Molecular dynamics simulation of discontinuous volume phase transitions in highly-charged crosslinked polyelectrolyte networks with explicit counterions in good solvent

Abstract

The volumetric properties of highly-charged defect-free polyelectrolyte networks with tetrafunctional crosslinks are studied through molecular dynamics simulations in the canonical ensemble. The network backbone monomers, which are monovalent, and the counterions, which are mono-, di-, or trivalent, are modeled explicitly in the simulations, but the solvent is treated implicitly as a dielectric medium of good solvation quality. The osmotic pressure of the network-solvent system is found to depend greatly on the strength of electrostatic interactions. Discontinuous volume phase transitions are observed when the electrostatic interactions are strong, and the onset of these transitions shifts to higher solvent dielectricity as the counterion valency increases. The roles of the various virial contributions to the osmotic pressure are examined. The network elasticity entropy is found to behave nearly classically. As the network contracts and collapses with increasing strength of electrostatic interactions, the loss of counterion entropy leads to increased counterion osmotic pressure contributions via two mechanisms. The reduction in available configurational space increases the counterion translational entropy contribution to the ideal part of the osmotic pressure, and the greater number of counterion-monomer contacts formed due to counterion condensation and confinement increases the counterion excluded-volume entropy contribution to the excess part of the osmotic pressure. These observations contrast the decrease in the single ideal-gas-like counterion translational entropy contribution to the osmotic pressure predicted by the counterion condensationcharge renormalization theory. An accompanying decrease in the total electrostatic energy balances the loss of counterion excluded-volume entropy as the polyelectrolyte networks collapse in low-dielectric solvents. This interplay between the electrostatic energy and the counterion excluded-volume entropy appears to be responsible for the discontinuous volume phase transitions that are observed in polyelectrolyte networks. The structure of the polyelectrolyte network is also found to be affine in the swollen state, with constituent chains nearly fully extended, and nonaffine in the collapsed state, with the chains adopting a Gaussian conformation.

Molecular simulation of the swelling of polyelectrolyte gels by monovalent and divalent counterions

“…Our calculations indicate that our previous findings 23 of an approximate cancellation between the electrostatic and excluded-volume contributions to the pressure for a pure species of counterions extend to mixtures of monovalent and divalent counterions. This result is of qualitative importance because it provides a numerical justification for treating for polyelectrolyte gels using the same theoretical expressions as those derived for neutral gels, as implicit in Eqs.…”

“…The relative standard error in the osmotic pressure is also of the order O͑10 −4 ͒ after 8.3ϫ 10 6 time steps. Overall the molecular simulation model and the integration scheme are essentially the same as those used in our previous study, 23 but with the difference that the system may contain a mixture of monovalent and divalent counterions. The extent of monovalentdivalent counterion exchange is denoted by the parameter ␣, describing the relative counterion concentration,…”

“…These studies show that the introduction of a multivalent salt leads to changes in the osmotic properties that are anomalous in com-parison to neutral gels ͑we summarize some of the main results of these measurements below͒, suggesting that the addition of multivalent salts might have an effect distinct from that of simply reducing the solvent quality, in the sense of this term as it pertains to neutral polymers. 6 With this proposition in mind, we generalize our previous simulations of polyelectrolyte gels with exclusively monovalent or divalent counterions 23 to describe gels that include a mixture of monovalent and divalent counterions. Our study is restricted to the salt-free case, where the counterions derive from those that dissociate from charged groups within the polymer chain.…”

“…The network has a defect-free tetrafunctionally crosslinked diamond network topology. 23,[28][29][30][31][32][33][34] We simulate only a unit cell containing 16 crosslinked chains. The individual constituent chains are of the freely jointed bead-spring type having 100 monomeric units and the chains are linked at their ends.…”

Theory of volume transition in polyelectrolyte gels with charge regularization

“…49 Thus it is necessary for theoretical formulations of charged polymer systems to take into effect this property of self-regularization of the effective charge, where the effective charge of the polymer, and hence the counterion concentration is determined by a balance between the electrostatic attraction between the counterions and the ionized polymer backbone, and the translational entropy of the counterions in the solution. 46,[50][51][52] There have been extensive experiments 4,[53][54][55][56][57][58][59][60][61][62][63] and simulations [64][65][66][67][68][69][70][71][72][73][74][75][76] that have studied the volume transition in ionic gels. In particular, Tanaka and co-workers have investigated the effect of added salt concentrations in the volume collapse both for monovalent and divalent salts.…”