With NSF support we have analyzed polyelectrolyte gels, and developed self-consistent models that account for their elastic properties as well as included ionic correlations in polymer electrolytes and developed a Lagrangian formulation of electrostatics in systems with dielectric heterogeneities.

Polyelectrolyte gels. Polymer gels are responsive materials that undergo large volume changes in response to external stimuli including salt, pH, light and electric fields. Their physical properties are determined by their degree of cross linking (elasticity), solvent quality and ionic conditions. Using molecular theory we studied the thermodynamics of a weak-polyacid hydrogel film that is chemically grafted to a solid surface. We investigated the response of the material to changes in the pH and salt concentration of the buer solution. We found that the pH-triggered swelling of the hydrogel film has a non-monotonic dependence on the acidity of the bath solution. At most salt concentrations, the thickness of the hydrogel lm presents a maximum when the pH of the solution is increased from acidic values. The quantitative details of such swelling behavior, which is not observed when the film is physically deposited on the surface, depend on the molecular architecture of the polymer network. This swelling-deswelling transition is the consequence of the complex interplay between the chemical free energy (acid-base equilibrium), the electrostatic repulsions between charged monomers, which are both modulated by the absorption of ions, and the ability of the polymer network to regulate charge and control its volume (molecular organization). In the absence of such competition, for example, for high salt concentrations, the film swells monotonically with increasing pH. A deswelling-swelling transition is similarly predicted as a function of the salt concentration at intermediate pH values. This reentrant behavior, which is due to the coupling between charge regulation and the two opposing effects triggered by salt concentration (screening electrostatic interactions and charging/discharging the acid groups), is similar to that found in end-grafted weak polyelectrolyte layers. Understanding how to control the response of the material to dierent stimuli, in terms of its molecular structure and local chemical composition, can help the targeted design of applications with extended functionality. We determined the response of the material to an applied pressure and an electric potential.

In the area of biological gels, Graham et al. has demonstrated concentration-dependent unbinding rates of proteins from DNA, using fluorescence visualization of the bacterial nucleoid protein Fis. The physical origin of this concentration-dependence was unexplained. Using a combination of coarse-grained simulation and theory we demonstrated that this behavior can be explained by taking into account the dimeric nature of the protein, which permits partial dissociation and exchange with other proteins in solution. This effect may play a major role in determining binding lifetimes of proteins in vivo where there are very high concentrations of solvated molecules.

Polymers and Copolymer Blends. Polyelectrolytes and electrolyte solutions display a rich array of phase behaviors due to the effects of long-ranged interactions inherent in Coulombic attractions and repulsions. While there is a wealth of literature examining these materials to provide some physical insight into their thermodynamics, all of these methods make strong approximations with regards to the nature of the ionic component. We developed a hybrid liquid-state integral equation and self-consistent field theory numerical theory that systematically demonstrates the ramications of local ion structure on the overall thermodynamics of segregated polymer blends. Furthermore, we demonstrated these effects on phase separation, such as suppression due to hard sphere interactions and enhancement due to ion cohesion, that are not described using traditional Poisson-Boltzmann mean-field theory.

Electrostatics. In simulating charged systems, it is useful to treat some ionic components of the system at the mean-field level and solve the Poisson-Boltzmann (PB) equation to get their respective density profiles. The numerically intensive task of solving the PB equation at each step of the simulation can be bypassed using variational methods that treat the electrostatic potential as a dynamic variable. But such approaches require the access to a true free-energy functional: a functional that not only provides the correct solution of the PB equation upon extremization, but also evaluates to the true free energy of the system at its minimum. Moreover, the numerical efficiency of such procedures is further enhanced if the free-energy functional is local and is expressed in terms of the electrostatic potential. Existing PB functionals of the electrostatic potential, while possessing the local structure, are not free energy functionals. We, however, have presented a variational formulation with a local free-energy functional of the potential. In addition, we also constructed a nonlocal free-energy functional of the electrostatic potential. These functionals are suited for employment in simulation schemes based on the ideas of dynamical optimization.

The results of this research have a wide range of possible applications in biological systems and in industry given the novelty of the techniques developed for soft-materials and complex fluids. 

Last Modified: 12/01/2016
Modified by: Monica Olvera