Osmotic pressure in polyelectrolyte solutions: cell-model and bulk simulations
Date
2018-06-22
Authors
Ullner, Magnus
Qamhieh, Khawla
Cabane, Bernard
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Abstract
The osmotic pressure of polyelectrolyte solutions as a function of concentration has been calculated by
Monte Carlo simulations of a spherical cell model and by molecular dynamics simulations with periodic
boundary conditions. The results for the coarse-grained polyelectrolyte model are in good agreement
with experimental results for sodium polyacrylate and the cell model is validated by the bulk simulations.
The cell model offers an alternative perspective on osmotic pressure and also forms a direct link to even
simpler models in the form of the Poisson–Boltzmann approximation applied to cylindrical and spherical
geometries. As a result, the non-monotonic behaviour of the osmotic coefficient seen in simulated
salt-free solutions is shown not to rely on a transition between a dilute and semi-dilute regime, as is
often suggested when the polyion is modelled as a linear flexible chain. The non-monotonic behaviour
is better described as the combination of a finite-size effect and a double-layer effect. Parameters that
represent the linear nature of the polyion, including an alternative to monomer concentration, make it
possible to display a generalised behaviour of equivalent chains, at least at low concentrations. At high
concentrations, local interactions become significant and the exact details of the model become
important. The effects of added salt are also discussed and one conclusion is that the empirical additivity rule,
treating the contributions from the polyelectrolyte and any salt separately, is a reasonable approximation,
which justifies the study of salt-free solutions.