Predictably Engineering the Viscoelastic Behavior of Dynamic Hydrogels via Correlation with Molecular Parameters.

Rational design of dynamic hydrogels with desirable viscoelastic behaviors relies on an in-depth understanding of the principles correlating molecular parameters and macroscopic properties. To quantitatively elucidate such principles, a series of dynamic covalent hydrogels crosslinked via hydrazone bonds is designed. The exchange rate of the hydrazone bond is tuned by varying the concentration of an organic catalyst, while maintaining the crosslinking density unchanged. This strategy of independently tuning exchange dynamics of crosslinks and crosslinking density allows unambiguous analysis of the viscoelastic response of the dynamic hydrogels as a function of their network parameters. It is found that the terminal relaxation time of the dynamic hydrogels is primarily determined by two factors: the exchange rate of crosslinks and the number of effective crosslinks per polymer chain, and is independent of the network architecture. Furthermore, a universal correlation is identified between the terminal relaxation time determined from stress relaxation and the exchange rate determined via reaction kinetics, which can be generalized to any viscoelastic hydrogel network, in principle. This quantitative correlation facilitates the development of dynamic hydrogels with a variable desired viscoelastic response based on molecular design.

Transferable Ion Force Fields in Water from a Simultaneous Optimization of Ion Solvation and Ion-Ion Interaction.

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.

Looping-in complexation and ion partitioning in nonstoichiometric polyelectrolyte mixtures.

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.

Overcharging of polyelectrolyte complexes: an entropic phenomenon.

Overcharging in complex coacervation, in which a polyelectrolyte complex coacervate (PEC) initially containing equal moles of the cationic and anionic monomers absorbs a large excess of one type of polyelectrolyte species, is predicted using a recently developed thermodynamic model describing complexation through a combination of reversible ion binding on the chains and long-range electrostatic correlations. We show that overcharging is favored roughly equally by the translational entropy of released counterions and the binding entropy of polyelectrolytes in the polyelectrolyte complex, thus helping resolve competing explanations for overcharging in the literature. We find that the extent of overcharging is non-monotonic in the concentration of added salt and increases with both strength of ion-pairing between polyions and chain hydrophobicity. The predicted extent of overcharging of the PEC is directly compared with that of multilayers made of poly(diallyldimethylammonium), PDADMA, and poly(styrene-sulfonate), PSS, overcompensated by the polycation in two different salts: KBr and NaCl. Accounting for the specificity of salt ion interactions with the polyelectrolytes, we find good qualitative agreement between theory and experiment.

Tunable Coacervation of Well-Defined Homologous Polyanions and Polycations by Local Polarity.

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.

Role of electrostatic correlations in polyelectrolyte charge association.

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.