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.     

Self‐sustained entropy‐driven flow in nano‐confined polymer melts

We present a Monte Carlo simulation study of the Brownian motion of polymer chains in a melt confined in a periodically asymmetric channel of nanometric dimensions. We assume no friction between the chains and the channel. A detailed analysis of the conformations of the chains reveals the presence of a favorable entropy gradient along the easy flow direction. For high molecular weight chains, this gradient is seen to drive a self‐sustained polymer flow with Peclet numbers as high as 0.9, which makes our observation experimentally accessible. Much weaker efficiences are observed at low molecular weights. We show that the unexpected directed Brownian motion of polymers in confined geometries is of significant importance in the design and stabilization of platelet nanocomposites which typically age over time under quiescent conditions. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 869–875     

Role of Hydrodynamic Interactions in the Deformation of Star Polymers in Poiseuille Flow

Stretching polymer in fluid flow is a vital process for studying and utilizing the physical properties of these molecules,such as DNA linearization in nanofluidic channels.We studied the role of hydrodynamic interactions(His)in stretching a free star polymer in Poiseuille flow through a tube using mesoscale hydrodynamic simulations.As increasing the flow strength,star polymers migrate toward the centerline of tube due to His,whereas toward the tube wall in the absence of His.By analyzing the end monomer distribution and the perturbed flow around the star polymer,we found that the polymer acts like a shield against the flow,leading to additional hydrodynamic drag forces that compress the arm chains in the front of the star center toward the tube axis and lift the arm chai ns at the back toward the tube wall.The balanced hydrodynamic forces freeze the polymer into a trumpet structure,where the arm chains maintain a steady strongly stretched state at high flow strength.In contrast,the polymer displays remarkably large conformational change when switching off His.Our simulation results explained the coupling between His and the structure of star polymers in Poiseuille flow.     

Cross-streamline migration of a semiflexible polymer in a pressure driven flow

Experiments and simulations on single α-actin filaments in the Poiseuille flow through a microchannel show that the center-of-mass probability density across the channel assumes a bimodal shape as a result of pronounced cross-streamline migration. We reexamine the problem and perform Brownian dynamics simulations for a bead-spring chain with bending elasticity. Hydrodynamic interactions between the pointlike beads are taken into account by the two-wall Green tensor of the Stokes equations. Our simulations reproduce the bimodal distribution only when hydrodynamic interactions are taken into account. Numerical results on the orientational order of the end-to-end vector of the model polymer are also presented together with analytical hard-needle expressions at zero flow velocity. We derive a Smoluchowski equation for the center-of-mass distribution and carefully analyze the different contributions to the probability current that causes the bimodal distribution. As for flexible polymers, hydrodynamic repulsion explains the depletion at the wall. However, in contrast to flexible polymers, the deterministic drift current mainly determines migration away from the centerline and thereby depletion at the center. Diffusional currents due to a position-dependent diffusivity become less important with increasing polymer stiffness.     

Pressure driven flow of polymer solutions in nanoscale slit pores

Polymer solutions subject to pressure driven flow and in nanoscale slit pores are systematically investigated using the dissipative particle dynamics approach. The authors investigated the effect of molecular weight, polymer concentration, and flow rate on the profiles across the channel of the fluid and polymer velocities, polymer density, and the three components of the polymers radius of gyration. They found that the mean streaming fluid velocity decreases as the polymer molecular weight and/or polymer concentration is increased, and that the deviation of the velocity profile from the parabolic profile is accentuated with increase in polymer molecular weight or concentration. They also found that the distribution of polymers conformation is highly anisotropic and nonuniform across the channel. The polymer density profile is also found to be nonuniform, exhibiting a local minimum in the center plane followed by two symmetric peaks. They found a migration of the polymer chains either from or toward the walls. For relatively long chains, as compared to the thickness of the slit, a migration toward the walls is observed. However, for relatively short chains, a migration away from the walls is observed.     

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)].     

Brownian dynamics simulation of polyelectrolyte dilute solutions: Relaxation time and elongational flow

The authors used the bead‐and‐spring model and the Brownian dynamics simulation technique including hydrodynamic interaction to study the behavior of dilute polyelectrolyte solutions under elongational flow. First they carried out simulations to determine the longest relaxation time of a polyelectrolyte, finding that the relaxation time depends on the ionic strength of the solution. Then, they studied the coil‐stretch transition of polyelectrolyte molecules in elongational flow and determined the critical value of the elongational rate necessary in order this transition to occur. In this way, they could compute the value of the Deborah number at which coil‐stretch transition sets in for polyelectrolyte dilute solutions. Finally, they studied the power law relationship that relates the critical elongational rate with the molecular weight of the polyelectrolyte. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 714–722, 2007     

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.     

Simulation of GPC‐Distribution Coefficients of Linear and Star‐Shaped Molecules in Spherical Pores

Simulations of the distribution coefficients of linear and star‐shaped polymers in spherical pores were performed in order to predict the GPC‐elution behavior of star‐shaped polymers relative to that of linear polymers. Self avoiding walks were generated on a tetrahedral lattice to simulate good solvent conditions. It was found that neither the molecular weight nor the mean squared radius of gyration of the polymer serves as a universal factor to determine the distribution coefficient. However, the calculated distribution coefficients correlate well with the calculated hydrodynamic radii even for different topologies. For molecules at same elution volume the ratios of molecular weights of star and linear polymer agree well with exact calculations for Gaussian chains. These ratios are nearly independent of pore geometry (spherical or cylindrical).     

DNA conformation in nanochannels: Monte Carlo simulation studies using a primitive DNA model

We have performed canonical ensemble Monte Carlo simulations of a primitive DNA model to study the conformation of 2.56 ~ 21.8 μm long DNA molecules confined in nanochannels at various ionic concentrations with the comparison of our previous experimental findings. In the model, the DNA molecule is represented as a chain of charged hard spheres connected by fixed bond length and the nanochannels as planar hard walls. System potentials consist of explicit electrostatic potential along with short-ranged hard-sphere and angle potentials. Our primitive model system provides valuable insight into the DNA conformation, which cannot be easily obtained from experiments or theories. First, the visualization and statistical analysis of DNA molecules in various channel dimensions and ionic strengths verified the formation of locally coiled structures such as backfolding or hairpin and their significance even in highly stretched states. Although the folding events mostly occur within the region of ~0.5 μm from both chain ends, significant portion of the events still take place in the middle region. Second, our study also showed that two controlling factors such as channel dimension and ionic strength widely used in stretching DNA molecules have different influence on the local DNA structure. Ionic strength changes local correlation between neighboring monomers by controlling the strength of electrostatic interaction (and thus the persistence length of DNA), which leads to more coiled local conformation. On the other hand, channel dimension controls the overall stretch by applying the geometric constraint to the non-local DNA conformation instead of directly affecting local correlation. Third, the molecular weight dependence of DNA stretch was observed especially in low stretch regime, which is mainly due to the fact that low stretch modes observed in short DNA molecules are not readily accessible to much longer DNA molecules, resulting in the increase in the stretch of longer DNA molecules.     

Fracture of flexible polymer chains in dilute solution under transient extensional flow

 Applying the technique of Brownian dynamics simulation, we have studied the fracture process of flexible polymer chains when they encounter an extensional flow field of transient character. For this purpose, a mathematical model was made of an experimental device used earlier by other authors to study fracture of polystyrene in dilute solution. The polymer/solvent system studied was a very dilute solution in theta conditions. The polymer molecule was modeled as a FENE bead-spring chain, including a modification to allow for chain fracture. The simulation results showed that the fracture yield depended strongly on flow rate and on molecular weight. We have characterized the molecular-weight dependence of the critical flow rate which is necessary for fracture to occur. The distribution of the result-ing fragments is interpreted in terms of the conformation of the chains prior to fracture. Received: 17 September 1996 Accepted: 29 May 1997     

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.     

Structure of flexible and semiflexible polyelectrolyte chains in confined spaces of slit micro/nanochannels

Understanding the behavior of a polyelectrolyte in confined spaces has direct relevance in design and manipulation of microfluidic devices, as well as transport in living organisms. In this paper, a coarse-grained model of anionic semiflexible polyelectrolyte is applied, and its structure and dynamics are fully examined with Brownian dynamics (BD) simulations both in bulk solution and under confinement between two negatively charged parallel plates. The modeling is based on the nonlinear bead-spring discretization of a continuous chain with additional long-range electrostatic, Lennard-Jones, and hydrodynamic interactions between pairs of beads. The authors also consider the steric and electrostatic interactions between the bead and the confining wall. Relevant model parameters are determined from experimental rheology data on the anionic polysaccharide xanthan reported previously. For comparison, both flexible and semiflexible models are developed accompanying zero and finite intrinsic persistence lengths, respectively. The conformational changes of the polyelectrolyte chain induced by confinements and their dependence on the screening effect of the electrolyte solution are faithfully characterized with BD simulations. Depending on the intrinsic rigidity and the medium ionic strength, the polyelectrolyte can be classified as flexible, semiflexible, or rigid. Confined flexible and semiflexible chains exhibit a nonmonotonic variation in size, as measured by the radius of gyration and end-to-end distance, with changing slit width. For the semiflexible chain, this is coupled to the variations in long-range bond vector correlation. The rigid chain, realized at low ionic strength, does not have minima in size but exhibits a sigmoidal transition. The size of confined semiflexible and rigid polyelectrolytes can be well described by the wormlike chain model once the electrostatic effects are taken into account by the persistence length measured at long length scale.     

Continuum theory of polymer crystallization

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with G approximately exp(1/TDeltaT), where G is the growth rate and DeltaT is the supercooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with G approximately DeltaT, for small DeltaT. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.     

SEGMENT DENSITY PROFILES OF COMPACT POLYMER CHAINS CONFINED BETWEEN TWO PARALLEL PLANE WALLS

We use the pruned-enriched Rosenbluth method to investigate systematically the segment density profiles of compact polymer chains confined between two parallel plane walls.The non-adsorption case of adsorption interaction energyε=0 and the weak adsorption case ofε=-1 are considered for the compact polymer chains with different chain lengths N and different separation distances between two walls D.Several special entropy effects on the confined compact polymer chains,such as a damped oscillation in the segment density profile for the large separation distance D,are observed and discussed for different separation distances D in the non-adsorption case.In the weak adsorption case,investigations on the segment density profiles indicate that the competition between the entropy and adsorption effects results in an obvious depletion layer.Moreover,the scaling laws of the damped oscillation period T_d and the depletion layer width L_d are obtained for the confined compact chains.Most of these results are obtained for the first time so far as we know,which are expected to understand the properties of the confined compact polymer chains more completely.     

Nanochannel confinement: DNA stretch approaching full contour length

Fully stretched DNA molecules are becoming a fundamental component of new systems for comprehensive genome analysis. Among a number of approaches for elongating DNA molecules, nanofluidic molecular confinement has received enormous attentions from physical and biological communities for the last several years. Here we demonstrate a well-optimized condition that a DNA molecule can stretch almost to its full contour length: the average stretch is 19.1 μm ± 1.1 μm for YOYO-1 stained λ DNA (21.8 μm contour length) in 250 nm × 400 nm channel, which is the longest stretch value ever reported in any nanochannels or nanoslits. In addition, based on Odijk's polymer physics theory, we interpret our experimental findings as a function of channel dimensions and ionic strengths. Furthermore, we develop a Monte Carlo simulation approach using a primitive model for the rigorous understanding of DNA confinement effects. Collectively, we present a more complete understanding of nanochannel confined DNA stretching via the comparisons to computer simulation results and Odijk's polymer physics theory.     

Viscosity of confined inhomogeneous nonequilibrium fluids

We use the nonlocal linear hydrodynamic constitutive model, proposed by Evans and Morriss [Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990)], for computing an effective spatially dependent shear viscosity of inhomogeneous nonequilibrium fluids. The model is applied to a simple atomic fluid undergoing planar Poiseuille flow in a confined channel of several atomic diameters width. We compare the spatially dependent viscosity with a local generalization of Newton's law of viscosity and the Navier-Stokes viscosity, both of which are known to suffer extreme inaccuracies for highly inhomogeneous systems. The nonlocal constitutive model calculates effective position dependent viscosities that are free from the notorious singularities experienced by applying the commonly used local constitutive model. It is simple, general, and has widespread applicability in nanofluidics where experimental measurement of position dependent transport coefficients is currently inaccessible. In principle the method can be used to predict approximate flow profiles of any arbitrary inhomogeneous system. We demonstrate this by predicting the flow profile for a simple fluid undergoing planar Couette flow in a confined channel of several atomic diameters width.     

聚羧酸系高性能减水剂分子在稀溶液中尺寸及其在体积排除色谱表征中表观分子量的模型研究

针对被称为"第一代聚羧酸高性能减水剂"(以下简称为MPEG-type PCE)的甲基丙烯酸(MAA)/烯酸甲酯(MAA-MPEG)梳状共聚物分子,从高分子物理基础理论出发,构建等效自由连接链模型,结合前人的理论结果和实验数据,得到了MPEG-type PCE分子的回转半径、流体力学半径及其相应的支化参数的数学表达式.在此基础上,报道了以下三方面的工作:首先,将计算结果与文献中的实验结果进行比较,检验模型的合理性;其次,利用所建立的数学模型考察主链分子量、侧链分子量和侧链接枝密度对PCE分子的回转半径和流体力学半径的影响;最后,结合近年来发展的体积排除色谱分离理论,对PCE分子的真实分子量与其常规体积排除色谱"表观分子量"(又被称为GPC分子量)两者之间的差异进行了分析.本文所提出的计算模型和数学表达式没有不确定的指前因子,可用来估算MPEG-type PCE分子在稀水溶液中的尺寸以及根据其GPC分子量估算真实分子量.     

Shear thinning in dilute polymer solutions

We use bead-spring models for a polymer coupled to a solvent described by multiparticle collision dynamics to investigate shear thinning effects in dilute polymer solutions. First, we consider the polymer motion and configuration in a shear flow. For flexible polymer models we find a sharp increase in the polymer radius of gyration and the fluctuations in the radius of gyration at a Weissenberg number approximately 1. We then consider the polymer viscosity and the effect of solvent quality, excluded volume, hydrodynamic coupling between the beads, and finite extensibility of the polymer bonds. We conclude that the excluded volume effect is the major cause of shear thinning in polymer solutions. Comparing the behavior of semiflexible chains, we find that the fluctuations in the radius of gyration are suppressed when compared to the flexible case. The shear thinning is greater and, as the rigidity is increased, the viscosity measurements tend to those for a multibead rod.     

Tumbling dynamics of individual absorbed polymer chains in shear flow

The tumbling dynamics of individual absorbed polymer chains in shear flow is studied by employing multi-particle collision dynamics simulation techniques combined with molecular dynamics simulations.We find that the dependence of tumbling frequencies on shear rate is independent of both adsorption strength and surface corrugate.