We develop a phenomenological
theory of electric double layer (EDL)
dynamics at complex bimodal electrode morphology, viz. arbitrary shaped
mesostructures with embedded heterogeneous micropores. The dynamics
of the diffuse layer at mesoscale is described through the Debye-Falkenhagen
(DF) model of EDL relaxation and dynamics at micropores is described
by employing the de Levie’s transmission line (TL) model. The
influence of mesostructure on the diffuse layer dynamics is incorporated
elegantly, employing a Green’s function (obtained through multiple
scattering formalism) expressing the local admittance of arbitrary
shaped mesostructure in surface mean and Gaussian curvatures of electrode.
The model also incorporates the finiteness of the molecular Stern
layer through correction in surface curvatures and generalizes the
EDL response for arbitrary shaped mesostructured electrodes. The contribution
of morphological parameters, namely, micropore depth, mesostructure
size, bimodal (micro- and meso-) structure combination, and surface
heterogeneity to impedance spectrum is discussed. In particular, at
low frequencies the surface heterogeneity causes distribution of relaxation
times resulting in constant phase element (CPE) behavior. At intermediate
frequencies, a significant influence of micropore length is found
to cause a slow rate of charge storage, which competes with the mesostructured
geometry, shape, and size causing the faster high frequency diffuse
layer dynamics. In general, the bimodal convex mesostructure has a
faster EDL reorganization than the concave mesostructure. We conclude
from the study that mesostructured morphology coupled with heterogeneous
microporous geometry can effectively increase or decrease the charging
dynamics of porous electrodes.