Reaction rates and phase diagrams in ElectrochemicalKinetics.jl

I will introduce ElectrochemicalKinetics.jl, a package that implements a variety of models for electrochemical reaction rates (such as Butler-Volmer or Marcus-Hush-Chidsey). It can also fit model parameters and construct nonequilibrium phase diagrams. While the package has already been of great use in electrochemical research applications, I will focus more on the design choices as well as the challenges that have come up in implementing automatic differentiation support.

In electrochemical reaction modeling, there are a variety of mathematical models (such as Butler-Volmer, Marcus, or Marcus-Hush-Chidsey kinetics) used to describe the relationship between the overpotential and the reaction rate (or electric current). Another important entity is the inverse of this function, i.e. given a current, what overpotential would be needed to drive it? Most of the models used do not have analytical inverses, so inverting them requires an optimization problem to be solved.

In ElectrochemicalKinetics.jl, I created a generic interface for computing these reaction rates and overpotentials, as well as using these quantities for other analyses such as fitting model parameters or constructing nonequilibrium phase diagrams, important for predicting, for example, behavior of a battery under fast charge or discharge conditions. Given a KineticModel object m we can always compute the rate constant at a given overpotential with the same syntax, no matter if m isa ButlerVolmer or m isa Marcus or any other implemented model type. This allows for easy comparison between these models, including when analyzing real data.

We can also construct nonequilibrium phase diagrams, to, for example, understand and predict lithium intercalation behavior in a battery at various charge or discharge rates. Building these phase diagrams requires calling the inverse function mentioned above and using it within another optimization (to satisfy the thermodynamic common-tangent condition), making automatic differentiation challenging. I will also discuss some of these challenges and the solutions I have found for them so far.