Dispersive ionic space charge relaxation in solid polymer electrolytes. II. Model and simulation

Abstract

Dynamic Monte-Carlo simulations of ionic space charge relaxations are carried out using a three-dimensional model for thermally activated ion hopping in a multiwell energy structure. In this model a solid polymer electrolyte is embedded between two ideal blocking electrodes. The polymer is subdivided into 100×100×100 lattice cells. Positive ions (typically 1000) are distributed on the cells. To provide charge neutrality a negative background charge, constant in space and time, is introduced. The positive ions are able to hop between neighboring cells, surmounting energy barriers of distributed heights. The barrier heights consist of an intrinsic part due to the polymer structure, a part due to the Coulomb interaction of the ions, and a part due to the externally applied field. To calculate the interaction between the ions and the electrodes a method of images is used. Periodical boundary conditions are used for those lattice surfaces which are not in contact with the electrodes. The ionic space charge polarization process is simulated as dependent on the time, the sample thickness, the ion concentration, and the externally applied voltage. The polarization current after a step of the electric field shows dispersion due to distributed energy barrier heights in the short time range and a Kohlrausch behavior due to image charges in the long time range.