GCMe: Efficient Implementation of the Gaussian Core Model with Smeared Electrostatic Interactions for Molecular Dynamics Simulations of Soft Matter 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 × 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.

Charge Asymmetry Suppresses Coarsening Dynamics in Polyelectrolyte Complex Coacervation.

Mixing solutions of oppositely charged macromolecules can result in liquid-liquid phase separation into a polymer-rich coacervate phase and a polymer-poor supernatant phase. Here, we show that charge asymmetry in the constituent polymers can slow down the coarsening dynamics, with an apparent growth exponent that deviates from the well-known 1/3 for neutral systems and decreases with increasing degrees of charge asymmetry. Decreasing solvent quality accelerates the coarsening dynamics for asymmetric mixtures but slows down the coarsening dynamics for symmetric mixtures. We rationalize these results by examining the interaction potential between merging droplets.

Using Implicit-Solvent Potentials to Extract Water Contributions to Enthalpy-Entropy Compensation in Biomolecular Associations.

Biomolecular assembly typically exhibits enthalpy-entropy compensation (EEC) behavior whose molecular origin remains a long-standing puzzle. While water restructuring is believed to play an important role in EEC, its contribution to the entropy and enthalpy changes, and how these changes relate to EEC, remains poorly understood. Here, we show that water reorganization entropy/enthalpy can be obtained by exploiting the temperature dependence in effective, implicit-solvent potentials. We find that the different temperature dependencies in the hydrophobic interaction, rooted in water reorganization, result in substantial variations in the entropy/enthalpy change, which are responsible for EEC. For lower-critical-solution-temperature association, water reorganization entropy dominates the free-energy change at the expense of enthalpy; for upper-critical-solution-temperature association, water reorganization enthalpy drives the process at the cost of entropy. Other effects, such as electrostatic interaction and conformation change of the macromolecules, contribute much less to the variations in entropy/enthalpy.

Driving force and pathway in polyelectrolyte complex coacervation.

There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation-polyanion complexation and polyion pair-pair condensation. We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we show that prior to contact, two neutral polyion pairs weakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.

Viscoelastic necking dynamics between attractive microgels.

HYPOTHESIS: Microgels can deform and interpenetrate and display colloid/polymer duality. The effective interaction of microgels in the collapsed state is governed by the interplay of polymer-solvent interfacial tension and bulk elasticity. A connecting neck is shown to mediate microgel interaction, but its temporal evolution has not been addressed. We hypothesize that the necking dynamics of attractive microgels exhibits liquid-like or solid-like behavior over different time and length scales. EXPERIMENTS: We simulate the merging and pinching of attractive microgels with different crosslinking densities in explicit solvent using dissipative particle dynamics. The temporal coalescence dynamics of microgels is investigated and compared with simple liquid and polymeric droplets. We model the neck growth on long time scales using Maxwell model of polymer relaxation and compare the theoretical prediction with simulation data. The mechanical strength of the neck is characterized systematically via simulated pinch-off of microgels by steered molecular dynamics. FINDINGS: We evidence a crossover in the coalescence dynamics reflecting the viscoelastic signature of microgels. In contrast to the common knowledge that viscoelastic materials respond elastically on short time scales, the early expansion of the microgel neck exhibits a linear behavior, similar to the viscous coalescence of liquid droplets. However, the late regime with arrested dynamics resembles sintering of solid particles. Through an analytical model relating microgel dynamics to neck growth, we show that the long-term behavior is governed by stress relaxation of the polymers in the neck region and predict an exponential decay in the rate of growth, which agrees favorably with the simulation. Different from coalescence, the thread thinning in microgel breakup primarily highlights its polymeric characteristics.

Elastocapillary interactions of thermoresponsive microgels across the volume phase transition temperatures.

HYPOTHESIS: Effective interactions of thermoresponsive microgels are known to be influenced by their volume phase transition. These soft colloids behave as repulsive spheres in the swollen state but show strong attraction in the collapsed state. We hypothesize that this transition in microgel interactions is governed by the interplay between surface tension and bulk elasticity. EXPERIMENTS: Using dissipative particle dynamics, we modeled the interactions between two coarse-grained microgel particles having a lower critical solution temperature around 32 °C, which are suspended in an explicit solvent. The potentials of mean force between microgels with different crosslinking densities were systematically characterized in the temperature range of 12-58 °C across the volume phase transition from steered molecular dynamics simulation trajectories. FINDINGS: The detailed dynamics of interaction is uncovered for microgels in different states. The simulations reveal the formation of capillary bridges between collapsed microgels at high temperatures, which contributes to strong attraction at contact. An elastocapillary model based on interface thermodynamics is proposed to describe microgel interactions and accurately predicts simulation data in a wide range of temperatures and overlapping distances. The results provide important physical insights into effective interactions between soft colloids that underpin broad applications of stimuli-responsive microgels.

Nanoparticle assembly modulated by polymer chain conformation in composite materials.

Mixing nanoparticles into a strategically selected polymer matrix yields nanocomposites with well-controlled microstructures and unique properties and functions. The modulation of nanoparticle assembly by polymer chain conformation can play a dominant role in determining nanocomposite structures, yet such a physical mechanism remains largely unexplored. We hypothesize that highly ordered microdomains of rigid linear polymers provide a template for nanoparticle assembly into open fractal structures. We conducted mesoscopic computer simulations and physical experiments to elucidate how polymer chain conformation regulates the dynamic evolution of nanoparticle structures during the drying processing of polymer nanocomposite films. The evaporation of polymer-nanoparticle mixtures with varying chain stiffnesses was simulated using dissipative particle dynamics. The formation of distinguished nanoparticle assemblies as a result of matrix selection was further corroborated by probing nanoparticle aggregation in different polymer nanocomposite coatings. The results show that polymer conformation not only influences the dispersion states of individual particles (dispersed vs. aggregated), but also modulates the morphologies of large-scale assembly (globular vs. fractal). The emergence of nematically ordered polymer clusters when the chain rigidity is increased creates local solvent-rich "voids" that promote anisotropic particle aggregates, which then percolate into open fractal structures upon solvent evaporation. The nanoparticle dynamics also exhibits an intriguing non-monotonic behavior attributed to the transitions between the coupling and decoupling with polymer dynamics. The nanoparticle assembly morphologies obtained in simulations match well with the electron microscopy images taken in physical experiments.

Janus Nanoparticles Enable Entropy-Driven Mixing of Bicomponent Hydrogels.

Mixing incompatible polymers in water to form homogeneous hydrogels possessing both hydrophilic and lipophilic components is challenging due to high enthalpic penalty and negligible entropic gain in total Gibbs free energy. Here we performed dissipative particle dynamics simulations and machine learning to uncover the influence of Janus nanoparticles on immiscible polymer mixtures with high water content and to predict the phase behavior of bicomponent hydrogels. An intriguing transition from kinetically arrested demixing to spontaneous mixing was observed with increasing particle concentration and decreasing particle size. The analysis reveals that the mixing is driven by a significant entropic gain of small nanoparticles being well dispersed in aqueous solvent of high-volume fraction. This finding highlights an entropy-driven mixing mechanism for nanocomposite bicomponent hydrogels. Supervised machine learning algorithms were used to establish a microstructure phase diagram with respect to particle concentration and radius, in which homogeneous, percolated, clustered, and separated phases, as well as corresponding phase boundaries, were clearly identified.

Morphology evolution of Janus dumbbell nanoparticles in seeded emulsion polymerization.

Emulsion polymerization is a versatile approach to produce different polymeric nanoparticle morphologies, which can be useful in a variety of applications. However, the detailed mechanism of the morphology formation is not entirely clear. We study the kinetics of nanoparticle morphology evolution during a seeded emulsion polymerization using both experimental and computational tools. Lightly crosslinked polystyrene seeds were first synthesized using dispersion polymerization. Then the seed particles were swollen in tert-butyl acrylate and styrene monomers, and subsequently polymerized into nanoparticles of dumbbell and multilobe morphologies. It was discovered that both the seed and final particle morphology were affected by the methanol concentration during the seed synthesis. Systematically adjusting the methanol amount will not only yield spherical seed particles of different size, but also dumbbell particles even without the second monomer polymerization. In addition to methanol concentration, morphology can be controlled by crosslinking density. The kinetics studies revealed an interesting transition from multilobe to dumbbell geometries during the secondary polymerization. Based on the results, a nucleation-growth model has been proposed to describe the morphology evolution and verification was offered by computer simulation. The key discovery is that nanoparticle morphology can be kinetically controlled by diffusion of the protrusions on the seed particles. The condition of seed synthesis and crosslinking density will drastically change the seed and final nanoparticle morphology.

Dissipative particle dynamics modeling of hydrogel swelling by osmotic ensemble method.

An osmotic ensemble method for dissipative particle dynamics (DPD) is developed for simulating the swelling behavior of polymer networks in aqueous solvent under constant solvent chemical potential, number of polymer beads, pressure, and temperature conditions. We apply a Langevin piston method to control the pressure of the polymer-solvent mixture. Chemical potential equilibrium is achieved via Monte Carlo insertions and deletions of solvent beads based on the total free energy change of the gel. The osmotic ensemble simulation produces swelling kinetics of hydrogels in excellent agreement with that obtained by previous methods but significantly reduces computational costs. The results show gel swelling as a result of the mechanical balance between osmotic pressure induced by the mixing of the polymer and solvent and elastic force originated from the network deformation. The simulations also elucidate the influence of solvent conditions and network topology on the degree of swelling. The bulk modulus of the model gel is probed at different solvency and its behavior is consistent with the prediction of Flory-Rehner theory. The osmotic ensemble DPD will permit the study of mechanical properties of hydrogels in mesoscale simulations and can be extended to model other complex fluid systems in chemical equilibrium under isothermal-isobaric conditions.