  Debye-Huckel (DH) theory is extended to treat two-component size- and
charge-asymmetric primitive models, focussing primarily on the 1:1 additive
hard-sphere electrolyte with, say, negative ion diameters, a--, larger than the
positive ion diameters, a++. The treatment highlights the crucial importance of
the charge-unbalanced ``border zones'' around each ion into which other ions of
only one species may penetrate. Extensions of the DH approach which describe
the border zones in a physically reasonable way are exact at high $T$ and low
density, $\rho$, and, furthermore, are also in substantial agreement with
recent simulation predictions for \emph{trends} in the critical parameters,
$T_c$ and $\rho_c$, with increasing size asymmetry. Conversely, the simplest
linear asymmetric DH description, which fails to account for physically
expected behavior in the border zones at low $T$, can violate a new lower bound
on the energy (which applies generally to models asymmetric in both charge and
size). Other recent theories, including those based on the mean spherical
approximation, have predicted trends in the critical parameters quite opposite
to those established by the simulations.

Statistical Mechanics