Primitive Path Networks Generated by Annealing and Geometrical Methods: Insights into Differences

Predicting compatibilized polymer blend toughness

Polymer blends can yield superior materials by merging the unique properties of their components. However, these mixtures often phase separate, leading to brittleness. While compatibilizers can toughen these blends, their vast design space makes optimization difficult. Here, we develop a model to predict the toughness of compatibilized glassy polymer mixtures. This theory reveals that compatibilizers increase blend toughness by creating molecular bridges that stitch the interface together. We validate this theory by directly comparing its predictions to extensive molecular dynamics simulations in which we vary polymer incompatibility, chain stiffness, compatibilizer areal density, and blockiness of copolymer compatibilizers. We then parameterize the model using self-consistent field theory and confirm its ability to make predictions for practical applications through comparison with simulations and experiments. These results suggest that the theory can optimize compatibilizer design for industrial glassy polymer blends in silico while providing microscopic insight, allowing for the development of next-generation mixtures.

Synthesis of Mechanically Robust Very High Molecular Weight Polyisoprene Particle Brushes by Atom Transfer Radical Polymerization

Linear polyisoprene (PI) and SiO2-g-PI particle brushes were synthesized by both conventional and activators regenerated by electron transfer (ARGET) atom transfer radical polymerization (ATRP). The morphology and solution state study on the particle brushes by transmission electron microscopy (TEM) and dynamic light scattering (DLS) confirmed the successful grafting of PI ligands on the silica surface. The presence of nanoparticle clusters suggests low grafting density (associated with the limited initiation efficiency of ARGET for PI). Nevertheless, particle brushes with very high molecular weights, Mn > 300,000, were prepared, which significantly improved the dispersion of silica nanoparticles and also contributed to excellent mechanical performance. The reinforcing effects of SiO2 nanofillers and very high molecular weight PI ligands were investigated by dynamic mechanical analysis (DMA) as well as computational simulation for the cured linear PI homopolymer/SiO2-g-PI particle brush bulk films.

Molecular Processes Leading to Shear Banding in Entangled Polymeric Solutions

The temporal and spatial evolution of shear banding during startup and steady-state shear flow was studied for solutions of entangled, linear, monodisperse polyethylene C3000H6002 dissolved in hexadecane and benzene solvents. A high-fidelity coarse-grained dissipative particle dynamics method was developed and evaluated based on previous NEMD simulations of similar solutions. The polymeric contribution to shear stress exhibited a monotonically increasing flow curve with a broad stress plateau at intermediate shear rates. For startup shear flow, transient shear banding was observed at applied shear rates within the steady-state shear stress plateau. Shear bands were generated at strain values where the first normal stress difference exhibited a maximum, with lifetimes persisting for up to several hundred strain units. During the lifetime of the shear bands, an inhomogeneous concentration distribution was evident within the system, with higher polymer concentration in the slow bands at low effective shear rate; i.e., γ˙<τR-1, and vice versa at high shear rate. At low values of applied shear rate, a reverse flow phenomenon was observed in the hexadecane solution, which resulted from elastic recoil of the molecules within the slow band. In all cases, the shear bands dissipated at high strains and the system attained steady-state behavior, with a uniform, linear velocity profile across the simulation cell and a homogeneous concentration.

Molecular Dynamics Simulation of Polymer Nanocomposites with Supramolecular Network Constructed via Functionalized Polymer End-Grafted Nanoparticles

Since the proposal of self-healing materials, numerous researchers have focused on exploring their potential applications in flexible sensors, bionic robots, satellites, etc. However, there have been few studies on the relationship between the morphology of the dynamic crosslink network and the comprehensive properties of self-healing polymer nanocomposites (PNCs). In this study, we designed a series of modified nanoparticles with different sphericity (η) to establish a supramolecular network, which provide the self-healing ability to PNCs. We analyzed the relationship between the morphology of the supramolecular network and the mechanical performance and self-healing behavior. We observed that as η increased, the distribution of the supramolecular network became more uniform in most cases. Examination of the segment dynamics of polymer chains showed that the completeness of the supramolecular network significantly hindered the mobility of polymer matrix chains. The mechanical performance and self-healing behavior of the PNCs showed that the supramolecular network mainly contributed to the mechanical performance, while the self-healing efficiency was dominated by the variation of η. We observed that appropriate grafting density is the proper way to effectively enhance the mechanical and self-healing performance of PNCs. This study provides a unique guideline for designing and fabricating self-healing PNCs with modified Nanoparticles (NPs).

Macroscopic analogue to entangled polymers

The entangled structure of polymeric materials is often described as resembling a bowl of spaghetti, swarms of earthworms, or snakes. These analogies not only illustrate the concept, but form the foundation of polymer physics. However, the similarity between these macroscopic, athermal systems and polymers in terms of topology remains uncertain. To better understand this relationship, we conducted an experiment using X-ray tomography to study the structure of arrays of linear rubber bands. We found that, similar to linear polymers, the average number of entanglements increases linearly with the length of the ribbons. Additionally, we observed that entanglements are less frequent near the surface of the container, where there are also more ends, similar to what has been seen in trapped polymers. These findings provide the first experimental evidence supporting the visualization of polymer structures using macroscopic, athermal analogues, confirming the initial intuitive insights of the pioneers of polymer physics.

Topological Analysis and Recovery of Entanglements in Polymer Melts

The viscous flow of polymer chains in dense melts is dominated by topological constraints whenever the single-chain contour length, N, becomes larger than the characteristic scale N_e, defining comprehensively the macroscopic rheological properties of the highly entangled polymer systems. Even though they are naturally connected to the presence of hard constraints like knots and links within the polymer chains, the difficulty of integrating the rigorous language of mathematical topology with the physics of polymer melts has limited somehow a genuine topological approach to the problem of classifying these constraints and to how they are related to the rheological entanglements. In this work, we tackle this problem by studying the occurrence of knots and links in lattice melts of randomly knotted and randomly concatenated ring polymers with various bending stiffness values. Specifically, by introducing an algorithm that shrinks the chains to their minimal shapes that do not violate topological constraints and by analyzing those in terms of suitable topological invariants, we provide a detailed characterization of the topological properties at the intrachain level (knots) and of links between pairs and triplets of distinct chains. Then, by employing the Z1 algorithm on the minimal conformations to extract the entanglement length N_e, we show that the ratio N/N_e, the number of entanglements per chain, can be remarkably well reconstructed in terms of only two-chain links.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

Microstructural evolution and reverse flow in shear-banding of entangled polymer melts

The temporal and spatial evolution of shear banding under startup of shear flow was simulated for highly entangled, linear, monodisperse polyethylene melts of differing molecular weight, C₇₅₀H₁₅₀₂, C₁₂₀₀H₂₄₀₂, and C₃₀₀₀H₆₀₀₂, using a high-fidelity coarse-grained dissipative particle dynamics method. It was determined that shear stress was dominated by segmental orientation of entangled strands at low shear rates, but at a critical shear rate below the reciprocal of the Rouse time, flow-induced disentanglement resulted in the onset of chain tumbling that reduced the average degree of orientation, leading to a regime of decreasing shear stress, with a commensurate onset of increasing average chain extension imposed by the strong flow kinematics that ultimately drove the steady-state shear stress higher. During startup of shear flow, shear band development began immediately after the maximum in the first normal stress difference, where distinct fast and slow bands formed. The slow bands consisted of relatively entangled and coiled molecules, whereas the fast bands consisted of more disentangled and extended chains that experienced quasiperiodic rotation/retraction cycles. The simulation results often exhibited a generation of temporary reverse flow, in which the local fluid velocity was temporarily opposite to that of the bulk flow direction, at the onset of the shear-banding phenomena; this effect was consistent with earlier experiments and theoretical results. The physical mechanism for the generation of reverse flow during shear-band formation was investigated and found to be related to the recoil of the molecules comprising the slow band. Overall, the phenomenon of shear banding appeared to arise due to flow-induced disentanglement from orientational ordering and segmental stretching that affected individual chains to different degrees, ultimately resulting in regions of relatively coiled and entangled chains that evolved into a slow band, whereas the locally disentangled chains, experiencing quasiperiodic stretch-rotation cycles, formed a fast band. The transitional period resulted in a kinematic instability that generated the temporary reverse-flow phenomenon.

Molecular Dynamics Simulation of Entangled Melts at High Rates: Identifying Entanglement Lockup Mechanism Leading to True Strain Hardening

In the present work, molecular dynamics simulations are carried out based on the bead-spring model to indicate how the entanglement lockup manifests in the late stage of fast Rouse-Weissnberg number (Wi_R >>1) uniaxial melt stretching of entangled polymer melts. At high strains, distinct features show up to reveal the emergence of an increasingly tightened entanglement network. Chain tension can build up, peaking at the middle of the chain, to a level for chain scission, through accumulated interchain interactions, as if there is a tug-of-war ongoing for each load-bearing chain. Thanks to the interchain uncrossability, network junctions form by the pairing of two or more hairpins. It is hypothesized that the interchain entanglement at junctions can lockup through prevailing twist-like interchain couplings as long as Wi_R > 9. In this limit, a significant fraction of chains act like cyclic chains to form a network held by interchain uncrossability, and appreciable chain tension emerges.

Coarse-Grained Molecular Dynamics Simulation of Polycarbonate Deformation: Dependence of Mechanical Performance by the Effect of Spatial Distribution and Topological Constraints

Polycarbonate is an engineering plastic used in a wide range of applications due to its excellent mechanical properties, which are closely related to its molecular structure. We performed coarse-grained molecular dynamics (CGMD) calculations to investigate the effects of topological constraints and spatial distribution on the mechanical performance of a certain range of molecular weights. The topological constraints and spatial distribution are quantified as the number of entanglements per molecule (Ne) and the radius of gyration (Rg), respectively. We successfully modeled molecular structures with a systematic variation of Ne and Rg by controlling two simulation parameters: the temperature profile and Kuhn segment length, respectively. We investigated the effect of Ne and Rg on stress-strain curves in uniaxial tension with fixed transverse strain. The result shows that the structure with a higher radius of gyration or number of entanglements has a higher maximum stress (σm), which is mainly due to a firmly formed entanglement network. Such a configuration minimizes the critical strain (εc). The constitutive relationships between the mechanical properties (σm and εc) and the initial molecular structure parameters (Ne and Rg) are suggested.

Computational Study of Mechanochemical Activation in Nanostructured Triblock Copolymers

Force-driven chemical reactions have emerged as an attractive platform for diverse applications in polymeric materials. However, the microscopic chain conformations and topologies necessary for efficiently transducing macroscopic forces to the molecular scale are not well-understood. In this work, we use a coarse-grained model to investigate the impact of network-like topologies on mechanochemical activation in self-assembled triblock copolymers. We find that mechanochemical activation during tensile deformation depends strongly on both the polymer composition and chain conformation in these materials. Activation primarily occurs in the tie chains connecting different glassy domains and in loop chains that are hooked onto each other by physical entanglements. Activation also requires a higher stress in materials having a higher glassy block content. Overall, the lamellar samples show the highest percent activation at high stress. In contrast, at low stress, the spherical morphology, which has the lowest glassy fraction, shows the highest activation. Additionally, we observe a spatial pattern of activation, which appears to be tied to distortion of the self-assembled morphology. Higher activation is observed in the tips of the chevrons formed during deformation of lamellar samples as well as in the centers between the cylinders in the cylindrical morphology. Our work shows that changes in the network-like topology in different morphologies significantly impact mechanochemical activation efficiencies in these materials, suggesting that this area will be a fruitful avenue for further experimental research.

Entanglement Characteristic Time from Complex Moduli via i-Rheo GT

Tassieri et al. have introduced a novel rheological tool called "i-Rheo GT" that allows the evaluation of the frequency-dependent materials' linear viscoelastic properties from a direct Fourier transform of the time-dependent relaxation modulus G(t), without artifacts. They adopted i-Rheo GT to exploit the information embedded in G(t) derived from molecular dynamics simulations of atomistic and quasi-atomistic models, and they estimated the polymers' entanglement characteristic time (τe) from the crossover point of the moduli at intermediate times, which had never been possible before because of the poor fitting performance, at short time scales, of the commonly used generalized Maxwell models. Here, we highlight that the values of τe reported by Tassieri et al. are significantly different (i.e., an order of magnitude smaller) from those reported in the literature, obtained from either experiments or molecular dynamics simulations of different observables. In this work, we demonstrate that consistent values of τe can be achieved if the initial values of G(t), i.e., those governed by the bond-oscillation dynamics, are discarded. These findings have been corroborated by adopting i-Rheo GT to Fourier transform the outcomes of three different molecular dynamics simulations based on the following three models: a dissipative particle dynamics model, a Kremer-Grest model, and an atomistic polyethylene model. Moreover, we have investigated the variations of τe as function of (i) the 'cadence' at which G(t) is evaluated, (ii) the spring constant of the atomic bone, and (iii) the initial value of the shear relaxation modulus G(O). The ensemble of these results confirms the effectiveness of i-Rheo GT and provide new insights into the interpretation of molecular dynamics simulations for a better understanding of polymer dynamics.

Effect of Slip-Spring Parameters on the Dynamics and Rheology of Soft, Coarse-Grained Polymer Models

Highly coarse-grained (hCG) linear polymer models allow for accessing long time and length scales by dissipative particle dynamics (DPD). This top-down strategy exploits the universal equilibrium behavior of long, flexible macromolecules by accounting only for the relevant interactions, such as molecular connectivity, and by parametrizing their strength via coarse-grained invariants, such as the mean-squared end-to-end distance. The description of the dynamics of long, entangled polymers, however, poses a challenge because (i) the noncrossability of the molecular backbones is not enforced by the soft interactions of an hCG model and (ii) the rheology involves multiple time and length scales, such as the Rouse-like dynamics on short scales and the reptation dynamics on long scales. One popular technique to effectively mimic the effect of entanglements in linear polymer melts via hCG models is slip-springs, and quantitative agreement with simulations that explicitly account for the noncrossability of molecular contours, experiments, and theoretical predictions has been achieved by identifying the time, length, and energy scales of the hCG model and adjusting the number of slip-springs per macromolecule. In the present work, we study how the spatial extent and the mobility of slip-springs affect the dynamics and discuss their implications in the choice of the degree of coarse-graining in computationally efficient hCG models.

Designing high performance polymer nanocomposites by incorporating robustness-controlled polymeric nanoparticles: insights from molecular dynamics

Introducing polymeric nanoparticles into polymer matrices is an interesting topic, and the robustness of the polymeric nanoparticles is crucial for the properties of the polymer nanocomposites (PNCs). In this study, by incorporating star-shaped polymeric nanoparticles (SSPNs) into the polymer, the effect of the sphericity (η) and arm length (L) of the SSPNs on the mechanical properties of PNCs is systematically investigated, using a coarse-grained molecular dynamics simulation. In addition, the linear and spherical nanoparticles (NPs) are compared with SSPNs by fixing the approximate diameter and mass fraction of the NPs. The radial distribution function, the second virial coefficient, mean-squared displacement, bond autocorrelation function, and primitive path analysis are employed to systematically characterize the structure and dynamics of these new PNCs. It is found that the dispersion of the NPs is enhanced with the increase of η, and the entanglement density reaches maximum, which both contribute to the greatest mechanical reinforcing effect. More significantly, it is found that the classical Payne effect, namely the storage as a function of the strain amplitude, decreases remarkably, and with a much smaller loss factor for these SSPN filled polymer nanocomposites, compared to conventional PNCs filled with rigid NPs. Furthermore, the change of the arm length of the SSPNs is found to exhibit the same effect on the mechanical and viscoelastic properties, as the variation of the number of the arms. In general, this work shows that these new SSPN filled polymer nanocomposites can exceed conventional PNCs, by manipulating the robustness of the SSPNs using, for example, the number and length of the arms. This research may provide guidelines for the investigation of the structure-property relationships of the topological structure of polymeric nanoparticles.

Shear Banding in Entangled Polymers: Stress Plateau, Banding Location, and Lever Rule

Using molecular dynamics simulation, we study shear banding of entangled polymer melts under a steady shear. The steady shear stress vs shear rate curve exhibits a plateau spanning nearly two decades of shear rates in which shear banding is observed, and the steady shear stress remains unchanged after switching the shear rates halfway in the range of shear rates within the plateau region. In addition, we find strong correlation in the location of the shear bands between different shear rates starting from the same microstate configurations at equilibrium, which suggests the importance of the inherent structural heterogeneity in the entangled polymer network for shear banding. Furthermore, for the steady shear bands persisting to the longest simulated time of 9.0τ_d0 (disengagement time), the shear rate in the slow band and the relative proportion of the bands do not change very much with the increase of imposed shear rate, but the shear rate in the fast band increases approximately in proportion to the imposed shear rates, in contradiction to the lever rule.

Investigation of Crystallization and Relaxation Effects in Coarse-Grained Polyethylene Systems after Uniaxial Stretching

In this study, we investigate the thermo-mechanical relaxation and crystallization behavior of polyethylene using mesoscale molecular dynamics simulations. Our models specifically mimic constraints that occur in real-life polymer processing: After strong uniaxial stretching of the melt, we quench and release the polymer chains at different loading conditions. These conditions allow for free or hindered shrinkage, respectively. We present the shrinkage and swelling behavior as well as the crystallization kinetics over up to 600 ns simulation time. We are able to precisely evaluate how the interplay of chain length, temperature, local entanglements and orientation of chain segments influences crystallization and relaxation behavior. From our models, we determine the temperature dependent crystallization rate of polyethylene, including crystallization onset temperature.

Heterogeneous Dynamics of Polymer Melts Exerted by Chain Loops Anchored on the Substrate: Insights from Molecular Dynamics Simulation

Understanding polymer-substrate interfacial dynamics at the molecular level is crucial for tailoring the properties of polymer ultrathin films (PUFs). Herein, through coarse-grained molecular dynamics simulation, the effect of length (N_loop) and rigidity (K_loop) of loop chains on the dynamics of linear chains is systematically explored, in which the loop chains are adsorbed on a solid substrate and the linear chains are covered on the loop chains. It is found that there is an optimal K_loop, which strongly confines the motion of the linear chains. Meanwhile, compared to increasing the rigidity of the loop chains, increasing the length of the loop chains can more effectively confine the motion of the linear chains. More interestingly, we observe that the mismatch of the length (ΔN) and rigidity (ΔK) between the loop and linear chains leads to dynamic asymmetry (ΔD_c). The relationship between the ΔN, ΔK, and ΔD_c are found to follow the mathematical expression of ΔD_c ∼ (ΔN)^α(ΔK)^β, in which the values of α and β are around 4.58 and 0.83, separately. Remarkably, using the Gaussian process regression model, we construct a master curve of diffusion coefficient on the segmental and chain length scales of the linear chains as a function of N_loop and K_loop, which is further validated by our simulated prediction. In general, this work provides a fundamental understanding of polymer interfacial dynamics at the molecular level, enlightening some rational principles for manipulating the physical properties of PUFs.

Shear-Thinning in Oligomer Melts-Molecular Origins and Applications

We investigate the molecular origin of shear-thinning in melts of flexible, semiflexible and rigid oligomers with coarse-grained simulations of a sheared melt. Entanglements, alignment, stretching and tumbling modes or suppression of the latter all contribute to understanding how macroscopic flow properties emerge from the molecular level. In particular, we identify the rise and decline of entanglements with increasing chain stiffness as the major cause for the non-monotonic behaviour of the viscosity in equilibrium and at low shear rates, even for rather small oligomeric systems. At higher shear rates, chains align and disentangle, contributing to shear-thinning. By performing simulations of single chains in shear flow, we identify which of these phenomena are of collective nature and arise through interchain interactions and which are already present in dilute systems. Building upon these microscopic simulations, we identify by means of the Irving-Kirkwood formula the corresponding macroscopic stress tensor for a non-Newtonian polymer fluid. Shear-thinning effects in oligomer melts are also demonstrated by macroscopic simulations of channel flows. The latter have been obtained by the discontinuous Galerkin method approximating macroscopic polymer flows. Our study confirms the influence of microscopic details in the molecular structure of short polymers such as chain flexibility on macroscopic polymer flows.

Supersonic Impact Response of Polymer Thin Films via Large-Scale Atomistic Simulations

Recent nanoscale ballistic tests have shown the applicability of nanomaterials for ballistic protection but have raised questions regarding the nanoscale structure-property relationships that contribute to the ballistic response. Herein, we report on multimillion-atom reactive molecular dynamics simulations of the supersonic impact, penetration, and failure of polyethylene (PE) and polystyrene (PS) ultrathin films. The simulated specific penetration energy (E_p*) versus impact velocity predicts to within 15% the experimentally determined E_p* for PS. For impact velocities less than 1 km s^-1, a crazing/petalling failure mode is observed due to chain disentanglement, transitioning to fragmentation coupled with large amounts of adiabatic heating at velocities greater than 1 km s^-1. Interestingly, the high entanglement density of PE provides enhanced penetration resistance at low velocities, whereas increased adiabatic heating in PS promotes greater penetration resistance at elevated velocities. By understanding nanoscale mechanisms of energy absorption, nanomaterials can be designed to provide superior penetration resistance.

Viscoelastic properties of wheat gluten in a molecular dynamics study

Wheat (Triticum spp.) gluten consists mainly of intrinsincally disordered storage proteins (glutenins and gliadins) that can form megadalton-sized networks. These networks are responsible for the unique viscoelastic properties of wheat dough and affect the quality of bread. These properties have not yet been studied by molecular level simulations. Here, we use a newly developed α-C-based coarse-grained model to study ∼ 4000-residue systems. The corresponding time-dependent properties are studied through shear and axial deformations. We measure the response force to the deformation, the number of entanglements and cavities, the mobility of residues, the number of the inter-chain bonds, etc. Glutenins are shown to influence the mechanics of gluten much more than gliadins. Our simulations are consistent with the existing ideas about gluten elasticity and emphasize the role of entanglements and hydrogen bonding. We also demonstrate that the storage proteins in maize and rice lead to weaker elasticity which points to the unique properties of wheat gluten.

During the breadmaking process, expanding gas bubbles cause the dough to increase volume. Gluten proteins act as an elastic scaffold in that process, allowing the wheat dough to grow more than other kinds of dough. Thus, explaining the unique viscoelastic properties of gluten at the molecular level may be of great interest to the baking industry. Assessing the structural properties of gluten is difficult because its proteins are disordered. We provide the first molecular dynamics model of gluten elasticity, that is able to distinguish gluten and proteins from different plants, like maize and rice. Our model shows the structural changes the gluten proteins undergo during their deformation, which mimics the mixing of dough during kneading. It also allows for a determination of the force required to extend gluten proteins, as during baking. The data confirms existing theories about gluten, but it also provides molecular-level information about the extraordinary elasticity of gluten.

Thermodynamically consistent incorporation of entanglement spatial fluctuations in the slip-link model

We evaluate the thermodynamic consistency of the anisotropic mobile slip-link model for entangled flexible polymers. The level of description is that of a single chain, whose interactions with other chains are coarse grained to discrete entanglements. The dynamics of the model consist of the motion of entanglements through space and of the chain through the entanglements, as well as the creation and destruction of entanglements, which are implemented in a mean-field way. Entanglements are modeled as discrete slip links, whose spatial positions are confined by quadratic potentials. The confinement potentials move with the macroscopic velocity field, hence the entanglements fluctuate around purely affine motion. We allow for anisotropy of these fluctuations, described by a set of shape tensors. By casting the model in the form of the general equation for the nonequilibrium reversible-irreversible coupling from nonequilibrium thermodynamics, we show that (i) since the confinement potentials contribute to the chain free energy, they must also contribute to the stress tensor, (ii) these stress contributions are of two kinds: one related to the virtual springs connecting the slip links to the centers of the confinement potentials and the other related to the shape tensors, and (iii) these two kinds of stress contributions cancel each other if the confinement potentials become anisotropic in flow, according to a lower-convected evolution of the confinement strength or, equivalently, an upper-convected evolution of the shape tensors of the entanglement spatial fluctuations. In previous publications, we have shown that this cancellation is necessary for the model to obey the stress-optical rule and the Green-Kubo relation, and simultaneously to agree with plateau modulus predictions of multichain models and simulations.

Crystallization of semiflexible polymers in melts and solutions

We studied the crystallization of semiflexible polymer chains in melts and poor-solvent solutions with different concentrations using dissipative particle dynamics (DPD) computer simulation techniques. We used the coarse-grained polymer model to reveal the general principles and microscopic scenario of crystallization in such systems at large time and length scales. It covers both primary and secondary nucleation as well as crystallites' merging. The parameters of the DPD model were chosen appropriately to reproduce the entanglements of polymer chains. We started from an initial homogeneous disordered solution of Gaussian chains and observed the initial stages of crystallization process caused in our model by orientational ordering of polymer chains and polymer-solvent phase separation. We found that the overall crystalline fraction at the end of the crystallization process decreases with the increasing polymer volume fraction while the steady-state crystallization speed at later stages does not depend on the polymer volume fraction. The average crystallite size has a maximal value in the systems with a polymer volume fraction from 0.7 to 0.95. In our model, these polymer concentrations represent an optimal value in the sense of balance between the amount of polymer material available to increase the crystallite size and chain entanglements, that prevent crystallites' growth and merging. On large time scales, our model allows us to observe lamellar thickening linear in logarithmic time scale.

Interaction of high-intensity focused ultrasound with polymers at the atomistic scale

Experiments show that high-intensity focused ultrasound (HIFU) is a promising stimulus with multiple superior and unique capabilities to induce localized heating and achieve temporal and spatial thermal effects in the polymers, noninvasively. When polymers are subjected to HIFU, they heat up differently compared to the case they are subjected to heat sources directly; however, the origins of this difference are still entirely unknown. We hypothesize that the difference in the macroscale response of polymers subjected to HIFU strongly depends on the polymer chains, composition, and structure, i.e. being crystalline or amorphous. In this work, this hypothesis is investigated by molecular dynamics studies at the atomistic level and verified by experiments at the macroscopic scale. The results show that the viscoelasticity, measured by stress-strain phase lag, the reptation motion of the chains, and the vibration-induced local mobility quantified by the root mean square fluctuation contribute to the observed difference in the HIFU-induced thermal effects. This unravels the unknown mechanisms behind stimulating the polymers by HIFU, and paves the way in front of using this method in future applications.

Combination of Hybrid Particle-Field Molecular Dynamics and Slip-Springs for the Efficient Simulation of Coarse-Grained Polymer Models: Static and Dynamic Properties of Polystyrene Melts

A quantitative prediction of polymer-entangled dynamics based on molecular simulation is a grand challenge in contemporary computational material science. The drastic increase of relaxation time and viscosity in high-molecular-weight polymeric fluids essentially limits the usage of classic molecular dynamics simulation. Here, we demonstrate a systematic coarse-graining approach for modeling entangled polymers under the slip-spring particle-field scheme. Specifically, a frequency-controlled slip-spring model, a hybrid particle-field model, and a coarse-grained model of polystyrene melts are combined into a hybrid simulation technique. Via a rigorous parameterization strategy to determine the parameters in slip-springs from existing experimental or simulation data, we show that the reptation behavior is clearly observed in multiple characteristics of polymer dynamics, mean-square displacements, diffusion coefficients, reorientational relaxation, and Rouse mode analysis, consistent with the predictions of the tube theory. All dynamical properties of the slip-spring particle-field models are in good agreement with classic molecular dynamics models. Our work provides an efficient and practical approach to establish chemical-specific coarse-grained models for predicting polymer-entangled dynamics.

Prediction of crossover in the molecular weight dependence of polyethylene viscosity using a polymer free volume theory

Based upon the Doolittle concept that viscosity and free volume are inversely related, we used the Boltzmann equation along with a polymer free volume theory to calculate the viscosity (η) of polyethylene with three different molecular structures - linear, ring and four-arm symmetrical star - over a molecular weight (M) range of 420-14 000 g mol-1. Free volume parameters were estimated using the Polymer Reference Interaction Site Model (PRISM) and generic van der Waals (GvdW) equation. The polymer free volume theory was able to describe the crossovers in the molecular weight dependence of the viscosity of the aforementioned molecular structures. In particular, the crossover for the linear structure was predicted at about 3000 g mole-1 with η ∼ M1.5 in the unentangled regime and η ∼ M3.3 in the entangled regime that agree reasonably well with experiment. The predictions for the other two structures also agree with the available simulation data. We also demonstrated that the accuracy of the viscosity prediction was sensitive to the difference between two free volume parameters (i.e., (φ+ - F)). Here, F signifies the probability of a bead finding free volume greater than the critical free volume while the fraction of such beads (φ+) can be used to calculate the activation energy. The theory also reproduced the temperature dependence of η for the linear structure at different M, giving apparent activation energy (Eappa) values in the range of 5.30-7.70 kcal mole-1 that are in good agreement with experimental values of 5.50-6.75 kcal mole-1. This work demonstrates for the first time that viscosity of polymer melts can be determined from the polymer free volume theory.

Effects of chain length and polydispersity on shear banding in simple shear flow of polymeric melts

The characteristics of shear banding were investigated in entangled, polydisperse, linear polymer melts under steady-state and startup conditions of simple shear flow. This virtual experimentation was conducted using course-grained nonequilibrium dissipative particle dynamics simulations expressed in terms of a force-field representation that faithfully models the atomistic system dynamics. We examined melts with two mean molecular bead numbers of Nn = 2 50 and 400 and polydispersity indexes of 1.0, 1.025, and 1.05. The wide range of relaxation timescales in the polydisperse melts decreased the nonmonotonic character of the steady-state shear stress vs. shear rate profile compared to a monodisperse linear melt. The polydispersity level required to observe a stress plateau in the shear stress profile at intermediate shear rates was correlated with the nominal entanglement density. Startup of shear flow simulations revealed the development of spatial inhomogeneities and dynamic instabilities in polydisperse fluids containing both monotonic and nonmonotonic shear stress flow curves. Although the shape and duration of instabilities were found to be correlated with the monotonicity of the shear stress profile, the onset and underlying mechanism leading to the formation of shear bands were generally universal. The simulations revealed that perturbations arose soon after the occurrence of a large stress overshoot under startup conditions, and that banded structures stemmed from local reorientation and subsequent deconstruction of the entanglement network. Furthermore, data indicated that the inception of strain localization occurred at shear rates near the reciprocal of the Rouse characteristic timescale, [small gamma, Greek, dot above] > τR-1. Transient shear banding was observed in shorter chain melts undergoing startup of shear flow in which instabilities arose after the appearance of a stress overshoot. These instabilities eventually decayed, but only long after the stresses had attained their steady-state values. The longer chain melt exhibited a shear band structure that remained indefinitely after the stresses had attained steady state.

On the diffusivity of ring polymers

A free volume theory of linear polyethylene (PE) melts [Soft Matter, 2019, 15, 9300-9309] was used to describe the crossover in the size dependence of the center-of-mass diffusion coefficients of ring PE melts from Dcm ∼ N-1.03±0.15 to Dcm ∼ N-1.88±0.14 at Nc ≈ 100. Parameters in the theory were determined theoretically by either the polymer reference interaction site model (PRISM) theory or molecular dynamics (MD) simulation data. The former method is computationally less expensive, whereas the latter gives more accurate results in calculating the temperature dependence of Dcm as different intermolecular and intramolecular potentials were explicitly included in the equation of motion. Both approaches were able to describe the dynamics below and above the crossover in the size dependence of Dcm.

Performance of Coarse Graining in Estimating Polymer Properties: Comparison with the Atomistic Model

Combining atomistic and coarse-grained (CG) models is a promising approach for quantitative prediction of polymer properties. However, the gaps between the length and time scales of atomistic and CG models still need to be bridged. Here, the scale gaps of the atomistic model of polyethylene melts, the bead–spring Kremer–Grest model, and dissipative particle dynamics with the slip-spring model were investigated. A single set of spatial and temporal scaling factors was determined between the atomistic model and each CG model. The results of the CG models were rescaled using the set of scaling factors and compared with those of the atomistic model. For each polymer property, a threshold value indicating the onset of static or dynamic universality of polymers was obtained. The scaling factors also revealed the computational efficiency of each CG model with respect to the atomistic model. The performance of the CG models of polymers was systematically evaluated in terms of both the accuracy and computational efficiency.

Protein droplets in systems of disordered homopeptides and the amyloid glass phase

We study phase diagrams and liquid droplet formation for systems of polyglutamine and polyalanine chains in a coarse-grained model.

An unexpected N-dependence in the viscosity reduction in all-polymer nanocomposite

Adding small nanoparticles (NPs) into polymer melt can lead to a non-Einstein-like decrease in viscosity. However, the underlying mechanism remains a long-standing unsolved puzzle. Here, for an all-polymer nanocomposite formed by linear polystyrene (PS) chains and PS single-chain nanoparticles (SCNPs), we perform large-scale molecular dynamics simulations and experimental rheology measurements. We show that with a fixed (small) loading of the SCNP, viscosity reduction (VR) effect can be largely amplified with an increase in matrix chain length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document}N, and that the system with longer polymer chains will have a larger VR. We demonstrate that such \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document}N-dependent VR can be attributed to the friction reduction experienced by polymer segment blobs which have similar size and interact directly with these SCNPs. A theoretical model is proposed based on the tube model. We demonstrate that it can well describe the friction reduction experienced by melt polymers and the VR effect in these composite systems.

Addition of small nanoparticles into polymer melt can lead to decrease in viscosity but the underlying mechanism for such viscosity reduction remains unclear. Here, the authors investigate the reduction in viscosity by large-scale molecular dynamics simulation and experimental rheology measurements for an all-polymer nanocomposite formed by linear polystyrene chains and PS single-chain nanoparticle.

Brush-Like Polymers and Entanglements: From Linear Chains to Filaments

Dynamics of melts and solutions of high molecular weight polymers and biopolymers is controlled by topological constraints (entanglements) imposing a sliding chain motion along an effective confining tube. For linear chains, the tube size is determined by universal packing number P_e, the number of polymer strands within a confining tube that is required for chains to entangle. Here we show that in melts of brush-like (graft) polymers, consisting of linear chain backbones with grafted side chains, P_e is not a universal number and depends on the molecular architecture. In particular, we use coarse-grained molecular dynamics simulations to demonstrate that the packing number is a nonmonotonic function of the ratio R_nsc/R_ng of the size of the side chains R_nsc to that of the backbone spacer between neighboring grafting points R_ng. This parameter characterizes the degree of mutual interpenetration between side chains of the same macromolecule. We show that P_e of brush-like polymers first decreases with increasing side chain grafting density in the dilute side chain regime (R_nsc < R_ng), then begins to increase in the regime of overlapping side chains (R_nsc > R_ng), approaching the value for linear chains in the limit of densely grafted side chains. This dependence of the packing number reflects a crossover from chain-like entanglements in systems with loosely grafted side chains (comb-like polymers) to entanglements between flexible filaments (bottlebrush-like polymers). Our simulation results are in agreement with the experimental data for the dependence of a plateau modulus on the molecular architecture of graft poly(n-butyl acrylates) and poly(norbornene)-graft-poly(lactide) melts.

Clustering of Entanglement Points in Highly Strained Polymer Melts

Polymer melts undergoing large deformation by elongation are studied by molecular dynamics simulations of bead-spring chains in melts. By applying a primitive path analysis to strongly deformed polymer melts, the role of topological constraints in highly entangled polymer melts is investigated and quantified. We show that the overall, large scale conformations of the primitive paths (PPs) of stretched chains follow affine deformation while the number and the distribution of entanglement points along the PPs do not. Right after deformation, PPs of chains retract in both directions parallel and perpendicular to the elongation. Upon further relaxation we observe a long-lived clustering of entanglement points. Together with the delayed relaxation time this leads to a metastable inhomogeneous distribution of topological constraints in the melts.