Thermal effects in a modified law of mass action

On the Nonequilibrium Thermodynamics of Large Departures from Butler−Volmer Behavior

“…In the limiting case when ν 2 , k B T/κ, the law of mass action and the Nernst equation can be recovered from eq 7. 2,3 The current in γ-space is given by the velocity averaged with the density in γ-space. Hence, the velocity can be taken to be proportional to the current Inserting eq 8 into eq 7 yields…”

“…MNET has been successfully used to describe a wide variety of ideal activation phenomena including nucleation, 11 aggregation and agglomeration, 12,13 evaporation and condensation, 14 and charge transfer through electrode surfaces. 2,3 The local equilibrium postulate of non-equilibrium thermodynamics is applicable to systems that, although far from equilibrium, may be approximated as a collection of equilibrium subsystems. 7 When changes in the spatial density occur simultaneously with changes in the velocities of the constituent elements, both the spatial and the velocity coordinates must be independently partitioned by the local equilibrium hypothesis.…”

“…1 Equation 12 presented here does not suffer from the restrictions bounding the applicability of the Butler-Volmer equation, but instead reduces to it when low electric currents are assumed such that j 2 , k B T/k 2 . 2,3 Figure 1 shows the performance of eq 12 against currentvoltage data from a polymer electrolyte fuel cell cathode with different oxygen partial pressures. 4,5 While the physical meaning of the fitting parameters remains to be investigated, the theory presented here offers better agreement with the data than kinetic models previously used for its analysis.…”

“…Chemical reactions, adsorption, nucleation, surface growth, elastoplasticity, and crossing of energy gaps in semiconductors are, to name a few, examples of activated processes. These processes obey a rate law often expressed as two Arrhenius terms accounting for the forward and the reverse rates, as is the case of the Butler−Volmer equation of electrochemistry. − The Butler−Volmer equation describes the rate of an electrochemical reaction as a function of the departure from the equilibrium voltage of the electrochemical cell. This equation, however, fails to reproduce the behavior of the system at high reaction rates, where nonideal effects in transport become significant (see, e.g., refs −6).…”

“…However, using mesoscopic nonequilibrium thermodynamics (MNET), − a description of activated dynamics is accessible while preserving the postulates of the classical theory. MNET has been successfully used to describe a wide variety of ideal activation phenomena including nucleation, aggregation and agglomeration, , evaporation and condensation, and charge transfer through electrode surfaces. , …”