Molecular Dynamics Studies of Collapse Stages in the chain folding process of Polyethylene

Althoughtheequilibriumpropertiesofthepolymerhavebeenextensivelystudied,kineticphenomenasuchasthecondensingprocessandcollapsetransitionstillhavemanyunclearaspects,andmucheffortwastakentomakeathoroughinvestigationandstudy.Moleculardynamic(MD)simulationsofthefoldingandcollapseprocessforapolyethylenechainwasrecentlycarriedoutbymanyauthors1'2'3.Itwasreportedthatatwo-stagecollapseprocesswasseenwithouttorsionpotential',andthreestageswerefoundbysimplificationofthecomputationalmodel5.ButthecollaPsesta…     

A molecular dynamics study on universal properties of polymer chains in different solvent qualities. Part I. A review of linear chain properties

This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the theta-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of "good solvents" and "theta-solvents" in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types.     

The collapse of polyethylene rings on an attractive surface

Polymers exhibit extended structures at high temperatures or in good solvents and collapsed configurations at low temperatures or in poor solvents. This fundamental property is crucial to the design of materials, and indeed has been extensively studied in recent years. In this paper, the collapse of polyethylene rings on an attractive surface was investigated by using molecular dynamics simulations. It is found that the collapse of ring chains on the attractive surface is of distinct difference from their free counterparts, where the collapse becomes more continuous and a one-stage instead of two-stage collapse can be identified by the specific heat. Some hairpin-like crystal structures are found at low temperatures, which are induced by the adsorption interaction of polymer-surface. For a given chain length, the results were further compared with those of the adsorbed linear chains. Due to the topological constraint of ring chains, the number of hairpin structures is clearly less than that of the linear chains. These numerical simulations may provide some new insights into the folding of ring polymers under adsorption interactions.     

Computer simulation study of the global phase behavior of linear rigid Lennard-Jones chain molecules: comparison with flexible models

The global phase behavior (i.e., vapor-liquid and fluid-solid equilibria) of rigid linear Lennard-Jones (LJ) chain molecules is studied. The phase diagrams for three-center and five-center rigid model molecules are obtained by computer simulation. The segment-segment bond lengths are L = sigma, so that models of tangent monomers are considered in this study. The vapor-liquid equilibrium conditions are obtained using the Gibbs ensemble Monte Carlo method and by performing isobaric-isothermal NPT calculations at zero pressure. The phase envelopes and critical conditions are compared with those of flexible LJ molecules of tangent segments. An increase in the critical temperature of linear rigid chains with respect to their flexible counterparts is observed. In the limit of infinitely long chains the critical temperature of linear rigid LJ chains of tangent segments seems to be higher than that of flexible LJ chains. The solid-fluid equilibrium is obtained by Gibbs-Duhem integration, and by performing NPT simulations at zero pressure. A stabilization of the solid phase, an increase in the triple-point temperature, and a widening of the transition region are observed for linear rigid chains when compared to flexible chains with the same number of segments. The triple-point temperature of linear rigid LJ chains increases dramatically with chain length. The results of this work suggest that the fluid-vapor transition could be metastable with respect to the fluid-solid transition for chains with more than six LJ monomer units.     

Chain collapse by lattice simulation

Monte Carlo simulations have been performed on a self-avoiding simple cubic lattice chain with the nearest-neighbor interactions for a range of chain lengths N from 40 to 1000 segments to investigate equilibrium properties of polymer chains from an athermal to a collapsed state. Both the fraction of segments in the clusters and the number of contacts exhibit the three stage process for the chain collapse, consistent with our previous molecular dynamics simulations of a fully atomistic chain. In the collapse region corresponding to the nearest-neighbor interaction parameter larger than 0.5 for a segment-solvent pair, polymer chains are quite spherical and both ends lie nearly randomized within the sphere. The peak height of the specific heat is proportional to N(In N)^3/11, as predicted by the renormalization group theory.     

聚乙烯单链松驰过程的分子模拟

利用分子模拟方法研究了不同链长聚乙烯单链折叠过程和相关的松弛和坍塌机理．发现在链长短于１０００ＣＨ２单元时,聚乙烯的链段主要通过整体塌缩机理进行折叠和取向;而链长超过１０００ＣＨ２单元时,可以明显地观察到局部取向团簇的形成,聚乙烯单链通过局部塌缩机理进行折叠和取向．通过对各阶段团簇数目,体系取向链段长度的表征,说明体系在模拟时间范围内表现了很强的松驰特性．     

Study on structure formation of short polyethylene chains via dynamic Monte Carlo simulation

Monte Carlo (MC) simulations of structure formation for short polyethylene chains at low temperature are performed based on a recent developed method that uses coarse-grained chains on a high coordination lattice. Local short-range interactions based on rotational isomeric state (RIS) model and long-range interactions obtained from Lennard–Jones (LJ) potential are introduced during the simulation. Properties evaluated from the simulations are the mean square dimensions, anisotropy of the radius of gyration tensor, local conformation determined by the occupancy of trans state and orientation correlation functions, energy of the system, and chain packing reflected by the pair correlation functions and structure factors. All of these parameters reveal an ordering process that produces an approximation to a hexagonal crystal phase. The hexagonal structure is imposed by the presence of a diamond lattice underlying the high coordination lattice on which the simulation is performed. Folding of the chains in the crystal is mandatory, because they have fully extended lengths in excess of the dimension of the simulated periodic box. Nevertheless, the simulations demonstrate that a high degree of crystallinity can be achieved in reasonable computer time. The simulation technique should be applicable to other choices of periodic boundary conditions that do not affect the results as strongly as in the present case.     

Structural correlations in comb heteropolymers in good and backbone-selective solvents

Molecular dynamics (MD) simulations of coarse-grained regular comb heteropolymers have been performed to explore structural correlations at equilibrium in a nonselective solvent and during the transition from coil to micelle in a backbone-selective solvent. We primarily consider the static structure factor measured directly from the simulations. In the good solvent, we consider cases ranging from short to long side chains, with respect to the spacer length. Reasonable agreement with a previously published theoretical structure factor is observed for a limited subset of the comb architectures in a small wavevector range. When the side chains are much longer than the spacers, the side-chain structure factor approaches that of starlike polymers. Additionally, plateau values of the structure factor scale with the side-chain length to the power of 0.736 when the side chains are shorter than the spacers. The transition from an open coil to a collapsed micelle is examined in MD simulations with explicit-solvent particles. Upon a sudden quench the from nonselective solvent to the backbone-selective solvent, the coil-to-micelle transition occurs via a side-chain clusterization mechanism. The time-dependent structure factors measured during the collapse process have plateau values that scale with the average cluster size to the power of 0.9. The origin of these two scaling exponents is still unknown. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 983-993, 2005     

Conformation of a flexible chain in explicit solvent: exact solvation potentials for short Lennard-Jones chains

The average conformation of a flexible chain molecule in solution is coupled to the local solvent structure. In a dense solvent, local chain structure often mirrors the pure solvent structure, whereas, in a dilute solvent, the chain can strongly perturb the solvent structure which, in turn, can lead to either chain expansion or compression. Here we use Monte Carlo (MC) simulation to study such solvent effects for a short Lennard-Lones (LJ) chain in monomeric LJ solvent. For an n-site chain molecule in solution these many-body solvent effects can be formally mapped to an n-body solvation potential. We have previously shown that for hard-sphere and square-well chain-in-solvent systems this n-body potential can be decomposed into a set of two-body potentials. Here, we show that this decomposition is also valid for the LJ system. Starting from high precision MC results for the n = 5 LJ chain-in-solvent system, we use a Boltzmann inversion technique to compute numerically exact sets of two-body solvation potentials which map the many-body chain-in-solvent problem to a few-body single-chain problem. We have carried out this mapping across the full solvent phase diagram including the dilute vapor, dense liquid, and supercritical regions and find that these sets of solvation potentials are able to encode the complete range of solvent effects found in the LJ chain-in-solvent system. We also show that these two-site solvation potentials can be used to obtain accurate multi-site intramolecular distribution functions and we discuss the application of these exact short chain potentials to the study of longer chains in solvent.     

Collapse kinetics of vibrated granular chains

The kinetics of the collapse of the coil state into condensed states is studied with vibrated granular chain composed of N metal beads partially immersed in water. The radius of gyration of the chain, R(g) is measured. For short chains (N < 140), disk-like condensed state is formed and R(g) decreases with time such that the function ΔR(g)(2) (≡ R(g)(2) - R(g)(2)(∞)) = A e(-t/τ), where the relaxation time τ follows a power-law dependence on the chain length N with an exponent γ = 1.9 ± 0.2. For the chains with length N ≥ 300, rod-like clusters are observed during the initial stage of collapse and R(g)(2) = R(g)(2)(0) - Bt(β), with β = 0.6 ± 0.1. In the coarsening stage, the exponential dependence of ΔR(g)(2) on time still holds, however, the relaxation time τ fluctuates and has no simple dependence on N. Furthermore, the time dependence of the averaged radius of gyration of the individual clusters, R(g,cl) can be described by the theory of Lifshitz and Slyozov. A peak in the structure function of long chains is observed in the initial stage of the collapse transition. The collapse transition in the bead chains is a first order phase transition. However, features of the spinodal decomposition are also observed.     

Thin-thick surface phase coexistence and boundary tension of the square-well fluid on a weak attractive surface

Prewetting transition is studied for the square-well fluid of attractive-well diameter lambda(ff)sigma(ff)=1.5 in the presence of a homogeneous surface modeled by the square-well potential of attractive well from 0.8sigma(ff) to 1.8sigma(ff). We investigate surface phase coexistence of thin-thick film transition using grand-canonical transition matrix Monte Carlo (GC-TMMC) and histogram reweighting techniques. Molecular dynamics (MD) and GC-TMMC are utilized to predict the properties of the fluid for various surface fluid affinities. Occurrences of prewetting transition with the variation of surface affinity are observed for a domain of reduced temperature from T(*)=0.62 to 0.75. We have used MD and GC-TMMC+finite size scaling (FSS) simulations to calculate the boundary tension as a function of temperature as well as surface affinity. Boundary tensions via MD and GC-TMMC+FSS methods are in good agreement. The boundary tension increases with the decrease of wall-fluid affinity. Prewetting critical properties are calculated using rectilinear diameter approach and scaling analysis. We found that critical temperature and density increase with the decrease of wall-fluid affinity.     

A Monte Carlo lattice model for chain diffusion in dense polymer systems and its interlocking with molecular dynamics simulation

The paper reports the development of a Monte Carlo lattice model (cubic F) of polymer chains which is able to access times where the diffusion of the centre-of-mass of the chains is the dominant process, even though the chain lengths are well above that for entanglement. The volume of the model is large when compared with the volume of gyration of the individual molecules. The model incorporates an algorithm, which allows for the possibility of co-operative motions over sections of the chains and increases the time efficiency of the simulation. Both the model and the modifying algorithm have been tested against the known scaling laws.The model, for shorter chains, is ‘reverse mapped’ into full atomic detail as polyethylene and the shorter time processes simulated using molecular dynamics (MD). The MD model is tested against experimental diffusion data for polyethylene, of the same molecular weight and at the same temperature, and then used to time-calibrate the lattice model.Both the fine grained MD model and the coarse grained MC model are thus interlocked to cover a time range from the individual atomic motions of MD up to the order of a microsecond, a range of six orders of magnitude.     

Template effect in the competition between Haeckelite and graphene growth on Ni(111): quantum chemical molecular dynamics simulations

Quantum chemical molecular dynamics (QM/MD) simulations of ensembles of C(2) molecules on the Ni(111) terrace show that, in the absence of a hexagonal template or step edge, Haeckelite is preferentially nucleated over graphene as a metastable intermediate. The nucleation process is dominated by the swift transition of long carbon chains toward a fully connected sp(2) carbon network. Starting from a pentagon as nucleus, pentagons and heptagons condense during ring collapse reactions, which results in zero overall curvature. To the contrary, in the presence of a coronene-like C(24) template, hexagonal ring formation is clearly promoted, in agreement with recent suggestions from experiments. In the absence of step edges or molecular templates, graphene nucleation follows Ostwald's "rule of stages" cascade of metastable states, from linear carbon chains, via Haeckelite islands that finally anneal to graphene.     

Phase behavior of a single polyethylene chain confined between two adsorption walls

The phase behavior of a single polyethylene chain confined between two adsorption walls is investigated by using molecular dynamics simulations. In the free space, it is confirmed in our calculation that the isolated polymer chain exhibits a disordered coil state at high temperatures, and collapses into a condensed state at low temperatures, that is, the coil‐to‐globule transition, and the finite chain length effects are considered since the critical region depends on chain lengths. When the chain is confined between two attractive walls, however, the equilibrium properties not only depend on the chain length but also depend on the adsorption energy and the confinement. Mainly, we focus on the influence of polymer chain length, confinement, and adsorption interaction on the equilibrium thermodynamic properties of the polyethylene chains. Chain lengths of N = 40, 80, and 120 beads, distances between the two walls of D = 10, 20, 30, 50, and 90 Å, and adsorption energies of w = 1.5, 2.5, 3.5, 6.5, and 8.5 kcal/mol are considered here. By considering the confinement–adsorption interactions, some new folding structures are found, that is, the hairpin structure for short chain of N = 40 beads, and the enhanced hairpin or crystal like structures for long chains of N = 80 and 120 beads. The results obtained in our simulations may provide some insights into the phase behaviors of confined polymers, which can not be obtained by previous studies without considering confinement–adsorption interactions. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 370–387, 2008     

Calculating thermodynamic properties from perturbation theory: II. An analytic representation for the square-well chain fluid

An analytic representation of thermodynamic properties of the freely jointed square-well chain fluid is developed based on the thermodynamic perturbation theory of Barker–Henderson, Zhang and Weitheim. By using a real function expression for the radial distribution function and incorporating structural information for square-well monomer of TPT1 model, an analytic expression for the Helmholtz energy of square-well chain fluid is expanded from Zhang’s analytic expressions for thermodynamic properties of square-well monomer. The expression leads to good predictions of the compressibility factor, residual internal energy and constant-volume heat capacity for 4-mer, 8-mer and 16-mer square-well fluids when compared with the Monte Carlo (MC) simulation results. The incorporating structural information for square-well dimer of TPT-D model is also calculated. To obtain the constant-volume heat capacity needed, NVT MC simulations were performed.     

Monte Carlo simulations of Lennard-Jones nonionic surfactant adsorption at the liquid/vapor interface

We present Monte Carlo simulations of nonionic surfactant adsorption at the liquid/vapor interface of a monatomic solvent. All molecules in the system, solvent and surfactant, are characterized by the Lennard-Jones (LJ) potential using differing interaction parameters. Surfactant molecules consist of an amphiphilic chain with a solvophilic head and a solvophobic tail. Adjacent atoms along the surfactant chain are connected by finitely extensible harmonic springs. Solvent molecules move via the Metropolis random-walk algorithm, whereas surfactant molecules move according to the continuum configurational bias Monte Carlo (CBMC) method. We generate quantitative thermodynamic adsorption and surface tension isotherms in addition to surfactant radius of gyration, tilt angles, and potentials of mean force. Surface tension simulations compared to those calculated from the simulated adsorbed amounts and the Gibbs adsorption isotherm agree confirming equilibrium in our simulations. We find that the classical Langmuir isotherm is obeyed for our LJ surfactants over the range of head and tail lengths studied. Although simulated surfactant chains in the bulk solution exhibit random orientations, surfactant chains at the interface orient roughly perpendicular and the tails elongate compared to bulk chains even in the submonolayer adsorption regime. At a critical surfactant concentration, designated as the critical aggregation concentration (CAC), we find aggregates in the solution away from the interface. At higher concentrations, simulated surface tensions remain practically constant. Using the simulated potential of mean force in the submonolayer regime and an estimate of the surfactant footprint at the CAC, we predict a priori the Langmuir adsorption constant, KL, and the maximum monolayer adsorption, Gammam. Adsorption is driven not by proclivity of the surfactant for the interface, but by the dislike of the surfactant tails for the solvent, that is by a "solvophobic" effect. Accordingly, we establish that a coarse-grained LJ surfactant system mimics well the expected equilibrium behavior of aqueous nonionic surfactants adsorbing at the air/water interface.     

Collapse of a two-state sticky hard sphere chain

The collapse of a homopolymer gaussian chain into a globule is represented as a transition between two states, viz., extended and collapsed. Appropriately, this model has been labeled as the all-or-none view of chain collapse. In the collapsed state, the single polymer partition function is expressed by a single Mayer diagram with the maximum number of f-bonds arising from nonbonded square well interactions. Our target is the dependence of the transition temperature on chain length and the interaction range of the square well, as indicated through the behavior of the radius of gyration and the constant volume heat capacity. Properties of the collapse transition are calculated exactly for chains with three to six backbone atoms and heuristically for long chains using arguments derived from the small chains and from conditions of integrability. Comparison with simulation studies is made.     

Polymer Structures and Glass Transition: A Molecular Dynamics Simulation Study

Full atomistic molecular dynamics (MD) simulations on five polymers with different chain backbone (C—C, Si—O, and C—O) and different side groups (—H, one —CH₃, and two —CH₃) are performed to study the effects of chain flexibility and side groups on the glass transition of polymers. Molecular dynamics simulations of NPT (constant pressure and constant temperature) dynamics are carried out to obtain specific volume as a function of temperature for polyethylene (PE), poly(propylene) (PP), polyisobutylene (PIB), poly(oxymethylene) (POM), and poly(dimethylsiloxane) (PDMS). The volumetric glass transition temperature has been determined as the temperature marking the discontinuity in slope of the plots of V–T simulation data. Various energy components at different temperatures of the polymers are investigated and their roles played in the glass transition process are analyzed. In order to understand the polymer chain conformations above and below the glass transition temperature, dihedral angle distributions of polymer chains at various temperatures are also studied.     

A Thermodynamic Model for Square-well Chain Fluid: Theory and Monte Carlo Simulation

A thermodynamic model for the freely jointed square-well chain fluids was developed based on the thermodynamic perturbation theory of Barker-Henderson, Zhang and Wertheim. In this derivation Zhang's expressions for square-well monomers improved from Barker-Henderson compressibility approximation were adopted as the reference fluid, and Wertheim's polymerization method was used to obtain the free energy term due to the bond connectivity. An analytic expression for the Helmholtz free energy of the square-well chain fluids was obtained. The expression without adjustable parameters leads to the thermodynamic consistent predictions of the compressibility factors, residual internal energy and constant-volume heat capacity for dimer, 4-mer, 8-mer and 16-mer square-well fluids. The results are in good agreement with the Monte Carlo simulation. To obtain the MC data of residual internal energy and the constant-volume heat capacity needed, NVT MC simulations were performed for these square-well chain fluids.     

Atomistic molecular-dynamics simulations of the size and shape of polyethylene in hexane at infinite dilution

Parameters characteristic of size and shape of single polyethylene chains consisting of 15-60 monomer units dissolved in hexane are calculated by use of molecular-dynamics simulations based on a fully atomistic representation of the system. Results are compared with corresponding calculations in vacuum as well as Monte Carlo simulations of coarse-grained chains. The major concern of the study is a careful check of actual limits and possibilities of atomistic simulations of global properties of polymers. As expected such simulations are still restricted to rather small chain lengths but are already large enough to obey the characteristics of polymer coils.