Temperature-Transferable Coarse-Grained Potentials for Ethylbenzene, Polystyrene, and Their Mixtures

A Temperature-Transferable Coarse-Grained Model for Poly(lactic Acid) Melts

We present a temperature-transferable coarse-grained (CG) model for poly(lactic acid) (PLA), specifically designed to replicate its volumetric properties and solubility parameter in the molten state. The CG-bonded potentials were derived by using the iterative Boltzmann inversion (IBI) optimization method to match structural properties from detailed atomistic models. A parametrization workflow was employed to determine nonbonded interaction parameters with temperature-dependent corrections that provide agreement with the target properties across the melting temperature range. The CG model successfully replicates key features of the PLA melt. It satisfactory reproduces the density and solubility parameter, maintains the dependence of chain conformation on molecular weight, and captures the dynamic behavior through agreement in scaled mean squared displacement and diffusion coefficients with the atomistic model. Additionally, the CG model offers much faster equilibration compared with the atomistic model. The proposed model is expected to be particularly useful for investigating the miscibility characteristics of PLA in various blends and composites that remain challenging to explore using fully atomistic simulations or experiments.

Self-Assembly Pathways of Triblock Janus Particles into 3D Open Lattices

The self-assembly of triblock Janus particles is simulated from a fluid to 3D open lattices: pyrochlore, perovskite, and diamond. The coarse-grained model explicitly takes into account the chemical details of the Janus particles (attractive patches at the poles and repulsion around the equator) and it contains explicit solvent particles. Hydrodynamic interactions are accounted for by dissipative particle dynamics. The relative stability of the crystals depends on the patch width. Narrow, intermediate, and wide patches stabilize the pyrochlore-, the perovskite-, and the diamond-lattice, respectively. The nucleation of all three lattices follows a two-step mechanism: the particles first agglomerate into a compact and disordered liquid cluster, which does not crystallize until it has grown to a threshold size. Second, the particles reorient inside this cluster to form crystalline nuclei. The free-energy barriers for the nucleation of pyrochlore and perovskite are ≈10 kBT, which are close to the nucleation barriers of previously studied 2D kagome lattices. The barrier height for the nucleation of diamond, however, is much larger (>20 kBT), as the symmetry of the triblock Janus particles is not perfect for a diamond structure. The large barrier is associated with the reorientation of particles, i.e., the second step of the nucleation mechanism.

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.

Physics-Informed Deep Learning Approach for Reintroducing Atomic Detail in Coarse-Grained Configurations of Multiple Poly(lactic acid) Stereoisomers

Multiscale modeling of complex molecular systems, such as macromolecules, encompasses methods that combine information from fine and coarse representations of molecules to capture material properties over a wide range of spatiotemporal scales. Being able to exchange information between different levels of resolution is essential for the effective transfer of this information. The inverse problem of reintroducing atomistic degrees of freedom in coarse-grained (CG) molecular configurations is particularly challenging as, from a mathematical point of view, it is an ill-posed problem; the forward mapping from the atomistic to the CG description is typically defined via a deterministic operator ("one-to-one" problem), whereas the reversed mapping from the CG to the atomistic model refers to creating one representative configuration out of many possible ones ("one-to-many" problem). Most of the backmapping methods proposed so far balance accuracy, efficiency, and general applicability. This is particularly important for macromolecular systems with different types of isomers, i.e., molecules that have the same molecular formula and sequence of bonded atoms (constitution) but differ in the three-dimensional configurations of their atoms in space. Here, we introduce a versatile deep learning approach for backmapping multicomponent CG macromolecules with chiral centers, trained to learn structural correlations between polymer configurations at the atomistic level and their corresponding CG descriptions. This method is intended to be simple and flexible while presenting a generic solution for resolution transformation. In addition, the method is aimed to respect the structural features of the molecule, such as local packing, capturing therefore the physical properties of the material. As an illustrative example, we apply the model on linear poly(lactic acid) (PLA) in melt, which is one of the most popular biodegradable polymers. The framework is tested on a number of model systems starting from homopolymer stereoisomers of PLA to copolymers with randomly placed chiral centers. The results demonstrate the efficiency and efficacy of the new approach.

Force matching and iterative Boltzmann inversion coarse grained force fields for ZIF-8

Despite the intense activity at electronic and atomistic resolutions, coarse grained (CG) modeling of metal-organic frameworks remains largely unexplored. One of the main reasons for this is the lack of adequate CG force fields. In this work, we present iterative Boltzmann inversion and force matching (FM) force fields for modeling ZIF-8 at three different coarse grained resolutions. Their ability to reproduce structure, elastic tensor, and thermal expansion is evaluated and compared with that of MARTINI force fields considered in previous work [Alvares et al., J. Chem. Phys. 158, 194107 (2023)]. Moreover, MARTINI and FM are evaluated for their ability to depict the swing effect, a subtle phase transition ZIF-8 undergoes when loaded with guest molecules. Overall, we found that all our force fields reproduce structure reasonably well. Elastic constants and volume expansion results are analyzed, and the technical and conceptual challenges of reproducing them are explained. Force matching exhibits promising results for capturing the swing effect. This is the first time these CG methods, widely applied in polymer and biomolecule communities, are deployed to model porous solids. We highlight the challenges of fitting CG force fields for these materials.

Insight into the Density-Dependence of Pair Potentials for Predictive Coarse-Grained Models

We investigate the temperature- and density-dependence of effective pair potentials for 1-site coarse-grained (CG) models of two industrial solvents, 1,4-dioxane and tetrahydrofuran. We observe that the calculated pair potentials are much more sensitive to density than to temperature. The generalized-Yvon-Born-Green framework reveals that this striking density-dependence reflects corresponding variations in the many-body correlations that determine the environment-mediated indirect contribution to the pair mean force. Moreover, we demonstrate, perhaps surprisingly, that this density-dependence is not important for accurately modeling the intermolecular structure. Accordingly, we adopt a density-independent interaction potential and transfer the density-dependence of the calculated pair potentials into a configuration-independent volume potential. Furthermore, we develop a single global potential that accurately models the intermolecular structure and pressure-volume equation of state across a very wide range of liquid state points. Consequently, this work provides fundamental insight into the density-dependence of effective pair potentials and also provides a significant step toward developing predictive CG models for efficiently modeling industrial solvents.

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.

Gaussian representation of coarse-grained interactions of liquids: Theory, parametrization, and transferability

Coarse-grained (CG) interactions determined via bottom-up methodologies can faithfully reproduce the structural correlations observed in fine-grained (atomistic resolution) systems, yet they can suffer from limited extensibility due to complex many-body correlations. As part of an ongoing effort to understand and improve the applicability of bottom-up CG models, we propose an alternative approach to address both accuracy and transferability. Our main idea draws from classical perturbation theory to partition the hard sphere repulsive term from effective CG interactions. We then introduce Gaussian basis functions corresponding to the system's characteristic length by linking these Gaussian sub-interactions to the local particle densities at each coordination shell. The remaining perturbative long-range interaction can be treated as a collective solvation interaction, which we show exhibits a Gaussian form derived from integral equation theories. By applying this numerical parametrization protocol to CG liquid systems, our microscopic theory elucidates the emergence of Gaussian interactions in common phenomenological CG models. To facilitate transferability for these reduced descriptions, we further infer equations of state to determine the sub-interaction parameter as a function of the system variables. The reduced models exhibit excellent transferability across the thermodynamic state points. Furthermore, we propose a new strategy to design the cross-interactions between distinct CG sites in liquid mixtures. This involves combining each Gaussian in the proper radial domain, yielding accurate CG potentials of mean force and structural correlations for multi-component systems. Overall, our findings establish a solid foundation for constructing transferable bottom-up CG models of liquids with enhanced extensibility.

Data-Driven Approach to Coarse-Graining Simple Liquids in Confinement

We propose a data-driven framework for identifying coarse-grained (CG) Lennard-Jones (LJ) potential parameters in confined systems for simple liquids. Our approach involves the use of a Deep Neural Network (DNN) that is trained to approximate the solution of the Inverse Liquid State (ILST) problem for confined systems. The DNN model inherently incorporates essential physical characteristics specific to confined fluids, enabling an accurate prediction of inhomogeneity effects. By utilizing transfer learning, we predict single-site LJ potentials of simple multiatomic liquids confined in a slit-like channel, which effectively replicate both the fluid structure and molecular force of the target All-Atom (AA) system when the electrostatic interactions are not dominant. In addition, we showcase the synergy between the data-driven approach and the well-known Bottom-Up coarse-graining method utilizing Relative-Entropy (RE) Minimization. Through the sequential utilization of these two methods, the robustness of the iterative RE method is significantly augmented, leading to a remarkable enhancement in convergence.

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.

Learning pair potentials using differentiable simulations

Learning pair interactions from experimental or simulation data is of great interest for molecular simulations. We propose a general stochastic method for learning pair interactions from data using differentiable simulations (DiffSim). DiffSim defines a loss function based on structural observables, such as the radial distribution function, through molecular dynamics (MD) simulations. The interaction potentials are then learned directly by stochastic gradient descent, using backpropagation to calculate the gradient of the structural loss metric with respect to the interaction potential through the MD simulation. This gradient-based method is flexible and can be configured to simulate and optimize multiple systems simultaneously. For example, it is possible to simultaneously learn potentials for different temperatures or for different compositions. We demonstrate the approach by recovering simple pair potentials, such as Lennard-Jones systems, from radial distribution functions. We find that DiffSim can be used to probe a wider functional space of pair potentials compared with traditional methods like iterative Boltzmann inversion. We show that our methods can be used to simultaneously fit potentials for simulations at different compositions and temperatures to improve the transferability of the learned potentials.

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.

Using molecular simulation to understand the skin barrier

Skin's effectiveness as a barrier to permeation of water and other chemicals rests almost entirely in the outermost layer of the epidermis, the stratum corneum (SC), which consists of layers of corneocytes surrounded by highly organized lipid lamellae. As the only continuous path through the SC, transdermal permeation necessarily involves diffusion through these lipid layers. The role of the SC as a protective barrier is supported by its exceptional lipid composition consisting of ceramides (CERs), cholesterol (CHOL), and free fatty acids (FFAs) and the complete absence of phospholipids, which are present in most biological membranes. Molecular simulation, which provides molecular level detail of lipid configurations that can be connected with barrier function, has become a popular tool for studying SC lipid systems. We review this ever-increasing body of literature with the goals of (1) enabling the experimental skin community to understand, interpret and use the information generated from the simulations, (2) providing simulation experts with a solid background in the chemistry of SC lipids including the composition, structure and organization, and barrier function, and (3) presenting a state of the art picture of the field of SC lipid simulations, highlighting the difficulties and best practices for studying these systems, to encourage the generation of robust reproducible studies in the future. This review describes molecular simulation methodology and then critically examines results derived from simulations using atomistic and then coarse-grained models.

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.

Roughness Volumes: An Improved RoughMob Concept for Predicting the Increase of Molecular Mobility upon Coarse-Graining

The reduced number of degrees of freedom in a coarse-grained molecular model compared to its parent atomistic model not only makes it possible to simulate larger systems for longer time scales but also results in an artificial mobility increase. The RoughMob method [Meinel, M. K. and Müller-Plathe, F. J. Chem. Theory Comput. 2020, 16, 1411.] linked the acceleration factor of the dynamics to the loss of geometric information upon coarse-graining. Our hypothesis is that coarse-graining a multiatom molecule or group into a single spherical bead smooths the molecular surface and, thus, leads to reduced intermolecular friction. A key parameter is the molecular roughness difference, which is calculated via a numerical comparison of the molecular surfaces of both the atomistic and coarse-grained models. Augmenting the RoughMob method, we add the concept of the region where the roughness acts. This information is contained in four so-called roughness volumes. For 17 systems of homogeneous hydrocarbon fluids, simple one-bead coarse-grained models are derived by the structure-based iterative Boltzmann inversion. They include 13 different homogeneous aliphatic and aromatic molecules and two different mapping schemes. We present a simple way to correlate the roughness volumes to the acceleration factor. The resulting relation is able to a priori predict the acceleration factors for an extended size and shape range of hydrocarbon molecules, with different mapping schemes and different densities.

Addressing Surface Effects at the Particle-Continuum Interface in a Molecular Dynamics and Finite Elements Coupled Multiscale Simulation Technique

Atomistic-to-continuum coupling methods are used to unravel molecular mechanisms of polymers and polymer composites. These multiscale techniques advantageously combine the computational efficiency of continuum approaches while keeping the accuracy of particle-based methods. The Capriccio method [Pfaller et al. Comput. Methods Appl. Mech. Eng. 2013, 260, 109-129.] is a well-proven multiscale technique, which connects finite elements (FE) with molecular dynamics (MD) in a partitioned-domain approach. A vital aspect of these multiscale methods is to provide physically sound boundary conditions to the particle domain suppressing any interface effects at the domain boundary occurring due to the coupling. These interfacial coupling artifacts still pose a significant problem, especially for amorphous polymers due to their highly irregular microstructure. We solve this problem by extending the particle-continuum interface by a layer of passive atoms which move with the outer continuum, thereby providing the missing interactions with a surrounding polymer bulk to the inner particle region. This solution allows us to successfully reproduce structural and mechanical properties obtained under conventional periodic boundary conditions, like density, stress, Young's modulus, and Poisson's ratio. Furthermore, we demonstrate the application of a nonaffine deformation by means of a simple bending test. In general, our revised method provides a framework to apply complex deformations for molecular scientists, while it allows the engineering community to examine challenging phenomena such as fracture behavior at a molecular level.

Data-Driven Methods for Accelerating Polymer Design

Optimal design of polymers is a challenging task due to their enormous chemical and configurational space. Recent advances in computations, machine learning, and increasing trends in data and software availability can potentially address this problem and accelerate the molecular-scale design of polymers. Here, the central problem of polymer design is reviewed, and the general ideas of data-driven methods and their working principles in the context of polymer design are discussed. This Review provides a historical perspective and a summary of current trends and outlines future scopes of data-driven methods for polymer research. A few representative case studies on the use of such data-driven methods for discovering new polymers with exceptional properties are presented. Moreover, attempts are made to highlight how data-driven strategies aid in establishing new correlations and advancing the fundamental understanding of polymers. This Review posits that the combination of machine learning, rapid computational characterization of polymers, and availability of large open-sourced homogeneous data will transform polymer research and development over the coming decades. It is hoped that this Review will serve as a useful reference to researchers who wish to develop and deploy data-driven methods for polymer research and education.

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.

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.

Solvent-Evaporation Induced and Mechanistic Entropy-Enthalpy-Balance Controlled Polymer Patch Formation on Nanoparticle Surfaces

The formation of polymer-patch nanoparticles (PNPs) involves a condensation process of grafted chains on a nanoparticle (NP) surface, which is conventionally achieved via a fine-tuning of the solvent quality. However, such a critical solvent condition differs dramatically between polymers, and the formation mechanism of different patchy structures remains under debate. In this study, we demonstrate by a combined simulation and experimental study that such a surface-patterning process can be easily achieved via a simple solvent evaporation process, which creates a natural nonsolvent condition and is, in principle, adaptable for all polymers. More importantly, we find that patchy structures are controlled by a delicate balance between enthalpic interaction and the entropy penalty of grafted chains. A small variation of cohesive energy density can lead to a dramatic change in patch structure. This work offers a robust yet easy approach for the fabrication of PNPs and provides new insights into polymer segregation on spherical surfaces.

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.

Block-copolymer-like self-assembly behavior of mobile-ligand grafted ultra-small nanoparticles

We use coarse-grained molecular dynamics simulations to study the self-assembly behavior of polyoxometalate (POM) nanoparticles (NPs) decorated with mobile polymer ligands under melt conditions. We demonstrate that due to the mobile nature of the grafted ligands on the NP surface, NPs have the ability to expose a part of their surfaces, leading to a block-copolymer-like self-assembly behavior. The exposed NP surface serves as one block and the grafted ligand polymers as another. This system has a strong ability to self-assemble into long-range ordered structures such as block copolymers due to large incompatibility between POM and ligand polymers, i.e., POM NPs can form lamellar, cylindrical, and spherical structures, which are consistent with previous experimental results. More importantly, these ordered structures are on the sub-10 nm scale, which is an important requirement for many applications. At low graft density, we find a new inverse-cylindrical structure formation where polymers form cylinders and POMs form a continuous network structure. A full self-assembly phase diagram is constructed which illustrates rules to manipulate the self-assembly structures of NPs decorated with mobile polymer ligands. We hope that these computational results will be useful for the new design of nanostructures with improved optical or electronic functions.

Uncertainty Quantification Guided Parameter Selection in a Fully Coupled Molecular Dynamics-Finite Element Model of the Mechanical Behavior of Polymers

The objective of investigating macroscopic polymer properties with a low computing cost and a high resolution has led to the development of efficient hybrid simulation tools. Systems generated from such simulation tools can fail in service if the effect of uncertainty of model inputs on its outputs is not accounted for. This work focuses on quantifying the effect of parametric uncertainty in our coarse-grained molecular dynamics-finite element coupling approach using uncertainty quantification. We consider uniaxial deformation simulations of a polystyrene sample at T = 100 K in our study. Parametric uncertainty is assumed to originate from parameters in the molecular dynamics model with a nonperiodic boundary (the force constant between polymer beads and anchor points, the number of anchor points, and the size of the surrounding dissipative particle dynamics domain) and a parameter to blend the energies of particles and continuum (weighting factor). Key issues that arise in uncertainty quantification are discussed on the basis of the quantities of interest including mass density, end-to-end distance, and radial distribution function. This work reveals the influence of key input parameters on the properties of polymer structure and facilitates the determination of those parameters in the application of this hybrid molecular dynamics-finite element approach.

Knotting behaviour of polymer chains in the melt state for soft-core models with and without slip-springs

We analyse the knotting behaviour of linear polymer melts in two types of soft-core models, namely dissipative-particle dynamics and hybrid-particle-field models, as well as their variants with slip-springs which are added to recover entangled polymer dynamics. The probability to form knots is found drastically higher in the hybrid-particle-field model compared to its parent hard-core molecular dynamics model. By comparing the knottedness in dissipative-particle dynamics and hybrid-particle-field models with and without slip-springs, we find the impact of slip-springs on the knotting properties to be negligible. As a dynamic property, we measure the characteristic time of knot formation and destruction, and find it to be (i) of the same order as single-monomer motion and (ii) independent of the chain length in all soft-core models. Knots are therefore formed and destroyed predominantly by the unphysical chain crossing. This work demonstrates that the addition of slip-springs does not alter the knotting behaviour, and it provides a general understanding of knotted structures in these two soft-core models of polymer melts.

Mechanisms of Nucleation and Solid-Solid-Phase Transitions in Triblock Janus Assemblies

A model, including the chemical details of core nanoparticles as well as explicit surface charges and hydrophobic patches, of triblock Janus particles is employed to simulate nucleation and solid-solid phase transitions in two-dimensional layers. An explicit solvent and a substrate are included in the model, and hydrodynamic and many-body interactions were taken into account within many-body dissipative particle dynamics simulation. In order not to impose a mechanism a priori, we performed free (unbiased) simulations, leaving the system the freedom to choose its own pathways. In agreement with the experiment and previous biased simulations, a two-step mechanism for the nucleation of a kagome lattice from solution was detected. However, a distinct feature of the present unbiased versus biased simulations is that multiple nuclei emerge from the solution; upon their growth, the aligned and misaligned facets at the grain boundaries are introduced into the system. The liquid-like particles trapped between the neighboring nuclei connect them together. A mismatch in the symmetry planes of neighboring nuclei hinders the growth of less stable (smaller) nuclei. Unification of such nuclei at the grain boundaries of misaligned facets obeys a two-step mechanism: melting of the smaller nuclei, followed by subsequent nucleation of liquid-like particles at the interface of bigger neighboring nuclei. Besides, multiple postcritical nuclei are formed in the simulation box; the growth of some of which stops due to introduction of a strain in the system. Such an incomplete nucleation/growth mechanism is in complete agreement with the recent experiments. The solid-solid (hexagonal-to-kagome) phase transition, at weak superheatings, obeys a two-step mechanism: a slower step (formation of a liquid droplet), followed by a faster step (nucleation of kagome from the liquid droplet).

Generalized equation of state for fluids: From molecular liquids to colloidal dispersions

In this work, a new parameterization for the Statistical Association Fluid Theory for potentials of Variable Range (SAFT-VR) is coupled to the discrete potential theory to represent the thermodynamic properties of several fluids, ranging from molecular liquids to colloidal-like dispersions. In this way, this version of the SAFT-VR approach can be straightforwardly applied to any kind of either simple or complex fluid. In particular, two interaction potentials, namely, the Lennard-Jones and the hard-core attractive Yukawa potentials, are discretized to study the vapor-liquid equilibrium properties of both molecular and complex liquids, respectively. Our results are assessed with Monte Carlo computer simulations and available and accurate theoretical results based on the self-consistent Ornstein-Zernike approximation.

Investigating the energetic and entropic components of effective potentials across a glass transition

By eliminating unnecessary details, coarse-grained (CG) models provide the necessary efficiency for simulating scales that are inaccessible to higher resolution models. However, because they average over atomic details, the effective potentials governing CG degrees of freedom necessarily incorporate significant entropic contributions, which limit their transferability and complicate the treatment of thermodynamic properties. This work employs a dual-potential approach to consider the energetic and entropic contributions to effective interaction potentials for CG models. Specifically, we consider one- and three-site CG models for ortho-terphenyl (OTP) both above and below its glass transition. We employ the multiscale coarse-graining (MS-CG) variational principle to determine interaction potentials that accurately reproduce the structural properties of an all-atom (AA) model for OTP at each state point. We employ an energy-matching variational principle to determine an energy operator that accurately reproduces the intra- and inter-molecular energy of the AA model. While the MS-CG pair potentials are almost purely repulsive, the corresponding pair energy functions feature a pronounced minima that corresponds to contacting benzene rings. These energetic functions then determine an estimate for the entropic component of the MS-CG interaction potentials. These entropic functions accurately predict the MS-CG pair potentials across a wide range of liquid state points at constant density. Moreover, the entropic functions also predict pair potentials that quite accurately model the AA pair structure below the glass transition. Thus, the dual-potential approach appears a promising approach for modeling AA energetics, as well as for predicting the temperature-dependence of CG effective potentials.

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

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

Temperature and Phase Transferable Bottom-up Coarse-Grained Models

Despite the high fidelity of bottom-up coarse-grained (CG) approaches to recapitulate the structural correlations in atomistic simulations, the general use of bottom-up CG methods is limited because of the nontransferable nature of these CG models under different thermodynamic conditions. Because bottom-up CG potentials usually correspond to configuration-dependent free energies of the system, recent studies have focused on adjusting enthalpic or entropic contributions to account for issues with transferability. However, these approaches can require a manual adjustment of the CG interaction a priori and are usually limited to constant volume ensembles. To overcome these limitations, we construct temperature and phase transferable CG models under constant pressure by developing the ultra-coarse-graining (UCG) methodology in the mean-field limit. In the mean-field ansatz, an embedded semi-global order parameter recapitulates global changes to the system by automatically adjusting the effective CG interactions, thus bridging free energy decompositions with UCG theory. The method presented is designed to faithfully capture structural correlations under different thermodynamic conditions, using a single UCG model. Specifically, we test the applicability of the developed theory in three distinct cases: (1) different temperatures at constant pressure in liquids, (2) different temperatures across thermodynamic phases, and (3) liquid/vapor interfaces. We demonstrate that the systematic construction of both temperature and phase transferable bottom-up CG models is possible using this generalized UCG theory. Based on our findings, this approach significantly extends the transferability and applicability of the bottom-up CG theory and method.

Multi-scale modeling of the polymer-filler interaction

We report mesoscopic simulations of the interaction between a silica nanoparticle and cis-1,4-polybutadiene chains with realistic coarse-(CG) grained models. The CG models are obtained with a bottom-up Bayesian method based on trajectory matching of atomistic configurations of the system. We then investigate the structural properties of the interfacial region as a function of the grafting density and polymer chain length. We take advantage of the realistic CG models to explore the dynamics of the nanoparticle over a period of 10 microseconds. We show that the dynamics of the nanoparticle is affected by the grafting density and the polymer chain length of the grafted chains.