The ionic complexation of polyelectrolytes is an important mechanism underlying many important biological processes and technical applications. The main driving force for complexation is electrostatic, which is known to be affected by the local polarity near charge centers, but the impact of which on the complexation of polyelectrolytes remains poorly explored. We developed a homologous series of well-defined polyelectrolytes with identical backbone structures, controlled molecular weights, and tunable local polarity to modulate the solvation environment near charged groups. A multitude of systematic, accurate phase diagrams were obtained by spectroscopic measurements of polymer concentrations via fluorescent labeling of polycations. These phase diagrams unambiguously revealed that the liquidlike coacervation is more stable against salt addition at reduced local polarity over a wide range of molecular weights. These trends were quantitatively captured by a theory of complexation that incorporates the effects of dispersion interactions, charge connectivity, and reversible ion-binding, providing the microscopic design rules for tuning molecular parameters and local polarity.

Reversible ion binding equilibria in polyelectrolyte solutions are strongly affected by interactions between dissociated ionic species. We examine how the structural correlations between ionic groups on polyelectrolytes impact the counterion binding. Treating the electrostatic correlation free energy using the classical Debye-Hückel expression leads to complete counterion dissociation in the concentrated regime. This unphysical behavior is shown to stem from improper regularization of the self-energy of dissociated ions and polyions and is mitigated by smearing point-like charges across a finite width. The influence of the self-energy on counterion binding is elaborated on by generalizing the Debye-Hückel free energy to polyelectrolytes with variable fractal dimension and stiffness. In the dilute regime, a greater propensity for binding is found for chains with more compact architectures, which in turn reduces the harsh self-repulsions of tightly packed arrangements of charge. In the concentrated regime, the effects of electrostatic correlations weaken due to screening and the extent of binding is governed by a balance of short-ranged interactions and the translational entropy of ions.

Doping of salt ions within stoichiometric polyelectrolyte complex coacervates (PECs) is modeled with a theory that includes polymer ion pairing and counterion adsorption as equilibrium reactions along with Flory−Huggins free energy and electrostatic correlations that capture the effects of polyelectrolyte charge connectivity. The model shows at low salt concentration a region in which the salt content in the PEC depends linearly on the salt concentration in the (external) supernatant, consistent with the experimental observations of the Schlenoff group. We find that only in the limit of strong salt ion adsorption are all salt ions in the PEC bound to polyelectrolytes; for binding free energies up to several k B T per ion, a significant fraction of the salt ions in the PEC are free (or unbound), even at the lowest salt concentration. When the salt concentration in the supernatant is increased to higher values beyond this linear regime, the PEC strongly swells with water and free salt ions, similar to that observed experimentally. The model also predicts that the partitioning behavior of salt ions into the PEC is primarily governed by ion-specific effects, which manifest themselves in the strength of salt ion adsorption and polyelectrolyte ion-pairing, in agreement with observations of Schlenoff and co-workers. With an appropriate choice of parameters, the theory provides good agreement with experimental doping and phase behavior data in the literature.

A wide variety of intracellular membraneless compartments are formed via liquid-liquid phase separation of charged proteins and nucleic acids. Understanding the stability of these compartments, while accounting for the compositional heterogeneity intrinsic to cellular environments, poses a daunting challenge. We combined experimental and theoretical efforts to study the effects of nonstoichiometric mixing on coacervation behavior and accurately measured the concentrations of polyelectrolytes and small ions in the coacervate and supernatant phases. For synthetic polyacrylamides and polypeptides/DNA, with unequal mixing stoichiometry, we report a general “looping-in” phenomenon found around physiological salt concentrations, where the polymer concentrations in the coacervate initially increase with salt addition before subsequently decreasing. This looping-in behavior is captured by a molecular model that considers reversible ion binding and electrostatic interactions. Further analysis in the low-salt regime shows that the looping-in phenomenon originates from the translational entropy of counterions that are needed to neutralize nonstoichiometric coacervates.

The poor performance of many existing nonpolarizable ion force fields is typically blamed on either the lack of explicit polarizability, the absence of charge transfer, or the use of unreduced Coulomb interactions. However, this analysis disregards the large and mostly unexplored parameter range offered by the Lennard-Jones potential. We use a global optimization procedure to develop water-model-transferable force fields for the ions K + , Na + , Cl – , and Br – in the complete parameter space of all Lennard-Jones interactions using standard mixing rules. No extra-thermodynamic assumption is necessary for the simultaneous optimization of the four ion pairs. After an optimization with respect to the experimental solvation free energy and activity, the force fields reproduce the concentration-dependent density, ionic conductivity, and dielectric constant with high accuracy. The force field is fully transferable between simple point charge/extended and transferable intermolecular potential water models. Our results show that a thermodynamically consistent force field for these ions needs only Lennard-Jones and standard Coulomb interactions.