# Temperature dependence of the primitive-model double-layer differential capacitance: A hypernetted chain/mean spherical approximation calculation

## Abstract

Calculations based on the hypernetted chain approximation (HNC/MSA version) for the differential capacitance are reported for the model double layer formed by charged hard spheres in a continuum dielectric medium and near a charged hard wall. The emphasis is on its temperature dependence. Rather than numerically differentiate a table of potential versus charge density, we formally differentiate the HNC/MSA equations and solve these equations simultaneously with the usual HNC/MSA equations. A finite element method that requires only a small number of iterations is used and is found to be very efficient. The resulting HNC/MSA values for C are considerably larger than the Gouy-Chapman (GC) values at high electrode charge density and, in contrast to the GC results, are found to decrease with increasing concentration. © 1988 American Chemical Society.