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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Mass transport at a long distance in systems with percolating features is reduced to a nonlinear diffusion equation, with a zero value of the diffusion coefficient below the percolation threshold. Two simple models for the concentration dependence of the diffusion coefficient are exploit above this value. The corresponding nonstationary concentration profiles after a stepwise increase of me boundary concentration have been analyzed for two initial conditions, a completely exhausted medium or with the initial concentration at the percolation threshold. In the former case the change of the boundary concentration to any value above the percolation threshold leads to the front, i.e. a jump of the concentration from zero to the threshold value, which propagates through the medium with a constant intensity. The latter initial condition in the case of the linear model for the diffusion coefficient leads to a profile with the fore edge, i.e. a stepwise change of the slope. This front or fore edge are followed by the "diffusional tail" where the concentration changes gradually between the threshold and boundary values. Its shape depends essentially on the model of the diffusion coefficient. In all above variants the profile is developing as the square root of time. We have proposed an approach to the charging process in conducting polymers based on the macroheterogeneous model (ensemble of elements with various redox potentials). Since such a system possesses percolation properties the above results have been applied to the description of the charging process after a stepwise change of the applied voltage. They are able to reproduce properly some essential features found experimentally, except for me observed constancy of me front propagation speed at each applied potential. The latter fact may be attributed to the considerable potential drop due to ionic transport resistance in such materials. Linear variation of the front position is predicted by such a theory if counterions are dominant ionic species inside the film, at least for its considerable charging levels.