Nonlinear coupled equations for electrochemical cells as developed by the general equation for nonequilibrium reversible-irreversible coupling

Abstract

We show how the Butler-Volmer and Nernst equations, as well as Peltier effects, are contained in the general equation for nonequilibrium reversible and irreversible coupling, GENERIC, with a unique definition of the overpotential. Linear flux-force relations are used to describe the transport in the homogeneous parts of the electrochemical system. For the electrode interface, we choose nonlinear flux-force relationships. We give the general thermodynamic basis for an example cell with oxygen electrodes and electrolyte from the solid oxide fuel cell. In the example cell, there are two activated chemical steps coupled also to thermal driving forces at the surface. The equilibrium exchange current density obtains contributions from both rate-limiting steps. The measured overpotential is identified at constant temperature and stationary states, in terms of the difference in electrochemical potential of products and reactants. Away from these conditions, new terms appear. The accompanying energy flux out of the surface, as well as the heat generation at the surface are formulated, adding to the general thermodynamic basis.

Fluctuating hydrodynamics of multi-species reactive mixtures

“…Here we assume that there is no cross-coupling between different reactions and thus associate an independent stochastic production rate with each reaction. Coupling between distinct reactions has been considered within a nonequilibrium thermodynamic framework only in some very specific cases [76,77] and a general formulation requires more detailed knowledge about the coupling mechanism than is available in practice.…”

A new perspective on the electron transfer: recovering the Butler–Volmer equation in non-equilibrium thermodynamics

“…Such a formulation in terms of the chemical potentials can also been found in Butler-Volmer equations which have been proposed recently for specific applications like Li-ion batteries or fuel cells. 13,18,19 We want to emphasize the importance of the chemical potentials for a consistent modeling: in the formulation of the constitutive eqn ( 14) and (15), we followed the approach of non-equilibrium thermodynamics that imposes compatibility constraints. This has the advantage, that the modeling is considerably simplified, because once the free energy density is specified, all constitutive equations are determined uniquely and in a compatible way, up to the choice of phenomenological coefficients.…”

“…16 Later on an attempt was taken to give a justification of the Butler-Volmer equation within a mesoscopic thermodynamic theory. 17 Recently a Butler-Volmer equation for oxidation reaction in fuel cells was derived within the GENERIC framework, 18 and in the context of phase separating electrode materials, a Butler-Volmer equation in non-equilibrium thermodynamics was derived. 19 In this paper we derive a general Butler-Volmer of the form (2) which is not restricted to a specific application scenario.…”

Mechanical approach to chemical transport

“…The importance of building simple models to connect thermodynamics with chemical transport has been clear for a long time and thus has been investigated extensively (3,(5)(6)(7). One way to make the connection (8)(9)(10)(11)(12) is to start with the Lagrangian L of a mechanical system with many particles "j" of a chemical component "i" at coordinate q ðiÞ j , where L equals the difference of the kinetic energy and potential energy of the whole system (13).…”