Coarse-grained Bead-spring Model Research Articles

Universal properties of a single polymer chain in slit: Scaling versus molecular dynamics simulations

We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyze their range of validity by means of comprehensive molecular dynamics simulations using a coarse-grained bead-spring model of a flexible polymer chain. The normal and parallel components of the average end-to-end distance, mean radius of gyration and their distributions, the density profile, the force exerted on the slit walls, and the local bond orientation characteristics are obtained in slits of width D=4/10 (in units of the bead diameter) and for chain lengths N=50/300. We demonstrate that a wide range of static chain properties in normal direction can be described quantitatively by analytic model-independent expressions in perfect agreement with computer experiment. In particular, the observed profile of confinement-induced bond orientation is shown to closely match theory predictions. The anisotropy of confinement is found to be manifested most dramatically in the dynamic behavior of the polymer chain. We examine the relation between characteristic times for translational diffusion and lateral relaxation. It is demonstrated that the scaling predictions for lateral and normal relaxation times are in good agreement with our observations. A novel feature is the observed coupling of normal and lateral modes with two vastly different relaxation times. We show that the impact of grafting on lateral relaxation is equivalent to doubling the chain length.

Phase separation of an asymmetric binary-fluid mixture confined in a nanoscopic slit pore: Molecular-dynamics simulations

As a generic model system of an asymmetric binary-fluid mixture, hexadecane dissolved in carbon dioxide is considered, using a coarse-grained bead-spring model for the short polymer, and a simple spherical particle with Lennard-Jones interactions for the carbon dioxide molecules. In previous work, it has been shown that this model reproduces the real phase diagram reasonably well, and also the initial stages of spinodal decomposition in the bulk following a sudden expansion of the system could be studied. Using the parallelized simulation package ESPResSo on a multiprocessor supercomputer, phase separation of thin fluid films confined between parallel walls that are repulsive for both types of molecules are simulated in a rather large system ( 1356 x 1356 x 67.8 A{3} , corresponding to about 3.2-million atoms). Following the sudden system expansion, a complicated interplay between phase separation in the directions perpendicular and parallel to the walls is found: In the early stages the hexadecane molecules accumulate mostly in the center of the slit pore, but as the coarsening of the structure in the parallel direction proceeds, the inhomogeneity in the perpendicular direction gets much reduced. Studying then the structure factors and correlation functions at fixed distances from the wall, the densities are essentially not conserved at these distances, and hence the behavior differs strongly from spinodal decomposition in the bulk. Some of the characteristic lengths show a nonmonotonic variation with time, and simple coarsening described by power-law growth is only observed if the domain sizes are much larger than the film thickness.

Brownian dynamics simulations of polyelectrolyte molecules traveling through an entropic trap array during electrophoresis

Using Brownian dynamics simulations of wormlike chain bead-spring models, the dynamics of linear and star-branched polyelectrolyte molecules traveling through an array of entropic traps during electrophoresis have been investigated. First, the effectiveness of using coarse-grained bead-spring systems for linear molecules to model the electrophoretic process was demonstrated and compared to previous bead-rod (Kramers) chain simulations by Panwar and Kumar [Macromolecules 39, 1297 (2006)]. Second, the coarse-grained bead-spring model has been extended to investigate the effect of branching on the dynamics of molecules through the entropic trap array. Initial studies indicate the reduced mobility of star-branched molecules as compared to equivalent linear molecules. The radius of gyration of the polymer molecule appears to be the dominating factor governing the time scales encountered during traversal of the entropic trapping array.

Comparison of dissipative particle dynamics and Langevin thermostats for out-of-equilibrium simulations of polymeric systems

In this work we compare and characterize the behavior of Langevin and dissipative particle dynamics (DPD) thermostats in a broad range of nonequilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion, polymeric liquids in Poiseuille and Couette flows, and brush-melt interfaces are used as model systems to analyze the efficiency and limitations of different Langevin and DPD thermostat implementations. Widely used coarse-grained bead-spring models under good and poor solvent conditions are employed to assess the effects of the thermostats. We considered equilibrium, transient, and steady state examples for testing the ability of the thermostats to maintain constant temperature and to reproduce the underlying physical phenomena in nonequilibrium situations. The common practice of switching off the Langevin thermostat in the flow direction is also critically revisited. The efficiency of different weight functions for the DPD thermostat is quantitatively analyzed as a function of the solvent quality and the nonequilibrium situation.

Polymer brushes in solvents of variable quality: Molecular dynamics simulations using explicit solvent

The structure and thermodynamic properties of a system of end-grafted flexible polymer chains grafted to a flat substrate and exposed to a solvent of variable quality are studied by molecular dynamics methods. The macromolecules are described by a coarse-grained bead-spring model, and the solvent molecules by pointlike particles, assuming Lennard-Jones-type interactions between pairs of monomers (epsilon(pp)), solvent molecules (epsilon(ss)), and solvent monomer (epsilon(ps)), respectively. Varying the grafting density sigma(g) and some of these energy parameters, we obtain density profiles of solvent particles and monomers, study structural properties of the chain (gyration radius components, bond orientational parameters, etc.), and examine also the profile of the lateral pressure P( parallel)(z), keeping in the simulation the normal pressure P( perpendicular) constant. From these data, the reduction of the surface tension between solvent and wall as a function of the grafting density of the brush has been obtained. Further results include the stretching force on the monomer adjacent to the grafting site and its variation with solvent quality and grafting density, and dynamic characteristics such as mobility profiles and chain relaxation times. Possible phase transitions (vertical phase separation of the solvent versus lateral segregation of the polymers into "clusters," etc.) are discussed, and a comparison to previous work using implicit solvent models is made. The variation of the brush height and the interfacial width of the transition zone between the pure solvent and the brush agrees qualitatively very well with corresponding experiments.

Simulation of nonlinear shear rheology of dilute salt-free polyelectrolyte solutions

Brownian dynamics simulations are used to conduct a systematic analysis of the nonlinear shear rheology of dilute polyelectrolyte solutions, exploring its relationship to shear rate, Bjerrum length, and concentration. A simple coarse-grained bead-spring chain model that incorporates explicit counterions is used. It is found that the polyelectrolyte chains exhibit a shear thinning behavior at high shear rate (as characterized by bead Peclet number Pe) that is independent of the electrostatic strength due to the stripping of ions from close proximity to the chain caused by the flow. In contrast, at low values of Pe, the viscosity increases monotonically with increasing Bjerrum length over the range studied here, in contrast to the nonmonotonic trend displayed by the chain size. Furthermore, at fixed Bjerrum length, the reduced viscosity increases monotonically with concentration. The mechanism underlying these observations is essentially the primary electroviscous effect; the ion cloud surrounding a polyelectrolyte chain deforms in flow, causing a significant increase in viscosity as concentration increases. Finally, the authors have also considered the role of hydrodynamic interactions in these simulations, finding that for low concentration studies in shear flow, these do not qualitatively affect the results.

2203 粗視化分子動力学シミュレーションを用いた磁気ディスク上における単分子層潤滑膜の流動特性の解析(要旨講演,マイクロナノ理工学)

A molecular dynamics simulation using a coarse-grained bead-spring model was applied to investigate the spreading characteristics of monolayer lubricant films on magnetic disks. One of the end beads of a perfluoropolyether molecule was fixed to the disk surface in order to model a bonded molecule. The simulated diffusion coefficient of mobile molecules for various coverages of the bonded molecules was in good agreement with previous experimental result using the half-dip method. The simulated relation between the coverage and bonding ratio was also in good agreement with the experimental one.

Static and dynamic properties of the interface between a polymer brush and a melt of identical chains

Molecular-dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model, which includes excluded volume and backbone connectivity of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and nonequilibrium molecular-dynamics simulations at constant temperature and volume using the dissipative particle dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The obtained boundary conditions and slip length show a rich behavior as a function of grafting density and shear velocity.

How Well Can Coarse-Grained Models of Real Polymers Describe Their Structure? The Case of Polybutadiene.

Coarse-graining of chemical structure of macromolecules in the melt is investigated using extensive molecular dynamics simulation data which are based on a united atom force-field model of polybutadiene. Systematically increasing the number, n, of the united atoms approximated by an effective coarse-grained monomer, we study the influence of degree of coarse-graining on the structure functions such as the segment-segment intermolecular and intramolecular correlation functions. These results are compared to Monte Carlo simulations of the corresponding coarse-grained bead-spring model and Chen-Kreglewski potential for chain molecules. In contrast to the atomistic chemically realistic model of polybutadiene, the bending and torsional potentials are not included into the coarse-grained models. Nevertheless, for a range of intermediate values of n a good qualitative agreement between intra- and intermolecular coarse-grained correlations of the atomistic model and the coarse-grained bead-spring model is found on large and intermediate length scales, but deviations occur on length scales well below one nanometer. The structure functions obtained for the Chen-Kreglewski chains exhibit many artificial features.

A successive fine-graining scheme for predicting the rheological properties of dilute polymer solutions

A new method for refining the predictions of a finitely extensible bead-spring chain model with hydrodynamic interactions is introduced. The suggested successive fine-graining procedure involves the representation of a long but finite macromolecule of NK Kuhn steps with a coarse-grained bead-spring chain model, and subsequently fine graining the representation by progressively increasing the number of beads, N. Extrapolating the results obtained using exact Brownian dynamics simulations for several values of N to the limit N−1→NK, leads to improved estimates for the behavior of the actual polymer chains. The extrapolated results for the extensional viscosity are found to be in good agreement with the recent experimental observations of Gupta et al. (2000). The scaling of the extensional viscosity with molecular weight is also examined.

Stability of thin polymer films: influence of solvents.

The interface and surface properties and the wetting behavior of polymer-solvent mixtures are investigated using Monte Carlo simulations and self-consistent field calculations. We carry out Monte Carlo simulations in the framework of a coarse-grained bead-spring model using short chains (oligomers) of N(P)=5 beads and a monomeric solvent, N(S)=1. The self-consistent field calculations are based on a simple phenomenological equation of state for compressible binary mixtures and we employ Gaussian chain model. The bulk behavior of the polymer-solvent mixture belongs to type III in the classification of van Konynenburg and Scott [Phil. Trans. R. Soc. London, Ser. A 298, 495 (1980)]. It is characterized by a triple line on which the polymer-liquid coexists with solvent-vapor and a solvent-rich liquid. The solvent is not homogeneously distributed across the dense polymer film but tends to accumulate at the surface and the polymer-vapor interface. This solvent enrichment at the interface and surface becomes more pronounced upon increasing the vapor pressure and alters the surface and interface tensions. This effect gives rise to a nonmonotonic dependence of the contact angle on the vapor pressure and one might observe reentrant wetting. The results of the Monte Carlo simulations and the self-consistent field calculations qualitatively agree. The profiles of drops are investigated by Monte Carlo simulations and a pronounced solvent enrichment is observed at the wedge formed by the substrate and the liquid-vapor interface at the three-phase contact line.

Transport Properties of Nanoscale Lubricant Films

Off-lattice molecular dynamics simulations based on the coarse-grained bead-spring model via the Langevin equation were performed to simulate the dynamics of a confined nanoscale perfluoropolyether film (i.e., the self-diffusion and relaxation processes). The effects of molecular weight and solid surface attraction on the film diffusion coefficient were studied using the Green-Kubo formula. Via a stretched-exponential model, we investigated the relaxation process of nanofilms, and found that the relaxation spectra were stretched from the exponential decay process for functional endgroups and/or surface attraction.

Growth, microstructure, and failure of crazes in glassy polymers.

We report on an extensive study of craze formation in glassy polymers. Molecular dynamics simulations of a coarse-grained bead-spring model were employed to investigate the molecular level processes during craze nucleation, widening, and breakdown for a wide range of temperature, polymer chain length N, entanglement length N(e), and strength of adhesive interactions between polymer chains. Craze widening proceeds via a fibril-drawing process at constant drawing stress. The extension ratio is determined by the entanglement length, and the characteristic length of stretched chain segments in the polymer craze is N(e)/3. In the craze, tension is mostly carried by the covalent backbone bonds, and the force distribution develops an exponential tail at large tensile forces. The failure mode of crazes changes from disentanglement to scission for N/N(e) approximately 10, and breakdown through scission is governed by large stress fluctuations. The simulations also reveal inconsistencies with previous theoretical models of craze widening, which were based on continuum level hydrodynamics.

Surface excess in dilute polymer solutions and the adsorption transition versus wetting phenomena

The adsorption of long flexible chains from dilute solution is studied by Monte Carlo simulation of a coarse-grained bead-spring model, and the results are interpreted in terms of phenomenological theories, using both mean field approaches and scaling concepts. It is shown that the surface excess, i.e., the integral of the local density difference of the monomers close to the surface relative to the bulk changes its sign very close to the adsorption transition (that is a sharp transition in the limit where the chain length diverges to infinity) for long chains, and it can be described in terms of the standard scaling description that has previously been tested for polymers with one end anchored on the surface (“polymer mushrooms”). Attention is also paid to the question on how this description changes when the temperature T of the polymer solution approaches the theta temperature Θ. Since the theta point can also be considered as an end point of a line of critical points, where the polymer solution phase separates into a dilute solution of collapsed chains and a more concentrated solution in the bulk, the adsorbing wall for T<Θ causes the existence of wetting layers. Conjectures about relations between wetting transitions for T near Θ and the adsorption transition are also presented.

Cooling rate dependence of the glass transition temperature of polymer melts: Molecular dynamics study

A coarse-grained bead spring model of short polymer chains is studied by constant pressure molecular dynamics (MD) simulations. Due to two competing length scales for the length of effective bonds and the energetically preferred distance between nonbonded beads, one observes a glass transition when dense melts are cooled down (as shown in previous work, at a pressure p=1 the mode coupling critical temperature is at Tc≈0.45 and the Vogel–Fulcher temperature is T0≈0.33, in Lennard-Jones units). The present work extends these studies, estimating a cooling-rate-dependent glass transition temperature Tg(Γ) by cooling the model system from T=0.6 down to T=0.3, applying cooling rates from Γ≈10−3 to Γ≈10−6 (in MD time units), and attempting to identify Tg(Γ) from a kink in the volume versus temperature or potential energy versus temperature curves. It is found that Tg(Γ) lies in the range 0.43⩽Tg(Γ)⩽0.47, for the cooling rates quoted, and the variation of Tg(Γ) for Γ is compatible with the expected logarithmic variations. We will show why a detailed distinction between competing theories on these cooling rate effects would need an excessive amount of computer time. To estimate also the melting transition temperature Tm of this model, the sytem was prepared in a crystalline configuration as an initial state and heated up. The onset of diffusion, accompanied by an isotropization of the pressure tensor was observed for Tm≈0.77. This implies that the model is suitable for studying deeply supercooled melts.

Polymer nanodroplets adsorbed on nanocylinders: A Monte Carlo study

The structure and the shape of polymer droplets of nanoscopic size on ultrathin cylindrical fibers (with diameters in the range of nanometers) is investigated by Monte Carlo simulation of a coarse-grained bead-spring type model. The interaction between atoms in the solid nanocylinder and the effective monomers is assumed to be of Lennard-Jones-type, but the detailed atomistic structure of the nanofiber is ignored, using a homogeneous cylinder with a perfectly smooth surface. Depending on the size of the droplet, the fiber radius, and the strength of the adsorption potential, droplets have either the (axially symmetric) “barrel shape,” or the asymmetric “clamshell shape,” or are unstable against spreading out along the fiber. For the barrel-shaped droplets, the dependence of the contact angle on the parameters mentioned above is estimated. For comparison, using the same model also the case of droplets on a flat horizontal surface and in a wedge with opening angle of 90° has been studied. When appropriate, the simulation results are interpreted in terms of current theoretical predictions.

Polymers near metal surfaces: selective adsorption and global conformations.

We study the properties of a polycarbonate melt near a nickel surface as a model system for the interaction of polymers with metal surfaces by employing a multiscale modeling approach. For bulk properties, a suitably coarse-grained bead-spring model is simulated by molecular dynamics methods with model parameters directly derived from quantum chemical calculations. The surface interactions are parametrized and incorporated by extensive quantum mechanical density functional calculations using the Car-Parrinello method. We find strong chemisorption of chain ends, resulting in significant modifications of the melt composition when compared to an inert wall.

Molecular simulation of thin polymer films with functional endgroups

An off-lattice Monte Carlo simulation using a coarse-grained bead-spring model was developed to analyze nanoconfined polymer films. The beads in the polymer chains are connected via finitely extensible, nonlinear elastic springs. In addition to nonpolar van der Waals interactions, functional endbeads have a short-range exponential interaction characteristic of endgroup coupling. Our simulated results qualitatively agree with experimental data for perfluoropolyether molecules with functional endgroups in ultrathin films. The chains exhibit an oblate conformation near the wall, but recover a spherical shape as they move farther away from it. The density profile of functional endbeads as a function of distance from the wall shows characteristic oscillation originating from endbead coupling and orientation near the wall. We examined the molecular layering of films via the analysis of an anisotropic radius of gyration for the chains, which is affected by the endgroup interactions.

Polymer melt droplets adsorbed on a solid wall: A Monte Carlo simulation

Using a coarse-grained bead-spring model of flexible polymers, we study the contact angle of polymer melt droplets sitting at a flat structureless wall, when the strength ε of the adsorption potential Vwall(z)=ε/z3 is varied. For this purpose, droplets containing 2048 or 4096 monomers for chain lengths N=16 and N=32 were carefully equilibrated at temperatures in the range from 74% to 82% of the Theta temperature, and the density profile of these droplets both in the z direction perpendicular to the substrate surface and in the radial direction was obtained. Beyond a critical value of ε we find that the contact angle vanishes, i.e., the droplets spread out and form a flat film. Such flat polymer films are also studied with considerably more polymers (up to 24 576 monomers contained in the simulation box). It is shown that the density profile ρ(z) is affected by the hard wall (exhibiting the characteristic layering oscillations) up to about z=5 (measuring lengths in units of the length of an effective bond), while at larger z the profile is flat and has the melt density at that temperature, with an interface to the “gas” at about z=20. Analyzing the capillary wave spectrum of the interfacial fluctuations, the surface tension of the polymer melt is extracted. Via the anisotropy of the local pressure near the wall, the wall excess free energy of the polymer melt is found as well, and the Young equation is tested. Thus methods have been developed that allow a systematic study of polymer–wall interactions and wetting vs dewetting behavior.

Formation of Surface Micelles from Adsorbed Asymmetric Block Copolymers: A Monte Carlo Study

The properties of surface micelles formed from flexible short block copolymers of composition AfB1-f with f = 1/4 and chain lengths of N = 8 and N = 16 effective monomers are obtained from Monte Carlo simulation of a coarse-grained bead spring model. We consider the case where the surface has a short-range attraction to the A monomers but is repulsive for the B monomers. Depending on the surface coverage and the strength EAA of the attractive energy between the A monomers, the adsorbed polymers may form “mushrooms”, or a polymer brush, or surface micelles. We show that a rather well-defined critical micelle concentration occurs, similar to that for micelle formation in bulk solutions, and we study the size distribution of the micelles as well as their internal structure. Large micelles exhibit a very dense solid core and are essentially immobile. Equilibration then is still possible via the exchange of single mobile chains between micelles.