Effective Ion Diffusion in Charged Nanoporous Materials

Multiscale models of ion transport in porous media relate microscopic material properties (e.g., pore size distribution and pore connectivity) to their macroscopic counterparts (e.g., porosity, effective diffusion coefficient and effective electrical conductivity). We derive a macroscopic model of ion transport in electrically charged nanoporous materials, and the corresponding effective diffusion coefficient, electric conductivity and transference numbers, that explicitly account for dynamic changes in electrical double layer (EDL) and possible overlap of EDLs in nanopores. The general equations comprising this model reduce to a model of an electrical double layer capacitor (EDLC) used to interpret measurements of the EDLC voltage response to charging. While the original representation relies on empirical coefficients (e.g., Bruggeman's relation), our effective coefficients are derived from the first principles and vary with a range of electrochemical conditions (e.g., initial concentration of ions in the electrolyte). The resulting model predictions of the EDLC voltage response match the experimental data better than the original model does. (C) 2017 The Electrochemical Society. All rights reserved.