Superprotonic Solid Acids: Structure, Pr

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Superprotonic Solid Acids: Structure, Properties, and Applications
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Boysen, Dane Andrew
(2004)
Superprotonic Solid Acids: Structure, Properties, and Applications.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/41BQ-3R07.
Abstract
In this work, the structure and properties of superprotonic MHₙXO₄-type solid acids (where M = monovalent cation, X = S, Se, P, As, and n = 1, 2) have been investigated and, for the first time, applied in fuel cell devices. Several MHₙXO₄-type solid acids are known to undergo a "superprotonic" solid-state phase transition upon heating, in which the proton conductivity increases by several orders of magnitude and takes on values of ~ 0.01 S/cm. The presence of superprotonic conductivity in fully hydrogen bonded solid acids, such as CsH₂PO₄, has long been disputed. In these investigations, through the use of pressure, the unequivocal identification of superprotonic behavior in both RbH₂PO₄ and CsH₂PO₄ has been demonstrated, whereas for chemically analogous compounds with smaller cations, such as KH₂PO₄ and NaH₂PO₄, superprotonic conductivity was notably absent. Such observations have led to the adoption of radius ratio rules, in an attempt to identify a critical ion size effect on the presence of superprotonic conductivity in solid acids. It has been found that, while ionic size does play a prominent role in the presence of superprotonic behavior in solid acids, equally important are the effects of ionic and hydrogen bonding. Next, the properties of superprotonic phase transition have been investigated from a thermodynamic standpoint. With contributions from this work, a formulation has been developed that accounts for the entropy resulting from both the disordering of both hydrogen bonds and oxy-anion librations in the superprotonic phase of solid acids. This formulation, fundamentally derived from Linus Pauling's entropy rules for ice, accurately accounts for the change in entropy through a superprotonic phase transition. Lastly, the first proof-of-principle fuel cells based upon solid acid electrolytes have been demonstrated. Initial results based upon a sulfate electrolyte, CsHSO₄, demonstrated the viability of solid acids, but poor chemical stability under the highly reducing H₂ gas environment of the fuel cell anode. Later experiments employing a CsH₂PO₄ electrolyte proved quite successful. The results of these solid acid-based fuel cell measurements suggest solid acids could serve as an alternative to current state-of-the-art fuel cell electrolytes.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
electrolytes; fuel cells; proton conductors; solid acids; superprotonic
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Haile, Sossina M.
Thesis Committee:
Haile, Sossina M. (chair)
Fultz, Brent T.
Asimow, Paul David
Goddard, William A., III
Johnson, William Lewis
Defense Date:
9 January 2004
Record Number:
CaltechETD:etd-05282004-155105
Persistent URL:
DOI:
10.7907/41BQ-3R07
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No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
2195
Collection:
CaltechTHESIS
Deposited By:
Imported from ETD-db
Deposited On:
28 May 2004
Last Modified:
03 Feb 2021 19:16
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Superprotonic Solid Acids:
Structure, Properties, and Applications

Thesis by

Dane Andrew Boysen

In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy

California Institute of Technology
Pasadena, California

2004
(Defended January 9, 2004)

2004

Dane Andrew Boysen

iii

To my grandfather, Sydney J. Wallace.

I am part of all that I have met;
Yet all experience is an arch wherethro’
Gleams the untravell’d world, whose margin fades
For ever and for ever when I move.
How dull it is to pause, to make an end,
To rust unburnish’d, not to shine in use!
As tho’ to breath were life. Life piled on life
Were all too little and of one to me
Little remains: but every hour is saved
From that eternal silence, something more,
A bringer of new things;
(excerpt from U lysses, by Lord Tennyson)

Acknowledgements
First and foremost, I would like to thank my advisor and mentor, Professor Sossina Haile,
for taking a chance on me. I am eternally grateful to Sossina for her patient and tireless
support throughout the course of my thesis work, even when my work was resulting in
perpetual failures. As a mentor, advisor, teacher, scientist, and mother—Sossina excels
at all. My awe and appreciation for having had the opportunity to work with such an
remarkable person can not be overstated.
Secondly, and for whose smiling face got me through the day, I have to thank my
officemate, co-conspirator, and friend, Dr. Calum Chisholm. As my complete anti-thesis,
Calum’s pure optimism and happy nature made life and work in the laboratory a true joy.
It has been my great pleasure to work with Calum.
Next, I would like thank Dr. Tetsuya Uda, whose timely addition to our research group
has allowed significant progress to be made in using solid acids as electrolytes for fuel cells.
I am fortunate to have had the opportunity to work with such an exceptional scientist.
In general, Caltech has provided me with the opportunity to meet and work with so
many exceptional people from all over the world. Among these extraordinay scientists and
coworkers, for whom I am thankful to have made their acquaintance are Jian Wu, Lisa
Cowan, Kwang Ryu, Paul Asimow, Jed Mosenfelder, Geoff Staneff, Chris Bielawski, Steven
Glade, Jörg Löffler, Boris Merinov, Lou Zaharopoulis, Carol Garland, Pam Albertson, and
Mike Vondrus.
I am in debt to Professor Richard Secco and Hongjian Liu at the University of Western
Ontario for their help with the high pressure measurements presented in this work.
Personally, I have to thank my parents for their steadfast support throughout my academic career, without which none of this work would have been possible. Also, I have to
thank my friend and fellow Netzchian optimist Yasser Rathore for his support and friendship. Thanks also to Ashish Bardwaj for being brilliant, honest, and a great friend. Finally,

I would also like to thank the Peik and Escot families for giving me a home away from
home.
Of course I must thank the California Institute and Technology, and specifically, the
Materials Science Department, for giving me this great opportunity to study at such a
remarkable institution. Caltech is like no other place, it is truly the ivory tower—a sanctuary
for the noble pursuits of truth, knowledge, and understanding. In a society which continues
to become increasingly anti-intellectual, Caltech is a last bastion for such high-minded
endevours—it has been a great honor to be a part of it. As caretakers of these high
endevours, I must give my humble thanks and appreciation to Professor Bill Johnson for
inspiring me in his course on thermodynamics and statistical mechanics and to Professor
Brent Fultz for taking the time to give me both professional and personal advice.
Lastly, I would like to thank the National Science Foundation, Office of Naval Research,
and Caltech for funding this work.

Abstract
In this work, the structure and properties of superprotonic MHn XO4 -type solid acids (where
M = monovalent cation, X = S, Se, P, As, and n = 1, 2) have been investigated and, for
the first time, applied in fuel cell devices. Several MHn XO4 -type solid acids are known to
undergo a “superprotonic” solid-state phase transition upon heating, in which the proton
conductivity increases by several orders of magnitude and takes on values of ∼ 10−2 Ω-1 cm-1 .
The presence of superprotonic conductivity in fully hydrogen bonded solid acids, such as
CsH2 PO4 , has long been disputed. In these investigations, through the use of pressure, the
unequivocal identification of superprotonic behavior in both RbH2 PO4 and CsH2 PO4 has
been demonstrated, whereas for chemically analogous compounds with smaller cations, such
as KH2 PO4 and NaH2 PO4 , superprotonic conductivity was notably absent. Such observations have led to the adoption of radius ratio rules, in an attempt to identify a critical ion
size effect on the presence of superprotonic conductivity in solid acids. It has been found
that, while ionic size does play a prominent role in the presence of superprotonic behavior
in solid acids, equally important are the effects of ionic and hydrogen bonding. Next, the
properties of superprotonic phase transition have been investigated from a thermodynamic
standpoint. With contributions from this work, a formulation has been developed that
accounts for the entropy resulting from both the disordering of both hydrogen bonds and
oxy-anion librations in the superprotonic phase of solid acids. This formulation, fundamentally derived from Linus Pauling’s entropy rules for ice, accurately accounts for the change
in entropy through a superprotonic phase transition. Lastly, the first proof-of-principle fuel
cells based upon solid acid electrolytes have been demonstrated. Initial results based upon
a sulfate electrolyte, CsHSO4 , demonstrated the viability of solid acids, but poor chemical
stability under the highly reducing H2 gas environment of the fuel cell anode. Later experiments employing a CsH2 PO4 electrolyte proved quite successful. The results of these
solid acid-based fuel cell measurements suggest solid acids could serve as an alternative to
current state-of-the-art fuel cell electrolytes.

vii

Contents
Acknowledgements

Abstract

1 Introduction

1.1

Solid Acids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2

Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2.1

Atomic Bonding 4,5,6 . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2.2

Hydrogen Bonding 4,7

. . . . . . . . . . . . . . . . . . . . . . . . . .

1.2.3

Coordination 11,12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2.4

Order–Disorder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3.1

Ionic Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Protonic Conductivity 18,19,20 . . . . . . . . . . . . . . . . .

1.3

1.3.1.1
1.3.2

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3.2.1

General Characterization 24 . . . . . . . . . . . . . . . . . .

1.3.2.2

Superprotonic Transitions . . . . . . . . . . . . . . . . . . .

Applications: Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4.1

Fuel Cell Description . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4.2

Types of Fuel Cells 29 . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4.3

Fuel Cell Performance 29 . . . . . . . . . . . . . . . . . . . . . . . . .

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4

Phase Transitions

2 Experimental Methods

2.1

Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2

Structural Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . .

viii
2.2.1

2.2.2

X-ray Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.1.1

Single Crystal X-ray Diffraction . . . . . . . . . . . . . . .

2.2.1.2

Powder X-ray Diffraction . . . . . . . . . . . . . . . . . . .

2.2.1.3

Rietveld Method 2,3 . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . .

Properties Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3.1

Impedance Spectroscopy 7 . . . . . . . . . . . . . . . . . . . . . . . .

2.3.2

High-Pressure Impedance Spectroscopy . . . . . . . . . . . . . . . .

2.3.3

Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3.4

Polarized Light Microscopy 12 . . . . . . . . . . . . . . . . . . . . . .

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3

Nuclear Magnetic Resonance Spectroscopy

3 Structure of Superprotonic MHn XO4 -type Solid Acids
3.1

Hydrogen Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1

CsH2 PO4 5

50
50

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1.1.1

Background . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1.1.2

Ambient Pressure Behavior . . . . . . . . . . . . . . . . . .

3.1.1.3

High Pressure Behavior . . . . . . . . . . . . . . . . . . . .

RbH2 PO4 32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1.2.1

Ambient Pressure Behavior . . . . . . . . . . . . . . . . . .

3.1.2.2

High Pressure Behavior . . . . . . . . . . . . . . . . . . . .

KH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1.3.1

Ambient Pressure Behavior . . . . . . . . . . . . . . . . . .

3.1.3.2

High Pressure Behavior . . . . . . . . . . . . . . . . . . . .

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Cation and Oxy-Anion Size Effects . . . . . . . . . . . . . . . . . . . . . . .

3.2.1

Radius Ratio Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.2

Atomic Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1.2

3.1.3

3.1.4
3.2

3.3

4 Properties of Superprotonic MHn XO4 -type Solid Acids
4.1

Pauling’s Entropy Rules for Ice 3 . . . . . . . . . . . . . . . . . . . . . . . .

94
95

ix
4.2

Entropy of Superprotonic Phases 1,2 . . . . . . . . . . . . . . . . . . . . . . .

4.2.1

Superprotonic Structures . . . . . . . . . . . . . . . . . . . . . . . .

4.2.2

Entropy Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

106

4.2.3

Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109

4.3

Entropy of Disordered Intra-Hydrogen Bond

. . . . . . . . . . . . . . . . .

110

4.4

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

113

4.5

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

114

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

116

5 Application of Superprotonic Solid Acids in Fuel Cells

119

State-of-the-Art Electolytes 1,2,3 . . . . . . . . . . . . . . . . . . . . . . . . .

119

5.1.1

Polymer Electrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . .

121

5.1.2

Solid Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

123

Solid Acid Electrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

125

5.2.1

CsHSO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

125

5.2.1.1

H2 /O2 Fuel Cell . . . . . . . . . . . . . . . . . . . . . . . .

126

5.2.1.2

Chemical Stability under H2 . . . . . . . . . . . . . . . . .

129

5.2.1.3

Chemical Stability under O2 . . . . . . . . . . . . . . . . .

135

5.2.1.4

O2 Concentration Cell . . . . . . . . . . . . . . . . . . . . .

142

5.2.2

Sulfates and Selenates 19 . . . . . . . . . . . . . . . . . . . . . . . . .

145

5.2.3

CsH2 PO4 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

146

5.2.3.1

Thermo-chemical Stability . . . . . . . . . . . . . . . . . .

146

5.2.3.2

H2 /O2 Fuel Cell . . . . . . . . . . . . . . . . . . . . . . . .

149

5.2.3.3

Direct Methanol Fuel Cell . . . . . . . . . . . . . . . . . . .

150

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

151

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

153

5.1

5.2

5.3

Appendix

156

A.1 Solid Acid Synthesis Recipes . . . . . . . . . . . . . . . . . . . . . . . . . .

156

A.1.1 CsH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

156

A.1.2 CsHSO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

156

A.1.3 KHSeO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

157

A.1.4 RbH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

157

A.1.5 TlH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

158

A.1.6 (NH4 )3 H(SO4 )2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

158

A.1.7 K3 H(SeO4 )2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

158

A.1.8 Rb3 H(SeO4 )2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

159

A.2 Thermal Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . . . . .

160

A.2.1 RbH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

160

A.2.2 TlH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

161

A.2.3 NaH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

162

A.2.4 LiH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

163

A.3 High Pressure Conductivity Results

. . . . . . . . . . . . . . . . . . . . . .

164

A.3.1 NaH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

164

A.3.2 LiH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

164

A.4 MHn XO4 -type Solid Acid Phase Behavior . . . . . . . . . . . . . . . . . . .

165

A.4.1 MH2 XO4 Phase Behavior . . . . . . . . . . . . . . . . . . . . . . . .

165

A.4.2 MHXO4 Phase Behavior

. . . . . . . . . . . . . . . . . . . . . . . .

166

A.5 Estimated Thermodynamic Values . . . . . . . . . . . . . . . . . . . . . . .

167

A.5.1 CsHSO4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

167

S298.15
and Cp . . . . . . . . . . . . . . . . . . . . . . . . .

167

A.5.2 Cs2 S2 O7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

168

, and Cp . . . . . . . . . . . . . . . . . . . . .
∆Hf◦ , S298.15

168

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

169

A.5.1.1

A.5.2.1

List of Figures
1.1

Symmetric and asymmetric hydrogen bonds . . . . . . . . . . . . . . . . . . .

1.2

Hydrogen bond networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3

Diagram of a coordinated atom . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4

Hydrogen bond disorder in KH2 PO4 . . . . . . . . . . . . . . . . . . . . . . .

1.5

Hydrogen bond disorder in CsH2 PO4

. . . . . . . . . . . . . . . . . . . . . .

1.6

Oxy-anion disorder in CsH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . .

1.7

Arrhenius plot of CsHSO4 conductivity . . . . . . . . . . . . . . . . . . . . .

1.8

Schematic diagram of basic H2 /O2 fuel cell . . . . . . . . . . . . . . . . . . .

1.9

Fuel cell performance curves . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1

Applied alternating electric field and current response . . . . . . . . . . . . .

2.2

Nyquist plot of AC impedance spectrum . . . . . . . . . . . . . . . . . . . . .

2.3

Equivalent RC circuit model . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4

Nyquist plots of RC and RQ equivalent circuits . . . . . . . . . . . . . . . .

2.5

Large-volume 1000-ton cubic anvil hydraulic press . . . . . . . . . . . . . . .

2.6

Schematic of high-pressure AC impedance cell . . . . . . . . . . . . . . . . .

2.7

Schematic of high-pressure ball drop cell

. . . . . . . . . . . . . . . . . . . .

2.8

Diagram of anisotropic crystal between cross-polarizers . . . . . . . . . . . .

3.1

Simple model for hydrogen bond disorder . . . . . . . . . . . . . . . . . . . .

3.2

Thermal analysis of CsH2 PO4 from literature . . . . . . . . . . . . . . . . . .

3.3

Conductivity of CsH2 PO4 from literature . . . . . . . . . . . . . . . . . . . .

3.4

Thermal analysis of CsH2 PO4 with various particle sizes . . . . . . . . . . . .

3.5

Thermal analysis of CsH2 PO4 at various heating rates . . . . . . . . . . . . .

3.6

Onset temperature of thermal events in CsH2 PO4 . . . . . . . . . . . . . . .

3.7

Polarized light microscopy of CsH2 PO4 . . . . . . . . . . . . . . . . . . . . .

xii
3.8

Conductivity of CsH2 PO4 under ambient pressure . . . . . . . . . . . . . . .

3.9

Nyquist plots of CsH2 PO4 at ambient pressure . . . . . . . . . . . . . . . . .

3.10

Nyquist plots of CsH2 PO4 at 200 ◦ C versus time . . . . . . . . . . . . . . . .

3.11

1 H-NMR of CsH PO

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.12

CsH2 PO4 P –T phase diagram CsH2 PO4 . . . . . . . . . . . . . . . . . . . . .

3.13

Conductivity of CsH2 PO4 at 1 GPa . . . . . . . . . . . . . . . . . . . . . . .

3.14

Nyquist plots of CsH2 PO4 at 1 GPa . . . . . . . . . . . . . . . . . . . . . . .

3.15

Powder X-ray diffraction patterns of CsH2 PO4 . . . . . . . . . . . . . . . . .

3.16

Thermal analysis of RbH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . .

3.17

RbH2 PO4 P –T phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . .

3.18

Conductivity of RbH2 PO4 at 1 GPa . . . . . . . . . . . . . . . . . . . . . . .

3.19

Nyquist plots of RbH2 PO4 at 1 GPa . . . . . . . . . . . . . . . . . . . . . . .

3.20

Thermal analysis of KH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.21

KH2 PO4 P –T phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.22

Conductivity of KH2 PO4 at 1 GPa . . . . . . . . . . . . . . . . . . . . . . . .

3.23

Nyquist plots of KH2 PO4 at 1 GPa . . . . . . . . . . . . . . . . . . . . . . .

3.24

MHSO4 and MH2 PO4 phase diagrams versus cation radius . . . . . . . . . .

3.25

Rotating oxy-anion coordinated cations . . . . . . . . . . . . . . . . . . . . .

3.26

Effective tetrahedral radius of an oxy-anion . . . . . . . . . . . . . . . . . . .

3.27

Radius ratios versus cation radius in MHn XO4 -type solid acids . . . . . . . .

3.28

Ionization potential and melting T versus cation size in MH2 PO4 . . . . . . .

3.29

H-bond strength and superprotonic transition T versus oxy-anion size . . . .

4.1

Structure of ice phase Ih . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2

Structure of paraelectric KH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . .

4.3

Plakida’s model for superprotonic phase transitions in CsHSO4 . . . . . . . .

4.4

Powder X-ray diffraction of RbHSeO4 at 170 ◦ C . . . . . . . . . . . . . . . .

100

4.5

Superprotonic structure of RbHSeO4 . . . . . . . . . . . . . . . . . . . . . . .

102

4.6

Superprotonic structure of CsHSO4

. . . . . . . . . . . . . . . . . . . . . . .

104

4.7

Proposed oxygen positions in superprotonic CsHSO4 . . . . . . . . . . . . . .

105

4.8

Superprotonic structure of CsH2 PO4 . . . . . . . . . . . . . . . . . . . . . . .

107

4.9

Paraelectric structure of CsH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . .

112

xiii
5.1

Conductivity of various fuel cell electrolytes . . . . . . . . . . . . . . . . . . .

120

5.2

Polymer electrolyte structure . . . . . . . . . . . . . . . . . . . . . . . . . . .

122

5.3

H2 /air fuel cell performance with Nafion r electrolyte . . . . . . . . . . . . . .

123

5.4

Solid oxide fuel cell configurations . . . . . . . . . . . . . . . . . . . . . . . .

124

5.5

Proof-of-principle H2 /O2 fuel cell with CsHSO4 electrolyte . . . . . . . . . .

126

5.6

Performance degradation in H2 /O2 fuel cell with CsHSO4 electrolyte . . . . .

129

5.7

Thermal analysis of CsHSO4 with Pt under H2 . . . . . . . . . . . . . . . . .

130

5.8

Powder X-ray diffraction of CsHSO4 after heating in H2 . . . . . . . . . . . .

131

5.9

Thermal analysis of CsHSO4 with different catalysts in H2

. . . . . . . . . .

132

5.10

Reaction equilibrium constants for CsHSO4 in H2 . . . . . . . . . . . . . . .

136

5.11

Cs–H2 O–SO3 chemical potential diagrams . . . . . . . . . . . . . . . . . . . .

140

5.12

CsHSO4 –Cs2 S2 O7 and CsHSO4 –Cs2 SO4 co-existence curves . . . . . . . . . .

141

5.13

Schematic diagram of O2 concentration cell . . . . . . . . . . . . . . . . . . .

143

5.14

Electric potential measurements of CsHSO4 in O2 concentration cell . . . . .

144

5.15

Thermal analysis of sulfates and selenates in H2 . . . . . . . . . . . . . . . .

145

5.16

Thermal analysis of CsH2 PO4 in H2 and O2 . . . . . . . . . . . . . . . . . . .

147

5.17

Dehydration of CsH2 PO4 versus pH2 O . . . . . . . . . . . . . . . . . . . . . .

148

5.18

H2 /O2 fuel cell performance with CsH2 PO4 electrolyte . . . . . . . . . . . . .

149

5.19

Direct methanol fuel cell performance with CsH2 PO4 electrolyte. . . . . . . .

151

A.1

Thermal analysis of RbH2 PO4 , constant V

. . . . . . . . . . . . . . . . . . .

160

A.2

Thermal analysis of TlH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . .

161

A.3

Thermal analysis of NaH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . .

162

A.4

Thermal analysis of LiH2 PO4 . . . . . . . . . . . . . . . . . . . . . . . . . . .

163

A.5

Conductivity of NaH2 PO4 at 1 GPa . . . . . . . . . . . . . . . . . . . . . . .

164

A.6

Conductivity of LiH2 PO4 at 1 GPa

164

. . . . . . . . . . . . . . . . . . . . . . .

xiv

List of Tables
1.1

Solid acid cations and oxy-anions . . . . . . . . . . . . . . . . . . . . . . . . .

1.2

Hydrogen bond strengths between oxygen atoms . . . . . . . . . . . . . . . .

1.3

Atomic coordination based on radius ratio rules . . . . . . . . . . . . . . . .

1.4

Mechanisms of proton motion . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.5

Basic fuel cell components . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.6

Common types of fuel cells . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1

Summary of onset temperatures of thermal events in CsH2 PO4 . . . . . . . .

3.2

High T thermal and electrical results of MH2 PO4 at 1 atm and 1 GPa . . . .

3.3

Shannon ionic radii for MHn XO4 -type solid acids . . . . . . . . . . . . . . . .

3.4

hX–Oi distance from MHn XO4 -structures compared to Shannon radii . . . .

3.5

MHn XO4 -type radius ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.1

Rietveld refinement results of RbHSeO4 at 175 ◦ C . . . . . . . . . . . . . . .

101

4.2

Superprotonic RbHSeO4 atomic coordinates . . . . . . . . . . . . . . . . . . .

102

4.3

Structural features of superprotonic MHn XO4 solid acids . . . . . . . . . . .

107

4.4

Calculated entropy of superprotonic MHn XO4 -structures . . . . . . . . . . .

110

4.5

Disordered hydrogen bond entropy in superprotonic MHn XO4 solid acids . .

112

4.6

Calculated and measured entropy of MHn XO4 superprotonic transitions . . .

114

5.1

Charateristics of catalysts used in thermal analysis of CsHSO4 in H2 . . . . .

131

5.2

Thermodynamic data for the reduction of CsHSO4 in H2 . . . . . . . . . . .

135

5.3

Thermodynamic data for the decomposition of CsHSO4 in O2 . . . . . . . . .

137

A.1

Thermodynamic and structural data of MH2 XO4 -type solid acids . . . . . . .

165

A.2

Thermodynamic and structural data of MHXO4 -type solid acids . . . . . . .

166

A.3

Thermodynamic data for M2 S2 O7 . . . . . . . . . . . . . . . . . . . . . . . .

168

Chapter 1

Introduction
The broad objective of this work is to develop a firm understanding of the correlation
between the structure and the properties of superprotonic solid acid compounds, so as to
allow the engineering of these compounds with the desired properties for the application
in devices. In this introduction, a brief description of solid acids will be given, then an
overview of the essential features governing the structure of solid acids, that is, the bonding
or cohesive forces between atoms, the coordination or packing arrangement of atoms, and the
concept of structural disorder. Moving then from structure to properties, the fundamental
material properties of interest in this work will be reviewed—specifically, ionic (protonic)
conductivity and phase transitions that lead to high protonic conductivity. Last of all, a
general introduction to fuel cells, the primary application of interest for superprotonic solid
acids, will be presented.
The overall structure of this work will be presented with the same basic outline as
this introduction, that is, following a review of the experimental methods, the structure,
properties, and finally application of superprotonic solid acids will be covered.

1.1

Solid Acids

Solid acids, or acid salts, are materials whose properties are intermediate those of a normal
salt and those of a normal acid. For example,
2 Cs2 SO4 (salt) + 2 H2 SO4 (acid) → CsHSO4 (solid acid).

Solid acids exhibit mechanical and electrical properties similar to a salt, i.e., brittle and
insulating. However, like acids, these compounds contain structural acid protons, which

can lead to high ionic conductivity (∼ 10−2 Ω-1 cm-1 ). In fact, it is precisely this structural acid proton in solid acids that is responsible for behavior such as ferroelectricity and
superprotonic conductivity.
The first systematic investigations of solid acid compounds began after the discovery
of ferroelectric behavior at low temperatures (T < 120 K) in solid acid KH2 PO4 1 . Today,
the low temperature properties (T < 100 ◦ C), such as piezoelectric, ferroelectric, electrooptical, and non-linear optical properties of these materials, are well characterized and
widely exploited in the construction of devices such as Kerr cells, high frequency light
modulators, and optical frequency doublers.
Largely ignored in most early studies were the high temperature behavior (T > 100
◦ C) and ionic conducting properties of solid acids. In 1982, a unique order–disorder phase

transition was observed in solid acid CsHSO4 , in which upon heating the proton conductivity
increased by ∼ 103 Ω-1 cm-1 to a so called “superprotonic” phase 2 . Despite unusually high
proton conductivity the application of solid acids in electrochemical devices was thought
to be impractical due to their solubility in water. However, as part of this work it was
demonstrated that, by simply operating above the boiling point of water (> 100 ◦ C), solid
acids may well be applicable as an electrolyte in fuel cells 3 —it is to this end that I have
investigated the nature of superprotonic behavior in solid acid compounds.

1.2

Structure

There are three essential concepts necessary to describe the structure of solid acids: (1)
atomic bonding, (2) coordination, and (3) order-disorder. Here, the nature of atomic bonding or the cohesive force between atoms will be briefly described, with a more in depth
characterization of hydrogen bonding, which plays a particularly prominent role in determining the structure and properties of solid acid compounds. Coordination, which describes
how atoms arrange themselves based upon size, is also a factor in determining the structure
of solid acids, and in particular superprotonic solid acids. Last of all, is the concept of
structural disorder, which is not only fundamental to the structure of solid acids, but is also
intimately related to their properties, such as ferroelectricity and superprotonic conductivity.
Solid acids can be represented by the general chemical formula: Ma Hb (XO4 )c , where

M is a monovalent or divalent cation, XO4 is a tetrahedral oxy-anion, and a, b, c are integers. The structure of solid acids are comprised of hydrogen-bonded tetrahedral oxy-anions
charge balanced by a host lattice of cations. All possible tetrahedral oxy-anions and cations
that are known to compose solid acids are listed in Table 1.1. Given the multitude of possible combinations of these tetrahedral oxy-anions and cations, solid acids represent a vast
number of compounds with a wide-range of possible structures.
Table 1.1: Solid acid cations (M+1,2 ) and tetrahedral oxy-anions (XO4−2,3,4 ).
Cations
M+

Tetrahedral Oxyanions
Li+ , Na+ , K+ , Tl+ ,

XO−2

−2
−2
SO−2
4 , SeO4 , CrO4 ,
−2
TeO−2
4 , MoO4 ,

Rb+ , NH+
4 , VO , Cs

WO−2
M+2

Be+2 , Mg+2 , Ca+2 ,

XO−3

−3
−3
PO−3
4 , AsO4 , VO4 ,
−3
NbO−3
4 , MnO4 ,

Sr+2 , Pb+2 , Ba+2

SbO−3
XO−4

1.2.1

−4
SiO−4
4 , GeO4

Atomic Bonding 4,5,6

The concept of atomic bonding is a useful construct for the characterization and prediction
of the structure of solids. Solids are held together via cohesive forces, which are represented
almost entirely by the electrostatic interaction between the negative charges of electrons and
the positive charges of the nuclei 5 . Magnetic forces in solids only weakly contribute to the
cohesion of crystals, and gravitational forces are negligible. As is conventional, we broadly
term these cohesive forces between atoms as chemical or atomic bonds. Furthermore, chemical bonds of different character are broadly classified as electrostatic bonds, covalent bonds,
and metallic bonds 4 . While bonding-type can exhibit character intemediate between these
broad classifications, the convention is nonetheless a useful one.
The structure of solid acids is typically dominated by electrostatic bonding, more specifically ionic bonding. The ionic bond results from the electrostatic attraction between posi-

tively and negatively charged ions, the formation of which occurs when one or more electrons
from one atom are transferred to another atom, forming a cation and anion, respectively.
Other electrostatic forces, such as Van der Waals interaction, in which dipole interaction
is caused by an induced polarization of the electronic charge distribution of an atom by a
neighboring atom, play only a minor role.

1.2.2

Hydrogen Bonding 4,7

Prominent in the structure of solid acids is a fourth type of bond, known as the hydrogen
bond. The hydrogen bond is defined as
an atom of hydrogen attracted by rather strong forces to two atoms, instead of
one, so that it may be considered to be acting as a bond between them. - Linus
Pauling
While relative to other types of bonds, the hydrogen bond is somewhat weak (2 to 10
kcal/mol) 4 , it nevertheless plays a significant role in determining the structure and properties of solid acids.
The hydrogen atom, containing only a single 1s electron, can form only one covalent
bond, and therefore, the attraction observed between hydrogen-bonded atoms must be due
largely to ionic forces. Especially relevant to solid acids are the hydrogen bonds between
two oxygen atoms. In this case, the two oxygen atoms are labeled as the proton donor
oxygen atom (Od ), in which the proton lies within the electron density of the oxygen atom
and bond most closely resembles a covalent bond, and the proton acceptor oxygen atom
(Oa ), which is hydrogen-bonded to Od via largely ionic forces.
For solid acid compounds, hydrogen bonds exhibit distinctive hydrogen bond geometries
within the hydrogen bonds, intra-hydrogen bonds, as well as arranging themselves spacially
within a crystalline lattice with a wide variety of geometries, inter-hydrogen bonds. Both
intra- and inter-hydrogen bonding observed in solid acid compounds will be discussed in
the following sections.
Intra-Hydrogen Bonds
Hydrogen bonds between oxygen atoms can be catagorized according to their strength,
which is related to the donor oxygen to hydrogen distance (dOd −H ), and the donor to ac-

ceptor oxygen distance (dOd ...Oa ), Table 1.2 8,7,9 . The strength of a hydrogen bond increases
inversely with the covalency of the Od –H bond, such that the hydrogen bond strength
increases as the hydrogen bond character transitions from being largely ionic to mostly
covalent.
Table 1.2: Categories of hydrogen bond types (strength) and the corresponding donor oxygen
to hydrogen atom distances (dOd −H ), donor to acceptor oxygen atom distances (dOd ···Oa ), Lewis
notation, and bond character of the hydrogen bond 8,7,9 .
Strength

dOd −H / Å

dOd ···Oa / Å

Lewis Notation

Character

strong

1.30 – 1.02

2.4 – 2.6

Od · · · H · · · Oa

covalent

medium

1.02 – 0.97

2.6 – 2.7

Od −H · · · Oa

polar covalent

weak

. 1

2.7 – 3

Od −H+

O−

ionic

Further distinction between types of hydrogen bonds between oxygen atoms in crystalline solids depends on the local symmetry of oxygen atoms participating in the hydrogen
bond. If both oxygen atoms participating in a hydrogen bond occupy crystallographically
equivalent positions, then the bond is symmetric, whereas, if the oxygen atoms occupy crystallographic distinct positions then the bond is asymmetric. In Figure 1.1 is a schematic
representation of the hydrogen bond potential energies E(r) (or potentials) as a function
of interatomic distance between two oxygen atoms for strong, medium, and weak symmetric and asymmetric bonds 9 . For symmetric and asymmetric strong hydrogen bonds, at
hydrogen bond distances less than 2.4 Å, there is no distinction between the donor and
acceptor oxygen atoms and the hydrogen atom sits equidistant between the oxygen atoms
in single-well potential. At medium bond strengths, with a hydrogen bond distance of ∼
2.6 Å, for symmetric and asymmetric bonds the hydrogen atom can reside near either oxygen atom, in one minimum of a double-well potential. At sufficiently high temperatures,
thermal oscillations can allow the hydrogen atom to overcome the potential barrier between
the minima in the double-well potential, partially occupying each position—this is known
as hydrogen bond disorder. In Figure 1.1, for medium strength asymmetric hydrogen bonds
both single-well potentials, case (1), which are not disordered, as well as, double-well potentials, case (2), which are disordered, are possible 9 . At hydrogen bond distances greater
than 2.9 Å (weak hydrogen bonds), symmetric bonds are not generally observed and for

asymmetric bonds the hydrogen atom lies within the minimum of a single-well potential,
close to the donor oxygen atom.
Bond Type

symmetric

asymmetric

strong

medium

weak

Figure 1.1: Schematic representation of symmetric and asymmetric strong, medium, and weak bond
potentials as a function of inter-atomic distance E(r) between hydrogen-bonded oxygen atoms 9 .

Inter-Hydrogen Bonds
Beyond intra-hydrogen bond geometry, the structure of solid acid compounds can also exhibit a wide variety of inter -hydrogen bond geometries, or networks, Figure 1.2 10 . The
number of hydrogen bonds per tetrahedral oxy-anions (XO4 s) can be as few as one hydrogen bond per XO4 , as is the case for K3 H(SO4 )2 , or as many as four, in which all the oxygen

atoms of the oxy-anion are hydrogen-bonded, as in KH2 PO4 . In general, the distribution
of hydrogen bonds can exhibit zero-, one-, two-, and three-dimensional networks depending
on the density of hydrogen bonds. As a general guide, the type of hydrogen bond network depends on the ratio of hydrogen to tetrahedral oxy-anions (H/XO4 ). Zero-dimension
hydrogen bond networks, in which there is only half a hydrogen atom per XO4 can take
the form of dimers. Solid acids that have one hydrogen atom per XO4 , tend to exhibit
one-dimensional networks in the form of cyclic dimers, rings, or chains. With one and a
half hydrogen atoms per XO4 , two-dimensional planar layers of hydrogen-bonded networks
of XO4 s are possible. Lastly, three-dimensionsal networks can be observed when all the
oxygen atoms are hydrogen bonded.

Dimesionality

Networks

H/XO4

Example

0–D

dimers

0.5

K3 H(SO4 )2

1–D

cyclic dimers

KHSO4

rings

Cs2 Na(HSO4 )3

chains

CsHSO4

2–D

planar layers

1.5

Cs2 HSO4 H2 PO4

3–D

3-dimensional networks

KH2 PO4

Figure 1.2: Diagrams of different inter-hydrogen bond networks exhibited by solid acids. Depending
on the number of hydrogen bonds (· · · ) per tetrahedral XO4 oxy-anions (
varying dimensionality are possible 10 .

) different networks of

1.2.3

Coordination 11,12

The coordination of an atom is defined by the number of surrounding nearest neighbor
atoms. Coordination plays a significant role in the arrangement of atoms in solids, and is
influenced principly by the type of bonding and the relative size of atoms (or ions) in a
solid. From simple geometric considerations and assuming a rigid sphere model for ions,
the structure of ionic solids can often be infered from the relative sizes of the consitutive
ions.

Figure 1.3: Two-dimensional depiction of an atom of radius r, coordinated by five other atoms of
radius R.

Consider a compound containing two different ions of radii r and R, as depicted in two
dimensions in Figure 1.3. Let r represent the radius of the smaller ion, usually the cation,
and let R represent the radius of the larger ion, usually the anion. The relationship between
the ratio of the radii r/R, and the resulting coordination number can be determined using
the following constraints: (1) cations “touch” anions, (2) the number of anions surrounding
a given cation will be as high as geometrically possible, and (3) the ions cannot overlap.
As the relative size of r to R increases (r/R → 1), the number of possible nearest neighbors increases (increasing coordination number) and the possible geometric arrangement of
atoms change. The expected geometries based on these radius ratio rules are presented in
Table 1.3, where for the geometries depicted, the vertices of the coordination polyhedron
represent the positions of atoms of radius R, and the coodinated atom of radius r is positioned at the center of the polyhedron. Values of ionic radii obtained from diffraction data
of ionic solids, such as those compiled by R.D. Shannon 13 , used in conjuction with these
radius ratio rules are of considerable utility in determining the structural arrangement of
ionic solids without any a priori knowledge of the structure.

Table 1.3: Coordination number of an atomic (ionic) species based on radius ratio (r/R) rules, where
the radius of the the smaller atomic species (r) lies central to the depicted coodination polyhedron,
and is coordinated by atomic species of larger radius (R) positioned at the vertices of the polyhedron
(from reference 11 ).
Coodination Number

Minimum Radius Ratio

Coordination Polyhedron

0.225

Tetrahedron

0.414

Octahedron

0.528

Trigonal prism

0.592

Capped octahedron

0.645

Square anti-prism

0.668

Dodecahedron

0.732

Cube

0.732

Tricapped trigonal prism

0.902

Icosahedron

1.000

Cuboctahedron

1.2.4

Order–Disorder

Order–disorder in solid acid structures is a central feature in determining the properties
of these compounds. There are many types of order–disorder phenomenon observed in
solids. The two main types of order–disorder phenomenon which describe the arrangement
of atoms are (1) structural disorder, in which a single atomic species partially occupies
multiple crystallographic positions; and (2) chemical disorder, in which multiple atomic
species occupy the same crystallographic position. Structural disorder can be broken into
two general catagories:
1. Static disorder, when a single atomic species is randomly distributed over multiple
crystallographic positions.
2. Dynamic disorder, resulting from thermally activated atomic species moving between
two or more crystallographic positions.
Of these types of structural disorder, dynamic disorder is the feature that is of greatest
interest for the present investigations into the properties of solid acid compounds.
Dynamic Disorder
Dynamic disorder is responsible for some of the truly spectacular properties exhibited by
solid acid compounds, such as ferroelectricity and superprotonic conductivity. The dynamic
disorder exhibited in solid acids are as follows: (1) Intra-hydrogen bond disorder, (2) Interhydrogen bond disorder, and (3) Oxy-anion disorder. The first of these is responsible for
ferroelectric transitions in solid acids, and the second and third, being intimately related to
one another, are responsible for superprotonic behavior.
Intra-Hydrogen Bond Disorder As mentioned previously, intra-hydrogen bond disorder occurs in medium strength symmetric and asymmetric hydrgen bonds, in which there
are two crystallographic positions separated by a potential barrier for a single hydrogen
atom. At low temperatures there is insufficient thermal energy for the hydrogen atom to
overcome the potential barrier, and the structure becomes ordered with respect to the intrahydrogren bond—the hydrogen atom resides in just one crystallographic position. Upon
heating, thermal oscillations of the hydrogen atom become sufficient to overcome the potential barrier between the two crystallographic positions and the crystallographic structure

12
becomes disordered with respect to the intra-hydrogen bond. In terms of properties, this
transition from order to disorder in solid acids leads to a ferroelectric to paraelectric transition. The most well-known solid acid exhibiting this behavior is KH2 PO4 , depicted in
Figure 1.4 in both its (a) ferroelectric phase (ordered intra-hydrogen bond), and (b) paraelectric phase (disordered intra-hydrogen bond). Crystallographically, upon tranforming
from order to disorder, a center of symmetry is created between the two oxygens atoms participating in the hydrogen bond and a higher symmetry space group is formed, for example
KH2 PO4 transitions from orthorhombic (F dd2) 14 to tetragonal (I 4̄2d) 15 .

(a) Ordered intra-hydrogen bond

(b) Disordered intra-hydrogen bond

Figure 1.4: Schematic representation of KH2 PO4 crystal structures in (a) orthorhombic (F dd2)
ferroelectric phase 14 , in which a single hydrogen atom is located at crystallographic position 1—
ordered intra-hydrogen bond, and (b) tetragonal (I 4̄2d) paraelectric phase 15 , in which a single
hydrogen atom is disordered between crystallographic positions 1 and 2—disordered intra-hydrogen
bond. Potassium atoms not shown for clarity.

Inter-hydrogen Bond Disorder Upon heating some solid acids the oxy-anions begin
to librate between crystallographically equivalent positions, while simultaneously breaking
and reforming new hydrogen bonds—a superprotonic phase transition. The hydrogen bond
is thus distributed among several crystallographic postions, i.e., the inter-hydrogen bonding
becomes disordered. For example, in Figure 1.5 (a) the ordered inter-hydrogen bond, and
(b) the disordered inter-hydrogen bond of CsH2 PO4 are depicted. Here, in two-dimensions
two hydrogen bonds (solid lines) per tetrahedral SO4 group can be observed in the ordered

13
paraelectric (ferroelastic) phase and four hydrogen bonds (dashed lines) in the disordered
superprotonic (paraelastic) phase (from a three-dimensional viewpoint, this would be four
and six hydrogen bonds per tetrahedral PO4 group, respectively). Clearly, there is an
intimate relationship between this inter-hydrogen bond disorder and the oxy-anion disorder
in solid acids, the former not occuring without the latter.

(a) Ordered inter-hydrogen bond

(b) Disordered inter-hydrogen bond

Figure 1.5: Schematic representation of CsH2 PO4 crystal structures in (a) monoclinic (P 21 /m)
phase 16 , in which the tetrahedral PO4 oxy-anions and inter-hydrogen bonds (solid lines) are ordered,
and (b) cubic (P m3̄m) superprotonic phase 17 , in which the tetrahedral PO4 oxy-anions and interhydrogen bonds (dashed lines) are dynamically disordered. Cesium atoms are not shown for clarity.

Oxy-Anion Disorder

Dynamic structural oxy-anion disorder occurs when the oxy-

gen atoms of structural tetrahedral oxy-anions partially occupy crystallographically equivalent positions. Due to the strong bonding between the oxygen atoms and the central
tetrahedral atom, the overall tetrahedral structure is maintained, leading to librations of
the tetrahedron between these crystallographically equivalent positions, and manifesting in
several possible orientations of the tetrahedron. In Figure 1.6, a three-dimensional depiction of ordered and disordered oxy-anion structures in CsH2 PO4 are presented. In (a) the
tetrahedral oxy-anion PO4 exists in only one orientation—ordered phase, and in (b) the
tetrahedron is rotationally disordered (as arrow indicates) among 6 possible orientations—
disordered phase. This dynamic tetrahedral disorder corresponds to an oxygen atom dis-

14
ordered over 4 oxygen positions (= 24 oxygen positions per tetrahedron ÷ 6 tetrahedron
positions). Given the appropriate structural prerequistes (cation to oxy-anion size), such a
transition is expected, based on entropic considerations, even in the absence of hydrogen
bonds. This expectation is, in part, confirmed by the observation of such phase transformations in salts such as Cs2 SO4 , in which disordered tetrahedral PO4 groups exist in absence
of any hydrogen-bonding. Therefore, while dynamic inter-hydrogen bond disorder requires
disordered oxy-anions, the reverse is not necessarily true.

(a) Ordered tetrahedral oxy-anions

(b) Disordered tetrahedral oxy-anions

Figure 1.6: Schematic representation of CsH2 PO4 crystal structures in (a) monoclinic (P 21 /m)
paraelectric (or ferroelastic) phase 16 , in which the tetrahedral PO4 oxy-anions resides in one
position—ordered, and (b) cubic (P m3̄m) superprotonic (or paraelastic) phase 17 , in which the
tetrahedral PO4 oxy-anions are rotationally disordered (as arrow indicates) among six different
tetrahedral orientations.

1.3

Properties

Electrolytes for application in fuel cells or batteries ideally have high ionic conductivity
and little or no electronic conductivity. Therefore, the ionic conductivity and specifically
protonic conductivity, is the principal material property of solid acids investigated here.
Solid acids exhibiting high proton or superprotonic conductivity are of particular interest.
To date, all known superprotonic behavior in solid acids is a result of a solid–solid order–
disorder phase transition and for this reason, significant effort has been made in this work

15
to characterize these transitions, and the subsequent superprotonic behavior.

1.3.1

Ionic Conductivity

A phenomenological review of some of the basic underlying principles of ionic conduction
is given here. Beginning with an isotropic solid the material property conductivity σ is a
scalar quantityi that relates the current density ~i to an applied electric field E~ according to
Ohm’s law
~i = σ E.

(1.1)

In an electrolyte with only one type of charge carrier, the current density ~i for a concentration of charged carriers n each with charge q traveling with an average velocity of h~v i
is
~i = nqh~v i.

(1.2)

The charge carrier mobility uii , defined as
h~v i
E~

(1.3)

σ = nqu.

(1.4)

u≡
can be used to express the conductivity as

When the concentration of particles n and the electric field E vary along the x-direction,
the subsequent flux J (or number of charged carriers passing through an area per time) of
charge carriers is equal to the product of the mean force on the particles hF i, n number of
particles per unit volume, charge q, and their mobility per charge u/q
−nu
−nu
hF i =
J=

∂µ
+ qE ,
∂x

(1.5)

where µ (= ∂G/∂n) is the chemical potential of the charge carriers. In the absence of an
ii

For anisotropic solids, the conductivity is a second rank tensor quantity.
Mobility is usually designated as µ, however in this case µ represents the chemical potential.

16
electric field (E = 0) this reduces to
J = −nuq

∂µ
∂x

(1.6)

The flux of particles can also be expressed in terms of a charge carrier diffusion coefficient
D according Fick’s first law
J = −D

∂n
∂x

(1.7)

Then, from the definition of chemical potential in dilute solutions
µ = µ0 + kB T ln n,

(1.8)

where kB is the Boltzmann constant, and T is temperature, and differentiating with respect
to x
kB T
∂µ
∂x

∂n
∂x

(1.9)

Now equating Equations 1.6 and 1.7, and using the previous relationship the diffusion
coefficient can be related to the mobility of the charge carriers according to the NernstEinstein equation,
u=

qD
kB T

(1.10)

and substituting this into Equation 1.4 yields
σ=

nq 2 D
kB T

(1.11)

Assuming uncorrelated motion of the charge carrying species a random walk model can
be adopted to describe the diffusion coefficient, such that
D = γa20 ν,

(1.12)

where γ is a geometric factor depending on the structure of the solid, a0 is the distance the
mobile charge carrier “jumps” between vacant crystallographic sites, and ν is the frequency
at which the charge carrier jumps. The jumping of charge carriers between crystallographic
sites is a thermally activated process, which is best described by an Arrhenius-type tem-

17
perature dependence,
ν = ν0 exp

−∆Ga
kB T

(1.13)

where ν0 is the attempt frequency and ∆Ga is the Gibbs free energy for activation of this
process. This leads to a diffusion coefficient that varies with an Arrhenius behaviour,
−∆Ga
D = γa20 ν0 exp
kB T
−∆Ga
= D0 exp
kB T

(1.14)
(1.15)

where the pre-exponential factor D0 = γa20 ν0 . The Gibbs free energy of activation can be
expressed in terms of an activation entropy ∆Sa and enthalpy ∆Ha
∆Ga = ∆Ha − T ∆Sa .

(1.16)

Similarly, the activation enthalpy can be expressed in terms of an activation energy ∆Ea
and volume ∆Va
∆Ha = ∆Ea + P ∆Va ,

(1.17)

where the activation volume is often neglected at ambient pressures. Using these thermodynamic relationships and combining Equations 1.4, 1.10, and 1.14 the Arrhenius relationship
for the conductivity of a solid can be written as
σT = A0 exp

−∆Ha
kB T

= A0 exp

−∆Ea − P ∆Va
kB T

(1.18)

where the pre-exponential factor A0 is
A0 =

D0 nq 2
∆Sa
exp
kB
kB
γa0 ν0 nq
∆Sa
exp
kB
kB

(1.19)
(1.20)

Thus, we have arrived at an expression for the ionic conductivity of an isotropic solid in
terms of intrinsic material properties as a function of temperature that closely models the
bulk behavior of real ionic solids.

18
1.3.1.1

Protonic Conductivity 18,19,20

The motion of protons in solids is unique among ionic species. The small size of protons
relative to other ionic species allows for high moblity of these ions. However, the relatively
small ratio of mass to charge leads to proton motion that is usually coupled with other
phenomenon within a solid, such as molecular diffusion, phonons, and molecular dynamics.
That is, unlike other ions, the proton rarely exists as a “bare” proton, prefering to lie within
the electron density of other atoms, and its movements are usually assisted by these other
phenomenon.
There are five basic mechanisms for proton motion in solids: (1) atomic diffusion, (2)
proton-displacement, (3) molecular reorientation, (4) vehicle mechanism, and (5) Grotthus
mechanism. A summary of these mechanisms, a brief description and depiction of each,
and an example is given in Table 1.4.
Atomic diffusion

This type of proton motion is simply coupled proton-electron dif-

fusion, which is common in materials such as metal hydrides, like Li3 AlH6 and Na3 AlH6 .
In such materials, the hydrogen can donate its electron density to the host matrix, accept
electron density, or simply remain neutral. Due to the inherent electronic conductivity
associated with these type of materials, they are of no practical interest for electrolyte
studies.
Proton displacement This proton motion occurs when a proton “hops” along a
hydrogen bond from one minima of a double-well potential to the other. As aforementioned,
this type of proton motion is quite common in solid acid compounds, and is responsible for
ferroelectric behavior in solid acids, such as KH2 PO4 .
Molecular reorientation Also referred to as dipole reorientation, in this process
a proton rides “piggy-back” a molecule undergoing a libration, rotation, or tumble. This
motion was first proposed to describe proton transport in ice, but is also commonly observed
in solid acid compounds, as well as liquid acids.
Vehicle mechanism

In this mechanism, proton translation is associated with the

diffusion of polyatomic species. In this type of proton motion, a proton rides “piggy-back”

19
on a mobile molecule, which may carry a positive charge (e.g. NH+
4 , OH3 , O2 H5 , O3 H7 ), a

negative charge (e.g. NH−2 , OH− ), or be neutral (e.g. NH3 , H2 O). The vehicle mechanism
is, perhaps, the most common type of proton transport mechanism, and is exhibited by
many fast-proton conductors, such as Nafion r , in which H3 O+ ions are transported along
sulfonic acid functional groups (—SO−
3 ), within a polymer host matrix.
Grotthus mechanism

This mechanism is a cooperative process involing both a

molecular (dipole) reorientation and proton-displacement. Superprotonic solid acids, such
as CsHSO4 , conduct protons via this process. In these superprotonic solid acids, the oxyanion librates between crystallographically equivalent positions while carrying a proton with
it, then the proton “hops” along a hydrogen bond to another oxy-anion, followed by another oxy-anion reorientation, and so on. Experimentally, it has been determined that the
reorientation of these oxy-anions occurs at a rate of ∼ 1012 Hz, and the proton transfer
(proton-displacement) rate at ∼ 109 Hz, therefore, the rate limiting step in this mechanism
for superprotonic solid acids is proton transfer 21,22,23 .

Table 1.4: Basic mechanisms of proton motion, descriptions, depictions of mechanisms, and examples.

(1)

Mechanism

Description

Example

Atomic diffusion

coupled proton-electron transla-

NaAlH6

tion

(2)

Proton-displacement

intra-hydrogen bond translation

KH2 PO4

(3)

Molecular reorientation

piggy-back rotation, libration, or

ice

tumble

(4)

Vehicle mechanism

piggy-back diffusion

Nafion r

(5)

Grotthus mechanism

proton diffusion via (2) + (3)

CsHSO4

1.3.2

Phase Transitions

Phase transitions are of fundamental importance to this work as, to date, no superprotonic
behavior has been observed in solid acid compounds that is not associated with a structural
phase transition. Here, a general description of phase transitions will be given, as well as a
specific description of superprotonic phase transitions.
1.3.2.1

General Characterization 24

A phase is a homogeneous solution of matter bounded by a surface so that it is mechanically
separate from any other portion 12 . Generally speaking, a phase transition is a transformation of matter induced by a change in a thermodynamic function, such as temperature T ,
pressure P , volume V , or entropy S, from one phase to another phase that is distinguishable
from the first. For the purpose of this work phase transitions are identified by a discontinuous change in an extensive thermodynamic variable of a substance, such as volume V ,
entropy S, magnetization M, polarization P, or derivatives thereof, while varying an intensive variable, such as pressure P , temperature T , magnetic field B, or electric field E.
Specifically, for transitions in which there is a discontinuous change in the entropy through
the phase transition while varying temperature, there will also be a change in enthalpy ∆H
or latent heat Q associated with the transition. This sort of phase transition is known as a
first order phase transition. If the entropy is continuous, but its first derivative with respect
to temperature, or heat capacity Cp is discontinuous,
Cp = T

∂S
∂T

(1.21)

the phase transition is said to be of second order, and if the entropy and heat capacity are
∂C

continous, and the derivative of the heat capacity ∂Tp is discontinous, the transition is third
order, and so on.
In this work, first order solid–solid phase transitions are of primary interest. For these
transitions the change in extensive thermodynamic variables such as V and M are negligible
compared to the change in S. Therefore, the conjugate thermodynamic variables: entropy
and temperature (which is the change in energy E with respect to entropy)
∂E
[S, T ] = S,
∂S

(1.22)

22
can be readily measured by calorimetry, and yield a complete thermodynamic description
of such first order phase transitions.
1.3.2.2

Superprotonic Transitions

Superprotonic transitions are characterized by a discontinuous “jump” in protonic conductivity by several orders of magnitude to a superprotonic phase, which exhibit conductivity of
∼ 10−2 Ω-1 cm-1 . These solid–solid, order–disorder transitions have a latent heat associated
with them, and therefore, are first order in nature. In Figure 1.7, the conductivity of the
prototypical superprotonic solid acid, CsHSO4 , is presented in an Arrhenius plot. At low
temperatures, CsHSO4 has a monoclinic (P 21 /c) crystal structure, and upon heating to the
superprotonic phase, the structure transforms to a tetragonal (I41 /amd) crystal structure
of higher symmetry. Optical studies have shown that associated with this transition is a
ferroelastic transition, in which a large spontaneous strain (∼ 10−2 ) is associated with the
low temperature (ferroelastic) phase 25 .

Figure 1.7: Arrhenius plot of the conductivity of CsHSO4 measured through the superprotonic
phase transition (this work), where the phase boundary is indicated by a dashed-line.

These superprotonic phase transitions exhibit properties not unlike those of solid–liquid
transitions. For example, upon heating through the superprotonic phase transition temperature the sound velocity drops by nearly 50%, which is comparable to that of a solid–liquid
transition 26 . The “liquid-like” properties of these superprotonic solid acids are the result of

23
the highly disordered tetrahedral oxy-anions. Strictly speaking, these superprotonic compounds are solids, as they exhibit long range translational order. However, while there is
no translation disorder, the rotation disorder of the oxy-anions in superprotonic solid acid
is comparable to that observed in liquid Hn XO4 acids. As one might expect, this rotational
disordering through the superprotonic phase transition, also leads to dramatic changes in
mechanical properties. For example, the superprotonic phase of CsHSO4 has been described
as having mechanical properties not unlike “clay or plasticine,” 27 whereas, at room temperature the mechanical properties are akin to conventional table salt. Ultimately, it is these
highly disordered oxy-anions that allow for the high conductivity observed in superprotonic
solid acids.

1.4

Applications: Fuel Cells

U.S. dependence on oil imports for energy is higher today than it was even during the “oil
shock” of the 1970s. Passenger vehicles alone consume 6 million barrels of oil every single
day, equivalent to 85% of oil imports. Fuel cell vehicles could dramatically affect these
numbers. Utilization of fuel cells could reduce urban air pollution, decrease oil imports,
reduce the trade deficit, and produce American jobs. The U.S. Department of Energy
(DOE) projects that if a mere 10% of automobiles nationwide were powered by fuel cells,
regulated air pollutants would be cut by one million tons per year and 60 million tons of the
greenhouse gas carbon dioxide would be eliminated. DOE projects that the same number of
fuel cell cars would cut oil imports by 800,000 barrels a day—about 13% of all oil imports 28 .
The application of solid acids in fuel cells is, therefore, motivated by this potential benefit
to society.
A fuel cell can be thought of a device which has characteristics that are intermediate
between those of an internal combustion engine and a battery. Like an internal combustion
engine, a fuel cell uses fuel as a source of energy, and therefore has the potential for high
energy densities, and does not need to be “charged up,” as with conventional batteries.
However, like a battery cell, a fuel cell converts chemical potential energy directly into
electricity, that is, it is an electrochemical device—thus, creating noiseless useful energy at
very high efficiencies, as compared to internal combustion engines. Due to these advantages,
fuel cells have captured the world’s attention and development is being aggressively pursued

24
by nearly every automobile manufacturer, as well as, manufacturers of power systems for
portable electronic devices. In this section, a brief review of the basic internal workings
of fuel cells, various types, and the characterization of a fuel cell’s performance will be
presented.

1.4.1

Fuel Cell Description

The basic internal workings of a fuel cell are best described by example. The simplest type
of fuel cell is a hydrogen/oxygen fuel cell at 25◦ C and 1 atm (standard conditions). The
thermodynamic driving force behind the operation of a fuel cell comes from the chemical
reactions of the fuels. For this simple case, the Gibbs free energy for the reaction of hydrogen
and oxygen can be described by two seperate half cell reactions to yield the overall chemical
reaction:
Anode:

H2 → 2H+ + 2e−

∆G◦f

= 0.0 kJ mol-1

Cathode:

2 O 2 + 2H + 2e → H2 O

∆G◦f

= -241.3 kJ mol-1

Overall:

H2 + 12 O 2 → H2 O

∆G◦rxn

= -241.3 kJ mol-1

This chemical potential energy can be related to an electric potential or electromotive force
E using the Nernst Equation,
∆G◦rxn = −nF E0◦ ,

(1.23)

where n is the stoichiometric number of charge carriers and F is Faraday’s contant, the
superscript ’◦’ refers to standard state conditions (25 ◦ C, 1 atm), and the subscript ’0’
identifies this potential as the theoretical open cell voltage (OCV ) or Nernst potential. For
this reaction, the E0◦ = 1.25 V. A schematic diagram of a hydrogen/oxygen fuel cell is shown
in Figure 1.8. The overall process by which this fuel cell operates can be described in 7
steps: (1) hydrogen fuel is fed into the anode of the fuel cell, while (2) oxygen is fed into the
cathode, (3) encouraged by a catalyst, the hydrogen atoms split into protons and electrons
(2H2 → 4H+ + 4e− ), (4) the protons are then transported through electrolyte, while (5)
the electrons provide useful electricity that can provide power to a device (load), before
finally (6) reuniting with the protons in the presence of oxygen gas and a catalyst, to (7)
generate H2 O exhaust at the cathode (2H2 + O 2 → 2H2 O).
While the previous example is the simplest case of a fuel cell the basic mode of operation
is the same for all fuel cells. However, the various types of fuel cells can differ significantly

25
in each of the separate components involved in the overall operation of the cell. These basic
components that comprise a fuel cell are: the anode, cathode, electrolyte, catalyst, load,
fuel, and oxidant. Fuel cell components can widely vary in the materials used, depending
upon the type of fuel cell. In Table 1.5, a description of the essential components for the
operation of a fuel cell and examples of each are given. Following is a general description
of some of the most common types of fuels cells.

Figure 1.8: Schematic diagram of a basic H2 /O2 fuel cell.

Table 1.5: The basic components essential to the operation of a fuel cell, and examples of each.
Component

Description

Examples

Fuel

source of chemical energy

Oxidant

used to oxidize fuel

H2 , methanol,
ethanol,
methane
O2 , air

Anode

porous electron conducting negative electrode

carbon paper,
Ni

Cathode

porous electron conducting positive electrode

carbon paper

Electrocatalyst

catalyzes electrochemical reactions at anode and cathode

Pt, Pd, Ni

Electrolyte

ion conducting, electron insulating membrane, separating fuel
and oxidant

Nafion r , ZrO2 ,
CsH2 PO4

1.4.2

Types of Fuel Cells 29

There are five common types of fuel cells, generally catagorized according to the type of
electrolyte used. Electrolytes operate optimally at different temperatures and transport
different ion species depending on the type of electrolyte. An overview of these five fuel cell
types is given in Table 1.6, and a brief description of each in the following sections.
Table 1.6: The most common types of fuel cells and their corresponding electrolyte, mobile ion
species, operating temperatures, and fuels used.
Type

Electolyte

Mobile Ion
Species

Operating
Temp.

Fuels

PEMFC
polymer electrolyte
membrane fuel cell

sulfonated polymer

H3 O+

70–110◦ C

H2 , CH3 OH

(Na,K)OH

OH−

100–250◦ C

PAFC
phosphoric acid
fuel cell

H3 PO4

H+

150–220◦ C

MCFC
molten carbonate
fuel cell

(Na,K)2 CO3

CO2−

500–700◦ C

hydrocarbons,
CO

SOFC
solid oxide
fuel cell

(Zr,Y)O2−δ

O2−

500–700◦ C

hydrocarbons,
CO

AFC
alkali fuel cell

Polymer Exchange Membrane Fuel Cell (PEMFC)

These cells operate at the

relatively low temperatures of 80–110 ◦ C. PEMFCs exhibit high power densities and are
very reliable, as long as they remain humidified and free from catalyst poisoning gases (CO,
H2 S, etc.). Most fuel cell systems now being developed for automotive and portable electronics are based on PEMFCs. Typical fuel cell stack outputs range from 50 W to 250 kW.
The polymer exchange membrane (PEM) is a thin plastic sheet (giving it good mechanical
properties) that allows hydrogen ions to pass through it when wet. The prototypical PEM,
Nafion r , developed by DuPont, is coated on both sides with highly dispersed metal alloy
particles (usually Pt with loadings ∼ 0.4 mg cm-2 ) that act to catalyse both the anode
and cathode reactions. In the process of proton conduction, water molecules travel from
the anode to the cathode resulting in the need for a water recirculation system. Due to

27
the limited operating temperatures and water balance issues, this type of fuel cell requires
high catalyst loadings at both the anode and cathode and very pure gases (< 50 ppm of
CO and S contaminants). These requirements ultimately lead to expensive gas purification
systems, costly and inefficient waste heat management, and expensive water maintenance
systems. Despite the drawbacks associated with PEMFCs, they continue to be the electrolyte of choice for the demonstration of automotive fuel cell power systems because of
the combination of very high conductivity and adequate mechanical properties of these
polymers.
Alkali Fuel Cell(AFC)

Long used by NASA on space missions (e.g. on the Apollo

spacecraft) to provide both electricity and drinking water, alkali fuel cells operate at temperatures of 100–250 ◦ C. They use an aqueous solution of alkaline potassium hydroxide
contained within an inert matrix as the electrolyte. They typically have a fuel cell stack
output from 300 W to 5 kW. Alkali fuel cells, while providing extremely high power densities, are considered by most to be impractical because of the need to remove trace CO2
from both the fuel and oxidant streams in order to prevent reaction of the electrolyte to
form solid, non-conducting alkali carbonates. Nevertheless, some commercialization efforts
are underway.
Phosphoric Acid Fuel Cell (PAFC)

PAFCs are the most mature fuel cell tech-

nology and this type of fuel cell is commercially available today. Principal use of this type
of fuel cell is for mid-to-large stationary power generation applications. Existing PAFCs
have outputs of up to 11 MW. Operating temperatures are in the range of 150–220 ◦ C.
The electrolyte is 100% liquid phosphoric acid contained within an inert matrix, such as
silicon carbide. PAFCs can withstand significant concentrations of the fuel cell catalyst
poison carbon monoxide ( 1.5%), a common by-product of reforming many hydrocarbon
fuels. Disadvantages of PAFCs include (1) necessity for expensive platinum catalysts, (2)
low current and power as compared to other types of fuel cells, (3) large in size and weight,
and (4) the corrosive liquid electrolyte which requires complex system designs and negatively impacts operating life/costs. Although the leading fuel cell technology in the early
1990s, PAFCs have been largely abandoned because of the inability of developers to reach
high power densities, and thus meet competitive cost targets on a per watt output basis.

28
Molten Carbonate Fuel Cell (MCFC)

These fuel cells use an electrolyte composed

of a liquid solution of lithium, sodium and/or potassium carbonates soaked in a matrix
support. Typical operational temperatures are 500–700 ◦ C. Because of these high operating
temperatures which are needed to achieve sufficient electrolyte conductivity, noble metal
catalysts are not required for the electrochemical oxidation and reduction processes of the
fuel cell. However, these fuel cells suffer from the difficulties of containing a corrosive liquid
electrolyte. In particular, dissolution of NiO at the cathode and its precipitation in the form
of Ni at the anode can result in electrical shorts across the electrolyte—few U.S. researchers
continue to pursue the developement of this technology.
Solid Oxide Fuel Cell (SOFC)

SOFCs are another highly promising type of fuel cell

for high-power applications, such as industrial and large-scale central generators. Today’s
demonstration SOFCs utilize yttria stabilized zirconia (YSZ), containing typically 8 mol%
Y, as the electrolyte, Ni-YSZ at the anode, and other electronically conducting ceramics at
the cathode, which can withstand the operating temperatures of 700–1000 ◦ C necessary for
adequate ionic conduction. Solid oxide fuel cells have shown tremendous reliability when
operated continuously. For example, a 100 kW system fabricated by Siemens-Westinghouse
has successfully produced power for over 20,000 hrs without any measurable degradation
in performance. In addition, such fuel cells offer good fuel flexibility, allowing a variety of
hydrocarbon fuels to be utilized. However, SOFCs are still much too costly for widespread
commercialization and they function poorly under intermittent operation. Furthermore, at
such high operating temperatures, the peripheral fuel cell components can not be composed
of inexpensive metals, and therefore costly ceramic components that are sensitive to thermal
cycling and can lead to failure are employed.

1.4.3

Fuel Cell Performance 29

A perfect fuel cell would be able to deliver as much power as fuel delivered, but in practice
the maximum power deliverable by a fuel cell is limited by several factors: (1) the electrolyte
conductivity, (2) catalytic activity, (3) gas transport processes, and (4) inherent “leakages”
across the electrolyte membrane. The performance of a fuel cell is generally characterzied
by measuring the electric potential, while drawing increasing amounts of current, which
is then used to generate a performance “polarization” curve, such as that depicted by

29
the solid–line in Figure 1.9. Deviations from the theoretical open cell voltage, E0 , result
from these aforementioned limitations. These “losses,” indicated in Figure 1.9, are termed
Ohmic polarization, activation polarization, and concentration polarization. A significant
limitation to the performance of a fuel cell is a result Ohmic losses, a direct consequence of
slow ionic conduction in the electrolyte. A second significant source of losses, are the result
of activation polarization, which is a consequence of sluggish reaction kinetics at the anode
and cathode, and is directly affected by the activity of the fuel cell catalyst. Losses can also
occur at high current densities, at which point concentration polarization losses result from
the generation of fuel cell reaction products at a rate faster than they can be transported out
of the cell—thereby diluting the fuel and lowering the overall chemical potential of the cell.
The sum of these losses limits the overall performance of a fuel cell such that the measured
power (I × E) output of a fuel cell, as a function of current, results in a characteristic peak
power, indicated by the dotted-line in Figure 1.9. Last of all, inherent leakages across an
electrolyte membrane can be the result of electronic conduction or fuel/oxidant cross-over
through the electrolyte membrane, both of which lower the open cell voltage.

Figure 1.9: Diagram of a typical fuel cell performance characterization curves. Polarization curve,
electric potential as a function of current—solid-line, and power as function of current—dotted-line.

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23. M. Pham-Thi, P. Colomban, A. Novak, and R. Blinc. Phase-transitions in superionic
protonic conductors CsHSO4 and CsHSeO4 . Solid State Communications, 55(4):265–
270, 1985.
24. D.L. Goodstein. States of Matter. Dover Publications, Inc., Mineola, NY, 1985.
25. A.I. Baranov, L.A. Shuvalov, and N.M. Shchagina. Superionic phase-transition in cesium deuterosulfate and its ferroelastic properties. Kristallografiya, 29(6):1203–1205,
1984.
26. R. Mizeris, J. Grigas, V. Samulionis, V. Skritski, A.I. Baranov, and L.A. Shuvalov.
Microwave and ultrasonic investigations of superionic phase-transitions in CsDSO4 and
CsDSeO4 . Physica Status Solidi A-Applied Research, 110(2):429–436, 1988.
27. L.F. Kirpichnikova, A.A. Urusovskaya, and V.I. Mozgovoi. Superplasticity of CsHSO4
crystals in the superionic phase. JETP Letters, 62(8):638–641, 1995.
28. Fuel Cells 2000. Fuel Cell Basics – Benefits. http://www.fuelcells.org/basics/benefits.html,
May 2004.
29. EG&G Services, Parsons, Inc. Fuel Cell Handbook. National Energy Technology Laboratory, Office of Fossil Energy, U.S. Department of Energy, P.O. Box 880, Morgantown,
West Virgina 26507-0880, 5th edition, October 2000.

Chapter 2

Experimental Methods

2.1

Synthesis

One advantage to carrying out research on solid acids is the relatively easy synthesis of
most compounds from aqueous solutions. In general, starting from the appropriate ions in
aqueous solution in stoichiometric quantities yields the desired MHn XO4 -type solid acid,
M+ (aq) + Hn XO4 − (aq) → MHn XO4 (s) + H2 O
where M = Li, Na, K, Rb, Tl, NH4 , and Cs; X = S, Se, P, and As; and n= 1, 2. Various
methods are employed in precipitating solid acids compounds from solution: (1) heating
to evaporate excess water, (2) freeze-drying to submilate excess water, and (3) solvent
introduction to exceed the solubility limit of the desired solid acid compound. The last
method is preferred, as it is an inexpensive and expeditious synthesis method. For each
solid acid some methods are more effective than others, and in the latter case some solvents
are more productive than others. Other factors which have an effect on the synthesis of solid
acid compounds are pH, synthesis temperature, and ion concentration. In the Appendix are
recipes for the preparation of various solid acid compounds. In this work, single crystals were
grown by slow evaporation of water at ambient temperature from aqueous solutions, where
the solutions were prepared from re-dissolved powders of the desired solid acid compounds.

2.2

Structural Characterization

Two techniques were employed for the structural characterization of solid acids: (1) X-ray
diffraction (XRD), and (2) nuclear magenetic resonance (NMR) spectroscopy. XRD was
the principal method used for phase identification, structure determination, and crystal

33
orientation. Single crystal X-ray diffraction was used primarily for phase identification and
crystal orientation. Phase identification and structure determination using the Rietveld
method were carried out using powder X-ray diffraction (PXRD) data. Pulsed Fourier
transform magic angle spinning (MAS) 1 H-NMR measurements were performed to identify
the local proton environment of solid acid compounds.

2.2.1

X-ray Diffraction

Single crystal and powder X-ray diffraction are essential techniques for determining the
atomic structure of crystalline solids. While single crystal X-ray diffraction techniques are
preferred for the unambiguous determination of crystal structures, due to the difficulty in
attaining single crystal samples and the polycrystallinity that is commonly induced by phase
transitions, we often defer to PXRD. When crystal samples were available, single crystal
X-ray diffraction was used primarily for phase identification and for the determination
of crystal axis (crystal orientation), which would, in turn, be used to characterize other
anisotropic properties of the crystal sample. In addition to routine phase identification,
PXRD was also used to determine new crystal structures which were refined using the
Rietveld method.
2.2.1.1

Single Crystal X-ray Diffraction

Single crystal diffraction data were collected using a Syntex four-circle diffractometer with
Mo Kα radiation (λ = 0.71073 Å). For phase identification small (∼ 0.15 mm across) single
crystals were cut from larger crystals, then attached to the end of a thin glass fiber using a
common two-part epoxy. Next, the glass fiber was mounted into a cylindrical brass holder,
which, in turn was placed in a goniometer. Finally, the crystal was aligned in the center of
the X-ray beam. The crystal axis orientation of large crystals (> 1 mm across) was carried
out by simply mounting the crystal on piece of clay attached to a goniometer head, and
then aligning in the center of the X-ray beam.
2.2.1.2

Powder X-ray Diffraction

PXRD data obtained in this work were taken using either a Siemens D500 or a Philips
X’Pert PRO diffractometer with Cu Kα radiation (λ = 1.5418 Å) and an applied voltage

34
and current of 45 kV and 40 mA, respectively. Data were collected at elevated temperatures
using the Philips X’Pert PRO diffractometer fitted with an Anton Paar HTK 1200 high
temperature furnace capable of temperatures up to 1200 ◦ C and non-ambient atmospheres.
For the identifications of phases, both ICSD (Inorganic Crystal Structure Database) and
ICDD (International Centre for Diffraction Data) databases were used in conjunction with
the commercial software package Philips X’Pert Highscore or the free software package
PowderCell for Windows 1 . When applicable, a silicon powder ground from single crystal
silicon was used as an internal 2θ standard. Refinements of unknown crystal structures and
the determination of lattice constants were carried out using the Rietveld method, see next
section for details.
2.2.1.3

Rietveld Method 2,3

Reitveld analysis was carried out using the free software package Rietica 4 , as well as the
commercially available software Philips X’Pert Plus. In principle the Rietveld method is
based on the equation:

yic = yib +

kz
XX

Gpik Ik ,

(2.1)

p k=kp

where yic is the net intensity calculated at point i in the pattern, yib is the background
intensity, Gik is a normalised peak profile function, Ik is the intensity of the kth Bragg
reflection, k1 . . . kz are the reflections contributing intensity to point i, and the superscript
p corresponds to the possible phases present in the sample. The intensity Ik is given by the
expression:
Ik = SMk Lk |Fk |2 Pk ,

(2.2)

where S is the scale factor, Mk is the multiplicity, Lk is the Lorentz polarization factor, and
Fk is the structure factor defined by
Fk =

fj exp 2πi(h|r rj − h|k Bj hk ),

(2.3)

j=1

where fj is the scattering factor or scattering length of atom j, and hk , rj and Bj are matrices representing the Miller indices, atomic coordinates, and anisotropic thermal vibration
parameters, respectively, and the superscript | indicates matrix transposition. The factor

35
Pk is used to describe the effects of preferred orientation, where no preferred orientation is
indicated Pk = 1.
The positions of the Bragg peaks from each phase are determined by their respective
set of cell dimensions, in conjunction with a zero parameter and the wavelength provided.
All of these parameters except the wavelength, may be refined simultaneously given a user
defined peak profile function and crystal structure parameters.
Of the commonly employed peak profile functions (Gaussian, Lorentzian, Pseudo-Voigt,
Pearson VII, and Voigt) Pseudo-Voight was selected and used for all Rietveld refinements
carried out in this work. The Pseudo-Voigt peak profile function (Gik ) is simply a linear
combination of Gaussian (GG ) and Lorentzian (GL ) peak profile functions:
Gik = ζ · GG + (1 − ζ) · GL
1/2

= ζ

(2.4)
1/2

c0
) + (1 − ζ) 1 1/2 exp (−c1 Xik
(1 + c0 Xik
),
Hk π
Hk π

(2.5)
(2.6)

where c0 = 4, c1 = 4 ln 2, Hk is the full width at half maximum (FWHM) of the kth
Bragg reflection, Xik = (2θi − 2θk )/Hk , and ζ (= 0 to 1) is a refinable “mixing” parameter
between pure Lorentzian and pure Gaussian peak profiles. The variation of the peak FWHM
is described by the function:
Hk = (U tan 2θ + V tan θ + W ),

(2.7)

where U , V , and W are refinable peak shape parameters.
The background yib was obtained by a least square refinement of data obtained at
positions where no peaks appear to contribute to the observed intensity using the function:

yib =

bm (2θi )m ,

(2.8)

m=−1

where bm is one of six refinable parameters.
The least-squares refinement procedure used here employs the Newton-Raphson algo-

36
rithm to minimize the quantity:

wi (yio − yic )2 ,

(2.9)

where yio is the set of observed diffraction intensities collected at each step across the
pattern, yic is the set of corresponding calculated values obtained from equation 2.1, and wi
is the weight assigned to each observation (see below). The minimization of R is undertaken
over all data points contributing to the peaks and the background.
Several values are used to determine the quality of a Reitveld refinement. They are
defined as follows:
• The profile R-value (Rp )
Rp =

|yio − yic |
yio

(2.10)

• The weighted profile R-value (Rwp )
P
Rwp =

wi (yio − yic )2
wi yio

1/2
(2.11)

• The Bragg R-value (RB )
RB =

|Iko − Ikc |
Iko

(2.12)

• The expected R-value (Rexp )
N −P
Rexp = P
wi yio

(2.13)

• The goodness of fit (GOF)
GOF =

Rwp
Rexp

• Durbin-Watson statistic (d)
PN
d=

i=2 (∆yi − ∆yi−1 )
Q
2
i=1 yi

where the parameters describing the values above are defined as follows:

(2.14)

37
yic

: calculated intensity at point i

yio

: observed intensity at point i

: reciprocal of the variance at the ith step, 1/σi2 = n/yic ≈ n/yio

: number of detectors contributing to the step intensity average

Iko

: observed intensity of reflection k

Ikc

: calculated intensity of reflection k

: number of observations

: number of adjusted parameters

∆yi

: difference between observed and calculated intensity at a given step

While, in theory, all parameters can be refined simultaneously in a Rietveld refinement,
highly unstable parameters often require that parameters be systematically refined independently. For such cases, the parameter refinement strategy recommended by R.A Young 3
was employed, where parameters were refined in the following order:

2.2.2

Scale of peak intensities

Specimen displacement

Zero point shift of instrument

First order background parameters

Lattice parameters: a, b, c, α, β, γ

Higher order background parameters

Peak shape parameter: W

Atomic coordinates: x, y, z

Site occupancy and isotropic thermal parameters: Nj , Bj

10.

Other peak shape parameters: U , V

11.

Anisotropic thermal parameters: Bj

Nuclear Magnetic Resonance Spectroscopy

Pulsed Fourier transform 1 H-NMR measurements were performed on finely ground samples
to characterize the proton environment of selected compounds, specifically, the number of
crystallographically distinct hydrogen atoms and their relative amounts. All measurements
were taken on a Bruker DSX 500 MHz NMR spectrometer using tetramethylsilane (TMS)
as a reference for measuring chemical shifts. Magic angle spinning (MAS) was employed

38
to reduce the proton-proton dipole broadening of the signal lines resulting from the local
interactions of a proton’s magnetic moment with the dipole fields generated by its neighbors.
For most measurements, a 12 kHz spinning rate was used in conjunction with a 4 µs, 90◦
pulse. The spin-lattice relaxation time t1 was on the order of 1000 s for all compounds
measured, revealing that the excited H+ nuclei in these solid acids interact weakly with
their surrounding lattices 5 . The observed chemical shifts for the crystallographic protons
were ∼ 10–12 ppm, typical values for protons residing in medium strength hydrogen bonds 5 .
Sharp peaks often observed at ∼ 6 ppm were attributed to surface adsorbed water based
upon simlar phenomenon observed in calcium phosphates 6 .

2.3

Properties Characterization

Protonic conductivity was the principal property of interest in the materials examined here.
For this, extensive use of alternating current (AC) impedance spectroscopy has been made to
characterize the protonic conductivity of solid acid compounds as a function of temperature
at both ambient and high pressures. Superprotonic behavior of solid acids compounds
is (to date) always preceded by an order-disorder phase transition. Therefore, extensive
effort has been made to characterize these phase transitions. Thermal analysis to measure
the enthalpy and temperature of these transitions, as well as to evaluate decomposition
behavior, has been an essential tool in these investigations. Furthermore, changes in optical
properties resulting from these order-disorder transitions observed through optical polarized
light microscopy were used to identify superprotonic phase transitions.

2.3.1

Impedance Spectroscopy 7

The advantage of an AC method is that there is no net movement of ions, thereby eliminating the need for an ion source. This method is implemented by placing an ionic conducting
material under an alternating electric field E, with an angular frequency of ω and amplitude
E0 , which can be described by the complex time (t) dependent wave function
E(t) = E0 · eiωt .

(2.15)

39
The current response I(t) generated by this electric field in the material being tested, as
depicted in Figure 2.1, can be described by a similar time dependent wave function with
some applitude I0 , plus some phase shift φ,
I(t) = I0 · ei(ωt+φ) .

(2.16)

Figure 2.1: Depiction of the real (<) component of an alternating applied electric field E(t) with an
amplitude E0 and angular frequency ω (solid line), and the real component of the induced current
response I(t) of a material with an amplitude I0 and angular frequency ω phase shifted by some
amount φ (dashed line).

From Ohm’s law,
E(t) = I(t) · Z,

(2.17)

where Z is the complex impedance characterized by a real component Z 0 and an imaginary
component Z 00 ,
Z = Z 0 + iZ 00 .

(2.18)

It is convenient to define the reciprocal of impedance, or admittance Y , as
= Y 0 + iY 00 .

(2.19)

I(t)
I0 eı(ωt+φ)
I0
= (cos φ + i sin φ).
ıωt
E(t)
E0 e
E0

(2.20)

Y ≡
Rewriting Ohm’s law using admittance
Y (φ) =

When a material’s current response is at frequency at which no phase shift occurs (φ = 0),

40
then equation 2.20 becomes
I0
= ,
E0

Y (0) =

(2.21)

where R is taken to be the real resistance of the material under test. As the frequency
ω increases, the material’s current response due to mobile charge carriers begins to lag
behind the applied electric field by some phase shift φ. This, in turn, leads to a capacitive
response from the material under test. This capacitive response is at a maximum at some
characteristic frequency ω0 , when the current response is exactly 90◦ out of phase with the
applied electric field, or when φ = π2 . Capacitance C, defined in terms of applied electric
field and charge q,
C≡

q(t)
E(t)

(2.22)

can be used to evaluate the imaginary component of the admittance, by substiting in for
q(t) into the definition of current,
I(t) ≡

q(t) = C E(t).
dt
dt

(2.23)

Now, substituting in for E(t), using equation 2.15, gives
I(t) = iωCE(t).

(2.24)

From Ohm’s law, equation 2.20, and the above result, the imaginary component of the
admittance for φ = π2 is

I(t)
= iωC.
E(t)

(2.25)

With the real and imaginary components (at φ = 0, and π2 , respectively) of the complex
admittance the complete polar form can be written:
Y = Y 0 + iY 00 =

+ iωC.

(2.26)

Similiarly, with some rearranging the complex impedance can be written:
Z=

1/R
ωC
−i
(1/R)2 + (ωC)2
(1/R)2 + (ωC)2

(2.27)

It should be noted that a similar analysis could have been carried out using the impedance,

41
rather than the admittance; however, the result is an expression in which the real component
of the impedance increases with frequency, which is not phenomenological.
In Figure 2.2, the complex impedance as a function of frequency ω or “Nyquist” plot
of equation 2.27 is presented. Here the apex is defined by a characteristic frequency ω0 in
terms of the resistive and capacitive response of the material under test,
ω0 =

(2.28)

and the diameter of the semi-circle is given by the real resistance of the material R. These
results lead naturally to a phenomenological equivalent RC circuit model, depicted in Figure 2.3, which is commonly employed in the analysis of AC impedance results.

Figure 2.2: Nyquist plot (Z 0 versus -iZ 00 ) of the AC impedance of a material as a function of
frequency ω. The diameter of the the semi-circle yields the real resistance R of a material, whereas
the apex occurs at a characteristic frequency ω0 equal to 1/RC.

Figure 2.3: A resistor (R) in parallel with a capacitor (C) circuit used to model the AC impedance
response of a material.

Real material impedance responses rarely exhibit perfect RC equivalent circuit behavior.
The most prominent deviation observed in real material impedance spectra is a depression
of the observed semi-circle in a Nyquist plot, shown in Figure 2.4. Phenomenologically,

42
this behavior is accounted for by introducing a new circuit element Q, or constant phase
element (CPE), in place of the capacitor. Where Q is defined as
Q ≡ (iω)n Y0 ,

(2.29)

where n and Y0 are parameters characterizing element Q. The admittance of an RQ circuit
is
Y =

+ Q = + (iω)n Y0 ,

(2.30)

where in the limit as n goes to one, we get our previous RC circuit,
lim

n→1

+ (iω)n Y0

+ iωC.

(2.31)

Unfortunately, no good physical description has yet been given for element Q, nevertheless
it is of considerable utility in least square refinements of real data sets.

Figure 2.4: Nyquist plots of RC and RQ equivalent circuits, where R is a resistor, C a capacitor,
and Q (= (iω)n Y0 ) a constant phase element depicting the apex depression often observed in real
AC impedance spectra.

The conductivity of materials was characterized by this method using an HP 4284A
Precision LCR Meter, in the frequency range of 20 Hz to 1 MHz and an applied voltage
of 1.0 V. Both single crystal samples and polycrystalline pellets were measured, with Ted
Pella silver paint serving as the electrode material. Data were collected on samples upon
heating and cooling in a tube furnace capable of temperatures up to 1200 ◦ C under various
atmospheres.
Least squares refinements using the previously described RQ equivalent circuit model
were carried out using the commercially available software package, ZView (Scribner &

43
Associates). The refined material resistance R was then normalized by a geometric factor
A/l, where A is the area of the sample and l is the thickness of the sample to obtain the
conductivity σ,
σ=

1/R
A/l

(2.32)

Then plotting the conductivity σ data as function of temperature T , in an Arrhenius plot
(ln σT versus 1/T ), the Arrhenius law:
A0
exp
σ(T ) =

−∆Ha
kB T

(2.33)

where kB is the Boltzmann constant, was used to extract the activation enthalpy ∆Ha and
pre-exponential factor A0 for protonic transport.

2.3.2

High-Pressure Impedance Spectroscopy

Though in principle high-pressure impedance measurements are no different than at ambient pressure, in reality these measurements are experimentally challenging to perform—
appropriate equipment and careful sample preparation are essential. For these measurement
a large-volume 1000-ton cubic anvil press (H.T. Hall Inc.) was employed, shown in Figure 2.5.

(a) Full view of experimental set-up

(b) Close-up view of anvils where cell is loaded

Figure 2.5: Photos of large-volume 1000-ton cubic anvil hydraulic press. (a) Full view of experimental setup, and (b) close-up view of anvils where high-pressure cell is loaded. (Photos courtesy
of R.A. Secco 8 )

Powder samples, lightly ground from single crystals, were packed into a boron nitride

44
(BN) cup with platinum electrodes on top and bottom. The cup was then placed into an AC
impedance high-pressure cell, a schematic of which is shown in Figure 2.6. The pressure cell
assembly was in turn loaded into a large-volume press, Figure 2.5(b). Each anvil, in electrical isolation from the other, makes contact through the faces of the cube with the Pt electrodes, Pt/Pt10%Rh thermocouple, and Nb foil heater. In such a design, quasi-hydrostatic
pressure is maintained by 12 gaskets formed by extrusion of the oversized pyrophyllite cube
along its edges. Details of the experimental apparatus and pressure calibration are given
elsewhere 9,10 . Impedance measurements were performed from room temperature up to ∼
375 ◦ C at 1.0 ± 0.2 GPa upon heating and cooling. A pressure-temperature correction was
applied to the readings obtained from the Pt/Pt10%Rh thermocouple 11 . AC impedance
data were collected using a Solartron SI 1260 Impedance/Gain-Phase Analyzer over the
frequency range 10 Hz to 1 MHz and with an applied voltage of 1.0 V. Data analysis was
again performed using the commercial software package, ZView (Scribner & Associates).

Figure 2.6: Cross-sectional schematic view of a high-pressure cell assembly used for AC impedance
measurements.

Because the sample cannot be directly observed in the high-pressure cell, one must
establish whether measured changes in conductivity are due to melting of the sample or to
a true solid-solid transition. To achieve this, a second high-pressure ball drop experiment
was performed. In this experiment, a 0.5 mm diameter ruby sphere and a 0.6 mm diameter
tungsten carbide (WC) sphere, with 1 atm 22◦ C densities of 4.0 g cm-3 and 14.9 g cm-3 ,
respectively, were placed on top of a powder sample packed into a BN cup, as shown in
the schematic in Figure 2.7. The pressure cell was loaded into the same large-volume
press utilized in the previous high-pressure impedance measurements, the pressure and
temperature raised to 1.0 ± 0.2 GPa and to the highest temperature attained for the high-

45
pressure impedance measurement, respectively, and held under these conditions for ∼ 10
minutes. Observation of recovered samples, in which the ruby and WC spheres remained
suspended over the sample indicated that melting had not occurred.

Figure 2.7: Cross-sectional schematic view of a high-pressure cell assembly used for ball drop
experiments.

2.3.3

Thermal Analysis

Thermal analysis was utilized for the characterization of phase transitions and decomposition behavior of solid acids. Analysis was performed using Perkin Elmer DSC 7, as well as a
Netzsch STA 449C thermal analyzer, capable of simultaneous differential scanning calorimetry (DSC) and thermal gravimetry (TG), equipped with a Pfeiffer Vacuum Thermal Star
mass spectrometer for the analysis of evolved gasses under various flowing atmopheres and
heating rates. Phase transitions were characterized by an endothermic or exothermic event
observed by DSC upon heating or cooling samples, whereby the enthalpy (heat) of the transition ∆Htr and transition temperature Ttr were measured to yield the changes in entropy
at the transition ∆Str ,
∆Str =

∆Htr
Ttr

(∆Gtr = 0).

(2.34)

Decomposition behavior was identified by weight-losses observed by TG and DTG (differential thermal gravimetry), and further aided by the analysis of evolved gasses by mass
spectroscopy.

2.3.4

Polarized Light Microscopy 12

Polarized light microscopy is an ideal tool for observing phase transitions in optically transparent anisotropic crystals. Isotropic materials, such as unstressed glasses and cubic crystals, demonstrate the same optical properties in all directions. They have only one refractive
index, and therefore, no restriction on the vibration direction of light passing through them.
Anisotropic materials, in contrast, have optical properties that vary with the orientation
of incident light with respect to the crystallographic axes. They demonstrate a range of
refractive indices depending both on the propagation direction of light through a substance
and on the vibrational plane coordinates. By placing an anisotropic crystal with unique
crystal axes, whose directions are represented by vectors a,
a = ax x̂ + ay ŷ,

(2.35)

b = bx x̂ + by ŷ,

(2.36)

and b,

between two crossed-polarizers, where the polarizing direction of the first polarizer p1 is
parallel to the x-axis,
p1 = x̂,

(2.37)

and orthogonal to the second polarizer p2 , which is then parallel to the y-axis,
p2 = ŷ,

(2.38)

and then rotating the crystal, the optical axes of the crystal can be identified. To achieve
this, we begin by describing how an anisotropic crystal behaves between cross-polarizers.
First of all, when the incident beam, travels though the first polarizer, all vibrational directions, except those parallel to the x-axis are filtered out, Figure 2.8. The remaining
“polarized” light beam then enters the crystal, which acts as beam splitter and divides
light ray into two parts, such that the polarized light vector, v1 , can be written as a linear
combination of the crystal vectors a and b,
v1 = a1 a + b1 b,

(2.39)

47
to give two new light ray vectors va and vb ,
va = a1 (ax x̂ + ay ŷ),

(2.40)

vb = b1 (bx x̂ + by ŷ).

(2.41)

After the light has passed through the crystal, it enters the second polarizer, which filters
out all light, but that which is along the y-axis, such that
p2 · va = a1 ay ŷ

(2.42)

p2 · vb = b1 by ŷ,

(2.43)

and the final observable light ray v2 is
v2 = (a1 ay + b1 by )ŷ.

(2.44)

Figure 2.8: Diagram of an anisotropic crystal beam-splitting light between crossed-polarizers.
If, for example, the first polarizer is parallel to the a direction of the crystal (akp1 ), then
all of the light passing through the crystal will be composed of a, such that after passing
through the second polarizer, no light will be observed
v2 = p2 · va = ŷ · a1 ax x̂ = 0.

(2.45)

This is known as the extinction position of the crystal, which can similarly be determined

48
for when b is parallel to the either of the polarizing axes. Therefore, by simply rotation
the crystal between the crossed-polarizers, the extinction positions, and thus, crystal axis
can quickly be identified. However, when the crystal is isotropic, no distinction can be
made between crystal axes, and therefore, the crystal is observed to be black if the crystal
is not optically active, or of uniform illumination if optically active, when rotated between
crossed-polarizers.
In this work, a transimission optical microscope, Leica DM LB polarized light microscope, was employed and fitted with an “in-house” built thermal stage cabable of temperatures of ∼ 270 ◦ C under ambient atmospheres. Order-disorder phase transitions were
identifited upon heating crystals under the microscope, and observing whether the optical
properties of the crystal became isotropic.

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11. F.P. Bundy. Effect of pressure on EMF of thermocouples. Journal of Applied Physics,
32(3):483, 1961.
12. Elizabeth A. Wood. Crystals and Light. Dover Publications, Inc., New York, NY, 2nd
edition, 1977.

Chapter 3

Structure of Superprotonic MHnXO4-type
Solid Acids
This chapter will address some of the structural features affecting the presence of superprotonic behavior in solid acid compounds—specifically, hydrogen bonding and cation to oxyanion size effects in MHn XO4 -type solid acid compounds (where M = monovalent cation,
X = S, Se, P, As, and n = 1, 2). An effort has been made, in this chapter, to focus on the
structural aspects of superprotonic solid acids, leaving inquiries relating to the properties
of superprotonic phase transitions to be addressed in the next chapter. However, there is
an intimate relationship between the structure and the properties of a material; that is, it
is the observable properties of a material that give us insight into its structure, while it is
the structure of a material that dictates its properties. This distinction between structure
and properties is particularly vague in the case of superprotonic solid acids, in which such
compounds exhibit a characteristic superprotonic transition to a highly disordered structure
that is identified by it high protonic conductivity. As such, it will often be the case here
that the structure of solid acids will be investigated by examining their properties, and vice
versa.

3.1

Hydrogen Bonding

While it is well known that in solid acids containing partially hydrogen-bonded oxy-anions,
such as CsHSO4 1 and Rb3 H(SeO4 )2 2 , the existence of a superprotonic phase in fully
hydrogen-bonded solid acids, such as CsH2 PO4 , RbH2 PO4 , and KH2 PO4 , has been under dispute for quite some time. In this work, significant effort has been made to determine
whether or not these fully hydrogen-bonded solid acids have superprotonic phase transi-

51
tions. Previous efforts to identify superprotonic conductivity in these compounds has been
impeded by dehydration processes that often mask high temperature phase behavior, complicating the identification of a superprotonic phase. Here we set out to answer the question:
Can fully hydrogen-bonded solid acids exhibit superprotonic phase transitions?
Because entropy drives all phase transitions, we began by looking at the entropic driving
forces that encourage superprotonic phase transitions. The superprotonic phase in CsHSO4
is known to exhibit hydrogen bond disorder 3 . In Figure 3.1, a simple two-dimensional
model depicting hydrogen-bonded tetrahedral oxy-anions is presented. CsHSO4 at room
temperature, like Figure 3.1(a), exhibits two hydrogen bonds (solid circles) per tetrahedron,
that is, 2 of the 4 possible hydrogen bond positions are occupied. Based upon this model,
the configurational entropy S, as a function of the number of possible configurations Ω that
would be gained by the hydrogen bonds being disordered is

S = R ln Ω = R ln
= R ln 6 = 14.9 J mol-1 K-1 ,

(3.1)

where R is the molar gas constant. This result is in close agreement with the reported
experimental value of 14.8(6) J mol-1 K-1 4 . Now, if we consider a fully hydrogen-bonded
solid acid as depicted in Figure 3.1(b), such as CsH2 PO4 , where there are 4 hydrogen bonds
for 4 hydrogen bond positions. Then, the configuration entropy using this model would be

S = R ln
= R ln 1 = 0 J mol-1 K-1 .

(3.2)

Therefore, based solely upon this simple model for hydrogen bond disorder, there would
be no entropic driving force for a superprotonic phase transition in fully hydrogen-bonded
solid acids, and thus, we would not expect such a transition.
In fact, this model is in incomplete, as it does not account for oxy-anion disorder. In
the following sections, background and experimental results of these investigations into the
high temperature behavior of CsH2 PO4 , RbH2 PO4 , and KH2 PO4 are presented. Evidence
is given that demonstrates that CsH2 PO4 and RbH2 PO4 do, in fact, exhibit superprotonic
transitions, while KH2 PO4 does not.

(a) Half-occupied hydrogen bonds

(b) Fully-occupied hydrogen bonds

Figure 3.1: A simple model depicting hydrogen-bonded (dashed-lines) oxy-anions (squares) in solid
acids, in which filled and empty circles represent occupied and unoccupied hydrogen bond positions,
respectively. (a) Half-occupied hydrogen bonds, in which 2 of the 4 positions are occupied, e.g.,
CsHSO4 . (b) Fully occupied hydrogen bonds, in which 4 of the 4 positions are occupied, e.g.,
CsH2 PO4 .

3.1.1

CsH2 PO4 5

The objective of this section study is to demonstrate unequivocally whether or not CsH2 PO4
undergoes a transition to a superprotonic phase prior to decomposition. In the first portion
of this study, the dehydration and phase transition behavior, and the effect of surface water
on conductivity at ambient pressures are presented. It is demonstrated that, even under
ambient pressure conditions, a high temperature phase transition occurs that is independent
of decomposition. The short-lived nature of this phase at ambient pressures, however,
precludes accurate measurement of its electrical properties. To address this challenge, in the
second portion, we employ high-pressure during conductivity measurements, with the aim
of suppressing dehydration and enabling complete characterization of the high temperature
phase. Before presenting the results of these sets of studies, a brief summary of the prior
state of knowledge regarding the behavior of CsH2 PO4 at elevated temperatures is given.
3.1.1.1

Background

Cesium dihydrogen phosphate, CsH2 PO4 , has received attention because of both its high
temperature proton transport properties and its low temperature ferroelectric properties.
While there is wide agreement on the low-temperature behavior of this material—that it
undergoes a ferroelectric phase transition at 154 K (P 21 /m → P 21 ) 6,7 —there is significant
discrepancy in the literature regarding its high temperature properties. It has been observed

53
that, upon heating, the conductivity of CsH2 PO4 undergoes a sharp increase at 230 ◦ C 8,9,10 .
Some, including Baranov et al. 8 , Romain and Novak 11 , Preisinger et al. 12 , and Luspin
et al. 13 attribute this behavior to a structural transition to a stable, high-temperature
phase (a so-called superprotonic transition), whereas others, including Lee 14 and Ortiz
et al. 9 , attribute the increase in conductivity to an artifact of water loss due to thermal
decomposition.
As aforementioned, whether or not CsH2 PO4 undergoes a superprotonic transition is of
particular relevance to understanding the role of hydrogen bonding in these phase transformations. Under ambient temperature and pressure conditions, this compound has a unique
hydrogen bond network in which PO3−
4 oxy-anions are linked via O–H· · · O bonds at all
corners of the phosphate tetrahedra, forming [H2 (PO4 )− ]∞ layers. Cesium cations reside
at sites between these layers. Plakida has treated the superprotonic phase transition in
the related solid acid compound, CsHSO4 , in terms of a microscopic model that assumes
an order-disorder relationship between the low and high temperature phases 15 . Although
not stated explicitly, such a model rules out the possibility of a superprotonic transition
in a compound such as CsH2 PO4 , in which all oxygen atoms participate in hydrogen bond
formation.
As an example of the controversy surrounding the high temperature behavior of CsH2 PO4 ,
the thermal gravimetric and differential thermal analysis (TGA and DTA) data reported
by Rashkovich et al. 16 , by Ortiz et al. 9 , and by Nirsha et al. 17 are presented in Figure 3.2.
It is immediately evident that there are significant discrepancies between these three sets
of results. Rashkovich et al. have reported two structural (polymorphic) phase transitions,
the onset of which occurs at 230 and 256 ◦ C, prior to decomposition, which begins at ∼
300 ◦ C. Data were collected only for temperatures of 180 ◦ C and higher. In a later paper,
Rashkovich and Meteva reported high temperature diffraction data and proposed that the
formation of an intermediate phase of “symmetry no higher than monoclinic” was responsible for the transition at 230 ◦ C 18 . In addition, they showed that the main peaks of cesium
phosphite, CsPO3 , appeared at temperatures as low as 100 ◦ C, and that this phase was
well-formed by 250 ◦ C, although weight loss was not observed until higher temperatures
were reached. Differential scanning calorimetry (DSC) measurements of Metcalfe and Clark
(not shown in Figure 3.2) indicate the presence of two polymorphic transitions, one at 149
◦ C (quasi-irreversible) and the latter at 230 ◦ C (reversible), with decomposition occurring

54
at temperatures above ∼ 250 ◦ C 19 , which is in relatively good agreement with Rashkovich
et al. for the temperature regime of mutual examination.

(a) Thermal gravimetric analysis

(b) Differential scanning calorimetry
and differential thermal analysis

Figure 3.2: Prior thermal analysis results reported for CsH2 PO4 by Ortiz et al. 9 , Nirsh et al. 17 ,
and Rashkovich et al. 18 ; (a) thermal gravimetric analysis (TGA), and (b) differential scanning
calorimetry (DSC) and differential thermal analysis (DTA) data.

In contrast, Nirsha et al. reported that thermal events occur at ∼ 220 and 255 ◦ C and
are both due to thermal decomposition, with the compound dicesium dihydrogen pyrophosphate, Cs2 H2 P2 O7 , forming over the temperature range 175–225 ◦ C and CsPO3 over the
range 235–285 ◦ C 17 . This interpretation was supported by high temperature diffraction
data and IR spectra. Thermal events evident in the DTA data at higher temperatures
were ascribed to the crystallization of the initially amorphous CsPO3 . The conclusions that
Ortiz et al. draw from their results are in general agreement with the findings of Nirsha et
al. although they differ in detail. Quite surprisingly, the DSC data of Ortiz et al. match
the DTA data of Rashkovich et al., but their TGA results differ significantly. Consistent
with the results of Rashkovich et al., Ortiz and coworkers observe thermal events at ∼
149, 231, and 273 ◦ C, all of which coincide with peaks in their differential thermal analysis
data. Accordingly, they ascribe all three, along with discontinuities in the conductivity of
CsH2 PO4 (see Figure 3.3, below) at 149 and 231 ◦ C, to thermal dehydration and partial
polymerization (i.e. polycondensation of phosphate groups).
A completely different interpretation of the high-temperature behavior of CsH2 PO4 has
been offered by a number of authors, specifically, that at ∼ 230 ◦ C the material transforms to

55
a phase of cubic symmetry with superprotonic conductivity. The conductivity of CsH2 PO4 ,
as reported by several authors 1,9,10 , is reproduced in Figure 3.3. It is evident that all
authors are in agreement that the conductivity increases sharply at ∼ 230 ◦ C, while only
Baranov et al. have attributed the increase to a transformation to a thermally stable,
superprotonic phase 1 . They report the activation energy for proton transport in this phase
to be 0.32 eV, and the magnitude of the conductivity at 230 ◦ C to be 2.3 × 10-2 Ω-1 cm-1 ,
somewhat higher than others have observed. In contrast, Ortiz et al. flatly ruled out
the possibility of a polymorphic phase transformation, as described above 9 . Haile et al.
observed that the conductivity of CsH2 PO4 immediately decreased after the transition at
230 ◦ C, and concluded that if a superprotonic phase did indeed exist, it was a highly
transient state, immediately followed by decomposition 10 . Prolonged examinations of the
electrical properties of CsH2 PO4 by Ortiz et al. showed a similar degradation in conductivity
with time 9 .

Figure 3.3: Prior conductivity data reported for CsH2 PO4 by Baranov et al. 8 , Ortiz et al. 9 , and
Haile et al. 10 , plotted in Arrhenius form.

Very convincing data for the presence of a cubic, high-temperature phase of CsH2 PO4
has been presented by Preisinger et al. (see also reference 20 ), who performed diffraction
experiments at elevated temperatures. Under dry atmospheres, dehydration and the formation of Cs2 H2 P2 O7 was observed, but under humidified conditions, a stable cubic phase
(P m3m, a = 4.961 Å) appeared at temperatures above 230 ◦ C 12 . Baranov et al. had earlier proposed that their superprotonic phase was cubic on the basis of optical microscopy

56
investigations, which showed the phase to be optically isotropic 8 . Further evidence for a
polymorphic transition at 230 ◦ C comes from the work of Romain and Novak, who showed
by high temperature Raman spectroscopy that there is no evidence of Cs2 H2 P2 O7 formation up to temperatures as high as 246 ◦ C 11 . In addition, in a comprehensive study of the
high-temperature, high-pressure behavior of CsH2 PO4 , Rapoport et al. observed a stable,
high-temperature phase, that transformed reversibly to and from the lower temperature
monoclinic form at elevated pressures 21 .
In addition to the competing views as to whether the transition at 230 ◦ C in CsH2 PO4
corresponds to decomposition or a polymorphic transition, there is significant discrepancy
regarding the behavior in the temperature regime 100–150 ◦ C. As noted above, Ortiz et al.
suggest that CsH2 PO4 undergoes a thermal decomposition event at a temperature of 149 ◦ C
which, much like the transition at 230 ◦ C, gives rise to an increase in conductivity 9 . Others have ascribed the transition at this temperature to a subtle, polymorphic, monoclinic
→ monoclinic transformation. Evidence for this interpretation is provided by Bronowska
and Pietraszko, who observed a slight change in the thermal expansion coefficients at this
temperature 20 , and by Luspin et al., who noted a small change in elastic constants 13 . Baranowski and coworkers 22 observed a subtle transition, not at 149 ◦ C, as most other groups
have reported, but rather at 107 ◦ C. What is quite clear from their work is that the thermal
behavior of CsH2 PO4 in this lower temperature regime is highly dependent on sample state
and environment, that is, whether the material is subjected to mechanical grinding or has
been freshly prepared, and whether the atmosphere is humid or dry. Moreover, in no case
have these transitions at 107 and 149 ◦ C been found to be reversible, nor are they associated
with superprotonic conductivity. Given that the presence or absence of these transitions is
not relevant to the question of whether or not a superprotonic phase can exist in a compound such as CsH2 PO4 , with its particular hydrogen bond network. Therefore, no effort
was made in this work to obtain a detailed understanding of the behavior of CsH2 PO4 in
this lower-temperature regime.

57
3.1.1.2

Ambient Pressure Behavior

Thermal Analysis
Typical thermal analysis results for CsH2 PO4 samples of different particle sizes and fixed
heating rate (5 ◦ C min-1 ) are presented in Figure 3.4. The thermal gravimetry (TG)
and differential thermal gravimetry (DTG) results are shown in the top panel, differential scanning calorimetry (DSC) in the middle panel, and mass spectroscopy measurements
of H2 O (m18.00) in the evolved gases in the bottom panel. For the complete dehydration
of CsH2 PO4 by the following reaction:
CsH2 PO4 (s) → CsPO3 (s) + H2 O(g) ,
a weight loss of 7.83% is expected, as noted in the top panel. It is evident from these thermal
measurements that surface area plays a significant role in the decomposition/dehydration
of CsH2 PO4 and may well explain the literature discrepancies noted above. For example, a
weight loss of 7% was observed at 278 ◦ C for the fine powder, while for single crystals the
same weight-loss was not observed until 352 ◦ C. Quite significantly, regardless of sample
surface area, in all cases a polymorphic transition, independent of decomposition, is clearly
evident at ∼ 230 ◦ C. Although the impact of this transition on conductivity cannot be
assessed from thermal analysis alone, we identify this transformation as the superprotonic
transition described earlier by Baranov et al. 8 At temperatures just beyond this structural
transformation, dehydration occurs via multiple steps. The superprotonic phase transition
(SP) and what are defined here as the first (I), second (II), third (III), and fourth (IV)
dehydration processes are indicated in Figure 3.4. For fine powders only dehydration processes I and II were observed, while the course powder and single crystals exhibited only
slight or no dehydration at I and II, with the majority of dehydration taking place at high
temperature processes III and IV.
The coincidence of the superprotonic phase transition with dehydration presents a challenge for the accurate measurements of the enthalpy ∆HSP of the superprotonic phase
transition. To address this challenge, the enthalpy of the transition was evaluated only
from single crystals, in which dehydration processes I and II are minimized. A value of 49.0
± 2.5 J g-1 was obtained for a heating rate of 5 ◦ C min-1 .
An inherent thermal lag in the thermal analysis can lead to systematic errors between
true and measured transition and reaction temperatures as a function of heating rate.

Figure 3.4: Thermal analysis of fine powder, course powder, and single crystals of CsH2 PO4 heated
at a rate of 5 ◦ C min-1 under flowing (40 cm3 min-1 ) dry Ar. Analysis consisted of simultaneous
thermal gravimetric (TG) and differential thermal gravimetric (DTG) analysis—top panel, differential scanning calorimetry (DSC)—middle panel, and mass spectroscopy of evolved H2 O vapor
(m18.00)—bottom panel.

The temperature difference ∆T between the measured peak temperature Tpeak and the
equilibrium onset temperature Tonset of a transition or reaction of a pure compound is
proportional to the heating rate υ, sample mass m, transition enthalpy ∆H, and the thermal
resistance % 23 :
∆T =

2mυ%∆H.

(3.3)

Assuming a constant % and utilizing samples of equal mass m, a linear relationship between
∆T and υ can be obtained. As the heating rate υ → 0, the difference in temperature
between the equilibrium onset and measured peak temperatures ∆T → 0, which implies that
Tpeak → Tonset . Therefore, by carrying out thermal analysis at several different heating rates
and extrapolating to a heating rate of zero, one can estimate the “true” onset temperature
for any thermal event.
As an example of the heating-rate dependent thermal behavior of CsH2 PO4 , a plot of
the TG and DSC traces obtained at several different heating rates from a fine powder of
CsH2 PO4 is shown in Figure 3.5. Analogous results were obtained for coarse powders and
single crystal samples. The Tpeak values for each process, as measured by DSC, DTG, and
mass spectroscopy, are plotted as a function of υ for fine powders in Figure 3.6. The

59
results obtained from these three thermal analysis techniques are in good agreement. More√
over, a linear relationship between Tpeak and υ is indeed evident. The true or equilibrium
onset temperatures, Tonset , determined by extrapolation to zero heating rate for each process and for each of the three sample types are summarized in Table 3.1. As is apparent
from these data, whereas TSP is relatively independent of surface area, the temperature of
the dehydration processes, I–IV, are not. Thus, for crystals of CsH2 PO4 heated rapidly,
the superprotonic phase transition will likely be observed before dehydration, however, if
sufficiently slow heating rates (< 0.3 ◦ C min-1 ) and large surface area powders are utilized,
dehydration can precede the superprotonic transition.

Figure 3.5: Thermal analysis of fine powders of CsH2 PO4 heated at rates of 0.5, 1, 5, 10, 15, and
25 ◦ C min-1 under flowing (40 cm3 min-1 ) dry Ar. Results of simultaneous thermal gravimetric (TG)
analysis—top panel, and differential scanning calorimetry (DSC)—bottom panel.

Figure 3.6: The peak temperature Tpeak of thermal events in fine powders of CsH2 PO4 as measured
by differential scanning calorimetry (DSC), differential thermal gravimetric (DTG)√analysis, and
mass spectroscopy (Mass Spec) of evolved H2 O vapor (m18.00) plotted as function of υ, the square
root of the heating rate employed for each measurement. Lines, calculated from a least squares fit
of the data, identify the thermal events resulting from the superprotonic phase transition (SP), first
dehydration process (I), and second dehydration
process (II). The equilibrium onset temperature
Tonset is indicated for each thermal event at υ = 0.

Table 3.1: Summary of measured onset temperatures for the superprotonic phase transition (TSP ),
and the first (TI ), second (TII ), third (TIII ), and fourth (TIV ) decomposition/dehydration processes
in CsH2 PO4 samples of various surface areas. Numbers in parentheses indicate the uncertainty in
the final digit(s).
Sample Type

TSP

TII

TIII

TIV

fine powders

228(2)

224(3)

258(5)

course powders

228(2)

230(4)

261(4)

292(5)

311(10)

single crystals

228(2)

230(5)

261(6)

298(8)

325(12)

/ ◦C

61
Polarized Light Microscopy
Optical polarized light microscopy studies support the conclusion that single crystal CsH2 PO4
undergoes a structural transition prior to decomposition. Typical images obtained under
cross-polarizers are shown in Figure 3.7. At room temperature (prior to heating), the optically anisotropic, monoclinic form of CsH2 PO4 was observed, Figure 3.7(a). Upon heating
to ∼ 245 ◦ C, a rainbow-colored phase-front traveled from left to right across the crystal,
leaving behind a new phase, which is optically isotropic (black) and presumably cubic, Figure 3.7(b) to (e). Upon cooling to room temperature, the crystal transformed back to an
optically anisotropic phase, Figure 3.7(e) to (f), with some evidence of slight damage to the
crystal quality. The reversible nature of this observed transformation is strong evidence for
a polymorphic phase transition as opposed to decomposition.

(a) 25 ◦ C

(d) 240 ◦ C

(b) 230 ◦ C

(e) 245 ◦ C

(f) 25 ◦ C

Figure 3.7: Polarized light microscopy images of a single crystal of CsH2 PO4 taken in the sequence
of temperatures: (a) 25 ◦ C → (b) 230 ◦ C → (c) 235◦ C → (d) 240 ◦ C → (e) 245 ◦ C → (f) 25 ◦ C.

63
Impedance Spectroscopy
The results of AC impedance measurements for both single crystal and polycrystalline samples under ambient pressure conditions are presented in Figure 3.8 in an Arrhenius plot.
Representative Nyquist plots obtained at temperatures above the superprotonic phase transition temperature TSP are presented in Figure 3.9. The conductivity of both sample types
increased sharply at the transition temperature, however, in neither case to the high value
reported by Baranov et al. 8 . Moreover the jump in conductivity was significantly lower for
the polycrystalline pellet than for the single crystal sample. Above TSP , neither sample type
exhibited a linear, Arrhenius region, as is typical for other superprotonic conductors. The
polycrystalline pellet exhibited a monotonic decrease in conductivity, also evident in Figure 3.9(b), whereas the single crystal sample exhibited more erratic behavior, although the
conductivity generally increased from 245 to 260 ◦ C, Figure 3.9(a). As might be expected,
the high-temperature behavior of CsH2 PO4 was highly sample dependent, with polycrystalline samples and small single crystals typically exhibiting lower conductivity and lower
stability above TSP than large single crystals. These results are consistent with previous investigations, in which the electrical behavior of the superprotonic phase could be observed,
such as by Baranov et al., 8 for sufficiently large crystals, whereas for smaller crystals, dehydration prevented such observations. 10 In almost every case, samples measured upon
cooling, either single crystals or polycrystalline pellets, did not exhibit conductivities as
high as that obtained upon heating (not shown), indicating that the sample had undergone
some degree of decomposition at elevated temperatures.
At temperatures below TSP , a large difference between the conductivities of the single
crystal (b-axis oriented) and polycrystalline samples is evident, Figure 3.8. Furthermore,
both appear more conductive than the CsH2 PO4 reported by Baranov et al. 8 Fitting the
conductivity σ of the CsH2 PO4 single crystal to an Arrhenius law (σT = A0 exp ∆Ha /kB T ),
yields a pre-exponential factor A0 of 4.0(2) × 106 Ω-1 cm-1 K and activation enthalpy ∆Ha
of 0.91(4) eV. Values of A0 and ∆Ha for the polycrystalline samples are not reported here
as they were highly dependent on sample history. Specifically, upon drying for long periods
the conductivity of polycrystalline pellets gradually decreased.
The apparent discrepancy between the conductivities of the single crystal and polycrystalline samples of CsH2 PO4 was further investigated by measuring the conductivity of a

Figure 3.8: Arrhenius plot of the conductivity upon heating at 0.5 ◦ C min-1 undering flowing dry
N2 a CsH2 PO4 single crystal and polycrystalline pellet, as compared to Baranov et al. results 8 .
The temperature of the superprotonic transition is indicated by TSP .

(a) Single crystal

(b) Polycrystalline pellet

Figure 3.9: Nyquist plots at various temperatures of CsH2 PO4 upon heating above the superprotonic transition temperature TSP for (a) a single crystal, and (b) a polycrystalline pellet.
polycrystalline pellet as a function of time at 200 ◦ C under flowing dry N2 . The pellet
was prepared from powders obtained by methanol-induced precipitation. The impedance
data initially showed a single arc in the Nyquist representation, but after approximately 24
hours a second low-frequency arc became evident, Figure 3.10(a). This low-frequency arc
was attributed to grain boundary conductivity (σgb ), and the high-frequency arc to bulk
conductivity (σbulk ). With increasing time, both σgb and σbulk decreased, and σbulk approached that of the conductivity of a CsH2 PO4 single crystal σxtal , Figure 3.10(b). These
results suggest that the apparently high conductivity measured in polycrystalline samples
is due to chemi-sorbed H2 O, which is very gradually desorbed at elevated temperatures.
Materials such as Zr(HPO4 )2 , in both hydrated and anhydrous form, are known to show a

65
somewhat similar humidity dependence in their transport behavior due to adsorbed water
between the layers of the highly layered crystal structure 24 . However, retention of water to
such high temperatures and for such long periods, as observed here, is unusual for a crystalline acid phosphate. Finally, we note that in this analysis, σgb has not been normalized
to account for the grain boundary density, as would be necessary to compare samples with
different grain sizes 25 .

(a) Nyquist plots with time

(b) Conductivity versus time

Figure 3.10: Impedance spectroscropy measurements on a polycrystalline pellet of CsH2 PO4 carried
out at 200 ◦ C under flowing dry N2 gas over 10 days. (a) Nyquist plots at various times, in which two
arcs are fit to the impedance data, the first, high frequency arc, attributed to the bulk conductivity
(σbulk ) , and the second, low frequency arc to the grain boundary conductivity (σgb ), as compared
to the conductivity of a single crystal (σxtal ). (b) Log plot of these conductivities as a function of
time.

NMR Spectroscopy
Presented in Figure 3.11 are 1 H- NMR spectra of two CsH2 PO4 powders: (1) produced
by methanol-induced precipitation, and (2) by grinding a single crystal. The methanolprecipitated powder was dried at 200 ◦ C for 24 hours prior to measurement, whereas the
ground single crystal was examined immediately after grinding. For both powders, peaks
were observed at 14.5 and 10.9 ppm, which correspond to the two crystallographically distinct hydrogen atoms observed in the room temperature structure of CsH2 PO4 26 . However,
for the methanol-precipitated powder an additional peak was observed at 6.6 ppm. On the
basis of extensive studies of chemically similar calcium phosphates, in which chemical shifts
of 5.5–6.2 ppm were observed for surface-adsorbed water, 27 it has been concluded that
this third peak corresponds to chemically surface-adsorbed water. It is thus evident that
chemi-sorbed surface water is particularly difficult to remove from CsH2 PO4 , and that this
water affects not only grain boundary conductivity, but also the AC impedance spectral

66
arc normally associated with bulk conductivity behavior. It is for this reason that welldried single crystals were used (in crushed form) in the following high pressure conductivity
experiments.

Figure 3.11: Solid-state 1 H-NMR spectra of CsH2 PO4 powders obtained by (1) methanol induced
precipitation and then dried for 24-hours at 200 ◦ C prior to measurement, and (2) from ground
single crystals.

3.1.1.3

High Pressure Behavior

Impedance Spectroscopy
The pressure–temperature (P –T ) conditions employed in these experiments can be compared to the phase diagram reported by Rapoport et al. 21 , as indicated in Figure 3.12. The
dashed horizontal line at 149 ◦ C in this figure refers to a quasi-irreversible phase transition
noted by those authors, from the room temperature phase III to an unidentified phase II.
The results of the conductivity measurements, which would be expected to traverse both the
III/II and II/I transitions, are presented in Figure 3.13. Upon heating for a first time (1), a
sharp increase in conductivity was first observed at 150 ◦ C. In response to further heating, a
second sharp increase in conductivity occurred at 260 ◦ C, beyond which Arrhenius behavior
was exhibited up to 375 ◦ C. Upon cooling (2), the high temperature transition exhibited a
large hysteresis, with the conductivity dropping by several orders of magnitude at about 240
◦ C. A second heating revealed no anomalous behavior at 150 ◦ C, indicating the irreversible

nature of this feature, consistent with earlier studies 21 . Upon further heating (3), the superprotonic transition at 260 ◦ C was reproduced. While cooling in this second thermal

67
cycle (4), a large hysteresis was again observed with a reverse transition at about 240 ◦ C.
In general, the magnitude of the conductivity at high temperature was highly reproducible
upon multiple heating and cooling cycles, whereas in the low temperature regime (25–260
◦ C) it was not.

Figure 3.12: P –T phase diagram of CsH2 PO4 from Rapoport et al. 21 showing the path over which
AC impedance measurements were performed in this work.

Representative Nyquist plots of the measured AC impedance spectra above and below
the superprotonic phase transition are presented in Figure 3.14. Below the transition (T <
TSP ), Figure 3.14(a), the intercept of the semi-circle with the real axis (Z’) is interpreted
as the resistivity of the sample, whereas above the transition (T > TSP ), Figure 3.14(b),
the intercept of the electrode response with Z’ is taken as the sample’s resistivity. In both
cases, the resistivity decreases with increasing temperature. This result differs markedly
from the ambient pressure behavior, Figure 3.9, for which the resistivity of the sample
increased with increasing temperature above the transition. With these data, we conclude
that the observed high temperature electrical behavior while under pressure is due to the
superprotonic phase of CsH2 PO4 , whereas at atmospheric pressure the electrical behavior
is complicated by dehydration processes.

Figure 3.13: Conductivity results of impedance spectroscopy measurements at 1 GPa on polycrystalline CsH2 PO4 upon a first heating (1) and cooling (2), and followed by a second heating (3) and
cooling (4), plotted in Arrhenius form. Phase boundaries are indicated by dashed lines.

(a) T < TSP

(b) T > TSP

Figure 3.14: Nyquist representation of impedance data obtained from polycrystalline CsH2 PO4 at
1 GPa and at temperatures (a) below and (b) above the superprotonic phase transition temperature
TSP .

Powder X-ray diffraction data collected from CsH2 PO4 under ambient conditions after heating to 350 ◦ C at 1 GPa, showed that the transformations undergone by CsH2 PO4
under high-temperature, high-pressure conditions are reversible. Figure 3.15 shows the calculated X-ray powder diffraction pattern for the P 21 /m paraelectric (ferroelastic) phase of
CsH2 PO4 7 along with those of the experimental diffraction patterns of samples “as prepared” and “after recovery” from the high temperature, high pressure conditions. The
similarity of the patterns demonstrates that the material did not undergo any kind of (irreversible) decomposition. Together with the results of the ball drop experiments described
in Chapter 2, these data confirm that all of the effects evident in Figure 3.15 are due to

69
solid–solid transformations.

Figure 3.15: Powder X-ray diffraction patterns of CsH2 PO4 : calculated 7 , as prepared, and after
recovery from conditions of 350 ◦ C and 1 GPa; backgrounds subtracted from experimental patterns.

The high temperature phase encountered in this work clearly corresponds to that identified as “phase I” by Rapoport et al. 21 Those authors reported a transition to this phase
at 258 ◦ C under 1 GPa pressure, comparable to the transition temperature of 260 ◦ C measured here. The dramatic increase in conductivity at the transition, along with the low
activation entalpy ∆Ha (see below), indicates phase I is ’superprotonic’ in nature. These
results thus support the findings of Baranov et al. that CsH2 PO4 undergoes a solid–solid
transformation that leads to high conductivity, independent of decomposition 8 . It can be
further concluded that this superprotonic phase corresponds to the cubic (P m3m) phase
reported by Preisinger et al. above 230 ◦ C at atmospheric pressure 12 . From their diffraction
studies, Preisinger and coworkers reported a change in volume (∆V ) at the superprotonic
transition of 3.6 Å3 . Using the Clausius-Clapeyron equation, this value of ∆V , along with
a ∆S of 22.4 J mol-1 K-1 , calculated from the enthalpy and transition temperature results
in the previous section, we would expect a transition that occurs at ∼ 330 ◦ C at 1 GPa,
much higher than observed here. One explaination for this could be the highly compressible
nature of the superprotonic phase, which has been experimentally observed in superprotonic
solid acid CsHSO4 28 .
In these measurements, an irreversible anomaly at ∼ 150 ◦ C was observed at 1 GPa upon
an initial heating. The nature of this apparent transition and the phase to which CsH2 PO4

70
transforms at this temperature, phase II, remain unclear; no signature of this phase was
observed at ambient pressures. As stated above, there is significant ambiguity concerning
this apparent transition, with researchers reporting transition temperatures ranging from
107 to 149 ◦ C at ambient pressure, and 149 to 167 ◦ C at 1 GPa 29 , depending on the details
of the sample preparation. Resolving these ambiguities is beyond the scope of this work.
Fitting the conductivity σ of superprotonic CsH2 PO4 to an Arrhenius law yields values
for A0 and ∆Ha of 3.2 × 104 Ω-1 cm-1 K and 0.35 eV, respectively. In comparison, the values
reported by Baranov et al. 8 for superprotonic, single-crystal CsH2 PO4 at ambient pressure
are A0 = 2 × 104 Ω-1 cm-1 K and ∆Ha = 0.32 eV. The difference between the two activation
enthalpies indicates that pressure increases the barrier to proton transport. This increase
in ∆Ha can be quantified in terms of the activation volume for proton conduction using the
relationship:
∆Ha = ∆Ea + P ∆Va ,

(3.4)

where P is pressure, ∆Ea the activation energy, and ∆Va the activation volume. The result,
∆Va = 2–3 cm3 mol-1 , corresponds to 3–4% of the unit cell volume. This value is comparable
to those determined from high pressure studies of other superprotonic solid acids, such as
CsHSO4 , Rb3 H(SeO4 )2 , and (NH4 )3 H(SO4 )2 30,31 . It is noteworthy, however, that in some
cases, for example CsHSO4 in its low temperature phase 30 , the activation volume for proton
conduction can be negative, reflecting the unique transport mechanism for this species as
compared to other ions for which steric hindrances to motion are more relevant.

3.1.2

RbH2 PO4 32

Rubidium dihydrogen phosphate, RbH2 PO4 , crystallizes in the tetragonal space group I42d
(referred to as phase III) 33 . Cooling RbH2 PO4 induces a well-documented transition at 145
K to an orthorhombic (F dd2) ferroelectric phase (phase IV) 34,33 . In contrast, heating produces a distinct series of transitions, which, like CsH2 PO4 , are of some debate in the literature. Upon heating, RbH2 PO4 transforms quasi-irreversibly to a monoclinic phase (phase
II) at a temperature of ∼ 90 ◦ C, depending on the details of the experimental conditions 19 .
The transition has been observed by numerous authors using primarily thermal analysis
methods 19,22,35,36 , but also high temperature powder X-ray diffraction 35 . The structure of
phase II was determined from single-crystal X-ray studies to be monoclinic (P 21 /c) 37 , in

71
which is in agreement with previous high temperature powder diffraction studies 35 . Though
not identical, the structure of RbH2 PO4 in phase II, closely resembles that of phase II in
CsH2 PO4 (P 21 /m) 7 . There have been reports, based primarily on high pressure thermal
analysis, that a second high temperature transition takes place at ∼ 280 ◦ C, to an as-of-yet
unidentified phase I, just prior to melting at ∼ 290 ◦ C 21,29,38 . To summarize, the reported
transitions for RbH2 PO4 take place as follows:

phase IV
(F dd2)

-128◦ C

←→

90◦ C

phase III ←→ phase II
(I42d)
(P 21 /c)

280◦ C

←→

phase I
(?)

290◦ C

←→

liquid

Despite the considerable evidence for high temperature phase transformations in RbH2 PO4 ,
Park and coworkers have argued in a series of papers, that none within the MH2 PO4 class of
compounds undergoes a polymorphic phase transition prior to decomposition/polymerization 39,40 ,
a position further supported by Ortiz and coworkers 9 . Both sets of authors conclude, primarily from thermal analysis measurements, that all anomalies in high temperature properties can be attributed to a decomposition process, which involves phosphate condensation
and polymerization. In fact these thermal dehydration events at ambient atmosphere, which
initiates at temperatures close to the II → I transition of RbH2 PO4 , has prevented previous
attempts to accurately characterization the electrical behavior of phase I 41 .
Ambient pressure thermal analysis results are presented here, confirming that dehydration processes readily masks any transition to phase I in RbH2 PO4 . However, through the
use of pressure, dehydration is suppressed, and the high temperature electrical behavior of
RbH2 PO4 phase I determined to be superprotonic in nature.
3.1.2.1

Ambient Pressure Behavior

Thermal analysis results obtained upon heating RbH2 PO4 powder to 500 ◦ C are presented
in Figure 3.16. The DTG and mass spectroscopy results correspond well to one another
and show at least two major dehydration events at 257 and 340 ◦ C. On the otherhand,
only one rather broad endothermic event at 261 ◦ Cis observed from the DSC measurements
and is perhaps the result of the two overlapping dehydration events observed by DTG and
mass spectroscopy. Analogous to CsH2 PO4 , the existence of multiple dehydration events
indicates a multi-step process, occurring via the formation of poly-phosphite intermediates.
Nevertheless, the overall dehydration can be described by the following reaction:

72
RbH2 PO4 (s) → RbPO3 (s) + H2 O(g) .
This would result in a loss of mass of 9.9 wt%—precisely that observed by TG, Figure 3.16.
Furthermore, samples recovered after thermal analysis, were identified by powder X-ray
diffraction as RbPO3 . No evidence of either polymorphic solid–solid or melting transitions
was observed under ambient pressures. The use of finely ground powder samples thus results
in high-temperature behavior that is dominated by thermal decomposition, as previously
observed in CsH2 PO4 .

Figure 3.16: Simultaneous differential scanning calorimetry (DSC), thermal gravimetry (TG), and
corresponding differential thermal gravimetry (DTG) of RbH2 PO4 powder upon heating to 500 ◦ C
at 10 ◦ C min-1 under flowing 40 cm3 min-1 dry N2 gas. H2 O in the evolved gas is identified by mass
spectroscopy (Mass Spec), m18.00.

3.1.2.2

High Pressure Behavior

To characterize the high-temperature behavior of RbH2 PO4 , and avoid the dehydration
observed at ambient pressure, high pressure impedance spectroscopy was carried out on
RbH2 PO4 powder ground from single crystals just prior to the measurement. Presented
in Figure 3.17 is a P –T phase diagram for RbH2 PO4 , reproduced from Rapaport et al. 21 ,
which indicates the region over which AC impedance data were collected.

Figure 3.17: P –T phase diagram of RbH2 PO4 from Rapoport et al. 21 showing the path over which
AC impedance measurements were performed in this work.

The conductivity results obtained from these high pressure impedance measurements
are presented in an Arrhenius plot in Figure 3.18. The arrows indicate the direction of
temperature change between data collections. The regions of phase stability expected from
the P –T phase diagrams in Figure 3.17 are overlaid and indicated by dashed-lines. Prior to
these measurements crystals of RbH2 PO4 were stored at 100 ◦ C, due to the hygroscopic nature of these compounds. In doing so, the quasi-irrevesible III → II transformation, which
occurs at 90 ◦ C, was induced. Therefore, the sample was in meta-stable (at room temperature) phase II prior to the initiation of the high pressure conductivity measurements.
Upon heating RbH2 PO4 above 327 ◦ C, a II → I phase transition is expected (see Figure
3.17). From the AC impedance results presented in Figure 3.18, a sharp “jump” in the
conductivity to a value of ∼ 6.8 × 10−2 Ω-1 cm-1 at 340 ◦ C is evident, and indicative of a
superprotonic phase transition. The solid–solid nature of this transition was confirmed by
a ball drop experiment (as described in Chapter 2). Reproducible Arrhenius behavior of
the superprotonic phase I was observed, with ∆Ha = 0.232(8) eV and A0 = 3.4(6)×103
Ω-1 cm-1 K, values fairly typical of superprotonic conductors 42 . Upon cooling, there was

74
some hysteresis (∼ 10 ◦ C). Like that CsH2 PO4 , the electrical behavior was somewhat irreproducible in the low temperature regime (phase II), between heating and cooling cycles,
yielding rather large uncertainties when fit to an Arrhenius-type behavior, ∆Ha = 0.77(2)
eV and A0 = 3(2) × 105 Ω-1 cm-1 K.

Figure 3.18: Arrhenius plot of conductivity results from AC impedance measurements performed
on RbH2 PO4 powder upon heating and cooling (as indicated by direction of arrows) from 25 to 350
C under 1.0 GPa of pressure. Phase boundaries are indicated by dashed lines.

Typical Nyquist plots of AC impedance spectra from these conductivity measurements
are presented in Figure 3.19 for selected temperatures. Below the superprotonic phase
transition (T < TSP ), Figure 3.19(a), well-resolved semi-circles were obtained. The real
resistance of the sample at low temperatures was identified by the intercept of the semicircle with the real axis (Z’). In contrast, at T > TSP , only an electrode response was
observed, Figure 3.19(b), and the intercept with Z’ was used as the estimated resistance of
the sample.
With these data, we conclude that the observed high temperature electrical behavior
while under pressure is due to the superprotonic phase of RbH2 PO4 , whereas at atmospheric
pressure the electrical behavior is complicated by dehydration processes. Furthermore, the
proton transport properties of RbH2 PO4 are quite comparable to those of CsH2 PO4 , from
which one would expect that phase I of RbH2 PO4 shares the same cubic structure, in which
phosphate groups are highly rotationally-disordered 43 .

(a) T < TSP

(b) T > TSP

Figure 3.19: Nyquist representation of impedance data obtained from polycrystalline RbH2 PO4 at
1 GPa and at temperatures (a) below and (b) above the superprotonic phase transition temperature
TSP .

3.1.3

KH2 PO4

Potassium dihydrogen phosphate, KH2 PO4 , is isostructural with RbH2 PO4 under ambient
conditions, crystallizing in the tetragonal space group I42d and commonly referred to as
phase II 44 . KH2 PO4 is well known for its ferroelectric phase transition, in which, upon
cooling below 123 K 45 , it transforms to a ferroelectric phase with orthorhombic symmetry
(F dd2) 46 (phase III). However, like the other MH2 PO4 compounds, the high-temperature
behavior of KH2 PO4 remains controversial.
Early studies of the high-temperature behavior of KH2 PO4 indicated two polymorphic
transitions, one at 180 ◦ C, to phase II’ 47 , and a second at 233 ◦ C 48 , to phase I. More recent
single crystal diffraction studies have confirmed the existence of both transitions and have
shown phase II’ to be triclinic (P 1), with entirely ordered phosphate groups, and phase
I to be monoclinic (P 21 /c) 49 . The existence of the II’ → I transition at 200–220 ◦ C has
been further confirmed by thermomechanical measurements, although little evidence for the
transition at 180 ◦ C was observed 50 . The structures of additional polymorphs that exist
under atmospheric conditions have also been reported 49,51 .
Still, as with the previous compounds, CsH2 PO4 and RbH2 PO4 , recent arguments have
been made claiming that the high-temperature behavior of this compound is dominated
by decomposition and polymerization processes 39,40,9 . Indeed, thermal dehydration, which
initiates at temperatures close to the II’ → I transition of KH2 PO4 and has prevented the
accurate electrical characterization of phase I 41 .
To summarize, it has been suggested that KH2 PO4 undergoes the following polymorphic
changes at atmospheric pressure and in the absence of dehydraton:

phase III
(F dd2)

-151◦ C

←→

phase II
(I42d)

180◦ C

←→

phase II’
(P 1/c)

233◦ C

←→

phase I
(P 21 /c)

280◦ C

←→

liquid

In this section, the aim is to identify the high temperature electrical properties of
KH2 PO4 phase I. First, thermal analysis results at ambient pressure for KH2 PO4 are presented, indicating that dehydration does mask any transition to phase I. Then results of
high pressure AC impedance are presented, which suggest that KH2 PO4 phase I is not
superprotonic in nature, as might have been expected based on its monoclinic structure.
3.1.3.1

Ambient Pressure Behavior

Thermal analysis results obtained upon heating powder of KH2 PO4 to 500 ◦ C are presented
in Figure 3.20. The DTG and mass spectroscopy results correspond well to one another and
show at least two major dehydration events at 233 and 320 ◦ C. The single endothermic event
at 241 ◦ C observed from the DSC measurements could be the result of the two overlapping
dehydration events observed by DTG and mass spectroscopy. The absence of a transition
for KH2 PO4 at ∼ 180 ◦ C, well before dehydration begins, cannot be readily explained,
but suggests that the II → II’ transformation is highly dependent on the details of sample
preparation and experimental conditions. No clear step-wise dehydration process observed
in the TG thermogram seems to suggest that dehydration must occur via a multi-step
process, whereby poly-phosphite intermediates are formed. The complete dehydration of
KH2 PO4 by the reaction:
KH2 PO4 (s) → KPO3 (s) + H2 O(g) ,
would result in a 13.2 wt% loss of mass for KH2 PO4 , which is in close agreement with
the TG results, Figure 3.20. Recovered samples after thermal analysis, were identified by
powder X-ray diffraction as KPO3 . From these results, no evidence of either polymorphic
solid–solid or melting transitions was observed under ambient pressures.
3.1.3.2

High Pressure Behavior

Given the difficulties in characterizing the electrical properties of KH2 PO4 phase I associated with dehydration at ambient pressures, high pressure impedance spectroscopy was
employed, the results of which are presented here. In Figure 3.21, a P –T phase diagram

Figure 3.20: Simultaneous differential scanning calorimetry (DSC), thermal gravimetry (TG), and
corresponding differential thermal gravimetry (DTG) of KH2 PO4 powder upon heating to 500 ◦ C
at 10 ◦ C min-1 under flowing 40 cm3 min-1 dry N2 gas. H2 O in the evolved gas is identified by mass
spectroscopy (Mass Spec), m18.00.

for KH2 PO4 , reproduced from Rapoport 48 , indicates the region over which AC impedance
data were collected. The conductivities obtained from the high pressure impedance measurements are presented in Arrhenius plots in Figure 3.22. The arrows indicate the direction
of temperature change between data collections. The regions of phase stability expected
from the P –T phase diagram in Figure 3.21 are overlaid and indicated by dashed-lines.
As synthesized KH2 PO4 crystallizes in phase II (tetragonal, I42d). Application of pressure (at 25 ◦ C) induces a transition to phase IV, however, the position of the II/IV phase
boundary has not been determined and the exact phase present at the initiation of the
high pressure conductivity measurements is thus not known. Regardless of this ambiguity, one expects KH2 PO4 to transform to phase I at 250 ◦ C upon heating under 1 GPa
(Figure 3.21). The conductivity, Figure 3.22, increases smoothly through this temperature;
there is no sharp increase that would be characteristic of a superprotonic phase transition.
This behavior is entirely in agreement with the reported monoclinic structure of phase I.
Upon further heating, one expects phase I to melt at 325 ◦ C, and here the conductivity
increases by more than two orders of magnitude to a value of ∼ 1.8 × 10−2 Ω-1 cm-1 at 345

Figure 3.21: P –T phase diagram of KH2 PO4 from Rapoport 48 showing the path over which AC
impedance measurements were performed in this work.

Figure 3.22: Arrhenius plot of conductivity results from AC impedance measurements performed
on KH2 PO4 powder upon heating and cooling (as indicated by direction of arrows) from 25 to 350
C under 1.0 GPa of pressure. Phase boundaries are indicated by dashed lines.
◦ C. Recovery of the KH PO sample from the ball drop experiment confirmed that this was

a solid–liquid transition and not a solid–solid superprotonic transition.
Typical Nyquist plots of AC impedance spectra are presented in Figure 3.23 for selected

79
temperatures. At low temperatures (T < Tm ), Figure 3.23(a), well-resolved semi-circles
were obtained, in which the real resistance is determined from the intercept of the spectral
arc with the real axis (Z’). In contrast, at high temperatures (T > Tm ), only an electrode
response was observed, Figure 3.23(b), and its intercept with Z’ is the estimated resistance
of the sample.

(a) T < Tm

(b) T > Tm

Figure 3.23: Nyquist representation of impedance data obtained from polycrystalline KH2 PO4 at
1 GPa and at temperatures (a) below and (b) above the melting temperature Tm .
Fitting the conductivity data of the liquid phase to an Arrhenius relationship yields:
∆Ha = 0.227(4) eV and A0 = 5.2(5)×103 Ω-1 cm-1 K. Upon cooling KH2 PO4 , some hysteresis
(∼ 20 ◦ C) from the melt phase and rather irreproducible electrical behavior in the low
conductivity solid phases was observed. It was not possible to distinguish between phases
I, II, and IV from these electrical measurements, and the conductivity was highly nonArrhenius in the low-temperature regime.
What is clear from these results is that none of the high temperature solid phases
of KH2 PO4 exhibit superprotonic conductivity. It is also noteworthy that the activation
enthalpy of the liquid-phase of KH2 PO4 is quite similar to that of the superprotonic phase I
of RbH2 PO4 and the overall difference in conductivity between the two is less than a factor
of two. This points to similar mechanisms for ionic transport between liquid KH2 PO4 and
superprotonic RbH2 PO4 .

3.1.4

Summary

At the onset of this work, the question was posed: Can fully-hydrogen bonded solid acids
exhibit superprotonic phase transitions? Here it has been shown that, yes, fully-hydrogen
bonded solid acids, such as CsH2 PO4 and RbH2 PO4 , can indeed exhibit superprotonic phase
transitions.

80
A summary of the high temperature thermal and electrical behavior of MH2 PO4 -type
compounds at atmospheric and 1 GPa pressures characterized here is given in Table 3.2.
Preliminary ambient pressure thermal analysis and high pressure impedance measurements
of LiH2 PO4 and NaH2 PO4 have been carried out (see Appendix for details) and the results included in Table 3.2. From these results, it is clear that at atmospheric pressure,
all MH2 PO4 -type compounds dehydrate at elevated temperatures. In general, the overall
dehydration reaction is:
MH2 PO4 (s) → MPO3 (s) + H2 O(g)

(M = Li, Na, K, Rb, Cs)

Contrary to what previous authors have suggested, such a dehydration reaction does not preclude a superprotonic phase transition at higher temperatures. Thermodynamically speaking, the previous reaction is in equilibrium when the Gibbs free energy is zero (∆Grxn = 0),
which is a function of water partial pressure (pH2 O ),
∆Grxn = ∆G◦rxn + RT ln pH2 O .

(3.5)

As such, thermal analysis in closed volume containers,i in which an equilibrium pH2 O is
reached with only minimal sample degradation, has allowed the accurate characterization
of the high temperature transition enthalpies of some of these compounds (see Appendix
for details), also included in Table 3.2.
What does seem to preclude superprotonic transitions in some MH2 PO4 -type compounds is the size of the cation. While large cation-sized MH2 PO4 compounds (M = Rb,
Cs) upon heating exhibit a superprotonic phase transition prior to melting, smaller cationsized MH2 PO4 compounds (M = K, Na, Li) simply melt. This effect has been observed in
other MHn XO4 -systems as well 4 , and will be discussed in detail in the next section.

The pressure rating of the closed volume containers was less than 1 MPa—resulting in a negligable
pressure change.

81
Table 3.2: Summary of thermal and electrical characterization at atmospheric and 1 GPa pressures
of MH2 PO4 -type compounds. Left—thermal decomposition/dehydration (d), melting (m), and superprotonic phase transition (SP) temperatures (T ) and enthalpies (∆H) at 1 atm. Right—high
temperature phase transition temperatures (Ttr ) and electrical behavior (∆Ha , σ0 ) at 1 GPa.

P = 1 atm

P = 1 GPa

Td†

TSP

Tm
/◦ C

∆HSP

∆Hm /kJ mol

Phase

Ttr /◦ C

∆Ha /eV

A0 /Ω-1 cm-1 K

CsH2 PO4

225

228(2)

346(2)

11.3(6)

25.2(5)

260

0.346(3)

2.1(2) × 104

RbH2 PO4

220

280(1)

290(2)

11.8(5)

22.7(8)

327

0.323(8)

3.4(6) × 103

KH2 PO4

210

259(4)

325

0.227(4)

5.2(5) × 103

NaH2 PO4

200

350

LiH2 PO4

195

255

-1

† Approximate values—dehydration onset is dependent upon experimental conditions.
‡ Values obtained by suppressing dehydration.

3.2

Cation and Oxy-Anion Size Effects

In this section, the effect of cation and oxy-anion size on the presence of superprotonic phase
transitions in MHn XO4 -type solid acids will be examined. In the previous section, a clear
cation size effect in MH2 PO4 -type solid acids was observed. In Figure 3.24, phase diagrams
of (a) MHSO4 and (b) MH2 PO4 compounds as function of cation radius are presented. From
these diagrams, increasing cation size appears to increase the melting temperature, while
at the same time, decrease the superprotonic phase transition temperature. From these
observations, superprotonic phase transitions appear to be favored in solid acids composed
of large cations. However, the effect of the oxy-anion size on phase transitions is somewhat
less clear. In the following sections, both the effect of the cation and oxy-anion size will be
considered. For the purpose of this study, the phase behavior of MHn XO4 -type compounds
has been compiled from this and other published work into Tables A.2 and A.1 given in the
Appendix, and these data are used throughout this section.
To begin with, radius ratio rules will be employed to examine the cation to oxy-anion
size effect with the hope of developing a method for predicting the presence of superprotonic
phase transitions in solid acids. Though moderately successful, cation to oxy-anion size effects alone do not give a complete picture of factors that govern the presence of superprotonic
phase transitions. Notable exceptions to these radius ratio rules will then presented, and
discussed in terms of bonding. From these investigations it will be shown that, while cation

(a) MHSO4 compounds

(b)MH2 PO4 compounds

Figure 3.24: MHSO4 and MH2 PO4 phase diagrams as a function of cation radius, where M = K,
Rb, and Cs. Cation radii were obtained from Shannon 52 for values of M+ with 8-fold coordination.

and oxy-anion size do play a significant role in the presence of superprotonic transitions,
the role of both ionic and hydrogen bonding are equally important.

3.2.1

Radius Ratio Rules

Superprotonic phases of solid acids are composed of a rotationally disordered tetrahedral
oxy-anion coordinated by cations, as depicted in Figure 3.25. We suppose that in order
for the oxy-anions (XO−
4 ) to become rotationally disordered, there must be sufficient space
between cations (M+ ) to be able to rotate freely, without the crystal falling apart (i.e.,
melt). By such rationale, we expect superprotonic phase transitions to be favored by larger
cation-cation distance (larger cations). But how large and what effect does the size of the
oxy-anion have?

Figure 3.25: Schematic representation in two-dimensions of a rotationally disordered oxy-anion
(XO−
4 ), coordinated by cations (M ).

Radius ratio rules have long been used to predict the likely structures of solids 53 . Here,

83
Table 3.3: Shannon ionic radii (IR) for elements relevant to MHn XO4 -type solid acids, where CN
is the ion coordination number 52 .
Cs

IR /Å

1.74
1.61
1.51

1.18

0.92

IR /Å

0.37

O/OH

IR /Å

−2

1.38

1.35

0.50

0.17

0.34

radius ratios rules will be adopted in attempt to predict the likelihood of a superprotonic
structure in MHn XO4 -type solid acids based upon cation and oxy-anion sizes alone. Technically speaking, the alkali cations in MHn XO4 -type solids acids are coordinated by oxygen
atoms, however, we will treat the entire oxy-anion as the coordinating species. In general,
the superprotonic structures of MHn XO4 -type solid acids are composed of oxy-anions, which
are coordinated by 8 cations (except for RbHSeO4 , see Section 4.2.1). For such 8-fold coordination, the expected geometries based upon the minimum cation (r) to anion (R) radius
ratios (r/R) rules are
r/R

≥ 0.732 → cube
≥ 0.668 → dodecahedron
≥ 0.645 → square anti-prism

R.D. Shannon has compiled a comprehensive list of ionic radii that is based upon systematic structural studies of interatomic distances in halide and chalcogenide compounds 52 .
These values of ionic radii are used throughout, and are reproduced in Table 3.3 for those
relevant to these studies. To begin with, the validity of the Shannon ionic radii was established from a comparison of the tetrahedral oxy-anion distances hX–Oi found in the room
temperature structures of MHn XO4 -types solid acids, the results of which are given in Tables 3.4. These results show excellent agreement with Shannon’s values for atomic radii.

84
Table 3.4: Average hX–Oi distances in MHn XO4 -type solids acid room temperature structures
compared to Shannon radii 52 .
hX–O(H)i /Å

MHSO4

MHSeO4

MH2 PO4

MH2 AsO4

Structures

1.540(4)

1.66(4)

1.47(9)

1.476(10)

Shannon

1.54

1.65

1.49

The first difficulty encountered in applying radius ratio rules to superprotonic solid acids
is in assigning a radius to a non-spherical tetrahedral oxy-anion. We begin this task by
defining the tetrahedral radius Rtetra as the distance from the center of the tetrahedral
oxy-anion to the vertices,

such that
Rtetra = 2IR(O−2 ) + IR(X+5,6 ).

(3.6)

Radius ratio rules assume that the cation and anions are “just touching.” Using Rtetra
as the anion radius, would result in the oxygen atom pointing directly into a cation—an
unlikely scenario, and, in fact, not observed in any known room temperature or superprotonic solid acid structures 54,12 . In the case of cubic superprotonic solid acids, the possible
orientations of tetrahedral oxy-anion are very limited due to the symmetry of the cell, and
therefore, can only be positioned as shown in Figure 3.26(a), plus the five symmetrically
equivalent positions. In this orientation, the tetrahedral oxy-anion radius Rtetra is positioned 36.4◦ away from hM–Xi. By definition, the cation must “touch” the oxy-anion along
hM–Xi, such that the “effective” oxy-anion radius R is
R = r − hM–Xi,

(3.7)

where r is the cation radius. Therefore, as depicted in Figure 3.26(b), the effective tetrahe-

85
dral radius can be related to the tetrahedral oxy-anion radius, such that
R = cos (36.4◦ )Rtetra = 0.805Rtetra .

(a) Orientation of tetrahedron in a cube

(3.8)

(b) Effective tetrahedral radius

Figure 3.26: The effective tetrahedral radius (R) of an oxy-anion situated in a cubic cell. (a) The
orientation of a tetrahedral oxy-anion in a cubic cell. (b) The effective tetrahedral radius of an
oxy-anion based upon the cation and oxy-anion “just touching,” and in relationship to the actual
tetrahedral radius Rtetra .
Using these results to calculate the radius ratios r/R for MHn XO4 -type compounds
generates the values given in Table 3.5, which in Figure 3.27 are presented graphically and
compared with known superprotonic (◦) and non-superprotonic (×) solid acid compounds.
The 8-fold coordination assumed here and exhibited by most known MHn XO4 -type superprotonic solid acids does in fact appear to follow these radius ratio rules. In particular, the
superprotonic structure of CsH2 PO4 has cubic coordination geometry and CsHSO4 has a
geometry that closely resembles the square anti-prism coordination geometry (see Section
4.21 for more structural details).

3.2.2

Atomic Bonding

While the previous results may be quite convincing that the effect of cation and oxy-anion
size are the key factors in identifying the presence of superprotonic conductivity in MHn XO4 type solid acids, two examples will be presented here that will show this is clearly not the
case.

86
Table 3.5: Cation to oxy-anion radius ratios (r/R) of MHn XO4 -type solid acids, where R is the
“effective” tetrahedral Hn XO−
4 radius and r is the M radius.
M+
Cs+
Rb+ K+
Na+
Li+
Hn XO−

R /Å

r /Å

1.74

1.61 1.515

1.18

0.92

HSO−
H2 PO−
HSeO−
H2 AsO−

2.31

r/R

0.755

0.698 0.655

0.512

0.399

2.33

0.746

0.690 0.647

0.506

0.394

2.43

0.715

0.661 0.620

0.485

0.378

2.47

0.705

0.653 0.612

0.478

0.373

Figure 3.27: Radius ratios (r/R) as function of cation radius, as compared to known
superprotonic—◦, and non-superprotonic—× conducting MHn XO4 -type solid acids.

Ionic Bonding
One may have noticed the conspicuous omission of other large cations such as NH+
4 and
Tl+ in these studies. These cations were purposefully left out because their behavior often
deviates substantially from alkali cations. However, at this point, using TlH2 PO4 as example, will help to illustrate the shortcomings of radius ratio rules as a predictive measure for
identifying superprotonic solid acids. The Shannon ionic radii of Tl+ is 1.7 Å, just slight
larger than Rb+ , therefore, since RbH2 PO4 and CsH2 PO4 both have superprotonic phase
transitions, we would expect TlH2 PO4 to follow suit. In fact, melting has been observed
in this compound at 180 ◦ C (see Appendix)—a melting temperature even lower than in

87
LiH2 PO4 . The reason proposed for this behavior is that Tl+ forms weak ionic bonds relative to the alkali ions. To verify the proposition, the ionization potential (IP ) of the alkali
ions as compared to Tl+ are plotted as a function ionic radius in Figure 3.28. In the same
figure, the melting temperature (Tm ) of MH2 PO4 -type compounds, where M = alkali and
Tl, is plotted above. The strong correlation between these data suggests that the large
ionization potential of Tl, and therefore, weak overall ionic bonding, plays a much more
significant role on melting than the cation size.

Figure 3.28: The ionization potential M and melting temperature of MH2 PO4 (where M = Li, Na,
K, Rb, Tl, Cs) as a function of M+ ionic radius.

Hydrogen Bonding
A second obervable phenonmenon that deviates from these cation to oxy-anion ratio rules
is the effect of the oxy-anion size on the superprotonic phase transition temperature (TSP ).
From radius ratio rules one would expect small oxy-anions to have lower superprotonic
transitions temperatures, but in fact, this is opposite with what is observed. For example,
CsH2 PO4 has a high superprotonic transition temperature of 230 ◦ C, while CsH2 AsO4 , with
a much larger oxy-anion, transforms at only 155 ◦ C. A simlar effect is observed between
the sulfates and selenates. This effect is likely caused, not by oxy-anion size, but rather,
by the difference in hydrogen bond strength between different oxy-anions. To consider this
possiblity, the difference in Gibbs free energies for the formation of ionic defects in aqueous

88
Hn XO4 acids are considered,
2−
2Hn XO−
4 (aq) → Hn−1 XO4 (aq) + Hn+1 XO4 (aq) , ∆Gf

where X = S, Se, P, As, and n = 1, 2. For the formation of such defects, acids exhibiting
strong hydrogen bonding are expected to have large positive values of ∆G◦f . The ∆G◦f
values calculated for the above defect formation are plotted as a function of oxy-anion
size in Figure 3.29. In the same figure, the superprotonic transition temperature (TSP ) for
CsHn XO4 compounds is similarly plotted as a function of oxy-anion size. The analogous
trend between these two curves suggests that hydrogen bonding plays a prominent role in
determining the superprotonic phase transition temperature, and furthermore, points out
the relatively insignificant role oxy-anion size plays.

Figure 3.29: The superprotonic transition temperature in CsHn XO4 compounds and the Gibbs
energy for ion defect formation in Hn XO4 -acids plotted as a function of oxy-anion size (where X =
S, Se, P, As).

3.3

Conclusions

The most substantial achievement presented in this chapter is the unequivocable identification of superprotonic behavior in fully hydrogen bonded solid acids, such as CsH2 PO4 and
RbH2 PO4 . This single result has (1) allowed significant progress to be made in understanding the role of hydrogen bonding in superprotonic solid acids, and (2) provided illumination

89
to the effect of cation and oxy-anion size. Moreover, as will be seen in the following chapters, this result has (3) aided in the characterization of the entropic driving force behind
superprotonic transitions, and (4) allowed for the successful application of solid acids in fuel
cells.
Finally, a clear cation to oxy-anion size effect in MHn XO4 -type superprotonic solid acids
has been explained in terms of radius ratio rules. However, while it has been observed that
ion size does play a role in superprotonic transitions, ultimately, the effect of both hydrogen
and ionic bonding are equally critical factors in allowing for superprotonic conductivity in
a MHn XO4 -type solid acids.

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Chapter 4

Properties of Superprotonic
MHnXO4-type Solid Acids
Superprotonic solid acids are known to undergo an order-disorder phase transition, upon
which the ionic conductivity increases by several orders of magnitude. In this chapter,
the thermodynamic driving force behind these phase transitions will be investigated. Phase
transitions are, in general, driven by a systems tendency towards maximum entropy. Therefore, an effort will be made here to account for the change in entropy through a superprotonic phase transition. While there are many forms of entropy, a detailed account of the
configurational entropy of superprotonic solid acids will be presented.
A methodology for calculating the configurational entropy of superprotonic solid acids
will be presented here, much of which has been pioneered by coworker, Calum Chisholm 1,2 .
Nonetheless, the incontrovertible proof of superprotonic conductivity in fully hydrogenbonded solid acids (presented in Chapter 3), was a key contribution to these developments.
Overall, the approach employed here has been fundamentally derived from the work of Linus
Pauling, and his landmark paper for evaluating the residual entropy in ice 3 .
This chapter will begin with a review of Pauling’s entropy rules for ice. Then, based
upon these entropy rules, a new set of entropy rules will be presented for superprotonic solid
acids. In this section, the structural details of superprotonic phases and calculations of the
configurational entropy of these phases will be presented. The section following will discuss
the configurational entropy associated with the intra-hydrogen bond disorder, which results
in ferro-paraelectric phase transitions in many of these solid acids. This is necessary to
compare the calculated with the experimentally measured values of the change in entropy
through the superprotonic transition ∆SSP , which is the entropy of the superprotonic phase

95
SSP , minus the entropy of the phase prior to the superprotonic transition, S0 ,
∆SSP = SSP − S0 .

(4.1)

Lastly, a summary of these calculations and a comparison with experimental results will be
presented.

4.1

Pauling’s Entropy Rules for Ice 3

Upon cooling H2 O to 0 K, it crystallizes in the hexagonal space group P 63 /mmc 4 , known as
ice phase Ih, depicted in Figure 4.1. It was observed that a “residual” entropy persists in this
phase to 0 K 5 . This residual entropy was explained by Pauling in terms of a configurational
entropy associated with statically disordered hydrogen bonds between oxygen atoms, as
indicated in Figure 4.1.

Figure 4.1: Depiction of the structure of hexagonal ice (P 63 /mmc), phase Ih 4 . Two hydrogen atoms
are statically disordered among the four possible hydrogen positions, 1 through 4, as indicated.

From original observations of the structure of hexagonal ice, Bernal and Fowler concluded that the structure of individual H2 O molecules in ice was not unlike those in steam,
and therefore, must follow these configuration rules 4 :
Rule 1 Two and only two protons can be bonded to an oxygen atom.
Rule 2 One and only one proton is allowed per hydrogen bond.
Later, Pauling added to these so-called ice rules, the following 3 :

96
Rule 3 The hydrogen bonds must be directed approximately toward two of the four neighboring oxygen atoms.
Rule 4 The interaction of non-neighboring water molecules does not energetically favor
one possible arrangement of protons with respect to other possible configurations so long as
they all satisfy Rules 1–3.
Using these four rules, Pauling estimated the number of configurations Ω per H2 O molecule
to be

number of
protons
number of proton
probability a proton
Ω =
configurations
site is open
2

4!
2 · 2!

(4.2)

giving a residual configurational entropy S of

S = R ln Ω = R ln
= 0.405R or 3.37 J mol-1 K-1 .

(4.3)

This result closely agrees with the experimentally determined residual entropy of 3.65 J
mol-1 K-1 , calculated from the difference between the entropy of ice estimated from thermal
data at very low temperature conditions (185.16 J mol-1 K-1 ) 5 and the spectroscopic value
of water vapor at standard conditions (188.81 J mol-1 K-1 ) 6 .
While the residual entropy in ice is due to statically disordered hydrogen bonds, others have extended these rules to account for the entropy of dynamically disordered hydrogen bonds in other H2 O-containing solids, such as ice-polymorphs, clathrate hydrates,
SnCl2 ·H2 O, Cu(HCO2 )2 ·H2 O, and (H31 O14 )(CdCu2 (CN)7 ) 7,8,9,10 . The successful application of Pauling’s Ice Rules to these dynamically disordered systems, which exhibit a wide
variety of hydrogen bonding and dimensionality of hydrogen bonded networks, demonstrates
the versatility of these rules.
While the aforementioned examples of the extension of Pauling’s Ice Rules all dealt with
the entropy associated with the disordering of hydrogen bonds between H2 O molecules, further extensions of these rules have been made by Slater to systems containing hydrogen
bonded tetrahedral oxy-anions 11 . Slater employed Pauling’s Ice Rules to account for the

97
entropy associated with the ferroelectric transition in KH2 PO4 , in which, upon cooling,
disordered hydrogen bonds become ordered at the ferroelectric transition temperature TFE
(-151 ◦ C). The structure of KH2 PO4 , depicted in Figure 4.2, is composed of PO4 tetrahedra, each of which partake in four disordered hydrogen bonds in the paraelectric room
temperature structure. Using the same formulation as used to determine the number of
configurations in ice, Equation 4.2, Slater arrived at an entropy for the disordered paraelectric phase of KH2 PO4 of R ln (3/2) or 3.37 J mol-1 K-1 (at T
TFE ). This value is not far
the experimental value of 3.51(12) J mol-1 K-1 from heat capacity measurements. 12,i

Figure 4.2: Depiction of the room temperature, paraelectric structure of KH2 PO4 , tetragonal
(I4amd) 13 . Disordered hydrogen bonds 1–4 of the central tetrahedral PO4 are indicated. Potassium
atoms not shown for clarity.

Pauling’s Ice Rules have, thus, successfully described the entropy changes of both disordered H2 O-containing systems and compounds containing tetrahedral oxy-anions. Further,
extension of these ice rules have even been made to superprotonic solid acids for the purpose
of distinguishing between the proton transport mechanisms of the ordered and disordered
phases, as well as, to describe phenomenologically, the arrangement of protons in the superprotonic phases 14 . Therefore, the development of anologous rules to quantitatively account
for the entropy associated with superprotonic solid acids, would seem a natural progression.

It is the author’s experience that literature values of entropy based upon heat capacity measurements
are highly variable—ultimately contingent upon the temperature range of the measurement and the baseline
used.

4.2

Entropy of Superprotonic Phases 1,2

In this section, an adaption of Pauling’s entropy rules for ice, that accounts for both the
disordered tetrahedral oxy-anions and hydrogen bond disorder in superprotonic MHn XO4 type solid acids, will be presented.
Previous entropic models of superprotonic phase transitions have failed to (1) provide
a general description of the entropic driving force for superprotonic phase transitions, and
(2) accurately account for the experimentally measured entropy in such transitions. Most
notable among these were the developments of Plakida, in which a Laudau theory approach was adopted to describe the superprotonic phase transition in CsHSO4 15,16 . In
this model, depicted in Figure 4.3, protons are (a) ordered at positions 2 and 4 at room
temperature, and upon passing through the superprotonic transition, the protons become
(b) disordered among positions 1–4. Assigning an order-parameter to proton positions 1
through 4 and incorporating the Silsbee-Jüling-Schmidt model 17 to account for short-range
proton correlations, Plakida obtains a first-order Slater type transition, identified by a discontinous “jump” in the order parameter at the transition temperature TSP . The calculated
change in entropy, ∆S ∼ 0.52R, differed somewhat from the experimental value of the time,
∆S = 1.32R, which, as Plakida explained, was on account of ignoring the disordering of
SO4 groups 15 . While this model does capture some aspects of the superprotonic phase transition, it falls short in accurately accounting for the entropy in the superprotonic phase, and
moreover, would forbid superprotonic phase transitions in solid acids with fully hydrogen
bonded tetrahedral oxy-anions.ii Furthermore, Plakida’s model relies upon a strict relationship between the low temperature and superprotonic structures, which is not necessarily
obeyed by the real structures
In order to develop a more complete picture of the disordered superprotonic phases of
MHn XO4 -type compounds, a new methodology for calculating the entropy of compounds
with rotationally disordered oxy-anions, randomly linked by disordered hydrogen bonds, is
presented.
ii

Discussed in the Section 3.1

(a) Ordered protons

(b) Disordered protons

Figure 4.3: Model proposed by for the superprotonic phase transitions in CsHSO4 . Squares represent SO4 groups and circles represent proton positions. (a) Ordered phase, in which positions 2 and
4 are occupied by protons. (b) Disordered superprotonic phase, in which, 2 protons are disordered
among 4 positions 15,16 .

4.2.1

Superprotonic Structures

In general, superprotonic MHn XO4 -type solid acids are known to exhibit one of two structures: tetragonal or cubic. Solid acids CsHSO4 and CsHSeO4 transform to an I41 /amd
tetragonal structure 18,19,20,21 , whereas CsH2 PO4 , RbH2 PO4 , and CsH2 AsO4 transform to
a P m3m cubic structure 22,23 . The structure of superprotonic RbHSeO4 , determined here,
also has a tetragonal structure (I4/mmm), however it differs significantly from the other
two structures in its atomic arrangement. Before delving into calculating the entropy, details of these structures and controversies pertaining to them, as well as the refinement of
the superprotonic structure of RbHSeO4 , will be presented. To summarize, the structures
of known superprotonic MHn XO4 -type solid acids are as follows:iii

RbHSeO4

 tetragonal
 (I4/mmm)

CsHSO4  tetragonal
CsHSeO4  (I41 /amd)

CsH2 PO4
CsH2 AsO4

cubic

 (P m3m)
RbH PO ? 

Tetragonal I4/mmm
The solid acid, rubidium hydrogen selenate (RbHSeO4 ), is known to undergo a superprotonic transition at 173 ◦ C 24 , however, as-of-yet there are no reported structures for this
superprotonic phase. Therefore, the structure of the superprotonic phase of RbHSeO4 has
iii

Structures not including mixed cation or oxy-anion compounds, such as Cs2 (HSO4 )(H2 PO4 ).

100
been investigated by high temperature powder X-ray diffraction, the results of which are
presented here.
The data from powder X-ray diffraction performed on RbHSeO4 with a Si-internal
standard at 175 ◦ C is presented in Figure 4.4. With these data, a Rietveld refinement was
carried out to determine the structure and atomic positions of the heavy atoms (Rb, Se).
The structure was refined in the body-centered tetragonal cell I/4mmm, a = 4.0309(2) Å,
c = 7.0436(3) Å, Z = 2, V = 114.4 Å3 . The structural results, measurement parameters,
and refinement parameters of the Rietveld refinement are given in Table 4.1. In Figure 4.4,
the calculated intensity (Icalc ) of the refined structure is compared with the experimentally
observed intensity (Iobs ) and below is the difference between these two curves (Icalc - Iobs ).

Figure 4.4: Powder X-ray diffraction pattern of RbHSeO4 at 170 ◦ Cwith a Si-internal standard.
The top-curve is the calculated intensities (Icalc ) from the refined superprotonic structure (I4/mmm,
a = 4.031, b = 7.044 Å) plus the Si-internal standard, the middle-curve the experimentally observed
intensities (Iobs ), and the bottom-curve the difference between the calculated and observed intensities
(Icalc - Iobs ).

The fractional atomic coordinates of the Rb and Se positions, determined from the

101
Table 4.1: Summary of structural data, measurement parameters, and refinement parameters of
the Rietveld analysis of powder X-ray diffraction data taken from RbHSeO4 with an Si-internal
standard at 170 ◦ C.
Structural Data
Compound Name
Chemical Formula
Molecular Weight/ g·mol-1
Weight Fraction/ %
Space Group (No.)
Lattice Parameters
a/ Å
b/ Å
c/ Å
α/ ◦
β/ ◦
γ/ ◦
Multiplicity, Z
Volume, V / Å3
Density, ρ/ g·cm-3

Rubidium hydrogen selenate
RbHSeO4
229.433
23.9(2)
I4/mmm (139)
4.03149(9)
4.03149(9)
7.0457(2)
90
90
90
114.513
2.41

Measurement Parameters
Generator Settings
Divergence Slit/ ◦
Scan-range, 2θ / ◦
Step Size, 2θ/ ◦
Scan Time per Step/ s
Scan Type
Radiation
Temperature, T / ◦ C
Atmosphere

45 kV, 40 mA
1.000
10.000–100.000
0.008
3.15
continuous
CuKα
170
ambient

Refinement Parameters
Number of Phases
Number of Variables
Displacement
Profile fit
Background
Coefficients for Peak FWHM
Preferred Orientation
Preferred Orientation Parameter
Asymmetry Parameter
Refinement Statistics
Rexp / %
Rp / %
Rwp / %
RB / %
GOF
d-statistic

21
0.1594(6)
Pseudo-Voigt
refined
0.000
0.012(1)
0.0017(3)
100
1.379(6)
1.0(1)
16.170
17.336
22.929
6.233
2.011
0.057

102
Table 4.2: Atomic fractional coordinates, Wycoff positions, and site occupancies of superprotonic
RbHSeO4 (I4/mmm). Rb and Se positions were determined from a Rietveld refinement. O positions
estimated (∗ ) from expected hSe–Oi bond lengths (1.66 Å), ∠O–Se–O bond angles (109.5◦ ), expected
12-fold coordination of Rb by O atoms, and crystal symmetry requirements.
Atom

Wyckoff
Position

Fractional Coordinates

Site
Occupancy

Rb
Se
O(1)∗
O(2)∗

2a
2b
32o
16n

0.125
0.250

1/8
1/4

0.348
1/2

1/2
0.116
0.330

Rietveld refinement, are given in Table 4.2. From these, the structure of superprotonic
RbHSeO4 is depicted in Figure 4.5(a). In this structure, Rb atoms are positioned at the
corners and body-center of the unit cell. The Se atoms are positioned in faces perpendicular
to the c-axis, and on the edges of the unit cell parallel to the c-axis. The SeO4 groups are
coordinated by 6 Rb atoms, forming an octahedral coordination polyhedra, Figure 4.5(b).

(a) Unit cell

(b) Octahedral coordination polyhedra

Figure 4.5: Depiction of the superprotonic structure of RbHSeO4 , tetragonal space group I4/mmm.
(a) The unit cell as viewed along the b-axis. (b) Octahedral coordination polyhedra of disorderd SeO4
groups by Rb cations, numbers 1–3 indicate disordered oxygen positions participating in hydrogen
bonding through the faces of the octahedra.

Attempts at refining the oxygen positions using the Rietveld method proved unsuccessful. Probable causes for this could be the low atomic number of oxygen (i.e., small scattering
cross section), however, a more likely cause is the high degree of disorder associated with
the rapid tetrahedral reorientations observed in superprotonic solid acids. Instead, the oxy-

103
gen positions are proposed based upon the optimization of four criteria: (1) the oxygen
to selenium distances must be approximately equal those found in the room temperature
structure of RbHSeO4 , hSe–Oi ≈ 1.66 Å, (2) the angles between two oxygen positions, with
selenium positioned at the vertex, must form a complete set of six tetrahedral angles, ∠ O–
Se–O ≈ 109.5◦ , (3) at least 12 oxygen positions must coordinate a Rb atom—the preferred
coordination of Rb+ by O2− ions 25 , (4) the symmetry of the crystal must be preserved by
the choice of any oxygen position. Based upon these criteria, approximate oxygen positions
are proposed, given in Table 4.2.
The structure of RbHSeO4 is unique among superprotonic MHn XO4 -type solid acids
in that, unlike the characteristic 8-fold coordination of the oxy-anions by cations normally
observed, superprotonic RbHSeO4 exhibits 6-fold octahedral coordination, Figure 4.5(b).
Disordered hydrogen bonds are expected to form through the faces of these octahedra, where
intra-tetrahedral oxygen distances are ∼ 2.4 Å—suggestive of strong symmetric hydrogen
bonds. Overall, 24 oxygen positions are suggested, resulting in 3 possible oxygen positions
per octahedral face, numbered 1–3 in Figure 4.5(b), and, therefore, 3 unique tetrahedral
orientations.
Tetragonal I41 /amd
Both superprotonic CsHSO4 and CsHSeO4 structures belong to the the tetragonal space
group I41 /amd 20,21 . The tetragonal structure of superprotonic of CsHSO4 , depicted in
Figure 4.6, is composed of Cs cations and SO4 oxy-anions arranged in alternating pairs along
the b-axis. Crystallographically equivalent and partially occupied oxygen positions result
in the overall rotational disorder of the oxy-anion between crystallographically equivalent
oxygen positions. These oxy-anions are coordinated by 8 Cs cations, forming a 6-sided
polyhedra, in which two triangular prisms lie orthogonal to one another, termed here as
a triangular anti-prism, Figure 4.6(b). The oxygen atoms of the rotationally disordered
tetrahedra are likely to participate in disordered hydrogen bonds through the rectangular
faces of the triangular anti-prism.
While reports of the superprotonic structure of both CsHSO4 and isostructural CsHSeO4 18,19,20,21
more or less agree on the symmetry, lattice parameters, and heavy atom positions; they
differ considerably in their assignment of oxygens positions, and consequently, tetrahedral
orientations and direction of hydrogen bonds 18,19,20 . This dissent is likely the result of highly

104

(a) Unit cell

(b) Triangular anti-prism coordination polyhedron

Figure 4.6: Depiction of the superprotonic structure of CsHSO4 , tetragonal space group I4/mmm.
(a) The unit cell as viewed along the c-axis. (b) Triangular anti-prism coordination polyhedra
of disorderd SO4 groups by Cs cations, where numbers 1–2 indicate disordered oxygen positions
according to structure proposed by Jirak 20 . Disordered hydrogen bonds are like to occur through
the rectangular faces of the cooridination polyhedron.

rotationally-disordered tetrahedral oxy-anions in the superprotonic phase—ultimately, leading to a “smearing out” of the oxygen positions. Experimental difficulties have also been
in encounterd in single crystal diffraction work of superprotonic CsHSO4 due to the loss of
structural integrity of the crystal while heating through the phase transition, resulting in
polycrytallinity 18 .
Many structural descriptions have been given for the superprotonic structure of CsHSO4 ,
each essentially differing in the assignment of oxygen positions. In Figure 4.7, three representative structures for the location of the tetrahedral oxygen positions are given, as
proposed by (a) Jirak 20 , (b) Merinov 18 , and (c) Belushkin 19 . In the structure suggested by
Jirak, there are 8 oxygen positions, corresponding to 2 tetrahedral orientations. Similarly,
Merinov has proposed a structure in which there are 8 oxygen positions and 2 tetrahedral orientations, except here the oxygen positions have been distinguished between oxygen
donor (Od ) and acceptor (Od ) positions. Belushkin, on the otherhand, proposed a structure
with 16 oxygen positions, and thus 4 tetrahedral positions, but like Merinov distinguished

105
between the donor and acceptor oxygen positions. Chisholm observed that by distinguishing
between the donor and acceptor oxygen positions, the number of possible tetrahedral orientations is subject to the symmetry imposed by the crystal. 2 . For example, in the structure
proposed by Merinov, the oxygen positions lie on mirror planes, which will generate a second
set of positions, resulting in a total of 4 tetrahedral configurations. Whereas, in the structure proposed by Belushkin, the oxygen positions do not lie on any special positions, and
therefore, each oxygen is associated with only one tetrahedral orientation—again, totaling
4 tetrahedral configurations. Consequently, both the structures of Merinov and Belushkin
yield a total of 4 tetrahedral configurations, to give a configuration entropy of R ln (4) or
11.52 J mol-1 K-1 —a value much lower than the 14.8 J mol-1 K-1 measured experimentally 1 .
In contrast, the structure given by Jirak does not distinguish between Od and Oa , hence,
each oxygen position can partake in any of the possible tetrahedral orientations, regardless of the placement of the hydrogen bond. In order to account for such a structure, a
more general entropic model is needed, which includes both tetrahedral reorientation and
hydrogen bond disorder.

2 orientations

4 orientations

(a) Jirak

(b) Merinov

Figure 4.7: Proposed oxygen positions for the superprotonic phase of CsHSO4 (I41 amd). (a)
Jirak—two tetrahedral orientations and does not distinguish between oxygen atoms 20 . (b)
Merinov—two tetrahedral orientations and distinguishes between oxygen donor Od and acceptor
Oa atoms. 18 (c) Belushkin—four tetrahedral positions and distinguishes between Od and Oa . 19
Based upon the previous discussion, the structure proposed by Jirak is adopted in the
following entropy calculations of tetragonal I41 /amd superprotonic MHn XO4 -type solid
acids. It will be seen that this structure, in fact, can be used to accurately account for
the entropy of the superprotonic phase. Beyond this self-consistent account of the entropy,
Chisholm has carried out molecular dynamic simulations of the superprotonic phase transition in CsHSO4 , the results of which, also favor the structure of Jirak 1 .

106
Cubic P m3m
Superprotonic CsH2 PO4 has a CsCl-type structure, belonging to the cubic space group
P m3m 22 . There has been only one structural study of this compound in its superprotonic
phase. While no explicit structural data exist for the superprotonic phases of CsH2 AsO4
or RbH2 PO4 , they are likely to be isostructural with superprotonic CsH2 PO4 . Observed
optical isotropy in superprotonic CsH2 AsO4 by polarized light investigations do, in fact,
suggest cubic symmetry in this crystal 23 . Likewise, comparable superprotonic transition
entropies between RbH2 PO4 and CsH2 PO4 , ∆SSP = 21.3 and 22.2 J mol-1 K-1 , respectively,
suggest these compounds have identical superprotonic structures.
The structure of superprotonic CsH2 PO4 is composed of disordered tetrahedral oxyanions positioned at the body centers of cubic coordination polyhedra composed of Cs
cations, depicted in Figure 4.8. Based upon inter-tetrahedral oxygen to oxygen bond distances, strong symmetric disordered hydrogen bonds (hO–Oi ≈ 2.48 Å) are expected to
form through each of the six faces of the cube. A total of 24 oxygen positions per cell
result in 6 tetrahedral orientations, and 4 disordered oxygen positions per hydrogen bond
direction, as indicated in Figure 4.8(b). Each Cs position is coordinated by a total of 12 O
positions—precisely that expected from radius ratio rules 25 .
Summary of Superprotonic Structures
A summary of some of the key structural features of these superprotonic MHn XO4 -type solid
acids is presented in Table 4.3. Since entropy is fundamentally a measure of the number
of configurational states (S = R ln Ω), particularly important to the following the entropy
calculations are the number of hydrogen bonds per polyhedra and the number of oxygen
positions per hydrogen bond direction. These two values represent both the hydrogen bond
and tetrahedral disorder, which should account for most of the entropy of the superprotonic
phase.

4.2.2

Entropy Rules

To generate a set of entropy rules for the superprotonic phases of MHn XO4 -type solid acids
we begin by modifying Pauling’s entropy rules for ice. First of all, in solid acids the number
of hydrogen atoms associated with each tetrahedral oxy-anion (H:XO4 ) can be 1 or 2,

107

(a) Four unit cells

(b) Cubic coordination polyhedra

Figure 4.8: Depiction of the superprotonic structure of CsH2 PO4 , cubic space group P m3m 22 . (a)
Four unit cells, where dashed lines represent possible hydrogen bonds based upon intra-tetrahedral
oxygen to oxygen distances (hO–Oi < 2.5 Å), and (b) cubic coordination polyhedra of disorderd PO4
groups by Cs cations, numbers 1–4 indicate disordered oxygen positions participating in hydrogen
bonds through the faces of the cube.

Table 4.3: Summary of key structural features observed in superprotonic MHn XO4 -type solid acids.
Superprotonic Structure

Tetragonal
I4/mmm

Tetragonal
I1 /amd

Cubic
P m3m

Solid Acids

RbHSeO4

CsHSO4
CsHSeO4

RbH2 PO4
CsH2 PO4
CsH2 AsO4

Oxy-Anion Coordination
Polyhedra

Octahedron

Triangular
Anti-Prism

Cube

Oxy-Anion/Cation
Coordination

Number of H-Bonds
/Polyhedra

Number of Tetrahedral
Orientations/Polyhedra

Number of Oxygen Positions
/H-bond Direction

108
whereas, in ice the number of hydrogen atoms per oxygen atom (H:O) is fixed at 2. Thus,
we modify Pauling’s Ice Rule 1 to read as follows:
Rule 1 One or two protons can be associated with a tetrahedral oxy-anion.
Since the nature of a hydrogen bond, itself, is essentially the same for all hydrogen bonded
materials, Ice Rules 2 and 3 remain effectively unchanged, adding only that the oxygen
atoms are associated with tetrahedral oxy-anions:
Rule 2 One and only one proton is allowed per hydrogen bond.
Rule 3 The hydrogen bonds must be directed approximately toward the oxygen atoms of a
neighboring tetrahedral oxy-anion.
Ice Rule 4 is essentially a statement that hydrogen bond configurations are only affected
by nearest-neighbor interactions. Here, we follow suit by assuming only nearest-neighbor
interactions between tetrahedral oxy-anions. However, one may ask, to what extent is the
proton and tetrahedral oxy-anion motion correlated? Here, we assume the independence
of the tetrahedral orientation between crystallographically equivalent positions from the
direction of the hydrogen bond. This is, perhaps, a reasonable assumption, considering
the relatively high degree of rotational disorder exhibited by the tetrahedral oxy-anions as
compared to the proton motion (∼ 100 times faster). Therefore, we modify Ice Rule 4 to
include the independent motion of the tetrahedral oxy-anions and its protons:
Rule 4 The interactions of non-adjacent tetrahedral oxy-anions do not affect the possible
configurations of a tetrahedral oxy-anion and its protons, so long as they all satisfy Rules 1–
3.
Carrying out these rules lead to a formulation for the number of configurational states
that accounts for both the tetrahedral oxy-anion disorder and the hydrogen bond disorder
in superprotonic solid acids:

number of
protons
number of proton
probability a proton
number of
Ω=
oxygen positions
configurations
site is open
{z
} |
{z
New Term
Pauling’s Ice Rules
(4.4)

109
Clearly, the first term is identical to Pauling’s formulation for ice (Equation 4.2), except
the total number of hydrogen positions around a tetrahedral oxy-anion need to be limited
to four, as is the case for the oxygen atoms in ice. The new term accounts for the reorientations of the tetrahedral oxy-anions, or rotational disorder, which results in multiple oxygen
positions for each hydrogen bond direction. With this formulation, which now accounts
for both hydrogen bond disorder and oxy-anion disorder, the number of configurational
states, and therefore, entropy of the superprotonic phase of MHn XO4 -type compounds can
be calculated.

4.2.3

Calculations

Utilizing Equation 4.4 and the necessary structural details from Table 4.3 the configuration entropy of the superprotonic phase, SSP , can be calculated for each of the known
superprotonic MHn XO4 -type structures. These calculations are summarized in Table 4.4.
Before the total change entropy through the superprotonic phase transition, ∆SSP can be
determined, the initial entropy before the superprotonic transition, S0 , must be established.
The most significant source of configurational entropy prior to the superprotonic phase
transition is the result of intra-hydrogen bond disorder.

110
Table 4.4: Calculations of the configuration entropies, SSP , in superprotonic MHn XO4 -type solid
acids, from the number of configurational states Ω.
Structure
Space Group

Tetragonal
I4/mmm

Tetragonal
I41 /amd

Cubic
P m3m

Compounds

RbHSeO4

CsHSO4
CsHSeO4

RbH2 PO4
CsH2 PO4

Polyhedra

Octahedron

Triangular Anti-prism

Cube

Coordination

6-fold

8-fold

Hydrogen Bond
Directions

Oxygen
Positions

Number of
Protons

Ω=

number of
protons
probability a proton
number of oxygen
number of proton
site is open
positions
configurations

1
(3) = 21

1
(2) = 6

2
(4) = 26.6

SSP = R ln Ω
SSP =

3.04R
-1

1.79R
-1

25.3 J mol K

4.3

-1

3.28R
-1

14.9 J mol K

27.3 J mol-1 K-1

Entropy of Disordered Intra-Hydrogen Bond

Many solid acids are known to undergo a ferroelectric transition upon cooling, in which
a disordered proton within a hydrogen bond double-well potential becomes ordered. This
disordered hydrogen bond can contribute significantly to the entropy of a solid acid prior to

111
the superprotonic phase transition. Classically, the entropy associated with the disordering
of a hydrogen bond (SH ) between the two positions in a double-well potential, is simply
SH = R ln Ω = R ln 2
= 0.69R or 5.76 J mol-1 K-1 .

(4.5)

The structures of RbHSeO4 , RbH2 PO4 , CsH2 PO4 , and CsH2 AsO4 all exhibit one disordered
hydrogen bond per XO4 group, just prior to heating through the superprotonic phase transition. 26,27,28,29,iv Solid acids CsHSO4 and CsHSeO4 do not exhibit any disordered hydrogen
bonds prior the superprotonic phase transtion, therefore, SH = 0 for these compounds.
The structure of the paraelectric phase of CsH2 PO4 is depicted in Figure 4.9. Here, zigzag chains of PO4 groups are connected via a disordered hydrogen bond along the b-axis.
In CsH2 PO4 , the classical configurational entropy of a disordered hydrogen bond of 5.76
J mol-1 K-1 , differs substantially from the measured ferroelectric transition entropy value
of 1.05 J mol-1 K-1 30 . This discrepancy can be explained by the formation of domains, in
which the motion of the disordered protons are likely to be correlated with the oxy-anions
on some small length scale λ. Take, for example, if the correlation length is limited to two
tetrahedral oxy-anions, λ2 in Figure 4.9, then the configurational entropy would be reduced
by half or 2.88 J mol-1 K-1 ( 21 R ln 2). Such local ordering effects, would yield erroneously
small transition entropies, if heat capacity measurements were performed over an insufficient
temperature range. In other words, the correlation length above the ferroelectric transition
temperature would be a function of temperature (λ = λ(T )). This proposition is further
supported by the rather high energy associated with the formation of oxy-anion defects,
which would favor correlations between the proton and oxy-anion. For example,
2−
-1
2H2 PO−
4 → HPO4 + H3 PO4 , ∆Gf = 76.5 kJ mol .

Such a large Gibbs free energy of formation, ∆G◦f , would certainly favor local ordering at low
temperatures, where the thermal energy per hydrogen bond would be too small to form such
ionic defects. Upon heating to higher temperatures, such defects would become increasingly
more likely, the correlation length would gradually approach the distance between hydrogen
iv

It should be noted that the ferroelectric transition of RbH2 PO4 and CsH2 AsO4 involve the disordering
of two hydrogen bonds per XO4 , but both compounds undergo structural modifications at intermediate
temperatures, in which only one disordered hydrogen bond remain up to TSP

112
bonded oxygens, and the disordering of the hydrogen bond would become eventually become
independent of (uncorrelated with) the oxy-anions.

Figure 4.9: Paraelectric phase of CsH2 PO4 depicting disordered hydrogen bond positions 1 and
2. The correlation length of the disordered hydrogen bond if correlated with 2 oxy-anions—λ2 , or
uncorrelated—λ0 , as indicated.

In these calculations, we have adopted the classical configurational entropy of a disordered hydrogen bond. In doing so we implicitly make the following assumption:
As T → TSP , the correlation length λ of the disordered hydrogen bond with
tetrahedral oxy-anions approaches λ0 , the distance between the hydrogen bonded
oxygen atoms (λ → λ0 ), such that the disordering of the hydrogen bond becomes
independent of the tetrahedral oxy-anions.
That is, as a solid acid is heated to the superprotonic transition temperature, the formation
of oxy-anion defects, like those just mentioned, become more and more likely, and therefore,
the disordering of the hydrogen bond becomes independent of the oxy-anion—ultimately
attaining the full entropy of a classically disordered hydrogen bond. Therefore, the entropy associated with disordered intra-hydrogen bonds employed here, are derived from the
entropy of a classically disordered hydrogen bond, Table 4.5.
Table 4.5: The entropy due to disordered intra-hydrogen bonds (SH ) in MHn XO4 -type solid acids
derived from the classical disorder of a hydrogen bond (R ln 2).
Solid Acid
-1

-1

SH / J mol K

CsHSO4

CsHSeO4

RbHSeO4

RbH2 PO4

CsH2 PO4

CsH2 AsO4

5.76

113

4.4

Results

In superprotonic MHn XO4 -type solid acids, the entropy of a superprotonic transition, ∆SSP ,
is the entropy of the superprotonic phase, SSP , minus the (configurational) entropy before
the phase transition, S0 . While several structural modifications exist in these compounds
prior to the superprotonic phase transition, none substantially increase the overall entropy
(< 1 J mol-1 K-1 )—with one exception, the ferroelectric transition. The entropy associated
with the ferro–paraelectric transition, is simply a result of intra-hydrogen bond disorder,
SH . Therefore, the approximate entropy prior to the superprotonic transition is
S0 ≈ SH .

(4.6)

Using the configuration entropy values of the superprotonic phases(SSP ) calculated in Table 4.4, and the intra-hydrogen bond disorder (SH ) values given in Table 4.5 the change in
entropy of the superprotonic phase transition can be calculated,
∆SSP = SSP − S0 .

(4.7)

The results of these calculations are compared with experimentally measured superprotonic phase transition entropies in Table 4.6. In all cases, except CsHSeO4 , the calculated
values of the superprotonic phase transition entropies are within experimental error of the
measured values. It is probable that the discrepancy observed, in the case of CsHSeO4 ,
is related to inaccurate measurements, as this is the only value reported here that was
obtained from an outside source. Similarly, previous experimental measurents of CsHSO4
ranged between 10.9 and 13.3 J mol-1 K-1 31,32 , before efforts were made by Chisholm 1 to
obtain an accurate measurement, resulting in a value of 14.8(6) J mol-1 K-1 . Regardless, the
general agreement between the calculated and experimental values presented here demonstrate that this new formulation can accurately account for the entropy of superprotonic
phase transitions.

114
Table 4.6: A comparison of calculated with measured values of the superprotonic phase transition entropy (∆SSP ) in MHn XO4 -type solid acids, where SSP and S0 are the calculated values of
configurational entropy of the superprotonic phase and the intra-hydrogen bond disorder prior the
superprotonic transition, respectively. † Represents the values obtained in this work.
Solid Acid

SSP
-1

4.5

S0
-1

-1

∆SSP

/J mol-1 K-1

Reference

/J mol K

calculated

measured

RbHSeO4

25.3

5.76

19.5

19.2(4)

CsHSO4

14.9

14.8(6)

Chisholm 1

CsHSeO4

14.9

16.0(5)

Hilczer 33

RbH2 PO4

27.3

5.76

21.5

21.3(9)

CsH2 PO4

27.3

5.76

21.5

22.2(12)

CsH2 AsO4

27.3

5.76

21.5

21.0(8)

Conclusions

A model that successfully accounts for the entropy of a superprotonic phase in MHn XO4 type solid acids has been developed, in collaboration with coworker Calum Chisholm. This
formulation is fundamentally based upon Pauling’s entropy rules for ice, and adapted to account for the rotational disorder of tetrahedral oxy-anions. Based upon the excellent agreement of these calculations with experiment, the previous assumption that intra-hydrogen
bond disorder is independent of the oxy-anion, appears to be valid.
These calculations have only been applied here to MHn XO4 -type solid acids, however Chisholm 1 has extended their application, with some modification, to mixed sulfatephosphate systems. Furthermore, this formulation, given sufficient structural knowledge,
should be broadly applicable to all superprotonic solid acids.
The limitations of these calculations are rooted in the necessity for an accurate structural
description of the superprotonic phase. Therefore, they cannot not serve as a tool for
predicting the presence of superprotonic phase transitions a priori. However, for a known
superprotonic solid acid, these calculations can be used as an effective tool in identifying
likely superprotonic structures. For example, in the case of CsHSO4 , of the structural models
presented, the structure which contains only two tetrahedral configurations is preferred by
this formulation. Similarly, for superprotonic RbHSeO4 , the entropy of the superprotonic
transition had long been known, but not the structure. Though chemically, one might
expect this superprotonic phase of this compound to be isostructural with CsHSeO4 , the

115
relatively high experimental value of superprotonic transition entropy led us to believe that
it was not—which, in fact, turned out to be the case.
Overall, the development of these entropy rules have led to a better understanding
of the thermodynamic driving force behind superprotonic phase transitions in solid acids.
These results also suggest that changes in entropy through superprotonic transition are
primarily due to changes in configurational entropy, and that other sources of entropy
(such as vibrational entropy) are the same in the low and high temperature phases. With
the characterization of parameters effecting superprotonic phase transition temperatures,
i.e., bonding and ionic size, both the conjugate thermodynamic variables, entropy and
temperature, [S, dE
dS ], can ultimately lead to a complete thermodynamic description of these
superprotonic phase transitions.

116

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affecting the presence and stability of superprotonic transitions in MHn XO4 family of
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Institute of Technology, 2002.
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hydrogen-bonded tetrahedra. in preparation.
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13. J. West. A quantitative X-ray analysis of potassium dihydrogen phosphate (KH2 PO4 ).
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crystals. Investiya Akademii Nauk SSSR. Seriya Fizicheskaya, 51(12):2146–2155, 1987.

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15. N.M. Plakida. Theory of the superionic phase-transition in CsHSO4 . JETP Letters,
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Solidi B–Basic Research, 135(1):133–139, 1986.
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at 505 K. Materials Science Forum, 166:511–516, 1994.
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100:135–141, 1989.
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44, 1984.
25. Linus Pauling. Nature of the Chemical Bond. Cornell University Press, New York, 1960.
26. I.P. Makarova, L.A. Muradyan, E.E. Rider, V.A. Sarin, I.P. Alexandrova, and V.I.
Simonov. Neutron-diffraction study of RbHSeO4 and NH4 HSeO4 single-crystals. Ferroelectrics, 107:281–286, 1990.
27. H. Matsunaga, K. Itoh, and E. Nakamura. X-ray structural study of ferroelectric cesium
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28. M.T. Averbuch-Pouchot and A. Durif. Structure of a new form of rubidium dihydrogenphosphate, RbH2 PO4 . Acta Crystallographica Section C–Crystal Structure Communications, 41(May):665–667, 1985.
29. S. Hart, P.W. Richter, J.B. Clark, and E. Rapoport. Phase-transitions in CsH2 AsO4
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30. E. Kanda, M. Yoshizawa, T. Yamakami, and T. Fujimura. Specific-heat study of
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Chapter 5

Application of Superprotonic Solid Acids
in Fuel Cells
Perhaps the most exciting potential application of superprotonic solid acids is as fuel cell
electrolytes. The high proton conductivity and intermediate temperature range (100–350
◦ C) of these compounds make them specifically well-suited for this application.

To fully

appreciate how solid acids are uniquely qualified as potential alternatives to current fuel
cell electrolytes, a brief review of some of the current state-of-art fuel cell electrolytes is
presented. Then the first “proof-of-principle” solid acid-based fuel cell, utilizing a CsHSO4
electrolyte is demonstrated, along with the unfortunate findings that CsHSO4 decomposes
under fuel cell conditions. This is followed by a detailed thermodynamic characterization of
CsHSO4 under oxidizing and reducing atmospheres. As a result of the chemical instablity
encountered in CsHSO4 , a search for a stable solid acid was undertaken. Next, thermal
analysis results confirming the chemical instability examined solid acid sulfates and selenates
under fuel cell conditions are presented. Finally, the potential of solid acid phosphates
as electrolytes is established through the demonstration of long-term stability and high
performance in both H2 /O2 and direct-methanol fuel cells based on a CsH2 PO4 electrolyte.

5.1

State-of-the-Art Electolytes 1,2,3

There are many types of fuel cells broadly characterized according to the electrolyte used.
Among these are (1) polymeric electrolyte membrane fuel cells (PEMFCs), (2) phophoric
acid fuel cells (PAFCs), (3) alkaline fuel cells (AFCs), (4) molten carbonate fuel cells
(MCFCs), and (5) solid oxide fuel cells (SOFCs). Over the last few years PEMFCs and
SOFCs have undergone the most intense research and development efforts, and significant

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progress has been made in both performance and long-term stability of these types of fuel
cells. The results of this progress has been primarily through the development and engineering of existing materials. However, the physical limitations of currently employed
electrolytes have inhibited the further progress of fuel cell development.

Figure 5.1: Arrhenius plot of the conductivity of various fuel cell electrolytes as compared to
solid acids. The dotted-line indicates the minimum value of conductivity, 10−2 Ω-1 cm-1 , at which
electrolytes are considered useful as fuel cell electolytes. Solid oxides,ref 3 (ZrO2 )0.9 (Y2 O3 )0.1 and
Ce0.9 Gd0.1 O1.95 are only applicable at temperatures above 500 ◦ C—indicated by a dashed-line; where
as, polymer electrolytes, such as Nafion r ,ref 3 due to dehydration, are only useful below 100 ◦ C—
also indicated by a dashed-line. Superprotonic solid acids, CsH2 PO4 ,ref 4 CsHSO4 ,ref 5 CsHSeO4 ,ref 5
Rb3 H(SeO4 )2 ,ref 6 K3 H(SO4 )2 ,ref 7 Cs2 (HSO4 )(H2 PO4 ),ref 8 and (NH4 )3 H(SO4 )2 ref 9 have potential
application in the temperature range between 100 and 350 ◦ C.

A pre-requisite for consideration of an electrolyte for fuel cell applications is high ionic
conducitivity. A typical area specific resistance (resistance × thickness) for a fuel cell
with competitive performance is ∼ 0.15 Ω cm2 3 . Through fairly routine processing techniques ∼ 20 µm thick membranes can be achieved. Then, for reasonable fuel cell performance, an electrolyte must have ionic conductivites on the order of 10−2 Ω-1 cm-1 . In
Figure 5.1, the conductivity is plotted on log scale versus the reciprocal of temperature
for Nafion r , the industrial standard for PEMFCs; two common solid oxide electolytes,
(ZrO2 )0.9 (Y2 O3 )0.1 or yttria-stabilized zirconia (YSZ) and Ce0.9 Gd0.1 O1.95 or gadolinium-

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doped cerate (CGO); and several superprotonic solid acid compounds—CsH2 PO4 , CsHSO4 ,
CsHSeO4 , Rb3 H(SeO4 )2 , K3 H(SO4 )2 , Cs2 (HSO4 )(H2 PO4 ), (NH4 )3 H(SO4 )2 . A dotted-line,
at a conductivity of 10−2 Ω-1 cm-1 , indicates the minimum ionic conductivity needed for a
fuel cell electolyte. Up to 100◦ C, Nafion r has spectacular ionic conductivity, while, the solid
oxides are only applicable at temperatures greater than 500 ◦ C. The operating temperatures
of these two leading fuel cell technologies, leaves a temperature gap between 100 and 500
◦ C, indicated by dashed-lines in Figure 5.1.

Operating at such intermediate temperatures

would have significant advantages, such as increased catalytic performance, as compared
to PEMFCs, and wider availablity of materials for cost-effective fuel cell components, as
compared to SOFCs. Solid acids, with high proton conductivities in the range of 100 to 350
◦ C, could potentially bridge this temperature gap and dramatically help to advance fuel

cell technology.

5.1.1

Polymer Electrolytes

Progress in fuel cells based upon polymer electolytes has been possibly the most rapid over
the last decade. Most notable and prevalent among these are fuel cells based on a polymer
electrolyte known as Nafion r made by DuPont. Polymeric membranes, such as Nafion r ,
are composed of a hydrophobic perfluorinated polymer backbone with covalently bonded
hydrophilic sulfonic acid functional groups. Upon hydration of these polymers, protons
are transported through the polymer matrix via a vehicle transport mechanism, in which
H3 O+ ions are the carriers. These H3 O+ ions travel through polymer via a network of
inter-connected nano-domains of hydrophilic sulfonic groups (SO−
3 ), depicted in Figure 5.2.
Due to the inherent need for water in polymer electrolytes, they might, in fact, be more
correctly termed as “polymer-water composite electrolytes.”
The performance of a H2 /air fuel cell using a Nafion r polymer electrolyte membrane is
shown in Figure 5.3 10 . For pure H2 fuel at the anode the performance is quite impressive,
with a peak power density of 0.5 W cm-2 at 0.5 V and maximum current density of almost
2 A cm-2 . However, competitive fuel cells must be able to withstand modest amounts of
CO, which is a by-product of hydrocarbon fuel reforming. In Figure 5.3, at just 100 ppm
of CO in the fuel stream, the fuel cell performance drops below 0.1 W cm-2 at 0.2 V and
has a maximum current density of less than 0.4 A cm-2 . This effect is not directly due to
the membrane itself, but a result of CO adsorbing to the surface of the Pt-catalyst, thereby

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Figure 5.2: Structure of perfluorinated sulfonated polymers (i.e. Nafion r and its close relatives)
depicting the nanoscale phase separated microstructure as determined by SAXS (small angle X-ray
scattering).

inhibiting the catalyst performance—this is commonly referred to as “catalyst poisoning.”
CO-tolerance of catalysts is strongly temperature dependent, for example at ∼ 200 ◦ C, COtolerance of Pt-catalysts is expected to increase to 2–3% 11 . Circumventing this problem is
non-trivial for fuel cells employing polymer electrolytes, due to their hydrated nature and
corresponding temperature limitations. Several approaches have been adopted to overcome
this problem, such as the use of CO-fuel scrubbers and utilizing pressure to access higher
temperatures, both of which effectively reduce the overall efficiency of the fuel cell. A third
approach has been through the replacement of water by an acid within a basic polymer
matrix, such as phosphoric acid (H3 PO4 ) into polybenzimidazole (PBI), however these
membranes suffer from issues similar to those encountered by PAFCs, such as acid leaching
out from the polymer matrix and large over potentials at the cathodes 12 .
Though polymer electrolytes exhibit excellent proton conductivity, the necessity for hydration, places severe limitations on them. For practical applications, some of the most
problematic of these are (1) limited operating temperature (0–100 ◦ C), (2) necessity for
complex and expensive hydration systems, (3) poor catalyst performance, (4) permeability

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Figure 5.3: H2 /air fuel cell performance with a Nafion r polymer electrolyte membrane. Both the
electric potentials (E) and power densities (P ) as a function of current density (i) measured on a
cell operated at 80 ◦ C under 2.4 atm H2 and 4.1 atm air at the anode and cathode, repectively, and
containing 0.13 mg Pt cm-2 . The solid line corresponds to the initial measurement, and the dashed
line after 100 ppm CO was introduced to the anode. Reproduced from reference 10 .

to fuels, and (5) costly and ineffecient waste heat management. To summarize, while polymeric electrolytes have exceptional laboratory performance, “real-world” limitations placed
upon them are perhaps too great to overcome through engineering and design alone.

5.1.2

Solid Oxides

Fuel cells utilizing solid oxide electrolytes can operate, in principle, in the high temperature regime 500–1000 ◦ C. Commercially available SOFCs can only operate efficiently at
temperatures above 800 ◦ C; however, significant effort has been put into bringing this temperature down to below 500 ◦ C. Solid oxides have the advantage of no liquid electrolyte and
the associated issues of electrolyte management and material corrosion, which limit design
configurations. Moreover, operating at temperatures above 800 ◦ C has the advantage of
rapid reaction kinetics, without the need for expensive precious metal catalysts, as well as
generating high quality heat for co-generation purposes. On the other hand, these high
temperatures demand robust materials capable of high temperatures under demanding fuel
cell environments. The development of suitable low-cost materials and ceramic fabrication
techniques are presently the key technical challenge facing SOFCs 13 .
The all-solid-state nature of SOFC components allows for flexible cell design configurations. Currently, two primary cell configurations are being developed, tubular and bi-

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(a) Tubular design

(b) Bi-polar plate design

Figure 5.4: Solid oxide fuel cell configurations: (a) tubular design, and (b) bi-polar plate design.
polar plate designs, depicted in Figure 5.4. In the 90’s, Siemens-Westinghouse Corporation
introduced a 100 kW capacity solid oxide fuel cell generator, based upon a tubular design, Figure 5.4(a)—which avoids the issue of sealing. In this cell, a porous cathode of
La(Sr)MnO3 is plasma sprayed with La(Sr)CrO3 for an interconnecting strip, then a thin
(30–40 µm) YSZ electrolyte layer is deposited by electro-chemical vapor deposition, and
finally a porous Ni-YSZ anode is slurry-spray deposited. Though technically successful, the
cost of electrochemical vapor deposition of YSZ has inhibited these fuel cells from being
competitive alternatives to gas-turbine generators. Furthermore, use of traditionally costeffective ceramic processing techniques, such as sintering are prevented by the reaction of
YSZ with the La(Sr)MnO3 cathode at temperatures above 1200 ◦ C 3 . Attempts at YSZ bipolar designs, Figure 5.4(b), have also been made through the use of compressive seals 14,15 .
However, gas leaks in this configuration have proven difficult to prevent, and high thermal
stresses at the interfaces between dissimilar materials leads to mechanical degradation of
the cell components upon thermal cycling.
As a result of temperature-imposed design constraints placed upon YSZ-based fuel cells,
a conserted effort has been made to find intermediate-temperature (< 600 ◦ C) solid oxide
electrolytes, in which more compliant high temperature gasket seals can be employed. One
such electrolyte, CGO has sufficiently high ionic conductivity (see Figure 5.1) that it could
be used at 500 ◦ C. However, at elevated temperatures (∼ 600 ◦ C), under the reducing
conditions encountered at the anode, Ce4+ reduces to Ce3+ , causing electrical conduction
in the electrolyte, and thereby shorting-circuiting the fuel cell. A further technological

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challenge for these electrolytes is the development of cathodes that can operate at 500 ◦ C,
while simulataneously having good oxidation resistance and electrical conduction.
In summary, solid oxides electrolytes, opposite to that of polymer electrolytes, suffer
issues arising from operating at too high of temperatures. At these temperatures, expensive
processing techniques and thermal-mechanical toughness of materials still remain technical
challenges to overcome—providing an impetus for research into intermediate temperature
electrolytes.

5.2

Solid Acid Electrolytes

Issues encountered in state-of-the-art electrolytes make the operation of fuel cells in an
intermediate temperature range, 100-500 ◦ C, highly desirable. These temperatures are low
enough that fuel cell component materials with appropriate properties can be choosen from
a wide-range of inexpensive materials, yet high enough to allow for good catalytic activity
and reaction kinetics. Fuel cells based on solid acid electrolytes, would operate in this highly
sought after temperature range.
Prior to the research conducted here at Caltech 16,17,18,19 , solid acids were known to
exhibit high proton conductivity, but were not considered for fuel cell applications. The
primary reason for this is the water-soluable nature of most solid acids. It was thought
that H2 O generated at the cathode of a fuel cell would dissolve away the solid acid when
employed as an electrolyte—eventually rendering the fuel cell useless. However, this issue
is easily circumvented by simply operating above the boiling point of water (100 ◦ C), at
which point H2 O in gas phase has no effect on the solid acid.

5.2.1

CsHSO4

In this work, we have selected the solid acid CsHSO4 for “proof-of-principle” investigations in fuel cell applications. This particular acid has been chosen because it is relatively
well-characterized and its superprotonic phase has a reasonably wide temperature range of
stability, from the transition at 141 ◦ C to decomposition/melting at ∼ 200-230 ◦ C 5,20 . Here
we demonstrate the feasiblity of a solid acid based fuel cell. Although these initial results
are quite promising, we show that the long-term viability of a fuel cell based on a CsHSO4 electrolyte is precluded by the reduction of the solid acid under hydrogen atmospheres in

126
the presence of typical anode electrocatalysts.
5.2.1.1

H2 /O2 Fuel Cell

Proof-of-Principle 16
To demonstrate a fuel cell based on a solid acid electrolyte a membrane electrode assembly
(MEA) was prepared as follows. A layer of the solid acid CsHSO4 was sandwiched between
two electrocatalysis layers comprised of CsHSO4 , Pt-black, C-black and Napthalene in a
mass ratio of 6:10:1:1. These layers were, in turn, placed between two sheets of porous,
graphite current collectors. The entire assembly was uniaxially pressed at 490 MPa, to
yield a dense electrolyte membrane with good contact to the electrocatalyst layers. Fuel
cell polarization curves were collected at 160 ◦ C from the MEA placed in a standard graphite
test station (Electrochem, Inc). Upon heating to the test temperature, the Naphthalene in
the electrode presumably evaporated, leaving behind a porous electrode structure.

Figure 5.5: Performance (polarization curve) of an H2 /O2 fuel cell based on a CsHSO4 electrolyte.
The electric potential (E) is plotted versus current density (i) for a cell operated at 160 ◦ C under
humidified (pH2 O = 3.13×10−2 atm) H2 and O2 gasses at the anode and cathode, respectively (total
pressure of 1 atm). The solid line represents the initial measurement, the dotted-line—after 18 hrs
of exposure to humidified air at both electrodes, and the dotted-line—the iRA -corrected result for
initial measurement. The cell was comprised of a 1.37 mm thick CsHSO4 electrolyte layer and a
catalyst loading of 18 mg Pt cm-2 .

The performance of this single cell fuel, characterized by the electric potential (E) measured as a function of current density (i) while exposed to H2 O-saturated H2 and O2 at
the anode and cathode, respectively, and held at 160 ◦ C, is presented in Figure 5.5. The

127
electrocatalyst content or “loading” was 18 mg Pt cm-2 at both the anode and cathode
and the membrane thickness was 1.37 mm. The solid curve reflects the initial measurement
and the dashed, the measurement after 18 hours of exposure to humid air. The anode and
cathode gases were humidified during fuel cell operation only in order to explicitly establish the open circuit potential. Similar results were obtained for operation with dry gases.
It is immediately apparent that despite the water solubility of CsHSO4 and its ability to
undergo extensive plastic deformation at high temperatures 21 , stable fuel cell performance
is possible. The slight drop in performance with time is likely due to degradation at the
anode, as a result of reduction by H2 , as described later, and not a result of interactions
with H2 O or any lack of dimensional integrity.
The open circuit potential of the cell in Figure 5.5 is 1.11 V. This compares favorably
with the theoretical value of 1.22 V, expected for the conditions T = 160 ◦ C, pO2 ≈ 1
atm, pH2 ≈ 1 atm, and pH2 O = 3.13 × 10−2 atm 22 . The difference between the measured
and theoretical open circuit voltages (OCV) is likely due to gas permeation through residual
pores within the polycrystalline electrolyte, or through leaks in the experimental apparatus.
Nevertheless, the OCV obtained here is significantly higher than that typically observed in
polymer based fuel cells, 0.9 - 1.0 V 23 . The humidification requirements of the polymer, as
well as its inherent permeability to H2 and O2 via molecular dissolution and transport, act
to lower the maximum OCV achievable. In the case of the solid acid, improved processing
will surely result in OCV values as high as theoretical, as has been reported, for example,
for KH2 PO4 24 and is routine for solid oxide fuel cells 13 .
The drop in fuel cell voltage with increasing current density, Figure 5.5, has many
causes 23 , the primary one being, for a relatively thick electrolyte as was used in this experiment the resistance of the membrane. This term is given by iRA , where i is the current
density, and RA is the area specific resistance or t/σ, where t is the electrolyte thickness
and σ is the conductivity. Thus, one expects a linear drop in voltage as a function of current density, the magnitude of which depends only on the properties and geometry of the
electrolyte. While the characteristics of the superprotonic phase transition of CsHSO4 are
well-established, the reported conductivity at 160 ◦ C varies from 3.70 × 10−3 Ω-1 cm-1 to
2.08 × 10−2 Ω-1 cm-1 20,5 . However, our measurements of CsHSO4 under H2 O-saturated air
indicate a conductivity of ∼ 8 × 10−3 Ω-1 cm-1 . Using this latter value and the electrolyte
thickness of 1.37 mm, the expected slope in Figure 5.5 is -17.1 Ω cm2 , which is significantly

128
smaller than the measured value of -22.7 Ω cm2 . Additional resistance effects are likely
due to slow charge transfer through the electrodes (also rather thick) and various contact
resistances. The dotted curve (Emeas + iRA ) in Figure 5.5 shows the magnitude of the losses
due to all non-electrolyte factors.
In the present work, rather thick membranes were necessary to obtain impermeable
MEAs and stable open circuit voltages. In order to achieve an area specific resistivity that
is directly comparable to that of Nafion r membranes (typically 0.025 to 0.0875 Ω cm2 at
90 ◦ C and under highly humidified atmospheres for membranes 50-175 µm in thickness 23 )
a dense CsHSO4 membrane with a thickness on the order of 2 to 20 µm would be necessary.
While such films may not be immediately achievable, routine fabrication of solid oxide
electrolytes with comparable dimensions 25 renders this target quite realistic.
Performance Degradation 19
The performance of a H2 /O2 fuel cell based on a CsHSO4 electrolyte is re-examined here
under prolonged exposure to standard fuel cell gases (humidified H2 and O2 at the anode
and cathode, respectively), as opposed to the previous measurement, in which, performance
was measured both prior to and after 18 hours of exposure of the cell to humidified air. The
performance of this second MEA, prepared in the same fashion as described in the previous
section, is shown in Figure 5.6.
Upon initial examination, the peak power density was 12 mW cm-2 , and a maximum
current density of 45 mA cm-2 . Damage to the fuel cell under operating conditions was
rapid. After five hours of continuous operation, the performance fell to a peak power
density of 6 mW cm-2 , and a maximum current density of 17 mA. After flushing both the
anode and cathode with compressed air and then holding the system in stagnant air for 5
hours, the fuel cell performance recovered to a level close to that measured initially (peak
power density of 10 mW cm-2 and maximum current density of 41 mA cm-2 ). In some
cases, the fuel cell recovery after flushing with air was such that the measured performance
had peak power densities higher than initial values. These results indicate that the loss
in performance cannot be associated with degradation of the membrane directly, which
would be irreversible, but some other reversible process. Adsorption of small quantities of
H2 S onto the surface of the Pt catalyst, and its desorption upon exposure of the anode to
air, is consistent with the observed fuel cell behavior, although other possibilities cannot

129

Figure 5.6: The degradation of H2 /O2 fuel cell performance with CsHSO4 -based electrolyte.
Electric potential (E) and power density (P ) measured as a function of current density (i) for a
CsHSO4 -based single cell fuel cell operated at 154 ◦ C. Solid curves represent the initial measurement
under humidified (pH2 O = 3.13×10−2 atm) H2 and O2 gasses at the anode and cathode, respectively,
the dashed curves after five hours of operation under these conditions, and the dotted curves after
an additional three hours exposure to air.
be unequivocally ruled out. It has been established, in the case of phosphoric acid fuel
cells, that as little as 50 ppm H2 S in the incoming fuel stream significantly degrades anode
performance, and that this degradation is similarly reversible 26 .
5.2.1.2

Chemical Stability under H2

To identify the cause for the loss in performance observed in the H2 /O2 fuel cell using a
CsHSO4 electrolyte from the previous section, thermal analysis of CsHSO4 , alone and with
various catalysts, under reducing H2 atmospheres, as well as thermodynamic calculations
of the stability of CsHSO4 in H2 gas were carried out and the results presented here.
Thermal Analysis 19
Thermal analysis results upon slowly heating CsHSO4 mixed with Pt catalyst while under
flowing H2 /Ar gasses are presented in Figure 5.7. From the DSC results (top panel) a sharp
endothermic peak is observed at 141 ◦ C, corresponding to the superprotonic phase transition
in CsHSO4 , and a second exothermic event at 201 ◦ C. From TG/DTG measurements (middle panel) slight weight loss is observed even before the superprotonic transition, with the
maximum amount of weight-loss occuring at 147 ◦ C and 199 ◦ C. Mass spectroscopy analysis

130
of resulting evolved gas species (bottom panel) indicate that the weight-loss observed by
TG/DTG correspond to H2 O and H2 S.

Figure 5.7: Combined differential scanning calorimetry (DSC—top panel), thermalgravimetry and
diffential thermalgravimetry (TG/DTG—middle panel), and evolved gas analysis by mass spectroscopy (Mass Spec—bottom panel) for gas species H2 O (m18.00) and H2 S (m34.00) while heating
at 1 ◦ C min-1 CsHSO4 mixed with 35 wt% Pt catalyst, under flowing 4% H2 –Ar (40 cm3 min-1 ).

A second sample of CsHSO4 mixed with 35 wt% Pt catatyst was heated to and held at
160 ◦ C for ∼ 15 hrs while exposed to H2 gas. A powder X-ray diffraction pattern taken from
the recovered sample is shown in Figure 5.8. The experimental diffraction pattern (solidcurve) corresponds well with the calculated patterns for Cs2 SO4 plus Pt (dashed-curve).
The combination of these thermal analysis and diffraction results suggests the following
decompositon reaction for CsHSO4 in a H2 atmosphere at elevated temperatures:
Reaction I:

2CsHSO4 (s) + 4H2 (g) → Cs2 SO4 (s) + 4H2 O(g) + H2 S(g)

The onset of this reaction appears to be nearly simultaneous with the superprotonic phase
transition at 141 ◦ C. Therefore, the successful application of a CsHSO4 -based H2 /O2 fuel
cell that uses Pt as a catalyst is prevented by this decomposition/dehydration reaction.

131

Figure 5.8: Powder X-ray diffraction pattern of the reaction by-product of H2 (g) with CsHSO4 (s)
with 35 wt% Pt catalyst held at 160 ◦ C for ∼ 15 hrs. Top curve represents the experimental
diffraction pattern and the bottom the calculated pattern of Cs2 SO4 .

Catalyst Effect
To establish the extent that catalysts promote the decomposition/dehydration reaction of
CsHSO4 under H2 atmospheres, and to possibly identify an alternative catalyst to Pt that
could be used in a CsHSO4 -based fuel cell, isothermal thermalgravimetric analysis at 160
◦ C was carried out on CsHSO alone, and with the various catalysts listed in Table 5.1

below, under flowing H2 /Ar gasses.
Table 5.1: Physical characteristics of catalyst materials used in thermal stability investagation of
CsHSO4 under H2 gas.
Surface Area / m2 g-1

Catalyst

Source

Particle Size

Pt black

Alfa Aesar

N/A

RuO (Ru)

Alfa Aesar

< 1 µm

45–65

Pd black

Aldrich

N/A

Aldrich

100 nm (1–2 µm agglomerates)

N/A

Ir black

Alfa Aesar

N/A

30–60

Ni/Al “Raney Ni”

Alfa Aesar

200 mesh (< 74 µm)

N/A

Alfa Aesar

< 1 µm

1.2–1.4

132
Here again, the results are undesirable for fuel cell applications. Even relatively inactive
catalysts such as Au lead to a significant increase of the rate of Reaction I compared to
its rate in the absence of catalysts. In general, the reaction rate increases according to
the sequence Au < Ni/Al < RuO2 < Pt < WC < Pd < Ir. Given the wide variation
in specific surface areas of the catalyst materials employed, Table 5.1, it is impossible to
establish whether this sequence is a direct consequence of catalyst chemistry. Nevertheless,
it is surprising that WC, with a relatively low specific surface area, serves as a very effective
catalyst for sulfur reduction.

Figure 5.9: Weight loss isotherms at 160 ◦ C of CsHSO4 under flowing H2 gas (20 cm3 min-1 ) in
the presence of various (potential) fuel cell catalysts (as indicated).

133
Thermodynamic Characterization 18
In exploring alternatives to CsHSO4 , a thorough investigation from a thermodynamic view
point of the decomposition of CsHSO4 could provide valuable insight into the thermochemical requirements necessary to create a stable solid acid-based electrolyte for fuel cell
applications.
For the purpose of such an exploration, the following thermodynamic data are obtained
from literature for each constitutive chemical species for the reaction of interest:
∆Hf,298.15

: enthalpy of formation at 298.15 K and 1 bar

S298.15

: standard entropy at 298.15 K and 1 bar

Cp◦ (T )

: heat capacity function at 1 bar

where empircally
Cp◦ (T ) = A + B · 10−3 T + C · 105 T −2 + D · 10−6 T 2

(5.1)

and coefficients A, B, C, and D are obtained from reported literature values. Using these
data, the standard enthalpy of formation ∆Hf◦ (T ) and standard entropy S ◦ (T ) functions
for each chemical species are extrapolated to elevated temperatures using the equations
∆Hf◦ (T ) = ∆Hf,298.15

Z T

Cp◦ (T ) dT +

298.15

and

S (T ) = S298.15

∆Htr

(5.2)

X ∆Htr
Cp◦ (T )
dT +
Tc
298.15
tr

Z T

(5.3)

where ∆Htr and Tc are the enthalpy and temperature of any relevant phase transitions.
◦ (T ) and entropy ∆S ◦ (T ) functions can be calculated
Now the reaction enthalpy ∆Hrxn
rxn
◦ (T ) and S ◦ (T ), respectively,
from the difference between the products and reactants of ∆Hf,i

of all chemical species i using

∆Hrxn
(T ) =

products

ni ∆Hf,i
(T ) −

reactants

and
∆Srxn
(T ) =

ni ∆Hf,i
(T )

(5.4)

ni Si◦ (T )

(5.5)

products

ni Si◦ (T ) −

reactants

134
where ni is the stoichiometric coefficient of chemical species i. Finally, the Gibbs free energy
function for the reaction ∆G◦rxn (T ) can be obtained from
∆G◦rxn (T ) = ∆Hrxn
(T ) − T ∆Srxn
(T )

(5.6)

and then used to evaluate the equilibrium constant Ki for reaction i, where
∆G◦rxn (T ) = −RT ln Ki .

(5.7)

For the reduction of CsHSO4 in H2 gas, thermal analysis from the previous section
suggests the decomposition reaction
Reaction I:

2 CsHSO4 (s) + H2 (g) → H2 O(g) + 4 H2 S(g) + 2 Cs2 SO4 (s)

while the further reduction of Cs2 SO4 to form CsOH would occur through
Reaction II:

4 Cs2 SO4 (s) + H2 (g) → 2 H2 O(g) + 4 H2 S(g) + 2 CsOH(s) .

Thermodynamic data for each constitutive chemical species of the chemical reactions above
are given in Table 5.2. Reported values are well-established for all chemical species, except
for CsHSO4 , in which it was necessary to estimate its S ◦ and Cp◦ (T ), see Appendix for
details. These estimates should be adequate given that accurate data for these values is
not essential for obtaining rough approximations of thermodynamic behavior. Also, the
transition enthalpies and temperatures of phase transitions in CsHSO4 were taken into
account. CsHSO4 undergoes two relevant phase transitions, (1) a monoclinic (P 21 /c)monoclinic (P 21 /m) transition at Tc = 60 ◦ C, ∆Htr = 0.53 kJ mol-1 , and (2) a superprotonic
transition at Tc = 141 ◦ C, ∆Htr = 6.13 kJ mol-1 . 27
The equilibrium constants (Ki ) for Reactions I and II can be written in terms of the
partial pressures pi ’s of relevant gaseous species i, such that
1/4

pH2 O · pH2 S
KI =
pH2
and

1/2

KII =

(5.8)

1/4

pH2 O · pH2 S
pH2

(5.9)

In Figure 5.10, KI and KII are plotted on a log scale in the temperature range 100-200 ◦ C.

135
Table 5.2: Reported values for standard (1 bar) enthalpy of formation ∆Hf,298.15
and entropy

S ◦ 298.15 at 298.15 K and the coefficients A, B, C, and D for the standard heat capacity function
Cp◦ (T ) of selected chemical species involved in the reduction of CsHSO4 in the presence of H2 gas.
Empirically, Cp◦ (T ) = A + B · 10−3 T + C · 105 T −2 + D · 10−6 T 2 .
Chemical Species

∆Hf◦ ,298.15
-1

S ◦ 298.15
-1

Cp◦ (T ) /J mol-1 K-1
-1

Source

/kJ mol

/J mol K

CsHSO4 (s)

-1158

189†

141.5

0†

CsOH(s)

-416.2

104.2

-46.24

394.5

24.78

-330.0

Gurvich 29

Cs2 SO4 (s)

-1442

211.8

99.72

113.4

-2.256

32.96

Barin 30

H2 (g)

31.23

25.86

4.837

1.584

-0.037

JANAF 31

H2 O(g)

-241.8

188.8

28.41

12.48

1.284

0.360

JANAF 31

H2 S(g)

-4.900

49.18

25.35

24.52

1.735

-4.015

Gurvich 32

NBS 28

Estimated values, see Appendix for details.

It is evident from Figure 5.10 that the reaction constant KI for the reduction of CsHSO4 to
Cs2 SO4 is substantial. Even at moderately reducing conditions, pH2 = 0.001 atm, suppression of the reduction of CsHSO4 would require pH2 O ·pH2 S 1/4 > 105 -107 atm, a condition that
is experimentally difficult, if not impossible, to achieve. Thus, the formation of Cs2 SO4 is a
thermodynamic expectation in almost any atmosphere which contains H2 gas. However, the
further reduction of Cs2 SO4 is not expected in the presence of even modest amounts of H2 O
and H2 S, because of the quite small equilibrium constant KII for this reaction. Alternative
reduction pathways of Cs2 SO4 accompanied with formation of SO2 were also considered,
however these reactions were deemed insignificant compared to the reduction accompanied
by the formation of H2 S. In conclusion, the reduction of CsHSO4 by H2 gas is expected to
form the products Cs2 SO4 and H2 S, which is in agreement with the previous experimental
findings.
5.2.1.3

Chemical Stability under O2

Thermodynamic characterization of CsHSO4 in the presence of O2 gas was carried out here,
however these results would also be equally valid for the thermal stability of CsHSO4 under
inert atmospheres. Such characterization will help to confirm that the degradation in fuel
cell performance observed when using a CsHSO4 electrolyte from the previous sections is,

136

Figure 5.10: Reaction equilibrium constant (Ki ) as a function of temperature (T ) for the reduction
of (I) CsHSO4 to Cs2 SO4 , and (II) Cs2 SO4 to CsOH in H2 gas.

in fact, solely the bi-product of an anode reaction with H2 to form H2 S and not a result of
any electrolyte instability at the cathode.
Thermodynamic Characterization 18
For this analysis of CsHSO4 under oxidizing conditions, the oxygen partial pressure was
assumed to be greater than 10−10 atm, at which all cations will remain in their maximum
valence states (Cs+ , H+ and S+6 ). That is, we can ignore species such as Cs, H2 , SO2
and other lower valence sulfur compounds. Consequently, degradation of CsHSO4 can only
take place via decomposition to compounds comprised of Cs2 O, SO3 , and H2 O. Of these,
Cs2 O and CsOH are unlikely products because of the strong chemical affinity of Cs2 O
and SO3 (Cs2 O(s) + SO3 (g) → Cs2 SO4 (s), ∆G◦f = -629 kJ mol-1 at 100 ◦ C). If we then
assume that there are no intermediate compounds between Cs2 S2 O7 (s) and CsHSO4 (s),
and between Cs2 S2 O7 (s) and Cs2 SO4 (s), the by-products of the decomposition of CsHSO4
in an oxidizing atmosphere are limited to H2 O(g), SO3 (g), H2 SO4 (g), Cs2 S2 O7 (s), and
Cs2 SO4 (s). Thermodynamic data for these chemical species are given in Table 5.3. Due to
a lack of reported data on Cs2 S2 O7 it was necessary to estimate its thermodynamic data, as
well as that of CsHSO4 , as was mentioned in the previous section, see Appendix for details.

137

Table 5.3: Reported values for standard (1 bar) enthalpy of formation ∆Hf,298.15
and entropy

S ◦ 298.15 at 298.15 K and the coefficients A, B, C, and D for the standard heat capacity function
Cp◦ (T ) of selected chemical species involved in the decomposition of CsHSO4 in the presence of O2
gas. Empirically, Cp◦ (T ) = A + B · 10−3 T + C · 105 T −2 + D · 10−6 T 2 .
Chemical Species

∆Hf◦ ,298.15

S ◦ 298.15

/kJ mol-1

/J mol-1 K-1

Cp◦ (T ) /J mol-1 K-1

Source

CsHSO4 (s)

-1158

189

141.5

0†

NBS 28

Cs2 SO4 (s)

-1442

211.8

99.72

113.4

-2.256

32.96

Barin 30

Cs2 S2 O7 (s)

-1990†

265†

105

0†

NBS 28

H2 O(g)

-241.8

188.8

28.41

12.48

1.284

0.360

JANAF 31

H2 SO4 (g)

-175.700

71.416

14.207

32.943

-2.316

-15.808

Barin 30

SO3 (g)

-94.590

61.370

4.826

29.879

0.042

-18.471

Barin 30

Estimated values, see Appendix for details.

138
The four relevant reactions inter-relating CsHSO4 and its possible decomposition products are given as
Reaction A:

2CsHSO4 (s) → Cs2 S2 O7 (s) + H2 O(g)

Reaction B:

2CsHSO4 (s) → Cs2 SO4 (s) + SO3 (s) + H2 O(g)

Reaction C:

Cs2 S2 O7 (s) → Cs2 SO4 (s) + SO3 (g)

Reaction D:

SO3 (g) + H2 O(g) → H2 SO4 (g)

For each of the above reactions, the corresponding equilibrium constant Ki for reaction i,
given as a function of the relative partial pressures pi of relevent gaseous species i are
KA = pH2 O

(5.10)

KB = pH2 O · pSO3

(5.11)

KC = pSO3
pH2 O · pSO3
KD =
pH2 SO4

(5.12)
(5.13)

Using equations 5.2 through 5.7, the data given in Table 5.3, and accounting for the phase
transitions in CsHSO4 , as in the previous section, the ∆G◦rxn was calculated at 100, 150,
and 200 ◦ C. From the ∆G◦rxn ’s, the above Ki ’s were used to generate stability domain
diagrams (or chemical potential diagrams) for the decomposition of CsHSO4 , shown as
Figure 5.11 at (a) 100 ◦ C, (b) 150 ◦ C, and (c) 200 ◦ C. The regions of stability of CsHSO4 (s),
Cs2 S2 O7 (s), Cs2 SO4 (s), and H2 SO4 –CsHSO4 or Cs2 S2 O7 solution are labeled. The region
of H2 SO4 –CsHSO4 or Cs2 S2 O7 solution is indicated as a gray area due to uncertainties in
thermodynamic data with respect to the activity of H2 SO4 and solubility of Cs compounds.
The partial pressure of H2 SO4 is indicated as dotted line at several different pressures
(pH2 SO4 = 10−2 , 10−3 and 10−4 atm). The equilibrium vapor pressures over liquid H2 SO4
(pH2 SO4 ) at the temperatures of interest, 100, 150, and 200 ◦ C are 10−3.7 , 10−2.5 , 10−1.6 atm,
respectively. To suppress dehydration of CsHSO4 , a pH2 O of greater than that indicated
by the co-existence of CsHSO4 with Cs2 S2 O7 (Reaction A) is required, shown as line A in
Figure 5.11. Similarly, to suppress the degradation of CsHSO4 to form Cs2 SO4 , a pH2 SO4
= 10−2 atm or greater than that indicated by the co-existence of CsHSO4 with Cs2 SO4
(Reactions B and C) is required, indicated line B. As temperature increases, the stability
field of Cs2 S2 O7 moves to higher pSO3 and pH2 SO4 , whereas that of CsHSO4 moves to
higher pH2 O —the stability field of CsHSO4 becomes quite small at 200 ◦ C. Given the direct

139
relationship between pH2 SO4 and those of pSO3 and pH2 O (equation 5.13) for the sake of
simplicity only the pH2 SO4 is considered, rather than pSO3 in further analysis.
Plots of the co-existence curve of (a) CsHSO4 –Cs2 S2 O7 –H2 O at a critical equilibrium
pH2 SO4 , and (b) CsHSO4 –Cs2 SO4 –H2 SO4 at a critical equilibrium pH2 O as function of temperature are presented in Figure 5.12. The CsHSO4 –Cs2 S2 O7 and CsHSO4 –Cs2 SO4 coexistence lines, indicated by lines A and B, respectively, correspond to those indicated in
Figure 5.11. For comparison, the liquid-vapor equilibrium pressure of H2 O liquid at 25
and 70 ◦ C, pH2 O = 0.031 and 0.31 atm, respectively, are also indicated in Figure 5.12(a).
Under an equilibrium pH2 O of liquid H2 O at 70 ◦ C, CsHSO4 will not begin to dehydrate
until temperatures greater than 200 ◦ C, whereas an equilibrium pH2 O at 25 ◦ C will retard
dehydration up to ∼ 170 ◦ C. Thus, dehydration of CsHSO4 can easily be suppressed by
simply heating under humidified gasses. Heating under pH2 SO4 to suppress decomposition
to Cs2 SO4 is a more challenging prospect because of the corrosive nature of this gas, but
would only be necessary at high temperatures. For example, at 170 ◦ C, only about 1 ppm
of H2 SO4 in the atmosphere is necessary to suppress degradation. For a sample exposed
to ambient atmospheres, a small amount of CsHSO4 degradation and H2 SO4 generation
would easily prevent further degradation as a result of limited H2 SO4 diffusion from the
electrolyte surface to the atmosphere. At higher temperatures, however, careful control of
pH2 SO4 would likely be necessary because of the exponential temperature dependence of the
equilibrium pH2 SO4 and increased diffusion rates.

140

Figure 5.11: Chemical potential diagrams (or stability domain diagrams) for the Cs–H2 O–SO3
system at temperatures (a) 100 ◦ C, (b) 150 ◦ C, and (c) 200 ◦ C. The co-existence line with H2 SO4 is
shown as a dotted line at various H2 SO4 partial pressures (pH2 SO4 s), as indicated on the right axis.
The co-existence lines of CsHSO4 (s)–Cs2 S2 O7 (s) are indicated by line A, and CsHSO4 (s)–Cs2 SO4 (s)
by line B.

141

(a) CsHSO4 –Cs2 S2 O7 co-existence curve

(b) CsHSO4 –Cs2 SO4 co-existence curve

Figure 5.12: Co-existence curves as a function of temperature for (a) CsHSO4 (s)–Cs2 S2 O7 (s) and
pH2 O at a critical equilibrium pH2 SO4 —line A, and (b) CsHSO4 (s)–Cs2 SO4 (s) and pH2 SO4 at a critical
equilibrium pH2 O —line B as a function of temperature.

142
5.2.1.4

O2 Concentration Cell

To experimentally verify the previous thermodynamic analysis of CsHSO4 in an O2 atmosphere, electromotive force (EMF) measurements were carried out on CsHSO4 in an O2
concentration cell. In addition to chemical stability, fuel cell electrolytes must also exhibit
sufficient mechanical integrity so as to prevent the development of leaks across the membrane over long-term operation. The large volume change accompanying the superprotonic
transition of solid acids, such as in CsHSO4 (1-2 vol%), renders mechanical integrity a particular concern for these compounds. Furthermore, it is essential that electrolytes under
consideration for fuel cell applications have an ionic (protonic) transference number close to
one; that is, the entirety of the current should be carried by protons rather than electronic
species, which would reduce fuel cell efficiencies. To address the issue of thermo-mechanical
stability, measurements are carried out while thermal cycling through the phase transition,
while the protonic transference number is determined by EMF measurements.
A schematic diagram of the experimental apparatus used is shown in Figure 5.13. Here
CsHSO4 powder was uniaxially pressed at 280 MPa into a pellet (2 mm thick by 19 mm in
diameter). Both sides were sputter-coated with platinum and then lightly polished with fine
sandpaper. Platinum gauze and leads were attached to both sides by applying moderate
pressure. A fluorocarbon O-ring was used as a seal between both chambers. Flowing
mixtures of Ar-O2 -3% H2 O gasses at 50 sccm were delivered to each chamber with different
O2 concentrations of 10 and 0.1% , respectively. The EMF across CsHSO4 in an oxygen
concentration cell was measured over several days, while the pellet was repeatedly cycled
through the phase transition temperature (141 ◦ C) between 129 (3 hrs) and 145 ◦ C (14
hrs). The resultant voltage generated across the sample was measured using an Agilent
34970A digital multimeter and the H2 O vapor pressure was monitored using an EdgeTech
650 capacitance manometer.
The results of the EMF measurements are shown in Figure 5.14. At temperatures
above the superprotonic phase transition (at 141 ◦ C), the measured voltages were, after
some equilibration period, consistent with the theoretical value of -41.5 mV within ± 2
mV. Thus, CsHSO4 is a purely ionic conductor above the superprotonic phase transition.
Furthermore, as expected on the basis of the thermodynamic analysis, the material was
stabilized against dehydration as a result of the 3% H2 O in the atmosphere—there were no

143

Figure 5.13: Schematic diagram of experimental apparatus used for elecromotive force measurements of CsHSO4 in an O2 concentration cell, where p1 and p2 represent the different O2 partial
pressures.

signs of CsHSO4 decomposition after 85 hrs of measurement. Rather unexpected is the drop
in voltage at temperatures below the transition. Given the nature of the chemical bonding
in CsHSO4 , it is unlikely that this can be a result of high electronic conductivity at 129 ◦ C.
It is instead believed that the low voltage is a result of microcracks which heal at elevated
temperatures. The possibility that microcracks can heal at high temperatures is proposed
on the basis of the reported “superplastic” behavior of CsHSO4 in the superprotonic phase,
in which it was observed that the mechanical properties were analogous to that of “clay or
plasticine” 21 . Whatever the cause of the low voltage at low temperature, it is clear that
it does not impact the high-temperature electrochemical behavior of CsHSO4 , for which
a large voltage is obtained in each thermal cycle. Furthermore, the unavoidable thermomechanical deformation of cesium hydrogen sulfate which occurs upon passing through
the phase transition can be prevented from causing device damage with the appropriate
experimental configuration.
These results demonstrate that CsHSO4 can, with the use of humidified gasses, be used
as an electrolyte in oxidizing atmospheres. Though it is clear that for fuel cell applications,
CsHSO4 is not an ideal candidate, this electrolyte could find it way into applications such
as oxygen and sulfuric acid sensors.

144

Figure 5.14: The electric potential as a function of time and temperature of a CsHSO4 -electrolytebased oxygen concentration cell. Flowing humidified gases (pH2 O = 0.3 atm) with O2 concentrations
of 10% and 0.1%, theoretical electric potential (E◦ ) of -41.5 mV at 145 ◦ C, were used while cycling
above and below the superprotonic phase transition temperature (Tc ) of CsHSO4 .

145

5.2.2

Sulfates and Selenates 19

After the discovery of chemical instability of CsHSO4 in H2 containing atmospheres a concerted effort was made to identify a superprotonic solid acid which is stable in H2 gas in the
presence of a fuel cell catalyst. To accomplish this, rapid characterization of many known
superprotonic solid acid sulfates and selenates by themal analysis under H2 in the presence
of a Pt-catalyst was carried out. Isothermal gravimetric analysis studies at 160 ◦ C under
flowing H2 gas in the presence of 35 wt% Pt on CsHSO4 , (NH4 )3 H(SO4 )2 , Rb3 H(SeO4 )2 ,
(NH4 )3 H(SeO4 )2 , Cs2 (HSO4 )(H2 PO4 ), and Cs2 SO4 (for reference), are presented in Figure 5.15. Each of the solid acid compounds undergoes a superprotonic transition at a temperature below the measurement temperature. It is apparent that the simple salt, Cs2 SO4 ,
is stable under reducing conditions, despite the 6+ oxidation state of sulfur, and thus it
is a likely final reaction product. Disappointingly, from an applications perspective, none
of the sulfate or selenate solid acids are stable under these conditions. The rate of weight
loss follows the sequence (NH4 )3 H(SO4 )2 > CsHSO4 > Rb3 H(SeO4 )2 > (NH4 )3 H(SeO4 )2
> Cs2 (HSO4 )(H2 PO4 ).

Figure 5.15: Weight loss isotherms at 160 ◦ C of various superprotonic solid acid sulfates and
selenates (as indicated) and Cs2 SO4 (for comparison) under flowing H2 gas (20 cm3 min-1 ) in the
presence 35 wt% Pt catalyst.

The reduction reaction for CsHSO4 in H2 gas, Reaction I from the previous sections,
can be expressed more generally to include all MHXO4 and M3 H(XO4 )2 compounds (where

146
M = monovalent cation, and X = S or Se):
2MHXO4 + 4H2 → M2 XO4 + 4H2 O + H2 X
2M3 H(XO4 )2 + 4H2 → 3M2 XO4 + 4H2 O + H2 X
Given the fractional weight change per formula unit reacted of the above reactions, one
would expect weight loss to occur more quickly for MHXO4 than M3 H(XO4 )2 compounds.
The rapid degradation of (NH4 )3 H(SO4 )2 reveals that this material is particularly unsuitable
for fuel cell applications. Indeed, attempts to demonstrate fuel cell performance using
(NH4 )3 H(SO4 )2 were uniformly unsuccessful 33 . The lower reactivity of Cs2 (HSO4 )(H2 PO4 )
may be a result of the lesser tendency of phosphorous to form H3 P than sulfur to form H2 S
and suggests that phosphate-based solid acids will likely have better chemical stability under
fuel cell conditions.

5.2.3

CsH2 PO4 17

In light of the chemical instablity observed in solid acid sulphates and selenates under
H2 atmospheres, here we have investigated the viability of CsH2 PO4 as an electrolyte in
fuel cells. A phosphate-based compound is not expected to suffer a reduction reaction
to form solid phosphorus or gaseous Hx P species, and therefore is a promising candidate
for fuel cell applications. It is well-known that CsH2 PO4 dehydrates in its superprotonic
phase under ambient pressures, which, if employed in a fuel cell, would render it useless.
This issue is addressed through (1) identifying the equilibrium partial pressure to suppress
this dehydration, and then (2) employing this knowledge to the measurement of fuel cell
performance under gasses, appropriately humidified so as to prevent dehydration.
5.2.3.1

Thermo-chemical Stability

First, to establish the stability of CsH2 PO4 under fuel cell conditions, thermal analysis was
carried out on CsH2 PO4 mixed with Pt-catalyst (4:1 wt ratio) under H2 and O2 atmospheres, respectively, Figure 5.16. From these results it is clear that thermal decomposition
of CsH2 PO4 , even when combined with Pt catalyst, is independent of whether the atmosphere is reducing (left panel, flowing H2 ) or oxidizing (right panel, flowing O2 ). In both
cases, weight loss begins at 223 ◦ C, and, as evident from analysis of the evolved gasses, is

147
due entirely to dehydration, that is, no phosphate fragments were detected. It has been proposed 34 that the dehydration reaction proceeds via the formation of amorphous hydrogen
pyrophosphate and polyphosphate intermediates until complete decomposition to CsPO3
occurs according to the following reaction:
CsH2 PO4 (s) → CsH2−2x PO4−x (s) + xH2 O(g)

(0 < x ≤ 1).

Regardless, what is clear from these results is that neither the presence of a Pt catalyst or
reducing/oxidizing atmospheres affect the dehydration behavior of CsH2 PO4 .

Figure 5.16: Thermal characterization of CsH2 PO4 with Pt-black (4:1 wt ratio) powder upon
heating to 400 ◦ C at 5 ◦ C min-1 by simultaneous differential scanning calorimetry (top—DSC),
thermalgravimetry and differential thermalgravimetry (middle—TG/DTG) with off-gasses analyzed
by mass spectrometry (bottom—Mass Spec) under 4 vol% H2 –Ar (left panel—H2 atmosphere) and
15 vol% O2 –Ar (right panel—O2 atmosphere) gasses, each at a flow rate of 60 cm3 min-1 .

Though unaffected by reducing or oxidizing atmospheres, the issue of thermal dehydration of CsH2 PO4 remains a barrier to its application as an electrolyte in fuel cells. However,
it has been recently shown that, in addition to the application of pressure 35 (Chapter 3), the
careful control of water partial pressure 36 can suppress the above dehydration reaction at

148
elevated temperatures. Thus, by retaining sufficient pH2 O in a CsH2 PO4 -based fuel cell, the
above reaction can be suppressed and, in principle, superprotonic behavior of the electrolyte
accessed.

0.1

0.2

0.3

0.4

0.5

300
280
260
240
220
200
0.0

(a)

(b)

Figure 5.17: (a) Arrhenius plot of the measured water partial pressure, pH2 O , as a function of
temperature upon heating CsH2 PO4 at 0.4◦ C min-1 to 300◦ C under closed volume at several different
initial water partial pressures. Here the onset of dehydration, Td , is indicated by a change in slope.
(b) Plot of the onset of dehydration temperatures as a function of water partial pressure. Here the
top-axis corresponds to the equivalent H2 O equilibrium liquid-vapor temperature, T (pH2 O ), at each
pH2 O given on the bottom-axis.
To this end powder samples of CsH2 PO4 at ten different starting water partial pressures
were slowly heated to ∼ 300 ◦ C in a closed volume container. The onset of dehydration (Td ),
indicated by a discontinuous change in the slope of log pH2 O as a function of 1/T , is shown
in Figure 5.17(a). Here no clear Arrhenius behaviour was observed that would indicate a
single dehydration reaction and corresponding Gibbs free energy (∆G◦rxn ) for the dehydration CsH2 PO4 . In Figure 5.17(b), the onset of CsH2 PO4 dehydration temperature (Td ) is
plotted as a function pH2 O . Here the top axis corresponds to the liquid-vapor equilibrium
temperature, T (pH2 O ), at each water partial pressure, pH2 O , indicated by the bottom axis.
These data show that humidification of gases in liquid water at ∼ 70 ◦ C, with an equivalent
pH2 O of ∼ 0.30 atm, is sufficient to suppress CsH2 PO4 dehydration up to a temperature
of ∼ 270 ◦ C. Only slightly greater water partial pressures are required if dehydration is to
be suppressed to temperatures as high as the melting point of CsH2 PO4 , 346 ◦ C 37 . From

149
these results, we can see that the operation of a fuel cell utilitzing a CsH2 PO4 electrolyte
without concern for dehydration is easily achievable by simply humidifying fuel cell gasses
by passing through water maintained at a temperature of 70 ◦ C or greater.
5.2.3.2

H2 /O2 Fuel Cell

To demonstrate the viability of using moderate water partial pressures to provide thermal
stability to a chemically stable solid acid, a membrane electrode assembly (MEA) was
prepared containing a 260 µm thick CsH2 PO4 electrolyte and Pt electrocatalyst at both
electrodes. The cell was operated under H2 /O2 configuration at 235 ◦ C, in which both anode
and cathode gases were humidified (pH2 O = 0.3 atm), where humidification was essential
to prevent dehydration of the CsH2 PO4 electrolyte. Electrical current (100 mA cm-2 ) was
drawn continuously for 35 hrs and polarization curves collected both before and after 35
hrs, Figure 5.18.

(a)

(b)

Figure 5.18: H2 /O2 fuel cell performance with CsH2 PO4 -based electrolyte. (a) Electric potential
(E) and water partial pressure (pH2 O ) as a function of time (t) while drawing 100 mA cm-2 continuous
current for 35 hrs. (b) Electric potential and power density (P ) versus current density (i) before
and after 35 hr measurement. The cell was operated at 235◦ C under humidified (pH2 O = 0.3 atm)
50 sccm flowing H2 and O2 gases at the anode and the cathode, respectively. Electrolyte thickness
was 260 µm and catalyst loading 18 mg cm-2 Pt.
During the continuous measurement, the cell showed remarkable stability; the voltage
very gradually increased from 0.538 to 0.567 V, with an average of 0.561 V. Water generated
at the cathode was in correspondence with that expected from drawing 100 mA cm-2 current.
The polarization curves obtained before and after the long-term evaluation were rather

150
similar to one another, although certainly not identical. The open cell voltage (OCV) was
initially 0.986 and dropped to 0.960 V after 35 hrs measurement. Both values are somewhat
lower than the theoretical open cell voltage (Nernst potential) of 1.15 V for this cell, and
the difference is attributed to small leaks across the fuel cell seals and possibly micro-cracks
within the electrolyte. The peak power and maximum current densities improved slightly
over the 35 hrs stability test, from 61.7 to 65.4 mW cm-2 and from 310 to 345 mA cm-2 ,
respectively. Performance limitations were primarily due to electrolyte resistance (Ohmic
or iRA losses), which can be reduced by up to a factor of ten by simply decreasing the
electrolyte thickness. Nonetheless, these power and current density values are about five
times those reported earlier for CsHSO4 and represent a substantial breakthrough both in
terms of electrolyte stability and fuel cell performance.
5.2.3.3

Direct Methanol Fuel Cell

Direct methanol fuel cells (DMFCs) based on a solid acid electrolyte are anticipated to
provide significant advantages over current state-of-the-art polymeric electrolytes due to
complete impermeability of the solid acids to methanol and elevated operating temperatures.
These features, in turn, translate into higher power densities, higher CO tolerance and,
ultimately, lower precious metal catalyst loadings.
In order to demonstrate the viability of a CsH2 PO4 electrolyte in vapor-fed direct
methanol fuel cells, a second MEA was constructed using PtRu (50:50 mol) as the anode electro-catalyst. Vapor-phase methanol and water (0.92:1 molar ratio), were fed into
the anode compartment using argon as a carrier gas, and humidified oxygen fed into the
cathode. The cell was operated at 243◦ C. Electrical current (80 mA cm-2 ) was drawn continuously for 35 hrs and polarization curves obtained both before and after the measurement,
Figure 5.19. As in the case of the H2 /O2 cell, the methanol cell showed remarkable stability,
with the voltage decreasing slightly from an initial value of 0.441 V to a final value of 0.381
V, and the majority of that decrease occurring in the first few hours. Moreover, the two
polarization curves are again quite similar. Peak power densities were 37.2 and 34.4 mW
cm-2 , respectively, for the two measurements. Open circuit voltages, measured at 0.897
and 0.865 V, respectively, before and after stability examination, cannot be compared to a
theoretical (Nernst) potential because, as is typical for DMFCs, the partial pressures of the
product gas, CO2 , and possible intermediates, e.g. CH4 , were not controlled or monitored.

151

(a)

(b)

Figure 5.19: Direct methanol fuel cell performance with CsH2 PO4 -based electrolyte. (a) Electric
potential (E) as a function of time (t) while drawing 80 mA cm-2 of current for 35 hrs. (b) Electric
potential and power density (P ) versus current density (i) before and after 35 hr measurement.
The cell was operated at 243◦ C. Gasses fed to the anode and cathode were, respectively, CH3 OH–
H2 O–Ar (23:25:52 mol%) flowing at 97 sccm and O2 –H2 O(67:33 mol%) flowing at 75 sccm. After
20 hrs, measurement was paused to replenish methanol supply. Electrolyte thickness was 260 µm
and catalyst loadings were 13 mg cm-2 PtRu (50:50 mol%) at the anode and 15 mg cm-2 Pt at the
cathode.

Nevertheless, the OCVs are greater than what is obtained from polymeric DMFCs (∼0.8
V) 38,39 presumably because of the higher methanol content utilized here and the lower
membrane permeability. The power densities reached in this work are within about a factor
of five of the most advanced DMFCs (100–200 mW cm-2 ). 38,39

5.3

Conclusions

Though initial results of solid acid fuel cells based on CsHSO4 were quite poor, much
was gained from these investigations including a “proof-of-principle” demonstration and
the identification of the thermo-chemical requirements necessary for the application of solid
acid in fuel cells. Thermodynamic characterization and stability studies of solid acid sulfates
and selenates indicated that solid acid phosphates may have the thermo-chemical stability
necessary for fuel cell applications. Further investigation into such compounds showed
that despite the apparently poor thermal stability of CsH2 PO4 in its superprotonic phase,
both H2 /O2 and direct methanol fuel cells based on this material have excellent long-term
performance when stabilized with water partial pressures of ∼ 0.3 atm, depending on the

152
temperature of operation. These “humidity-stabilized” solid acid fuel cells exhibit higher
open circuit voltages than polymer electrolyte fuel cells and thus may ultimately yield better
overall system efficiencies. More importantly, high temperature operation and much less
demanding humidification requirements lead to system simplifications. In conclusion, fuel
cells based on solid acid phosphates operating in an intermediate temperature range ∼ 230300 ◦ C, may offer significant advantages over current state-of-the-art electrolytes, and could
significantly help to advance the current state of fuel cell technology.

153

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156

Appendix
A.1

Solid Acid Synthesis Recipes

A.1.1

Cesium dihydrogen phosphate (CsH2 PO4 )

(1) Weigh out 10.0 g of Cs2 CO3 powder
(2) Measure out 6.01 mL H3 PO4 (phosphoric acid, 85% assay)
(3) Slowly add (2) to (1)
(4) Add DI-H2 O to (3) while stirring, until complete dissolution (∼ 5 mL)
(5) Add 50–100 mL methanol, until massive precipitation
(6) Vacuum filter precipitate
(7) Dry precipitate in an oven at 60 ◦ C for several hours
→ theoretical yield = 14.1 g CsH2 PO4

A.1.2

Cesium hydrogen sulfate (CsHSO4 )

(1) Weigh out 10.0 g of Cs2 SO4 powder
(2) Measure out 3.10 mL H2 SO4 (sulfuric acid, 85% assay)
(3) Add DI-H2 O to (1) until completely dissolved (∼ 5 mL)
(4) Add (2) to (3)
(5) Add 50–100 mL acetone, until massive precipitation
(6) Vacuum filter precipitate

157
(7) Dry precipitate in an oven at 60 ◦ C for several hours
→ theoretical yield = 12.7 g CsHSO4

A.1.3

Potassium hydrogen selenate (KHSeO4 )

(1) Weigh out 1.00 g of K2 SeO4 powder
(2) Weigh out 1.94 g H2 Se4 (60% aqueous solution)
(3) Add (1), (2), and 6 mL DI-H2 O
(4) Repeatedly heat and cool, until massive precipitation
(5) Vacuum filter precipitate
(6) Dry precipitate in an oven at 60 ◦ C for several hours
→ theoretical yield = 1.65 g KHSeO4

A.1.4

Rubidium dihydrogen phosphate (RbH2 PO4 )

(1) Weigh out 1.00 g of Rb2 CO3 powder
(2) Add DI-H2 O to (1) until dissolution
(3) Weigh out 1.00 g H3 PO4 (phosphoric acid, 85% assay)
(4) Slowly add (3) to (2)
(5) Add methanol, until massive precipitation
(6) Vacuum filter precipitate
(7) Dry precipitate in an oven at 60 ◦ C for several hours
→ theoretical yield = 2.53 g RbH2 PO4

158

A.1.5

Thallium dihydrogen phosphate (TlH2 PO4 )

(1) Weigh out 1.00 g of Tl2 CO3 powder
(2) Add 20 mL DI-H2 O to (1)
(3) Weigh out 0.492 g H3 PO4 (phosphoric acid, 85% assay)
(4) Slowly add (3) to (2)
(5) Add 50 mL methanol, until massive precipitation
(6) Vacuum filter precipitate
(7) Dry precipitate in an oven at 60 ◦ C for several hours
→ theoretical yield = 1.28 g TlH2 PO4

A.1.6

Triammonium hydrogen disulfate ((NH4 )3 H(SO4 )2 )

(1) Weigh out 5.0 g of (NH4 )2 SO4 powder
(2) Measure out 3.8 mL H2 SO4 (sulfuric acid, 95% assay)
(3) Add DI-H2 O to (1) until completely dissolved (∼ 10 mL)
(4) Add (2) to (3)
(5) Add 150 mL acetone, until massive precipitation
(6) Vacuum filter precipitate
(7) Dry precipitate in an oven at 60 ◦ C for several hours
→ theoretical yield = 6.23 g (NH4 )3 H(SO4 )2

A.1.7

Tripotassium hydrogen diselenate (K3 H(SeO4 )2 )

(1) Weigh out 1.0 g of KOH powder
(2) Weigh out 12.9 g H2 Se4 (60% aqueous solution)
(3) Add (1) to (2)

159
(4) Add 30 mL methanol, until massive precipitation
(5) Vacuum filter precipitate
(6) Dry precipitate in an oven at 60 ◦ C for several hours
→ theoretical yield = 2.4 g K3 H(SeO4 )2

A.1.8

Trirubidium hydrogen diselenate (Rb3 H(SeO4 )2 )

(1) Weigh out 15.9 g of Rb2 CO3 powder
(2) Weigh out 100 g H2 Se4 (60% aqueous solution)
(3) Add (1) to (2)
(4) Add 200 mL methanol, until massive precipitation
(5) Vacuum filter precipitate
(6) Dry precipitate in an oven at 60 ◦ C for several hours
→ theoretical yield = 10.6 g Rb3 H(SeO4 )2

160

A.2

Thermal Analysis Results

A.2.1

RbH2 PO4

Figure A.1: Differential scanning calorimetry (DSC) data taken on RbH2 PO4 powders in sealedcontainers (constant volume) at heating rates of 1, 5, and 10 ◦ C min-1 upon heating and cooling
from 25 to 350 ◦ C. Both the melting (Tm ) and the superprotonic transition (TSP ) temperatures are
indicated.

161

A.2.2

TlH2 PO4

Figure A.2: Simultaneous differential scanning calorimetry (DSC), thermal gravimetry (TG), and
corresponding differential thermal gravimetry (DTG) of TlH2 PO4 powder upon heating to 500 ◦ C
at 10 ◦ C min-1 under flowing 40 cm3 min-1 dry N2 gas. H2 O in the evolved gas is identified by mass
spectroscopy (Mass Spec), m18.00.

162

A.2.3

NaH2 PO4

Figure A.3: Simultaneous differential scanning calorimetry (DSC), thermal gravimetry (TG), and
corresponding differential thermal gravimetry (DTG) of NaH2 PO4 powder upon heating to 500 ◦ C
at 10 ◦ C min-1 under flowing 40 cm3 min-1 dry N2 gas. H2 O in the evolved gas is identified by mass
spectroscopy (Mass Spec), m18.00.

163

A.2.4

LiH2 PO4

Figure A.4: Simultaneous differential scanning calorimetry (DSC), thermal gravimetry (TG), and
corresponding differential thermal gravimetry (DTG) of LiH2 PO4 powder upon heating to 500 ◦ C
at 10 ◦ C min-1 under flowing 40 cm3 min-1 dry N2 gas. H2 O in the evolved gas is identified by mass
spectroscopy (Mass Spec), m18.00.

164

A.3

High Pressure Conductivity Results

A.3.1

NaH2 PO4

Figure A.5: Arrhenius plot of conductivity results from AC impedance measurements performed
on NaH2 PO4 powder upon heating and cooling (as indicated by direction of arrows) from 25 to 400
C under 1.0 GPa of pressure.

A.3.2

LiH2 PO4

Figure A.6: Arrhenius plot of conductivity results from AC impedance measurements performed
on LiH2 PO4 powder upon heating and cooling (as indicated by direction of arrows) from 25 to 400
C under 1.0 GPa of pressure.

165

A.4

MHn XO4 -type Solid Acid Phase Behavior

A.4.1

MH2 XO4 Phase Behavior

Table A.1: Summary of phase transition temperatures (Ttr ), entropies (∆Str ), and stuctures in
MH2 XO4 -type solid acids, where M = Li, Na, K, Rb, and Cs, and X = P, As. † Represents data
obtained in this work.
Compound
Phase

Ttr

∆Str
J/mol·K

Crystal
System

Space
Group

Lattice Parameters
c /Å α

CsH2 PO4
IV ferroelectric 1
III paraelectric
İI
superprotonic 6
liq melt

154
380
510
619

1.05 2
1.18 5
22.2†
25.2†

monoclinic 3
monoclinic 4

P 21
P 21 /m

7.870
7.912

6.320 4.890
6.383 4.880

90.0 108.3 90.0
90.0 107.7 90.0

230.9
234.8

cubic 7

P m3m

4.961

4.961 4.961

90.0 90.0 90.0

122.1

RbH2 PO4
IV ferroelectric 8
III paraelectric
II
superprotonic†
liq melt

77
352
553
563

2.86 9
1.5 5
21.3†
22.7†

orthorhombic 10
tetragonal 10
monoclinic 11
cubic†

F dd2
I42d
P 21 /a

10.800 10.672 7.242
7.607 7.607 7.299
9.606 6.236 7.738

90.0 90.0 90.0
90.0 90.0 90.0
90.0 109.1 90.0

834.7
422.4
438.1

KH2 PO4
III ferroelectric 1
II paraelectric
II’
liq melt

122
2.89
453 14
506 14
532 14

orthorhombic 12
tetragonal 13
triclinic 15
monoclinic 15

F dd2
I42d
P1
P 21 /c

10.530 10.440 6.900
7.430 7.430 6.970
7.438 7.393 7.200
6.141 4.499 8.966

90.0
90.0
88.5
90.0

90.0
90.0
87.8
90.0

758.5
384.4
394.9
394.2

NaH2 PO4

monoclinic 16

P 21 /c

6.808 13.491 7.331

90.0 92.9 90.0

672.4

LiH2 PO4

orthorhombic 17

P na21

6.253

7.656 6.881

90.0 90.0 90.0

329.4

CsH2 AsO4
IV ferroelectric 18
III paraelectric
II
superprotonic 22
liq melt

139
3.72 19
396
1.31 21
438
17.9 21
569 21

orthorhombic 20
tetragonal 20

F dd2
I42d

11.516 11.103 7.870
7.985 7.985 7.893

90.0 90.0 90.0
90.0 90.0 90.0

1006.3 8
502.6 4

RbH2 AsO4
III ferroelectric 23
II paraelectric

110
4.17 24
423 26

tetragonal 25

I42d

7.720

7.720 7.420

90.0 90.0 90.0

454.6

KH2 AsO4
III ferroelectric
II paraelectric

96
4.21 27
403 29

tetragonal 28

I42d

7.623

7.623 7.155

90.0 90.0 90.0

415.7

P na21

6.416

7.727 7.298

90.0 90.0 90.0

361.8

90.0
90.0
86.9
91.6

γ /◦ V /Å3 Z

cubic 22

NaH2 AsO4
no information available
LiH2 AsO4

orthorhombic 30

166

A.4.2

MHXO4 Phase Behavior

Table A.2: Summary of phase transition temperatures (Ttr ), entropies (∆Str ), and stuctures in
MHXO4 -type solid acids, where M = Li, Na, K, Rb, and Cs, and X = S, Se.
obtained in this work.

Represents data

Compound
Phase

Ttr

∆Str
J/mol·K

Crystal
System

Space
Group

Lattice Parameters
c /Å α

CsHSO4
III
II
superprotonic 33
liq melt

330
415
484

0.10 5
14.94 34
27.27 5

monoclinic 31
monoclinic 32
tetragonal 35

P 21 /m
P 21 /c
I41 /amd

7.304
7.781
5.718

5.810 5.491
8.147 7.722
5.718 14.232

90.0 101.5 90.0
90.0 110.8 90.0
90.0 90.0 90.0

228.3
457.7
465.3

RbHSO4
IV ferroelectric 36
III paraelectric
II
liq melt

263
439
0.50 5
455 39
481 39

monoclinic 37
monoclinic 38

Pc
P 21 /c

14.235 4.582 14.679
14.360 4.636 14.814

90.0 121.0 90.0
90.0 120.9 90.0

820.9
844.5

KHSO4
II
liq melt

451
488

4.68 41
34.02 41

orthorhombic 40

P bca

8.429

9.807 18.976

90.0 90.0

1568.6 16

NaHSO4
I’

triclinic 42
monoclinic 43

P1
P 21 /n

7.005
8.759

7.125
7.500

6.712
5.147

95.9 87.6 104.5
90.0 99.5 90.0

322.5
333.5

LiHSO4

monoclinic 44

P 21 /c

5.234

7.322

8.363

90 90.02

320.5

CsHSeO4
II
II’
superprotonic 47

355
400

0.61 46
16.1 48

monoclinic 45

P 21 /c

7.970

8.446

7.784

90.0 111.3 90.0

488.3

tetragonal 45

I41 /amd

5.880

5.880 14.415

90.0 90.0

90.0

498.5

RbHSeO4
III ferroelectric 49
II paraelectric
superprotonic†
liq melt

386
446
474

0.84 5
19.2†
12.8†

triclinic 50
monoclinic 50

P1
I1

10.622 4.622
19.443 4.629

89.4 110.8 102.1
90.0 90.0 90.8

339.0
687.1

KHSeO4

orthorhombic 51

P bca

8.690 10.053 19.470

90.0 90.0

1700.9 16

NaHSeO4

monoclinic 52

P 21 /n

5.295

90.0 101.3 90.0

LiHSeO4
no information available

7.873

7.575
7.635

8.911

γ /◦ V /Å3 Z

90.0

364.1

167

A.5

Estimated Thermodynamic Values

A.5.1

CsHSO4

A.5.1.1

S298.15
and Cp

The entropy of CsHSO4 at 298.15 K (S298.15
) was estimated from the reported values for

KHSO4 and NaHSO4 entropy of formation ∆Sf◦ (298.15 K),
M(cr) + 12 H2 (g) + S(cr) + 2O2 (g) → MHXO4 (cr)

M = Na, K

of -434 and -445 J mol-1 K-1 , respectively 53 . Then the estimated ∆Sf◦ (298.15 K) of CsHSO4 ,
by analogy to the previous compounds, is -439 J mol-1 K-1 (average value) and S298.15
= 189

J mol-1 K-1 .
For condensed phase reactions, such as those calculated in this work, it is often acceptable to neglect the heat capacity altogether, by employing the Neumann and Kopp rule 54 .
However, for completeness we have estimated the heat capacity of CsHSO4 . Therefore, in a
similar fashion as with the entropy, the reported values for the heat capacity of formation
of KHSO4 (∆f Cp ),
M(cr) + 12 H2 (g) + S(cr) + 2O2 (g) → MHXO4 (cr),

M=K

of 13.567 J mol-1 K-1 53 was used to estimate the heat capacity of CsHSO4 , Cp = 141.5 J
mol-1 K-1 .

168

A.5.2
A.5.2.1

Cs2 S2 O7
∆Hf◦ , S298.15
, and Cp

Since there are virtually no reported thermodynamic data for solid Cs2 S2 O7 , the enthalpy
of the formation of Cs2 S2 O7 (s) (∆Hf◦ = -1990 kJ mol-1 ) was estimated from the reported
formation enthalpy of aqueous Cs2 S2 O7 (aq) and from analogous reported values of other
aqueous and solid M2 S2 O7 (M = Na, K) compounds, given in Table A.3. Using reported
values for the Gibbs energy of formation for these analogous compounds (also listed in
Table A.3), the entropy of formation (∆Sf◦ (298.15 K) = 536 J mol-1 K-1 ) was estimated for
Cs2 S2 O7 (s), and finally the entropy S298.15
= 265 J mol-1 K-1 .

Table A.3: Thermodynamic data for M2 S2 O7 compounds (M = Na, K, Cs) used to estimate the
∆Hf◦ and S298.15
of Cs2 S2 O7 , from reference 55 .

∆G◦f

∆Hf◦

Cs2 S2 O7 (aq)
K2 S2 O7 (aq)
Na2 S2 O7 (aq)

-1917.9
-1914.6
-1888.2

K2 S2 O7 (s)
Na2 S2 O7 (s)

-1791.5
-1722.0

-1986.6
-1925.1

/kJ mol-1

169

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