The Thermodynamic Characterization of Spontaneous Electrochemical
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
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.