4.6 Calculated Transition Entropies for the CsHSO 4 -CsH 2 PO 4 System of
4.6.8 Application of the adjusted ice rules to other superprotonic transitions 163
CsHXO4) of CsH2PO4 is almost twice that of CsHSO4. The intermediate compounds, however, fall far from the line connecting the two end members and it can only be said very generally that increasing phosphate/hydrogen content correlates to higher molar hydrogen bond energies.
It is then even more pleasing that Pauling’s ice rules, adjusted to properly
describe the superprotonic phases of these cesium sulfate-phosphate compounds, produce transition entropies that compare very well with the measured values. Since these rules combine the positional disorder of the proton system with the rotational disorder of the tetrahedra, it should be applicable to any transition that involves a disordering of a hydrogen-bonded network via disorder of the hydrogen carriers. This has already been shown to be true in compounds where the hydrogen-bonded network is composed of water molecules and would now appear to be true for systems containing hydrogen- bonded tetrahedra.
4.6.8 Application of the adjusted ice rules to other superprotonic
hydrogen bonds, similar to CsH2PO4, but here all bonds are disordered, so that CsH2AsO4 will have an entropy of 2*R*ln(2) associated with its room temperature structure. Using the calculated configurational entropy of the superprotonic tetragonal and cubic phases (Eqs. (4-9) and (4-11), respectively), the transition entropies can then be calculated. The resulting entropies match up very well with the measured values, Table 4.7. Having successfully applied these ice rules to the CsHSO4-CsH2PO4 system and to the end members CsHSeO4 and CsH2AsO4, one would expect that they should apply equally well to any mixed Cs-S-Se-P-As compounds. Some of these mixed compounds have already been synthesized, such as Cs4(SeO4)(HSeO4)2(H3PO4),
Cs3(HSeO4)2(H2PO4), and Cs5(HSeO4)3(H2PO4)2, (NH4)2(HSO4)(H2AsO4), however their properties have not been reported162,163.
Table 4.7 Application of ice rules to other solid acid supeprotonic phase transitions Compound Tc-mean
(K)
Scalc – RT (J/mol*K)
Scalc – HT
(J/mol*K) ∆Scalc
(J/mol*K)
∆Sexp=∆Hexp/Tc (J/mol*K)
ref
CsHSeO4 140 0 14.90 14.90 16.0(5) 157
164
CsH2AsO4 186 11.53 27.30 15.77 17.4(6) 158 K3H(SeO4)2 121 5.76 13.38 7.62 7.8(3) 165
101
CsHPO3H 140 0 30.67 30.67 30.1(11) 166
RbHSeO4 182 2.88 ? ? 23.9(4) 167
NH4HSeO4 157 2.88 + 9? ? ? 15.1(5) 167
Until now, only compounds with Cs cations have been examined, but this theory places no limitation on the type or number of cations present. The prevalence for Cs cations is directly linked with the cation size effect discussed in Chapter 3, in that superprotonic transitions are more often found in compounds with large cations. These
ice rules should then also be applicable to the superprotonic transitions of MHXO4
compounds (where M = Li, Na, K, NH4, Rb, Tl, Cs; X = S, Se, P, As). These compounds could have varying M:XO4 ratios, mixed cations, or both, such as (NH4)4H2(SeO4)3, Cs0.9Rb0.1HSO4, and Rb4LiH3(SeO4)4, respectively, all of which have reported superprotonic transitions (without, unfortunately, the transition enthalpies or
entropies)168, 97,169. And, of course, the intersection of these two sets, compounds with mixed anions and mixed cations, will be equally susceptible to having these ice rules applied to any uncovered superprotonic phase transitions.
Also, the disordered network of hydrogen bonds need not be three-dimensional, as with all the previous examples, for these rules to apply. The class of compounds M3H(XO4)2 (M= Na, K, NH4, Rb, Cs: X = S, Se) exhibits superprotonic phase transitions where the proton transport occurs within planes170. The compounds are pseudo-trigonal in their room temperature phases and most of them transform into a trigonal phase at
elevated temperatures100. For the compounds with such transitions, these ice rules should reproduce the measured transition enthalpies quite well, as can be seen for the
K3H(SeO4)2 compound in Table 4.6.
Finally, these ice rules also appear valid for compounds with alternative anion chemistries, such as CsHPO3H, where one of the tetrahedral oxygens has been replaced by a hydrogen atom. This compound exhibits a superprotonic phases transition at 137°C, transforming into the same cubic CsCl like structure as the mixed cesium sulfate
phosphates166. Adjusting the ice like rules developed here for the dissimilarity of the tetrahedra’s coordinating ions will cause two changes. First, no hydrogen bonds can be formed to the tetrahedral hydrogens. The tetrahedral hydrogen then effectively acts as an
OH group and the probablility of a direction being open will be 4/6 rather than the normal 5/6 for a hydrogen to tetrahedron ratio of 1:1. Second, there will be three distinguishable configurations of the two possible acceptor oxygen atoms and the tetrahedral hydrogen for every configuration of the proton/donor oxygen system. This will cause an extra factor of three. The number of configurations for this compound in its cubic phase is then
( ) ( ) 1 * 4 * ( 3 ) 48
6 *
* 4 1 1
6 =
=
Ω
(4-32)which results in a calculated enthalpy very close to the measure value, Table 4.6.
This exposition of applications serves to prove the flexibility of these ice rules; a flexibility that allows for a certain amount of prediction concerning poorly characterized compounds or entirely new systems. For example, the high temperature structures of RbHSeO4 and NH4HSeO4 are not well determined and so an evaluation of their entropy is not possible87,91. However, the measured transition entropies of 24 and 15 J/mol*K for RbHSeO4 and NH4HSeO4, respectively, and these ice rules indicate that the high temperature phase cannot be the tetragonal phase of CsHSO4167. These compounds are isostructural to each other in their room temperature phase with one disordered hydrogen bond per two tetrahedra (S = 1/2*Rln(2) = 2.88 J/mol*K)171. The ammonium compound also has orientational disorder associated with the SeO4 and NH4 ions, which most probably accounts for the difference in transition entropies between the two
compounds102. There is then a considerable amount of entropy incorporated into the room temperatures of these compounds and yet the transition entropies are both above the calculated 14.9 J/mol*K maximal transition entropy for the tetragonal phase of CsHSO4.
It is also possible that entirely new systems of compounds with superprotonic transitions will be discovered, systems with perhaps mixed M+2 and M+1cations or including various other anion groups (i.e., SiO4, ClO4, PO3F, SiF6, COF3, etc.). It would be very nice to estimate the probability of an order-disorder transition in such new compounds so as to narrow the focus of experiments to those compounds most likely to exhibit superprotonic conduction. After all, the entire purpose of this work is to better understand what causes superprotonic phases to exist and to then apply that to making materials more suited for application.
With this purpose in mind, it is suggested that a hypothetical transition
temperature could be derived from an observed correlation between the transition ∆V and
∆H, and liberal use of these ice rules in estimating a transition entropy. For the CsHSO4- CsH2PO4 compounds, the correlation between transition enthalpy and volume is quite clear, Figure 4.22. Since the variation of the data is so small, it seems possible that if one estimated a transition volume from the predicted room and high temperature structures, it would be possible to derive a fairly accurate transition enthalpy. Also, using the predicted structures and these ice-like rules, a likely entropy could also be obtained. Taking the ratio of these two values would then give an approximate transition temperature,
hopefully telling the investigator whether a compound was worth investigating or not. In other systems, a similar relationship could be calculated from existing data, or perhaps extrapolated from structurally and chemically related compounds. This process could save a vast amount of experimental time as synthesis of even these water soluble compounds was not trivial.
0 5 10 15 20 25 4
6 8 10 12 14 16
CsH2PO4
Cs3(HSO4)2.25(H2PO4)0.75
R
2= 0.96
Y = 5.4(7) + 0.39(5)*X
∆
H (kJ/mol CsHXO
4)
∆
V (m
3/mol CsHXO
4x 10
-7)
Figure 4.22 Transition volume versus enthalpy. The apparent correlation between the two values suggests the possibility of estimating a transition enthalpy from a predicted volume change.
It would be interesting to add the transition enthalpies and volumes of the other known superprotonic conductors to Figure 4.22. Alas, even though the room and high temperature structures have been measured for most of the known superprotonic
compounds, accurate thermal expansion coefficients are almost universally lacking. Since the difference between the temperature at which the room and high temperature structures are measured is usually in the hundreds of degrees, the expansion (or contraction) of the phases with temperature would greatly effect the transition volumes. If and when more accurate transition volumes become available, it will be very interesting to see if the
linear trend seen in Figure 4.22 holds for all the known superprotonic conductors, or if different structural and chemical families of compounds require their own categorization.
Chapter 5. Superprotonic Phase Transition of CsHSO
4: A Molecular Dynamics Simulation
Study with New MSXX Force Field
5.1 Introduction
This molecular dynamics (MD) study of the superprotonic phase transition of CsHSO4 was undertaken with two aims: to determine whether the transition could be simulated without allowing proton migration and to develop a procedure for creating MD force fields (FF) applicable to other solid acids. The first objective was motivated by the desire to know whether proton hopping or tetrahedra reorientations are the essential ingredient in stimulating a transition from the ordered room temperature structure to the highly disordered superprotonic phase. The latter goal comes from the desire to greatly speed up the search for new superprotonic compounds with properties ideal for
application. It was hoped that a simple process could be developed to predict
superprotonic phase transitions of, as yet unknown, compounds without first synthesizing the material, which can take untold time in the laboratory.
Success in simulating the transition of CsHSO4 gave sufficient confidence in the new FF that the effects of changing various FF parameters on the transition were
investigated. The adjusted parameters included the charge distribution of the oxygen atoms, hydrogen bond strength and torsional barrier height. In each case, a single parameter was changed and the simulations re-run with all other FF and simulation
variables held constant. Thus, the superprotonic phase transition of CsHSO4 was probed in a manner not possible by experimental methods.
The results of this chapter will then compliment those of the experimental chapters (3 and 4) in that all three chapters aim to better our understanding of which parameters favor superprotonic transitions. In particular, this chapter gives atomistic information (you can even watch them if you like!) not available from physical measurements. Also, the success of this chapter’s FF in simulating the superprotonic transition of CsHSO4 suggests that the same procedure could be employed to generate FF’s for other cations and anions. Combining these FF could then give us a powerful tool for predicting novel superprotonic conducting solid acids.