A Chemically Accurate Implicit-Solvent Coarse-Grained Model for Polystyrenesulfonate Solutions

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.

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.

Consistent and Transferable Force Fields for Statistical Copolymer Systems at the Mesoscale

The statistical trajectory matching (STM) method was applied successfully to derive coarse grain (CG) models for bulk properties of homopolymers. The extension of the methodology for building CG models for statistical copolymer systems is much more challenging. We present here the strategy for developing CG models for styrene-butadiene-rubber, and we compare the quality of the resulting CG force fields on the structure and thermodynamics at different chemical compositions. The CG models are used through the use of a genuine mesoscopic method called the dissipative particle dynamics method and compared to high-resolution molecular dynamics simulations. We conclude that the STM method is able to produce coarse-grained potentials that are transferable in composition by using only a few reference systems. Additionally, this methodology can be applied on any copolymer system.

Multiscale modeling of thermomechanical properties of stereoregular polymers

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

Molecular Simulation Approaches to the Study of Thermotropic and Lyotropic Liquid Crystals

Over the last decade, the availability of computer time, together with new algorithms capable of exploiting parallel computer architectures, has opened up many possibilities in molecularly modelling liquid crystalline systems. This perspective article points to recent progress in modelling both thermotropic and lyotropic systems. For thermotropic nematics, the advent of improved molecular force fields can provide predictions for nematic clearing temperatures within a 10 K range. Such studies also provide valuable insights into the structure of more complex phases, where molecular organisation may be challenging to probe experimentally. Developments in coarse-grained models for thermotropics are discussed in the context of understanding the complex interplay of molecular packing, microphase separation and local interactions, and in developing methods for the calculation of material properties for thermotropics. We discuss progress towards the calculation of elastic constants, rotational viscosity coefficients, flexoelectric coefficients and helical twisting powers. The article also covers developments in modelling micelles, conventional lyotropic phases, lyotropic phase diagrams, and chromonic liquid crystals. For the latter, atomistic simulations have been particularly productive in clarifying the nature of the self-assembled aggregates in dilute solution. The development of effective coarse-grained models for chromonics is discussed in detail, including models that have demonstrated the formation of the chromonic N and M phases.

Overlap Concentration of Sodium Polystyrene Sulfonate in Solution

The overlap concentration c* of sodium polystyrene sulfonate in water is calculated using multichain atomistic and coarse grained (CG) simulations for a range of chain lengths. Fully atomistic molecular dynamics simulations are carried out for N = 32-192 monomers. The CG model was parameterized to match the end-to-end distance from the atomistic simulations at small N and allows us to simulate a much larger N. Treating the hydrophobic backbone by inclusion of attraction between monomers is an essential addition to the CG model. The simulation c* are in agreement with experimental data, yet at c*, the chains are not fully stretched, even for N as large as 1200. This implies that none of the experimental systems are in the scaling regime and to reach the scaling regime for NaPSS chains much longer than N = 1200 are required.

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.

Atomistic simulation studies of ionic cyanine dyes: self-assembly and aggregate formation in aqueous solution

Cyanine dyes are known to form large-scale aggregates of various morphologies via spontaneous self-assembly in aqueous solution, akin to chromonic liquid crystals. Atomistic molecular dynamics simulations have been performed on four cyanine dyes: pseudoisocyanine chloride (PIC), pinacyanol chloride (PCYN), 5,5',6,6'-tetrachloro-1,1',3,3'-tetraethylbenzimidazolylcarbocyanine chloride (TTBC) and 1,1'-disulfopropyl-3,3'-diethyl-5,5',6,6'-tetrachloro-benzimidazolylcarbocyanine sodium salt (BIC). Simulations employed an optimised general AMBER force field and demonstrate the organisation of the dyes into stacked structures at dilute concentrations. The thermodynamics of self-assembly was studied by calculating potentials of mean force for n-mers (n = 2, 3 or 4), from which the free energies of association are determined. We report binding free energies in the range of 8 to 15k_BT for dimerisation, concordant with typical values for ionic chromonics (7 to 14k_BT), and examine the enthalpic and entropic contributions to the aggregation process. The self-assembly of these dyes yields two distinct classes of structures. We observe the formation of H-aggregate stacks for PCYN, with further complexity in these assemblies for PIC; where the aggregates contain shift and Y junction defects. TTBC and BIC associate into a J-aggregate sheet structure of unimolecular thickness, and is composed of a brickwork arrangement between molecules. These sheet structures are characteristic of the smectic chromonic mesophase, and such assemblies provide a route to the emergence of nanoscale tubular architectures.

Coarse-Grained Molecular Dynamics (CG-MD) Simulation of the Encapsulation of Dexamethasone in PSS/PDDA Layer-by-Layer Assembled Polyelectrolyte Nanocapsules

Experimental studies have reported the fundamental and applied science aspects of polyelectrolyte (PE) layer-by-layer (LbL) self-assembly. LbL nanocoating is a simple and robust technique that can be used to modify the surface properties of nearly any material. These modifications take place by adsorption of mere nanometers of PE to impart previously absent properties to the nanocoated substrate. Paper manufacturing, drug delivery, and antimicrobial applications have since been developed. LbL self-assembly has become a very lucrative field of research. Computational modeling of LbL nanocoating has received limited attention. PE simulations often require significant computational resources and make computational modeling studies challenging. In this study, atomic-level PE and dexamethasone models are developed and then converted into coarse-grained (CG) models. This modeling study is based on experimental results that were previously reported. The CG models showed the effect of salt concentration and the number of PE layers on the LbL drug nanocapsule. The suitability of the model was evaluated and showed that this model can serve as a predictive tool for an LbL-nanocoated drug delivery system. It is suggested that this model can be used to simulate LbL drug delivery systems before the experimental evaluation of the real systems take place.

Molecular Modeling Investigations of Sorption and Diffusion of Small Molecules in Glassy Polymers

With a wide range of applications, from energy and environmental engineering, such as in gas separations and water purification, to biomedical engineering and packaging, glassy polymeric materials remain in the core of novel membrane and state-of the art barrier technologies. This review focuses on molecular simulation methodologies implemented for the study of sorption and diffusion of small molecules in dense glassy polymeric systems. Basic concepts are introduced and systematic methods for the generation of realistic polymer configurations are briefly presented. Challenges related to the long length and time scale phenomena that govern the permeation process in the glassy polymer matrix are described and molecular simulation approaches developed to address the multiscale problem at hand are discussed.

Machine-Learning Enabled New Insights into the Coil-to-Globule Transition of Thermosensitive Polymers Using a Coarse-Grained Model

We present a computational framework that integrates coarse-grained (CG) molecular dynamics (MD) simulations and a data-driven machine-learning (ML) method to gain insights into the conformations of polymers in solutions. We employ this framework to study conformational transition of a model thermosensitive polymer, poly( N-isopropylacrylamide) (PNIPAM). Here, we have developed the first of its kind, a temperature-independent CG model of PNIPAM that can accurately predict its experimental lower critical solution temperature (LCST) while retaining the tacticity in the presence of an explicit water model. The CG model was extensively validated by performing CG MD simulations with different initial conformations, varying the radius of gyration of chain, the chain length, and the angle between the adjacent monomers of the initial configuration of PNIPAM (total simulation time = 90 μs). Moreover, for the first time, we utilize the nonmetric multidimensional scaling (NMDS) method, a data-driven ML approach, to gain further insights into the mechanisms and pathways of this coil-to-globule transition by analyzing CG MD simulation trajectories. NMDS analysis provides entirely new insights and shows multiple metastable states of PNIPAM during its coil-to-globule transition above the LCST.

Depletion attraction of sheet-like ion aggregates in low-dielectric ionomer melts

Ionomers are polymers in which an ionic group is covalently bonded to the polymer backbone. Ion aggregates in ionomers have morphologies that allow for the packing of the attached polymer backbone. Using ion-only coarse-grained molecular dynamics, we observe that string-like ion aggregates become flat and sheet-like at lower dielectric constants. A consequence of the changing morphology is that the sheet-like aggregates self-assemble to form ordered, lamellar structures. We use a simple thermodynamic model to demonstrate that depletion attraction mediated by small aggregates can explain the observed order. Our results suggest that depletion attraction can drive ions to form structures that have the size scale suggested by direct visualization, produce the commonly observed experimental correlation peak from X-ray and neutron scattering, and satisfy chain-packing constraints that have been demonstrated to be important in simulations.

A Review of Multiscale Computational Methods in Polymeric Materials

Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.

Thermodynamics of the self-assembly of non-ionic chromonic molecules using atomistic simulations. The case of TP6EO2M in aqueous solution

Atomistic molecular dynamic simulations have been performed for the non-ionic chromonic liquid crystal 2,3,6,7,10,11-hexa-(1,4,7-trioxa-octyl)-triphenylene (TP6EO2M) in aqueous solution. TP6EO2M molecules consist of a central poly-aromatic core (a triphenylene ring) functionalized by six hydrophilic ethyleneoxy (EO) chains, and have a strong tendency to aggregate face-to-face into stacks even in very dilute solution. We have studied self-assembly of the molecules in the low concentration range corresponding to an isotropic solution of aggregates, using two force fields GAFF and OPLS. Our results reveal that the GAFF force field, even though it was successfully used previously for modelling of ionic chromonics, overestimates the attraction of TP6EO2M molecules in water. This results in an aggregation free energy which is too high, a reduced hydration of EO chains and, therefore, molecular self-assembly into compact disordered clusters instead of stacks. In contrast, use of the OPLS force field, leads to self-assembly into ordered stacks in agreement with earlier experimental studies of triphenylene-based chromonics. The free energy of association follows a "quasi-isodesmic" pattern, where the binding free energy of two molecules to form a dimer is of the order of 2.5 RT larger than the corresponding energy of addition of a molecule into a stack. The obtained value for the binding free energy, ΔG=-12 RT, is found to be in line with the published values for typical ionic chromonics (-7 to -12 RT), and agrees reasonably well with the experimental results for this system. The calculated interlayer distance between the molecules in a stack is 0.37 nm, which is at the top of the range found for typical chromonics (0.33-0.37 nm). We suggest that the relatively large layer spacing can be attributed to the repulsion between EO side chains.

Solvation effects on like-charge attraction

We present results of molecular dynamics simulations of the electrostatic interaction between two parallel charged rods in the presence of divalent counterions. Such polyelectrolytes have been considered as a simple model for understanding electrostatic interactions in highly charged biomolecules such as DNA. Since there are correlations between the free charge carriers, the phenomenon of like charge attraction appears for specific parameters. We explore the role of solvation effects and the resulting deviations from Coulomb's law on the nanoscale on this peculiar phenomenon. The behavior of the force between the charged rods in a simulation with atomistic representation of water molecules is completely different from a model in which water is modeled as a continuum dielectric. By calculating counterion-rodion pair correlation functions, we find that the presence of water molecules changes the structure of the counterion cloud and results in both qualitative and quantitative changes of the force between highly charged polyelectrolytes.