Brownian dynamics algorithm for bead-rod semiflexible chain with anisotropic friction

A model of semiflexible bead-rod chain with anisotropic friction can mimic closely the hydrodynamics of a slender filament. We present an efficient algorithm for Brownian dynamics simulations of this model with configuration dependent anisotropic bead friction coefficients. The algorithm is an extension of that given previously for the case of configuration independent isotropic friction coefficients by Grassia and Hinch [J. Fluid Mech. 308, 255 (1996)]. We confirm that the algorithm yields predicted values for various equilibrium properties. We also present a stochastic algorithm for evaluation of the stress tensor, and we show that in the limit of stiff chains the algorithm recovers the results of Kirkwood and Plock [J. Chem. Phys. 24, 665 (1956)] for rigid rods with hydrodynamic interactions.     

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)].     

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.     

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.     

Electroviscous sphere-wall interactions

A theoretical analysis is presented to determine the forces of interaction between an electrically charged spherical particle and a charged plane wall when the particle translates parallel to the wall and rotates around its axis in a symmetric electrolyte solution at rest. The electroviscous effects, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, derived from Cox's general theory [R.G. Cox, J. Fluid Mech. 338 (1997) 1], for electroviscous ion concentration, electroviscous potential and electroviscous flow field. It is a priori assumed that the double layer thickness surrounding each charged surfaces is much smaller than the particle size. Using the matched asymptotic expansion technique, the electroviscous forces experienced by the sphere are explicitly determined analytically for small particle-wall distances, but low and intermediate Peclet numbers.     

Comparison of Brownian dynamics algorithms with hydrodynamic interaction

The hydrodynamic interaction is an essential effect to consider in Brownian dynamics simulations of polymer and nanoparticle dilute solutions. Several mathematical approaches can be used to build Brownian dynamics algorithms with hydrodynamic interaction, the most common of them being the exact but time demanding Cholesky decomposition and the Chebyshev polynomial expansion. Recently, Geyer and Winter [J. Chem. Phys. 130, 1149051 (2009)] have proposed a new approximation to treat the hydrodynamic interaction that seems quite efficient and is increasingly used. So far, a systematic comparison among those approaches has not been clearly made. In this paper, several features and the efficiency of typical implementations of those approaches are evaluated by using bead-and-spring chain models. The different sensitivity to the bead overlap detected for the different implementations may be of interest to select the suitable algorithm for a given simulation.     

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.     

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.     

Nondriven Polymer Translocation Through a Nanopore:Scaling for Translocation Time with Chain Length

We investigated the dynamics of the passage for a polymer chain through a nanopore in the absence of any external driving force with Weeks-Chandler-Andersen potential in two-dimensional simulations, in particular, focused our attention on the scaling law of the mean translocation time. We found that the effect of hydrodynamic interactions is the major factor in determining the scaling exponents with increasing pore size. The scaling close to N1+2v was observed when the hydrodynamic interactions were screened in the cases of small pore sizes, while the scaling close to N3v was obtained when the hydrodynamic interactions were present in the cases of large pore sizes.     

Hydrodynamic screening near planar boundaries: effects on semiflexible polymer dynamics

The influence of hydrodynamic screening near a surface on the dynamics of a single semiflexible polymer is studied by means of Brownian dynamics simulations and hydrodynamic mean field theory. The polymer motion is characterized in terms of the mean squared displacements of the end-monomers, the end-to-end vector, and the scalar end-to-end distance. In order to control hydrodynamic screening effects, the polymer is confined to a plane at a fixed separation from the wall. When gradually decreasing this separation, a crossover from Zimm-type towards Rouse (free-draining) polymer dynamics is induced. However, this crossover is rather slow and the free-draining limit is not completely reached--substantial deviations from Rouse-like dynamics are registered in both simulations and theory--even at distances of the polymer from the wall on the order of the monomer size. Remarkably, the effect of surface-induced screening of hydrodynamic interactions sensitively depends on the type of dynamic observable considered. For vectorial quantities such as the end-to-end vector, hydrodynamic interactions are important and therefore surface screening effects are sizeable. For a scalar quantity such as the end-to-end distance, on the other hand, hydrodynamic interactions are less important, but a pronounced dependence of dynamic scaling exponents on the persistence length to contour length ratio becomes noticeable. Our findings are discussed against the background of single-molecule experiments on f-actin [L. Le Goff et al., Phys. Rev. Lett. 89, 258101 (2002)].     

Theoretical analysis and computer simulation of fluorescence lifetime measurements. I. Kinetic regimes and experimental time scales

The configuration-controlled regime and the diffusion-controlled regime of conformation-modulated fluorescence emission are systematically studied for Markovian and non-Markovian dynamics of the reaction coordinate. A path integral simulation is used to model fluorescence quenching processes on a semiflexible chain. First-order inhomogeneous cumulant expansion in the configuration-controlled regime defines a lower bound for the survival probability, while the Wilemski-Fixman approximation in the diffusion-controlled regime defines an upper bound. Inclusion of the experimental time window of the fluorescence measurement adds another dimension to the two kinetic regimes and provides a unified perspective for theoretical analysis and experimental investigation. We derive a rigorous generalization of the Wilemski-Fixman approximation [G. Wilemski and M. Fixman, J. Chem. Phys. 60, 866 (1974)] and recover the 1/D expansion of the average lifetime derived by Weiss [G. H. Weiss, J. Chem. Phys. 80, 2880 (1984)].     

Fourth‐order hydrodynamic contribution to the polymer self‐diffusion coefficient

A hydrodynamic scattering treatment of interacting polymer chains is extended to obtain the five‐point chain–chain–chain–chain–chain hydrodynamic interaction tensor. The tensor is used to calculate the second‐order concentration correction to the self‐diffusion coefficient of a polymer in solution. The self‐similarity assumption of the hydrodynamic scaling model of polymer dynamics is tested against these calculations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1663–1670, 2004     

Sliding friction between polymer surfaces: a molecular interpretation

For two contacting rigid bodies, the friction force F is proportional to the normal load and independent of the macroscopic contact area and relative velocity V (Amonton's law). With two mutually sliding polymer samples, the surface irregularities transmit deformation to the underlying material. Energy loss along the deformation cycles is responsible for the friction force, which now appears to depend strongly on V [see, e.g., N. Maeda et al., Science 297, 379 (2002)]. We base our theoretical interpretation on the assumption that polymer chains are mainly subjected to oscillatory "reptation" along their "tubes." At high deformation frequencies-i.e., with a large sliding velocity V-the internal viscosity due to the rotational energy barriers around chain bonds hinders intramolecular mobility. As a result, energy dissipation and the correlated friction force strongly diminish at large V. Derived from a linear differential equation for chain dynamics, our results are basically consistent with the experimental data by Maeda et al. [Science 297, 379 (2002)] on modified polystyrene. Although the bulk polymer is below T(g), we regard the first few chain layers below the surface to be in the liquid state. In particular, the observed maximum of F vs V is consistent with physically reasonable values of the molecular parameters. As a general result, the ratio FV is a steadily decreasing function of V, tending to V(-2) for large velocities. We evaluate a much smaller friction for a cross-linked polymer under the assumption that the junctions are effectively immobile, also in agreement with the experimental results of Maeda et al. [Science 297, 379 (2002)].     

Molecular simulation of the shear viscosity and the self-diffusion coefficient of mercury along the vapor-liquid coexistence curve

In earlier work [G. Raabe and R. J. Sadus, J. Chem. Phys. 119, 6691 (2003)] we reported that the combination of an accurate two-body ab initio potential with an empirically determined multibody contribution enables the prediction of the phase coexistence properties, the heats of vaporization, and the pair distribution functions of mercury with reasonable accuracy. In this work we present molecular dynamics simulation results for the shear viscosity and self-diffusion coefficient of mercury along the vapor-liquid coexistence curve using our empirical effective potential. The comparison with experiment and calculations based on a modified Enskog theory shows that our multibody contribution yields reliable predictions of the self-diffusion coefficient at all densities. Good results are also obtained for the shear viscosity of mercury at low to moderate densities. Increasing deviations between the simulation and experimental viscosity data at high densities suggest that not only a temperature-dependent but also a density-dependent multibody contribution is necessary to account for the effect of intermolecular interactions in liquid metals. An analysis of our simulation data near the critical point yields a critical exponent of beta = 0.39, which is identical to the value obtained from the analysis of the experimental saturation densities.     

Dynamics of self-assembled chaining in magnetorheological fluids

The aggregation dynamics of paramagnetic spherical particles embedded in a viscous fluid is investigated via numerical simulations using a fully coupled three-dimensional model. Particles experience simultaneously Brownian motion, dipolar magnetic attraction, and multibody hydrodynamic interactions. When the dipole strength characterizing the ratio of magnetic attraction to random diffusion exceeds a critical value, particles join together forming supraparticle structures. As time evolves, particle/chain and chain/ chain interactions lead to a continuous increase of the cluster size. The mean length of particle chains has a power-law dependence with respect to time, as predicted by the theory of diffusion-limited aggregation. Both the exponent and the characteristic time scale agree very well with the experimental results of Promislow et al.     

How a single stretched polymer responds coherently to a minute oscillation in fluctuating environments: An entropic stochastic resonance

Within the cell, biopolymers are often situated in constrained, fluid environments, e.g., cytoskeletal networks, stretched DNAs in chromatin. It is of paramount importance to understand quantitatively how they, utilizing their flexibility, optimally respond to a minute signal, which is, in general, temporally fluctuating far away from equilibrium. To this end, we analytically study viscoelastic response and associated stochastic resonance in a stretched single semi-flexible chain to an oscillatory force or electric field. Including hydrodynamic interactions between chain segments, we evaluate dynamics of the polymer extension in coherent response to the force or field. We find power amplification factor of the response at a noise-strength (temperature) can attain the maximum that grows as the chain length increases, indicative of an entropic stochastic resonance (ESR). In particular for a charged chain under an electric field, we find that the maximum also occurs at an optimal chain length, a new feature of ESR. The hydrodynamic interaction is found to enhance the power amplification, representing unique polymer cooperativity which the fluid background imparts despite its overdamping nature. For the slow oscillatory force, the resonance behavior is explained by the chain undulation of the longest wavelength. This novel ESR phenomenon suggests how a biopolymer self-organizes in an overdamping environment, utilizing its flexibility and thermal fluctuations.     

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.     

Viscoelastic properties of an isolated polymer chain with arbitrary flexibility,chain length and hydrodynamic interactions from 4‐dimensional Dirac propagator

Kholodenko's theory of semiflexible polymer chains, the conformation and properties of which are obtained from the Dirac propagator, shows applicability to dilute solutions of semiflexible polymers of arbitrary persistence and contour lengths by calculating the static scattering function and the squared end‐to‐end distance of the polymer chain. In the present work, the theory is extended and applied to obtain the intrinsic viscosity with consideration of hydrodynamic interactions. The intrinsic viscosity formula is derived as function of chain length and persistence length. The hydrodynamic interactions are also taken into account following the Kirkwood and Riseman scheme. From this calculation, we obtain the general expression for the intrinsic viscosity and diffusion coefficients covering the whole range of chain flexibilities without confusion with the excluded volume effects. Calculated limiting values of hydrodynamical observables are in complete agreement with those known for random coils and rigid rods.