The classical Voorn-Overbeek thermodynamic theory of complexation and phase separation of oppositely charged polyelectrolytes is generalized to account for the charge accessibility and hydrophobicity of polyions, size of salt ions, and pH variations. Theoretical predictions of the effects of pH and salt concentration are compared with published experimental data and experiments we performed, on systems containing poly(acrylic acid) (PAA) as the polyacid and poly(N,N-dimethylaminoethyl methacrylate) (PDMAEMA) or poly(diallyldimethyl ammonium chloride) (PDADMAC) as the polybase. In general, the critical salt concentration below which the mixture phase separates, increases with degree of ionization and with the hydrophobicity of polyelectrolytes. We find experimentally that as the pH is decreased below 7, and PAA monomers are neutralized, the critical salt concentration increases, while the reverse occurs when pH is raised above 7. We predict this asymmetry theoretically by introducing a large positive Flory parameter (= 0.75) for the interaction of neutral PAA monomers with water. This large positive Flory parameter is supported by molecular dynamics simulations, which show much weaker hydrogen bonding between neutral PAA and water than between charged PAA and water, while neutral and charged PDMAEMA show similar numbers of hydrogen bonds. This increased hydrophobicity of neutral PAA at reduced pH increases the tendency towards phase separation despite the reduction in charge interactions between the polyelectrolytes. Water content and volume of coacervate are found to be a strong function of the pH and salt concentration.

Polymeric nanogels undergo large reversible volume changes with moderate changes in environmental conditions. We report the results of a theoretically informed coarse-grained Monte Carlo simulation of a polymeric nanogel placed in a solvent bath. The nanogel is modelled as a regular network of Gaussian strands, each discretized with coarse-grained polymer beads (“particles”). The non-bonded interactions are evaluated from the local densities (“fields”), and include the Flory-like contribution for polymer-solvent interactions, the translational entropy of mobile ions, and the Coulomb energy obtained by solution of Poisson's equation. While an artificial grid is employed for convenience of implementation, the results are independent of contour and grid discretization within a resolution specified by the level of coarse-graining. We analyze the effects of degree of crosslinking, solvent quality, and charge fraction of polymer backbone, on the volume phase transition behavior of nanogels.

Nanoparticles functionalized with photo-switchable ligands can be assembled into a broad range of structures by controlled light exposure. In particular, alternating light exposures provide the means to control formation of assemblies of various sizes and symmetries. Here, we use scaling arguments and Kinetic Monte Carlo simulations to study the evolution of reversible aggregates in a solution of periodically irradiated photo-switchable nanoparticles. Scaling estimates of the characteristic size and the mean separation of aggregates agree with the simulations. The transition probabilities in the Kinetic Monte Carlo scheme are derived from a renormalized master equation of the diffusion process. Simulations on a system of nanoparticles, interacting through Lennard-Jones pair potentials that change their character from repulsive to attractive depending on the light exposure, show that the slow diffusion of particles at low effective temperatures (where the attractions are much higher than the thermal energy) results in the formation of small, “kinetically frozen” aggregates. On the other hand, aggregation does not occur at high effective temperatures, where the attractions are comparable to the thermal energy. In the intermediate range of effective temperatures, “fluctuating” aggregates form that can be stabilized by applying light pulses of specific lengths and frequencies. The aggregate sizes increase by increasing the packing fraction and the aggregates undergo transition to a percolated “network” at high packing fractions. Light-control of inter-particle interactions can either inhibit or promote nucleation and growth, and can reduce gel and glass formation.