Entropy Evaluation of the Superprotonic Phase of CsHSO_4: Pauling’s Ice Rules Adjusted for Systems Containing Disordered Hydrogen-Bonded Tetrahedra

Abstract

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 Jirak² 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.