Transition in swollen polymer networks induced by intramolecular condensation

We present a theory for polyelectrolyte gels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gel elasticity, free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the selfregularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.

Section: A Polyelectrolyte Gel In a Salt-free Solutionmentioning

confidence: 99%

Theory of volume transition in polyelectrolyte gels with charge regularization

Hua

Mitra²,

Muthukumar³

2012

“…[7][8][9][10] A series of reports on the experimental observation of the discontinuous volume a͒ Present address: Synopsys, Inc., 2025 NW Cornelius Pass Rd., Hillsboro, OR 97124 b͒ Author to whom correspondence should be addressed. Electronic mail: depablo@engr.wisc.edu phase transition in polyacrylamide and polyacrylic acid networks was first presented by Tanaka et al 1,6,[11][12][13] A general theoretical prediction of the volume phase transition phenomenon in polymer networks formed by crosslinking linear polymer chains that are swollen in a solvent had been presented by Dušek and Patterson, 14 and several theoretical models concerning phase transitions in polyelectrolyte gels had been presented earlier by Hill in the context of muscle contraction and the ␣-␤ transformation in fibrous proteins. [7][8][9] Theories on neutral polymer networks are relatively well established [15][16][17][18] and have been verified by computer simulation studies.…”

Section: Introductionmentioning

confidence: 99%

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

Yin

Yan

Pablo

2005

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.

“…12 While the latter theory adequately describes the discontinuous phase transitions that may be observable in neutral polymer gels, the theory behind the phase transitions in polyelectrolyte gels, particularly with respect to the treatment of charge interactions, needs further development.…”

Section: Introductionmentioning

confidence: 99%

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

Yin

Horkay

Douglas

et al. 2008

Permanently crosslinked polyelectrolyte gels are known to undergo discontinuous first-order volume phase transitions, the onset of which may be caused by a number of factors. In this study we examine the volumetric properties of such polyelectrolyte gels in relation to the progressive substitution of monovalent counterions by divalent counterions as the gels are equilibrated in solvents of different dielectric qualities. We compare the results of coarse-grained molecular dynamics simulations of polyelectrolyte gels with previous experimental measurements by others on polyacrylate gels. The simulations show that under equilibrium conditions there is an approximate cancellation between the electrostatic contribution and the counterion excluded-volume contribution to the osmotic pressure in the gel-solvent system; these two contributions to the osmotic pressure have, respectively, energetic and entropic origins. The finding of such a cancellation between the two contributions to the osmotic pressure of the gel-solvent system is consistent with experimental observations that the swelling behavior of polyelectrolyte gels can be described by equations of state for neutral gels. Based on these results, we show and explain that a modified form of the FloryHuggins model for nonionic polymer solutions, which accounts for neither electrostatic effects nor counterion excluded-volume effects, fits both experimental and simulated data for polyelectrolyte gels. The Flory-Huggins interaction parameters obtained from regression to the simulation data are characteristic of ideal polymer solutions, whereas the experimentally obtained interaction parameters, particularly that associated with the third virial coefficient, exhibit a significant departure from ideality, leading us to conclude that further enhancements to the simulation model, such as the inclusion of excess salt, the allowance for size asymmetric electrolytes, or the use of a distance-dependent solvent dielectricity model, may be required. Molecular simulations also reveal that the condensation of divalent counterions onto the polyelectrolyte network backbone occurs preferentially over that of monovalent counterions.