The Coupled Nernst-Planck-Poisson and Darken Formalisms: Interdiffusion in the Presence of the Electric Field

The coupled Nernst-Planck-Poisson and Darken formalisms are presented. The intrinsic diffusion fluxes are defined in the material (lattice) fixed frame of reference and  the Nernst-Planck flux formula is used. The overall fluxes of the components (defined in the laboratory reference frame) are sum of diffusion and drift (convection), that is to say we follow the Darken approach. The resulting set of differential equations has been solved numerically for planar systems by using the method of lines and the Radau solver. The method has been used for predictions of mass and charge transport in polymeric and glassy multicomponent systems. The obtained results are consistent with physical limitations, e.g. allowed to overcome a virtual phenomenon of non-physical values predicted by the NPP model solely in ion-selective electrodes.