Field theoretical approach to inhomogeneous ionic systems: thermodynamic consistency with the contact theorem,Gibbs adsorption and surface tension |
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Authors: | D DI CAPRIO J STAFIEJ J P BADIALI |
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Institution: | 1. Laboratoire d'électrochimie et Chimie Analytique , UMR 7575, Université P. et M. Curie, Paris VI, Bat. , F74, BP 39, 4, Place Jussieu , 75230 , Paris Cedex 05 , France;2. Department of Electrode Processes , Institute of Physical Chemistry of the Polish Academy of Sciences , ul. Kasprzaka 44/52, 01-224 , Warsaw , Poland |
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Abstract: | Using a statistical field approach we investigate the structure of an electrolyte solution in contact with a neutral impenetrable wall. The Hamiltonian contains the Coulomb interaction and the ideal entropy. At the level of the quadratic approximation, the Hamiltonian yields the Debye-Hückel theory in the bulk. Analytic expressions of the charge-charge and potential-potential inhomogeneous correlation functions are obtained. Exact asymptotic results for point ion charge correlation functions are obtained and the profile for the fluctuation of the electric potential is calculated. We also consider the term beyond the quadratic expansion of the ideal entropy in the Hamiltonian. With this term a higher order coupling between charge density and number density produces a non-trivial profile for the total ion density. This density profile is consistent with the contact theorem and the related surface tension calculated from the Gibbs adsorption isotherm. |
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