Non-linear Poisson-Boltzmann theory for swollen clays

The non-linear Poisson-Boltzmann (PB) equation for a circular, uniformly charged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semianalytically 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.