Charge Distribution Around Nanoscale Nonhomogeneities in Solid State Ionics

Abstract

The system of Nernst-Planck-Poisson equations is modified by including the gradient terms in the chemical potential expression. The gradient terms are important in the regions of significant inhomogeneities, e. g. near the interface boundaries. These modified equations are used for investigating the particle density distribution in the vicinity of interphase boundary of a solid electrolyte. The differential equation of the fourth order for the problem of contact between two solid phases is formulated. Its analytic solution which describes non monotonic distribution of charge in both phases is obtained. It is shown that the gradient component added in the transport equations makes a decisive contribution in the double layer region. The approach is further expanded to the system composed of bulk phases and the intergrain layer between them. The particle density distributions at different conditions are investigated. The quasy-one dimensional lattice model of the fuel cell is considered in the frame of kinetic Monte Carlo simulation. It is shown that the electrostatic interaction between ions makes a significant contribution to the activation energy of migration of the particles. On the other hand, the fluctuations of the energy barriers slightly increase the particle migration activation energy. It is found that at blocked electrodes in the near electrode regions electrical double layers are formed. The thickness of the electrical double layer is around few lattice constants.