Energy-Renormalization for Achieving Temperature Transferable Coarse-Graining of Polymer Dynamics

Do Specific Ion Effects on Collective Relaxation Arise from Perturbation of Hydrogen-Bonding Network Structure?

The change in the transport properties (i.e., water diffusivity, shear viscosity, etc.) when adding salts to water has been used to classify ions as either being chaotropic or kosmotropic, a terminology based on the presumption that this phenomenon arises from respective breakdown or enhancement of the hydrogen-bonding network structure. Recent quasi-elastic neutron scattering measurements of the collective structural relaxation time, τC, in aqueous salt solutions were interpreted as confirming this proposed origin of ion effects on the dynamics of water. However, we find similar changes in τC in the same salt solutions based on molecular dynamics (MD) simulations using a coarse-grained water model in which no hydrogen bonding exists, challenging this conventional interpretation of mobility change resulting from the addition of salts to water. A thorough understanding of specific ion effects should be useful in diverse material manufacturing and biomedical applications, where these effects are prevalent, but poorly understood.

A Molecular Dynamics Study of Mechanical and Conformational Properties of Conjugated Polymer Thin Films

Understanding and predicting the mechanical and conformational properties of conjugated polymer (CP) thin films are a central focus in flexible electronic device research. Employing molecular dynamics simulations with an architecture-transferable chemistry-specific coarse-grained (CG) model of poly(3-alkylthiophene)s (P3ATs), developed by using an energy renormalization approach, we investigate the mechanical and conformational behavior of P3AT thin films during deformation. The density profiles and measures of local mobility identify a softer interfacial layer for all films, the thickness of which does not depend on M w or side-chain length. Remarkably, Young's modulus measured via nanoindentation is more sensitive to M w than for tensile tests, which we attribute to distinct deformation mechanisms. High-M w thin films show increased toughness, whereas longer side-chain lengths of P3AT resulted in lower Young's modulus. Fractures in low-M w thin films occur through chain pullout due to insufficient chain entanglement and crazing in the plastic region. Importantly, stretching promoted both chain alignment and longer conjugation lengths of P3AT, potentially enhancing its electronic properties. For instance, at room temperature, stretching P3HT thin films to 150% increases the conjugated length of P3HT thin films from 2.7 nm to 4.7 nm, aligning with previous experimental findings and all-atom simulation results. Furthermore, high-M w thin films display elevated friction forces due to the chain accumulation on the indenter, with negligible variations in the friction coefficient across all thin film systems. These findings offer valuable insights that enhance our understanding and guide the rational design of CP thin films in flexible electronics.

Structural Coarse-Graining via Multiobjective Optimization with Differentiable Simulation

In the realm of multiscale molecular simulations, structure-based coarse-graining is a prominent approach for creating efficient coarse-grained (CG) representations of soft matter systems, such as polymers. This involves optimizing CG interactions by matching static correlation functions of the corresponding degrees of freedom in all-atom (AA) models. Here, we present a versatile method, namely, differentiable coarse-graining (DiffCG), which combines multiobjective optimization and differentiable simulation. The DiffCG approach is capable of constructing robust CG models by iteratively optimizing the effective potentials to simultaneously match multiple target properties. We demonstrate our approach by concurrently optimizing bonded and nonbonded potentials of a CG model of polystyrene (PS) melts. The resulting CG-PS model effectively reproduces both the structural characteristics, such as the equilibrium probability distribution of microscopic degrees of freedom and the thermodynamic pressure of the AA counterpart. More importantly, leveraging the multiobjective optimization capability, we develop a precise and efficient CG model for PS melts that is transferable across a wide range of temperatures, i.e., from 400 to 600 K. It is achieved via optimizing a pairwise potential with nonlinear temperature dependence in the CG model to simultaneously match target data from AA-MD simulations at multiple thermodynamic states. The temperature transferable CG-PS model demonstrates its ability to accurately predict the radial distribution functions and density at different temperatures, including those that are not included in the target thermodynamic states. Our work opens up a promising route for developing accurate and transferable CG models of complex soft-matter systems through multiobjective optimization with differentiable simulation.

Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties

The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.

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.

Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB)

The MSCG/FM (multiscale coarse-graining via force-matching) approach is an efficient supervised machine learning method to develop microscopically informed coarse-grained (CG) models. We present a theory based on the principle of maximum entropy (PME) enveloping the existing MSCG/FM approaches. This theory views the MSCG/FM method as a special case of matching the thermodynamic forces from the extended ensemble described by the set of thermodynamic (relevant) system coordinates. This set may include CG coordinates, the stress tensor, applied external fields, and so forth, and may be characterized by nonequilibrium conditions. Following the presentation of the theory, we discuss the consistent matching of both bonded and nonbonded interactions. The proposed PME formulation is used as a starting point to extend the MSCG/FM method to the constant strain ensemble, which together with the explicit matching of the bonded forces is better suited for coarse-graining anisotropic media at a submolecular resolution. The theory is demonstrated by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a well-known insensitive molecular energetic material, which exhibits highly anisotropic mechanical properties.

Energy renormalization for temperature transferable coarse-graining of silicone polymer

The bottom-up prediction of thermodynamic and mechanical behaviors of polymeric materials based on molecular dynamics (MD) simulation is of critical importance in polymer physics. Although the atomistically informed coarse-grained (CG) model can access greater spatiotemporal scales and retain essential chemical specificity, the temperature-transferable CG model is still a big challenge and hinders widespread application of this technique. Herein, we use a silicone polymer, i.e., polydimethylsiloxane (PDMS), having an incredibly low chain rigidity as a model system, combined with an energy-renormalization (ER) approach, to systematically develop a temperature-transferable CG model. Specifically, by introducing temperature-dependent ER factors to renormalize the effective distance and cohesive energy parameters, the developed CG model faithfully preserved the dynamics, mechanical and conformational behaviors compared with the target all-atomistic (AA) model from glassy to melt regimes, which was further validated by experimental data. With the developed CG model featuring tremendously improved computational efficiency, we systematically explored the influences of cohesive interaction strength and temperature on the dynamical heterogeneity and mechanical response of polymers, where we observed consistent trends with other linear polymers with varying chain rigidity and monomeric structures. This study serves as an extension of our proposed ER approach of developing temperature transferable CG models with diverse segmental structures, highlighting the critical role of cohesive interaction strength on CG modeling of polymer dynamics and thermomechanical behaviors.

Perspectives on Theoretical Models and Molecular Simulations of Polymer Brushes

Polymer brushes have witnessed extensive utilization and progress, driven by their distinct attributes in surface modification, tethered group functionality, and tailored interactions at the nanoscale, enabling them for various scientific and industrial applications of coatings, sensors, switchable/responsive materials, nanolithography, and lab-on-a-chips. Despite the wealth of experimental investigations into polymer brushes, this review primarily focuses on computational studies of antifouling polymer brushes with a strong emphasis on achieving a molecular-level understanding and structurally designing antifouling polymer brushes. Computational exploration covers three realms of thermotical models, molecular simulations, and machine-learning approaches to elucidate the intricate relationship between composition, structure, and properties concerning polymer brushes in the context of nanotribology, surface hydration, and packing conformation. Upon acknowledging the challenges currently faced, we extend our perspectives toward future research directions by delineating potential avenues and unexplored territories. Our overarching objective is to advance our foundational comprehension and practical utilization of polymer brushes for antifouling applications, leveraging the synergy between computational methods and materials design to drive innovation in this crucial field.

Temperature-Transferable Coarse-Grained Models for Volumetric Properties of Poly(lactic Acid)

A new coarse-grained (CG) model, for which each monomer is mapped as one bead at its center of mass, was developed for simulating the volumetric properties of the polylactide (PLA) bulk. The three bonded CG potentials are first parametrized against the strain energies of the dimer, trimer, and tetramer, and the nonbonded CG potentials are then optimized to match the melt densities of the decamer. With the derived CG potentials, molecular dynamics (MD) simulations are found to reproduce thermal expansion and glass transition. By rescaling the dihedral and nonbonded potentials with temperature-independent factors, the glass transition temperature (Tg) is also satisfactorily restored with little modifications on the volumetric expansive coefficients at both rubbery and glassy states. Therefore, the finally optimized CG potentials exhibit excellent temperature transferability, as rationalized by the Simha-Boyer relation. Furthermore, it is confirmed that the dihedral torsions and nonbonded interactions play key roles in glass transition. Also, the simulated bulk moduli and conformational properties in a wide temperature range compare well with the referenced data. The proposed multiscale scheme has great potential in simulating thermo-mechanical properties of PLA and other polymers.

An Accurate and Transferable Coarse-Graining Method for the Investigation of Microscopic Fracture Behaviors of Epoxy Thermosets

Coarse-grained modeling shows potential in exploring the thermo-mechanical behaviors of polymers applied in harsh conditions such as cryogenic environment, but its accuracy in simulating fracture behaviors of highly cross-linked epoxy thermosets is largely limited due to the complex molecular structures of the cross-linked networks. We address this fundamental problem by developing a CG modeling method where the backbones and electrostatic interaction (EI) contributions in the cross-linked networks are retained, and thus the potentials of the CG model can be directly extracted, or parametrized on the basis of, existing all-atomistic (AA) force fields. A multilevel parametrization procedure was adopted, where the bond potentials were parametrized relying on the results of density functional theory (DFT) simulation, whereas the nonbond potentials were parametrized by renormalizing the cohesive interaction strength. Remarkably, the CG model can reproduce stress-strain responses highly consistent with the AA simulation results at multiple stages, including elastic deformation, yielding, plastic flow, strain hardening, etc., and the straightforward parametrization procedure can be easily transferred to different materials and thermodynamic conditions. The CG modeling method was then used to build a large-scale representative volume element (RVE) to investigate the microscopic fracture behavior of an epoxy thermoset. It has been discovered that EI contributions play a significant role in generating correct mechanical responses and fracture morphologies. The influences of temperature (i.e., from room to cryogenic temperatures) and strain rates were discussed, and the fracture morphology in the RVE was unveiled and analyzed in a quantitative manner.

Diffusion Coefficients of Variable-Size Amphiphilic Additives in a Glass-Forming Polyethylene Matrix

Diffusion of additives in polymers is an important issue in the plastics industry since migratory-type molecules are widely used to tune the properties of polymeric composites. Predicting the diffusional behavior of new additives can minimize the need for repetitive experiments. This work presents molecular dynamics simulations at the microsecond time scale and uses the MARTINI force field to estimate self-diffusion coefficients, D, of six monounsaturated amides and their analogs carboxylic acids in polyethylene matrices (PE, MW = 5600 Da). The results are strongly influenced by the glass-forming properties of the PE matrix, which we characterize by three distinct temperatures. The metastability region (T < 325 K), the glass transition temperature (Tg = 256-260 K), and the end of the transition (T ≅ 200 K). Self-diffusion mechanisms are inferred from the results of the dependence of D on the molecular mass of the additive, observing a Rouse-like behavior at high temperatures and deviations from it within the metastability region of the matrix. Interestingly, D values are nonsensitive to the nature of the considered polar head for additives of similar size. The temperature-dependent behavior of D follows, at fixed additive size, a linear Arrhenius pattern at high temperatures and a super Arrhenius trend at lower temperatures, which is well represented with a power law equation as predicted by the Mode Coupling Theory (MCT). We offer a conceptual explanation for the observed super-Arrhenius behavior. This explanation draws on Truhlar and Kohen's interpretation of the available energies at both the initial and the transition states along the diffusion pathway. The matrix's mobility significantly affects solute self-diffusion, yielding equal activation enthalpies for the Arrhenius region or the same power law parameters for the super-Arrhenius regime. Finally, we establish a one-to-one time-equivalence of the self-diffusion processes between CG and all-atom systems for the largest additives and the PE matrix in the high-temperature regime.

Competing Effects of Molecular Additives and Cross-Link Density on the Segmental Dynamics and Mechanical Properties of Cross-Linked Polymers

The introduction of molecular additives into thermosets often results in changes in their dynamics and mechanical properties that can have significant ramifications for diverse applications of this broad class of materials such as coatings, high-performance composites, etc. Currently, there is limited fundamental understanding of how such additives influence glass formation in these materials, a problem of broader significance in glass-forming materials. To address this fundamental problem, here, we employ a simplified coarse-grained (CG) model of a polymer network as a model of thermoset materials and then introduce a polymer additive having the same inherent rigidity and polymer-polymer interaction strength as the cross-linked polymer matrix. This energetically "neutral" or "self-plasticizing" additive model gives rise to non-trivial changes in the dynamics of glass formation and provides an important theoretical reference point for the technologically more important case of interacting additives. Based on this rather idealized model, we systematically explore the combined effect of varying the additive mass percentage (m) and cross-link density (c) on the segmental relaxation dynamics and mechanical properties of a model thermoset material with additives. We find that increasing the additive mass percentage m progressively decreases both the glass-transition temperature Tg and the fragility of glass formation, a trend opposite to increasing c so that these thermoset variables clearly have a competing effect on glass formation in these model materials. Moreover, basic mechanical properties (i.e., bulk, shear, and tensile moduli) likewise exhibit a competitive variation with the increase of m and c, which are strongly correlated with the Debye-Waller parameter ⟨u2⟩, a measure of material stiffness at a molecular scale. Our findings prove beneficial in the development of structure-property relationships for the cross-linked polymers, which could help guide the design of such network materials with tailored physical properties.

Understanding the thermomechanical behavior of graphene-reinforced conjugated polymer nanocomposites via coarse-grained modeling

Graphene-reinforced conjugated polymer (CP) nanocomposites are attractive for flexible and electronic devices, but their mechanical properties have been less explored at a fundamental level. Here, we present a predictive multiscale modeling framework for graphene-reinforced poly(3-alkylthiophene) (P3AT) nanocomposites via atomistically informed coarse-grained molecular dynamics simulations to investigate temperature-dependent thermomechanical properties at a molecular level. Our results reveal reduced graphene dispersion with increasing graphene loading. Nanocomposites with shorter P3AT side chains, lower temperatures, and higher graphene content exhibit stronger mechanical responses, which correlates with polymer dynamics. The elastic modulus increases linearly with the graphene content, which slightly deviates from the "Halpin-Tsai" micromechanical model prediction. Local stiffness analysis shows that graphene possesses the highest stiffness, followed by the P3AT backbone and side chains. Deformation-induced stronger chain alignment of the P3AT backbone compared to graphene may further promote conductive behavior. Our findings provide insights into the dynamical heterogeneity of nanocomposites, paving the way for understanding and predicting their thermomechanical properties.

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.

Hierarchical Machine Learning of Low-Resolution Coarse-Grained Free Energy Potentials

A force-matching-based method for supervised machine learning (ML) of coarse-grained (CG) free energy (FE) potentials─known as multiscale coarse-graining via force-matching (MSCG/FM)─is an efficient method to develop microscopically informed CG models that are thermodynamically and statistically equivalent to the reference microscopic models. For low-resolution models, when the coarse-graining is at supramolecular scales, objective-oriented clustering of nonbonded particles is required and the reduced description becomes a function of the clustering algorithm. In the present work, we explore the dependence of the ML of the CG Helmholtz FE potential on the clustering algorithm. We consider coarse-graining based on partitional (k-means, leading to Voronoi diagram) and hierarchical agglomerative (bottom-up) clustering algorithms common in unsupervised ML and develop theory connecting the MSCG/FM learned CG Helmholtz potential and the clustering statistics. By combining the agglomerative clustering and the MSCG/FM learning in a recursive manner, we propose an efficient ML methodology to develop the fine-to-low resolution hierarchies of the CG models. The methodology does not suffer from degrading accuracy or increased computational cost to construct larger hierarchies and as such does not impose an upper size limitation of the CG particles resulting from the extended hierarchies. The utility of the methodology is demonstrated by obtaining the bottom-up agglomerative hierarchy for liquid nitromethane from all-atom molecular dynamics (MD) simulations. For agglomerative hierarchies, we prove the existence of renormalization group transformations that indicate self-similarity and allow for learning the low-resolution MSCG/FM potentials at low computational cost by rescaling and renormalizing the certain finer-resolution members of the hierarchy. The hierarchies of the CG models can be used to carry out simulations under constant-pressure conditions.

Understanding Nanocellulose-Water Interactions: Turning a Detriment into an Asset

Modern technology has enabled the isolation of nanocellulose from plant-based fibers, and the current trend focuses on utilizing nanocellulose in a broad range of sustainable materials applications. Water is generally seen as a detrimental component when in contact with nanocellulose-based materials, just like it is harmful for traditional cellulosic materials such as paper or cardboard. However, water is an integral component in plants, and many applications of nanocellulose already accept the presence of water or make use of it. This review gives a comprehensive account of nanocellulose-water interactions and their repercussions in all key areas of contemporary research: fundamental physical chemistry, chemical modification of nanocellulose, materials applications, and analytical methods to map the water interactions and the effect of water on a nanocellulose matrix.

Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.

Approaches and Perspective of Coarse-Grained Modeling and Simulation for Polymer-Nanoparticle Hybrid Systems

Molecular modeling and simulations have emerged as effective and indispensable tools to characterize polymeric systems. They provide fundamental and essential insights to design a product of the required properties and to improve the understanding of a phenomenon at the molecular level for a particular system. The polymer-nanoparticle hybrids are materials with outstanding properties and correspondingly large applications whose study has benefited from this new paradigm. However, despite the significant expansion of modern day computational powers, investigation of the long time and large length scale phenomenon in polymeric and polymer-nanoparticle systems is still a challenging task to complete through all-atom molecular dynamics (AA-MD) simulations. To circumvent this problem, a variety of coarse-grained (CG) models have been proposed, ranging from the generic CG models for qualitative properties predictions to more realistic chemically specific CG models for quantitative properties predictions. These CG models have already delivered some success stories in the study of several spatial and temporal evolutions of many processes. Some of these studies were beyond the feasibility of traditional atomistic resolution models due to either the size or the time constraints. This review captures the different types of popular CG approaches that are utilized in the investigation of the microscopic behavior of polymer-nanoparticle hybrid systems. The rationale of this article is to furnish an overview of the popular CG approaches and their applications, to review several important and most recent developments, and to delineate the perspectives on future directions in the field.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

Understanding the role of cross-link density in the segmental dynamics and elastic properties of cross-linked thermosets

Cross-linking is known to play a pivotal role in the relaxation dynamics and mechanical properties of thermoset polymers, which are commonly used in structural applications because of their light weight and inherently strong nature. Here, we employ a coarse-grained (CG) polymer model to systematically explore the effect of cross-link density on basic thermodynamic properties as well as corresponding changes in the segmental dynamics and elastic properties of these network materials upon approaching their glass transition temperatures (T_g). Increasing the cross-link density unsurprisingly leads to a significant slowing down of the segmental dynamics, and the fragility K of glass formation shifts in lockstep with T_g, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τ_α becomes almost a universal function of reduced temperature, (T - T_g)/T_g, a phenomenon that underlies the applicability of the "universal" Williams-Landel-Ferry (WLF) relation to many polymer materials. We also test a mathematical model of the temperature dependence of the linear elastic moduli based on a simple rigidity percolation theory and quantify the fluctuations in the local stiffness of the network material. The moduli and distribution of the local stiffness likewise exhibit a universal scaling behavior for materials having different cross-link densities but fixed (T - T_g)/T_g. Evidently, T_g dominates both τ_α and the mechanical properties of our model cross-linked polymer materials. Our work provides physical insights into how the cross-link density affects glass formation, aiding in the design of cross-linked thermosets and other structurally complex glass-forming materials.

Multiscale modeling of thermomechanical properties of stereoregular polymers

Multiscale coarse-grained (CG) models are expected to play the critical roles in molecular simulations of complex polymers. However, this poses a great challenge for accurately simulating their thermomechanical properties, for which excellent representability and transferability are required for the CG potentials. In this work, virtual sites and elastic network bonds are introduced to improve the structural and volumetric property-based CG models including explicit electrostatic interactions, which is exemplarily applied to the iso- and syndio-tactic poly(methyl methacrylate). A variety of thermomechanical properties of the two stereoregular polymer bulks are reasonably reproduced by the extensive molecular dynamics simulations with the so-parameterized CG potentials. In particular, the attractive nature of electrostatic interactions and tacticity effects on glass transition temperatures (T_g) are well captured. Furthermore, stronger electrostatic interactions lead to higher mass density and bulk modulus, and their effects on Young's modulus, Poisson's ratio, and shear modulus depend upon the chain tacticity. It is also demonstrated that all these elastic constants can be effectively modulated by imposing external electric field. The proposed multiscale scheme can be very valuable to molecular designs of polar polymer materials.

Temperature-Transferable Coarse-Grained Model for Poly(propylene oxide) to Study Thermo-Responsive Behavior of Triblock Copolymers

Thermo-responsive behavior of ethylene oxide (EO)-propylene oxide (PO) copolymers makes them suitable for many potential applications. Reproducing the origins of the tunable properties of EO-PO copolymers using coarse-grained (CG) models such as the MARTINI force field is critically important for building a better understanding of their behavior. In the present work, we have investigated the effects of coarse-graining on the water-polymer interaction across a temperature range. We compared the performance of different all-atom force fields to find the most appropriate one for the purpose of PO block parameterization in the MARTINI platform. We parameterized a CG temperature-dependent PO model based on the reproduction of the atomistic free energy of transfer of propylene oxide trimer from octane to water over a range of temperatures (20-60 °C) and compared the atomistic bond and angle distributions. Then, we used the model to study the effects of EO/PO ratio, molecular weight, and concentration on the thermo-responsive behavior of EO-PO copolymers in water. The results show an excellent agreement with experiments in different areas. Our temperature-dependent model reproduces (1) micellar phase above critical micelle temperature (CMT) and unimer phase below CMT for different Pluronics (a class of EO-PO triblock copolymers) spanning many EO/PO ratios and molecular weights; (2) spherical-to-rodlike micellar shape transition for Pluronics with 60 wt % of PO content or more; (3) diffusion coefficients for Pluronics with high PO content (P104 Pluronic with a PO mass of 3500 g mol^-1) across a broad range of temperatures; and (4) micelle core size and micelle diameter similar to experimental results. Overall, our model improves the temperature sensitivity of EO-PO copolymers of existing models significantly, particularly for copolymers that are dominated by PO agents.

Combined description of polymer PVT and relaxation data using a dynamic "SL-TS2" mean-field lattice model

We develop a combined model to describe the pressure-volume-temperature (PVT) thermodynamics and the α- and β-relaxation time dynamics in glass-forming amorphous materials. The PVT results are described using a two-state modification of the Sanchez-Lacombe equation of state (SL-EoS). The minimization of the Sanchez-Lacombe free energy expression allows one to calculate the density (or specific volume) and the "solid fraction" as a function of temperature and pressure. The solid fraction, ψ(T,P), is then substituted into the TS2 mean-field model (V. V. Ginzburg, Soft Matter, 2020, 16, 810), and the equilibrium relaxation times and the glass transition temperature are calculated. Finally, we use a dynamic model of a Tool-Narayanaswami-Moynihan (TNM)-type to describe the density relaxation as a function of the cooling rate. We applied the new framework to describe experimental data for polystyrene and poly(methylmethacrylate) and found a good qualitative and quantitative agreement.

Systematic Coarse-graining of Epoxy Resins with Machine Learning-Informed Energy Renormalization

A persistent challenge in predictive molecular modeling of thermoset polymers is to capture the effects of chemical composition and degree of crosslinking (DC) on dynamical and mechanical properties with high computational efficiency. We established a new coarse-graining (CG) approach that combines the energy renormalization method with Gaussian process surrogate models of the molecular dynamics simulations. This allows a machine-learning informed functional calibration of DC-dependent CG force field parameters. Taking versatile epoxy resins consisting of Bisphenol A diglycidyl ether combined with curing agent of either 4,4-Diaminodicyclohexylmethane or polyoxypropylene diamines, we demonstrated excellent agreement between all-atom and CG predictions for density, Debye-Waller factor, Young's modulus and yield stress at any DC. We further introduce a surrogate model enabled simplification of the functional forms of 14 non-bonded calibration parameters by quantifying the uncertainty of a candidate set of high-dimensional/flexible calibration functions. The framework established provides an efficient methodology for chemistry-specific, large-scale investigations of the dynamics and mechanics of epoxy resins.

A microcanonical approach to temperature-transferable coarse-grained models using the relative entropy

Bottom-up coarse-graining methods provide systematic tools for creating simplified models of molecular systems. However, coarse-grained (CG) models produced with such methods frequently fail to accurately reproduce all thermodynamic properties of the reference atomistic systems they seek to model and, moreover, can fail in even more significant ways when used at thermodynamic state points different from the reference conditions. These related problems of representability and transferability limit the usefulness of CG models, especially those of strongly state-dependent systems. In this work, we present a new strategy for creating temperature-transferable CG models using a single reference system and temperature. The approach is based on two complementary concepts. First, we switch to a microcanonical basis for formulating CG models, focusing on effective entropy functions rather than energy functions. This allows CG models to naturally represent information about underlying atomistic energy fluctuations, which would otherwise be lost. Such information not only reproduces energy distributions of the reference model but also successfully predicts the correct temperature dependence of the CG interactions, enabling temperature transferability. Second, we show that relative entropy minimization provides a direct and systematic approach to parameterize such classes of temperature-transferable CG models. We calibrate the approach initially using idealized model systems and then demonstrate its ability to create temperature-transferable CG models for several complex molecular liquids.

An Enhanced Scheme for Multiscale Modeling of Thermomechanical Properties of Polymer Bulks

While multiscale modeling significantly enhances the capability of molecular simulations of polymer systems, it is well realized that the systematically derived coarse-grained (CG) models generally underestimate the thermomechanical properties. In this work, a charge-based mapping scheme has been adopted to include explicit electrostatic interactions and benchmarked against two typical polymers, atactic poly(methyl methacrylate) (PMMA) and polystyrene (PS). The CG potentials are parameterized against the oligomer bulks of nine monomers per chain to match the essential structural features and the two basic pressure-volume-temperature (PVT) properties, which are obtained from the all-atomistic (AA) molecular dynamics (MD) simulations at a single elevated temperature. The so-parameterized CG potentials are extended with the MD method to simulate the two polymer bulks of one hundred monomers per chain over a wide temperature range. Without any scaling, all the simulated results, including mass densities and bulk moduli at room temperature, thermal expansion coefficients at rubbery and glassy states, and glass transition temperatures (T_g), compare well with the corresponding experimental data. The proposed scheme not only contributes to realistically simulating various thermomechanical properties of both apolar and polar polymers but also allows for directly simulating their electrical properties.

Transfer learning of memory kernels for transferable coarse-graining of polymer dynamics

The present work concerns the transferability of coarse-grained (CG) modeling in reproducing the dynamic properties of the reference atomistic systems across a range of parameters. In particular, we focus on implicit-solvent CG modeling of polymer solutions. The CG model is based on the generalized Langevin equation, where the memory kernel plays the critical role in determining the dynamics in all time scales. Thus, we propose methods for transfer learning of memory kernels. The key ingredient of our methods is Gaussian process regression. By integration with the model order reduction via proper orthogonal decomposition and the active learning technique, the transfer learning can be practically efficient and requires minimum training data. Through two example polymer solution systems, we demonstrate the accuracy and efficiency of the proposed transfer learning methods in the construction of transferable memory kernels. The transferability allows for out-of-sample predictions, even in the extrapolated domain of parameters. Built on the transferable memory kernels, the CG models can reproduce the dynamic properties of polymers in all time scales at different thermodynamic conditions (such as temperature and solvent viscosity) and for different systems with varying concentrations and lengths of polymers.

Dynamical properties across different coarse-grained models for ionic liquids

Room-temperature ionic liquids (RTILs) stand out among molecular liquids for their rich physicochemical characteristics, including structural and dynamic heterogeneity. The significance of electrostatic interactions in RTILs results in long characteristic length- and timescales, and has motivated the development of a number of coarse-grained (CG) simulation models. In this study, we aim to better understand the connection between certain CG parameterization strategies and the dynamical properties and transferability of the resulting models. We systematically compare five CG models: a model largely parameterized from experimental thermodynamic observables; a refinement of this model to increase its structural accuracy; and three models that reproduce a given set of structural distribution functions by construction, with varying intramolecular parameterizations and reference temperatures. All five CG models display limited structural transferability over temperature, and also result in various effective dynamical speedup factors, relative to a reference atomistic model. On the other hand, the structure-based CG models tend to result in more consistent cation-anion relative diffusion than the thermodynamic-based models, for a single thermodynamic state point. By linking short- and long-timescale dynamical behaviors, we demonstrate that the varying dynamical properties of the different CG models can be largely collapsed onto a single curve, which provides evidence for a route to constructing dynamically-consistent CG models of RTILs.

Dynamically consistent coarse-grain simulation model of chemically specific polymer melts via friction parameterization

Coarse-grained (CG) models of polymers involve grouping many atoms in an all-atom (AA) representation into single sites to reduce computational effort yet retain the hierarchy of length and time scales inherent to macromolecules. Parameterization of such models is often via "bottom-up" methods, which preserve chemical specificity but suffer from artificially accelerated dynamics with respect to the AA model from which they were derived. Here, we study the combination of a bottom-up CG model with a dissipative potential as a means to obtain a chemically specific and dynamically correct model. We generate the conservative part of the force-field using the iterative Boltzmann inversion (IBI) method, which seeks to recover the AA structure. This is augmented with the dissipative Langevin thermostat, which introduces a single parameterizable friction factor to correct the unphysically fast dynamics of the IBI-generated force-field. We study this approach for linear polystyrene oligomer melts for three separate systems with 11, 21, and 41 monomers per chain and a mapping of one monomer per CG site. To parameterize the friction factor, target values are extracted from the AA dynamics using translational monomer diffusion, translational chain diffusion, and rotational chain motion to test the consistency of the parameterization across different modes of motion. We find that the value of the friction parameter needed to bring the CG dynamics in line with AA target values varies based on the mode of parameterization with short-time monomer translational dynamics requiring the highest values, long-time chain translational dynamics requiring the lowest values, and rotational dynamics falling in between. The friction ranges most widely for the shortest chains, and the span narrows with increasing chain length. For longer chains, a practical working value of the friction parameter may be derived from the rotational dynamics, owing to the contribution of multiple relaxation modes to chain rotation and a lack of sensitivity of the translational dynamics at these intermediate levels of friction. A study of equilibrium chain structure reveals that all chains studied are non-Gaussian. However, longer chains better approximate ideal chain dimensions than more rod-like shorter chains and thus are most closely described by a single friction parameter. We also find that the separability of the conservative and dissipative potentials is preserved.

Development of Coarse-Grained Models for Poly(4-vinylphenol) and Poly(2-vinylpyridine): Polymer Chemistries with Hydrogen Bonding

In this paper, we identify the modifications needed in a recently developed generic coarse-grained (CG) model that captured directional interactions in polymers to specifically represent two exemplary hydrogen bonding polymer chemistries-poly(4-vinylphenol) and poly(2-vinylpyridine). We use atomistically observed monomer-level structures (e.g., bond, angle and torsion distribution) and chain structures (e.g., end-to-end distance distribution and persistence length) of poly(4-vinylphenol) and poly(2-vinylpyridine) in an explicitly represented good solvent (tetrahydrofuran) to identify the appropriate modifications in the generic CG model in implicit solvent. For both chemistries, the modified CG model is developed based on atomistic simulations of a single 24-mer chain. This modified CG model is then used to simulate longer (36-mer) and shorter (18-mer and 12-mer) chain lengths and compared against the corresponding atomistic simulation results. We find that with one to two simple modifications (e.g., incorporating intra-chain attraction, torsional constraint) to the generic CG model, we are able to reproduce atomistically observed bond, angle and torsion distributions, persistence length, and end-to-end distance distribution for chain lengths ranging from 12 to 36 monomers. We also show that this modified CG model, meant to reproduce atomistic structure, does not reproduce atomistically observed chain relaxation and hydrogen bond dynamics, as expected. Simulations with the modified CG model have significantly faster chain relaxation than atomistic simulations and slower decorrelation of formed hydrogen bonds than in atomistic simulations, with no apparent dependence on chain length.

Coarse-graining strategy for modeling effective, highly diffusive fluids with reduced polydispersity: A dynamical study

We present a coarse-graining strategy for reducing the number of particle species in mixtures to achieve a simpler system with higher diffusion while preserving the total particle number and characteristic dynamic features. As a system of application, we chose the bidisperse Lennard-Jones-like mixture, discovered by Kob and Andersen [Phys. Rev. Lett. 73, 1376 (1994)], possessing a slow dynamics due to the fluid's multi-component character with its apparently unconventional choice for the pair potential of the type-A-type-B arrangement. We further established in a so-formed coarse-grained and temperature-independent monodisperse system an equilibrium structure with a radial distribution function resembling its mixture counterpart. This one-component system further possesses similar dynamic features such as glass transition temperature and critical exponents while subjected to Newtonian mechanics. This strategy may finally lead to the manufacturing of new nanoparticle/colloidal fluids by experimentally modeling only the outcoming effective pair potential(s) and no other macroscopic quantity.

Revisiting stress-strain behavior and mechanical reinforcement of polymer nanocomposites from molecular dynamics simulations

Through coarse-grained molecular dynamics simulations, the effects of nanoparticle properties, polymer-nanoparticle interactions, chain crosslinks and temperature on the stress-strain behavior and mechanical reinforcement of polymer nanocomposites (PNCs) are comprehensively investigated. By regulating the filler-polymer interaction (miscibility) in a wide range, an optimal dispersion state of nanoparticles is found at moderate interaction strength, while the mechanical properties of PNCs are improved monotonically with the increase of the particle-polymer interaction due to the tele-bridge structures of nanoparticles via polymer chains. Although smaller-sized fillers more easily build interconnected structures, the elastic moduli of PNCs at the percolation threshold concentration where a three-dimensional filler network forms are almost independent of nanoparticle size. Compared with spherical nanoparticles, anisotropic rod-like ones, especially with larger aspect ratio and rod stiffness, contribute exceptional reinforcement towards polymer materials. In addition, the elastic modulus with the strain, derived from the stress-strain curve, shows an analogous nonlinear behavior to the amplitude-dependence of the storage modulus (Payne effect). Such a behavior originates essentially from the failure/breakup of the microstructures contributing to the mechanical reinforcement, such as bound polymer layers around nanoparticles or nanoparticle networking structures. The Young's modulus as a function of the nanoparticle volume fraction greatly exceeds that predicted by the Einstein-Smallwood model and Guth-Gold model, which arises primarily from the contribution of the local/global filler network. The temperature dependence of the Young's modulus is further examined by mode coupling theory (MCT) and the Vogel-Fulcher-Tammann (VFT) equation, and the results indicate that the time-temperature superposition principle holds modestly above the critical temperature on the short-time (small-length) scale of elastic response. This work is expected to provide some guidance on controlling and improving the mechanical properties and nonlinear behavior of PNCs.

Exploring a unified description of the super-Arrhenius region above and below the glass transition temperature

A new approach is presented in order to check whether the hypothesis of an Arrhenius component surviving in the α-relaxation region is consistent with experimental data. The temperature dependence of the dynamics in the whole glassy regime is described by an equation which assumes an Arrhenius component in the cooperative diffusion. Based on thermodynamic arguments, the dynamic heterogeneities close to the glass transition region are related to structural heterogeneities in a manner consistent with the idea of a sigmoidal shape in the cohesion energy. By doing so, a characteristic temperature which can be identified as the glass transition temperature (T_g) emerges, while an additional parameter for the extension of the super-Arrhenius region is introduced. In the analysis of experimental data, the activation energy parameter, determined from the temperature dependence of the β-relaxation, is fixed, and the relation between the experimental and the predicted glass transition temperature is examined. The results of this comparison support the idea that dynamics above and below T_g can be described in a unified manner. The proposed model is tested against experimental data of glass-forming liquids, polymers and polymer composites. In the latter systems, it is shown that the Arrhenius-like behavior characterizing the dynamics of the polymeric bound-layer can be accounted for by such an extension of the super-Arrhenius region.