Non-linear Poisson-Boltzmann theory for swollen clays

¹ Laboratoire de Physique, Ecole Normale Supérieure de Lyon (URA CNRS 1325 ) 46 Allée d'Italie, 69364 Lyon Cedex 07, France
² Department of Chemistry, University of Cambridge Lensfield Road, Cambridge CB2 1EW, UK

Received: 22 April 1998
Accepted: 27 June 1998

Abstract

The non-linear Poisson-Boltzmann (PB) equation for a circular, uniformly char ged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semi-analytically by transforming it into an integral equation and solving the latter iteratively. This method proves efficient and robust, and can be readily generalized to other problems based on cell models, treated within non-linear Poisson-like theory. The solution to the PB equation is computed over a wide range of physical conditions, and the resulting osmotic equation of state is shown to be in semi-quantitative agreement with recent experimental data for Laponite clay suspensions, in the concentrated gel phase.