A Review of Multiscale Computational Methods in Polymeric Materials

Thermal Conductivity Enhancement of Polymeric Composites Using Hexagonal Boron Nitride: Design Strategies and Challenges

With the integration and miniaturization of chips, there is an increasing demand for improved heat dissipation. However, the low thermal conductivity (TC) of polymers, which are commonly used in chip packaging, has seriously limited the development of chips. To address this limitation, researchers have recently shown considerable interest in incorporating high-TC fillers into polymers to fabricate thermally conductive composites. Hexagonal boron nitride (h-BN) has emerged as a promising filler candidate due to its high-TC and excellent electrical insulation. This review comprehensively outlines the design strategies for using h-BN as a high-TC filler and covers intrinsic TC and morphology effects, functionalization methods, and the construction of three-dimensional (3D) thermal conduction networks. Additionally, it introduces some experimental TC measurement techniques of composites and theoretical computational simulations for composite design. Finally, the review summarizes some effective strategies and possible challenges for the design of h-BN fillers. This review provides researchers in the field of thermally conductive polymeric composites with a comprehensive understanding of thermal conduction and constructive guidance on h-BN design.

Revealing the Role of Chain Conformations on the Origin of the Mechanical Reinforcement in Glassy Polymer Nanocomposites

Understanding the mechanism of mechanical reinforcement in glassy polymer nanocomposites is of paramount importance for their tailored design. Here, we present a detailed investigation, via atomistic simulation, of the coupling between density, structure, and conformations of polymer chains with respect to their role in mechanical reinforcement. Probing the properties at the molecular level reveals that the effective mass density as well as the rigidity of the matrix region changes with filler volume fraction, while that of the interphase remains constant. The origin of the mechanical reinforcement is attributed to the heterogeneous chain conformations in the vicinity of the nanoparticles, involving a 2-fold mechanism. In the low-loading regime, the reinforcement comes mainly from a thin, single-molecule, 2D-like layer of adsorbed polymer segments on the nanoparticle, whereas in the high-loading regime, the reinforcement is dominated by the coupling between train and bridge conformations; the latter involves segments connecting neighboring nanoparticles.

Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution

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

Integrating Machine Learning in the Coarse-Grained Molecular Simulation of Polymers

Machine learning (ML) is having an increasing impact on the physical sciences, engineering, and technology and its integration into molecular simulation frameworks holds great potential to expand their scope of applicability to complex materials and facilitate fundamental knowledge and reliable property predictions, contributing to the development of efficient materials design routes. The application of ML in materials informatics in general, and polymer informatics in particular, has led to interesting results, however great untapped potential lies in the integration of ML techniques into the multiscale molecular simulation methods for the study of macromolecular systems, specifically in the context of Coarse Grained (CG) simulations. In this Perspective, we aim at presenting the pioneering recent research efforts in this direction and discussing how these new ML-based techniques can contribute to critical aspects of the development of multiscale molecular simulation methods for bulk complex chemical systems, especially polymers. Prerequisites for the implementation of such ML-integrated methods and open challenges that need to be met toward the development of general systematic ML-based coarse graining schemes for polymers are discussed.

Multiscale equilibration of highly entangled isotropic model polymer melts

We present a computationally efficient multiscale method for preparing equilibrated, isotropic long-chain model polymer melts. As an application, we generate Kremer-Grest melts of 1000 chains with 200 entanglements and 25 000-2000 beads/chain, which cover the experimentally relevant bending rigidities up to and beyond the limit of the isotropic-nematic transition. In the first step, we employ Monte Carlo simulations of a lattice model to equilibrate the large-scale chain structure above the tube scale while ensuring a spatially homogeneous density distribution. We then use theoretical insight from a constrained mode tube model to introduce the bead degrees of freedom together with random walk conformational statistics all the way down to the Kuhn scale of the chains. This is followed by a sequence of simulations with carefully parameterized force-capped bead-spring models, which slowly introduce the local bead packing while reproducing the larger-scale chain statistics of the target Kremer-Grest system at all levels of force-capping. Finally, we can switch to the full Kremer-Grest model without perturbing the structure. The resulting chain statistics is in excellent agreement with literature results on all length scales accessible in brute-force simulations of shorter chains.

Hierarchically structured bioinspired nanocomposites

Next-generation structural materials are expected to be lightweight, high-strength and tough composites with embedded functionalities to sense, adapt, self-repair, morph and restore. This Review highlights recent developments and concepts in bioinspired nanocomposites, emphasizing tailoring of the architecture, interphases and confinement to achieve dynamic and synergetic responses. We highlight cornerstone examples from natural materials with unique mechanical property combinations based on relatively simple building blocks produced in aqueous environments under ambient conditions. A particular focus is on structural hierarchies across multiple length scales to achieve multifunctionality and robustness. We further discuss recent advances, trends and emerging opportunities for combining biological and synthetic components, state-of-the-art characterization and modelling approaches to assess the physical principles underlying nature-inspired design and mechanical responses at multiple length scales. These multidisciplinary approaches promote the synergetic enhancement of individual materials properties and an improved predictive and prescriptive design of the next era of structural materials at multilength scales for a wide range of applications.

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.

Emerging polymeric material strategies for cartilage repair

Cartilage is found throughout the body, serving an array of essential functions. Owing to the limited healing capacity of cartilage, damage or degeneration is often permanent and so requires clinical intervention. Established surgical techniques generally rely on biological grafting. However, recent advances in polymeric materials provide an encouraging alternative to overcome limits of auto- and allografts. For regenerative engineering of cartilage, a polymeric scaffold ideally supports and instructs tissue regeneration while also providing mechanical integrity. Scaffolds direct regeneration via chemical and mechanical cues, as well as delivery and support of exogenous cells and bioactive factors. Advanced polymeric scaffolds aim to direct regeneration locally, replicating the heterogeneities of native tissues. Alternatively, new cartilage-mimetic hydrogels have potential to serve as synthetic cartilage replacements. Prepared as multi-network or composite hydrogels, the most promising candidates have simultaneously realized the hydration, mechanical, and tribological properties of native cartilage. Collectively, the recent rise in polymers for cartilage regeneration and replacement proposes a changing paradigm, with a new generation of materials paving the way for improved clinical outcomes.

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review

Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality.

Modeling Polyzwitterion-Based Drug Delivery Platforms: A Perspective of the Current State-of-the-Art and Beyond

Drug delivery platforms are anticipated to have biocompatible and bioinert surfaces. PEGylation of drug carriers is the most approved method since it improves water solubility and colloid stability and decreases the drug vehicles’ interactions with blood components. Although this approach extends their biocompatibility, biorecognition mechanisms prevent them from biodistribution and thus efficient drug transfer. Recent studies have shown (poly)zwitterions to be alternatives for PEG with superior biocompatibility. (Poly)zwitterions are super hydrophilic, mainly stimuli-responsive, easy to functionalize and they display an extremely low protein adsorption and long biodistribution time. These unique characteristics make them already promising candidates as drug delivery carriers. Furthermore, since they have highly dense charged groups with opposite signs, (poly)zwitterions are intensely hydrated under physiological conditions. This exceptional hydration potential makes them ideal for the design of therapeutic vehicles with antifouling capability, i.e., preventing undesired sorption of biologics from the human body in the drug delivery vehicle. Therefore, (poly)zwitterionic materials have been broadly applied in stimuli-responsive “intelligent” drug delivery systems as well as tumor-targeting carriers because of their excellent biocompatibility, low cytotoxicity, insignificant immunogenicity, high stability, and long circulation time. To tailor (poly)zwitterionic drug vehicles, an interpretation of the structural and stimuli-responsive behavior of this type of polymer is essential. To this end, a direct study of molecular-level interactions, orientations, configurations, and physicochemical properties of (poly)zwitterions is required, which can be achieved via molecular modeling, which has become an influential tool for discovering new materials and understanding diverse material phenomena. As the essential bridge between science and engineering, molecular simulations enable the fundamental understanding of the encapsulation and release behavior of intelligent drug-loaded (poly)zwitterion nanoparticles and can help us to systematically design their next generations. When combined with experiments, modeling can make quantitative predictions. This perspective article aims to illustrate key recent developments in (poly)zwitterion-based drug delivery systems. We summarize how to use predictive multiscale molecular modeling techniques to successfully boost the development of intelligent multifunctional (poly)zwitterions-based systems.

Coarse-Grained Modeling of Ion-Containing Polymers

Ion-containing polymers have continued to be an important research focus for several decades due to their use as an electrolyte in energy storage and conversion devices. Elucidation of connections between the mesoscopic structure and multiscale dynamics of the ions and solvent remains incompletely understood. Coarse-grained modeling provides an efficient approach for exploring the structural and dynamical properties of these soft materials. The unique physicochemical properties of such polymers are of broad interest. In this review, we summarize the current development and understanding of the structure-property relationship of ion-containing polymers and provide insights into the design of such materials determined from coarse-grained modeling and simulations accompanying significant advances in experimental strategies. We specifically concentrate on three types of ion-containing polymers: proton exchange membranes (PEMs), anion exchange membranes (AEMs), and polymerized ionic liquids (polyILs). We posit that insight into the similarities and differences in these materials will lead to guidance in the rational design of high-performance novel materials with improved properties for various power source technologies.

Polyply; a python suite for facilitating simulations of macromolecules and nanomaterials

Molecular dynamics simulations play an increasingly important role in the rational design of (nano)-materials and in the study of biomacromolecules. However, generating input files and realistic starting coordinates for these simulations is a major bottleneck, especially for high throughput protocols and for complex multi-component systems. To eliminate this bottleneck, we present the polyply software suite that provides 1) a multi-scale graph matching algorithm designed to generate parameters quickly and for arbitrarily complex polymeric topologies, and 2) a generic multi-scale random walk protocol capable of setting up complex systems efficiently and independent of the target force-field or model resolution. We benchmark quality and performance of the approach by creating realistic coordinates for polymer melt simulations, single-stranded as well as circular single-stranded DNA. We further demonstrate the power of our approach by setting up a microphase-separated block copolymer system, and by generating a liquid-liquid phase separated system inside a lipid vesicle.

Optimization of Polymer Processing: A Review (Part I-Extrusion)

Given the global economic and societal importance of the polymer industry, the continuous search for improvements in the various processing techniques is of practical primordial importance. This review evaluates the application of optimization methodologies to the main polymer processing operations. The most important characteristics related to the usage of optimization techniques, such as the nature of the objective function, the type of optimization algorithm, the modelling approach used to evaluate the solutions, and the parameters to optimize, are discussed. The aim is to identify the most important features of an optimization system for polymer processing problems and define the best procedure for each particular practical situation. For this purpose, the state of the art of the optimization methodologies usually employed is first presented, followed by an extensive review of the literature dealing with the major processing techniques, the discussion being completed by considering both the characteristics identified and the available optimization methodologies. This first part of the review focuses on extrusion, namely single and twin-screw extruders, extrusion dies, and calibrators. It is concluded that there is a set of methodologies that can be confidently applied in polymer processing with a very good performance and without the need of demanding computation requirements.

Atomistic-scale analysis of the deformation and failure of polypropylene composites reinforced by functionalized silica nanoparticles

Interfacial adhesion between polymer matrix and reinforcing silica nanoparticles plays an important role in strengthening polypropylene (PP) composite. To improve the adhesion strength, the surface of silica nanoparticles can be modified by grafted functional molecules. Using atomistic simulations, we examined the effect of functionalization of silica nanoparticles by hexamethyldisilazane (HMDS) and octyltriethoxysilane (OTES) molecules on the deformation and failure of silica-reinforced PP composite. We found that the ultimate tensile strength (UTS) of PP composite functionalized by OTES (28 MPa) is higher than that of HMDS (25 MPa), which is in turn higher than that passivated only by hydrogen (22 MPa). To understand the underlying mechanistic origin, we calculated the adhesive energy and interfacial strength of the interphase region, and found that both the adhesive energy and interfacial strength are the highest for the silica nanoparticles functionalized by OTES molecules, while both are the lowest by hydrogen. The ultimate failure of the polymer composite is initiated by the cavitation in the interphase region with the lowest mass density, and this cavitation failure mode is common for all the examined PP composites, but the cavitation position is dependent on the tail length of the functional molecules. The present work provides interesting insights into the deformation and cavitation failure mechanisms of the silica-reinforced PP composites, and the findings can be used as useful guidelines in selecting chemical agents for surface treatment of silica nanoparticles.

Effect of Nanoparticles Surface Bonding and Aspect Ratio on Mechanical Properties of Highly Cross-Linked Epoxy Nanocomposites: Mesoscopic Simulations

The paper aims to study the mechanical properties of epoxy resin filled with clay nanoparticles (NPs), depending on their shapes and content on the surface of a modifying agent capable of forming covalent bonds with a polymer. The cylindrical clay nanoparticles with equal volume and different aspects ratios (disks, barrel, and stick) are addressed. The NPs' bonding ratio with the polymer (RGC) is determined by the fraction of reactive groups and conversion time and varies from RGC = 0 (non-bonded nanoparticles) to RGC = 0.65 (more than half of the surface groups are linked with the polymer matrix). The performed simulations show the so-called load-bearing chains (LBCs) of chemically cross-linked monomers and modified nanoparticles to determine the mechanical properties of the simulated composites. The introduction of nanoparticles leads to the breaking of such chains, and the chemical cross-linking of NPs with the polymer matrix restores the LBCs and strengthens the composite. At small values of RGC, the largest value of the elastic modulus is found for systems filled with nanoparticles having the smallest surface area, and at high values of RGC, on the contrary, the systems containing disk-shaped particles with the largest surface area have a larger elastic modulus than the others. All calculations are performed within the framework of a mesoscopic model based on accurate mapping of the atomistic structures of the polymer matrix and nanoparticles into coarse-grained representations, which, if necessary, allow reverse data mapping and quantitative assessment of the state of the filled epoxy resin. On the other hand, the obtained data can be used to design the functional materials with specified mechanical properties based on other practically significant polymer matrices and nanofillers.

A network model of transient polymers: exploring the micromechanics of nonlinear viscoelasticity

Dynamic networks contain crosslinks that re-associate after disconnecting, imparting them with viscoelastic properties. While continuum approaches have been developed to analyze their mechanical response, these approaches can only describe their evolution in an average sense, omitting local, stochastic mechanisms that are critical to damage initiation or strain localization. To address these limitations, we introduce a discrete numerical model that mesoscopically coarse-grains the individual constituents of a dynamic network to predict its mechanical and topological evolution. Each constituent consists of a set of flexible chains that are permanently cross-linked at one end and contain reversible binding sites at their free ends. We incorporate nonlinear force-extension of individual chains via a Langevin model, slip-bond dissociation through Eyring's model, and spatiotemporally-dependent bond attachment based on scaling theory. Applying incompressible, uniaxial tension to representative volume elements at a range of constant strain rates and network connectivities, we then compare the mechanical response of these networks to that predicted by the transient network theory. Ultimately, we find that the idealized continuum approach remains suitable for networks with high chain concentrations when deformed at low strain rates, yet the mesoscale model proves necessary for the exploration of localized stochastic events, such as variability of the bond kinetics, or the nucleation of micro-cavities that likely conceive damage and fracture.

Structure-Property Relationship on the Example of Gas Separation Characteristics of Poly(Arylene Ether Ketone)s and Poly(Diphenylene Phtalide)

Three poly(arylene ether ketone)s (PAEKs) with propylidene (C1, C2) and phtalide (C3) fragments, and one phtalide-containing polyarylene (C4), were synthesized. Their chemical structures were confirmed via 1H NMR, 13C NMR and 19F NMR spectroscopy. The polymers have shown a high glass transition temperature (>155 °C), excellent film-forming properties, and a high free volume for this polymer type. The influence of various functional groups in the structure of PAEKs was evaluated. Expectedly, due to higher free volume the introduction of hexafluoropropylidene group to PAEK resulted in higher increase of gas permeability in comparison with propylidene group. The substitution of the fluorine-containing group on a rigid phtalide moiety (C3) significantly increases glass transition temperature of the polymer while gas permeation slightly decreases. Finally, the removal of two ether groups from PAEK structure (C4) leads to a rigid polymer chain that is characterized by highest free volume, gas permeability and diffusion coefficients among the PAEKs under investigation. Methods of modified atomic (MAC) and bond (BC) contributions were applied to estimate gas permeation and diffusion. Both techniques showed reasonable predicted parameters for three polymers while a significant underestimation of gas transport parameters was observed for C4. Gas solubility coefficients for PAEKs were forecasted by "Short polymer chain surface based pre-diction" (SPCSBP) method. Results for all three prediction methods were compared with the ex-perimental data obtained in this work. Predicted parameters were in good agreement with ex-perimental data for phtalide-containing polymers (C3 and C4) while for propylidene-containing poly(arylene ether ketone)s they were overestimated due to a possible influence of propylidene fragment on indices of oligomeric chains. MAC and BC methods demonstrated better prediction power than SPCSBP method.

Multidimensional Nano-Imaging of Structure, Coupling, and Disorder in Molecular Materials

A hierarchy of intramolecular and intermolecular interactions controls the properties of biomedical, photophysical, and novel energy materials. However, multiscale heterogeneities often obfuscate the relationship between microscopic structure and emergent function, and they are generally difficult to access with conventional optical and electron microscopy techniques. Here, we combine vibrational exciton nanoimaging in variable-temperature near-field optical microscopy (IR s-SNOM) with four-dimensional scanning transmission electron microscopy (4D-STEM), and vibrational exciton modeling based on density functional theory (DFT), to link local microscopic molecular interactions to macroscopic three-dimensional order. In the application to poly(tetrafluoroethylene) (PTFE), large spatio-spectral heterogeneities with C-F vibrational energy shifts ranging from sub-cm^-1 to ≳25 cm^-1 serve as a molecular ruler of the degree of local crystallinity and disorder. Spatio-spectral-structural correlations reveal a previously invisible degree of highly variable local disorder in molecular coupling as the possible missing link between nanoscale morphology and associated electronic, photonic, and other functional properties of molecular materials.

Physics of the Nuclear Pore Complex: Theory, Modeling and Experiment

The hallmark of eukaryotic cells is the nucleus that contains the genome, enclosed by a physical barrier known as the nuclear envelope (NE). On the one hand, this compartmentalization endows the eukaryotic cells with high regulatory complexity and flexibility. On the other hand, it poses a tremendous logistic and energetic problem of transporting millions of molecules per second across the nuclear envelope, to facilitate their biological function in all compartments of the cell. Therefore, eukaryotes have evolved a molecular "nanomachine" known as the Nuclear Pore Complex (NPC). Embedded in the nuclear envelope, NPCs control and regulate all the bi-directional transport between the cell nucleus and the cytoplasm. NPCs combine high molecular specificity of transport with high throughput and speed, and are highly robust with respect to molecular noise and structural perturbations. Remarkably, the functional mechanisms of NPC transport are highly conserved among eukaryotes, from yeast to humans, despite significant differences in the molecular components among various species. The NPC is the largest macromolecular complex in the cell. Yet, despite its significant complexity, it has become clear that its principles of operation can be largely understood based on fundamental physical concepts, as have emerged from a combination of experimental methods of molecular cell biology, biophysics, nanoscience and theoretical and computational modeling. Indeed, many aspects of NPC function can be recapitulated in artificial mimics with a drastically reduced complexity compared to biological pores. We review the current physical understanding of the NPC architecture and function, with the focus on the critical analysis of experimental studies in cells and artificial NPC mimics through the lens of theoretical and computational models. We also discuss the connections between the emerging concepts of NPC operation and other areas of biophysics and bionanotechnology.

Computational Tools to Rationalize and Predict the Self-Assembly Behavior of Supramolecular Gels

Supramolecular gels form a class of soft materials that has been heavily explored by the chemical community in the past 20 years. While a multitude of experimental techniques has demonstrated its usefulness when characterizing these materials, the potential value of computational techniques has received much less attention. This review aims to provide a complete overview of studies that employ computational tools to obtain a better fundamental understanding of the self-assembly behavior of supramolecular gels or to accelerate their development by means of prediction. As such, we hope to stimulate researchers to consider using computational tools when investigating these intriguing materials. In the concluding remarks, we address future challenges faced by the field and formulate our vision on how computational methods could help overcoming them.

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.

The Martini Model in Materials Science

The Martini model, a coarse-grained force field initially developed with biomolecular simulations in mind, has found an increasing number of applications in the field of soft materials science. The model's underlying building block principle does not pose restrictions on its application beyond biomolecular systems. Here, the main applications to date of the Martini model in materials science are highlighted, and a perspective for the future developments in this field is given, particularly in light of recent developments such as the new version of the model, Martini 3.

A systematic approach to the scale separation problem in the development of multiscale models

Throughout engineering there are problems where it is required to predict a quantity based on the measurement of another, but where the two quantities possess characteristic variations over vastly different ranges of time and space. Among the many challenges posed by such 'multiscale' problems, that of defining a 'scale' remains poorly addressed. This fundamental problem has led to much confusion in the field of biomedical engineering in particular. The present study proposes a definition of scale based on measurement limitations of existing instruments, available computational power, and on the ranges of time and space over which quantities of interest vary characteristically. The definition is used to construct a multiscale modelling methodology from start to finish, beginning with a description of the system (portion of reality of interest) and ending with an algorithmic orchestration of mathematical models at different scales within the system. The methodology is illustrated for a specific but well-researched problem. The concept of scale and the multiscale modelling approach introduced are shown to be easily adaptable to other closely related problems. Although out of the scope of this paper, we believe that the proposed methodology can be applied widely throughout engineering.

Crystallization of semiflexible polymers in melts and solutions

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

A survey of multiscale modeling: Foundations, historical milestones, current status, and future prospects

Research problems in the domains of physical, engineering, biological sciences often span multiple time and length scales, owing to the complexity of information transfer underlying mechanisms. Multiscale modeling (MSM) and high-performance computing (HPC) have emerged as indispensable tools for tackling such complex problems. We review the foundations, historical developments, and current paradigms in MSM. A paradigm shift in MSM implementations is being fueled by the rapid advances and emerging paradigms in HPC at the dawn of exascale computing. Moreover, amidst the explosion of data science, engineering, and medicine, machine learning (ML) integrated with MSM is poised to enhance the capabilities of standard MSM approaches significantly, particularly in the face of increasing problem complexity. The potential to blend MSM, HPC, and ML presents opportunities for unbound innovation and promises to represent the future of MSM and explainable ML that will likely define the fields in the 21st century.

Heterogeneity Effects in Highly Cross-Linked Polymer Networks

Despite their level of refinement, micro-mechanical, stretch-based and invariant-based models, still fail to capture and describe all aspects of the mechanical properties of polymer networks for which they were developed. This is for an important part caused by the way the microscopic inhomogeneities are treated. The Elastic Network Model (ENM) approach of reintroducing the spatial resolution by considering the network at the level of its topological constraints, is able to predict the macroscopic properties of polymer networks up to the point of failure. We here demonstrate the ability of ENM to highlight the effects of topology and structure on the mechanical properties of polymer networks for which the heterogeneity is characterised by spatial and topological order parameters. We quantify the macro- and microscopic effects on forces and stress caused by introducing and increasing the heterogeneity of the network. We find that significant differences in the mechanical responses arise between networks with a similar topology but different spatial structure at the time of the reticulation, whereas the dispersion of the cross-link valency has a negligible impact.

Iterative integral equation methods for structural coarse-graining

In this paper, new Newton and Gauss-Newton methods for iterative coarse-graining based on integral equation theory are evaluated and extended. In these methods, the potential update is calculated from the current and target radial distribution function, similar to iterative Boltzmann inversion, but gives a potential update of quality comparable with inverse Monte Carlo. This works well for the coarse-graining of molecules to single beads, which we demonstrate for water. We also extend the methods to systems that include coarse-grained bonded interactions and examine their convergence behavior. Finally, using the Gauss-Newton method with constraints, we derive a model for single bead methanol in implicit water, which matches the osmotic pressure of the atomistic reference. An implementation of all new methods is provided for the open-source VOTCA package.

Digital Transformation in Materials Science: A Paradigm Change in Material's Development

The ongoing digitalization is rapidly changing and will further revolutionize all parts of life. This statement is currently omnipresent in the media as well as in the scientific community; however, the exact consequences of the proceeding digitalization for the field of materials science in general and the way research will be performed in the future are still unclear. There are first promising examples featuring the potential to change discovery and development approaches toward new materials. Nevertheless, a wide range of open questions have to be solved in order to enable the so-called digital-supported material research. The current state-of-the-art, the present and future challenges, as well as the resulting perspectives for materials science are described.

Effectiveness of coarse graining degree and speedup on the dynamic properties of homopolymer

Evaluation of effective coarse graining (CG) degree and reasonable speedup relative to all-atomistic (AA) model was conducted to provide a basis for building appropriate larger-scale model. The reproducibility of atomistic conformation and temperature transferability both act as the analysis criteria to resolve the maximum acceptable CG degree. Taking short- and long time spans into account simultaneously in the estimation of computational speedup, a dynamic scaling factor is accessible in fitting mean squared displacement ratio of CG to AA as an exponential function. Computing loss in parallel running is an indispensable component in acceleration, which was also added in the evaluation. Subsequently, a quantified prediction of CG speedup arises as a multiplication of dynamic scaling factor, computing loss, time step, and the square of reduction in the number of degrees of freedom. Polyethylene oxide was adopted as a reference system to execute the direct Boltzmann inversion and iterative Boltzmann inversion. Bonded and non-bonded potentials were calculated in CG models with 1~4 monomers per bead. The effective CG degree was determined as two at the most with a speedup of four orders magnitude over AA in this study. Determination of effectiveness CG degree and the corresponding speedup prediction provide available tools in larger spatiotemporal-scale calculations.

Molecular Modelling Guided Modulation of Molecular Shape and Charge for Design of Smart Self-Assembled Polymeric Drug Transporters

Nanomedicine employs molecular materials for prevention and treatment of disease. Recently, smart nanoparticle (NP)-based drug delivery systems were developed for the advanced transport of drug molecules. Rationally engineered organic and inorganic NP platforms hold the promise of improving drug targeting, solubility, prolonged circulation, and tissue penetration. However, despite great progress in the synthesis of NP building blocks, more interdisciplinary research is needed to understand their self-assembly and optimize their performance as smart nanocarriers. Multi-scale modeling and simulations provide a valuable ally to experiment by mapping the potential energy landscape of self-assembly, translocation, and delivery of smart drug-loaded NPs. Here, we highlight key recent advances to illustrate the concepts, methods, and applications of smart polymer-based NP drug delivery. We summarize the key design principles emerging for advanced multifunctional polymer topologies, illustrating how the unusual architecture and chemistry of dendritic polymers, self-assembling polyelectrolytes and cyclic polymers can provide exceptional drug delivery platforms. We provide a roadmap outlining the opportunities and challenges for the effective use of predictive multiscale molecular modeling techniques to accelerate the development of smart polymer-based drug delivery systems.

Energetics of Electron Pairs in Electrophilic Aromatic Substitutions

The interacting quantum atoms approach (IQA) as applied to the electron-pair exhaustive partition of real space induced by the electron localization function (ELF) is used to examine candidate energetic descriptors to rationalize substituent effects in simple electrophilic aromatic substitutions. It is first shown that inductive and mesomeric effects can be recognized from the decay mode of the aromatic valence bond basin populations with the distance to the substituent, and that the fluctuation of the population of adjacent bonds holds also regioselectivity information. With this, the kinetic energy of the electrons in these aromatic basins, as well as their mutual exchange-correlation energies are proposed as suitable energetic indices containing relevant information about substituent effects. We suggest that these descriptors could be used to build future reactive force fields.

Computational and Experimental Approaches to Investigate Lipid Nanoparticles as Drug and Gene Delivery Systems

Lipid nanoparticles (LNPs) have been widely applied in drug and gene delivery. More than twenty years ago, DoxilTM was the first LNPs-based drug approved by the US Food and Drug Administration (FDA). Since then, with decades of research and development, more and more LNP-based therapeutics have been used to treat diverse diseases, which often offer the benefits of reduced toxicity and/or enhanced efficacy compared to the active ingredients alone. Here, we provide a review of recent advances in the development of efficient and robust LNPs for drug/gene delivery. We emphasize the importance of rationally combining experimental and computational approaches, especially those providing multiscale structural and functional information of LNPs, to the design of novel and powerful LNP-based delivery systems.

From adaptive resolution to molecular dynamics of open systems

ABSTRACT

We provide an overview of the Adaptive Resolution Simulation method (AdResS) based on discussing its basic principles and presenting its current numerical and theoretical developments. Examples of applications to systems of interest to soft matter, chemical physics, and condensed matter illustrate the method's advantages and limitations in its practical use and thus settle the challenge for further future numerical and theoretical developments.

A Novel Multiscale Methodology for Simulating Droplet Morphology Evolution during Injection Molding of Polymer Blends

The morphology of polymer blends plays a critical role in determining the properties of the blends and performance of resulting injection-molded parts. However, it is currently impossible to predict the morphology evolution during injection molding and the final micro-structure of the molded parts, as the existing models for the morphology evolution of polymer blends are still limited to a few simple flow fields. To fill this gap, this paper proposed a novel model for droplet morphology evolution during the mold filling process of polymer blends by coupling the models on macro- and meso-scales. The proposed model was verified by the injection molding experiment of PP/POE blends. The predicted curve of mold cavity pressure during filling process agreed precisely with the data of the corresponding pressure sensors. On the other hand, the model successfully tracked the moving trajectory and simulated morphology evolution of the droplets during the mold-filling process. After mold-filling ended, the simulation results of the final morphology of the droplets were consistent with the observations of the scanning electron microscope (SEM) experiment. Moreover, this study revealed the underlying mechanism of the droplet morphology evolution through the force analysis on the droplet. It is validated that the present model is a qualified tool for simulating the morphology evolution of polymer blends during injection molding and predicting the final microstructure of the products.

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.

Effect of Poly(vinyl butyral) Comonomer Sequence on Adhesion to Amorphous Silica: A Coarse-Grained Molecular Dynamics Study

Modulating a comonomer sequence, in addition to the overall chemical composition, is the key to unlocking the true potential of many existing commercial copolymers. We employ coarse-grained molecular dynamics (MD) simulations to study the behavior of random-blocky poly(vinyl butyral-co-vinyl alcohol) (PVB) melts in contact with an amorphous silica surface, representing the interface found in laminated safety glass. Our two-pronged coarse-graining approach utilizes both macroscopic thermophysical data and all-atom MD simulation data. Polymer-polymer nonbonded interactions are described by the fused-sphere SAFT-γ Mie equation of state, while bonded interactions are derived using Boltzmann inversion to match the bond and angle distributions from all-atom PVB chains. Spatially dependent polymer-surface interactions are mapped from a hydroxylated all-atom amorphous silica slab model and all-atom monomers to an external potential acting on the coarse-grained sites. We discovered an unexpected complex relationship between the blockiness parameter and the adhesion energy. The adhesion strength between PVB copolymers with intermediate VA content and silica was found to be maximal for random-blocky copolymers with a moderately high degree of blockiness rather than for diblock copolymers. We attribute this to two main factors: (1) changes in morphology, which dramatically alter the number of VA beads interacting with the surface and (2) a non-negligible contribution of vinyl butyral (VB) monomers to adhesion energy because of their preference to adsorb to zones with low hydroxyl density on the silica surface.

Data-driven coarse-grained modeling of polymers in solution with structural and dynamic properties conserved

We present data-driven coarse-grained (CG) modeling for polymers in solution, which conserves the dynamic as well as structural properties of the underlying atomistic system. The CG modeling is built upon the framework of the generalized Langevin equation (GLE). The key is to determine each term in the GLE by directly linking it to atomistic data. In particular, we propose a two-stage Gaussian process-based Bayesian optimization method to infer the non-Markovian memory kernel from the data of the velocity autocorrelation function (VACF). Considering that the long-time behaviors of the VACF and memory kernel for polymer solutions can exhibit hydrodynamic scaling (algebraic decay with time), we further develop an active learning method to determine the emergence of hydrodynamic scaling, which can accelerate the inference process of the memory kernel. The proposed methods do not rely on how the mean force or CG potential in the GLE is constructed. Thus, we also compare two methods for constructing the CG potential: a deep learning method and the iterative Boltzmann inversion method. With the memory kernel and CG potential determined, the GLE is mapped onto an extended Markovian process to circumvent the expensive cost of directly solving the GLE. The accuracy and computational efficiency of the proposed CG modeling are assessed in a model star-polymer solution system at three representative concentrations. By comparing with the reference atomistic simulation results, we demonstrate that the proposed CG modeling can robustly and accurately reproduce the dynamic and structural properties of polymers in solution.

Molecular Modeling and Simulations of Peptide–Polymer Conjugates

Peptide–polymer conjugates are a class of soft materials composed of covalently linked blocks of protein/polypeptides and synthetic/natural polymers. These materials are practically useful in biological applications, such as drug delivery, DNA/gene delivery, and antimicrobial coatings, as well as nonbiological applications, such as electronics, separations, optics, and sensing. Given their broad applicability, there is motivation to understand the molecular and macroscale structure, dynamics, and thermodynamic behavior exhibited by such materials. We focus on the past and ongoing molecular simulation studies aimed at obtaining such fundamental understanding and predicting molecular design rules for the target function. We describe briefly the experimental work in this field that validates or motivates these computational studies. We also describe the various models (e.g., atomistic, coarse-grained, or hybrid) and simulation methods (e.g., stochastic versus deterministic, enhanced sampling) that have been used and the types of questions that have been answered using these computational approaches.

Domain Heterogeneity in Radiofrequency Therapies for Pain Relief: A Computational Study with Coupled Models

The objective of the current research work is to study the differences between the predicted ablation volume in homogeneous and heterogeneous models of typical radiofrequency (RF) procedures for pain relief. A three-dimensional computational domain comprising of the realistic anatomy of the target tissue was considered in the present study. A comparative analysis was conducted for three different scenarios: (a) a completely homogeneous domain comprising of only muscle tissue, (b) a heterogeneous domain comprising of nerve and muscle tissues, and (c) a heterogeneous domain comprising of bone, nerve and muscle tissues. Finite-element-based simulations were performed to compute the temperature and electrical field distribution during conventional RF procedures for treating pain, and exemplified here for the continuous case. The predicted results reveal that the consideration of heterogeneity within the computational domain results in distorted electric field distribution and leads to a significant reduction in the attained ablation volume during the continuous RF application for pain relief. The findings of this study could provide first-hand quantitative information to clinical practitioners about the impact of such heterogeneities on the efficacy of RF procedures, thereby assisting them in developing standardized optimal protocols for different cases of interest.

Modeling the Full Time-Dependent Phenomenology of Filled Rubber for Use in Anti-Vibration Design

Component design of rubber-based anti-vibration devices remains a challenge, since there is a lack of predictive models in the typical regimes encountered by anti-vibration devices that are deformed to medium dynamic strains (0.5 to 3.5) at medium strain rates (0.5/s to 10/s). An approach is proposed that demonstrates all non-linear viscoelastic effects such as hysteresis and cyclic stress softening. As it is based on a free-energy, it is fast and easily implementable. The fitting parameters behave meaningfully when changing the filler volume fraction. The model was implemented for use in the commercial finite element software ABAQUS. Examples of how to fit experimental data and simulations for a variety of carbon black filled natural rubber compounds are presented.

Special Issue on “Computational Methods for Polymers”

Polymers play a key role in our daily lives [...]