The Thermodynamic Characterization of Spontaneous Electrochemical Reactions

By: Joseph W. Jerome

We consider whether the association of charged species of opposite parity in a chemical cell constitutes a spontaneous reaction. The initial distributions of the species are modeled as a steady-state phenomenon, characterized by a drift-diffusion system and two coupled constraints: (1) the electroneutrality of net system charge; and, (2) a coupled thermodynamic inequality constraint, reflecting the net decrease of the Gibbs' free energy in the closed system required for any spontaneous chemical reaction leading to uniform association of the species. A useful analytical technique of partial convexity allows the reformulation of thermodynamic compatibility. A control theory interpretation of the Dirichlet boundary conditions allows the selection of an invariant region for the range of the solution components, which ensures that the reaction is spontaneous. A specific application is the production of hydrogen in an electrochemical cell. This is contained in a larger modeling context: reduction processes in electrochemistry. The final section describes extensions of the modeling in which an open mathematical problem and a pointer to the nonisothermal case are identified. This paper has been presented at WCNA-4, held in Orlando in July, 2004, and has appeared: Nonlinear Analysis: vol. 63 (2005), pp. 754--762. The posted article includes an additional final section 3.5, which removes a minor gap in the proof of the main theorem, Theorem 2.1, of the published article.