RATE EQUATIONS IN THE HOPPING TRANSPORT .2. BOUNDARY-CONDITIONS AND LIMITING PROCESSES IN A SIMPLE 1D-MODEL

The usual kinetic equations for the site occupation probabilities in an external field are solved exactly in a simple one-dimensional periodic model with two kinds of atoms using a) free boundary conditions and order of limits N→∞, ω→0 needed for a proper treatment of the dc conductivity here b) boundary conditions with metallic contacts and order of limits N→∞, ω→0 and c) the same boundary conditions but reversed order of limiting processes ω→0, N→∞ typical of e.g. numerical and percolation treatments. (N and ω are the number of sites and frequency.) It is demonstrated that though the bulk dc conductivity is the same in all three cases, local bulk properties of the material are strongly dependent on the régime used. The role of the order of all three limiting processes ω→0, N→+∞ and n→+∞ (N-n→+∞) for local shifts of the chemical potential δμn in the dc limit is examined (n is the number of the relevant site calculated from a boundary of the chain). It is shown especially that the rate equation treatment (régime a) on the one hand and numerical or percolation treatments (régime c) on the other hand never yield the same bulk values of δμr. © 1979 Academia, Publishing House of the Czechoslovak Academy of Sciences.