Field theory for ionic systems. From fluctuations and structure at a hard wall to thermodynamics

We use a field theoretical approach to study ionic systems. In this paper we illustrate this formalism in a grand canonical ensemble for the long range Coulomb potential. For the inhomogeneous system near a hard neutral plane wall we go beyond the well known Debye-Huckel electrolyte results and predict the existence of a desorption profile. The results are compared with well established sum rules for ionic systems and thermodynamic relations are verified. We also calculate the differential capacitance in a slab using the linear response theory. The capacitance is calculated from the charge-charge correlations for the neutral system using the fluctuation-dissipation theorem. (C) 2003 Elsevier Ltd. All rights reserved.