Electrochemistry and capacitive charging of porous electrodes in asymmetric multicomponent electrolytes

We present porous electrode theory for the general situation of electrolytes containing mixtures of mobile ions of arbitrary valencies and diffusion coefficients (mobilities). We focus on electrodes composed of primary particles that are porous themselves. The predominantly bimodal distribution of pores in the electrode consists of the interparticle or macroporosity outside the particles through which the ions are transported (transport pathways), and the intraparticle or micropores inside the particles, where electrostatic double layers (EDLs) are formed. Both types of pores are filled with electrolyte (solvent plus ions). For the micropores we make use of a novel modified-Donnan (mD) approach valid for strongly overlapped double layers. The mD-model extends the standard Donnan approach in two ways: (1) by including a Stern layer in between the electrical charge and the ions in the micropores, and (2) by including a chemical attraction energy for the ions to go from the macropores into the micropores. This is the first paper where the mD-model is used to model ion transport and electrochemical reactions in a porous electrode. Furthermore we investigate the influence of the charge transfer kinetics on the chemical charge in the electrode, i.e., a contribution to the electrode charge of an origin different from that stemming from the Faradaic reaction itself, e.g. originating from carboxylic acid surface groups as found in activated carbon electrodes. We show that the chemical charge depends on the current via a shift in local pH, i.e. "current-induced charge regulation." We present results of an example calculation where a divalent cation is reduced to a monovalent ion which electro-diffuses out of the electrode.