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

Yannick Hallez, LGC Toulouse

par Salmon Jean-Baptiste - publié le , mis à jour le

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.