Electrolyte Butler-Volmer treatment

Activation polarization arises from kinetics hindrances of the charge-transfer reaction taking place at the electrode/electrolyte interface. This type of kinetics is best understood using the absolute reaction rate theory or the transition state theory. In these treatments, the path followed by the reaction proceeds by a route involving an activated complex, where the rate-limiting step is the dissociation of the activated complex. The rate, current flow, i (/ = HA and lo = lolA, where A is the electrode surface area), of a charge-transfer-controlled battery reaction can be given by the Butler—Volmer equation as... 

But before dying to understand the behavior of electrochemical systems, or cells, it was considered useful to disassemble, or analyze, them conceptually into two isolated electrode/electrolyte interfaces and then to study single interfaces. This has been done. The whole treatment so far has concerned itself with a single electrode/ solution interface98 and with the current-potential laws that govern its behavior. The Butler-Volmer equation is the key equation for a single interface. The behavior of an electrochemical system, or cell, must be conceptually synthesized from the behavior of the individual interfaces that combine to form a cell... 

Contrary to outer sphere electron transfer reactions, the validity of the Butler-Volmer law for ion transfer reactions is doubtful. Conway and coworkers [225] have collected data for a number of proton and ion transfer reactions and find a pronounced dependence of the transfer coefficient on temperature in all cases. These findings were supported by experiments conducted in liquid and frozen aqueous electrolytes over a large temperature range [226, 227]. On the other hand, Tsionskii et al. [228] have claimed that any apparent dependence of the transfer coefficient on temperature is caused by double layer effects, a statement which is difficult to validate because double layer corrections, in particular their temperature dependence, depend on an exact knowledge of the distribution of the electrostatic potential at the interface, which is not available experimentally. Here, computer simulations may be helpful in the future. Theoretical treatments of ion transfer reactions are few they are generally based on variants of electron transfer theory, which is surprising in view of the different nature of the elementary act [229]. 

Integration of KMC simulations with larger-scale models such as finite element continuum approaches can enhance the impact of a KMC simulation. In many cases, certain components of an electrochemical device can be effectively approximated by a bulk continuum treatment (e.g., ionic diffusion through the bulk of an electrolyte) while other components of a device that involve interfacial transport require discrete treatments like either Butler-Volmer empiricism or an atomistic treatment to capture important details related to the distribution of charge in the double layer. 

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