Modeling of Donnan Equilibrium in Charged Porous Materials - a Scale Transition Analysis

Knowledge of location and magnitude of charge density, together with the pore morphology allows one to calculate the Donnan potential, characterizing ion exclusion in charged porous materials. Use of the electro-chemical potential together with Gauss’ electrostatic theorem allows the computation of the ion and voltage distribution at the microscale. On the other hand, commonly used macroscopic counterparts of these equations allow the estimation of the Donnan potential and ion concentration on the macroscale. However, it turns out that the classical macroscopic equations describing phase equilibrium do not account for the non-homogeneous distribution of ion and voltage at the microscale, leading to inconsistencies in estimating the Donnan potential (at the macroscale) from microscale information. In this paper we derive a new generalized macroscopic equilibrium equation by means of volume averaging of the microscale electro-chemical potential.