## Abstract

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 language | English (US) |
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Pages (from-to) | 754-762 |

Number of pages | 9 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 63 |

Issue number | 5-7 |

DOIs | |

State | Published - Nov 30 2005 |

## Keywords

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

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics