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.     

Universal consequences of the presence of excluded volume interactions in dilute polymer solutions undergoing shear flow

The role of solvent quality in determining the universal material properties of dilute polymer solutions undergoing steady simple shear flow is examined. A bead-spring chain representation of the polymer molecule is used, and the influence of solvent molecules on polymer conformations is modelled by a narrow Gaussian excluded volume potential that acts pairwise between the beads of the chain. Brownian dynamics simulations data, acquired for chains of finite length, and extrapolated to the limit of infinite chain length, are shown to be model independent. This feature of the narrow Gaussian potential, which leads to results identical to a delta-function repulsive potential, enables the prediction of both universal crossover scaling functions and asymptotic behavior in the excluded volume limit. Universal viscometric functions, obtained by this procedure, are found to exhibit increased shear thinning with increasing solvent quality. In the excluded volume limit, they are found to obey power law scaling with the characteristic shear rate beta, in close agreement with previously obtained renormalization group results. The presence of excluded volume interactions is also shown to lead to a weakening of the alignment of the polymer chain with the flow direction.     

Depletion and pair interactions of proteins in polymer solutions

We study the depletion, pair interaction, and phase behavioral characteristics of proteins in polymer solutions. We use a McMillan-Mayer-like approach [W. G. McMillan, Jr. and J. E. Mayer, J. Chem. Phys. 13, 276 (1945)] to suggest that the depletion characteristics should be studied at an effective polymer concentration which is a function of both the average polymer and the protein concentrations. In the protein limit, we show that the volume of the polymer depletion layers exceeds the size of the proteins, leading to effective polymer concentrations typically in the semidilute and concentrated regimes even when the average polymer concentrations are in the dilute regimes. We propose an approximate approach that accounts for the multibody depletion overlaps, and use an accurate numerical solution of polymer mean-field theory to address depletion characteristics in these regimes which are characterized by both the importance of polymer interactions as well as the curvature of the proteins relative to the correlation length of polymers. We show that the depletion characteristics of the protein-polymer mixture can be quite different when viewed in this framework, and this can have profound consequences for the phase behavior of the mixture. Our theoretical predictions for the phase diagram match semiquantitatively with published experimental results.     

A simple and effective boundary model in nonequilibrium molecular dynamics method

We propose a simple and effective boundary model in a nonequilibrium molecular dynamics (NEMD) simulation to study the out-of-equilibrium dynamics of polymer fluids. The present boundary model can effectively weaken the depletion effect and the slip effect near the boundary, and remove the unwanted heat instantly. The validity of the boundary model is checked by investigating the flow behavior of dilute polymer solution driven by an external force. Reasonable density distributions of both polymer and solvent particles, velocity profiles of the solvent and temperature profiles of the system are obtained. Furthermore, the studied polymer chain shows a cross-streaming migration towards center of the tube, which is consistent with that predicted in previous literatures. These numerical results give powerful evidences for the validity of the present boundary model. Besides, the boundary model can also be used in other flows in addition to the Poiseuille flow.     

Polymer-particle mixtures: depletion and packing effects

The structure of polymers in the vicinity of spherical colloids is investigated by Monte Carlo simulations and integral equation theory. Polymers are represented by a simple bead-spring model; only repulsive Lennard-Jones interactions are taken into account. Using advanced trial moves that alter chain connectivity, depletion and packing effects are analyzed as a function of chain length and density, both at the bond and the chain level. Chain ends segregate to the colloidal surface and polymer bonds orient parallel to it. In the dilute regime, the polymer chain length governs the range of depletion and has a negligible influence on monomer packing in dense polymer melts. Polymers adopt an ellipsoidal shape, with the larger axis parallel to the surface of the particle, as they approach larger colloids. The dimensions are perturbed within the range of the depletion layer.     

Molecular dynamics simulations of polymer transport in nanocomposites

Molecular dynamics simulations on the Kremer-Grest bead-spring model of polymer melts are used to study the effect of spherical nanoparticles on chain diffusion. We find that chain diffusivity is enhanced relative to its bulk value when polymer-particle interactions are repulsive and is reduced when polymer-particle interactions are strongly attractive. In both cases chain diffusivity assumes its bulk value when the chain center of mass is about one radius of gyration R(g) away from the particle surface. This behavior echoes the behavior of polymer melts confined between two flat surfaces, except in the limit of severe confinement where the surface influence on polymer mobility is more pronounced for flat surfaces. A particularly interesting fact is that, even though chain motion is strongly speeded up in the presence of repulsive boundaries, this effect can be reversed by pinning one isolated monomer onto the surface. This result strongly stresses the importance of properly specifying boundary conditions when the near surface dynamics of chains are studied.     

Monte Carlo simulation of structure and nanoscale interactions in polymer nanocomposites

Off-lattice Monte Carlo simulations in the canonical ensemble are used to study polymer-particle interactions in nanocomposite materials. Specifically, nanoscale interactions between long polymer chains (N=550) and strongly adsorbing colloidal particles of comparable size to the polymer coils are quantified and their influence on nanocomposite structure and dynamics investigated. In this work, polymer-particle interactions are computed from the integrated force-distance curve on a pair of particles approaching each other in an isotropic polymer medium. Two distinct contributions to the polymer-particle interaction potential are identified: a damped oscillatory component that is due to chain density fluctuations and a steric repulsive component that arises from polymer confinement between the surfaces of approaching particles. Significantly, in systems where particles are in a dense polymer melt, the latter effect is found to be much stronger than the attractive polymer bridging effect. The polymer-particle interaction potential and the van der Waals potential between particles determine the equilibrium particle structure. Under thermodynamic equilibrium, particle aggregation is observed and there exists a fully developed polymer-particle network at a particle volume fraction of 11.3%. Near-surface polymer chain configurations deduced from our simulations are in good agreement with results from previous simulation studies.     

Multiple dynamic regimes in colloid‐polymer dispersions: New insight using X‐ray photon correlation spectroscopy

We present an X‐ray photon correlation spectroscopy (XPCS) study of dynamic transitions in an anisotropic colloid‐polymer dispersion with multiple arrested states. The results provide insight into the mechanism for formation of repulsive glasses, attractive glasses, and networked gels of colloids with weakly adsorbing polymer chains. In the presence of adsorbing polymer chains, we observe three distinct regimes: a state with slow dynamics consisting of finite particles and clusters, for which interparticle interactions are predominantly repulsive; a second dynamic regime occurring above the saturation concentration of added polymer, in which small clusters of nanoparticles form via a short‐range depletion attraction; and a third regime above the overlap concentration in which dynamics of clusters are independent of polymer chain length. The observed complex dynamic state diagram is primarily governed by the structural reorganization of a nanoparticle cluster and polymer chains at the nanoparticle‐polymer surface and in the concentrated medium, which in turn controls the dynamics of the dispersion. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 752–760     

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)].     

Effects of grafted polymer chains on lamellar membranes

We have investigated the effects of grafted polymer chains [poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide)] on the bending modulus and the intermembrane interactions of lamellar membranes (C(12)E(5) water) by means of a neutron spin-echo and a small-angle x-ray scattering technique. In this study the hydrophilic chain takes the mushroom configuration on the membrane. The bending modulus of the polymer-grafted membranes increases in proportion to the square of the end to end distance of the polymer chain, which agrees well with the theoretical prediction of Hiergeist and Lipowsky [J. Phys. II 6, 1465 (1996)]. From the interlamellar interaction point of view, the mushroom layer is renormalized to the membrane thickness, which enhances the repulsive Helfrich interaction. When the size of the decorated polymer chain increases to the interlamellar distance, however, the mushroom is squeezed so as to optimize the interlamellar potential. Further increase of the grafted polymer size brings a lamellar-lamellar phase separation, where the grafted polymer chains are localized in the dilute lamellar phase and the concentrated lamellar phase forms the onionlike texture.     

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.     

Chain overlap and entanglements in dilute polymer solutions: Brownian dynamics simulation

We have analyzed chain conformations and the existence — or otherwise — of chain overlaps and entanglements in dilute polymer solutions (at concentrations c < C^*, c^* = critical concentration). The fundamental problem of existence of chain overlaps in dilute solutions is also related to the drag reduction phenomenon (DR). Some experimental results pertinent to DR are explained in terms of entanglements even for solutions at concentrations defined in ppm. We report results of Brownian dynamics simulations of polymer solutions in which the equations of motion of the chains are solved by using the Langevin equation. Chains move according to actions of a systematic frictional force and a randomly fluctuating force w(t), where t is time. In addition, a shear flow field can be introduced into the model. To evaluate the structure of polymer chains in solution we have devised a measure of interchain contacts and two different measures of entanglements. The results for c = 0.3 c^* demonstrate that both chain entanglements and overlaps take place even in dilute solution. They also confirm predictions from an earlier combinatorial model.     

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.     

Effect of grafting on nanoparticle segregation in polymer/nanoparticle blends near a substrate

Nanoparticles in polymer films have shown the tendency to migrate to the substrate due to an entropic-based attractive depletion interaction between the particles and the substrate. It is also known that polymer-grafted nanoparticles show better dispersion in a polymer matrix. Here, molecular dynamics simulations are employed to study the effect of grafting on the nanoparticle segregation to the substrate. The nanoparticles were modeled as spheres and the polymers as bead-spring chains. The polymers of the grafts and the matrix are identical in nature. For a purely repulsive system, the nanoparticle density near the surface was found to decrease as the length of grafted chains and the number of grafts increased and in the bulk, the nanoparticles are well-dispersed. Whereas, in case of attractive systems with interparticle interactions on the order of thermal energy, the nanoparticles segregated to the substrate even more strongly, essentially forming clusters on the wall and in the bulk. However, due to the presence of grafted chains on the nanoparticles, the clusters formed in the bulk are structurally anisotropic. The effect of grafts on nanoparticle segregation to the surface was found to be qualitatively similar to the purely repulsive case.     

Design and fabrication of a multilayered polymer microfluidic chip with nanofluidic interconnects via adhesive contact printing

The design and fabrication of a multilayered polymer micro-nanofluidic chip is described that consists of poly(methylmethacrylate) (PMMA) layers that contain microfluidic channels separated in the vertical direction by polycarbonate (PC) membranes that incorporate an array of nanometre diameter cylindrical pores. The materials are optically transparent to allow inspection of the fluids within the channels in the near UV and visible spectrum. The design architecture enables nanofluidic interconnections to be placed in the vertical direction between microfluidic channels. Such an architecture allows microchannel separations within the chip, as well as allowing unique operations that utilize nanocapillary interconnects: the separation of analytes based on molecular size, channel isolation, enhanced mixing, and sample concentration. Device fabrication is made possible by a transfer process of labile membranes and the development of a contact printing method for a thermally curable epoxy based adhesive. This adhesive is shown to have bond strengths that prevent leakage and delamination and channel rupture tests exceed 6 atm (0.6 MPa) under applied pressure. Channels 100 microm in width and 20 microm in depth are contact printed without the adhesive entering the microchannel. The chip is characterized in terms of resistivity measurements along the microfluidic channels, electroosmotic flow (EOF) measurements at different pH values and laser-induced-fluorescence (LIF) detection of green-fluorescent protein (GFP) plugs injected across the nanocapillary membrane and into a microfluidic channel. The results indicate that the mixed polymer micro-nanofluidic multilayer chip has electrical characteristics needed for use in microanalytical systems.     

Nanoparticle stability in semidilute and concentrated polymer solutions

The wetting of PDMS-grafted silica spheres (PDMS- g-silica) is connected to their depletion restabilization in semidilute and concentrated PDMS/cyohexane polymer solutions. Specifically, we found that a wetting diagram of chemically identical graft and free homopolymers predicts stability of hard, semisoft, and soft spheres as a function of the bulk free polymer volume fraction, graft density, and the graft and free polymer chain lengths. The transition between stable and aggregated regions is determined optically and with dynamic light scattering. The point of demarcation between the regions occurs when the graft and free polymer chains are equal in length. When graft chains are longer than free chains, the particles are stable; in contrast, the particles are unstable when the opposite is true. The regions of particle stability and instability are corroborated with theoretical self-consistent mean-field calculations, which not only show that the grafted brush is responsible for particle dispersion in the complete wetting region but also aggregation in the incomplete wetting region. Ultimately, our results indicate that depletion restabilization depends on the interfacial properties of the nanoparticles in semidilute and concentrated polymer solutions.     

Effect of polymer size and chain length on depletion interactions between two colloids

A density functional theory based on the weighted density has been developed to investigate the depletion interactions between two colloids immersed in a bath of the binary polymer mixtures, where the colloids are modeled as hard spheres and the polymers as freely jointed tangent hard-sphere chain mixtures. The theoretical calculations for the depletion forces between two colloids induced by the polymer are in good agreement with the computer simulations. The effects of polymer packing fraction, degree of polymerization, polymer/polymer size ratio, colloid/polymer size ratio on the depletion interactions, and colloid-colloid second virial coefficient B2 due to polymer-mediated interactions have been studied. With increasing the polymer packing fraction, the depletion interaction becomes more long ranged and the attractive interaction near the colloid becomes deeper. The effect of degree polymerization shows that the long chain gives a more stable dispersion for colloids rather than the short chain. The strong effective colloid-colloid attraction appears for the large colloid/polymer and polymer/polymer size ratio. The location of maximum repulsion Rmax is found to appear Rmax approximately sigmac+Rg2 for the low polymer packing fraction and this is shifted to smaller separation Rmax approximately sigmac+sigmap2 with increasing the polymer packing fraction, where sigmap2 and Rg2 are the small-particle diameter and the radius of gyration of the polymer with the small-particle diameter, respectively.     

Molecular dynamics simulations of supramolecular polymer rheology

Using equilibrium and nonequilibrium molecular dynamics simulations, we studied the equilibrium and rheological properties of dilute and semidilute solutions of head-to-tail associating polymers. In our simulation model, a spontaneous complementary reversible association between the donor and the acceptor groups at the ends of oligomers was achieved by introducing a combination of truncated pseudo-Coulombic attractive potential and Lennard Jones repulsive potential between donor, acceptor, and neighboring groups. We have calculated the equilibrium properties of supramolecular polymers, such as the ring/chain equilibrium, average molecular weight, and molecular weight distribution of self-assembled chains and rings, which all agree well with previous analytical and computer modeling results. We have investigated shear thinning of solutions of 8- and 20-bead associating oligomers with different association energies at different temperatures and oligomer volume fractions. All reduced viscosity data for a given oligomer length can be collapsed into one master curve, exhibiting two power-law regions of shear-thinning behavior with an exponent of -0.55 at intermediate ranges of the reduced shear rate β and -0.8 (or -0.9) at larger shear rates. The equilibrium viscosity of supramolecular solutions with different oligomer lengths and associating energies is found to obey a power-law scaling dependence on oligomer volume fraction with an exponent of 1.5, in agreement with the experimental observations for several dilute or semidilute solutions of supramolecular polymers. This implies that dilute and semidilute supramolecular polymer solutions exhibit high polydispersity but may not be sufficiently entangled to follow the reptation mechanism of relaxation.