Molecular dynamics study of tethered polymers in shear flow

Single macromolecules can now be isolated and characterized experimentally using techniques such as optical tweezers and videomicroscopy. An interesting and important single-molecule problem is that of the dynamics of a polymer chain tethered to a solid surface and subjected to a shear flow. An experimental study of such a system was reported by Doyle et al. (Phys. Rev. Lett. 84, 4769 (2000)), and their results showed a surprising recirculating motion of the DNA chain. We explore this problem using molecular dynamics computer simulations with explicit hydrodynamic interactions. The dynamical properties of a Freely Jointed Chain (FJC) with Finitely Extensible Nonlinear Elastic (FENE) links are examined in similar conditions (i.e., confined between two surfaces and in the presence of a Poiseuille flow). We see the remarkable cyclic polymer motion observed experimentally, and we show that a simple cross-correlation function can be used to measure the corresponding period of motion. We also propose a new empirical equation relating the magnitude of the shear flow to the amount of chain deformation, an equation that appears to apply for both weak and strong flows. Finally, we report on packing effects near the molecularly flat wall, an associated chain-sticking phenomenon, and the impact of the chain hydrodynamic drag on the local fluid flow.     

Stochastic Event-Driven Molecular Dynamics

A novel Stochastic Event-Driven Molecular Dynamics (SEDMD) algorithm is developed for the simulation of polymer chains suspended in a solvent. SEDMD combines event-driven molecular dynamics (EDMD) with the Direct Simulation Monte Carlo (DSMC) method. The polymers are represented as chains of hard-spheres tethered by square wells and interact with the solvent particles with hard-core potentials. The algorithm uses EDMD for the simulation of the polymer chain and the interactions between the chain beads and the surrounding solvent particles. The interactions between the solvent particles themselves are not treated deterministically as in EDMD, rather, the momentum and energy exchange in the solvent is determined stochastically using DSMC. The coupling between the solvent and the solute is consistently represented at the particle level retaining hydrodynamic interactions and thermodynamic fluctuations. However, unlike full MD simulations of both the solvent and the solute, in SEDMD the spatial structure of the solvent is ignored. The SEDMD algorithm is described in detail and applied to the study of the dynamics of a polymer chain tethered to a hard-wall subjected to uniform shear. SEDMD closely reproduces results obtained using traditional EDMD simulations with two orders of magnitude greater efficiency. Results question the existence of periodic (cycling) motion of the polymer chain.     

Hybrid MC/RISM technique for simulation of polymer solutions: Monte Carlo+ RISM integral equations

A new (hybrid) method is reported for modelling complex macromolecular systems. The approach combines the traditional atomistic Monte Carlo (MC) computer simulation of flexible polymer chains with the numerical solution of the site-site Ornstein-Zernike-like (RISM) integral equations. The method is used for calculating properties of a linear polymer in dilute solution. Since the condensed-phase environment of a flexible macromolecule affects the equilibrium configuration probability distribution of the macromolecule, the site-site intramolecular correlation function and the intramolecular potential field are treated in a self-consistent manner. Briefly, the MC method is applied to generate the configurations of a single chain molecule. Using the coordinates of chain beads, the averaged intrapolymer correlation function is obtained. Then, solving the coupled RISM equations for a given density of solvent particles, we find the polymer-solvent correlation functions. This yields the medium-induced intrapolymer potential and the corresponding effective intramolecular energies, which are used in the standard Metropolis MC procedure. The structural properties of the polymer chain are computed by averaging over the statistically representative set of configurations. As a result of many such iterations, the intramolecular structure is determined self-consistently. Using the hybrid MC/RISM method, extensive studies have been made of static properties of flexible polymer chains surrounded by LJ particles with purely repulsive interactions between the particles and chain beads. Also, direct molecular dynamics simulations have been carried out and have demonstrated that the hybrid MC/RISM approach gives a quite accurate prediction for condensed-phase effects.     

Hybrid Particle–Continuum Simulations of Polymer Brushes in Shear Flow

A hybrid particle–continuum method is used to study the shear flow confined between two opposing walls, one of which is coated with polymer chains. Molecular dynamics (MD) is used in the particle region near the brush and Navier–Stokes (NS) equations are applied in the remaining region where the continuum assumption holds. The information exchange from the continuum region to the particle region is implemented using the constrained particle dynamics. Both Couette shear flow and oscillatory flow are considered in the present work. The effect of the shear flow on the conformational characteristics of polymer brushes is analyzed. In the overlap region, the velocities obtained from MD simulations are smoothly connected with those from NS equations. Our investigations demonstrate that the hybrid particle–continuum model is valid in exploring the shear behavior of polymer brushes.     

自扩散泳微观转动马达的介观模拟

转动的微尺度马达是一类重要的微流器件.近年来,因为其重要的应用及理论价值引起了学术界的广泛关注.本文提出了一种新型的自扩散泳驱动的微观转动马达模型.通过介观动力学模拟,验证了该模型的有效性.模拟结果表明,该自扩散泳微观转动马达可以单向地自驱动转动,并且转动速度和马达表面发生的催化化学反应速率(即自产生的浓度梯度场强弱)、以及液体分子与马达之间的相互作用有关.此外,研究了两个转动马达共存时的运动行为,重点考察了马达之间的流体力学相互作用和浓度梯度场效应对马达转动的影响.该自扩散泳微观转动马达为设计实用的微流器件提供了新的思路和参考,也为研究活性胶体系统的集体行为提供了理想模型.     

微通道中流体流动的分子动力学模拟

本文建立了周期外力作用下流体在微通道间流动模型.以此模型为基础,模拟计算了氩在亲水性和憎水性平行平板壁面间的流动过程,并对速度分布、温度分布等进行了统计.模拟结果表明在憎水性壁面附近,易观察到速度滑移和温度阶跃现象,而亲水性壁面上则反之.与N-S方程和能量方程的解进行了比较,亲水性通道速度和温度的模拟结果与分析解吻合较好,憎水性通道的模拟结果与分析解相差较大.同时,对300℃下不同密度水的流动进行了模拟,随着密度的增大,在壁面附近流体流动特性发生了变化.     

Imaging of Flow Patterns with Fluorescent Molecular Rotors

Molecular rotors are a group of fluorescent molecules that form twisted intramolecular charge transfer states (TICT) upon photoexcitation. Some classes of molecular rotors, among them those that are built on the benzylidene malononitrile motif, return to the ground state either by nonradiative intramolecular rotation or by fluorescence emission. In low-viscosity solvents, intramolecular rotation dominates, and the fluorescence quantum yield is low. Higher solvent viscosities reduce the intramolecular rotation rate, thus increasing the quantum yield. We recently described a different mechanism whereby the fluorescence quantum yield of the molecular rotor also depends on the shear stress of the solvent. In this study, we examined a possible application for shear-sensitive molecular rotors for imaging flow patterns in fluidic chambers. Flow chambers with different geometries were constructed from polycarbonate or acrylic. Solutions of molecular rotors in ethylene glycol were injected into the chamber under controlled flow rates. LED-induced fluorescence (LIF) images of the flow chambers were taken with a digital camera, and the intensity difference between flow and no-flow images was visualized and compared to computed fluid dynamics (CFD) simulations. Intensity differences were detectable with average flow rates as low as 0.1 mm/s, and an exponential association between flow rate and intensity increase was found. Furthermore, a good qualitative match to computed fluid dynamics simulations was seen. On the other hand, prolonged exposure to light reduced the emission intensity. With its high sensitivity and high spatial and temporal resolution, imaging of flow patterns with molecular rotors may become a useful tool in microfluidics, flow measurement, and control.     

Cyclic motion of a grafted polymer under shear flow

The long-time dynamics of a single end-tethered chain under shear flow are studied using molecular and Brownian dynamics simulations of a flexible polymer. As observed in previous experiments with tethered DNA [Phys. Rev. Lett. 84, 4769 (2000)], under a flow sheared at constant rate the chain performs a cyclic motion. But, contrary to what has been previously suggested, a well-defined characteristic period exists and it is clearly revealed in the cross spectra of the chain extension along flow and gradient directions. The main cycling time scales like the time needed to stretch the polymer by convection, being about 10 times the relaxation time of the chain in flow. This coherent recursive motion introduces long memory in the fluid and suggests resonance effects under periodic external forcing.     

Lattice boltzmann versus molecular dynamics simulation of nanoscale hydrodynamic flows

A fluid flow in a simple dense liquid, passing an obstacle in a two-dimensional thin film geometry, is simulated by molecular dynamics (MD) computer simulation and compared to results of lattice Boltzmann (LB) simulations. By the appropriate mapping of length and time units from LB to MD, the velocity field as obtained from MD is quantitatively reproduced by LB. The implications of this finding for prospective LB-MD multiscale applications are discussed.     

Influence of dispersive long-range interactions on properties of vapour–liquid equilibria and interfaces of binary Lennard-Jones mixtures

The influence of dispersive long-range interactions on properties of vapour–liquid equilibria and interfaces of six binary Lennard-Jones (LJ) mixtures was studied by molecular dynamics (MD) simulations and density gradient theory (DGT). The mixtures were investigated at a constant temperature T, at which the low-boiling component, which is the same in all mixtures, is subcritical. Two different high-boiling components were considered: one is subcritical, the other is supercritical at T. Furthermore, the unlike dispersive interaction was varied such that mixtures with three different types of phase behaviour were obtained: ideal, low-boiling azeotrope, and high-boiling azeotrope. In a first series of simulations, the full LJ potential was used to describe these mixtures. To assess the influence of the long-range interactions, these results were compared with simulations carried out with the LJ truncated and shifted (LJTS) potential applying the corresponding states principle. The dispersive long-range interactions have a significant influence on the surface tension and the interfacial thickness of the studied mixtures, whereas the relative adsorption and the enrichment are hardly affected. Furthermore, the influence of the long-range interactions on Henry's law constants and the phase envelopes of the vapour–liquid equilibrium was investigated. The long-range interactions have practically no influence on the composition dependency of the investigated mixture properties.     

A comprehensive molecular dynamics study of a single polystyrene chain in a good solvent

In this study, molecular characteristics of polystyrene (PS) was calculated measuring its dilute-solution properties in toluene at 288.15 K via molecular dynamics (MD) simulations. The solution models consisted of PS chains with different number of repeating units all of which were in a dilute regime. In order to investigate the compatibility between the polymer and the solvent molecules, interaction energy and Flory-Huggins (FH) interaction parameter were estimated. The simulation results indicate that increasing the chain repeating units enhanced the interaction between the solute and the solvent. Additionally, the chain dimensions were evaluated calculating the radius of gyration (R_g) and end-to-end distance, r0. To determine the dynamic behavior of the chains in the solutions, mean square displacement (MSD) and diffusivity coefficient were calculated. The simulation results indicated that the chain rigidity at low molecular weight and chain flexibility with increasing the molecular weight influenced chains dynamic behavior and diffusivity. Moreover, radial distribution function (RDF) illustrated the effect of steric hindrance of the chains in dilute solution on capturing the solvent molecules. In addition, solution viscosity was calculated by performing non-equilibrium molecular dynamics simulation (NEMD). The obtained results of chain characteristics and viscosity showed a good agreement with experimental results published previously. This agreement confirms the accuracy of the applied simulation method to characterize the dilute solutions and the chains characteristics.     

Molecular-dynamics simulations with explicit hydrodynamics I: On the friction coefficients of deformed polymers

We implement large-scale Molecular-Dynamics (MD) simulations which incorporate hydrodynamic interactions via the inclusion of explicit Lennard-Jones solvent to examine the behaviour of polymer chains in sieving media. We begin by examining the friction coefficients of polymers in long-lived states responsible for inducing length-dependent mobility, i.e., allowing separation of polymers (or polyelectrolytes) by molecular weight. In particular, the conformations we examine occur in devices which utilize arrays of molecular obstacles or dilute solutions of polymers. We compare the results from our MD simulations with expressions from macroscopic hydrodynamics for four specific cases: i) a random coil excluded-volume Zimm polymer, ii) a rigid polymer moving perpendicular to its major axis iii) a rigid polymer moving parallel to its major axis and iv) a rigid polymer, folded at different points along its contour. We also examine the behaviour of the friction coefficient of a fully flexible molecule pulled by its middle monomer as a function of an applied force F and show that there are several distinct frictional regimes.PACS: 83.10.Mj Molecular dynamics, Brownian dynamics - 61.41. + e Polymers, elastomers, and plastics - 82.20.Wt Computational modeling; simulation     

Perturbation and variational approach for the equation of state for hard-sphere and Lennard-Jones fluids

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard–Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.     

Simple theoretical model of shear viscosity in isotopic fluid mixtures

We propose a simple hybrid model for the shear viscosity of isotopic fluid mixtures by coupling the contribution of the Stokes–Einstein relation with the existing linear model of Roults's law for the shear viscosity. The calculated values of shear viscosity using this simple hybrid model are found to be in excellent agreement with the molecular dynamics (MD) simulation results. The calculated value of the shear viscosity obtained from the theoretical model as well as the MD simulation increases with increasing mass ratio.     

Roles of V/III ratio and mixture degree in GaN growth: CFD and MD simulation study

To understand the mechanism of Gallium nitride (GaN) film growth is of great importance for their potential applica- tions. In this paper, we investigate the growth behavior of the GaN film by combining computational fluid dynamics (CFD) and molecular dynamics (MD) simulations. Both of the simulations show that V/III mixture degree can have important impacts on the deposition behavior, and it is found that the more uniform the mixture is, the better the growth is. Besides, by using MD simulations, we illustrate the whole process of the GaN growth. Furthermore, we also find that the V/III ratio can affect the final roughness of the GaN film. When the V/III ratio is high, the surface of final GaN film is smooth. The present study provides insights into GaN growth from the macroscopic and microscopic views, which may provide some suggestions on better experimental GaN preparation.     

A classical density functional approach to depletion interaction of Lennard-Jones binary mixtures

In this article, we apply classical density functional theory to investigate the characteristics of depletion interaction in Lennard-Jones (LJ) binary fluid mixtures. First, to confirm the validity of our adopted density functional formalism, we calculate the radial distribution functions using a theoretical approach and compare them with results obtained by molecular dynamics simulation. Then, this approach is applied to two colloids immersed in LJ solvent systems. We investigate the variation of depletion interaction with respect to the distance of two colloids in LJ binary systems. We find that depletion interaction may be attractive or repulsive, mostly depending on the bulk density of the solvent and the temperature of the binary system. For high bulk densities, the repulsive barrier of depletion force is remarkable when the total excluded volume of colloids touches each other and reaches a maximum. The height of the repulsive barrier is related to the parameters of the LJ potential and bulk density. Moreover, the depletion force may exhibit attractive wells if the bulk density of the solvent is low. The attractive well tends to appear when the surface–surface distance of colloids is half of the size of the polymer and deepens with temperature lowering in a fixed bulk density. In contrast with the hard-sphere system, no oscillation of depletion potential around zero is observed.     

Crooks Fluctuation Theorem for Single Polymer Dynamics in Time-Dependent Flows: Understanding Viscoelastic Hysteresis

Nonequilibrium work relations have fundamentally advanced our understanding of molecular processes. In recent years, fluctuation theorems have been extensively applied to understand transitions between equilibrium steady-states, commonly described by simple control parameters such as molecular extension of a protein or polymer chain stretched by an external force in a quiescent fluid. Despite recent progress, far less is understood regarding the application of fluctuation theorems to processes involving nonequilibrium steady-states such as those described by polymer stretching dynamics in nonequilibrium fluid flows. In this work, we apply the Crooks fluctuation theorem to understand the nonequilibrium thermodynamics of dilute polymer solutions in flow. We directly determine the nonequilibrium free energy for single polymer molecules in flow using a combination of single molecule experiments and Brownian dynamics simulations. We further develop a time-dependent extensional flow protocol that allows for probing viscoelastic hysteresis over a wide range of flow strengths. Using this framework, we define quantities that uniquely characterize the coil-stretch transition for polymer chains in flow. Overall, generalized fluctuation theorems provide a powerful framework to understand polymer dynamics under far-from-equilibrium conditions.     

高超声速可压缩流中粗糙壁热流研究

用计算流体力学（CFD）数值模拟和理论方法对高超声速可压缩湍流中粗糙壁面热增量进行研究. 着重考虑粗糙单元密度和粗糙单元形状对粗糙表面热流的影响. 结果表明： ①粗糙单元密度变化时, CFD数值方法计算所得的粗糙单元等效热流随着粗糙单元密度的降低而增加, 理论方法预测结果的规律随方法不同而不同;②在相同粗糙单元密度和高度时,如果粗糙单元形状改变,CFD计算结果也随之发生改变. 理论预测方法所得结果不发生变化.