Shensheng Chen

Partial vitrimer elastomers that combine static and dynamic covalent crosslinks provide a promising route to reconcile creep resistance with network reconfigurability; however, the mechanistic understanding of their cooperative roles under large deformation remains limited. Here, we report a high-performance silicone rubber system based on polymethylvinylsiloxane (PMVS) incorporating dynamic boronic ester bonds and static covalent crosslinks with tunable compositions. The resulting materials exhibit exceptional stretchability (>1200%) together with enhanced tensile strength and improved elastic recovery under large strains. Rheological and mechanical analyses reveal that dynamic covalent crosslinks (DCCs) enable topological rearrangement, leading to enhanced damping, extensibility, and rate-dependent response, while static covalent crosslinks (SCCs) provide a persistent elastic backbone and impose topological constraints that suppress long-time flow and delay DCC-mediated relaxation. To quantitatively describe this behavior, we develop a constitutive model that integrates non-Gaussian chain elasticity with finite extensibility, stress-assisted bond-exchange kinetics, and static-crosslink induced topological constraints. The model accurately reproduces rate- and strain-dependent mechanical behavior and enables direct partitioning of viscoelastic contributions from the static and dynamic subnetworks. This work establishes a quantitative constitutive framework linking effective bond exchange kinetics and hybrid network topology to the macroscopic nonlinear mechanics of partial vitrimer elastomers under large strains.

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.

Inert polymer crowders ubiquitously promote the liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs), yet the underlying mechanisms remain elusive. By evaluating the potential of mean force between polyampholyte-like IDPs, we demonstrate that the presence of inert polymer crowders induces conformational transitions by screening the excluded-volume interactions of the IDPs, indirectly enhancing interchain electrostatic correlations. Under physiological conditions, this enhanced correlation is sufficient to trigger LLPS of highly charged IDPs that would otherwise remain dispersed. Our work highlights a universal crowder-conformation-electrostatics coupling in driving LLPS.

Polymerization-driven liquid-liquid phase separation (LLPS) underpins critical biological processes and biomaterial innovations, yet its underlying kinetic pathway and domain growth law remain unclear. Here we report the first computational study of LLPS dynamics in polymerization-driven polyelectrolyte complex coacervation, where the degree of macromolecular charge asymmetry and polymer connectivity are dynamically changing during polymerization. We show that the polymerization-driven LLPS leads to two-stage kinetics in domain growth L(t): At an early stage, an exponential growth L(t) ∼ exp(t) emerges due to polymerization-driven collapse of conjugated polyions; at later stage, the coupling between polymerization and coarsening lead to a single power-law in domain growth with near-linear scaling L(t) ∼ t. Both stages show drastically faster LLPS dynamics in domain growth compared to the classical prediction of L(t) ∼ t^1/3.

The Kremer–Grest (KG) model [Kremer and Grest, J. Chem. Phys. 92(8), 5057–5086 (1990)] laid the groundwork for molecular dynamics (MD) simulations of entangled polymer dynamics and remains the standard approach for investigating both equilibrium and nonequilibrium behavior. However, simulating highly entangled systems with chain lengths exceeding 10 entanglement strands (Ne) in the diffusive regime is still computationally challenging. In this work, we report MD simulations based on a Gaussian soft-core potential to study entangled polymer dynamics over time scales that extend into the diffusive regime, for melts with chain lengths up to N = 2000 ≈ 80Ne. Compared to the classical KG model at the same N, our approach results in a smaller entanglement length Ne and a larger invariant degree of polymerization N̄, while offering significantly improved computational efficiency, enabling it to cover the full time spectrum of entanglement dynamics. The monomer mean-squared displacement, g1(t), exhibits a distinct and robust t1/4 scaling over nearly three decades in time. Notably, for chains with N > 1000, the stress relaxation function G(t) develops a weak, power-law-like quasi-plateau, which is subsequently followed by an exponential decay. For chain lengths up to N = 2000 ≈ 80Ne, both chain diffusion and zero-shear viscosity follow the experimentally observed trends, D ∼ N−2.3 and η ∼ N3.4, respectively, with no clear indication of crossover toward D ∼ N−2.0 or η ∼ N3.0.

Highly-charged intrinsically disordered proteins (IDPs) underpin biomolecular condensate formation through liquid–liquid phase separation, yet the influence of charge sequences on the dynamics within the condensate phase remains poorly understood. Using extensive molecular dynamics simulations with explicit hydrodynamics and electrostatics, we study the dynamics in IDP condensates across different length and time scales, by systematically varying the charge sequences of the constituent IDPs. Contrary to the expectation that long-range interactions are heavily screened in dense semidilute polymer solutions, we find hydrodynamics and electrostatics significantly influence the dynamics in IDP condensates and their effects are strongly coupled to the charge sequence of the constituent IDPs. For condensates of low to intermediate-κ IDPs, where κ is a measure of the charge blockiness of the charge sequence, we find hydrodynamics dominates the dynamics up to the length scale of the chain and beyond. On the sub-chain level, segmental relaxation is highly coupled to intra-chain electrostatic correlations due to local charge patterns, where sections with more charge-balanced blocks have faster relaxation. Furthermore, the viscosity in IDP condensates is significantly length-scale-dependent, with condensates of high-κ IDPs exhibiting large difference between microscopic and macroscopic viscosity. Such length-scale-dependent viscosity may be the key to understanding the experimentally observed extremely fast molecule-level dynamics in biocondensates of highly-charged IDPs. Our findings highlight the intricate relationship between charge sequences, hydrodynamics, and electrostatics in shaping the dynamics in IDP condensates at different length and time scales.

Polyelectrolyte complex coacervation underpins many critical biological processes, yet how different initial mixing protocols determine its liquid-liquid phase separation (LLPS) dynamics remains unclear. Using molecular dynamics simulations, we show that when polycations and polyanions are initially randomly mixed, coacervate domain growth exhibits transient t^1/2 scaling, driven by polymer network formation. This phase is followed by either t¹ scaling due to hydrodynamic pumping or t^1/3 scaling from droplet coarsening, depending on the initial mixing degree. Conversely, starting with spatially separated domains of polycations and polyanions-mimicking LLPS in certain marine organisms-leads to rapid coacervate formation, with early-stage growth following distinct t^2/3 scaling due to strong electrostatic attraction, followed by continued growth via polymer accumulation. Both protocols yield significantly faster dynamics than systems initialized with preformed polyion pairs, which exhibit classical t^1/3 scaling characteristic of droplet coarsening. These findings highlight the profound impact of initial conditions on LLPS dynamics in polyelectrolyte systems.

It is generally assumed that hydrodynamics in dense polyelectrolyte (PE) solutions, such as semidilute PE solutions and PE complex coacervates, is heavily screened and inconsequential. Here, using mesoscale molecular dynamics that explicitly accounts for hydrodynamics, we show that segmental dynamics in the subdiffusive regime show strong signatures of hydrodynamic interactions that persist well beyond the correlation length of semidilute PE solutions with moderately short chains. The strong hydrodynamic effects are also observed in coacervate systems containing moderately short chains, even with PE concentration as high as 30%. Our work fills a gap in the existing simulation literature on dense PE solutions and hints at the importance of hydrodynamics in the transport and rheological properties in broader polymer/polyelectrolyte solution systems.

The functionalities and applications of complex coacervates -- liquid condensates resulting from liquid-liquid phase separation of charged polymers -- are significantly influenced by the dispersion and aggregation states of guest macromolecules. Intriguingly, guest macromolecules exhibit a strong tendency to aggregate within coacervates even in the absence of apparent chemical incompatibility, indicating a universal aggregation mechanism at play in these environments. Using extensive MD simulations, we identify electrostatic depletion -- a strong force arising from electrostatic correlations within the host polyelectrolyte network that drives guest aggregations. Due to electrostatic depletion, neutral polymers, low-charge-density polyelectrolytes, and intrinsically disordered proteins (IDPs) exhibit effective attractions in coacervates, in stark contrast to their behavior in dilute solutions. Unlike traditional depletion effect that requires mismatched length scale and morphology, electrostatic depletion is relevant in fluid systems where solute and solvent are both polymers with comparable size. Our discovery bridges a critical knowledge gap in the molecular physics of densely charged, crowded liquids and holds significant implications for the design of synthetic protocells and advanced drug delivery systems.

In recent years, molecular dynamics (MD) simulations have emerged as an essential tool for understanding the structure, dynamics, and phase behavior of charged soft matter systems. To explore phenomena across greater length and time scales in MD simulations, molecules are often coarse-grained for better computational performance. However, commonly used force fields represent particles as hard-core interaction centers with point charges, which often overemphasizes the packing effect and short-range electrostatics, especially in systems with bulky deformable organic molecules and systems with strong coarse-graining. This underscores the need for an efficient soft-core model to physically capture the effective interactions between coarse-grained particles. To this end, we implement a soft-core model uniting the Gaussian core model with smeared electrostatic interactions that is phenomenologically equivalent to recent theoretical models. We first parametrize it generically using water as the model solvent. Then, we benchmark its performance in the OpenMM toolkit for different boundary conditions to highlight a computational speedup of up to 34 x compared to commonly used force fields and existing implementations. Finally, we demonstrate its utility by investigating how boundary polarizability affects the adsorption behavior of a polyelectrolyte solution on perfectly conducting and nonmetal boundaries.