Polyelectrolyte complexes are omnipresent both in nature and in the technological world, including nucleotide condensates, biological marine adhesives, food stabilizers, encapsulants, and carriers for gene therapy. However, the true phase behavior of complexes, resulting from associative phase separation of oppositely charged polyelectrolytes, remains poorly understood. Here, we rely on complementary experimental and simulation approaches to create a complete quantitative description of the phase behavior of polyelectrolyte complexes that represents a significant advance in our understanding of the underlying physics of polyelectrolyte complexation. Experiments employing multiple approaches with model polyelectrolytesoppositely charged polypeptides poly­(l-lysine) and poly­(d,l-glutamic acid) of matched chain lengthsled to phase diagrams with compositions of the complex and the supernatant that were in excellent agreement with simulation results. Contrary to the widely accepted theory for complexation, we found preferential partitioning of salt ions into the supernatant phase. Additionally, the salt partitioning into the supernatant phase was found to initially increase and then decrease on increasing the salt concentrations, manifesting as a distinct minimum in the salt partition coefficients. These trends were shown by simulations to be strongly influenced by the excluded volume interactions in the complex phase, which were not accounted for in their entirety in earlier theories. We believe the comprehensive data we present will be conducive to the development of an accurate physical theory for polyelectrolyte complexation with predictive capabilities.

Assembly of oppositely charged triblock copolyelectrolytes into phase-separated gels at low polymer concentrations (<1% by mass) has been observed in scattering experiments and molecular dynamics simulations. Here we show that in contrast to uncharged, amphiphilic block copolymers that form discrete micelles at low concentrations and enter a phase of strongly interacting micelles in a gradual manner with increasing concentration, the formation of a dilute phase of individual micelles is prevented in polyelectrolyte complexation-driven assembly of triblock copolyelectrolytes. Gel phases form and phase separate almost instantaneously on solvation of the copolymers. Furthermore, molecular models of self-assembly demonstrate the presence of oligo-chain aggregates in early stages of copolyelectrolyte assembly, at experimentally unobservable polymer concentrations. Our discoveries contribute to the fundamental understanding of the structure and pathways of complexation-driven assemblies, and raise intriguing prospects for gel formation at extraordinarily low concentrations, with applications in tissue engineering, agriculture, water purification and theranostics.

It is widely appreciated that the addition of salts to water leads to significant changes in the thermodynamic and dynamic properties of these aqueous solutions that have great significance in biology and manufacturing applications. However, no theoretical framework currently exists that describes these property changes in an internally consistent fashion. In previous work, we developed a coarse-grained model of electrolyte solutions capable of reproducing basic trends on how salts influence the viscosity and water diffusion coefficient. The present work explores the predictions of this model for basic thermodynamic properties of electrolyte solutions, namely, the density, isothermal compressibility, and surface tension. On the basis of our model, we find that ion-specific effects on thermodynamics properties, and by extension the dynamics of electrolyte solutions, derive primarily from ion solvation.

The idea that the dynamics of concentrated, high-molecular weight polymers are largely governed by entanglements is now widely accepted and typically understood through the tube model. Here we review alternative approaches, slip-link models, that share some similarities to and offer some advantages over tube models. Although slip links were proposed at the same time as tubes, only recently have detailed, quantitative mathematical models arisen based on this picture. In this review, we focus on these models, with most discussion limited to mathematically well-defined objects that conform to state-of-the-art beyond-equilibrium thermodynamics. These models are connected to each other through successive coarse graining, using nonequilibrium thermodynamics along the way, and with a minimal parameter set. In particular, the most detailed level of description has four parameters, three of which can be determined directly from atomistic simulations. Once the remaining parameter is determined for any system, all parameters for all members of the hierarchy are determined. We show how, using this hierarchy of slip-link models combined with atomistic simulations, we can make predictions about the nonlinear rheology of monodisperse homopolymer melts, polydisperse melts, or blends of different architectures. Mathematical details are given elsewhere, so these are limited here, and physical ideas are emphasized. We conclude with an outlook on remaining challenges that might be tackled successfully using this approach, including complex flow fields and polymer blends.

Ion-specific solvation has fundamental implications in biochemistry, and the thermodynamics and dynamics of aqueous salt solutions have correspondingly been investigated intensively. Nonetheless, there are fundamental unresolved issues in modeling the dynamics of aqueous salt solutions and the related problem of polymers dissolved in these solutions. In particular, experiments show that the self-diffusion coefficient, D, of water molecules in electrolyte solutions can be either enhanced or suppressed by particular salts having the same valence where the observed changes correlate with the Hofmeister series governing the relative solubility of proteins and water-soluble polymers in the same salt solutions. Recent studies have demonstrated that common atomistic models of aqueous electrolyte solutions completely fail to reproduce this basic phenomenon. Drawing on similar trends observed in the field of polymer nanocomposites, we propose a coarse-grained model of aqueous electrolyte solutions that captures the observed trends and that offers physical insight into the influence of salt on the thermodynamic and dynamic properties of electrolyte solutions.