Properties of simple models of polymer networks. A Monte Carlo simulation

A model polymer network was constructed from branched chains. Each chain was built on a simple cubic lattice forming a star-branched polymer consisting of f = 3 arms of equal lengths. The fragment of network under consideration consisted of 1, 2 and 3 star polymers with different topology of connections. The only potential used was excluded volume (athermal chains). The properties of the network were determined by the means of computer simulations using the classical Metropolis sampling algorithm (local micromodifications of chain conformation). The behaviour of linear chains of the same molecular weight was also studied as a state of reference. The influence of attaching the next star-branched chain to the network on its static and dynamic properties was studied. The short-time dynamic behaviour of chain fragments was determined and discussed.     

Mixed brushes consisting of oppositely charged Y-shaped polymers in salt free,monovalent, and divalent salt solutions

The conformation and the internal stratification of mixed brushes formed from oppositely charged Y(−) and Y(+)-shaped chains in salt free, monovalent, and divalent salt solutions were studied by means of molecular dynamics simulations using the primitive model. Scaling relations of mixed brush height with respect to the grafting surface per chain, the ratio of the total positive to the total negative charge of polyelectrolyte chains, and salt concentrations were obtained. The simulations predicted that mixed brushes show a unique response to divalent salt (1:2) solutions. For symmetric brushes having the same spacer lengths, number of chains and charged units fractions the increase of the salt concentration leads to the enrichment of the outer brush surface with Y(+) units and the lamella microphase separation. For asymmetric brushes in high salt concentration cylindrical domain microphases are formed.     

Interdiffusion of polymers across interfaces

Neutron Reflection (NR) and Dynamic Secondary Ion Mass Spectroscopy (DSIMS) experiments were conducted on symmetrically deuterated polystyrene triblock bilayers (HDH/DHD) which directly probed the interdiffusion dynamics of the chains during welding. The HDH chains had their centers deuterated 50%, the DHD chains had their ends deuterated (25% at each end) such that each chain contained approximately 50% D. During welding, anisotropic motion of the chains produces a time-dependent oscillation (ripple) in the H and D concentration at the interface, which bears the characteristic signature of the polymer dynamics. These oscillations were compared with those predicted by Rouse, polymer mode coupling (PMC), and reptation dynamics. The following conclusions can be made from this study. (a) During the interdiffusion of high molecular weight HDH/DHD pairs, higher mobility of the chain ends caused a concentration oscillation which increased to a maximum amplitude, and eventually vanished at times, t > τ_D. The amplitude, or excess enrichment found, was appreciably more than that predicted by Rouse and PMC simulations, and was only slightly less than that predicted from reptation simulations. (b) The oscillations were completely missing in the 30 and 50K HDH/DHD polymers, which are only weakly entangled. The lack of oscillations for the 30 and 50K pairs may be due to a combination of surface roughness and fluctuations of order 30 Å. (c) It was found that the position of the maximum in this ripple stayed at the interface during its growth. This is also consistent with reptation and has not been explained by other theories. (d) All dynamics models for linear polymers produce ripples, many of which are qualitatively similar to that predicted for reptation. However, each ripple bears the fingerprint of the dynamics in terms of its time-dependent shape, position, and magnitude, and the models are clearly distinguishable. Our results, in summary, support reptation as a candidate mechanism of interdiffusion at polymer(SINGLEBOND) polymer interfaces and its uniqueness is being further pursued. © 1996 John Wiley & Sons, Inc.     

Atomistic hybrid particle‐field molecular dynamics combined with slip‐springs: Restoring entangled dynamics to simulations of polymer melts

In hybrid particle‐field (hPF) simulations (J. Chem. Phys., 2009 130, 214106), the entangled dynamics of polymer melts is lost due to chain crossability. Chains cross, because the field‐treatment of the nonbonded interactions makes them effectively soft‐core. We introduce a multi‐chain slip‐spring model (J. Chem. Phys., 2013 138, 104907) into the hPF scheme to mimic the topological constraints of entanglements. The structure of the polymer chains is consistent with that of regular molecular dynamics simulations and is not affected by the introduction of slip‐springs. Although slight deviations are seen at short times, dynamical properties such as mean‐square displacements and reorientational relaxation times are in good agreement with traditional molecular dynamics simulations and theoretical predictions at long times.     

疏水高分子单链在疏水表面上吸附和扩散过程的分子动力学模拟

采用分子动力学模拟方法研究不同聚合度(N)的聚乙烯(PE)单链在Si(111)表面上的吸附和扩散行为. 分别设置相对介电常数为1和78模拟无溶剂和不良溶剂环境. PE单链的平衡吸附构象均呈现为二维吸附构象, 但在这两种截然不同的环境中呈现不同的构象和动力学特征, 说明溶剂环境对于疏水高分子单链在疏水表面上的吸附和扩散起到了很大的作用. 吸附能与聚合度呈线性关系, 单位链长的平均吸附能是-0.38 kJ·mol^-1. 另外, 扩散系数(D)与聚合度之间的标度关系是D~N^-3/2.     

良溶剂中接枝型聚两性电解质单链构象的布朗动力学模拟

采用布朗动力学研究了在良溶剂中荷电平衡的接枝聚两性电解质(GPA)的单链构象转变行为,讨论了主链链长、支链数及电荷密度对GPA分子链构象转变的影响.研究发现,随着静电相互作用的增强,GPA分子链构象转变过程由线团、主链与支链间的折叠、链段塌缩和电荷配对形成偶极子与四极子等4个阶段构成.与线型聚两性电解质不同,GPA存在的额外支链间空间排斥与静电排斥作用随着分子结构的变化而改变,并影响构象转变行为.在强静电相互作用下,良溶剂中的GPA链由于溶剂化作用会再伸展,以保证偶极子完全配对成四极子.减小主链长度或电荷密度或增加支链数目都会增大体系的排斥力和主链的刚性,阻滞分子链的塌缩,并使得分子链再伸展的幅度增大.     

Properties of Star-Branched Polymer Chains Near a Surface

We considered two model systems of star-branched polymers near an impenetrable surface. The model chains were constructed on a simple cubic lattice. Each star polymer consisted of f = 3 arms of equal length and the total number of segments was up to 799. The excluded volume effect was included into these models only and therefore the system was studied at good solvent conditions. In the first model system polymer chain was terminally attached with one arm to the surface. The grafted arm could slide along the surface. In the second system the star-branched chain was adsorbed on the surface and the strength of adsorption was were varied. The simulations were performed using the dynamic Monte Carlo method with local changes of chain conformations. The internal and local structures of a polymer layer were determined. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. It was shown that the behavior of grafted and weakly adsorbed chains was similar to that of a free three-dimensional polymer, while the strongly adsorbed chains behave as a two-dimensional system.     

Dynamics of grafted star-branched polymers. A Monte Carlo study

Monte Carlo simulations of simple models of star-branched polymers were carried out. The model chains were confined to simple cubic lattice and consisted of f = 3 branches of equal length and the total number of polymer segments as well as the density of grafted chains on the surface were varied. The chains have had one arm end attached to an impenetrable plate. The simulations were performed by employing the set of local micromodifications of the chain conformations. The model chains were athermal, i.e. good solvent conditions were modeled, the excluded volume effect was present at the model. The density of grafted chains on the surface was varied from a single chain up to 0.3. The static and dynamic properties of the system were studied. The influence of polymer concentration as well as the polymer length on static and dynamic properties of the system studied was shown. The relation between the structure and short-time dynamics (relaxation times) was discussed.     

线形、梳形和星形高分子静态和动态性质的模拟

以梳形高分子为纽带,基于粗粒化分子动力学模拟方法,研究了线形、梳形和星形拓扑结构高分子的静态和动态性质,以揭示稀溶液中高分子链行为与链拓扑结构依赖关系的一般性规律.研究结果表明,随着线形-梳形-星形的链拓扑结构转变,回转半径的标度关系由仅依赖分子聚合度转变为同时依赖链聚合度与臂数或侧链数.分析了星形高分子和梳形高分子的静态和动态性质的特征规律.星形高分子的臂数增加使其尺寸迅速减小,形状则由长椭球形转变为类球形,且扩散系数也随之增加;其均方回转半径(〈R_g〉)和扩散系数(D)与分子聚合度(N)及臂数(f)的标度规律为〈R_g〉~N~(0.581)f~(-0.402),D~N~(-0.763)f~(0.227).梳形高分子的静态与动态性质与分子聚合度及侧链数的依赖关系为〈R_g〉~N~(0.597)f~(-0.212)(每个支化点只有一条侧链)和〈R_g〉~N~(0.599)f~(-0.316)(每个支化点有多条侧链).     

Heterogeneities in Polymer Structural and Dynamic Properties in Graphene and Graphene Oxide Nanocomposites: Molecular Dynamics Simulations

The effect of graphene (G) and graphene oxide (GO), used as the nanofiller in polymer nanocomposites (NC), on the structural and dynamic properties of polymer chains, has been studied by means of molecular dynamics (MD) simulations. Two polymers, i.e., poly(propylene) and poly(vinyl alcohol), are employed as matrices to cover a wider range of polymer–filler interactions. The local structural properties, e.g., density profile, average R _g, and end‐to‐end distance as well as dynamic properties, e.g., estimated translational and orientational relaxation times, of polymer chains are studied. In addition, the interaction energies are estimated between polymers and nanofillers for different hybrid systems using MD pullout simulations. Strong heterogeneities in polymer structural and dynamic properties have been observed such that chains are more oriented and exhibit slower dynamics in the vicinity of the nanofillers (G and GO) as compared to bulk. It is also found that the orientation of polymer chains at the interface is more influenced by the nanofiller in such a way that the more oriented polymer chains are observed in G‐based NC for both polymers. However, the immobilization of polymer chains at the interface proves to be very much dependent on the polymer–filler interactions.

     

Shear-induced effects in hyperbranched-linear polyelectrolyte complexes

Static and dynamic properties of complexes formed by hyperbranched polymers with linear polyelectrolytes are studied under the influence of steady shear flow by means of Brownian dynamics simulations. Models of peripherally charged hyperbranched molecules bearing two extreme topological structures and different molecular weights complexed with linear neutralizing chains are subjected to a range of shear rates starting from a low-shear regime toward the complex-breaking point. Examination of the stability limit, shape and mass distribution parameters, and dynamics in different lengths and timescales is performed as a function of the applied shear. The results described illustrate features of the generic behavior that should be expected from such systems under conditions of steady shear flow.     

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.     

Monte Carlo Simulations of Self-Assembling Copolymer Brushes

We studied a simplified model of a polymer brush formed by linear chains, which were restricted to vertices of a simple cubic lattice. The macromolecules consisted of a sequence of two different kinds of united atoms arranged in a specific sequence. The chains were grafted to an impenetrable surface, i.e. they were terminally attached to the surface with one end. The model system was studied at different solvent quality from good to poor solvent. The properties of this model system were determined by means of Monte Carlo simulation using a Metropolis-like sampling algorithm based on local changes of chain's conformations. The size and the structure of the brush were determined.     

Coarse grained model of diffusion in entangled bidisperse polymer melts

Chain diffusion is studied in mixtures of bidisperse linear polymers of same chemical identity by means of simulations. The two subpopulations are moderately to highly entangled, with the shorter chain length N(S), fulfilling N(S)N(e)> or =5. To this end, a coarse grained model calibrated to reproduce both the structure and dynamics of chains in monodisperse entangled melts is used [A. Rakshit and R. C. Picu, J. Chem. Phys. 125, 164907 (2006)]. Its performance in reproducing chain dynamics in a polydisperse melt is tested by extensively comparing the results with those obtained from an equivalent fine scale representation of the same system (a bead-spring model). The coarse grained model is used further to investigate the scaling of the diffusion coefficient with the length of the two types of chains and its dependence on the respective fractions. The model reproduces many features observed experimentally. For example, the diffusion coefficient of one of the chain types decreases with increasing the length of the other type chains. It is shown that, in this model, this effect is not linked to constraint release. When the matrix chains become sufficiently long, their length does not influence the diffusion coefficient of the short chains anymore. The diffusion coefficient of the short chains scales with their weight fraction in a manner consistent with experimental observations. In mixtures, the dynamics of the short chains is slower and that of the long chains is marginally faster than in their respective monodisperse melts.     

Contribution of omega-3 fatty acids to the thermodynamics of membrane protein solvation

Recent NMR experiments and molecular dynamics simulations have indicated that rhodopsin is preferentially solvated by omega-3 fatty acids compared to saturated chains. However, to date no physical theory has been advanced to explain this phenomenon. The present work presents a novel thermodynamic explanation for this preferential solvation based on statistical analysis of 26,100 ns all-atom molecular dynamics simulations of rhodopsin in membranes rich in polyunsaturated chains. The results indicate that the preferential solvation by omega-3 chains is entropically driven; all chains experience an entropic penalty when associating with the protein, but the penalty is significantly larger for saturated chains.     

Dynamics of free chains in polymer nanocomposites

The dynamics of entangled polymeric chains in a polymer filled with nanoparticles is studied by means of molecular dynamics simulations of a model system. The primary objective is to study to what extent the reptation of polymers not in direct contact with fillers is modified with respect to the neat material. To this end, two systems are considered: A regular filled material in which the filler-polymer affinity is controlled, and a system in which the beads in contact with the filler at the beginning of the production phase of the simulation are tethered to the filler surface. This second system represents the limit case of long polymer-filler attachment time. In this case attention is focused on the free chains of the melt. The dynamics in the two models is different. In the filled system uniform slowing down for all Rouse modes is observed. The effect varies monotonically with the filler-polymer affinity. Up to saturation, this behavior may be captured by usual models with an effective, affinity-dependent, friction coefficient. In the system with grafted chains, the free chain Rouse dynamics is identical to that in the neat material, except for the longest modes which are significantly slowed down. More interestingly, the dynamics of the free chains depends in a nonmonotonic way on the polymer-filler affinity, although the free chains do not come in direct contact with the filler. This effect is due to small changes in the structure of the polydisperse brush upon modification of the affinity. Specifically, the density of the brush and the amount of interpenetration of free and grafted chains depend on the filler-polymer affinity. The use of a reptation model with modified tube diameter to capture this behavior is discussed.     

Relation between Polymer Conformational Structure and Dynamics in Linear and Ring Polyethylene Blends

Atomistic molecular dynamics simulations of ring‐linear polyethylene blends are employed to understand the relationship between chain conformational structure and the melt dynamics of these blends. As observed in previous studies, this study confirms that ring polymers in pure melts do not exhibit screened excluded volume interactions, contrary to linear polymers. Moreover, the average molecular shapes of the rings are quite distinct from both swollen and ideal ring polymers under theta conditions, and instead rather resemble branched polymers with screened binary excluded volume interactions, e.g., percolation clusters. Upon adding linear chains to a melt of pure rings, we find significant swelling of the rings and a corresponding shape change that is qualitatively similar to dissolving rings in a small molecule good solvent. This swelling, arising from altered self‐excluded volume interactions, translates into a large decrease in ring diffusivity, an effect that becomes more amplified when the polymer melt is entangled.     

Molecular dynamics with the United-residue force field: ab initio folding simulations of multichain proteins

The implementation of molecular dynamics with the united-residue (UNRES) force field is extended to treat multichain proteins. Constant temperature was maintained in the simulations with Berendsen or Langevin thermostats. The method was tested on three alpha-helical proteins (1G6U and GCN4-p1, each with two chains, and 1C94, with four chains). Simulations were carried out for both the isolated single chains and the multichain complexes. The proteins were folded by starting from the extended conformation with random initial velocities and with the chains parallel to each other. No symmetry constraints or structure information were included for the single chains or the multichain complexes. In the case of single-chain simulations, a high percentage of the trajectories (100% for 1G6U, 90% for GCN4-p1, and 80% for 1C94) converged to nativelike structures (assumed as the experimental structure of a monomer in the multichain complex), showing that, for the proteins studied in this work with the UNRES force field, the interactions between chains are not critical for stabilization of the individual chains. In the case of multichain simulations, the native structures of the 1G6U and GCN4-p1 complexes, but not that of 1C94, are predicted successfully. The association of the subunits does not follow a unique mechanism; the monomers were observed to fold both before and simultaneously with their association.     

Conformational behavior of comb-like polyelectrolytes in selective solvent: computer simulation study

In this work, we present molecular dynamics simulations of comb-like polyelectrolytes in selective solvent. The studied polymers have a neutral backbone and polyelectrolyte side chains. The solvent is poor for the backbone and the theta solvent for the side chains. The polymers are modeled on a coarse-grained level with implicit solvent. The simulations show that the comb-like polyelectrolytes tend to form intramolecular self-organized structures of the pearl necklace type. This type of conformational behavior has been predicted by Borisov and Zhulina (Borisov, O. V.; Zhulina, E. B. Macromolecules 2005, 38, 2506) for neutral comb-like copolymers in selective solvent. The present study shows that comb-like polyelectrolytes in selective solvent exhibit the same type of behavior; however, it can be controlled by one additional parameter, the degree of dissociation of the grafts. The local conformational characteristics are studied using the ensemble-averaged bond angle cosines as functions of monomer position in the chain, which reveal structural details invisible by other means.     

Reduction of the effective shear viscosity in polymer solutions due to crossflow migration in microchannels: Effective viscosity models based on DPD simulations

Molecular dynamics simulations (dissipative particle dynamics–DPD) were developed and used to quantify wall-normal migration of polymer chains in microchannel Poseuille flow. Crossflow migration due to viscous interaction with the walls results in lowered polymer concentration near the channel walls. A larger fraction of the total flow volume becomes depleted of polymer when the channel width h decreases into the submicron range, significantly reducing the effective viscosity. The effective viscosity was quantified in terms of channel width and Weissenberg number Wi, for 5% polymer volume fraction in water. Algebraic models for the depletion width δ(Wi, h) and effective viscosity μ_e(δ/h, Wi) were developed, based on the hydrodynamic theory of Ma and Graham and our simulation results. The depletion width model can be applied to longer polymer chains after a retuning of the polymer persistence length and the corresponding potential/thermal energy ratio.