Dynamics and Rheology of Polymer Melts via Hierarchical Atomistic, Coarse-Grained, and Slip-Spring Simulations

Salt Effects on the Mechanical Properties of Ionic Conductive Polymer: A Molecular Dynamics Study

Functional polymers can be used as electrolyte and binder materials in solid-state batteries. This often requires performance targets in terms of both the transport and mechanical properties. In this work, a model ionic conductive polymer system, i.e., poly(ethylene oxide)-LiTFSI, was used to study the impact of salt concentrations on mechanical properties, including different types of elastic moduli and the viscoelasticity with both nonequilibrium and equilibrium molecular dynamics simulations. We found an encouragingly good agreement between experiments and simulations regarding Young's modulus, bulk modulus, and viscosity. In addition, we identified an intermediate salt concentration at which the system shows high ionic conductivity, high Young's modulus, and short elastic restoration time. Therefore, this study laid the groundwork for investigating ionic conductive polymer binders with self-healing functionality from molecular dynamics simulations.

Resolving the dynamic properties of entangled linear polymers in non-equilibrium coarse grain simulation with a priori scaling factors

The molecular weight of polymers can influence the material properties, but the molecular weight at the experiment level sometimes can be a huge burden for property prediction with full-atomic simulations. The traditional bottom-up coarse grain (CG) simulation can reduce the computation cost. However, the dynamic properties predicted by the CG simulation can deviate from the full-atomic simulation result. Usually, in CG simulations, the diffusion is faster and the viscosity and modulus are much lower. The fast dynamics in CG are usually solved by a posteriori scaling on time, temperature, or potential modifications, which usually have poor transferability to other non-fitted physical properties because of a lack of fundamental physics. In this work, a priori scaling factors were calculated by the loss of degrees of freedom and implemented in the iterative Boltzmann inversion. According to the simulation results on 3 different CG levels at different temperatures and loading rates, such a priori scaling factors can help in reproducing some dynamic properties of polycaprolactone in CG simulation more accurately, such as heat capacity, Young's modulus, and viscosity, while maintaining the accuracy in the structural distribution prediction. The transferability of entropy-enthalpy compensation and a dissipative particle dynamics thermostat is also presented for comparison. The proposed method reveals the huge potential for developing customized CG thermostats and offers a simple way to rebuild multiphysics CG models for polymers with good transferability.

Impact of Molecular-level Structural Disruption on Relaxation Dynamics of Polymers with End-on and Side-on Liquid Crystal Moieties

In side-chain liquid crystal polymers (SCLCPs), short side chains are attached on a flexible polymer backbone, and each side chain can have a liquid crystal (LC) group attached at the final bead in either an end-on or a side-on configuration. SCLCPs with random sequences of end-on and side-on LC moieties exhibit nonmonotonic thermal behavior as a function of composition, with some mixed sequences having a lower isotropic to LC phase transition than either purely end-on or side-on configurations. The origin of this nonmonotonic thermal trend lies in the disruption of molecular-level positional ordering and alignment due to the different preferred types of ordering of the different LC attachment types. We compare coarse-grained molecular dynamics (MD) simulations and experiments on SCLCP systems with only one type of LC moiety and demonstrate qualitative agreement in the observed mesophases of end-on and side-on SCLCP systems. Specifically, end-on SCLCPs display a smectic B-like mesophase, with layers of polymer between LC layers, while side-on SCLCPs exhibit a quasi-hexagonal columnar structure of polymer and a nematic surrounding the LC mesophase. Detailed analysis of SCLCP systems with various compositions of these types of LC attachments via MD reveals structural disruption in systems with intermediate compositions. Simulation snapshots and anisotropy ratio measurements show how random SCLCP systems deviate from the expected behavior of prolate or oblate systems in terms of their conformation. This molecular disruption in random SCLCP systems, particularly with a high composition of side-on LC moieties, also significantly impacts the relaxation dynamics. Modifying the composition of the LC type of attachment (molecular structure) is a possible route to tuning both the phase behavior and mechanical response of these systems.

Entanglements via Slip Springs with Soft, Coarse-Grained Models for Systems Having Explicit Liquid-Vapor Interfaces

Recent advances in nano-rheology require that new techniques and models be developed to precisely describe the equilibrium and non-equilibrium characteristics of entangled polymeric materials and their interfaces at a molecular level. In this study, a slip-spring (SLSP) model is proposed to capture the dynamics of entangled polymers at interfaces, including those between liquids, liquids and vapors, and liquids and solids. The SLSP model employs a highly coarse-grained approach, which allows for comprehensive simulations of entire nano-rheological characterization systems using a particle-level description. The model relies on many-body dissipative particle dynamics (MDPD) non-bonded interactions, which permit explicit description of liquid-vapor interfaces; a compensating potential is introduced to ensure an unbiased representation of the shape of the liquid-vapor interface within the SLSP model. The usefulness of the proposed MDPD + SLSP approach is illustrated by simulating a capillary breakup rheometer (CaBR) experiment, in which a liquid droplet splits into two segments under the influence of capillary forces. We find that the predictions of the MDPD + SLSP model are consistent with experimental measurements and theoretical predictions. The proposed model is also verified by comparison to the results of explicit molecular dynamics simulations of an entangled polymer melt using a Kremer-Grest chain representation, both at equilibrium and far from equilibrium. Taken together, the model and methods presented in this study provide a reliable framework for molecular-level interpretation of high-polymer dynamics in the presence of interfaces.

Comparison of Friction Parametrization from Dynamics and Material Properties for a Coarse-Grained Polymer Melt

In this work, we extend an approach to coarse-grained (CG) modeling for polymer melts in which the conservative potential is parametrized using the iterative Boltzmann inversion (IBI) method and the accelerated dynamics inherent to IBI are corrected using the dissipative Langevin thermostat with a single tunable friction parameter (J. Chem. Phys. 2021, 154, 084114). Diffusive measures from picoseconds to nanoseconds are used to determine the Langevin friction factor to apply to the CG model to recover all-atom (AA) dynamics; the resulting friction factors are then compared for consistency. Here, we additionally parametrize the CG dynamics using a material property, the zero-shear viscosity, which we measure using the Green-Kubo (GK) method. Two materials are studied, squalane as a function of temperature and the same polystyrene oligomers previously studied as a function of chain length. For squalane, the friction derived from the long-time diffusive measures and the viscosity all strongly increase with decreasing temperature, showing an Arrhenius-like dependence, and remain consistent with each other over the entire temperature range. In contrast, the friction required for the picosecond diffusive measurement, the Debye-Waller factor, is somewhat lower than the friction from long-time measures and relatively insensitive to temperature. A time-dependent friction would be required to exactly reproduce the AA measurements during the caging transition connecting these two extremes over the entire timespan at this level of coarse-graining. For the polystyrene oligomers for which we previously characterized the diffusive friction, the viscosity-parametrized frictions are consistent with the diffusive measures for the smallest chain length. However, for the longer chains, we find different trends based on measurement method with friction derived from rotational diffusion remaining nearly constant, friction derived from translational diffusion showing a modestly increasing trend, and viscosity-derived friction showing a modest decreasing trend. This seems to indicate that there is some sensitivity of the friction measurement method for systems with increased relaxation times and that in particular, the unsteady dynamics of the individual parametrization schemes plays a role in this. Increased difficulty in applying the GK method with increasing relaxation time of the longer chain systems is also discussed. Overall, we find that when the material is in a high-temperature melt state and the viscosity measurement is reliable, the friction parametrization from the diffusive friction measures is consistent and the lower cost diffusive parametrization is a reliable means for modeling viscosity. Our data give insight into the time-dependent friction one might compute using a non-Markovian approach to enable the recovery of AA dynamics over a wider range of time scales than can be computed using a single friction.

Open Macromolecular Genome: Generative Design of Synthetically Accessible Polymers

A grand challenge in polymer science lies in the predictive design of new polymeric materials with targeted functionality. However, de novo design of functional polymers is challenging due to the vast chemical space and an incomplete understanding of structure-property relations. Recent advances in deep generative modeling have facilitated the efficient exploration of molecular design space, but data sparsity in polymer science is a major obstacle hindering progress. In this work, we introduce a vast polymer database known as the Open Macromolecular Genome (OMG), which contains synthesizable polymer chemistries compatible with known polymerization reactions and commercially available reactants selected for synthetic feasibility. The OMG is used in concert with a synthetically aware generative model known as Molecule Chef to identify property-optimized constitutional repeating units, constituent reactants, and reaction pathways of polymers, thereby advancing polymer design into the realm of synthetic relevance. As a proof-of-principle demonstration, we show that polymers with targeted octanol-water solubilities are readily generated together with monomer reactant building blocks and associated polymerization reactions. Suggested reactants are further integrated with Reaxys polymerization data to provide hypothetical reaction conditions (e.g., temperature, catalysts, and solvents). Broadly, the OMG is a polymer design approach capable of enabling data-intensive generative models for synthetic polymer design. Overall, this work represents a significant advance, enabling the property targeted design of synthetic polymers subject to practical synthetic constraints.

Correlations of tensor field components in isotropic systems with an application to stress correlations in elastic bodies

Correlation functions of components of second-order tensor fields in isotropic systems can be reduced to an isotropic fourth-order tensor field characterized by a few invariant correlation functions (ICFs). It is emphasized that components of this field depend in general on the coordinates of the field vector variable and thus on the orientation of the coordinate system. These angular dependencies are distinct from those of ordinary anisotropic systems. As a simple example of the procedure to obtain the ICFs we discuss correlations of time-averaged stresses in isotropic glasses where only one ICF in reciprocal space becomes a finite constant e for large sampling times and small wave vectors. It is shown that e is set by the typical size of the frozen-in stress components normal to the wave vectors, i.e., it is caused by the symmetry breaking of the stress for each independent configuration. Using the presented general mathematical formalism for isotropic tensor fields this finding explains in turn the observed long-range stress correlations in real space. Under additional but rather general assumptions e is shown to be given by a thermodynamic quantity, the equilibrium Young modulus E. We thus relate for certain isotropic amorphous bodies the existence of finite Young or shear moduli to the symmetry breaking of a stress component in reciprocal space.

Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution

The transient elongational viscosity ηe(t) of the polymer melt is known to exhibit strain hardening, which depends on the strain rate ε˙. This phenomenon was elucidated by the difference of chain stretching in the entanglement network between extension and shear. However, to date, the microscopic evolution of polymer melt has not been fully statistically analyzed. In this work, the radial size distributions P(Rg,t) of linear polymers are explored by dissipative particle dynamics during the stretching processes. In uniaxial extensional flow, it is observed that the mean radius of gyration R¯g(t) and standard deviation σ(t) remain unchanged until the onset of strain hardening, corresponding to linear viscoelasticity. Both R¯g and σ rise rapidly in the non-linear regime, and bimodal size distribution can emerge. Moreover, the onset of strain hardening is found to be insensitive to the Hencky strain (ε˙Ht) and chain length (N).

Simulating Stress-Strain Behavior by Using Individual Chains: Uniaxial Deformation of Amorphous Cis- and Trans-1,4-Polybutadiene

This work develops a probability-based numerical method for quantifying mechanical properties of non-Gaussian chains subject to uniaxial deformation, with the intention of being able to incorporate polymer-polymer and polymer-filler interactions. The numerical method arises from a probabilistic approach for evaluating the elastic free energy change of chain end-to-end vectors under deformation. The elastic free energy change, force, and stress computed by applying the numerical method to uniaxial deformation of an ensemble of Gaussian chains were in excellent agreement with analytical solutions that were obtained with a Gaussian chain model. Next, the method was applied to configurations of cis- and trans-1,4-polybutadiene chains of various molecular weights that were generated under unperturbed conditions over a range of temperatures with a Rotational Isomeric State (RIS) approach in previous work (Polymer2015, 62, 129-138). Forces and stresses increased with deformation, and further dependences on chain molecular weight and temperature were confirmed. Compression forces normal to the imposed deformation were much larger than tension forces on chains. Smaller molecular weight chains represent the equivalent of a much more tightly cross-linked network, resulting in greater moduli than larger chains. Young's moduli computed from the coarse-grained numerical model were in good agreement with experimental results.

Hairy Gels: A Computational Study

We present results of MD and MC simulations of the equilibrium properties of swelling gels with comb-like or bottlebrush subchains and compare them to scaling-theory predictions. In accordance with theory, the simulation results demonstrate that swelling coefficient of the gel increases as a function of the polymerization degree of the main chains and exhibits a very weak maximum (or is virtually constant) as a function of the polymerization degree and grafting density of side chains. The bulk osmotic modulus passes through a shallow minimum as the polymerization degree of the side chains increases. This minimum is attributed to the onset of overlap of side chains belonging to different bottlebrush strands in the swollen gel.

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.

Deep convolutional neural networks for generating atomistic configurations of multi-component macromolecules from coarse-grained models

Despite the modern advances in the available computational resources, the length and time scales of the physical systems that can be studied in full atomic detail, via molecular simulations, are still limited. To overcome such limitations, coarse-grained (CG) models have been developed to reduce the dimensionality of the physical system under study. However, to study such systems at the atomic level, it is necessary to re-introduce the atomistic details into the CG description. Such an ill-posed mathematical problem is typically treated via numerical algorithms, which need to balance accuracy, efficiency, and general applicability. Here, we introduce an efficient and versatile method for backmapping multi-component CG macromolecules of arbitrary microstructures. By utilizing deep learning algorithms, we train a convolutional neural network to learn structural correlations between polymer configurations at the atomistic and their corresponding CG descriptions, obtained from atomistic simulations. The trained model is then utilized to get predictions of atomistic structures from input CG configurations. As an illustrative example, we apply the convolutional neural network to polybutadiene copolymers of various microstructures, in which each monomer microstructure (i.e., cis-1,4, trans-1,4, and vinyl-1,2) is represented as a different CG particle type. The proposed methodology is transferable over molecular weight and various microstructures. Moreover, starting from a specific single CG configuration with a given microstructure, we show that by modifying its chemistry (i.e., CG particle types), we are able to obtain a set of well equilibrated polymer configurations of different microstructures (chemistry) than the one of the original CG configuration.

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.

Molecular simulations and hydrodynamic theory of nonlocal shear stresscorrelations in supercooled fluids

A supercooled fluid close to the glass transition develops nonlocal shear stress correlations that anticipate the emergence of elasticity. We performed molecular dynamics simulations of a binary Lennard-Jones mixture at different temperatures and investigated the spatiotemporal autocorrelation function of the shear stressfor different wavevectors, q, from a locally measured and Fourier-transformed stress tensor. Anisotropic correlations are observed at non-zero wavevectors, exhibiting strongly damped oscillations with a characteristic frequency ω(q). A comparison with a recently developed hydrodynamic theory [Maier et al., Phys. Rev. Lett. 119, 265701 (2017)] shows a remarkably good quantitative agreement between the particle-based simulations and the theoretical predictions.

Slip-Spring Hybrid Particle-Field Molecular Dynamics for Coarse-Graining Branched Polymer Melts: Polystyrene Melts as an Example

The topology of chains significantly modifies the dynamical properties of polymer melts. Here, we extend a recently developed efficient simulation method, namely the slip-spring hybrid particle-field (SS-hPF) model, to study the structural and dynamical properties of branched polymer melts over large spatial-temporal scales. In the coarse-grained SS-hPF simulation of polymers, the bonded potentials are derived by iterative Boltzmann inversion from the underlying fine-grained model. The nonbonded potentials are computed from a density functional field instead of pairwise interactions used in standard molecular dynamics simulations, which increases the computational efficiency by a factor of 10-20. The entangled dynamics is lost due to the soft-core nature of density functional field interactions. It is recovered by a multichain slip-spring model that is rigorously parametrized from existing experimental or simulation data. To quantitatively predict the relaxation and diffusion of branched polymers, which are dominated by arm retraction rather than chain reptation, the slip-spring algorithm is augmented to improve the polymer dynamics near the branch point. Multiple dynamical observables, e.g., diffusion coefficients, arm relaxations, and tube survival probabilities, are characterized in an example coarse-grained model of symmetric and asymmetric star-shaped polystyrene melts. Consistent dynamical behaviors are identified and compared with theoretical predictions. With a single rescaling factor, the prediction of diffusion coefficients agrees well with the available experimental measurements. In this work, an efficient approach is provided to build chemistry-specific coarse-grained models for predicting the dynamics of branched polymers.

Analysis of Elongational Viscosity of Entangled Poly (Propylene Carbonate) Melts by Primitive Chain Network Simulations

It has been established that the elongational rheology of polymers depends on their chemistry. However, the analysis of experimental data has been reported for only a few polymers. In this study, we analyzed the elongational viscosity of poly (propylene carbonate) (PPC) melts in terms of monomeric friction via primitive chain network simulations. By incorporating a small polydispersity of materials, the linear viscoelastic response was semi-quantitatively reproduced. Owing to this agreement, we determined units of time and modulus to carry out elongational simulations. The simulation with constant monomeric friction overestimated elongational viscosity, whereas it nicely captured the experimental data if friction decreased with increasing segment orientation. To see the effect of chemistry, we also conducted the simulation for a polystyrene (PS) melt, which has a similar entanglement number per chain and a polydispersity index. The results imply that PPC and PS behave similarly in terms of the reduction of friction under fast deformations.

Nonequilibrium Processes in Polymer Membrane Formation: Theory and Experiment

Porous polymer and copolymer membranes are useful for ultrafiltration of functional macromolecules, colloids, and water purification. In particular, block copolymer membranes offer a bottom-up approach to form isoporous membranes. To optimize permeability, selectivity, longevity, and cost, and to rationally design fabrication processes, direct insights into the spatiotemporal structure evolution are necessary. Because of a multitude of nonequilibrium processes in polymer membrane formation, theoretical predictions via continuum models and particle simulations remain a challenge. We compiled experimental observations and theoretical approaches for homo- and block copolymer membranes prepared by nonsolvent-induced phase separation and highlight the interplay of multiple nonequilibrium processes─evaporation, solvent-nonsolvent exchange, diffusion, hydrodynamic flow, viscoelasticity, macro- and microphase separation, and dynamic arrest─that dictates the complex structure of the membrane on different scales.

Coupling between Polymer Conformations and Dynamics Near Amorphous Silica Surfaces: A Direct Insight from Atomistic Simulations

The dynamics of polymer chains in the polymer/solid interphase region have been a point of debate in recent years. Its understanding is the first step towards the description and the prediction of the properties of a wide family of commercially used polymeric-based nanostructured materials. Here, we present a detailed investigation of the conformational and dynamical features of unentangled and mildly entangled cis-1,4-polybutadiene melts in the vicinity of amorphous silica surface via atomistic simulations. Accounting for the roughness of the surface, we analyze the properties of the polymer chains as a function of their distance from the silica slab, their conformations and the chain molecular weight. Unlike the case of perfectly flat and homogeneous surfaces, the monomeric translational motion parallel to the surface was affected by the presence of the silica slab up to distances comparable with the extension of the density fluctuations. In addition, the intramolecular dynamical heterogeneities in adsorbed chains were revealed by linking the conformations and the structure of the adsorbed chains with their dynamical properties. Strong dynamical heterogeneities within the adsorbed layer are found, with the chains possessing longer sequences of adsorbed segments ("trains") exhibiting slower dynamics than the adsorbed chains with short ones. Our results suggest that, apart from the density-dynamics correlation, the configurational entropy plays an important role in the dynamical response of the polymers confined between the silica slabs.

Connecting the complex microstructure of LDPE to its rheology and processing properties via a combined fractionation and modelling approach

Well-defined mini-plant low density polyethylene samples were fractionated preparatively according to their crystallizability via preparative temperature rising elution fractionation and according to molecular weight via preparative solvent gradient fractionation (pSGF). Rheology of the fractions was measured in both the small amplitude oscillatory shear (SAOS) and the non-linear extension regimes. The linear and non-linear rheology of the pTREF fractions were dominated by molecular weight effects, while the impact of the higher degree of long chain branching for the pSGF fractions with higher molecular weights was observed in van Gurp–Palmen plots and in strain hardening behavior in the extensional rheology measurements. Additionally, the experimental fractionation process was mimicked via modelling. The branching topologies of the bulk samples were obtained by coupled kinetic and Monte Carlo calculations. These topologies were fractionated computationally and the result were used to predict the rheological behavior of the individual fractions by applying the BoB algorithm with no parameter adjustment. The experimental observed trends were predicted by the model and the overall agreement was acceptable. This study demonstrates, that polymer fractionation is possible on a preparative scale and allows for the polymer flow properties characterization of the individual fractions, a method that is highly relevant during processing. Moreover, the fractionation process is followed and understood from the modelling point of view.

The complex microstructure of LDPE regarding branching and molecular weight was correlated to its rheology and processing properties via preparative fractionation and modelling.