The thermodynamic characterization of spontaneous electrochemical reactions

Joseph W Jerome*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 a trapping 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.

Original languageEnglish (US)
Pages (from-to)754-762
Number of pages9
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number5-7
StatePublished - Nov 30 2005


  • Electrochemical cells
  • Electrode control variables
  • Electroneutrality
  • Gibbs free energy
  • Partial convexity
  • Spontaneous association

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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