MICROSCOPIC DERIVATION OF THE HUBBARD-ONSAGER-ZWANZIG EXPRESSION OF LIMITING IONIC-CONDUCTIVITY

An outstanding problem in the theory of ionic conductivity is a deriva tion of the well-known Hubbard-Onsager-Zwanzig expression for the diel ectric friction on an ion from first principles. In fact, microscopic theories have repeatedly failed to reproduce the Hubbard-Onsager-Zwanz ig expression under any limiting conditions. We show in this article t hat the existing molecular theories and the continuum model treatments calculate two entirely different contributions to the friction on the ion. While the former calculates the contribution from the solvent de nsity mode alone, the latter includes only the contribution from the c urrent mode. Thus the existing molecular theories can never be reduced to the Hubbard-Onsager (H-O) theory. In addition, we show that the ex isting molecular theories become inconsistent for larger ions where th e H-O theory is accurate. The reverse is true for smaller ions. An exp ression is derived here which is valid at both the Limits and for all ion sizes and its consequences discussed. (C) 1998 American Institute of Physics. [S0021-9606(98)50234-6].