Entropy evaluation of the superprotonic phase of CsHSO4:: Pauling's ice rules adjusted for systems containing disordered hydrogen-bonded tetrahedra

The entropy of the superprotonic transition (phase II -> phase I) of CsHSO4 is evaluated both experimentally and theoretically. Calorimetric measurements reveal a value of 14.75(22) J mol(-1) K-1. Under the assumption that the entropy is entirely configurational, arising from both sulfate group orientational disorder and disorder in the hydrogen-bond network, we evaluated several structural models of CsHSO4 for their consistency with the measured entropy. For a structure in which hydrogen-bond disorder is independent of sulfate-group orientational disorder, simple methods of calculating the number of structural configurations are inadequate. Thus, the configurational entropy of the superprotonic, disordered phase of CsHSO4 is evaluated using an approach similar to that employed by Pauling to describe the residual entropy of ice at 0 K. Analogous to ice and the so-called ice rules, superprotonic CsHSO4 is assumed to obey a set of structural rules. Key among these are that there is only one proton per sulfate tetrahedron and only one proton per hydrogen bond. Defects are argued to make a negligible contribution to the transition entropy. The transition entropy obtained from this model, 14.9 J mol(-1) K-1, is in excellent agreement with the measured value. Such a match between theoretical and experimental values suggests that of all published Phase I structures, the structure proposed by Jirak(2) more correctly describes the arrangements of the sulfate tetrahedra and protons attached to them. The assumption of a low defect concentration implies that the jump in proton conductivity at the transition is due to an increase in the mobility of charge carriers rather than their concentration.