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

Network Topology and Percolation in Model Covalent Adaptable Networks

Incorporating dynamic covalent linkages into thermosets can endow previously unrecyclable materials with new functionality and reprocessing options. Recent work has shown that the properties of the resulting covalent adaptable networks (CANs) are highly dependent on network topology, specifically the phenomenon of percolation, when permanent linkages form a connected skeleton that spans the material. Here, we use a model glassy disulfide based CAN to assess the merits of mean-field percolation theory as a tool to describe the network topology of CANs. After challenging the theory with both experimental data and a coarse-grained molecular dynamics simulation, we find that the mean-field approach is surprisingly accurate, despite its simplifying assumptions. The theory is particularly well suited to the unique context of mixed-composition CANs and provides practical guidance on how to design for reprocessability.

Modeling-driven materials by design for conjugated polymers: insights into optoelectronic, conformational, and thermomechanical properties

Conjugated polymers (CPs) have emerged as pivotal functional materials in the realm of flexible electronics and optoelectronic devices due to their unique blend of mechanical flexibility, solution processability, and tunable optoelectronic properties. This review synthesizes the latest molecular simulation-driven insights obtained from various multiscale modeling techniques, including quantum mechanics (QM), all-atomistic (AA) molecular dynamics (MD), coarse-grained (CG) modeling, and machine learning (ML), to elucidate the optoelectronic, structural, and thermomechanical properties of CPs. By integrating findings from our recent computational work with key experimental studies, we highlight the molecular mechanisms influencing the multifunctional performance of CPs. This comprehensive understanding aims to guide future research directions and applications in the modeling assisted design of high-performance CP-based materials and devices.

Characterizing the shear response of polymer-grafted nanoparticles

Grafting polymer chains to the surface of nanoparticles overcomes the challenge of nanoparticle dispersion within nanocomposites and establishes high-volume fractions that are found to enable enhanced material mechanical properties. This study utilizes coarse-grained molecular dynamics simulations to quantify how the shear modulus of polymer-grafted nanoparticle (PGN) systems in their glassy state depends on parameters such as strain rate, nanoparticle size, grafting density, and chain length. The results are interpreted through further analysis of the dynamics of chain conformations and volume fraction arguments. The volume fraction of nanoparticles is found to be the most influential variable in deciding the shear modulus of PGN systems. A simple rule of mixture is utilized to express the monotonic dependence of shear modulus on the volume fraction of nanoparticles. Due to the reinforcing effect of nanoparticles, shortening the grafted chains results in a higher shear modulus in PGNs, which is not seen in linear systems. These results offer timely insight into calibrating molecular design parameters for achieving the desired mechanical properties in PGNs.

Improved Ballistic Impact Resistance of Nanofibrillar Cellulose Films with Discontinuous Fibrous Bouligand Architecture

Natural protective materials offer unparalleled solutions for impact-resistant material designs that are simultaneously lightweight, strong, and tough. Particularly, the Bouligand structure found in the dactyl club of mantis shrimp and the staggered structure in nacre achieve excellent mechanical strength, toughness, and impact resistance. Previous studies have shown that hybrid designs by combining different bioinspired microstructures can lead to enhanced mechanical strength and energy dissipation. Nevertheless, it remains unknown whether combining Bouligand and staggered structures in nanofibrillar cellulose (NFC) films, forming a discontinuous fibrous Bouligand (DFB) architecture, can achieve enhanced impact resistance against projectile penetration. Additionally, the failure mechanisms under such dynamic loading conditions have been minimally understood. In our study, we systematically investigate the dynamic failure mechanisms and quantify the impact resistance of NFC thin films with DFB architecture by leveraging previously developed coarse-grained models and ballistic impact molecular dynamics simulations. We find that when nanofibrils achieve a critical length and form DFB architecture, the impact resistance of NFC films outperforms the counterpart films with continuous fibrils by comparing their specific ballistic limit velocities and penetration energies. We also find that the underlying mechanisms contributing to this improvement include enhanced fibril sliding, intralayer and interlayer crack bridging, and crack twisting in the thickness direction enabled by the DFB architecture. Our results show that by combining Bouligand and staggered structures in NFC films, their potential for protective applications can be further improved. Our findings can provide practical guidelines for the design of protective films made of nanofibrils.

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.

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.

Rapid and accurate predictions of perfect and defective material properties in atomistic simulation using the power of 3D CNN-based trained artificial neural networks

This article introduces an innovative approach that utilizes machine learning (ML) to address the computational challenges of accurate atomistic simulations in materials science. Focusing on the field of molecular dynamics (MD), which offers insight into material behavior at the atomic level, the study demonstrates the potential of trained artificial neural networks (tANNs) as surrogate models. These tANNs capture complex patterns from built datasets, enabling fast and accurate predictions of material properties. The article highlights the application of 3D convolutional neural networks (CNNs) to incorporate atomistic details and defects in predictions, a significant advancement compared to current 2D image-based, or descriptor-based methods. Through a dataset of atomistic structures and MD simulations, the trained 3D CNN achieves impressive accuracy, predicting material properties with a root-mean-square error below 0.65 GPa for the prediction of elastic constants and a speed-up of approximately 185 to 2100 times compared to traditional MD simulations. This breakthrough promises to expedite materials design processes and facilitate scale-bridging in materials science, offering a new perspective on addressing computational demands in atomistic simulations.

Tensile Stress Reduction and Strain Concentration of Epoxy Resin Caused by Heterogeneity: A Multiscale Approach Combining Molecular Dynamics Simulation and Finite Element Method

In this study, we investigated the effect of heterogeneity on the mechanical properties of epoxy resin by combining coarse-grained molecular dynamics (CG-MD) and finite element method (FEM) simulations. To evaluate the heterogeneity effect in the uniaxial elongation, heterogeneous and homogeneous FEM models of micrometer-scale cubic epoxy resin were constructed. For the heterogeneous FEM model, parameters of nanometer-scale elements were determined by CG-MD simulations, where nanometer-scale blocks have different cross-linked structures. For the homogeneous FEM model, the averaged parameters were used for all elements. The calculated stress-strain (S-S) curves of the heterogeneous model exhibit similar tensile stress values when compared to the experimental data, whereas the homogeneous model yields notably higher values. Moreover, a clear strain concentration associated with the formation of the shear band-like structure was observed in the heterogeneous model and not in the homogeneous model.

B-factor prediction in proteins using a sequence-based deep learning model

B factors provide critical insight into protein dynamics. Predicting B factors of an atom in new proteins remains challenging as it is impacted by their neighbors in Euclidean space. Previous learning methods developed have resulted in low Pearson correlation coefficients beyond the training set due to their limited ability to capture the effect of neighboring atoms. With the advances in deep learning methods, we develop a sequence-based model that is tested on 2,442 proteins and outperforms the state-of-the-art models by 30%. We find that the model learns that the B factor of a site is prominently affected by atoms within a 12-15 Å radius, which is in excellent agreement with cutoffs from protein network models. The ablation study revealed that the B factor can largely be predicted from the primary sequence alone. Based on the abovementioned points, our model lays a foundation for predicting other properties that are correlated with the B factor.

Atomistic to Mesoscopic Modelling of Thermophysical Properties of Graphene-Reinforced Epoxy Nanocomposites

This research addresses the need for a multiscale model for the determination of the thermophysical properties of nanofiller-enhanced thermoset polymer composites. Specifically, we analyzed the thermophysical properties of an epoxy resin containing bisphenol-A diglyceryl ether (DGEBA) as an epoxy monomer and dicyandiamide (DICY) and diethylene triamine (DETA) as cross-linking agents. The cross-linking process occurs at the atomistic scale through the formation of bonds among the reactive particles within the epoxy and hardener molecules. To derive the interatomic coarse-grained potential for the mesoscopic model and match the density of the material studied through atomic simulations, we employed the iterative Boltzmann inversion method. The newly developed coarse-grained molecular dynamics model effectively reproduces various thermophysical properties of the DGEBA-DICY-DETA resin system. Furthermore, we simulated nanocomposites made of the considered epoxy additivated with graphene nanofillers at the mesoscopic level and verified them against continuum approaches. Our results demonstrate that a moderate amount of nanofillers (up to 2 wt.%) increases the elastic modulus and thermal conductivity of the epoxy resin while decreasing the Poisson's ratio. For the first time, we present a coarse-grained model of DGEBA-DICY-DETA/graphene materials, which can facilitate the design and development of composites with tunable thermophysical properties for a potentially wide range of applications, e.g., automotive, aerospace, biomedical, or energy ones.

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.

Automatic Multiscale Method of Building up a Cross-linked Polymer Reaction System: Bridging SMILES to the Multiscale Molecular Dynamics Simulation

An automatic method is introduced to generate the initial configuration and input file from SMILES for multiscale molecular dynamics (MD) simulation of cross-linked polymer reaction systems. Inputs are a modified version of SMILES of all the components and conditions of coarse-grained (CG) and all-atom (AA) simulations. The overall process comprises the following steps: (1) Modified SMILES inputs of all the components are converted to 3-dimensional coordinates of molecular structures. (2) Molecular structures are mapped to the coarse-grained scale, followed by a CG reaction simulation. (3) CG beads are backmapped to the atomic scale after the CG reaction. (4) An AA productive run is finally performed to analyze volume shrinkage, glass transition, and atomic detail of network structure. The method is applied to two common epoxy resin reactions, that is, the cross-linking process of DGEVA (diglycidyl ether of vanillyl alcohol) and DHAVA (dihydroxyaminopropane of vanillyl alcohol) and that of DGEBA (diglycidyl ether of bisphenol A) and DETA (diethylenetriamine). These components form network structures after the CG cross-linking reaction and are then backmapped to calculate properties in the atomic scale. The result demonstrates that the method can accurately predict volume shrinkage, glass transition, and all-atom structure of cross-linked polymers. The method bridges from SMILES to MD simulation trajectories in an automatic way, which shortens the time of building up cross-linked polymer reaction model and suitable for high-throughput computations.

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.

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.