End-Bridging Monte Carlo: A Fast Algorithm for Atomistic Simulation of Condensed Phases of Long Polymer Chains

Equilibration of linear polyethylene melts with pre-defined molecular weight distributions employing united atom Monte Carlo simulations

Possessing control over the molecular size (molecular weight/chain length/degree of polymerization) distribution of a polymeric material is extremely important in applications. This is manifested de facto by the extensive contemporary scientific literature on processes for controlling this distribution experimentally. Yet, the literature on computational techniques for achieving prescribed molecular size distributions in simulations and exploring their impact on properties is much less abundant than its experimental/technical counterpart. Here, we develop-on the basis of united atom melt simulations employing connectivity-altering Monte Carlo moves-a new Metropolis selection criterion that drives the multichain system to a prescribed but otherwise arbitrary distribution of molecular sizes. The new formulation is a generalization of that originally proposed [P. V. K. Pant and D. N. Theodorou, Macromolecules 28, 7224 (1995)], but simpler and more computationally efficient. It requires knowledge solely of the target distribution, which need not be normalized. We have implemented the new formulation on long-chain linear polyethylene melts, obtaining excellent results. The target molecular size distribution can be provided in tabulated form, allowing absolute freedom as to the types of chain size profiles that can be simulated. Distributions for which equilibration has been achieved here for linear polyethylene include a truncated most probable, a truncated Schulz-Zimm, an arbitrary one defined in tabulated form, a broad truncated Gaussian, and a bimodal Gaussian. The last two are comparable to those encountered in industrial applications. The impact of the molecular size distribution on the properties of the simulated melts, such as density, chain dimensions, and mixing thermodynamics, is explored.

A Tale of Two Chains: Geometries of a Chain Model and Protein Native State Structures

Linear chain molecules play a central role in polymer physics with innumerable industrial applications. They are also ubiquitous constituents of living cells. Here, we highlight the similarities and differences between two distinct ways of viewing a linear chain. We do this, on the one hand, through the lens of simulations for a standard polymer chain of tethered spheres at low and high temperatures and, on the other hand, through published experimental data on an important class of biopolymers, proteins. We present detailed analyses of their local and non-local structures as well as the maps of their closest contacts. We seek to reconcile the startlingly different behaviors of the two types of chains based on symmetry considerations.

Capillary filling dynamics of polymer melts in a bicontinuous nanoporous scaffold

Polymer infiltrated nanoporous gold is prepared by infiltrating polymer melts into a bicontinuous, nanoporous gold (NPG) scaffold. Polystyrene (PS) films with molecular weights (Mw) from 424 to 1133 kDa are infiltrated into a NPG scaffold (∼120 nm), with a pore radius (Rp) and pore volume fraction of 37.5 nm and 50%, respectively. The confinement ratios (Γ=RgRp) range from 0.47 to 0.77, suggesting that the polymers inside the pores are moderately confined. The time for PS to achieve 80% infiltration (τ80%) is determined using in situ spectroscopic ellipsometry at 150 °C. The kinetics of infiltration scales weaker with Mw, τ80%∝Mw1.30±0.20, than expected from bulk viscosity Mw3.4. Furthermore, the effective viscosity of the PS melt inside NPG, inferred from the Lucas-Washburn model, is reduced by more than one order of magnitude compared to the bulk. Molecular dynamics simulation results are in good agreement with experiments predicting scaling as Mw1.4. The reduced dependence of Mw and the enhanced kinetics of infiltration are attributed to a reduction in chain entanglement density during infiltration and a reduction in polymer-wall friction with increasing polymer molecular weight. Compared to the traditional approach involving adding discrete particles into the polymer matrix, these studies show that nanocomposites with higher loading can be readily prepared, and that kinetics of infiltration are faster due to polymer confinement inside pores. These films have potential as actuators when filled with stimuli-responsive polymers as well as polymer electrolyte and fuel cell membranes.

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.

Crystallization of Flexible Chains of Tangent Hard Spheres under Full Confinement

We present results from extensive Monte Carlo simulations on the crystallization of athermal polymers under full confinement. Polymers are represented as freely jointed chains of tangent hard spheres of uniform size. Confinement is applied through the presence of flat, parallel, and impenetrable walls in all dimensions. We analyze crystallization as the summation of two contributions: one that occurs in the bulk volume of the system (bulk crystallization), and one on the wall surfaces (surface crystallization). Depending on volume fraction initially amorphous (disordered) hard-sphere chain packings transit to the stable crystal phase. The established ordered morphologies consist primarily of hexagonal close-packed (HCP) crystals in the bulk volume and of triangular (TRI) crystals on the surface. As in the case of athermal packings in the bulk (without confinement), a structural competition is observed between the 5-fold local symmetry and the formation of close-packed crystallites. Effectively, the full confinement inside a cube favors the growth of the HCP crystal, as the FCC one is quite incompatible with the imposed spatial constraints. Consequently, we observe the formation of noncompact ordered motifs which grow from the surface to the inner volume of the simulation cell. We further compare the 2D and 3D crystals formed by monomeric hard spheres under the same simulation conditions. Significant differences are observed at low densities that tend to diminish as concentration increases.

Semiflexible oligomers crystallize via a cooperative phase transition

Semicrystalline polymers are ubiquitous, yet despite their fundamental and industrial importance, the theory of homogeneous nucleation from a melt remains a subject of debate. A key component of the controversy is that polymer crystallization is a non-equilibrium process, making it difficult to distinguish between effects that are purely kinetic and those that arise from the underlying thermodynamics. Due to computational cost constraints, simulations of polymer crystallization typically employ non-equilibrium molecular dynamics techniques with large degrees of undercooling that further exacerbate the coupling between thermodynamics and kinetics. In a departure from this approach, in this study, we isolate the near-equilibrium nucleation behavior of a simple model of a melt of short, semiflexible oligomers. We employ several Monte Carlo methods and compute a phase diagram in the temperature-density plane along with two-dimensional free energy landscapes (FELs) that characterize the nucleation behavior. The phase diagram shows the existence of ordered nematic and crystalline phases in addition to the disordered melt phase. The minimum free energy path in the FEL for the melt-crystal transition shows a cooperative transition, where nematic order and monomer positional order move in tandem as the system crystallizes. This near-equilibrium phase transition mechanism broadly agrees with recent evidence that polymer stiffness plays an important role in crystallization but differs in the specifics of the mechanism from several recent theories. We conclude that the computation of multidimensional FELs for models that are larger and more fine-grained will be important for evaluating and refining theories of homogeneous nucleation for polymer crystallization.

Simu-D: A Simulator-Descriptor Suite for Polymer-Based Systems under Extreme Conditions

We present Simu-D, a software suite for the simulation and successive identification of local structures of atomistic systems, based on polymers, under extreme conditions, in the bulk, on surfaces, and at interfaces. The protocol is built around various types of Monte Carlo algorithms, which include localized, chain-connectivity-altering, identity-exchange, and cluster-based moves. The approach focuses on alleviating one of the main disadvantages of Monte Carlo algorithms, which is the general applicability under a wide range of conditions. Present applications include polymer-based nanocomposites with nanofillers in the form of cylinders and spheres of varied concentration and size, extremely confined and maximally packed assemblies in two and three dimensions, and terminally grafted macromolecules. The main simulator is accompanied by a descriptor that identifies the similarity of computer-generated configurations with respect to reference crystals in two or three dimensions. The Simu-D simulator-descriptor can be an especially useful tool in the modeling studies of the entropy- and energy-driven phase transition, adsorption, and self-organization of polymer-based systems under a variety of conditions.

Load-bearing entanglements in polymer glasses

Through a combined approach of experiment and simulation, this study quantifies the role of entanglements in determining the mechanical properties of glassy polymer blends. Uniaxial extension experiments on 100-nm films containing a bidisperse mixture of polystyrene enable quantitative comparison with molecular dynamics (MD) simulations of a coarse-grained model for polymer glasses, where the bidisperse blends allow us to systematically tune the entanglement density of both systems. In the MD simulations, we demonstrate that not all entanglements carry substantial load at large deformation, and our analysis allows the development of a model to describe the number of effective, load-bearing entanglements per chain as a function of blend ratio. The film strength measured experimentally and the simulated film toughness are quantitatively described by a model that only accounts for load-bearing entanglements.

Effect of Surface Nanopatterning on Slip: The Case of Couette Flow of Long-Chain Polyethylene Melt Flowing Past Gold Surfaces

The manifestation of slip during flow of a polymer melt past a solid surface depends on several parameters, such as film thickness, the strength of polymer-solid interactions compared to the cohesive energy of the polymer, and the roughness of the surface. Understanding the role of these molecular aspects for slip is crucial in microfluidics, friction-tuning, polymer extrusion, and nanocomposites applications. The present article investigates the effect of surface nanopatterning on slip, via Couette-flow simulations of long chain polyethylene melts past nanopatterned gold surfaces. Slip is quantified in terms of the true and effective slip velocity, and the slip length. When polymer chains are adsorbed to surfaces with periodic features (e.g., crystal planes), they develop preferential ordering in a way that enables them to minimize their free energy. The orientation of a chain is affected by that of its neighbors; thus, when several chains come together, they are prone to form regions with crystal-like orientation. We show that, in some cases, the introduction of nanopatterns on the surface can perturb and induce reorganization of these regions, and in turn affect slip. The nanopatterns are realized as periodic defect stripes of variable width, depth, areal density, and orientation angle. In situations in which the width of the defects becomes comparable to the diameter of individual chain backbones, slip is minimized (stick conditions). Cutting the nanopatterns in low symmetry directions can affect the quality of their edges and lead to enhanced friction. To characterize these edges we have devised a scheme for the quantification of the mean square roughness and mean position of the surface, which is general and applicable in 2 and 3 dimensions for any kind of material, either crystalline of amorphous. Applying the patterns on the opposing solid surfaces in a symmetric or antisymmetric manner has a profound effect on flow. We show that the application of nanopatterns in symmetric configurations generates zero net flow and induces additional shear along directions normal to the direction of the flow. The application of symmetry-breaking configurations can guide flow toward preferential directions, a result with possible applications in microfluidic devices.

Entropy-Driven Heterogeneous Crystallization of Hard-Sphere Chains under Unidimensional Confinement

We investigate, through Monte Carlo simulations, the heterogeneous crystallization of linear chains of tangent hard spheres under confinement in one dimension. Confinement is realized through flat, impenetrable, and parallel walls. A wide range of systems is studied with respect to their average chain lengths (N = 12 to 100) and packing densities (ϕ = 0.50 to 0.61). The local structure is quantified through the Characteristic Crystallographic Element (CCE) norm descriptor. Here, we split the phenomenon into the bulk crystallization, far from the walls, and the projected surface crystallization in layers adjacent to the confining surfaces. Once a critical volume fraction is met, the chains show a phase transition, starting from regions near the hard walls. The established crystal morphologies consist of alternating hexagonal close-packed or face-centered cubic layers with a stacking direction perpendicular to the confining walls. Crystal layer perfection is observed with an increasing concentration. As in the case of the unconstrained phase transition of athermal polymers at high densities, crystal nucleation and growth compete with the formation of sites of a fivefold local symmetry. While surface crystallites show perfection with a predominantly triangular character, the morphologies of square crystals or of a mixed type are also formed. The simulation results show that the rate of perfection of the surface crystallization is not significantly faster than that of the bulk crystallization.

Enhancement in Flux and Antifouling Properties of Polyvinylidene Fluoride/Polycarbonate Blend Membranes for Water Environmental Improvement

In this work, to overcome the fouling phenomenon of hydrophobic polymer membranes, polyvinylidene fluoride (PVDF) was blended with hydrophilic polycarbonate (PC) to prepare ultrafiltration membranes via the nonsolvent-induced phase separation method. The effects of PC content on membrane morphology, pore size distribution, and surface porosity were characterized and investigated by FE-SEM and image analyzer software. Solubility parameters calculated by molecular dynamics (MD) simulation showed that PVDF and PC are compatible and the results were confirmed by differential scanning calorimetry and wide angle X-ray diffractometry. The long-term chemical stability against NaOH and mechanical property before and after the abrasion test of the prepared membranes were also characterized by dynamic thermomechanical analysis. It was found that the hydrophilicity, water flux, abrasion resistance, and antifouling properties as the performance criteria of polymeric membranes were improved because of the presence of PC, and the separation efficiency of PVDF/PC membranes is much higher than that of the pristine PVDF membrane. The exemplary water filtration performances of these polymer membranes are harnessed here in this work to purify raw water polluted by natural organic matters, addressing the key environmental issue of water contamination.

Self-Avoiding Random Walks as a Model to Study Athermal Linear Polymers under Extreme Plate Confinement

Monte Carlo (MC) simulations, built around chain-connectivity-altering moves and a wall-displacement algorithm, allow us to simulate freely-jointed chains of tangent hard spheres of uniform size under extreme confinement. The latter is realized through the presence of two impenetrable, flat, and parallel plates. Extreme conditions correspond to the case where the distance between the plates approaches the monomer size. An analysis of the local structure, based on the characteristic crystallographic element (CCE) norm, detects crystal nucleation and growth at packing densities well below the ones observed in bulk analogs. In a second step, we map the confined polymer chains into self-avoiding random walks (SAWs) on restricted lattices. We study all realizations of the cubic crystal system: simple, body centered, and face centered cubic crystals. For a given chain size (SAW length), lattice type, origin of SAW, and level of confinement, we enumerate all possible SAWs (equivalently all chain conformations) and calculate the size distribution. Results for intermediate SAW lengths are used to predict the behavior of long, fully entangled chains through growth formulas. The SAW analysis will allow us to determine the corresponding configurational entropy, as it is the driving force for the observed phase transition and the determining factor for the thermodynamic stability of the corresponding crystal morphologies.

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.

Mathematical foundations of an ultra coarse-grained slip link model

The master equation underlying ecoSLM, an ultra-coarse-grained slip link model, is presented. In the absence of constraint release, the equilibrium and dynamic properties of the discrete master equation for large chains are found to be virtually identical to the continuous Fokker-Planck equation for Brownian particles diffusing in a potential. A single-chain microscopic model with repulsion between adjacent slip links is described. It is approximately consistent with the quadratic fluctuation potential used in ecoSLM. Mapping ecoSLM with fine-grained slip link models or experiments requires specification of an effective friction as a function of molecular weight. Methods to accomplish this are discussed. Collectively, the mathematical framework described provides an interface for fine-grained slip link models to potentially use ecoSLM for extreme coarse-graining.

Nonequilibrium Monte Carlo simulations of entangled polymer melts under steady shear flow

We present a nonequilibrium Monte Carlo (MC) methodology based on expanded nonequilibrium thermodynamic formalism to simulate entangled polymeric materials undergoing steady shear flow. Motivated by the standard kinetic theory for entangled polymers, a second-rank symmetric conformation tensor based on the entanglement segment vector was adopted in the expanded statistical-ensemble based MC method as the nonequilibrium structural variable that properly represents the deformed structure of the system by the flow. The corresponding (second-rank symmetric) conjugate thermodynamic force variable was introduced to simulate an external flow field. As a test case, we applied the GENERIC MC to C₄₀₀H₈₀₂ entangled linear polyethylene melts in a wide range of shear rates. Detailed analysis of the GENERIC MC results for various structural and rheological properties (such as chain size, chain orientation, mesoscale chain configuration, topological properties, and material functions) was carried out via direct comparison with the corresponding NEMD results. Overall, the GENERIC MC is shown to predict the general trends of the nonequilibrium properties of polymer systems reasonably for a wide range of flow strengths (i.e., 0.5 ≤ De ≤ 540). In conjunction with NEMD, the present MC method can thus be used to extract fundamental thermodynamic information (nonequilibrium entropy and free energy functions) of entangled polymeric systems under various flow types. Despite the general consistency between the GENERIC MC and NEMD results, some quantitative discrepancies appear in the intermediate-to-strong flow regime. This behavior stems from the inherent mean-field nature of the MC force field which is applied to the individual entanglement segments independently and uniformly along the chain, without accounting for any flow-induced structural or dynamical correlations between segments.

Hierarchical modelling of polystyrene melts: from soft blobs to atomistic resolution

We demonstrate that hierarchical backmapping strategies incorporating generic blob-based models can equilibrate melts of high-molecular-weight polymers, described with chemically specific, atomistic models. The central idea is first to represent polymers by chains of large soft blobs (spheres) and efficiently equilibrate the melt on large scales. Then, the degrees of freedom of more detailed models are reinserted step by step. The procedure terminates when the atomistic description is reached. Reinsertions are feasible computationally because the fine-grained melt must be re-equilibrated only locally. We consider polystyrene (PS) which is sufficiently complex to serve method development because of stereo-chemistry and bulky side groups. Our backmapping strategy bridges mesoscopic and atomistic scales by incorporating a blob-based, a moderately coarse-grained (CG), and a united-atom model of PS. We demonstrate that the generic blob-based model can be parameterised to reproduce the mesoscale properties of a specific polymer - here PS. The moderately CG model captures stereo-chemistry. To perform backmapping we improve and adjust several fine-graining techniques. We prove equilibration of backmapped PS melts by comparing their structural and conformational properties with reference data from smaller systems, equilibrated with less efficient methods.

Effect of Chain Length Dispersity on the Mobility of Entangled Polymers

While nearly all theoretical and computational studies of entangled polymer melts have focused on uniform samples, polymer synthesis routes always result in some dispersity, albeit narrow, of distribution of molecular weights (Đ_{M}=M_{w}/M_{n}∼1.02-1.04). Here, the effects of dispersity on chain mobility are studied for entangled, disperse melts using a coarse-grained model for polyethylene. Polymer melts with chain lengths set to follow a Schulz-Zimm distribution for the same average M_{w}=36  kg/mol with Đ_{M}=1.0 to 1.16, were studied for times of 600-800  μs using molecular dynamics simulations. This time frame is longer than the time required to reach the diffusive regime. We find that dispersity in this range does not affect the entanglement time or tube diameter. However, while there is negligible difference in the average mobility of chains for the uniform distribution Đ_{M}=1.0 and Đ_{M}=1.02, the shortest chains move significantly faster than the longest ones offering a constraint release pathway for the melts for larger Đ_{M}.

Influence of Liquid Structure on Fickian Diffusion in Binary Mixtures of n-Hexane and Carbon Dioxide Probed by Dynamic Light Scattering, Raman Spectroscopy, and Molecular Dynamics Simulations

This study contributes to a fundamental understanding of how the liquid structure in a model system consisting of weakly associative n-hexane ( n-C₆H₁₄) and carbon dioxide (CO₂) influences the Fickian diffusion process. For this, the benefits of light scattering experiments and molecular dynamics (MD) simulations at macroscopic thermodynamic equilibrium were combined synergistically. Our reference Fickian diffusivities measured by dynamic light scattering (DLS) revealed an unusual trend with increasing CO₂ mole fractions up to about 70 mol %, which agrees with our simulation results. The molecular impacts on the Fickian diffusion were analyzed by MD simulations, where kinetic contributions related to the Maxwell-Stefan (MS) diffusivity and structural contributions quantified by the thermodynamic factor were studied separately. Both the MS diffusivity and the thermodynamic factor indicate the deceleration of Fickian diffusion compared to an ideal mixture behavior. Computed radial distribution functions as well as a significant blue-shift of the CH stretching modes of n-C₆H₁₄ identified by Raman spectroscopy show that the slowing down of the diffusion is caused by a structural organization in the binary mixtures over a broad concentration range in the form of self-associated n-C₆H₁₄ and CO₂ domains. These networks start to form close to the infinite dilution limits and seem to have their largest extent at a solute-solvent transition point at about 70 mol % CO₂. The current results not only improve the general understanding of mass diffusion in liquids but also serve to develop sound prediction models for Fick diffusivities.

Multiscale Molecular Simulations of Polymer-Matrix Nanocomposites: or What Molecular Simulations Have Taught us About the Fascinating Nanoworld

Following the substantial progress in molecular simulations of polymer-matrix nanocomposites, now is the time to reconsider this topic from a critical point of view. A comprehensive survey is reported herein providing an overview of classical molecular simulations, reviewing their major achievements in modeling polymer matrix nanocomposites, and identifying several open challenges. Molecular simulations at multiple length and time scales, working hand-in-hand with sensitive experiments, have enhanced our understanding of how nanofillers alter the structure, dynamics, thermodynamics, rheology and mechanical properties of the surrounding polymer matrices.

Multiscale approach to equilibrating model polymer melts

We present an effective and simple multiscale method for equilibrating Kremer Grest model polymer melts of varying stiffness. In our approach, we progressively equilibrate the melt structure above the tube scale, inside the tube and finally at the monomeric scale. We make use of models designed to be computationally effective at each scale. Density fluctuations in the melt structure above the tube scale are minimized through a Monte Carlo simulated annealing of a lattice polymer model. Subsequently the melt structure below the tube scale is equilibrated via the Rouse dynamics of a force-capped Kremer-Grest model that allows chains to partially interpenetrate. Finally the Kremer-Grest force field is introduced to freeze the topological state and enforce correct monomer packing. We generate 15 melts of 500 chains of 10.000 beads for varying chain stiffness as well as a number of melts with 1.000 chains of 15.000 monomers. To validate the equilibration process we study the time evolution of bulk, collective, and single-chain observables at the monomeric, mesoscopic, and macroscopic length scales. Extension of the present method to longer, branched, or polydisperse chains, and/or larger system sizes is straightforward.

Influence of molecular architecture on the entanglement network: topological analysis of linear, long- and short-chain branched polyethylene melts via Monte Carlo simulations

We present detailed results on the effect of chain branching on the topological properties of entangled polymer melts via an advanced connectivity-altering Monte Carlo (MC) algorithm. Eleven representative model linear, short-chain branched (SCB), and long-chain branched (LCB) polyethylene (PE) melts were employed, based on the total chain length and/or the longest linear chain dimension. Directly analyzing the entanglement [or the primitive path (PP)] network of the system via the Z-code, we quantified several important topological measures: (a) the PP contour length Lpp, (b) the number of entanglements Zes per chain, (c) the end-to-end length of an entanglement strand des, (d) the number of carbon atoms per entanglement strand Nes, and (e) the probability distribution for each of these quantities. The results show that the SCB polymer melts have significantly more compact overall chain conformations compared to the linear polymers, exhibiting, relative to the corresponding linear analogues, (a) ∼20% smaller values of 〈Lpp〉 (the statistical average of Lpp), (b) ∼30% smaller values of 〈Zes〉, (c) ∼20% larger values of 〈des〉, and (d) ∼50% larger values of 〈Nes〉. In contrast, despite the intrinsically smaller overall chain dimensions than those of the linear analogues, the LCB (H-shaped and A3AA3 multiarm) PE melts exhibit relatively (a) 7-8% larger values of 〈Lpp〉, (b) 6-11% larger values of 〈Zes〉 for the H-shaped melt and ∼2% smaller values of 〈Zes〉 for the A3AA3 multiarm, (c) 2-5% smaller values of 〈des〉, and (d) 7-11% smaller values of 〈Nes〉. Several interesting features were also found in the results of the probability distribution functions P for each topological measure.

Classical force field for hydrofluorocarbon molecular simulations. Application to the study of gas solubility in poly(vinylidene fluoride)

A classical all-atoms force field for molecular simulations of hydrofluorocarbons (HFCs) has been developed. Lennard-Jones force centers plus point charges are used to represent dispersion-repulsion and electrostatic interactions. Parametrization of this force field has been performed iteratively using three target properties of pentafluorobutane: the quantum energy of an isolated molecule, the dielectric constant in the liquid phase, and the compressed liquid density. The accuracy and transferability of this new force field has been demonstrated through the simulation of different thermophysical properties of several fluorinated compounds, showing significant improvements compared to existing models. This new force field has been applied to study solubilities of several gases in poly(vinylidene fluoride) (PVDF) above the melting temperature of this polymer. The solubility of CH4, CO2, H2S, H2, N2, O2, and H2O at infinite dilution has been computed using test particle insertions in the course of a NpT hybrid Monte Carlo simulation. For CH4, CO2, and their mixtures, some calculations beyond the Henry regime have also been performed using hybrid Monte Carlo simulations in the osmotic ensemble, allowing both swelling and solubility determination. An ideal mixing behavior is observed, with identical solubility coefficients in the mixtures and in pure gas systems.