良溶剂中环形高分子单链的结构与动力学性质的模拟研究

本文采用多粒子碰撞动力学与分子动力学耦合的模拟方法研究了环形高分子单链在良溶剂中的静态与动态性质,并与线形分子进行了对比.研究发现,环形高分子链内粒子之间的平均距离小于线形链,即粒子排列得更加紧密;相应的均方回转半径也小于线形链,线形链与环形链的均方回转半径的比值为1.77;同时,环形链扩散的速度也比线形链快,两者比值为1.10.模拟结果揭示了扩散行为是排斥体积作用和流体力学相互作用耦合的结果,在扩散过程中,流体力学相互作用消减了排斥体积作用对扩散行为的贡献.此外,通过对有和没有流体力学相互作用的多粒子碰撞动力学得到的结果作对比,研究了流体力学相互作用对高分子静态和动态行为的影响,结果表明,流体力学相互作用使高分子链在极稀溶液中的扩散速度变快.     

Mesoscopic description of solvent effects on polymer dynamics

Solvent effects on polymer dynamics and structure are investigated using a mesoscopic solvent model that accounts for hydrodynamic interactions among the polymer beads. The simulation method combines molecular dynamics of the polymer chain, interacting with the solvent molecules through intermolecular forces, with mesoscopic multiparticle collision dynamics for the solvent molecules. Changes in the intermolecular forces between the polymer beads and mesoscopic solvent molecules are used to vary the solvent conditions from those for good to poor solvents. Polymer collapse and expansion dynamics following changes in solvent conditions are studied for homopolymer and block copolymer solutions. The frictional properties of polymers are also investigated.     

高分子动力学的单链模型

高分子单链模型是高分子稀溶液理论研究的基本模型.对其进行深入地分析,不仅有助于解决高分子稀溶液体系中溶液黏度和分子链扩散等基本问题,而且能够增进人们对高分子链结构与溶液性质间关联性的理解.虽然基于经典连续性介质力学的流体动力学理论可以定性,甚至半定量地获得稀溶液的一些重要性质,但是,随着科学技术的发展,人们从分子水平上建立了许多描述高分子稀溶液性质的模型和理论,期望能够定量地描述高分子稀溶液的性质.本文以高分子稀溶液中3个典型的单链模型为例(包括:不含流体力学相互作用的Rouse模型、含二体流体力学相互作用的Zimm模型和含多体流体力学相互作用的部分穿透球模型),综述高分子稀溶液的重要性质,并详细地给出其动力学方程的推导过程及其重要的研究进展.特别是,对于Rouse模型,本文还将其预言结果拓展到了短链高分子流体体系;此外,还介绍了这一领域的关键科学问题、发展前景和研究方向.     

Effect of molecular topology on the transport properties of dendrimers in dilute solution at Theta temperature: a Brownian dynamics study

Structure and transport properties of dendrimers in dilute solution are studied with the aid of Brownian dynamics simulations. To investigate the effect of molecular topology on the properties, linear chain, star, and dendrimer molecules of comparable molecular weights are studied. A bead-spring chain model with finitely extensible springs and fluctuating hydrodynamic interactions is used to represent polymer molecules under Theta conditions. Structural properties as well as the diffusivity and zero-shear-rate intrinsic viscosity of polymers with varied degrees of branching are analyzed. Results for the free-draining case are compared to and found in very good agreement with the Rouse model predictions. Translational diffusivity is evaluated and the difference between the short-time and long-time behavior due to dynamic correlations is observed. Incorporation of hydrodynamic interactions is found to be sufficient to reproduce the maximum in the intrinsic viscosity versus molecular weight observed experimentally for dendrimers. Results of the nonequilibrium Brownian dynamics simulations of dendrimers and linear chain polymers subjected to a planar shear flow in a wide range of strain rates are also reported. The flow-induced molecular deformation of molecules is found to decrease hydrodynamic interactions and lead to the appearance of shear thickening. Further, branching is found to suppress flow-induced molecular alignment and deformation.     

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 Soret effect in dilute polymer solutions: influence of chain length, chain stiffness, and solvent quality

Thermal diffusion in dilute polymer solutions is studied by reverse nonequilibrium molecular dynamics. The polymers are represented by a generic bead-spring model. The influence of the solvent quality on the Soret coefficient is investigated. At constant temperature and monomer fraction, a better solvent quality causes a higher affinity for the polymer to the cold region. This may even go to thermal-diffusion-induced phase separation. The sign of the Soret coefficient changes in a symmetric nonideal binary Lennard-Jones solution when the solvent quality switches from good to poor. The known independence of the thermal diffusion coefficients of the molecular weight is reproduced for three groups of polymers with different chain stiffnesses. The thermal diffusion coefficients reach constant values at chain lengths of around two to three times the persistence length. Moreover, rigid polymers have higher Soret coefficients and thermal diffusion coefficients than more flexible polymers.     

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.     

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.     

Flow-induced translocation of polymers through a fluidic channel: a dissipative particle dynamics simulation study

The dynamics of flow-induced translocation of polymers through a fluidic channel has been studied by dissipative particle dynamics (DPD) approach. Unlike implicit solvent models, the many-body energetic and hydrodynamic interactions are preserved naturally by incorporating explicit solvent particles in this approach. The no-slip wall boundary and the adaptive boundary conditions have been implemented in the modified DPD approach to model the hydrodynamic flow within a specific wall structure of fluidic channel and control the particles' density fluctuations. The results show that the average translocation time versus polymer chain length satisfies a power-law scaling of τ ～N(1.152). The conformational changes and translocation dynamics of polymers through the fluidic channel have also been investigated in our simulations, and two different translocation processes, i.e., the single-file and double-folded translocation events, have been observed in detail. These findings may be helpful in understanding the conformational and dynamic behaviors of such polymer and/or DNA molecules during the translocation processes.     

Brownian dynamics simulations of a flexible polymer chain which includes continuous resistance and multibody hydrodynamic interactions

Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the "freely draining" case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.     

Lattice cluster theory of associating polymers. IV. Phase behavior of telechelic polymer solutions

The newly developed lattice cluster theory (in Paper I) for the thermodynamics of solutions of telechelic polymers is used to examine the phase behavior of these complex fluids when effective polymer-solvent interactions are unfavorable. The telechelics are modeled as linear, fully flexible, polymer chains with mono-functional stickers at the two chain ends, and these chains are assumed to self-assemble upon cooling. Phase separation is generated through the interplay of self-assembly and polymer/solvent interactions that leads to an upper critical solution temperature phase separation. The variations of the boundaries for phase stability and the critical temperature and composition are analyzed in detail as functions of the number M of united atom groups in a telechelic chain and the microscopic nearest neighbor interaction energy ε(s) driving the self-assembly. The coupling between self-assembly and unfavorable polymer/solvent interactions produces a wide variety of nontrivial patterns of phase behavior, including an enhancement of miscibility accompanying the increase of the molar mass of the telechelics under certain circumstances. Special attention is devoted to understanding this unusual trend in miscibility.     

A Brownian dynamics study on the self-diffusion of charged tracers in dilute polyelectrolyte solutions

Brownian dynamics simulations with hydrodynamic interactions are conducted to investigate the self-diffusion of charged tracer particles in a dilute solution of charged polymers, which are modeled by bead-spring chains. The Debye-Hückel approximation is used for the electrostatic interactions. The hydrodynamic interactions are implemented by the Ewald summation of the Rotne-Prager tensor. Our simulations find that the difference in short- and long-time diffusivities is very slight in uncharged short-chain solutions. For charged systems, to the contrary, the difference becomes considerable. The short-time diffusivity is found to increase with increasing chain length, while an opposite behavior is obtained for the long-time diffusivity. The former is attributed to the hydrodynamic screening among beads in a same chain due to the bead connectivity. The latter is explained by the memory effect arising from the electrostatic repulsion and chain length. The incorporation of hydrodynamic interactions improves the agreement between the simulation prediction and the experimental result.     

流场驱动高分子链迁移穿过微通道的耗散粒子动力学模拟

利用耗散粒子动力学模拟方法研究了高分子链在流场驱动作用下迁移穿过微通道过程中的链构象变化和动力学行为.在足够大的流场力驱动作用下,高分子链在沿着流场方向逐渐被拉伸,从而能够穿过管径小于其自身尺寸的微通道.耗散粒子动力学模拟结果表明高分子链的迁移过程主要分为3个步骤:(1)在流场驱动作用下,高分子链漂移并逐渐靠近微通道入口;(2)高分子链逐渐调整自身构象,并使其部分进入微通道;(3)高分子链成功穿过微通道.同时,模拟还发现当高分子链尺寸大于微通道细管道管径时,高分子链穿过微通道所需的平均迁移时间随着流量的增加而逐渐减小.此外,为了研究高分子链刚性对高分子链穿过微通道的影响,模型中还引入了蠕虫状高分子链模型.模拟结果发现,高分子链的链刚性越强,其迁移穿过微通道的时间越长.     

Two-particle friction in a mesoscopic solvent

The effects of hydrodynamic interactions on the friction tensors for two particles in solution are studied. The particles have linear dimensions on nanometer scales and are either simple spherical particles interacting with the solvent through repulsive Lennard-Jones forces or are composite cluster particles whose atomic components interact with the solvent through repulsive Lennard-Jones forces. The solvent dynamics is modeled at a mesoscopic level through multiparticle collisions that conserve mass, momentum, and energy. The dependence of the two-particle relative friction tensors on the interparticle separation indicates the importance of hydrodynamic interactions for these nanoparticles.     

Motion of star‐branched chains in polymer networks: a Monte Carlo study

A simple model of branched polymers in confined space is developed. Star‐branched polymer molecules are built on a simple cubic lattice with excluded volume and no attractive interactions (good solvent conditions). A single star molecule is trapped in a network of linear polymer chains of restricted mobility. The simulations are carried out using the classical Metropolis algorithm. Static and dynamic properties of the star‐branched polymer are determined using various networks. The dependence of the longest relaxation time and the self‐diffusion coefficient on chain length and network properties are discussed and the proper scaling laws formulated. The possible mechanism of motion is discussed. The differences between the motion of star‐branched polymers in such a network are compared with the cases of a dense matrix of linear chains and regular rod‐like obstacles.     

Stochastic entangled chain dynamics of dense polymer solutions

We propose an adjustable-parameter-free, entangled chain dynamics model of dense polymer solutions. The model includes the self-consistent dynamics of molecular chains and solvent by describing the former via coarse-grained polymer dynamics that incorporate hydrodynamic interaction effects, and the latter via the forced Stokes equation. Real chain elasticity is modeled via the inclusion of a Pincus regime in the polymer's force-extension curve. Excluded volume effects are taken into account via the combined action of coarse-grained intermolecular potentials and explicit geometric tracking of chain entanglements. We demonstrate that entanglements are responsible for a new (compared to phantom chain dynamics), slow relaxation mode whose characteristic time scale agrees very well with experiment. Similarly good agreement between theory and experiment is also obtained for the equilibrium chain size. We develop methods for the solution of the model in periodic flow domains and apply them to the computation of entangled polymer solutions in equilibrium. We show that the number of entanglements Π agrees well with the number of entanglements expected on the basis of tube theory, satisfactorily reproducing the latter's scaling of Π with the polymer volume fraction φ. Our model predicts diminishing chain size with concentration, thus vindicating Flory's suggestion of excluded volume effects screening in dense solutions. The predicted scaling of chain size with φ is consistent with the heuristic, Flory theory based value.     

The effect of hydrodynamic interactions on the dynamics of DNA translocation through pores

In this work, we investigate the effect of hydrodynamic interactions on the dynamics of DNA translocation through micropores. We simulate DNA as a bead-spring chain and use a lattice Boltzmann method to simulate the flow field that arises from the motion of the molecule. We investigate the free-draining entrance of DNA to the pore by diffusion and find that, consistent with experiments, molecules have a higher probability of entering the pore from one end. We then consider the electric-field driven translocation of 21-210 microm DNA with and without hydrodynamic interactions. Consistent with experiments, we study translocation events that are much shorter than the relaxation time of DNA. We find that the effect of hydrodynamic interactions on this process is to cause different regions of a molecule, other than the ones pulled by voltage or chain connectivity into the pore, to move toward the pore. We quantify this effect and show that it is smaller than the difference in the translocation dynamics of chains that arises from different initial configurations of the molecules. A power-law scaling of translocation time with chain length is observed, with exponents of 1.28+/-0.03 and 1.31+/-0.03 in simulations with and without hydrodynamic interactions, respectively. Our results are in good agreement with recent translocation experiments conducted in small pores and show that, for the regime considered in this work, hydrodynamic interactions play a minor role in the relation of the translocation time to chain length. For fast translocation processes, the effect of hydrodynamic interactions is local and the main factor determining the dynamics of DNA is the initial configuration of the molecules.     

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.     

Equilibrium conformational dynamics of a polymer in a solvent

Molecular dynamics simulations were used to study the conformational dynamics of a bead-spring model polymer in an explicit solvent under good solvent conditions. The dynamics of the polymer chain were investigated using an analysis of the time autocorrelation functions of the Rouse coordinates of the polymer chain. We have investigated the variation of the correlation functions with polymer chain length N, solvent density rho, and system size. The measured initial decay rates gamma(p) of the correlation functions were compared with the predictions from a theory of polymer dynamics which uses the Oseen tensor to describe hydrodynamic interactions between monomers. Over the range of chain lengths considered (N = 30-60 monomers), the predicted scaling of gamma(p) proportional to N(-3nu) was observed at high rho, where nu is the polymer scaling exponent. The predicted gamma(p) are generally higher than the measured values. This discrepancy increases with decreasing rho, as a result in the breakdown in the conditions required for the Oseen approximation. The agreement between theory and simulation at high rho improves considerably if the theoretical expression for gamma(p) is modified to avoid sum-to-integral approximations, and if the values of (R(p)2), which are used in the theory, are taken directly from the simulation rather than being calculated using approximate scaling relations. The observed finite-size scaling of gamma(p) is not quantitatively consistent with the theoretical predictions.