Bottom-Up Multiscale Approach to Estimate Viscoelastic Properties of Entangled Polymer Melts with High Glass Transition Temperature

A multiscale computational method is presented for the prediction of the viscoelastic properties of entangled homopolymer melts with high glass transition temperatures. Starting from an atomistic model of a polymer, two coarser representations are introduced─a coarse-grained model and a slip-spring representation─which successively operate at longer time and length scales. The three models are unified by renormalizing the time and modulus scales, which is achieved through matching their normalized chain mean squared displacement and stress relaxation modulus, respectively. To facilitate the relaxation of entangled chains, the simulations are performed at temperatures higher than those accessible in experiments. Time–temperature superposition is then applied to extrapolate the viscoelastic properties calculated at high temperatures to experimentally accessible lower temperatures. This proposed approach can predict the linear rheology of the melt starting from an atomistic model and does not require experimental parameters as an input. Here, it is demonstrated for syndiotactic and atactic polystyrene, where good agreement with experimental measurements is observed

Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates: Insights from Molecular Simulations

Electrostatic interactions in polymeric systems are responsible for a wide range of liquid-liquid phase transitions that are of importance for biology and materials science. Such transitions are referred to as complex coacervation, and recent studies have sought to understand the underlying physics and chemistry. Most theoretical and simulation efforts to date have focused on oppositely charged linear polyelectrolytes, which adopt nearly ideal-coil conformations in the condensed phase. However, when one of the coacervate components is a globular protein, a better model of complexation should replace one of the species with a spherical charged particle or colloid. In this work, we perform coarse-grained simulations of colloid-polyelectrolyte coacervation using a spherical model for the colloid. Simulation results indicate that the electroneutral cell of the resulting (hybrid) coacervates consists of a polyelectrolyte layer adsorbed on the colloid. Power laws for the structure and the density of the condensed phase, which are extracted from simulations, are found to be consistent with the adsorption-based scaling theory of coacervation. The coacervates remain amorphous (disordered) at a moderate colloid charge, $Q$, while an intra-coacervate colloidal crystal is formed above a certain threshold, at $Q > Q^{*}$. In the disordered coacervate, if $Q$ is sufficiently low, colloids diffuse as neutral non-sticky nanoparticles in the semidilute polymer solution. For higher $Q$, adsorption is strong and colloids become effectively sticky. Our findings are relevant for the coacervation of polyelectrolytes with proteins, spherical micelles of ionic surfactants, and solid organic or inorganic nanoparticles

Transport coefficient approach for characterizing nonequilibrium dynamics in soft matter

Nonequilibrium states in soft condensed matter require a systematic approach to characterize and model materials, enhancing predictability and applications. Among the tools, X-ray photon correlation spectroscopy (XPCS) provides exceptional temporal and spatial resolution to extract dynamic insight into the properties of the material. However, existing models might overlook intricate details. We introduce an approach for extracting the transport coefficient, denoted as $J(t)$, from the XPCS studies. This coefficient is a fundamental parameter in nonequilibrium statistical mechanics and is crucial for characterizing transport processes within a system. Our method unifies the Green–Kubo formulas associated with various transport coefficients, including gradient flows, particle–particle interactions, friction matrices, and continuous noise. We achieve this by integrating the collective influence of random and systematic forces acting on the particles within the framework of a Markov chain. We initially validated this method using molecular dynamics simulations of a system subjected to changes in temperatures over time. Subsequently, we conducted further verification using experimental systems reported in the literature and known for their complex nonequilibrium characteristics. The results, including the derived $J(t)$ and other relevant physical parameters, align with the previous observations and reveal detailed dynamical information in nonequilibrium states. This approach represents an advancement in XPCS analysis, addressing the growing demand to extract intricate nonequilibrium dynamics. Further, the methods presented are agnostic to the nature of the material system and can be potentially expanded to hard condensed matter systems

Chameleon-like elastomers with molecularly encoded strain-adaptive stiffening and coloration

Active camouflage is widely recognized as a soft-tissue feature, and yet the ability to integrate adaptive coloration and tissuelike mechanical properties into synthetic materials remains elusive. We provide a solution to this problem by uniting these functions in moldable elastomers through the self-assembly of linear-bottlebrush-linear triblock copolymers. Microphase separation of the architecturally distinct blocks results in physically cross-linked networks that display vibrant color, extreme softness, and intense strain stiffening on par with that of skin tissue. Each of these functional properties is regulated by the structure of one macromolecule, without the need for chemical cross-linking or additives. These materials remain stable under conditions characteristic of internal bodily environments and under ambient conditions, neither swelling in bodily fluids nor drying when exposed to air

Computer Simulations of Continuous 3‑D Printing

3-D printing is a revolutionary manufacturing technique which makes it possible to fabricate objects of any shape and size that are hard to reproduce by traditional methods. We develop a coarse-grained molecular dynamics simulation approach to model the continuous liquid interface production (CLIP) 3-D printing technique. This technique utilizes a continuous polymerization and cross-linking of the liquid monomeric precursor by the UV light within a thin layer while pulling the cross-linked polymeric object out of a pool of monomers. Simulations show that the quality of the shape of the 3-D printed objects is determined by a fine interplay between elastic, capillary, and friction forces. Using simulation results, we identify the source of the object shape deformations and develop a set of rules for calibration of the parameters to meet the accuracy requirements. Comparison between different continuous 3-D printing setups shows that proposed modifications of the printing process could improve quality and accuracy of the printed parts

Isotropic-to-Nematic Transition in Salt-Free Polyelectrolyte Coacervates from Coarse-Grained Simulations

Recent interest in complex coacervation between oppositely charged polyelectrolytes (PEs) has been fueled by its relevance to biology in the context of membraneless organelle formation within living cells. For PEs with limited flexibility (such as double-stranded DNA), theoretical treatments and recent experiments have reported the emergence of liquid crystalline order (LCO) within the resulting coacervate phases. In this work, we study the underlying physics of this phenomenon using coarse-grained molecular dynamics simulations of symmetric semiflexible–semiflexible and asymmetric semiflexible–flexible coacervates. By comparing coacervates with the corresponding semidilute solutions of neutral polymers, we demonstrate that the presence of Coulomb interactions in coacervates facilitates orientational ordering, in agreement with theoretical predictions. Quantitative comparisons between our simulations and theory indicate that, for asymmetric nematic coacervates, the strong orientational ordering of stiff polyanions induces a weak ordering of the flexible polycations─an effect that was not anticipated by available theoretical studies. Simulations reveal that, for nematic coacervates, the preferred orientation of the PE chains at the liquid–liquid coacervate–supernatant interface is parallel, and the alignment of semiflexible PEs is homogeneous. The results presented here provide new molecular-level insights into the intra-coacervate LCO and will help motivate further experimental and theoretical activities in this area

Supersoft and Hyperelastic Polymer Networks with Brushlike Strands

Using a combination of the scaling analysis and molecular dynamics simulations, we study relationship between mechanical properties of networks of graft polymers and their molecular architecture. The elastic response of such networks can be described by replacing the brushlike strands with wormlike strands characterized by the effective Kuhn length which is controlled by the degree of polymerization of the side chains <i>n</i>_sc and their grafting density 1/<i>n</i>_g. In the framework of this approach we have established relationships between the network structural shear modulus <i>G</i>, strands extension ratio β, and architectural triplet [<i>n</i>_sc, <i>n</i>_g, <i>n</i>_x], where <i>n</i>_x is the degree of polymerization of the backbone strand between cross-links. Analysis of the simulation data shows that <i>G</i> could increase with β (<i>G</i> ∝ β), which reflects the “golden rule” of elastomers: softer materials are more deformable. However, networks of graft polymers can also break this rule and demonstrate an increase of the modulus <i>G</i> with decreasing extension ratio β such as <i>G</i> ∝ β^–2. This can be achieved by changing the grafting density of the side chains 1/<i>n</i>_g and keeping <i>n</i>_x and <i>n</i>_sc constant. This peculiar mechanical response of graft polymer networks is in agreement with experimental studies of poly­(dimethylsiloxane) graft polymer elastomers

Multiscale rheology model for entangled Nylon 6 melts

A multiscale simulation method is used to calculate the rheological properties of entangled Nylon 6 melts, including the stress relaxation modulus, storage and loss moduli, and the melt viscosity. The three-level multiscale approach includes all-atom, coarse-grained and slip-spring models, each operating at different levels of resolution and encompassing a wide range of length scales and over nine orders of magnitude in time. These models are unified by matching the polymer chain structure and dynamics as well as the stress relaxation, and together predict the rheological master curves at various temperatures using time–temperature superposition. The calculated viscosity agrees reasonably with experiment. The effect of polydispersity on rheology is also studied by simulating a polydisperse melt with chain lengths follow the Schulz-Zimm distribution. Under the same weight-average molecular weight, the polydisperse melt shows faster stress relaxation and lower viscosity compared to the monodisperse melt. For polymers that undergo rapid degradation at elevated temperatures, such as Nylon, the proposed approach offers a useful means to investigate rheology over a wide range of conditions. Importantly, the approach is fully predictive in that calculations of rheology are generated without relying on experimental information, and it therefore offers potential for design of polymeric materials on the basis of purely molecular models

Surface Stress and Surface Tension in Polymeric Networks

Understanding of how surface properties could change upon deformation is of paramount importance for controlling adhesion, friction, and lubrication of soft polymeric materials (i.e., networks and gels). Here, we use a combination of the theoretical calculations and coarse-grained molecular dynamics simulations to study surface stress dependence on deformation in films made of soft and rigid polymeric networks. Simulations have shown that films of polymeric networks could demonstrate surface properties of both polymer melts and elastic solids depending on their deformation. In particular, at small film deformations the film surface stress ϒ is equal to the surface tension obtained at zero film strains, γ₀, and surface properties of networks are similar to those of polymer melts. The surface stress begins to show a strain dependence when the film deformation ratio λ approaches its maximum possible value λ_max corresponding to fully stretched network strands without bond deformations. In the entire film deformation range the normalized surface stress ϒ­(λ)/γ₀ is a universal function of the ratio λ/λ_max. Analysis of the simulation data at large film deformations points out that the significant increase in the surface stress can be ascribed to the onset of the bond deformation. In this deformation regime network films behave as elastic solids

Surface Stresses and a Force Balance at a Contact Line

Results of the coarse-grained molecular dynamics simulations are used to show that the force balance analysis at the triple-phase contact line formed at an elastic substrate has to include a quartet of forces: three surface tensions (surface free energies) and an elastic force per unit length. In the case of the contact line formed by a droplet on an elastic substrate an elastic force is due to substrate deformation generated by formation of the wetting ridge. The magnitude of this force <i>f</i>_el is proportional to the product of the ridge height <i>h</i> and substrate shear modulus <i>G</i>. Similar elastic line force should be included in the force analysis at the triple-phase contact line of a solid particle in contact with an elastic substrate. For this contact problem elastic force obtained from contact angles and surface tensions is a sum of the elastic forces acting from the side of a solid particle and an elastic substrate. By considering only three line forces acting at the triple-phase contact line, one implicitly accounts the bulk stress contribution as a part of the resultant surface stresses. This “contamination” of the surface properties by a bulk contribution could lead to unphysically large values of the surface stresses in soft materials