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.
Highlights
The osmotic pressure of a solution measures its ability to gain or retain solvent molecules in an exchange with the surroundings, i.e., the chemical potential of the solvent
The deviation from the ideal pressure is expressed by the osmotic coefficient, which is the ratio between the real osmotic pressure and the ideal pressure
A notable exception is the case of osmotic stress measurements (N = 375),[5] which gives significantly lower values. This could possibly be due to the equation of state used for the osmotic pressure of the reference polyethylene glycol (PEG) solution
Summary
The osmotic pressure of a solution measures its ability to gain or retain solvent molecules in an exchange with the surroundings, i.e., the chemical potential of the solvent. The practical problem is to maintain a high net pressure in gels equilibrated with a solution at significant ionic concentration This situation is reproduced in experimental setups where the polyelectrolyte solution is contained by a semipermeable membrane that allows solvent, small ions and other small solutes to pass through, but not polymers. The simplest possible description of a polyelectrolyte solution is a cell model,[20,21,22,23] where the solution is treated as independent cells, each containing one chain with neutralising counterions and salt, if present It is attractive, because, computational benefits aside, it allows us to focus on the interactions between the polyion and the ions, which dominate the polyelectrolyte effect on osmotic pressure. The main discussion is based on salt-free cases, which is justified in a discussion of the effects of adding salt
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