Nonlinear Effects in the Nanophase Segregation of Polyelectrolyte Gels

Electrostatic correlations and the polyelectrolyte self energy

We address the effects of chain connectivity on electrostaticfluctuations in polyelectrolyte solutions using a field-theoretic, renormalizedGaussian fluctuation (RGF) theory. As in simple electrolyte solutions [Z.-G. Wang,Phys. Rev. E 81, 021501 (2010)], the RGF provides a unified theory forelectrostatic fluctuations, accounting for both dielectric and charge correlationeffects in terms of the self-energy. Unlike simple ions, the polyelectrolyte self energydepends intimately on the chain conformation, and our theory naturally provides aself-consistent determination of the response of intramolecular chain structure topolyelectrolyte and salt concentrations. The effects of the chain-conformation on theself-energy and thermodynamics are especially pronounced for flexiblepolyelectrolytes at low polymer and salt concentrations, where application of thewrong chain structure can lead to a drastic misestimation of the electrostaticcorrelations. By capturing the expected scaling behavior of chain size from dilute tosemi-dilute regimes, our theory provides improved estimates of the self energy at lowpolymer concentrations and correctly predicts the eventual N-independenceof the critical temperature and concentration of salt-free solutions of flexiblepolyelectrolytes. We show that the self energy can be interpreted in terms of aninfinite-dilution energy μ_m,0^el and a finite concentrationcorrelation correction μ^corr which tends to cancel out the formerwith increasing concentration.

Non-Gaussian elasticity and charge density-dependent swelling of strong polyelectrolyte poly(N-isopropylacrylamide-co-sodium acrylate) hydrogels

The mechanical properties and charge density-dependent swelling of strong polyelectrolyte poly(N-isopropylacrylamide-co-sodium acrylate) P(NIPA-co-NaA) hydrogels prepared at a fixed total monomer concentration and crosslinker ratio, but at various charge densities, i.e. NaA content in the feed between 0 and 90 mol%, were investigated. The elasticity results were discussed to explain the relationship between the elastic free energy ΔG_el and the swelling ratio α as well as to fit the existing theories to the swelling data. The implications of the obtained results for the deviation from the Gaussian chain statistics were considered. Given the swollen elastic modulus and the dependence of charge density on the equilibrium gel volume, it would seem that the latter factor is an important determinant of non-Gaussian elasticity of polyelectrolyte P(NIPA-co-NaA) hydrogels containing strongly dissociated groups. The dependence of the reduced modulus on the equilibrium gel volume was found to be G_r ≈ (V_eq)^-0.47 at low swelling degree and G_r ≈ (V_eq)^0.64 at high swelling degree and the deviation was interpreted as the non-Gaussian elasticity of equilibrium swollen P(NIPA-co-NaA) hydrogels. The detailed theoretical treatments of non-Gaussian elasticity of P(NIPA-co-NaA) hydrogels and, in particular, the influence of the charge density on the elasticity showed that the knowledge of several swollen state parameters and the effective charge density distribution of hydrogels were strongly required to explain the variation of the elastic properties depending on the ionic group content. Within this framework, the dominant mechanism responsible for the deviation from Gaussian elasticity and the finite chain extensibility of ionic P(NIPA-co-NaA) hydrogels was described and the results were used to explain the dependence of the elastic modulus on the equilibrium gel volume.

Two regions of microphase separation in ion-containing polymer solutions

The phenomenon of spinodal decomposition in weakly charged polyelectrolyte solutions is studied theoretically within the random phase approximation. A novel feature of the theoretical approach is that it accounts for the effects of ionic association, i.e. ion pair and multiplet formation between counterions and ions in polymer chains, as well as the dependence of local dielectric permittivity on the polymer volume fraction Φ. The main focus is on the spinodal instability of polyelectrolyte solutions towards microscopic phase separation. It has been shown that increasing the binding energy of ions decreases the classical microphase separation region (possible at low polymer concentrations) due to the effective neutralization of the chains. A qualitatively new type of microphase separation is found in the presence of a dielectric mismatch between polymer and solvent. This new branch of microphase separation is realized at high polymer concentrations where ion association processes are the most pronounced. Typical microstructures are shown to have a period of a few nanometers like in ionomers. The driving force for the microphase formation of a new type is more favourable ion association in polymer-rich domains where ionomer-type behavior takes place. Effective attraction due to ion association promotes microscopic as well as macroscopic phase separation, even under good solvent conditions for uncharged monomer units of polymer chains. Polyelectrolyte-type behavior at low Φ and ionomer-type behavior at high Φ result in the presence of two critical points on the phase diagrams of polyelectrolyte solutions as well as two separate regions of possible microscopic structuring. Our predictions on the new type of microphase separation are supported by experimental data on polymer solutions, membranes and gels.

A polymer microgel at a liquid-liquid interface: theory vs. computer simulations

We propose a mean-field theory and dissipative particle dynamics (DPD) simulations of swelling and collapse of a polymer microgel adsorbed at the interface of two immiscible liquids (A and B). The microgel reveals surface activity and lowers A-B interfacial tension. Attempting to occupy as large an interfacial area as possible, the microgel undergoes anisotropic deformation and adopts a flattened shape. Spreading over the interface is restricted by polymer subchain elasticity. The equilibrium shape of the microgel at the interface depends on its size. Small microgels are shown to be more oblate than the larger microgels. Increasing microgel cross-link density results in stronger reduction of the surface tension and weaker flattening. As the degree of immiscibility of A and B liquids increases, the microgel volume changes in a non-monotonous fashion: the microgel contraction at moderate immiscibility of A and B liquids is followed by its swelling at high incompatibility of the liquids. The segregation regime of the liquids within and outside the microgel is different. Being segregated outside the microgel, the liquids can be fully (homogeneously) mixed or weakly segregated within it. The density profiles of the liquids and the polymer were plotted under different conditions. The theoretical and the DPD simulation results are in good agreement. We hope that our findings will be useful for the design of stimuli responsive emulsions, which are stabilized by the microgel particles, as well as for their practical applications, for instance, in biocatalysis.

Mixing of Two Immiscible Liquids within the Polymer Microgel Adsorbed at Their Interface

We report on the behavior of two immiscible liquids within polymer microgel adsorbed at their interface. By means of dissipative particle dynamics (DPD) simulations and theoretical analysis in the framework of the Flory-Huggins (FH) lattice theory, we demonstrate that the microgel acts as a "compatibilizer" of these liquids: their miscibility within the microgel increases considerably. If the incompatibility of the liquids is moderate, although strong enough to induce phase separation in their 1:1 composition, they form homogeneous mixture in the microgel interior. The mixture of highly incompatible liquids undergoes separation into two (micro)phases within the microgel likewise out of it; however, the segregation regime is weaker and the concentration profiles are characterized by a weaker decay (gradient) in comparison with those of two pure liquids. The enhanced miscibility is a result of the screening of unfavorable interactions between unlike liquid molecules by polymer subchains. We have shown that better miscibility of the liquids is achieved with densely cross-linked microgels. Our findings are very perspective for many applications where immiscible species have to be mixed at interfaces (like in heterogeneous catalysis).

Free-energy functionals of the electrostatic potential for Poisson-Boltzmann theory

In simulating charged systems, it is often 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 present a variational formulation with a local free-energy functional of the potential. In addition, we also construct 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.

Transient modeling for kinetic swelling/deswelling of the ionic-strength-sensitive hydrogel

The multi-effect-coupling ionic-strength-stimulus (MECis) model is presented for transient simulation of the kinetic deformation behavior of the ionic-strength-sensitive hydrogel, based on the laws of conservation of mass and momentum, where the chemical, electrical and mechanical effects are considered on the kinetics of the hydrogel. The simulated kinetic swelling/shrinking characteristics by the MECis model are compared with the experiments. It is concluded that the model is able to predict well the responsive variation of the ionic-strength-sensitive hydrogel with time.