Zhen-Gang Wang

Weak polyelectrolyte hydrogels are emerging as a versatile platform for ion transport and separation, desalination, and energy applications. However, a predictive understanding of how dynamic charge regulation at the nanoscopic scale influences ionic mobility in these polymer networks remains elusive. Here, using large-scale molecular simulations, we dissect the coupled mechanisms governing small-ion transport in weak polyelectrolyte hydrogels, and reveal how charge density, competitive binding, and dynamic charge regulation jointly control ion mobility. By systematically isolating these effects, we uncover a pronounced nonmonotonic dependence of ion self-diffusion on hydrogel pKa and salt concentration for multivalent ions. Strikingly, allowing the hydrogel backbone to dynamically regulate its charge eliminates this nonmonotonicity and leads to dramatic enhancements in ion mobility, with diffusion coefficients increasing by more than a factor of 2 for trivalent ions. We attribute this effect to a protonation-assisted hopping mechanism that continuously remodels the local electrostatic landscape, providing an additional molecular-scale pathway for ion unbinding beyond translational escape and accelerating ion-pair kinetics without affecting the fraction of free ions. Our results demonstrate that dynamic nanoscale charge regulation can decouple ion mobility from equilibrium binding strength, offering a powerful design lever unavailable in fixed-charge materials. Building upon these insights, we propose simple molecular design principles for next-generation ion-conducting hydrogels and suggest alternative strategies for nanostructured membranes, energy materials, and biologically inspired charge-adaptive soft matter.

Complex coacervates─liquid condensates resulting from liquid–liquid phase separation of oppositely charged polymers─have attracted broad interest in artificial cells, drug delivery vehicles, and smart nanoreactors. The functionality of these applications is significantly influenced by the coacervate’s ability to encapsulate guest macromolecules, where the guest interactions determine their loading efficiency and activity. Using MD simulations, analytical theory, and experiments, we demonstrate that the intrinsic electrostatic correlations within the coacervate matrix significantly modify the effective interactions of guest polymers in the dense phase, resulting in the strong dependence of encapsulation on guest chain length, charge density, and charge sequence observed experimentally. Even in the absence of chemical incompatibility, neutral polymers are strongly excluded from the coacervate phase as a result of disrupting electrostatic correlations within coacervates. Consequently, the encapsulation efficiency of neutral polymers exponentially decays with increasing guest chain length. For polyampholyte-like intrinsically disordered proteins (IDPs), their effective interaction within coacervates is largely determined by charge sequence: IDPs with more-disordered sequences experience strict rejection from the dense phase, whereas those with more blocky charges are dispersed within coacervates. Interestingly, for all the guest species tested, their effective interactions are opposite to those observed in dilute solutions, where the sign of the effective two-body interaction reverses when going from the dilute phase to the dense coacervate phase. We elucidate that the non-trivial guest selectivity in complex coacervates originates from the disruption of polycation–polyanion electrostatic correlations by the guest, which combines an energetic penalty (dilution of charge density) with an entropic penalty (loss of chain conformational freedom of the host). These findings have significant implications for understanding guest behavior in coacervate and biocondensate systems.

Electric double layers in concentrated electrolytes exhibit a range of complex phenomena, including steric crowding, overscreening, and voltage-dependent capacitance. Mean-field theories offer a mathematically and conceptually simple framework for describing these phenomena and relating them to experimentally relevant observables. Here, we develop a spread-charge theory for the double layer in which ions carry finite-width charge distributions. In this formulation, nonlocal electrostatic response arises from the spatial extent of ionic charges, without altering the underlying Coulomb operator. The resulting model reproduces the key features of concentrated electrolyte double layers without any phenomenological electrostatic terms or ad hoc boundary conditions. Charge spreading produces a Kirkwood crossover from monotonic to damped oscillatory decay in bulk solutions, which in turn governs the long-range decay of the electrostatic potential, differential capacitance, and disjoining pressure in confined geometries. We show that in systems with no external charge, the Bazant–Storey–Kornyshev (BSK) theory emerges as the long-wavelength limit of the spread-charge model. This correspondence gives the phenomenological nonlocal electrostatic correction in BSK a microscopic interpretation in terms of the finite spatial extent of ionic charge. The spread-charge framework provides a physically interpretable mean-field route for connecting bulk screening, interfacial structure, and measurable double-layer response in concentrated electrolytes and ionic liquids.

Block copolymers self-assemble into ordered nanostructures whose geometry is governed by a competition between interfacial energy and chain conformational entropy. While this competition produces a rich sequence of morphologies, topologically complex “frustrated” phases, such as the primitive cubic network and single networks, incur severe packing penalties and are difficult to access in neutral systems. Here we show that ions functionalized at the termini of one block in an AB diblock copolymer melt introduce a qualitatively new stabilization mechanism. Strong ion correlations drive chain-end association and generate a curvature preference toward the charged domain; the resulting tendency of end-localized ion clusters to adopt compact, curved geometries selectively favors the highly frustrated single-primitive-cubic network ( P m 3 ¯ m ) and single-gyroid network ( I 4 ₁ 32) over the classical phases, in a region of parameter space with a segregation strength lying below the order–disorder transition of the neutral system. Free energy decomposition reveals that the electrostatic energy, arising almost entirely from beyond-mean-field ion correlations, becomes increasingly negative with increasing interfacial curvature. In the primitive cubic network, pronounced local segregation of ions into the cylindrical struts generates compact curved clusters whose correlation energy gain more than offsets the enhanced packing frustration, so the very geometry that is the source of packing frustration in neutral systems becomes the source of its stability here. Increasing ion size weakens correlations and suppresses the network phases, consistent with experimental observations. Our results establish curvature-selective end-group association as a general principle for accessing frustrated topologies in block copolymer systems.

Asymmetry in chain lengths between polycations and polyanions plays a pivotal role in determining the structure and dynamics of polyelectrolyte complex coacervates, yet how such asymmetry modulates the energetics underlying the complexation between polycation and polyanion chains remains poorly understood. Here we develop an efficient Monte Carlo technique to calculate the Helmholtz free energy as a function of the electrostatic coupling parameter Γ for polyelectrolyte solutions in an implicit dielectric continuum. We apply this method to investigate the conformation and energetics in both single-chain systems with their monovalent counterions and mixtures composed of one polycation and one polyanion chain along with their respective counterions, all under the salt-free conditions. Comparison between the two-chain systems and the corresponding single-chain systems allows us to quantify the complexation free energy ΔF between two oppositely charged polyions. We further examine the energetic and entropic contributions of ΔF by either neglecting or incorporating the temperature dependence of dielectric constant. We find that only the latter can reproduce the experimentally observed entropy-dominated driving force over a wide range of Γ. At weak to moderate Γ, the entropy gain mainly arises from the orientation degrees of freedom of solvent molecules. As Γ increases, the contribution of counterion-release entropy gradually becomes dominant. In addition, ΔF of asymmetric pairs is mainly governed by the shorter chain and varies weakly with increasing the chain length of the longer polyion. Our study offers valuable insights into the thermodynamic nature of polyelectrolyte complexation with asymmetric chain lengths, which is crucial for understanding the structure and stability of biomolecular condensates and the rational design of coacervate-based polymeric materials.

Weak polyelectrolyte hydrogels are emerging as a versatile platform for ion transport and separation, desalination, and energy applications. However, a predictive understanding how charge regulation influences ionic mobility in these polymer networks remains elusive. Here, using large-scale molecular simulations, we dissect the coupled mechanisms governing small-ion transport in weak polyelectrolyte hydrogels, and reveal how charge density, competitive binding, and dynamic charge regulation jointly control ion mobility. By systematically isolating these effects, we uncover a pronounced non-monotonic dependence of ion self-diffusion on hydrogel pKa and salt concentration for multivalent ions. Strikingly, allowing the hydrogel backbone to dynamically regulate its charge eliminates this non-monotonicity and leads to dramatic enhancements in ion mobility, with diffusion coefficients increasing by up to an order of magnitude for trivalent ions. We attribute this effect to a protonation-assisted hopping mechanism, which provides an additional pathway for ion unbinding beyond translational escape and accelerates ion-pair kinetics without affecting the fraction of free ions. Our results demonstrate that charge regulation can decouple ion mobility from equilibrium binding strength, offering a powerful design lever unavailable in fixed-charge materials. Building upon these insights, we propose simple molecular design principles for next-generation ionconducting hydrogels and suggest new strategies for membranes, energy materials, and biologically inspired charge-adaptive soft matter.

Weak polyelectrolyte hydrogels are emerging as a versatile platform for ion transport and separation, desalination, and energy applications. However, a predictive understanding how charge regulation influences ionic mobility in these polymer networks remains elusive. Here, using large-scale molecular simulations, we dissect the coupled mechanisms governing small-ion transport in weak polyelectrolyte hydrogels, and reveal how charge density, competitive binding, and dynamic charge regulation jointly control ion mobility. By systematically isolating these effects, we uncover a pronounced non-monotonic dependence of ion selfdiffusion on hydrogel pKa and salt concentration for multivalent ions. Strikingly, allowing the hydrogel backbone to dynamically regulate its charge eliminates this non-monotonicity and leads to dramatic enhancements in ion mobility, with diffusion coefficients increasing by up to an order of magnitude for trivalent ions. We attribute this effect to a protonation-assisted hopping mechanism, which provides an additional pathway for ion unbinding beyond translational escape and accelerates ion-pair kinetics without affecting the fraction of free ions. Our results demonstrate that charge regulation can decouple ion mobility from equilibrium binding strength, offering a powerful design lever unavailable in fixed-charge materials. Building upon these insights, we propose simple molecular design principles for next-generation ionconducting hydrogels and suggest new strategies for membranes, energy materials, and biologically inspired charge-adaptive soft matter.

The tube model has long served as a cornerstone of entangled polymer dynamics and rheology. We test some of the key concepts of the tube model by investigating the equilibrium dynamics of a free chain in a fixed-topology polymer network using molecular dynamics simulation. Our results reveal significant position-dependent dynamical heterogeneity manifested as a rugged free energy landscape for the longitudinal motion, resulting in additional friction due to the topological interactions, and a "tube dilation" mechanism arising from the relaxation of entanglements formed by loop strands in the network in a "flip-flop" motion. On timescales less than the Rouse time, the mean-square displacement of the center of mass of the free chain displays a subdiffusive behavior that is slower than the expected t^{1/2} scaling. On longer timescales, the effects of topological friction amount to a renormalized monomer friction that is several times the intrinsic value. These results challenge some of the fundamental assumptions of the tube model, even under equilibrium conditions.

Shifting the point dipole from the center of a Stockmayer particle is a simple geometric modification, whose implications on liquid structure, dielectric response, and phase behavior remain incompletely understood. We combine molecular dynamics simulations with analytical theory to provide a unified physical interpretation of how dipole shifts reshape microscopic correlations and propagate to macroscopic properties. We show that dipole-shifting breaks the fore–aft symmetry of the local electrostatic field, producing only modest changes in radial packing but strong alterations in angular structure within the first solvation shell. Enhanced alignment near the dipole head is accompanied by frustrated orientational correlations near the tail, leading to broader angular distributions and a shift away from axial configurations at strong coupling. These structural asymmetries weaken cooperative ordering and result in a systematic reduction in the dielectric constant, despite locally stronger interactions. For large shifts, the dielectric response approaches the Debye limit, indicating effective suppression of dipole–dipole correlations. The same geometric frustration governs vapor–liquid equilibria: while increasing dipole strength raises the critical temperature, even modest shifts disrupt the highly polarized liquid state that emerges at strong coupling and can suppress ferroelectric-like ordering. Predictions from a reparameterized co-oriented fluid functional equation for electrostatic interactions theory capture these trends within its domain of validity, highlighting the connection between local structure and macroscopic observables. Overall, this work demonstrates that dipole location, not only magnitude, provides a powerful control parameter in dipolar fluids and offers a clear framework for understanding geometric frustration in electrostatic liquids.

We investigate the properties of the liquid–vapor interface in the shifted-dipole Stockmayer fluid using molecular dynamics simulations in the canonical ensemble. We study the role of dipole moment strength and the degree of asymmetry on equilibrium interfacial characteristics, including density profiles, polar order, nematic order, interfacial polarization, electric field, and electrostatic potential. In addition, we compute angular distribution functions across the interface to gain insight into how the dipole shift affects the molecular orientation. We find that the shift significantly affects angular distribution functions by altering the polar order while leaving the nematic order relatively unaffected, relative to the reference regular Stockmayer fluid. These results can be explained using an image-dipole construct that has been previously applied to regular Stockmayer fluids. We find remarkable agreement between the simple theory and the simulations in the qualitative shape of the distribution functions for both the liquid and vapor phases in proximity to the interface. Surprisingly, the spontaneous polarization at the interface, and therefore the generated electric field, changes sign as the dipole moment strength increases, leading to an inversion of the sign of the potential difference across the interface.