Prediction of the osmotic pressure in charged colloidal dispersions : from approximate theories to many-body electrostatics

One of the classical methods to compute an osmotic pressure in a dispersion of interacting objects is to prescribe a model of pairwise interactions and invoke integral equation theories such as the Ornstein-Zernike (OZ) equation with a suitable closure. The assumption of pairwise additivity however breaks down for highly charged colloids and concentrated suspensions.

The cell model is a fast and relatively easily implemented model used to estimate the osmotic pressure of a highly charged colloidal dispersion. It yields accurate approximations of the pressure in dispersions with a low salt content and performs well when long-ranged interactions are involved and the structure of the dispersion is solid-like. It includes (to some extent) many-body electrostatics.

In this presentation, the accuracy of the cell model is quantified by comparing the osmotic pressure it predicts to reference values obtained from Poisson-Boltzmann Brownian dynamics simulations including many-body electrostatics. The comparison is performed for various colloidal sizes and charges, salt contents, and volume fractions.