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Fine-graining without coarse-graining: An easy and fast way to equilibrate dense polymer melts
Abstract
A technique to prepare well-equilibrated polymer melts is presented. The method, named fine-graining, consists of two steps: the generation of continuum random walks characterized by different Kuhn lengths and the insertion of the atomistic units on the "parent" random walk chains. The procedure ensures a good equilibration at long as well as short length-scales and it is very easy to implement. Melts of polyethylene, atactic polystyrene and polyamide-66 are equilibrated with this technique and their long and short range structural properties can be successfully compared with previous simulation and experimental data.
... Variants of the double-bridging algorithm 6-10 introduce connectivity-altering moves allowing pivot-like 11 moves in dense systems for the equilibration of the large-scale chain structure. Schemes building on the Flory ideality hypothesis 12 superpose pre-equilibrated chain configurations with the proper large-scale random walk statistics in the simulation box and gradually remove the local overlap between monomers 9,[13][14][15][16] . This approach can be generalized to a systematic multi-scale approach, which equilibrates density fluctuations and chain conformations from the largest scales down to the monomer [16][17][18] or even atomic scale 19 . ...
... [3][4][5] In particle-based models, the resolution ranges from the atom scale to DPD-like descriptions, where entire chains are represented by one or two soft spheres or ellipsoids 78,79 . While systematic coarse-graining is an important aspect of the multi-scale view of polymeric systems, the framework also lends itself to fine-graining, i.e. the insertion of additional molecular details into a more coarse-grain model [3][4][5]14 . ...
... Refs. 14,19,28,83 . ...
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 $25000$-$2000$ beads per 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.
... Configuration assembly [10,[14][15][16][17] algorithms construct the initial sample by putting together polymer chains under fixed average density. Implementations vary in details, but in all cases chains are generated to reproduce prescribed distributions of conformations. ...
... Subsequently local conformations and liquid packing are recovered through a "push off" procedure, which gradually [14] reinserts the microscopic excluded volume into the ensemble. The strategy has been successful with generic [14,15] and chemistry specific [10,16,17] microscopic models. However, the postulative construction of starting configurations is a drawback. ...
... Note that several different methods for re-introducing atomistic detail in CG polymer chain conformations have been appeared in the literature. [9,12,16,40,57] Here, inspired from the above works, we propose a generic approach that is based on a "lego-like" construction of consecutive monomers along a macromolecular chain. The backmapping algorithm consists of the following stages: ...
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 behind these strategies, is first to represent polymers by chains of large soft blobs (spheres) and efficiently equilibrate the melt on mesoscopic scale. 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. To develop the method, we choose a polymer with sufficient complexity. We consider polystyrene (PS), characterized by stereochemistry and bulky side groups. Our backmapping strategy bridges mesoscopic and atomistic scales by incorporating a blob-based, a moderately CG, and a united-atom model of PS. We demonstrate that the generic blob-based model can be parameterized to reproduce the mesoscale properties of a specific polymer -- here PS. The moderately CG model captures stereochemistry. 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.
... Chain dimensions are important static properties of polymers and are given by the mean-squared end-to-end distance (〈R 0 2 〉) and the mean-squared radius of gyration (〈R g 2 〉) of the equilibrated systems. Both 〈R 0 2 〉 and 〈R g 2 〉 are available from MC and MD simulations of all-atomistic (AA) [80], united atoms (UA) [40,[46][47][48]53,58,[61][62][63][64]69,[71][72][73][74][81][82][83][84][85][86][87][88] and coarse-graining (CG) [89][90][91][92][93][94][95][96][97] models at different temperatures ranging from 413 to 600 K. Within the broad range of molecular lengths available (up to N = 6000, where N is the number of carbons in the backbone) the value of 〈R 0 2 〉/6〈R g 2 〉 decreases as the molecular weight increases and a final trend towards the Gaussian approximation (〈R 0 2 〉/6〈R g 2 〉 = 1) is observed while the molecular weight N is > 150 [98]. Significantly, near N = 15, irrespective of the use of SKS-UA [81] and PYS-UA [98] FFs, the largest deviation from Gaussian statistics (maximum 〈R 0 2 〉/6〈R g 2 〉) is observed, a phenomenon noted in earlier MC simulations [99]. ...
... By far, MD simulations are the most used computational techniques to study PE properties. Among others, MD simulations have been performed to calculate static equilibrium properties (radius of gyration, end-to-end distances, PVT properties, static structure factor, pair-distribution functions etc.) [47,48,53,58,[61][62][63][64][65][66][67][68][69][70][71][72][73][74]81,85,86,100,112], dynamic properties (mean-square displacements, diffusion coefficient, dynamic structure factors, etc.) and rheological properties (intrinsic viscosity, entanglement molecular weight, entanglement relaxation time etc.) [70,[72][73][74]76,[142][143][144]153]. Crystallization [73,308,356] and melting [273,315,349,356,426] processes for semi-crystalline PE have been also simulated using atomistic MD methods. ...
... However, as far as we know, this method has not been applied to obtain a full PE system; rather a CG Kremer-Grest representation is obtained [149]. A second method has been proposed by Carbone et al. [86] for the long length-scale. In this case, the chains are built as a random walk using the characteristic Kuhn length of the polymer under study. ...
This feature article reviews several aspects of computational approaches to polyethylene melt and solid state properties in relation to existing experimental results. Based on 40 years of experience in the field, we offer a personal view of how computer simulations are helping to understand the physics of polyethylene as a model polymer. The first issue discussed is the molten state of polyethylene, including static and dynamic properties and entanglement features along with their impacts on rheological behaviour. We then examine the glass transition, crystallization process and solid state structure, including the interlamellar region. This is followed by brief descriptions of the latest advances in simulating mechanical properties and of the various methodologies used to simulate the physics of polyethylene. Throughout the manuscript, references are made to our own work and also to studies by many other authors that have nicely contributed to developments in simulating the physics of polyethylene in close agreement with experimental results.
... Consequently, a reverse mapping is also needed to reproduce atomistic details such as chemical characteristics from the CG model. The reverse mapping procedure is also referred to as fine-graining or backmapping in the literature [423,424]. ...
... As for the latter, Wu [431] utilized a special backmapping procedure to capture tacticity effects on the structure and dynamics of poly(methyl methacrylate) melts. Moreover, a general backmapping technique to prepare equilibrated polymer melts was proposed by Carbone et al. [424] which consists of (i) the generation of random walk chains with various Kuhn lengths; and (ii) the insertion of atoms on the underlying random walk chains. The steps of this approach for PA-66 are shown in Figure 9. ...
... Finally, the validity of a reverse-mapped atomistic structure is often tested by comparing relevant structural information simulated using atomistic models based on the reverse-mapped configurations with the original AA simulations initially used to develop the CG force field [424,430,434]. Radial distribution function of a specific chemical group, bond and angle distributions, torsion angle distribution, and the number of hydrogen bonds are mostly used for such comparisons. ...
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.
... Thus developing non-dynamic approaches for efficient sampling of configuration space of polymeric liquids is an area of active research. Several strategies are available, including advanced rebridging Monte Carlo (MC) algorithms [2,3], configuration assembly procedures [4,5,6,7], and hierarchical backmapping approaches [8,9,10,11,12,13,14,15]. This classification is not strict, e.g. it is possible to combine concepts from configuration assembly and hierarchical backmapping [16,17]. ...
... In configuration assembly procedures the polymer liquid is first described with crude resolution, aiming to reproduce equilibrium long-wavelength structural and conformational properties. This is typically achieved by assembling an ideal gas of chains, reproducing conformational distributions expected [4,5,6,7] in the polymer liquid. Correlations are then partially recovered, e.g. by reducing density fluctuations through a MC optimization [4,5,7]. ...
Understanding properties of polymer alloys with computer simulations frequently requires equilibration of samples comprised of microscopically described long molecules. We present the extension of an efficient hierarchical backmapping strategy, initially developed for homopolymer melts, to equilibrate high-molecular-weight binary blends. These mixtures present significant interest for practical applications and fundamental polymer physics. In our approach, the blend is coarse-grained into models representing polymers as chains of soft blobs. Each blob stands for a subchain with N <sub>b</sub> microscopic monomers. A hierarchy of blob-based models with different resolution is obtained by varying N <sub>b</sub>. First the model with the largest N <sub>b</sub> is used to obtain an equilibrated blend. This configuration is sequentially fine-grained, reinserting at each step the degrees of freedom of the next in the hierarchy blob-based model. Once the blob-based description is sufficiently detailed, the microscopic monomers are reinserted. The hard excluded volume is recovered through a push-off procedure and the sample is re-equilibrated with Molecular Dynamics (MD), requiring relaxation on the order of the entanglement time. For the initial method development we focus on miscible blends, described on microscopic level through a generic bead-spring model which reproduces hard excluded volume, strong covalent bonds, and realistic liquid density. The blended homopolymers are symmetric with respect to molecular architecture and liquid structure. To parameterize the blob-based models and validate equilibration of backmapped samples we benefit from the symmetry of the blends, to obtain reference data from independent hybrid simulations combining MD and identity exchange Monte Carlo (MC) moves. The potential of the backmapping strategy is demonstrated by equilibrating blend samples with different degree of miscibility, containing 500 chains with 1000 monomers each. Equilibration is verified by comparing chain conformations and liquid structure in backmapped blends with data from samples prepared using the hybrid MD/MC. Possible directions for further methodological developments are discussed.
... Hence alternative methods of setting up a polymer melt must be explored. We were successful in employing a method termed "fine-graining" or "back mapping" [55,56]. Fine graining is a method used to add atomistic detail to a more abstract, a coarse grained, polymer model. ...
... Firstly it must be decided what the ratio λ of CG beads to UA monomers should be. It is argued that [56] it is best to choose a large λ of the order of s p , the number of monomers per persistence length. The UA model can then be mapped onto a freely jointed chain. ...
The Flory ideality hypothesis states that flexible polymer chains in a melt assume the shape of three-dimensional random walks leading to so called Gaussian coils. The basis of this hypothesis is that any local conformational information decays exponentially along the chain backbone and thus has no influence on the long range conformation. Additionally it is argued that the excluded volume shielding of neigbor chains cancels out any swelling effects. Neutron scattering (NS) experiments dating back 30 years confirm the postulated Gaussian coil shape of polymers. This leads to a pillar of polymer theory: Any flexible polymer can be described as a three-dimensional random walk. Advances in simulation technics and computing power have opened the door to the possibility of studing very long chains. This allowed for a closer look at the chain structure of polymer melts and revealed deviations from ideality. This deviation is very slight and thus great care must be taken to distinguish it from noise. So far the deviation from the Gaussian coil structure was only studied for coarse-grained models. The scope of this thesis is to explore if these deviations are also measurable in atomistically realistic simulations and modern day NS experiments.
... Here, initially relaxed configura- tions for mixtures of CO 2 in PMMA are chosen. To in- clude the effect of system size on gas solubility, reported by Neyertz and Brown, 29 we have prepared long chains (100 re- peat units) of PMMA using a direct reverse-mapping (fine graining) technique developed by Carbone et al. 30 to generate relaxed chains. The main idea of this method of chain gen- eration is that the polymer displays random-walk conforma- tional properties on length-scales larger than the Kuhn length. ...
... The method consists of the following steps: (1) Generation of continuum random walks characterized by the Kuhn length of PMMA, 1.53 nm. 30 To prepare the mixture, we used our GCE simulation technique, to insert CO 2 molecules in the polymeric matrix, by setting the target excess chemical potential to a high value. Starting from an initially relaxed PMMA + CO 2 configura- tion we did simulations in the GCE to obtain the density of CO 2 in the PMMA phase as well as the equilibrium CO 2 pres- sure. ...
Molecular dynamics simulations are performed to determine the solubility and diffusion coefficient of carbon dioxide and nitrogen in poly(methyl methacrylate) (PMMA). The solubilities of CO2 in the polymer are calculated employing our grand canonical ensemble simulation method, fixing the target excess chemical potential of CO2 in the polymer and varying the number of CO2 molecules in the polymer matrix till establishing equilibrium. It is shown that the calculated sorption isotherms of CO2 in PMMA, employing this method well agrees with experiment. Our results on the diffusion coefficients of CO2 and N2 in PMMA are shown to obey a common hopping mechanism. It is shown that the higher solubility of CO2 than that of N2 is a consequence of more attractive interactions between the carbonyl group of polymer and the sorbent. While the residence time of CO2 beside the carbonyl group of polymer is about three times higher than that of N2, the diffusion coefficient of CO2 in PMMA is higher than that of N2. The higher diffusion coefficient of CO2, compared to N2, in PMMA is shown to be due to the higher (≈3 times) swelling of polymer upon CO2 uptake.
... Chain entanglement is a physical interaction caused by non-bonded interactions and steric hindrance of the chain topology (Park and Lee, 2021;Carbone et al., 2010). Chain entanglement occurs when two chains are in contact with each other. ...
The coupling mechanism of chain entanglement and crosslinking remains unelucidated at the atomic scale. The network-forming dynamics and mechanical properties of pure-entangled matrix (PEM) and crosslinked & entangled matrix (CEM) were explored using all-atomic molecular dynamics simulations. The generation of side chains and local networks significantly affects the mechanical properties. For the PEM, as the reaction degree (r) increased , the dominant factor affecting the mechanical properties of materials changed from the movement of the main chain to entanglement. For the CEM, as r increased, the system first produced a local cross-linked structure and then formed a complete matrix. At extremely large strain, the CEM directly ruptured; the PEM showed a strain-hardening behavior before the final rupture because of the redistribution of chain entanglements. The PEM and CEM exhibited almost the same elasticity but demonstrated a large difference in viscosity owing to the presence of long side chains in the CEM.
... the insertion of additional molecular details into a more coarse-grain model. 3,73,74,77 In the present context, pre-packing and push-off schemes can be generalised to a systematic multi-scale approach, which equilibrates density fluctuations and chain conformations from the largest scales down. Zhang et al. 14,78,79 represented the chains in a polymer melt via a hierarchy of soft blob models with matching invariant degrees of polymerization. ...
We present a computationally efficient multiscale method for preparing very well equilibrated, isotropic long chain model polymer melts. As an application we generate Kremer-Grest melts of $1000$ chains with $200$ entanglements and $25000$-$2000$ beads per 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 force-capped bead-spring models slowly introducing the local bead packing. 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.
... 15,41 As shown in Table VI, 4.761 is much lower than C∞ values from experiments 64,70,71 and previous atomistic simulations. 15,41,60,62 This is consistent with the fact that the SDK model has less rigid coarse-grain bond angles compared to atomistic PE (e.g., the CHARMM forcefield 74 that was used to parameterize the SDK model). For the SDK PE melts, ⟨lCG⟩ 2 (λ⟨l⟩ 2 ) = 1.866, so the SDK PE model corresponds to an atomistic polymer with C∞ = 8.884 ± 0.002, which is slightly elevated, but still reasonable for PE (see Table VI). ...
The Shinoda-DeVane-Klein (SDK) model is herein demonstrated to be a viable coarse-grain model for performing molecular simulations of polyethylene (PE), affording new opportunities to advance molecular-level, scientific understanding of PE materials and processes. Both structural and dynamical properties of entangled PE melts are captured by the SDK model, which also recovers important aspects of PE crystallization phenomenology. Importantly, the SDK model can be used to represent a variety of materials beyond PE and has a simple functional form, making it unique among coarse-grain PE models. This study expands the suite of tools for studying PE in silico and paves the way for future work probing PE and PE-based composites at the molecular level.
... For long-chain polymers, the time scale to fully equilibrate the chain conformation, i.e., the longest polymer relaxation time, is well beyond the reach of brute-force MD. For this reason, the development of methods for polymer structure generation has remained an active area of research after more than three decades [4][5][6][7][8][9]. For dynamical properties and phenomena, the limited time scale accessible by MD is a more direct challenge. ...
Bottom-up prediction that links materials chemistry to their properties is a constant theme in polymer simulation. Rheological properties are particularly challenging to predict because of the extended time scales involved as well as large uncertainty in the stress output from molecular simulation. This review focuses on the application of molecular simulation in the prediction of such properties, including approaches solely based on molecular simulation and its integration with rheological models. Most attention is given to the prediction of quantitative properties, in particular, those most studied such as shear viscosity and linear viscoelasticity. Studies on the fundamental understanding of rheology are referenced only when they are directly relevant to the property prediction. The review starts with an overview of the major methods for extracting rheological properties from molecular simulation, using bead-spring chain models as a sandbox system. It then discusses materials-specific prediction using chemically-realistic models, including systematically coarse-grained models that allow the mapping between scales. Finally, integrating molecular simulation with rheological models extends the prediction to highly entangled polymers. Recent development of several multiscale predictive frameworks allowed the successful prediction of rheological properties from the chemical structure for polymers of experimentally relevant molecular weights.
... Even so, only the generic anharmonic multibead-spring microscopic (Kremer-Grest) model 16 was used to describe the coarse-grained representations, where the final reinsertion of chemical detail at atomistic resolution remains non-trivial. Carbone et al. 17 considered a similar fine-graining procedure to produce well-equilibrated polymer melts at UA resolution. In this method, both the long and short length scales are considered sequentially to equilibrate the melt. ...
Equilibrated systems of entangled polymer melts cannot be produced using direct brute force equilibration due to the slow reptationdynamics exhibited by high molecular weight chains. Instead, these dense systems are produced using computational techniques such as Monte Carlo-Molecular Dynamics hybrid algorithms, though the use of soft potentials has also shown promise mainly for coarse-grained polymeric systems. Through the use of soft-potentials, the melt can be equilibrated via molecular dynamics at intermediate and long length scales prior to switching to a Lennard-Jones potential. We will outline two different equilibration protocols, which use various degrees of information to produce the starting configurations. In one protocol, we use only the equilibrium bond angle, bond length, and target density during the construction of the simulation cell, where the information is obtained from available experimental data and extracted from the force field without performing any prior simulation. In the second protocol, we moreover utilize the equilibrium radial distribution function and dihedral angle distribution. This information can be obtained from experimental data or from a simulation of short unentangled chains. Both methods can be used to prepare equilibrated and highly entangled systems, but the second protocol is much more computationally efficient. These systems can be strictly monodisperse or optionally polydisperse depending on the starting chain distribution. Our protocols, which utilize a soft-core harmonic potential, will be applied for the first time to equilibrate a million particle system of polyethylene chains consisting of 1000 united atoms at various temperatures. Calculations of structural and entanglement properties demonstrate that this method can be used as an alternative towards the generation of entangled equilibrium structures.
... The scaling of the radius of gyration with the polymer size is in good agreement with the theory, being best fitted by a ∝M w 0.58 function for both PE and PP. In Figure 4 we plot also a comparison with the data by Liu et al., 52 who performed static and dynamic light 40 Foteinopoulou et al., 41 and Carbone et al. 42 (the last using the force field developed by Smit et al. 43 ). Small angle neutron scattering (SANS) data are from Fetters et al. 44 and Horton et al. 45 For PP, UA data are from Boland et al. 46 and Neelakatan et al. 47 The original SANS data by Ballard et al. ...
The understanding of the interaction of nanoplastics with living organisms is crucial both to assess the health hazards of degraded plastics and to design functional polymer nanoparticles with biomedical applications. In this paper, we develop two coarse-grained models of every-day use polymers, polyethylene (PE) and polypropylene (PP), aimed at the study of the interaction of hydrophobic plastics with lipid membranes. The models are compatible with the popular MARTINI force field for lipids, and they are developed using both structural and thermodynamic properties as targets in the parameterization. The models are then validated by showing their reliability at reproducing structural properties of the polymers, both linear and branched, in dilute conditions, in the melt and in a PE-PP blend. Partitioning of PP and PE oligomers in phosphatidylcholine membranes as obtained at CG level reproduces well atomistic data.
... In DPD, instead of simulating all atomic degrees of freedom, one lumps groups of atoms in so-called coarse-grained particles or beads connected by harmonic springs [11,12]. The coarse graining of the structure and the soft interactions used in DPD simulations allow for larger systems (~1 μm) to be modeled over significantly longer times (~1 ms) than is possible with conventional particle-based simulations methods such as Monte Carlo or molecular dynamics. ...
Surfactant formulations are currently being used by the oil industry in chemical enhanced oil recovery. Given a properly selected formulation, a microemulsion is formed between the (crude) oil and brine that resides in the reservoir. The formed microemulsion typically has an ultralow interfacial tension (~0.001 mN/m) that will restore the oil flow in the reservoir. Here we discuss a simulation protocol for computing the properties of oil–brine–surfactant microemulsions. The protocol is based on dissipative particle dynamics, a coarse grained simulation technique that allows for a fast screening of parameter space. The “Method of Moments” [Fraaije et al., Langmuir 2013, 29, 2136–2151], which looks at the bending properties of the surface film, is introduced and applied to a set of anionic sulfonate and sulfate surfactants. For the set of surfactants, we compute the optimum salinities and address the effect of surfactant tail length and the co-solvent. We find that the computed optimum salinities for neat oil–brine–surfactant interfaces quantitatively agree with experimentally obtained values. In addition, the Method of Moments correctly predicts that the optimum salinity decreases with increasing surfactant tail length. Furthermore, the simulations show that the addition of a co-solvent leads to lower salinity, again in good agreement with experiments. We finally discuss how to extend the Method of Moments to industrially relevant mixtures that include surfactant mixtures and crude oils.
... This mapping procedure establishes a one-to-one correspondence between both atomistic and CG representations and enables an interchange between them (backmapping procedure). [10][11][12][13] With the IBI procedure, simulations of polymer melts of molecular weight comparable to the experimental ones can be carried out. Among the advantages of this procedure, there are the relatively easy implementation, the possibility to retain different chemical features of the atomistic model by choosing appropriately the position of the CG beads, and the correspondence between the state point of the CG and atomistic models that should help in constructing hybrid models where atoms and CG beads are mixed together. ...
Polymers are multiscale systems by construction. They are formed by several monomeric units connected by covalent bonds whose chemical nature defines the rigidity of the chain. The interconnection between the monomeric units determines the interdependence of the motion of the different chain segments and the intrinsic multiscale nature of polymeric materials. This characteristic is reflected on the different modeling techniques that can be used to simulate polymeric materials. Because of the large conformational space that needs to be sampled when simulating polymers, coarse‐grained (CG) models are commonly used and depending on which part of the system free energy (enthalpy, entropy, or both) is relevant for the properties of interest, the appropriate modeling techniques should be used. Each model is characterized by advantages and limitations that can have a great impact on the quality of the results obtained. In this overview, we address some of the more common CG techniques presented in the literature for the modeling of polymeric materials at different length scales. WIREs Comput Mol Sci 2014, 4:62–70. doi: 10.1002/wcms.1149
This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods
Hydrogen is a clean and sustainable energy carrier which plays a major role in the transition of the global energy market to a less fossil fuel dependent future. Polymer-based materials are crucial in the production, storage, transportation, and energy extraction of hydrogen. More insights in the hydrogen-polymers interactions are required to guide material design and product development, especially for hydrogen solubility in polymers, which is crucial in many applications. The current study aims at rationalizing the determining factors of hydrogen solubility in two relevant polymers: polyamide-6 (PA-6) and high density polyethylene (HDPE). Based on atomistic molecular dynamics simulations and experimental data, we have reached several conclusions related to hydrogen and oxygen solubility in these two polymers. The crystal phases of PA-6 and HDPE are impenetrable to hydrogen and oxygen at elevated pressures, despite the small molecular size of hydrogen and oxygen. The practical implication for gas barrier applications is that polymer crystals act as impermeable obstacles and gas migration takes place primarily in the amorphous phase. Experimental hydrogen and oxygen solubilities in PA-6 and HDPE at elevated pressures can be predicted in a semiquantitative manner by molecular simulations. The discrepancies between experimental and predicted values could be attributed to neglect of the effect of crystal regions on the amorphous polymer domains. Although hydrogen is smaller than oxygen, it has been experimentally observed that hydrogen has a lower solubility in PA-6 and HDPE than oxygen. This observation has been confirmed by molecular simulations and attributed to the more favorable energetic interactions of oxygen with PA-6 and PE than of hydrogen. These interactions dominate the solubility behavior over the distribution of the accessible volume in the polymers.
Decades of work in the field of computational study of semiconducting polymers using atomistic models illustrate the challenges of generating equilibrated models for this class of materials. While adopting a coarse-grained model can be helpful, the process of developing a suitable model is particularly non-trivial and time-consuming for semiconducting polymers due to a large number of different interactions with some having an anisotropic nature. This work introduces a procedure for the rapid generation of a hybrid model for semiconducting polymers where atoms of secondary importance (those in the alkyl side chains) are transformed into coarse-grained beads to reduce the computational cost of generating an equilibrated structure. The parameters are determined from easy-to-equilibrate simulations of very short oligomers and the model is constructed to enable a very simple back-mapping procedure to reconstruct geometries with atomistic resolution. The model is illustrated for three related polymers containing DPP (diketopyrrolopyrrole) to evaluate the transferability of the potential across different families of polymers. The accuracy of the model, determined by comparison with the results of fully equilibrated simulations of the same material before and after back-mapping, is fully satisfactory for two out of the three cases considered. We noticed that accuracy can be determined very early in the workflow so that it is easy to assess when the deployment of this method is advantageous. The hybrid representation can be used to evaluate directly the electronic properties of structures sampled by the simulations.
Optimal design of polymers is a challenging task due to their enormous chemical and configurational space. Recent advances in computations, machine learning, and increasing trends in data and software availability can potentially address this problem and accelerate the molecular-scale design of polymers. Here, the central problem of polymer design is reviewed, and the general ideas of data-driven methods and their working principles in the context of polymer design are discussed. This Review provides a historical perspective and a summary of current trends and outlines future scopes of data-driven methods for polymer research. A few representative case studies on the use of such data-driven methods for discovering new polymers with exceptional properties are presented. Moreover, attempts are made to highlight how data-driven strategies aid in establishing new correlations and advancing the fundamental understanding of polymers. This Review posits that the combination of machine learning, rapid computational characterization of polymers, and availability of large open-sourced homogeneous data will transform polymer research and development over the coming decades. It is hoped that this Review will serve as a useful reference to researchers who wish to develop and deploy data-driven methods for polymer research and education.
Multiscale‐computational‐chemistry (MSCC) simulations are employed—bridging quantum chemistry, coarse‐grained dissipative particle dynamics (DPD), and molecular dynamics (MD)—to derive solubility and diffusivity of dibutylamine (DBA)—a residual moiety in commercially available poly(phenylene ether) (PPE) resins—in PPE and food simulants. Coarse‐grained DPD simulations are used for computationally inexpensive and faster equilibration of high‐molecular‐weight PPE chains, with a final MD step to estimate mean squared displacement (diffusivity) of DBA in PPE. State‐of‐the‐art algorithms involving quasichemical methods and thermodynamic‐integration in DPD are employed to estimate solubility of DBA in various mediums. Such approaches are not hitherto widely employed for polymers. The constants derived using MSCC approaches, implemented in CULGI, a commercially available tool, are used as inputs for estimating migration of DBA from PPE into food simulants using a commercial migration‐estimation software AKTS‐SML. The migration estimates from AKTS‐SML simulations, using parameters derived from MSCC, as well as those derived from in‐built thermodynamic models (Piringer, Brandsch) are compared with experimentally measured migration. Multiscale computational‐chemistry simulations—combining quantum chemistry, coarse‐grained simulations, and molecular dynamics simulations—are employed to arrive at estimates of solubility and diffusivity of large permeant moieties through poly(phenylene ether) (PPE). These values are employed to arrive at accurate estimates of migration using the AKTS‐SML software.
Similar to macroscopic ropes and cables, long polymers create knots. We address the fundamental question whether and under which conditions it is possible to describe these intriguing objects with crude models that capture only mesoscale polymer properties. We focus on melts of long polymers which we describe by a model typical for mesoscopic simulations. A worm-like chain model defines the polymer architecture. To describe nonbonded interactions, we deliberately choose a generic “soft” repulsive potential that leads to strongly overlapping monomers and coarse local liquid structure. The soft model is parametrized to accurately reproduce mesoscopic structure and conformations of reference polymer melts described by a microscopic model. The microscopically resolved samples retain all generic features affecting polymer topology and provide, therefore, reliable reference data on knots. We compare characteristic knotting properties in mesoscopic and microscopically resolved melts for different cases of chain stiffness. We conclude that mesoscopic models can reliably describe knots in those melts, where the length scale characterizing polymer stiffness is substantially larger than the size of monomer–monomer excluded volume. In this case, simplified local liquid structure influences knotting properties only marginally. In contrast, mesoscopic models perform poorly in melts with flexible chains. We qualitatively explain our findings through a free energy model of simple knots available in the literature.
State‐of‐the‐art multiscale computational chemistry simulations is employed to predict diffusivity of small gaseous molecules in a generic polyphenylene ether (PPE). The diffusivities are obtained from trajectory analysis of gaseous molecules in molecular dynamics simulations using coarse‐grained dissipative particle dynamics (DPD) simulations to design the amorphous starting structure. Required intra‐ and intermolecular parameters of the DPD simulations are automatically generated using the automated fragmentation and parametrization protocol. A comparison of calculated diffusion coefficients with experimental data for five gaseous molecules in PPE shows adequate accuracy of computational‐chemistry‐based approaches in the prediction of diffusion coefficients. These estimates, validated against measurements reported in the literature, serve as proof of concept for applicability of these new multiscale modeling strategies for complex polymers with aromatic backbones.
The Kremer−Grest (KG) polymer model is a
standard model for studying generic polymer properties in
molecular dynamics simulations. It owes its popularity to its
simplicity and computational efficiency, rather than its ability to
represent specific polymers species and conditions. Here we show
that by tuning the chain stiffness it is possible to adapt the KG
model to model melts of real polymers. In particular, we provide
mapping relations from KG to SI units for a wide range of
commodity polymers. The connection between the experimental
and the KG melts is made at the Kuhn scale, i.e., at the crossover
from the chemistry-specific small scale to the universal large scale
behavior. We expect Kuhn scale-mapped KG models to faithfully represent universal properties dominated by the large scale
conformational statistics and dynamics of flexible polymers. In particular, we observe very good agreement between entanglement
moduli of our KG models and the experimental moduli of the target polymers.
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 stereochemistry 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 blobbased model can be parameterized to reproduce the mesoscale properties of a specific polymer – here PS. The moderately CG model captures stereochemistry. 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.
Using full-atom molecular simulation, we report the first systematic investigation of common phthalate plasticizers for PVC. A multistep model generation and equilibration protocol are proposed for amorphous polymer–plasticizer mixtures, from which statistically robust prediction of materials properties is achieved. Plasticizer performance is evaluated with our molecular models, which considers both their plasticization efficacy and thermodynamic compatibility with the host polymer. Effects of the alkyl side chain configuration in these phthalates are systematically discussed. The results agree well with all known experimental observations. In addition to the size of the alkyl chains, their branching configuration is another factor affecting the phthalate compatibility with PVC. Relaxation of the alkyl side chains is found to be the limiting step in the diffusion of phthalates in PVC, making it a key design parameter for better migration resistance. With the addition of plasticizers, the dynamics of PVC backbones remain the same in the short-time relaxation process, but an earlier onset of the cooperative motion between molecules allows it to enter the long-time diffusive regime earlier. The main outcomes of this study include (1) a molecular modeling protocol validated with commonly used phthalates, which can be used to predict the performance of alternative plasticizers, and (2) molecular insight that can better inform the molecular design of new plasticizers. As a side outcome, we also report a nontrivial chain-length dependence of the cohesive energy and solubility parameter of long-chain polymers, which is an important consideration in the calculation of these quantities using molecular simulation.
We present a thorough analysis of the dynamic behaviour of hybrid atomistic/coarse-grained (CG) models of polymer melts. While structural properties are well preserved in a dual-resolved model, we show how the dynamic of the chains can be influenced by the simultaneous presence of atoms and beads. We show that although the polymer chains are long enough to exhibit reptation, the corresponding CG model is unable to capture the expected subdiffusive regimes and seems to still follow the Rouse dynamics. The introduction of atoms in the chain restores the correct dynamic regime, and the dynamics of hybrid systems becomes comparable to that of the atomistic dynamics as the atoms/beads ratio is increased.
Molecular modeling of crosslinked polymers often follows arbitrary pathways for network generation, with different precursor topology from experimental systems. We use coarse-grained molecular simulation to study the effects of precursor choice on the predicted network structure and properties. Three sets of precursors with different molecular architectures are designed such that they would form identical networks at the limit of perfect conversion. Little difference is observed between the resulting networks in typical properties including the radial distribution function, macroscopic statistics of network connectivity, and glass transition behaviors. However, the stress-strain relationship in tensile deformation clearly depends on the formation pathway when compared at the same crosslinking density. The elastic modulus of the network is found to correlate strongly with the number of elastic strands in the network, except at the highly-crosslinked limit where substantial discrepancy is observed between networks from different precursors. Although these final networks contain a similar average density of structural defects, the choice of precursor has significant impact on their spatial distribution, leading to the precursor dependence of their mechanical properties. Uniform defect distribution and fast defect elimination can be achieved by designing precursor units with a proper stoichiometric ratio of different monomers.
The extent of phase separation and water percolation in sulfonated membranes are the key to their performance in fuel cells. Toward this, the effect of hydration on the morphology and transport characteristics of sulfonated poly(ether ether ketone), sPEEK, membrane is investigated using atomistic molecular dynamics (MD) simulation at various hydration levels ({\lambda}: number of water molecules per sulfonate group) between 4 and 15. At the molecular level, the evolution of local morphology is investigated in terms of structural pair correlations and minimum pair distances, and the transport properties are studied in terms of mean squared displacements (MSDs) and diffusion coefficients. The water-sulfur interaction in sPEEK is found to be stronger than that in Nafion, as observed in experiments. As opposed to Nafion, a weaker interaction of hydronium, with sulfonate, than water is observed. The behavior of water in sPEEK membrane is found to remain far from bulk as indicated by its diffusion coefficient. Analysis of simulation data indicate that at low {\lambda}, the largest water cluster forms a narrow connected path of water molecules and hydronium ions. With increasing {\lambda}, larger water domains appear, spanning more than half of the simulation box at {\lambda} = 15. Small isolated clusters are present at all hydration levels, demonstrating the extent of phase separation in sPEEK to be lesser than that in Nafion. Various analyses, both at molecular and collective level, suggest the occurrence of a percolation transition between {\lambda} = 8 and 10, which leads to a connected network of water channels in the membrane, thereby boosting the mobility of hydronium ions.
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 straight forward.
Using systematic coarse-grained (CG) techniques such as iterative Boltzmann inversion (IBI) is an efficient means to simulate high molecular weight polymer melts within reasonable computational time. One drawback of such an approach is however the need to carry out extensive atomistic simulations in order to extrapolate the necessary distributions to derive the inter and intrabead force field parameters. Here it is shown that it is possible to use atomistic simulations of relative short oligomers to develop the CG model for high molecular weight polymers. In particular for the specific case of polycarbonates, it is found that the structural properties (end-to-end distance, radius of gyration and their distributions) are similar irrespective of whether the CG potentials are derived from 5-mer or 10-mer melt systems. Dynamical properties of the CG systems are smoother and faster than the atomistic ones. Scaling factor, derived by overlapping the CG mean square displacement curves (obtained from different CG IBI potentials) over the atomistic ones, also scales the autocorrelation functions. A prediction of the dynamical scaling factor in the case of the unavailability of atomistic simulations is also discussed. The dynamical properties of the CG melts are modeled reasonably well by all the CG potentials derived from atomistic simulations of short oligomers.
The influence of the inclusion of a silica nanoparticle on the spatial distribution of the local stresses and the locally resolved excess Helmholtz free energy of sorption of small penetrants (He, H2, O2, and CO2) in a polystyrene matrix is studied by molecular dynamics simulations. The local deviations of these quantities from their bulk averages are correlated with spatial peculiarities in structural and dynamical properties, for instance in the mass density, the segmental orientation, and the mean-square atomic positional fluctuations in the polymer matrix. Relative to the bulk, stress anisotropies are slightly enhanced in the neighborhood of a nanoparticle. This is demonstrated by the spatial variations of the local shear stress and the local von Mises shear stress. For all penetrants considered, the region near the interphase is found to be a preferential sorption site. The two stress estimators are compared against one of the most frequently adopted descriptors, i.e., the radial mass density distribution. We show that the estimated interphase width depends on the quantity considered. The interphase width based on variations of the local stresses is considerably shorter than the estimate obtained using the mass density distribution. Furthermore, we find that the interphase width derived from the locally resolved Helmholtz free energy strongly depends on the size of the inserted molecule. For the smallest particle, the helium atom, a broader interphase is found than for the larger molecular species. In the case of carbon dioxide insertion, we estimate an extension similar to the one derived by stress profiles. By artificially reducing the interactions between the nanoparticle atoms and those of the polymer matrix, an attempt has been made to identify links between different ways to define the interphase thickness. It is shown that the quantities under consideration lead to interphase widths which are independent of each other.
In the framework of a hybrid particle-field simulation technique where self-consistent field (SCF) theory and molecular dynamics (MD) are combined, specific coarse-grained (CG) models for Pluronic block copolymers are developed. In particular, the behavior of the model in the correct reproduction of micellar and non-micellar phases has been tested for Pluronic L62 and L64. At different temperature and polymer contents of the water-polymer mixture, the proposed model is able to correctly describe the different morphologies that are experimentally found. The proposed CG models, still very close to atomistic ones, allow the reconstruction of full atomistic structures by applying suitable reverse mapping techniques. This opens the way to all atom description of these systems.
The chain tacticity of a polymer is a key influence on its structure and dynamics, which ultimately determine its properties. While they have great potential to elucidate the influence of chain tacticity, all-atom molecular simulations are often restricted to short chains and small systems. In this work, two typical stereoregular poly(methyl methacrylate) melts were investigated via multiscale simulations. To improve computational efficiency, systematic coarse-graining was first performed. While the coarse-grained molecular dynamics simulations were able to show the effects of tacticity on intramolecular structure and intermolecular interactions, they were not able to reproduce the exact structural distribution or even the effects of tacticity on the dynamics. An alternative reverse-mapping scheme was therefore developed specifically to treat chain configurations in a direct geometric way. The backmapped all-atomistic simulations were found to accurately reproduce the microscopic features of the polymers. Since the effects of tacticity are rather subtle and therefore difficult to discern, this multiscale simulation scheme is a very important method of investigating complex high molecular weight polymer systems.
A simulation strategy for the creation of equilibrated nanostructured copolymer melt morphologies is proposed. Molecular dynamics simulations of bead-spring chains with a soft pair potential are used for efficient modeling of phase separation, while preserving Gaussian chain statistics and chain conformations of an underlying microscopic model. In a second step, hard excluded volume interactions are reintroduced that match the copolymer segregation strength but only require reequilibration of local packing structure. We show that substantial computational gains can be achieved for equilibrating moderately entangled bead-spring polymers. The resultant configurations can be used for further studies of structural and mechanical properties in melts or glasses.
In hybrid particle models where coarse-grained beads and atoms are used simultaneously, two clearly separate time scales are mixed. If such models are used in molecular dynamics simulations, a multiple time step (MTS) scheme can therefore be used. In this manuscript, we propose a simple MTS algorithm which approximates for a specific number of integration steps the slow coarse-grained bead–bead interactions with a Taylor series approximation while the atom–atom ones are integrated every time step. The procedure is applied to a previously developed hybrid model of a melt of atactic polystyrene (di Pasquale, Marchisio, and Carbone, J. Chem. Phys. 2012, 137, 164111). The results show that structure, local dynamics, and free diffusion of the model are not altered by the application of the integration scheme which can confidently be used to simulate multiresolved models of polymer melts. © 2014 Wiley Periodicals, Inc.
Flexible possess promising perspectives in opto-electronic technologies, where high mobility and/or large-scale applicability are important. However, their usefulness in such applications is currently still limited due to the low level of optimization of their performance and durability. For the improvement of these properties, a better understanding and control of small-scale annihilation phenomena involved in the process, such as loss and loss, is necessary, which typically implicates multiple length- and time-scales. Here, we study the causes for their occurrence on the example of nanostructured diblock- and triblock-copolymer systems by making use of a novel solar-cell simulation algorithm and explore new routes to optimize their properties. A particular focus is set on the investigation of and loss phenomena and their dependence on the inter-monomeric interaction strength, chain architecture, and external mechanical loading. Our simulation results reveal that in the regime from low up to intermediate χ-parameters an increasing number of continuous percolation paths is created. In this parameter range, the internal quantum efficiency increases up to a maximum, characterized by a minimum in the number of losses due to recombination. In the regime of high χ-parameters both block-copolymer systems form nanostructures with a large number of bottlenecks and dead ends. These lead to a large number of losses due to recombination, trapping, and a deteriorated resulting in a significant drop in the Moreover, we find that the performance of the triblock-copolymer material decreases with increasing mechanical loading, caused by a growing number of losses due to recombination and accumulation. Finally, we demonstrate that the process of trapping in defects can be reversed by changing the polarity of the which confers these materials the ability to be used as storage media.
We consider the effective interaction between dendrimers affected by pH and counterions of solution as well as terminal modification of dendrimers through the calculation of the free energy with coarse-grained molecular dynamics simulations. We find that the decrease of the pH value can induce the increase in the effective size of dendrimers and that multivalent counterions can lead to like-charged attraction between dendrimers. Under high-valent counterion conditions, the attractive force between the two dendrimers displays the ''M''-like profiles induced by the competition of various interactions. Moreover, short modification of surface does not change their trend of aggregation no matter what the terminal monomers of the dendrimers are. Our results are helpful for designing a novel class of dendrimers to achieve optimal functionalities.
We present a simple hybrid model for macromolecules where the single molecules are modelled with both atoms and coarse-grained beads. We apply our approach to two different polymer melts, polystyrene and polyethylene, for which the coarse-grained potential has been developed using the iterative Boltzmann inversion procedure. Our results show that it is possible to couple the two potentials without modifying them and that the mixed model preserves the local and the global structure of the melts in each of the case presented. The degree of resolution present in each single molecule seems to not affect the robustness of the model. The mixed potential does not show any bias and no cluster of particles of different resolution has been observed.
This article introduces a simple and fast method to reinsert atomistic details into mesoscale models of polymers with rigid side groups. We describe our backmapping scheme from a coarse-grained (CG) resolution to an atomistic picture in the framework of molecular dynamics (MD) simulations of a silica–atactic polystyrene (PS) composite. The CG model of Qian et al. [ Macromolecules 2008, 41, 9919] has been used in the coarse-graining; it combines the atoms of one repeat unit of PS to a CG bead. In the reverse mapping only the centers of mass of these units and their chiralities are known. We show that this information is sufficient for the reverse mapping which requires simple geometrical and mechanical considerations. The capability of the suggested method is demonstrated by comparing MD results from the original atomistic model with those emerging from the reverse mapping. Because of its simplicity, the suggested technique offers the opportunity to study relaxed structures of melt chains with large molecular weights.
We present a multiscale modeling protocol to generate realistic amorphous polymer surfaces. Our computational approach consists of several steps having different levels of molecular detail. Initially, we generate a course-grained polymer surface that is completely relaxed using mesoscopic simulation methods. In the second step we transform the equilibrated coarse-grained polymer surface to atomistic detail with a special “mapper” that takes as input the mesoscopic morphology and uses Monte Carlo techniques to generate the atomistic structure. In the final step the atomistically detailed surface is equilibrated by performing a short molecular dynamics simulation. The great advantage of this multiscale approach is that it allows the study of compounds that have intrinsically (very) slow equilibration dynamics such as polymers, which would be difficult to study with conventional simulation methods only. In addition, the multiscale approach makes it straightforward to “move” between different levels of molecular detail and even zoom in on a relevant part of the mesoscopic structure and map only that part. As test cases we applied the multiscale modeling protocol to polyethylene, polypropylene, and polyacrylonitrile.
By means of molecular dynamics simulations of model dendrimers, we analyze the dependence of the bulk density and molecular packing on the dendrimer molecular weight and intrinsic stiffness. We find that the density is consistently higher in flexible dendrimers than in the rigid ones with a large bending angle. The density values change slightly within the first two generations to reach a plateau. We interpret these results in terms of free volume, showing that the enhanced accessible free volume that characterizes the end-dendron monomers is counterbalanced by the higher number of internal monomers, leading to a constant bulk density for generations larger than three. The added stiffness affects the geometrical properties and the molecular rearrangement of the bulk, reducing the short-range local order and the packing efficiency favoring the dendrimer interpenetration. Our prediction for the bulk density matches and rationalizes experimental and previous all-atom simulation results.
In the framework of a recently developed scheme for a hybrid particle-field simulation technique where self-consistent field theory (SCF) and molecular dynamics (MD) are combined [ J. Chem. Phys. 2009, 130, 214106], specific coarse-grained models for phospholipids and water have been developed. We optimized the model parameters, which are necessary in evaluating the interactions between the particles and the density fields, so that the coarse-grained model can reproduce the structural properties of the reference particle–particle simulations. The development of these specific coarse-grained models suitable for hybrid particle-field simulations opens the way toward simulations of large-scale systems employing models with chemical specificity, especially for biological systems.
We propose an ellipsoid-chain model which may be routinely parameterized to capture large-scale properties of semiflexible, amphiphilic conjugated polymers in various solvent media. The model naturally utilizes the defect locations as pivotal centers connecting adjacent ellipsoids (each currently representing ten monomer units), and a variant umbrella-sampling scheme is employed to construct the potentials of mean force (PMF) for specific solvent media using atomistic dynamics data and simplex optimization. The performances, both efficacy and efficiency, of the model are thoroughly evaluated by comparing the simulation results on long, single-chain (i.e., 300-mer) structures with those from two existing, finer-grained models for a standard conjugated polymer (i.e., poly(2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylenevinylene) or MEH-PPV) in two distinct solvents (i.e., chloroform or toluene) as well as a hybrid, binary-solvent medium (i.e., chloroform/toluene = 1:1 in number density). The coarse-grained Monte Carlo (CGMC) simulation of the ellipsoid-chain model is shown to be the most efficient--about 300 times faster than the coarse-grained molecular dynamics (CGMD) simulation of the finest CG model that employs explicit solvents--in capturing elementary single-chain structures for both single-solvent media, and is a few times faster than the coarse-grained Langevin dynamics (CGLD) simulation of another implicit-solvent polymer model with a slightly greater coarse-graining level than in the CGMD simulation. For the binary-solvent system considered, however, both of the two implicit-solvent schemes (i.e., CGMC and CGLD) fail to capture the effects of conspicuous concentration fluctuations near the polymer-solvent interface, arising from a pronounced coupling between the solvent molecules and different parts of the polymer. Essential physical implications are elaborated on the success as well as the failure of the two implicit-solvent CG schemes under varying solvent conditions. Within the ellipsoid-chain model, the impact of synthesized defects on local segmental ordering as well as bulk chain conformation is also scrutinized, and essential consequences in practical applications discussed. In future perspectives, we remark on strategy that takes advantage of the coordination among various CG models and simulation schemes to warrant computational efficiency and accuracy, with the anticipated capability of simulating larger-scale, many-chain aggregate systems.
We report on Monte Carlo simulations of a single coarse-grained polystyrene chain in spherical confinement. To this end we employ a variant of the freely rotating chain model, the parameters of which are chosen to mimic polystyrene in good solvent conditions. Entanglements are analyzed as a function of molecular weight and capsid radius to provide an educated guess about the structure of a single polystyrene chain in a miniemulsion droplet. We also show that significant knotting occurs first when the radius of the confining sphere falls below the chainʼs radius of gyration.
Hybrid simulations of molecular systems, which combine all-atom (AA) with simplified (or coarse grain, CG) representations, propose an advantageous alternative to gain atomistic details on relevant regions while getting profit from the speedup of treating a bigger part of the system at the CG level. Here we present a reduced set of parameters derived to treat a hybrid interface in DNA simulations. Our method allows us to forthrightly link a state-of-the-art force field for AA simulations of DNA with a CG representation developed by our group. We show that no modification is needed for any of the existing residues (neither AA nor CG). Only the bonding parameters at the hybrid interface are enough to produce a smooth transition of electrostatic, mechanic and dynamic features in different AA/CG systems, which are studied by molecular dynamics simulations using an implicit solvent. The simplicity of the approach potentially permits us to study the effect of mutations/modifications as well as DNA binding molecules at the atomistic level within a significantly larger DNA scaffold considered at the CG level. Since all the interactions are computed within the same classical Hamiltonian, the extension to a quantum/classical/coarse-grain multilayer approach using QM/MM modules implemented in widely used simulation packages is straightforward.
Understanding mesoscopic phenomena in terms of the fundamental motions of atoms and electrons poses a severe challenge for molecular simulation. This challenge is being met by multiscale modeling techniques that aim to bridge between the microscopic and mesoscopic time and length scales. In such techniques different levels of theory are combined to describe a system at a number of scales or resolutions. Here we review recent advancements in adaptive hybrid simulations, in which the different levels are used in separate spatial domains and matter can diffuse from one region to another with an accompanying resolution change. We discuss what it means to simulate such a system, and how to enact the resolution changes. We show how to construct efficient adaptive hybrid quantum mechanics/molecular mechanics (QM/MM) and atomistic/coarse grain (AA/CG) molecular dynamics methods that use an intermediate healing region to smoothly couple the regions together. This coupling is formulated to use only the native forces inherent to each region. The total energy is conserved through the use of auxiliary bookkeeping terms. Error control, and the choice of time step and healing region width, is obtained by careful analysis of the energy flow between the different representations. We emphasize the CG → AA reverse mapping problem and show how this problem is resolved through the use of rigid atomistic fragments located within each CG particle whose orientation is preconditioned for a possible resolution change through a rotational dynamics scheme. These advancements are shown to enable the adaptive hybrid multiscale molecular dynamics simulation of macromolecular soft matter systems.
For petrochemical applications knowledge of the critical properties of the n‐alkanes is of interest even at temperatures where these molecules are thermally unstable. Computer simulations can determine the vapor–liquid coexistence curve of a large number of n‐alkanes ranging from pentane (C5) through octatetracontane (C48). We have compared the predicted phase diagrams of various models with experimental data. Models which give nearly identical properties of liquid alkanes at standard conditions may have critical temperatures that differ by more than 100 K. A new n‐alkane model has been developed by us that gives a good description of the phase behavior over a large temperature range. For modeling vapor–liquid coexistence a relatively simple united atom model was sufficient to obtain a very good agreement with experimental data; thus it appears not necessary to take the hydrogen atoms explicitly into account. The model developed in this work has been used to determine the critical properties of the long‐chain alkanes for which experiments turned out to be difficult and contradictory. We found that for the long‐chain alkanes (C8–C48) the critical density decreases as a function of the carbon number. These simulations were made possible by the use of a recently developed simulation technique, which is a combination of the Gibbs‐ensemble technique and the configurational‐bias Monte Carlo method. Compared with the conventional Gibbs‐ensemble technique, this method is several orders of magnitude more efficient for pentane and up to a hundred orders of magnitude for octatetracontane. This recent development makes it possible to perform routinely phase equilibrium calculations of complex molecules.
Polymer-RISM (Reference-interaction-site-model) theory is used to examine the local structure of a dense polyethylene melt near the freezing point. Predictions for the static structure factor are found to be in near quantitative agreement with new x-ray diffraction data obtained at 430 K and 1 atm.
A numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated. The relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration. The method is applied to a molecular dynamics simulation of a liquid of 64 n-butane molecules and compared to a simulation using generalized coordinates. The method should be useful for molecular dynamics calculations on large molecules with internal degrees of freedom.
In molecular dynamics (MD) simulations the need often arises to maintain such parameters as temperature or pressure rather than energy and volume, or to impose gradients for studying transport properties in nonequilibrium MD. A method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling. The method is easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints. The influence of coupling time constants on dynamical variables is evaluated. A leap‐frog algorithm is presented for the general case involving constraints with coupling to both a constant temperature and a constant pressure bath.
We propose a novel approach that allows efficient numerical simulation of systems consisting of flexible chain molecules. The method is especially suitable for the numerical simulation of dense chain systems and monolayers. A new type of Monte Carlo move is introduced that makes it possible to carry out large scale conformational changes of the chain molecule in a single trial move. Our scheme is based on the selfavoiding random walk algorithm of Rosenbluth and Rosenbluth. As an illustration, we compare the results of a calculation of mean-square end to end lengths for single chains on a two-dimensional square lattice with corresponding data gained from other simulations.
We develop and test a new elementary Monte Carlo move for use in the
efficient simulation of polymer systems. The move consists of a
concerted rotation around up to seven adjacent skeletal bonds that
leaves the rest of the chain unaffected. No assumption is made
concerning the backbone geometry other than that bond lengths and bond
angles are held constant during the elementary move. Special sampling
techniques are needed because the new move involves a correlated change
in seven degrees of freedom along the chain backbone. We use the new
move in conjunction with reptation in an isothermal-isobaric Monte Carlo
simulation of a bulk tetracosane melt system and find that it improves
computational efficiency relative to a purely reptation-based Monte
Carlo scheme. Comparisons are also made between a concerted
rotation-based Monte Carlo simulation and a molecular dynamics
simulation of an oligomer of atactic polypropylene.
A model to perform coarse grained molecular dynamics simulations of room temperature ionic liquids of the family 1-n-alkyl-3-methylimidazolium hexafluorophosphate has been developed. Large scale simulations of ionic liquids with butyl, heptyl, and decyl side chains have been carried out. Calculated structure factors demonstrate intermediate range ordering in these liquids. The spatial correlations between anions are shown to dominate the neutron or X-ray scattering at low wave vectors. Ionic liquids with long side chains exhibit a bicontinuous morphology, one region consisting of polar moieties and the other of non-polar, alkyl tails.
This work is concerned with the atomistic simulation of the volumetric, conformational and structural properties of monodisperse polyethylene (PE) melts of molecular length ranging from C78 up to C1000. In the past, polydisperse models of these melts have been simulated in atomistic detail with the end-bridging Monte Carlo algorithm [Pant and Theodorou, Macromolecules 28, 7224 (1995); Mavrantzas et al., Macromolecules 32, 5072 (1999)]. In the present work, strictly monodisperse as well as polydisperse PE melts are simulated using the recently introduced double bridging and intramolecular double rebridging chain connectivity-altering Monte Carlo moves [Karayiannis et al., Phys. Rev. Lett. 88, 105503 (2002)]. These algorithms constitute generalizations of the EB move, since they entail the construction of two trimer bridges between two properly chosen pairs of dimers along the backbones of two different chains or along the same chain. In the simulations, a new molecular model is employed which is a hybrid of the united-atom TraPPE model [Martin and Siepmann, J. Phys. Chem. B 102, 2569 (1998)] and the anisotropic united-atom model [Toxvaerd, J. Chem. Phys. 107, 5197 (1997)]. Results are first presented documenting the efficiency of the algorithm in equilibrating long-chain PE melts and its dependence on chain length and polydispersity. Simulation data concerning the volumetric, conformational and structural properties of the monodisperse PE melts, obtained with the new simulation algorithm, are found to be in excellent agreement with available experimental data. © 2002 American Institute of Physics.
Results are presented for the thermodynamic, conformational, and structural properties of cis-1,4 polyisoprene (PI) melts from detailed atomistic Monte Carlo simulations. All simulations have been executed by employing the very efficient end-bridging move, which alters chain connectivity and induces fast conformational and structural equilibration over the entire range of length scales in the melt. To use the end-bridging move, a geometric mapping of a cis-1,4 PI monomer onto an equivalent three-bead monomer is utilized. In the acceptance criterion of the move, however, the energy terms are calculated from the actual atomistic cis-1,4 PI chains, obtained after performing the reverse mapping. Simulation results are obtained at T = 413 K with cis-1,4 PI melts of mean molecular length ranging from C40 to C200. The performance of the end-bridging Monte Carlo (EBMC) algorithm is explored as a function of average chain length. Results for the specific volume of the cis-1,4 PI melt are found to be within 1% of experimentally reported values and analytical fits to those values. Additional predictions concerning the conformational properties, the equilibrium mean square chain end-to-end distance 〈R2〉0, and the wide-angle neutron and x-ray diffraction patterns, demonstrate that our force field predicts reliably the physical properties of polyisoprene in the molten state. © 2001 American Institute of Physics.
The configurations of oligomers of polyimide and polyetherketone polycyclic polymers in the melt are predicted by a new hybrid pivot Monte Carlo (PMC)/molecular dynamics (MD) single-chain sampling technique restricted to a limited number of near-neighbor interactions. These are then compared to configurations obtained for the same models by running MD simulations on the corresponding multichain systems in the bulk melt. A new phantom-atom technique is introduced which avoids interlocking rings during construction of the bulk melt samples. Similar to earlier work carried out on polyethylene, polyvinylchloride and uncharged polyethylene oxide, both theoretical and bulk melt sampled conformational and configurational properties are found to be in very good agreement. This confirms that the new hybrid PMC/MD sampling is a promising and cost-effective technique for preparing polymer samples prior to subsequent MD simulations of the bulk amorphous phase. © 2001 American Institute of Physics.
Polyethylene at equilibrium is studied by computer simulation. Configuration space is sampled efficiently by a novel Monte Carlo simulation scheme developed for the study of long molecules at high densities. Simulations are carried out in an isobaric‐isothermal statistical‐mechanical ensemble which permits calculation of the density of the polymer matrix at specified conditions of pressure and temperature. A systematic study of the polymer at different temperatures indicates a phase transition; in agreement with experiment, at low temperatures, the polyethylene model studied here crystallizes spontaneously. At temperatures above the melting point, the simulated melt is described accurately by the model.
Membrane remodelling plays an important role in cellular tasks such as endocytosis, vesiculation and protein sorting, and in the biogenesis of organelles such as the endoplasmic reticulum or the Golgi apparatus. It is well established that the remodelling process is aided by specialized proteins that can sense as well as create membrane curvature, and trigger tubulation when added to synthetic liposomes. Because the energy needed for such large-scale changes in membrane geometry significantly exceeds the binding energy between individual proteins and between protein and membrane, cooperative action is essential. It has recently been suggested that curvature-mediated attractive interactions could aid cooperation and complement the effects of specific binding events on membrane remodelling. But it is difficult to experimentally isolate curvature-mediated interactions from direct attractions between proteins. Moreover, approximate theories predict repulsion between isotropically curving proteins. Here we use coarse-grained membrane simulations to show that curvature-inducing model proteins adsorbed on lipid bilayer membranes can experience attractive interactions that arise purely as a result of membrane curvature. We find that once a minimal local bending is realized, the effect robustly drives protein cluster formation and subsequent transformation into vesicles with radii that correlate with the local curvature imprint. Owing to its universal nature, curvature-mediated attraction can operate even between proteins lacking any specific interactions, such as newly synthesized and still immature membrane proteins in the endoplasmic reticulum.
One of the main accepted views in the detailed structure of glassy polymers is Flory's hypothesis, according to which the chain conformation in the glassy state is close to that in the melt or in solutions under θ conditions. On the basis of Flory's hypothesis, an approximate algorithm to generate atomistic structures of bulk glassy polymers, known as the `amorphous-cell' method, has been introduced. Atomistic simulations of bulk a-PS and amorphous isotactic polystyrene (i-PS) with chain conformations close to the rotational-isomeric-state (RIS) models were presented. These structures were generated with PolyPack and agree well with solid-state NMR measurements sensitive to the chain conformation.
The recently introduced end-bridging (EB) Monte Carlo move is revisited, and a thorough analysis of its geometric formulation and numerical implementation is given. Detailed results are presented from applying the move, along with concerted rotation, in atomistic simulations of polyethylene (PE) melt systems with mean molecular lengths ranging from C78 up to C500, flat molecular weight distributions, and polydispersity indices I ranging from 1.02 to 1.12. To avoid finite system-size effects, most simulations are executed in a superbox containing up to 5000 mers and special neighbor list strategies are implemented. For all chain lengths considered, excellent equilibration is observed of the thermodynamic and conformational properties of the melt at all length scales, from the level of the bond length to the level of the chain end-to-end vector. In sharp contrast, if no end bridging is allowed among the Monte Carlo moves, no equilibration is achieved, even for the C78 system. The polydispersity index I is found to have no effect on the equilibrium properties of the melt. To quantify the efficiency of the EB Monte Carlo move, the CPU time t0 required for the chain center of mass to travel a distance equal to the root-mean-square end-to-end distance is estimated by simple analytical arguments. It is found that t0 should scale as n/(X̄Δ2.5), where n is the total number of mers in the system, X̄ is the average chain length, and Δ [3(I − 1)]1/2 is the reduced width of the chain-length distribution function. This means that, if the size of the model system and the shape of the chain-length distribution are kept constant, systems of larger average molecular weight equilibrate faster, a remarkable attribute of the EB Monte Carlo method. The simulation results obey the estimated scaling of t0 with X̄, n, and Δ remarkably well in the range of chain lengths and polydispersities for which the premises of the analysis are not violated (mean chain lengths greater than C156 and polydispersity indices above about 1.07). Results for volumetric behavior, structure, and chain conformation at temperature T = 450 K and pressure P ranging from 1 to 800 atm are presented, using three different PE united atom models proposed in the recent literature. All three models are shown to overestimate the density by ca. 4% and also overestimate the stiffness of chains. The Yoon et al. model is in best agreement with experimental characteristic ratios. Simulation predictions for the structure factor and for the chain-length dependence of the density are in excellent agreement with experiment.
NMR measurements of polarization-transfer between carbon-13 nuclei in specifically labeled amorphous atactic and isotactic polystyrenes allow the conformational characterization of meso and racemo dyads separately. For racemo dyads, the experimental data are well explained by considering only conformations near those two used in rotational-isomeric-state (RIS) models. At least half of the racemo dyads in atactic polystyrene are near the trans−trans conformation. Calculations based on different RIS models for meso dyads are compared with measurements in isotactic polystyrene. RIS models with exclusively trans−gauche and gauche−gauche states fail to account for the measurements. RIS models with a small (5−10%), but significant, amount of meso dyads near the trans−trans state agree better with the experimental results. A comparison of the experimental data with calculations from atomistic simulations of atactic polystyrene shows that in the simulations, conformations which do not correspond to those considered in RIS models are overpopulated for both types of dyads.
A method is developed for predicting the elasticity of a polymer melt through detailed atomistic simulations. The Helmholtz energy of a melt oriented by flow is postulated to be of the form A(T,ρ,c̃), where T is the temperature, ρ is the mass density, and c̃, the conformation tensor, is defined as the end-to-end tensor reduced by one-third the mean squared unperturbed end-to-end distance and averaged over all chains. The conjugate thermodynamic variable to c̃, α, is a tensorial orienting field intimately related to the strain rate in a flow situation. Assuming affine deformation of chain ends, the stress tensor τ can be expressed in terms of c̃ and α. We have mapped out c̃, A, and τ for melts subjected to elongational flow by conducting Monte Carlo (MC) simulations at various values of αxx, all other components of α being zero. Two linear polyethylene melts, of mean chain lengths C24 and C78 and polydispersity index 1.09, have been studied. Efficient sampling of oriented melt configurations has been made possible through the use of the end-bridging MC algorithm. Comparison of the melt response to that of isolated chains subjected to the same orienting field shows that, while at low fields the two responses are similar, at high fields more anisotropy develops in the melt due to favorable lateral interactions between the oriented chains. Comparison against simple models used in flow calculations shows that FENE dumbbells and freely-jointed chains are more representative of the actual melt response than Hookean dumbbells, because they account for the finite extensibility of the polymer. Partitioning A into its energetic and entropic components shows that the melt response is purely entropic for long chains and low orienting fields, which leave the intrinsic shape of chains (averaged in the coordinate frame of their principal axes) practically unaltered. A significant energetic contribution develops for small chains and high orienting fields, where the chain intrinsic shape becomes more elongated and attractive lateral interchain interactions are intensified. Values of τ calculated from c̃ and α are consistent with virial theorem predictions.
A formulation is presented for the calculation of the excess chemical potential μex(ntest) of ntest-mer chains mixed at infinite dilution with a bulk n-mer fluid and of the excess segmental chemical potential = μex(n + 1) − μex(n) from detailed atomistic simulations. The formulation is applied for ntest = 6 to 16 in n-hexadecane (C16, n = 16) in the liquid (P = 50 atm) and vapor (P = 1.02 atm) states at T = 580 K using a configurational bias Monte Carlo (MC) scheme. Two different reference states (ideal gas and continuous unperturbed chains) are examined for the definition of μex, and simulations are conducted with two united-atom model representations from the recent literature. In parallel, μex and with reference to the ideal gas are derived from two cubic equations of state (EoS) for the same systems and conditions. Both the MC and the EoS calculations for both models and reference states examined give a linear dependence of μex(ntest) on ntest, confirming that chemical potentials for long chains can be reliably estimated from small test chain and test segment insertions. This confirmation of the “chain increment ansatz” is of great practical value for phase equilibrium calculations in long-chain systems. Predictions for the structure of the C16 liquid and vapor are in good agreement with existing experimental and simulation evidence. Chain conformations in the liquid and vapor are indistinguishable from unperturbed and ideal gas chain conformations, respectively. In lower temperature liquids (T = 450 K, P = 20 atm), insertions of long test chains cannot provide adequate sampling, but the chain increment ansatz remains useful for estimating chemical potentials.
The radii of gyration for a series of poly(ethylene−1-butene) copolymers of varying ethyl branch content were measured as a function of temperature in the melt via small angle neutron scattering (SANS), and their temperature coefficients, d ln C∞/dT = κ, changed from negative to positive. The characteristic ratio C∞ decreased with increasing ethyl branch frequency. When possible, these results were compared with those obtained from ϑ solvents and from rotational isomeric (RIS) state theory. The SANS-based chain dimensions were slightly larger than those obtained from ϑ solvents. The values of κ differed significantly from those extracted from ϑ-solvent measurements. Serious discrepancies with RIS-based calculations were observed.
A technique is presented for generating atomistic models of amorphous polymer structures starting from chain configurations on lattice. The method guarantees Gaussian chain statistics and enables control of chain tacticity and monomer sequence while avoiding severe overlaps between the atoms in the structure. We show that the single polymer chain, which completely occupies the lattice with periodic boundary conditions, is Gaussian with chain statistics equivalent to that obtained for a nonreversing random walk on the cubic lattice. The method enables efficient generation of the chain topology, which can then be populated with specific chemical units. Large models of glassy, atactic polystyrene have been generated, and the effects of system size are examined in terms of calculated X-ray scattering intensities. These results demonstrate the efficacy of this new method for generating more realistic polymer glass structures.
We report atomistically detailed molecular dynamics simulations of benzene−polystyrene systems (0−84.2 wt % polystyrene). We have calculated solvent diffusion coefficients and have found that their composition dependence not only shows good agreement with experiment but also follows quite well the predictions by lattice models. We also show that, for the polystyrene−benzene system studied here, it is not possible to separate solvent molecules into slow ones, tightly bound to the polymer, and fast ones, not bound to the polymer. This would suggest that, in a gel, the polymer chains alone act as obstacles to solvent diffusion and not polymer decorated by a shell of solvent molecules. We have found the reorientation of benzene molecules in the gel to be nonexponential and anisotropic, the reorientation of the ring normal being slower than the in-plane reorientation. This anisotropy increases dramatically with polystyrene concentration. At the highest polymer concentration, the time scales for the two motions are separated by 3 orders of magnitude. The changes of polymer solvation and polymer dynamics with concentration are discussed. For all polymer concentrations above 50 wt %, the polymer turns out to be essentially rigid on a nanosecond time scale with only local fluctuations possible.
A quantitative understanding and prediction of the dynamics of entangled polymer melts is a long-standing problem. In this work we present results about the dynamical and rheological properties of atactic polystyrene melts, obtained from a hierarchical approach that combines atomistic and coarse-grained dynamic simulations of unentangled and entangled systems. By comparing short chain atomistic and coarse-grained simulations, the time mapping constant is determined. Self-diffusion coefficients, after correcting for the chain end free volume effect, show a transition from Rouse to reptation-like behavior. In addition, the entanglement molecular weight is calculated through a primitive path analysis. All properties are compared to experimental data.
Using molecular dynamics simulations, we study the hydrogen bond dynamics and thermodynamics of the bulk of polyamide-66 over a broad temperature range (300−600 K). We show that different dynamic properties (the structure relaxation time, the orientational time correlation function of the amide groups, and the self-diffusion coefficient) of unentangled polyamide-66 undertake a crossover transition in the same small temperature range ( 413 K) above the experimental glass transition temperature (350 K). The data can be fitted to a Vogel−Fulcher−Tammann law when T > 413 K and to an Arrhenius equation when T < 413 K. Our results show that the global dynamics of polyamide-66 is intimately related to the relaxation of the hydrogen bond network formed among the amide groups. The presence of a dynamic crossover at a temperature slightly higher than the glass transition one is in agreement with the more recent experimental data and glass theories.
A method is presented to obtain well-equilibrated atactic polystyrene (aPS) samples for molecular simulations. The method starts with equilibrating the polymer in the melt at length scales beyond the Kuhn length lK, using end-bridging Monte Carlo techniques; at this level a (2:1)-coarse-grained description of aPS is being employed. Subsequently atomistic detail is reintroduced, and the sample is equilibrated at the smallest length scales as well. At length scales beyond lK the simulated polymer chain conformations fulfill the random-coil hypothesis of Flory, and C∞ = 8.7 ± 0.1 at 463 K. Eventually various glassy samples are created by subjecting the melt sample to different cooling rates. Pair correlations are in agreement with existing X-ray data, and the amount of dihedral angles in the trans (t) state agrees with NMR data. On the level of dyads, the conformations of racemic dyads agree well with existing NMR results. At the same time, meso dyads conformations do not agree: 65% of meso dyads is in the gt/tg state (NMR: 80%); 25% is in tt state (NMR: <10%). An attempt has been made to relate the observation in simulations, namely that an increase in cooling time causes an increase in yield stress, to effects of the cooling rate on the polymer structure.
Neutron coherent scattering techniques have been used for the determination of the conformation of polymer in bulk and experimental details are given about the application of this method to the study of polymeric systems. Measurements have been made for small and intermediate momentum ranges on a series of eight monodisperse deuterated polystyrenes of molecular weight ranging from 21,000 to 1,100,000. The results lead to the concluson that in amorphous state the conformation of the polymer molecule is indistinguishable from that in θ solvent and that the Debye scattering function which is valid for unperturbed chains applies for q-1 as low as 10 Å.
The very efficient end-bridging Monte Carlo (EBMC) method has been employed in order to simulate an amorphous, polydisperse 80-chain large C156 polyethylene (PE) system in atomistic detail over a wide range of temperatures (from 600 down to 150 K) and determine its glass transition temperature (Tg). Two sets of simulations have been performed: one with a bulk, isotropic sample and the other with a thin film in which all the 80 PE chains were grafted on a hard substrate on one side (corresponding to a high grafting density equal to σ = 1.75 nm-2) and exposed to vacuum on the other side. In the simulations, a united-atom model was employed for PE ensuring that only the purely amorphous phase of PE was simulated at all temperatures. In all cases, very long simulations were carried out in order to give enough time for the system to relax at all length scales. For all temperatures studied, the longest relaxation time was found to be present by descriptors associated with the system's long-range conformational characteristics. In contrast, more local, internal structural features were always faster in equilibrating. As a result, the time autocorrelation function for the chain end-to-end unit vector, fu(t), was found to drop to zero and then clearly fluctuate around this value only for temperatures higher than about 220 K for both systems. For lower temperatures, fu(t) did not relax completely, even after 2 × 107 CPU seconds. Additional volumetric simulation data demonstrated a sharp change in the density and potential energy of both systems in the neighborhood of the 230 K, which are considered as features of the glass transition for amorphous PE. The Tg value suggested by the present EBMC simulations for amorphous (bulk or grafted) PE is (230 ± 10) K, which is consistent with the value of 237 K measured experimentally by Wunderlich [J. of Chem. Phys. 1962, 37, 1203] and Loufakis and Wunderlich [J. Phys. Chem. 1988, 92, 4205] for PE in the limit of zero crystallinity. Further, the predicted change in the heat capacity at constant pressure at the glass transition is Δcp = 1.2 × 10-4 kcal g-1 K-1, which is very close to the value of 1.5 × 10-4 kcal g-1 K-1 measured experimentally by Wunderlich [J. of Chem. Phys. 1962, 37, 1203]. Additional results on the temperature dependence of the conformational and structural properties in the two PE systems are also reported and discussed in detail.
The reverse nonequilibrium molecular dynamics (RNEMD) method is implemented to predict the viscosity of a coarse-grained model of short-chain polystyrene. The coarse-grained model has been derived to reproduce the structure of polystyrene. It is therefore not a generic model, but polymer-specific. Here, its performance for dynamical quantities is tested. The zero-shear viscosity is compared with experimental data. The pronounced difference can be mainly attributed to the inherent dynamic properties of the coarse-grained model. The qualitative results are compared to previous results calculated via conventional nonequilibrium molecular dynamics (NEMD) and more generic polymer models, and the agreement is reasonable. The structural alterations under shear are investigated by characterizing the molecular deformation and birefringence extinction angle.
A coarse-grained model of atactic polystyrene, in which meso and racemo diads are represented as single “superatoms,” parametrized using Iterative Boltzmann Inversion, has been subjected to connectivity-altering Monte Carlo simulations in order to simulate monodisperse atactic polystyrene melts of molar mass up to 210000 g mol-1 at 500 or 413 K and 1 bar. Analysis of the Monte Carlo results reveals excellent equilibration of chain conformations at all length scales. Chain dimensions, as determined from the mean square end-to-end distance, the mean square radius of gyration, and simulated Kratky plots of the single-chain scattering function, are in excellent agreement with experiment. The equilibrated long-chain configurations are reduced to entanglement networks via topological analysis with the CReTA algorithm. The resulting Kuhn length of primitive paths provides an excellent estimate of the molar mass between entanglements and of the entanglement tube diameter extracted from plateau modulus measurements. The distribution of strand lengths between entanglements, when appropriately reduced, follows the same master curve as previously determined distributions of polyethylene, cis-1,4 polybutadiene, and poly(ethylene terephthalate). A new strategy is introduced for reverse mapping the long-chain coarse-grained configurations into detailed united-atom configurations in a manner that preserves the sequence of diad types along the chains. This strategy employs local “flip” Monte Carlo moves to relax the reverse-mapped configurations. Relaxation starts using bonded interactions only, and proceeds by gradually introducing nonbonded interactions. Final relaxation is achieved via short-time canonical molecular dynamics simulation. Predicted wide-angle X-ray diffraction patterns from reverse-mapped configurations are indistinguishable from those of short-chain melts equilibrated directly in the united atom representation using molecular dynamics, and in favorable agreement with experiment. Distributions of torsion angles and pairs of successive torsion angles in the reverse-mapped configurations exhibit some deviations from the corresponding distributions of directly equilibrated short-chain united atom melts and from experimental NMR measurements.
Coarse-grained interaction potentials for poly(ethylene terephthalate) (PET) have been developed using the concept of potential of mean force and employing results of atomistic molecular dynamics simulations of ethylene terephthalate dimer. The end bridging Monte Carlo method has been adopted to handle coarse-grained PET chains. The resulting method permits for thorough, multiscale equilibration of a 100-mer PET melt, and is applicable to a wide range of industrially important polymers. The coarse-grained melt density, characteristic ratio and other conformational properties agree with experiment. Topological analyses of the melt using the CReTA and Z algorithms reveal that the melt is also well equilibrated with respect to entanglement density.
We present a hierarchical approach that combines atomistic and mesoscopic simulations that can generally be applied to vinyl polymers. As a test case, the approach is applied to atactic polystyrene (PS). First, a specific model for atactic PS is chosen. The bonded parameters in the coarse-grained force field, based on data obtained from atomistic simulations of isolated PS dimers, are chosen in a way which allows to differentiate between meso and racemic dyads. This approach in principle allows to study isotactic and syndiotactic melts as well. Nonbonded interactions between coarse-grained beads were chosen as purely repulsive. The proposed mesoscopic model reproduces both the local structure and the chain dimensions properly. An explicit time mapping is performed, based on the atomistic and CG mean-square displacements of short chains, demonstrating an effective speed up of about 3 orders of magnitude compared to brute force atomistic simulations. Finally the equilibrated coarse-grained chains are back mapped onto the atomistic systems. This opens new routes for obtaining well equilibrated high molecular weight polymeric systems and also providing very long dynamic trajectories at the atomistic level for these polymers.
We develop a mesoscale polystyrene model based on atomistic simulations of oligomers using the iterative Boltzmann inversion method. The potential is optimized against the atomistic simulation until the radial distribution function generated from the mesoscale model is consistent with the atomistic simulation. The mesoscale model allows to elucidate the polymer dynamics of long chains. The dynamics of polystyrene melts are investigated at various chain lengths between 15 and 240 monomers. Mean-squared displacements are analyzed to capture the dynamics changing from the Rouse to the reptation behavior. The reorientation behavior of segmental vectors is investigated to identify the heterogeneity along the chain. Diffusion constants of various systems are calculated to verify the crossover from the unentangled to entangled dynamics. Rouse mode analysis shows that the Rouse model is applicable from chain length between 50 and 100 monomers. The entanglement length of this polystyrene model is around 85 monomers at 450 K, in fair agreement with experiments.
To understand, at a molecular scale, the effect of water on the structure of the amorphous region of polyamide 6,6 (PA6,6), atomistic molecular dynamics simulations have been carried out. Our results concerning the very local water organization relative to PA moieties agree qualitatively with a two-step sorption model. The first sorption mode seems to be saturated well below the lowest water concentration studied (5% relative to the amorphous phase). Moreover, above this saturation, the overall water organization displays at 300 K larger clusters than the 2−3 molecules usually assumed in the literature. The temperature dependence of free volume, hole size, and hydrogen bonding has also been investigated. It shows a transition between plasticized and antiplasticized behavior.
Connectivity-altering Monte Carlo simulations have been used to study structure−property relationships of poly(ethylene glycol) (PEG) and poly(ethylene oxide) dimethyl ether (PEODME) using the recently developed transferable potentials for phase equilibria united atom (TraPPE-UA) ether and alkanol force fields. The combination of end-bridging and double-bridging Monte Carlo simulation techniques is shown to do a good job of equilibrating moderate to high molecular weight polymer melts. Results give excellent agreement between experiment and simulation for liquid densities at a variety of temperatures, pressures, and molecular weights. Comparisons are also made with experiment for structural properties, including the structure factor, chain mean squared end-to-end distance, and radius of gyration, showing good agreement with experiment. Moreover, a thorough microscopic analysis is performed on the different end group effects of PEG and PEODME, determining the excluded volume and liquid structure around the end groups, and linking these to their volumetric properties.
A combined coarse-graining and back-mapping approach to preparing relaxed systems of amorphous polymers with atomistic detail is presented and applied to the case of bulk amorphous cellulose. The coarse-grained model is first developed using results from a standard molecular dynamics atomistic simulation of octaose, i.e., the short 8-ring oligomer of cellulose. The change to a coarse-grained scale leads to an effective speed-up in excess of 2000 for the computational efficiency of the relaxation of the chains. A representation of one ring by one bead is used in order to maintain a good description of the envelope of the molecule and this allows for a subsequent seamless reintroduction of the atoms. The back-mapping procedure has been successfully tested on dense bulk systems of both octaose and hectaose, i.e., 100-ring cellulose chains. The principal advantage and motivation for this approach is that it adapts well to cases where interfaces are present and spatial isotropy of chain conformations is no longer assured or easily predictable.
The apparent mean-square radius of gyration, 〈S2〉s, was measured by small-angle X-ray scattering for 12 samples of atactic oligo- and polystyrenes (a-PS) in the range of weight-average molecular weight Mw from 578 (pentamer) to 97 300 in cyclohexane at 34.5°C (Θ temperature). The mean-square radius of gyration 〈S2〉 for the chain contour was calculated from the values of 〈S2〉s thus obtained by making correction for the finite thickness of the polymer chain. The ratio of 〈S2〉 to the weight-average degree of polymerization rather steeply increased with increasing Mw and leveled off at Mw higher than 105.
Transport studies of CO2 in several solvent-cast poly(styrene-co-butadiene) block copolymers of controlled morphology are presented. The morphology is documented by means of transmission electron microscopy and the transport is examined by means of sorption. The transport properties predicted by simple models involving ordered microstructures agree surprisingly well with the experimental results. Transport studies are a sensitive measure of the connectedness of the most conductive phase (polybutadiene). By change of the composition of the copolymer or the casting solvent, the microdomain morphology, i.e., the connectedness of the polybutadiene domains, can be systematically changed. The variation in effective diffusion as a function of domain morphology is well captured by the models.
We have performed a molecular dynamics simulation study of atactic polystyrene (a-PS) and its dimer 2,4-diphenylpentane (DPP) using a previously derived quantum chemistry based explicit atom force field. The X-ray structure factor of a-PS obtained from simulations was found to be in good agreement with experiment, reproducing the “amorphous” peak at around 1.4 Å-1 as well as the “polymerization peak” at around 0.75 Å-1 and its anomalous temperature dependence (increasing intensity with increasing temperature). We found that the amorphous peak in a-PS arises primarily from phenyl−phenyl correlations, with important intramolecular and intermolecular contributions. While the intermolecular component was found to shift to lower q with increasing temperature, the intramolecular component was found to be insensitive to temperature, resulting in a weak temperature dependence of the amorphous peak. Simulations revealed the presence of the polymerization peak in DPP, indicating that the designation “polymerization peak” for this feature is a misnomer. The polymerization peak in both a-PS and DPP was found to be due primarily to intermolecular correlations of backbone atoms. This underlying correlation showed the expected decrease in intensity and shifting to lower q with increasing temperature. The shifting to lower q of intermolecular phenyl−phenyl and phenyl−backbone correlations with increasing temperature was found to lead to the observed anomalous temperature dependence of the polymerization peak.
The critical molecular weight Mc of 36 flexible and semirigid polymers has been studied. A unique correlation between the critical end-to-end distance 〈Rc〉 for entanglements and the average polymer chain diameter D is found. This correlation is discussed in the light of the reptation concept.
Wide-angle X-ray diffraction measurements were performed on polymer melts of isotactic and syndiotactic polypropylene (IPP and SPP), poly(ethylenepropylene) (PEP), polystyrene (PS), polyisobutylene (PIB), and polyethylene (PE), to study the dependence of the short-range structure of polymer liquids on chain architecture. Total structure functions, which comprise intra- and intermolecular contributions, were derived from the scattering data. The trivial Fourier components of the intramolecular structure (C(SINGLE BOND)>C ≃ 1.54 Å and C(SINGLE BOND)C(SINGLE BOND)C ≃ 2.55 Å) were subtracted from the total structure functions. The remaining functions contain only those intramolecular contributions dependent on the chain's conformational degrees of freedom, plus the intramolecular contributions. The structural differences between the polymers in momentum space are discerned only when the trivial components are subtracted. This subtraction also reduces the effects of truncation errors on Fourier transformation to real space. The short-range structure of PIB appears very different compared to all the others, which correlates with anomalies in a number of physical properties for this polymer. © 1996 John Wiley & Sons, Inc.
In this article, we present coarse-grained potentials of ethylbenzene developed at 298 K and of amorphous polystyrene developed at 500 K by the pressure-corrected iterative Boltzmann inversion method. The potentials are optimized against the fully atomistic simulations until the radial distribution functions generated from coarse-grained simulations are consistent with atomistic simulations. In the coarse-grained polystyrene melts of different chain lengths, the Flory exponent of 0.58 is obtained for chain statistics. Both potentials of polystyrene and ethylbenzene are transferable over a broad range of temperature. The thermal expansion coefficients of the fully atomistic simulations are well reproduced in the coarse-grained models for both systems. However, for the case of ethylbenzene, the coarse-grained potential is temperature-dependent. The potential needs to be modified by a temperature factor of √ T/T 0 when it is transferred to other temperatures; T 0) 298 K is the temperature at which the coarse-grained potential has been developed. For the case of polystyrene, the coarse-grained potential is temperature-independent. An optimum geometrical combination rule is proposed with the combination constant x) 0.4 for mutual interactions between the polystyrene monomer and ethylbenzene molecules in their mixtures at different composition and different temperature.
The challenge of controlled sampling of the conformations of internal sections of chain molecules, subject to constrained interatomic bond lengths and angles, is central to many areas of macromolecular science. A new method for overcoming this challenge via an internal configuration bias (ICB) Monte Carlo algorithm is described. It is demonstrated that the algorithm obeys the detail balance (microscopic reversibility) criterion necessary for performing rigorous molecular simulations in equilibrium ensembles. The algorithm is applied to a study of the molecular conformations of cyclic alkane molecules in a vacuum, where it is shown to be up to ∼2 orders of magnitude more efficient than standard molecular dynamics simulation techniques. Qualitative transitions between constrained ring and flexible chain behavior are observed between 16 and 30 backbone atoms for local structure (torsion angle distribution) and between 30 and 50 backbone atoms for global ring dimensions.
A continuum mean field approach based on Generalized Flory Theory and the Polymer Reference Interaction Site Model is developed
to describe the structural and equation of state properties of normal alkane liquids and linear polyethylene melts. Efficient
Monte Carlo simulations based on a new algorithm that employs concerted rotations around up to seven consecutive skeletal
bonds along a chain are also conducted on the same systems. A realistic united-atom model is chosen to describe the geometry
and energetics of the molecules and used throughout the study. Comparisons between the simulations and experimental thermodynamic
and structural results are good and those between the mean field theory and the exact simulation results are reasonable. A
method is described for quickly sampling the conformation of unperturbed chains in continuous space. The statistics of these
chains compare very well with conformationally equilibrated chain statistics from the bulk simulation; this provides a confirmation
of Flory's Random Coil Hypothesis. The need for improving the mean field theory and for enhancing the equilibration rate of
the Monte Carlo simulations are identified. A new neighbor-list scheme is introduced for use in polymer Monte Carlo simulations.
Details of the implementation, user interface and file formats of the YASP molecular dynamics program (version 3.0) are described. Version 3.0 has been extensively rewritten with respect to earlier versions. The features now include Coulombic interactions, reaction field approximation, external forces, position restraining, fully vectorised treatment of bond constraints, constraint contributions to the pressure, efficient and well-vectorised evaluation of bonded and nonbonded interactions.