We couple the Leaky Membrane Model, which describes the diffusion and
electromigration of ions in a homogenized porous medium of fixed background
charge, with Butler-Volmer reaction kinetics for flat electrodes separated by
such a medium in a simple mathematical theory of voltammetry. The model is
illustrated for the prototypical case of copper electro-deposition/dissolution
in aqueous charged porous media. We first consider the steady state with three
different experimentally relevant boundary conditions and derive analytical or
semi-analytical expressions for concentration profiles, electric potential
profiles, current-voltage relations and overlimiting conductances. Next, we
perform nonlinear least squares fitting on experimental data, consider the
transient response for linear sweep voltammetry and demonstrate good agreement
of the model predictions with experimental data. The experimental datasets are
for copper electrodeposition from copper(II) sulfate solutions in a variety of
nanoporous media, such as anodic aluminum oxide, cellulose nitrate and
polyethylene battery separators, whose internal surfaces are functionalized
with positively and negatively charged polyelectrolyte polymers.Comment: 39 pages, 12 figures, 5 tables; clarified where other parameters are
taken from and fixed typo
