This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels.

We present results of MD and MC simulations of the equilibrium properties of swelling gels with comb-like or bottlebrush subchains and compare them to scaling-theory predictions. In accordance with theory, the simulation results demonstrate that swelling coefficient of the gel increases as a function of the polymerization degree of the main chains and exhibits a very weak maximum (or is virtually constant) as a function of the polymerization degree and grafting density of side chains. The bulk osmotic modulus passes through a shallow minimum as the polymerization degree of the side chains increases. This minimum is attributed to the onset of overlap of side chains belonging to different bottlebrush strands in the swollen gel.

Conformational transitions and nanoscale self-organization triggered in double pH- and thermo-responsive molecular brushes by varying environmental conditions are studied by means of analytical mean-field theory and numerical Scheutjens–Fleer self-consistent field modelling. Such molecular brushes are composed of multiple thermo-responsive side chains end-grafted onto the main chain (backbone) and are capable of acquiring ionic charges via reversible (de)protonation of the monomer units. Competition of long-range Coulomb repulsion with short-range solvophobic interactions leads to complex patterns in the intramolecular self-organization of molecular brushes. In particular, we observed formation of pearl necklace-like structures with multiple dense nanodomains formed by weakly ionized collapsed side chains and stabilized by a fraction protruding into the solution and strongly ionized ones. Such structures are thermodynamically stable in a certain parameter range and can be termed as intramolecular micelles. The stimuli-induced intramolecular nanopatterning occurs via a sequence of quasi-first order phase transitions corresponding to splitting/fusion of collapsed domains accompanied by jumps in the average degree of ionization and macromolecular dimensions. A re-entrant sequence of transitions is observed when the salt concentration is used as a control parameter. These theoretical predictions provide guidelines for design of smart unimolecular devices, for example multicompartment nanocarriers of active substances or nanosensors.

Polyelectrolyte hydrogels can absorb a large amount of water across an osmotic membrane as a result of their swelling pressure. On the other hand, the insoluble cross-linked hydrogel network enables dewatering under the influence of external (thermal and/or mechanical) stimuli. Moreover, from a thermodynamic perspective, a polyelectrolyte hydrogel is already an osmotic membrane. These properties designate hydrogels as excellent candidates for use in desalination, at the same time avoiding the use of expensive membranes. In this article, we present our recent theoretical study of polyelectrolyte hydrogel usage for water desalination. Employing a coarse-grained model and the Gibbs ensemble, we modeled the thermodynamic equilibrium between the coexisting gel phase and the supernate aqueous salt solution phase. We performed a sequence of step-by-step hydrogel swellings and compressions in open and closed systems, i.e., in equilibrium with a large and with a comparably small reservoir of aqueous solution. The swelling in an open system removes ions from the large reservoir, whereas the compression in a closed system decreases the salt concentration in the small reservoir. We modeled this stepwise process of continuous decrease of water salinity from seawater up to freshwater concentrations and estimated the energy cost of the process to be comparable to that of reverse osmosis.