| The volumetric properties and swelling behavior of polyelectrolyte gels are studied using molecular dynamics and Monte Carlo simulations. The model polyelectrolyte network consists of highly charged linear polyelectrolyte chains of the same length, ranging from 50 to 300 monomeric units, that are tetrafunctionally crosslinked at the ends to form a defect-free diamond-like network backbone, and the network is immersed in an implicit solvent. For polyelectrolyte gels with no added salt, explicit mono-, di-, or trivalent counterions neutralize the charges on the polymer and molecular dynamics in the canonical ensemble is used for the simulations. For polyelectrolyte gels in equilibrium with an electrolyte solution reservoir, explicit coions are also present in the model, and the thermodynamic equilibrium between the gel and the reservoir is simulated using osmotic ensemble Monte Carlo, which combines the grand canonical and isothermal-isobaric Monte Carlo methods. In the salt-free cases the polyelectrolyte gels are found to undergo discontinuous volume phase transitions when the Bjerrum length of the implicit solvent is sufficiently high. An approximate cancellation between the counterion excluded volume contribution to the osmotic pressure and the electrostatic contribution to the osmotic pressure shows that the interplay between the counterion excluded volume entropy and electrostatic energy appears to drive the discontinous volume phase transitions in the gels, and also results in polyelectrolyte gels having swelling characteristics that have resemblance to the swelling characteristics of nonionic gels. In the cases where the polyelectrolyte gel is in equilibrium with an external electrolyte reservoir, the swelling behavior of the gel is continuous rather than discontinuous, and polyelectrolyte gels with long constituent chain lengths are shown to have very large swelling capacities. A disordered percolated nanostructure of regions containing high concentrations of monomers and divalent counterions separated by regions rich in coions is revealed as the polyelectrolyte gels undergo a volume collapse transition with increasing external electrolyte concentration. |
