Entropy of Metal/Solution Interfaces: Thermodynamic Framework, Theoretical Models, and Roles of Interfacial Water

Entropy is a basic thermodynamic property of the electrical double layer (EDL) at metal/solution interfaces, yet, its definition, measurement, and theoretical treatment are dispersed in the literature, and, in some cases, ambiguous. In this paper, we revisit the thermodynamic theory of EDL, from which two variants of entropy, excess entropy and formation entropy, are obtained and compared. In terms of the formation entropy, two calculation routes are validated in the context of a primitive EDL model, namely, the Gouy-Chapman (GC) model. After clarifying the concepts and calculation routes, we investigate interfacial water effects on the EDL entropy, using a refined Gouy-Chapman-Stern (GCS) model accounting for chemical potential difference between oxygen- and hydrogen-down water molecules, denoted δµ. The model-derived differential capacitance and entropy are compared with experimental data for the EDL at Au(111) in an aqueous electrolyte solution. The model reveals that the charge of maximum entropy (CME) is negative when water molecules have higher tendency to take oxygen-down configuration at the uncharged surface. Moreover, the formation entropy profile becomes asymmetric around the CME, when δµ is potential-dependent. However, the model fails to simultaneously reproduce capacitance and entropy measurements on the same system taken from two separate studies, indicating deficiencies of the model or experimental errors. Nevertheless, this work stresses the importance of measuring both capacitance and entropy of EDLs at the same time.