Conformation and diffusion behavior of ring polymers in solution: a comparison between molecular dynamics, multiparticle collision dynamics, and lattice Boltzmann simulations

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.     

Communication: consistent picture of lateral subdiffusion in lipid bilayers: molecular dynamics simulation and exact results

This communication presents a molecular dynamics simulation study of a bilayer consisting of 128 dioleoyl-sn-glycero-3-phosphocholine molecules, which focusses on the center-of-mass diffusion of the lipid molecules parallel to the membrane plane. The analysis of the simulation results is performed within the framework of the generalized Langevin equation and leads to a consistent picture of subdiffusion. The mean square displacement of the lipid molecules evolves as ∝ t(α), with α between 0.5 and 0.6, and the fractional diffusion coefficient is close to the experimental value for a similar system obtained by fluorescence correlation spectroscopy. We show that the long-time tails of the lateral velocity autocorrelation function and the associated memory function agree well with exact results which have been recently derived by asymptotic analysis [G. Kneller, J. Chem. Phys. 134, 224106 (2011)]. In this context, we define characteristic time scales for these two quantities.     

Computer Simulation of Polymer Diffusion Under External Electric Field

Molecular dynamics simulations were carried out to investigate the diffusion of polymer chains in solvent under an external electric field. Polyethylene‐like polymer and methyl chloride molecule were chosen as solute and solvent. The external DC electric field strength was varied from 10 to 50 (4.3×10⁸ V/m). Both polar and non‐polar polymer chains in polar and non‐polar solvents were investigated. The simulation shows that the center of mass diffusion coefficient of polymer is sensitive to the polarities of polymer and solvent, field strength, polymer concentration and the density of the system. Various factors that affect the diffusion constant of the polymer are discussed. The present simulation is consistent with the results from light scattering experiments.     

The properties of a single polymer chain in solvent confined in a slit: A molecular dynamics simulation

A single polymer chain in solvent confined in a slit formed by two parallel plates is studied by using molecular dynamics simulation method. The square radii of gyration and diffusion behaviors of polymers are greatly affected by the distance between the two plates, but they do not follow the same way. The chain size decays drastically with increasing h (h is the distance between two plates), until a basin occurs, and a universal h/〈R _g〉₀ dependence for polymer chains with different degrees of polymerization can be obtained. While, for the chain’s diffusion coefficient, it decays monotonously and there is no such basin-like behavior. Furthermore, we studied the radial distribution function of confined polymer chains to explain the reason why there is a difference for the decay behaviors between dynamic properties and static properties. Besides, we also give the degree of confinement dependence of the static scaling exponent for a single polymer chain. Our work provides an efficient way to estimate the dynamics and static properties of confined polymer chains, and also helps us to understand the behavior of polymer chains under confinement.     

类蛋白质分子扩散系数的模拟计算

蛋白质分子是一类比较特殊的高分子，一方面它的性质与氨基酸序列密切相关，另一方面其二级结构（如α螺旋以及β折叠等）极大地影响着它的性质．另外它的内部结构又非常紧密，与一般的高分子链完全不同．同时随着计算机技术的发展，计算机模拟日益作为一种有效的手段广泛应用于高分子科学的研究．但是由于蛋白质分子比一般的高分子结构更加复杂，如氨基酸之间有复杂的互相作用等，因此对蛋白质性质的研究往往建立在简化模型的基础上，如基于格点的HP紧密高分子模型等．虽然建立在格点模型上的蛋白质分子和真实的蛋白质分子存在着一定的差异，但基本上能体现蛋白质分子的主要特征，因此把这一类分子称为类蛋白质分子．     

Polymer chain diffusion in polymer blends: A theoretical interpretation based on a memory function formalism

The diffusion of polymer chains in miscible polymer blends with large dynamic asymmetry—those where the two blend components display very different segmental mobility—is not well understood yet. In the extreme case of the blend system of poly(ethylene oxide) (PEO) and poly(methyl methacrylate)(PMMA), the diffusion coefficient of PEO chains in the blend can change by more than five orders of magnitude while the segmental time scale hardly changes with respect to that of pure PEO. This behavior is not observed in blend systems with small or moderate dynamic asymmetry as, for instance, polyisoprene/poly(vinyl ethylene) blends. These two very different behaviors can be understood and quantitatively explained in a unified way in the framework of a memory function formalism, which takes into account the effect of the collective dynamics on the chain dynamics of a tagged chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1239–1245     

Lattice-Boltzmann simulations of the dynamics of polymer solutions in periodic and confined geometries

A numerical method to simulate the dynamics of polymer solutions in confined geometries has been implemented and tested. The method combines a fluctuating lattice-Boltzmann model of the solvent [Ladd, Phys. Rev. Lett. 70, 1339 (1993)] with a point-particle model of the polymer chains. A friction term couples the monomers to the fluid [Ahlrichs and Dunweg, J. Chem. Phys. 111, 8225 (1999)], providing both the hydrodynamic interactions between the monomers and the correlated random forces. The coupled equations for particles and fluid are solved on an inertial time scale, which proves to be surprisingly simple and efficient, avoiding the costly linear algebra associated with Brownian dynamics. Complex confined geometries can be represented by a straightforward mapping of the boundary surfaces onto a regular three-dimensional grid. The hydrodynamic interactions between monomers are shown to compare well with solutions of the Stokes equations down to distances of the order of the grid spacing. Numerical results are presented for the radius of gyration, end-to-end distance, and diffusion coefficient of an isolated polymer chain, ranging from 16 to 1024 monomers in length. The simulations are in excellent agreement with renormalization group calculations for an excluded volume chain. We show that hydrodynamic interactions in large polymers can be systematically coarse-grained to substantially reduce the computational cost of the simulation. Finally, we examine the effects of confinement and flow on the polymer distribution and diffusion constant in a narrow channel. Our results support the qualitative conclusions of recent Brownian dynamics simulations of confined polymers [Jendrejack et al., J. Chem. Phys. 119, 1165 (2003) and Jendrejack et al., J. Chem. Phys. 120, 2513 (2004)].     

The influence of the polymer chain stiffness on tracer diffusion in polymeric matrices

The diffusion of penetrants in polymers is of technological importance in many areas including chromatography and fuel cell membranes. In this work, the effect of chain conformations on tracer diffusion is studied using molecular simulations and a percolation theory. The polymeric matrix is composed of tangent hard sphere chains that are fixed in space; conformations are changed by tuning the stiffness of the chains. The tracer diffusion coefficient is relatively insensitive to the chain stiffness when polymer chains are frozen as in polymer glasses with the local chain dynamics switched off. An analysis of the matrix using percolation theory shows that the polymer volume fraction at the free volume percolation threshold is also relatively insensitive to the chain stiffness, consistent with the diffusion results. This is surprising because the site‐site intermolecular pair correlation functions in the matrix are quite sensitive to the chain stiffness. In contrast, the tracer diffusion coefficient in a melt of mobile chains decreases significantly as the chain stiffness is increased. We conclude that tracer diffusion is only weakly correlated with the chain conformations and local chain dynamics plays an important role. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Structure and dynamics of short chain molecules in disordered porous materials: a molecular dynamics simulation study

The static and dynamic properties of short polymer chains in disordered materials are studied using discontinuous molecular dynamics simulations. The polymers are modeled as chains of hard spheres and the matrix is a collection of fixed hard spheres. The simulations show that the chain size is a nonmonotonic function of the matrix concentration for all polymer concentrations. The dependence of polymer diffusion D on the degree of polymerization N becomes stronger as the matrix concentration is increased. At high matrix concentrations we observe a decoupling between translational and rotational diffusion, i.e., the rotational relaxation time becomes very large but the translational diffusion is not affected significantly. We attribute this to the trapping of a small number of polymers. Under these conditions the polymer chains diffuse via a hopping mechanism.     

Density functional theory of homopolymer mixtures confined in a slit

A density functional theory (DFT) is developed for polymer mixtures with shorted-ranged attractive interparticle interactions confined in a slit. Different weighting functions are used separately for the repulsive part and the attractive part of the excess free energy functional by applying the weighted density approximation. The predicted results by DFT are in good agreement with the corresponding simulation data indicating the reliability of the theory. Furthermore, the center-of-mass profiles and the end-to-end distance distributions are obtained by the single chain simulation; the predictions also agree well with simulation data. The results reveal that both the attraction of the slit wall and the temperature has stronger effect on longer chains than on shorter ones because the intrasegment correlation of chains increases with increasing chain length.     

氧气在聚丙烯内吸附和扩散的分子模拟

采用巨正则Monte Carlo和分子动力学模拟相结合的方法研究了氧气在不同聚合度的聚丙烯内的吸附和扩散. 模拟结果表明, 随聚丙烯聚合度的增加, 聚丙烯对氧气的吸附量逐渐增加, 而氧气在聚丙烯内的扩散系数减小; 当聚合度增大到一定程度时, 吸附量和扩散系数都趋于一稳定值. 随温度的升高, 氧气在聚丙烯内的吸附量减少, 而扩散系数增大. 本文还应用自由体积理论探讨了氧气在聚合物内扩散的机理, 发现氧气在聚丙烯内以空穴形式存在的自由体积之间扩散, 即氧气先在一个空穴内不停振动, 然后通过聚丙烯链段运动形成的通道跳跃到下一个空穴来完成扩散. 结果表明, 较高聚合度的聚合物材料在常温及低温下使用对于其在食品包装材料中的应用是有利的, 这为食品包装材料行业相关产品的应用开发提供了一定的指导和依据.     

Interactions between colloidal particles in polymer solutions: A density functional theory study

We present a density functional theory study of colloidal interactions in a concentrated polymer solution. The colloids are modeled as hard spheres and polymers are modeled as freely jointed tangent hard sphere chains. Our theoretical results for the polymer-mediated mean force between two dilute colloids are compared with recent simulation data for this model. Theory is shown to be in good agreement with simulation. We compute the colloid-colloid potential of mean force and the second virial coefficient, and analyze the behavior of these quantities as a function of the polymer solution density, the polymer chain length, and the colloid/polymer bead size ratio.     

Influence of molecular topology on the static and dynamic properties of single polymer chain in solution

The influence of molecular topology on the structural and dynamic properties of polymer chain in solution with ring structure, three-arm branched structure, and linear structure are studied by molecular dynamics simulation. At the same degree of polymerization (N), the ring-shaped chain possesses the smallest size and largest diffusion coefficient. With increasing N, the difference of the radii of gyration between the three types of polymer chains increases, whereas the difference of the diffusion coefficients among them decreases. However, the influence of the molecular topology on the static and the dynamic scaling exponents is small. The static scaling exponents decrease slightly, and the dynamic scaling exponents increase slightly, when the topology of the polymer chain is changed from linear to ring-shaped or three-arm branched architecture. The dynamics of these three types of polymer chain in solution is Zimm-like according to the dynamic scaling exponents and the dynamic structure factors.     

Chain confinement in polymer nanocomposites and its effect on polymer bulk properties

The issue of chain confinement in nanocomposites remains largely unanswered because experimental systems are plagued by additional complicating variables such as particle–polymer interactions and free volume increases brought upon by the addition of the particles. Using computer simulation of high length chain polymers, we show that simple excluded volume interactions between polymer and nanoparticles lead to a wealth of changes in the diffusion coefficient and entanglement density of the chains. This opens up the possibility of using nanoparticles for tuning polymer properties, such as toughness, melt viscosity, and transient rubberlike behavior. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 687–692, 2010     

Monitoring Diffusion of Reptating Polymer Chains by a Direct Energy Transfer Method: A Monte Carlo Simulation

A kinetic Monte Carlo method was used to simulate the diffusion of reptating polymer chains across an interface. A time‐resolved fluorescence technique in conjunction with a direct energy transfer method was used to measure the extent of diffusion of dye‐labeled reptating polymer chains. The diffusion of donor‐ and acceptor‐labeled polymer chains between adjacent compartments was randomly generated. The fluorescence decay profiles of donor molecules were simulated at several diffusion steps to produce mixing of the polymer chains. Mixing ratios of donor‐ and acceptor‐labeled polymer chains in compartments were measured at various stages (snapshots) of diffusion. It was observed that for a given molecular weight, the average interpenetration contour length was found to be proportional to the mixing ratio. Monte Carlo analysis showed that the curvilinear diffusion coefficient is inversely proportional to the weight of polymer chains during diffusion.     

The kinetics of free radical polymerizing systems at low conversion, 1. On the rate determining step of the bimolecular termination reaction

Using a styrene bulk system as a model, this paper examines rates of termination at very low conversions in bulk and solution polymerizations. No definitive answer to the question of what determines such rates of termination is arrived at. Indeed, it is argued that on the basis of existing kinetic information, no such definitive answer is possible. However several things may be said with conviction. To begin with, it is rigorously shown that low conversion rates of termination cannot be explained by assuming that all radical chain end encounters result in termination, and then using center-of-mass diffusion coefficients of polymer in free solution to calculate rates of chain end encounter. However this does not mean that rates of center-of-mass diffusion do not determine rates of low conversion termination, as is shown; the idea that it may be the case that not all chain end encounters result in termination, this a manifestation of a spin multiplicity effect, is especially worthy of mention. It is also possible to explain low conversion rates of termination, as has traditionally been done, in terms of chain end motions being hindered by the presence of another polymer chain. However in concentrating on interactions between overlapping long chain macroradical coils, this traditional picture is certainly inaccurate, for it is shown that most termination interactions must involve at least one radical of shorter than expected degree of polymerization. This has the important consequence that an understanding of overall rates of dilute solution termination must be founded on an understanding of the diffusional behavior of the ends of short and intermediate length polymer chains.     

Structural modes of a polymer in the repton model

Using extensive computer simulations, the behavior of the structural modes-more precisely, the eigenmodes of a phantom Rouse polymer-are characterized for a polymer in the three-dimensional repton model and are used to study the polymer dynamics at time scales well before the tube renewal. Although these modes are not the eigenmodes for a polymer in the repton model, we show that numerically the modes maintain a high degree of statistical independence. The correlations in the mode amplitudes decay exponentially with (p∕N)(2)A(t), in which p is the mode number, N is the polymer length, and A(t) is a single function shared by all modes. In time, the quantity A(t) causes an exponential decay for the mode amplitude correlation functions for times <1; a stretched exponential with an exponent 1∕2 between times 1 and τ(R) ～ N(2), the time-scale for diffusion of tagged reptons along the contour of the polymer; and again an exponential decay for times t > τ(R). Having assumed statistical independence and the validity of a single function A(t) for all modes, we compute the temporal behavior of three structural quantities: the vectorial distance between the positions of the middle monomer and the center-of-mass, the end-to-end vector, and the vector connecting two nearby reptons around the middle of the polymer. Furthermore, we study the mean-squared displacement of the center-of-mass and the middle repton, and their relation with the temporal behavior of the modes.     

The dynamics of single chains within a model polymer melt

Discontinuous molecular dynamics simulations are performed on a system containing 32 hard chains of length 192 at a volume fraction of phi = 0.45 to explore the idea that localized entanglements have a significant effect on the dynamics of the individual chains within an entangled polymer melt. Anomalous behavior can still be observed when studying the dynamics of the individual chains, although increased time averaging causes the anomalous relaxation-memory-release behavior that was observed previously in the system to smooth out. First, the individual chain mean squared displacements and apparent diffusion coefficients are calculated, and a wide distribution of diffusive behavior is found. Although the apparent diffusion coefficient curve averaged over all chains displays the predicted long-time diffusive behavior, the curves for the individual chains differ both qualitatively and quantitatively. They display superdiffusive, diffusive, and subdiffusive behavior, with the largest percentage of chains exhibiting superdiffusive behavior and the smallest percentage exhibiting the predicted diffusive behavior. Next, the individual chain end-to-end vector autocorrelation functions and relaxation times are determined, and a wide distribution of stress relaxation behavior is found. The times when the end-to-end vector autocorrelation functions relax completely span almost an order of magnitude in reduced time. For some chains, the end-to-end vector autocorrelation function relaxes smoothly toward zero similar to the system average; however, for other chains the relaxation is slowed greatly, indicating the presence of additional entanglements. Almost half of the chains exhibit the anomalous behavior in the end-to-end vector autocorrelation function. Finally, the dynamic properties are displayed for a single chain exhibiting anomalous relaxation-memory-release behavior, supporting the idea that the relaxation-memory-release behavior is a single-chain property.     

Hybrid method coupling fluctuating hydrodynamics and molecular dynamics for the simulation of macromolecules

We present a hybrid computational method for simulating the dynamics of macromolecules in solution which couples a mesoscale solver for the fluctuating hydrodynamics (FH) equations with molecular dynamics to describe the macromolecule. The two models interact through a dissipative Stokesian term first introduced by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We show that our method correctly captures the static and dynamical properties of polymer chains as predicted by the Zimm model. In particular, we show that the static conformations are best described when the ratio sigma/b=0.6, where sigma is the Lennard-Jones length parameter and b is the monomer bond length. We also find that the decay of the Rouse modes' autocorrelation function is better described with an analytical correction suggested by Ahlrichs and Dunweg. Our FH solver permits us to treat the fluid equation of state and transport parameters as direct simulation parameters. The expected independence of the chain dynamics on various choices of fluid equation of state and bulk viscosity is recovered, while excellent agreement is found for the temperature and shear viscosity dependence of center of mass diffusion between simulation results and predictions of the Zimm model. We find that Zimm model approximations start to fail when the Schmidt number Sc < or approximately 30. Finally, we investigate the importance of fluid fluctuations and show that using the preaveraged approximation for the hydrodynamic tensor leads to around 3% error in the diffusion coefficient for a polymer chain when the fluid discretization size is greater than 50 A.