Theory of the Electrochemical Impedance of Mesostructured Electrodes Embedded with Heterogeneous Micropores

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.