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.     

Shear thickening in a model colloidal suspension

We study the rheology of model colloidal suspensions using molecular-dynamics simulations. We relate the onset of shear thickening to the transition from a low-viscosity regime, in which the solvent facilitates the flow of colloids, to a high-viscosity regime associated with jamming of the colloids and the formation of chains of colloids. In the low-viscosity regime, the colloidal particles are, on average, surrounded by two layers of solvent particles. On the contrary, in the high-viscosity regime, the solvent is expelled from the interstice between the jammed colloids. The thickening in suspensions is shown to obey the same criterion as in simple fluids. This demonstrates that jamming, even without the divergence of lubrication interactions, is sufficient to observe shear thickening.     

Structure and transport properties of polymer grafted nanoparticles

We perform molecular dynamics simulations on a bead-spring model of pure polymer grafted nanoparticles (PGNs) and of a blend of PGNs with a polymer melt to investigate the correlation between PGN design parameters (such as particle core concentration, polymer grafting density, and polymer length) and properties, such as microstructure, particle mobility, and viscous response. Constant strain-rate simulations were carried out to calculate viscosities and a constant-stress ensemble was used to calculate yield stresses. The PGN systems are found to have less structural order, lower viscosity, and faster diffusivity with increasing length of the grafted chains for a given core concentration or grafting density. Decreasing grafting density causes depletion effects associated with the chains leading to close contacts between some particle cores. All systems were found to shear thin, with the pure PGN systems shear thinning more than the blend; also, the pure systems exhibited a clear yielding behavior that was absent in the blend. Regarding the mechanism of shear thinning at the high shear rates examined, it was found that the shear-induced decrease of Brownian stresses and increase in chain alignment, both correlate with the reduction of viscosity in the system with the latter being more dominant. A coupling between Brownian stresses and chain alignment was also observed wherein the non-equilibrium particle distribution itself promotes chain alignment in the direction of shear.     

Calculation of the nonlinear stress of polymers in oscillatory shear fields

Complex moduli are calculated for the lowest-order deviations from linearity of the stress in an oscillatory shear field. The calculations involve solution of an equation, recently proposed by Doi, which goes beyond the “independent alignment approximation” of the Doi-Edwards theory of polymer dynamics. The new equation incorporates various reptative motions of a polymer in the effective constraining tube induced by entanglements, viz. Brownian motion along the tube and the systematic motion in response to changes in the length of the tube accompanying affine deformation.     

Structure of electrorheological fluids under an electric field and a shear flow: experiment and computer simulation

It is known that macroscopic properties of colloidal suspensions are often determined by the microstructure of the particles in the suspensions, depending on the interparticle, Brownian, and hydrodynamic (if any) forces. We take electrorheological (ER) fluids as an example. By using a computer simulation and an experimental approach, we investigate the structure of ER fluids subjected to both an electric field and a shear flow. The microstructure evolution from random structure, to chains, and then to stable lamellar patterns, observed in the experiments, agrees very well with that obtained in the simulations. It is shown that the formation of such lamellar patterns originates from the difference between the dipole moment induced in the particles suspended in the ER fluids without shear and the one with shear. The results on the relaxation process of structural formation and the internal structure of layers are also presented. Thus, it seems possible to achieve various structures and hence desired macroscopic properties of colloidal suspensions by adjusting external fields and, simultaneously, a shear flow.     

Electroosmotic flow of non‐Newtonian fluids in a constriction microchannel

Insulator‐based dielectrophoresis has to date been almost entirely restricted to Newtonian fluids despite the fact that many of the chemical and biological fluids exhibit non‐Newtonian characteristics. We present herein an experimental study of the fluid rheological effects on the electroosmotic flow of four types of polymer solutions, i.e., 2000 ppm xanthan gum (XG), 5% polyvinylpyrrolidone (PVP), 3000 ppm polyethylene oxide (PEO), and 200 ppm polyacrylamide (PAA) solutions, through a constriction microchannel under DC electric fields of up to 400 V/cm. We find using particle streakline imaging that the fluid elasticity does not change significantly the electroosmotic flow pattern of weakly shear‐thinning PVP and PEO solutions from that of a Newtonian solution. In contrast, the fluid shear‐thinning causes multiple pairs of flow circulations in the weakly elastic XG solution, leading to a central jet with a significantly enhanced speed from before to after the channel constriction. These flow vortices are, however, suppressed in the strongly viscoelastic and shear‐thinning PAA solution.     

Rheo-SANS studies on shear-thickening/thinning in aqueous rodlike micellar solutions

Shear-induced thickening/thinning phenomena of aqueous rodlike micellar solutions of cetyltrimethylammonium bromide (CTAB) and sodium p-toluene sulfonate (NapTS) were investigated by means of simultaneous measurements of rheology and small-angle neutron scattering (SANS), the so-called Rheo-SANS. The aqueous CTAB/NapTS solutions were classified into five different categories dependent on their flow behavior and micellar structure. By increasing salt concentration and/or shear rates, the micelles underwent morphological transition from (i) spherical or short rodlike micelles to (ii) long rodlike micelles without entanglements, followed by (iii) those with entanglements. These transitions were recognized as changes in flow behavior from Newtonian to shear-thickening and shear-thinning flow, respectively. In the latter two cases, anisotropic SANS patterns appeared around these critical shear rates. The physical meaning of the anisotropic SANS patterns accompanied by shear-thickening flow behavior is discussed in conjunction with other shear-thickening systems.     

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.     

Mechanical structures in polymer melts. II. Roles of entanglements in viscosity and elastic turbulence

Current theories of polymer flow processes often sacrifice realistic molecular models for simplicity of their mathematical equations. An analysis of what might happen to molecules of more realistic sizes and shapes under shear flow, shows the importance of the rapid Brownian motion of chain segments, the elastic deformations of polymer random coils, and the dissipation of this elastic random coil energy by the relatively slow slippage of the chains past each other at a few entanglements where steric hindrance causes long relaxation times. This makes the energy loss depend on the time at each local deformation, and not on the overall shear rate. At high shear rates this model leads to “cluster flow” and low loss cyclic deformations, rather than the high loss processes of steady-state shear. This model gives reasonable qualitative explanations for many anomalous flow properties, and it has predicted new effects that have since been observed.     

Shear and extensional rheology of solutions of mixtures of poly(ethylene oxide) and anionic surfactants in ionic environments

Interactions between a high molecular weight poly(ethylene oxide) (PEO) and the anionic surfactant sodium dodecyl benzene sulfonate (SDBS) in aqueous solutions were investigated by shear and extensional rheometry. Results for mixtures between PEO and sodium dodecyl sulfate (SDS) are also presented for comparison purposes. Addition of anionic surfactants to PEO solutions above the critical aggregation concentration (CAC), at which micellar aggregates attach to the polymer chain, results in an increase in shear viscosity due to PEO coil expansion, and a strengthening of interchain interactions. In extensional flows, these interactions result in a decrease of the critical shear rate for the onset of the characteristic extension thickening of the PEO solutions that is due to transient entanglements of polymer molecules. The relaxation times associated with these transient entanglements are not directly proportional to the shear viscosity of the solutions, but rather vary more rapidly with surfactant concentration. In the presence of an electrolyte, coil contraction results in lower shear viscosities and a decrease in the extension thickening effects at surfactant concentrations just beyond the CAC. The relaxation times associated with transient entanglement reach a minimum at the same surfactant concentration as the shear viscosity, which indicates that coil contraction is responsible for the observed effects in both types of flow. However, the increase in extensional-flow entanglement relaxation times is much more abrupt than the decrease in shear viscosity. All these results point to a greater sensitivity of extensional flows on the molecular conformation of PEO/surfactant complexes.     

Influence of poly(ethylene oxide) brushes on the rheological properties of MgO colloidal suspensions in water

A combined experimental and multiscale simulation study of the influence of polymer brush modification on interactions of colloidal particles and rheological properties of dense colloidal suspensions has been conducted. Our colloidal suspension is comprised of polydisperse MgO colloidal particles modified with poly(ethylene oxide) (PEO) brushes in water. The shear stress as a function of shear rate was determined experimentally and from multiscale simulations for a suspension of 0.48 volume fraction colloids at room temperature for both bare and PEO-modified MgO colloids. Bare MgO particles exhibited strong shear thinning behavior and a yield stress on the order of several Pascals in both experiments and simulations. In contrast, simulations of PEO-modified colloids revealed no significant yielding or shear thinning and viscosity only a few times larger than solvent viscosity. This behavior is inconsistent with results obtained from experiments where modification of colloids with PEO brushes formed by adsorption of PEO-based comb-branched chains resulted in relatively little change in suspension rheology compared to bare colloids over the range of concentration of comb-branch additives investigated. We attribute this discrepancy in rheological properties between simulation and experiment for PEO-modified colloidal suspensions to heterogeneous adsorption of the comb-branch polymers.     

Particle laden fluid interfaces: Dynamics and interfacial rheology

We review the dynamics of particle laden interfaces, both particle monolayers and particle + surfactant monolayers. We also discuss the use of the Brownian motion of microparticles trapped at fluid interfaces for measuring the shear rheology of surfactant and polymer monolayers. We describe the basic concepts of interfacial rheology and the different experimental methods for measuring both dilational and shear surface complex moduli over a broad range of frequencies, with emphasis in the micro-rheology methods. In the case of particles trapped at interfaces the calculation of the diffusion coefficient from the Brownian trajectories of the particles is calculated as a function of particle surface concentration. We describe in detail the calculation in the case of subdiffusive particle dynamics. A comprehensive review of dilational and shear rheology of particle monolayers and particle + surfactant monolayers is presented. Finally the advantages and current open problems of the use of the Brownian motion of microparticles for calculating the shear complex modulus of monolayers are described in detail.     

Periodic orientational motions of rigid liquid-crystalline polymers in shear flow

The collective periodic motions of liquid-crystalline polymers in a nematic phase in shear flow have, for the first time, been simulated at the particle level by Brownian dynamics simulations. A wide range of parameter space has been scanned by varying the aspect ratio L/D between 10 and 60 at three different scaled volume fractions Lphi/D and an extensive series of shear rates. The influence of the start configuration of the box on the final motion has also been studied. Depending on these parameters, the motion of the director is either characterized as tumbling, kayaking, log-rolling, wagging, or flow-aligning. The periods of kayaking and wagging motions are given by T=4.2(Lphi/D)gamma(-1) for high aspect ratios. Our simulation results are in agreement with theoretical predictions and recent shear experiments on fd viruses in solution. These calculations of elongated rigid rods have become feasible with a newly developed event-driven Brownian dynamics algorithm.     

Structure-defined c60/polymer colloids supramolecular nanocomposites in water

We report a new supramolecular method for the synthesis of well-defined pristine C 60/polymer colloid nanocomposites in water. The colloids include polymer micelles and emulsion particles. To a polymer colloid solution in water or alcohol, we introduced C 60 solution in a solvent that is miscible with water or alcohol. After the two solutions mixed, polymer colloids and C 60 spontaneously assembled into stable colloidal nanocomposites. After a dialysis process, a nanocomposite dispersion in pure water was obtained. As characterized by DLS and (Cryo-)TEM, the nanocomposites have a core-shell structure with C 60 aggregated on the surface of emulsion particles or micellar cores. The resulting nanocomposites have many potential applications such as biomedicals and photovoltaics.     

Critical flux of hard sphere suspensions in crossflow filtration: Hydrodynamic force bias Monte Carlo simulations

A Monte Carlo method is developed for crossflow membrane filtration to determine the critical flux of hard sphere suspensions. Brownian and shear-induced diffusion are incorporated into an effective hydrodynamic force exerted on the hard spheres in a concentrated shear flow. Effects of shear rate and particle size on the critical flux are investigated using hydrodynamic force bias Monte Carlo simulations, providing a baseline of the critical flux.     

Theory of Liquid-crystalline Ordering in Polymer Brushes

Summary: We present a review of the works devoted to investigation of LC ordering in polymer brushes. This series has been carried out by the group of T. M. Birshtein and covers the following aspects of the problem: thermotropic LC phase transition in LCP brushes, microphase segregation, homeotropic and planar LC phases, LC polymer in LC solvent, lyotropic LCP brushes, LC transitions under normal or lateral force (shear flow). Analytical theory is developed for simplified model of polymer brush with accounting for thermotropic attraction in Mayer-Saupe approximation and lyotropic repulsion in DiMarzio formalism; numerical calculations are fulfilled in self-consistent field approximation (method of Scheutjens and Fleer). Brownian dynamics simulations are applied for modeling polymer brush in a shear flow.     

Rheology of aqueous poly(ethylene oxide) solutions reinforced with bentonite clay

The rheological properties of bentonite clay-filled aqueous solutions of high-molecular-mass poly(ethylene oxide) (PEO) have been studied. The PEO solution is a typical polymer solution characterized by the highest Newtonian viscosity and the range of non-Newtonian flow. The addition of small amounts of bentonite to the PEO solution causes passage to a viscoplastic behavior that manifests itself as the appearance of the yield stress. Therewith, the flow at the highest Newtonian viscosity in the region of low shear stresses (rather than rates) remains possible. After passing through the yield stress, the effect of antithixotropy, i.e., an increase in the viscosity with the deformation rate in a certain shear rate region, has been observed for the multicomponent systems. The data obtained have been interpreted assuming that the addition of the solid filler to the polymer solution destroys the random network of entanglements between macromolecules, while the presence of the polymer in the clay suspension reduces the strength of the coagulation structure of bentonite.     

Structure of a semidilute polymer solution under steady shear

We use Brownian dynamics computer simulations to investigate the structure of a semidilute polymer solution undergoing a steady, uniform shear flow. We find that the contributions to structure factor from intra- and interchain correlations, which cancel each other almost completely for an equilibrium semidilute solution, are modified in different ways by the shear flow. Incomplete cancellation of these contributions leads to anisotropic patterns that resemble those observed in light scattering experiments on sheared semidilute solutions [Wu et al., Phys. Rev. Lett. 66, 2408 (1991)]. For small wave vectors the structure factor change is dominated by the interchain contribution. We also monitor the distortion of the pair correlation function and show that for small distances it is dominated by the intrachain contribution. Finally, we investigate nonlinear shear viscosity and find that, like the short-distance part of the distortion of the pair correlation function, it is predominantly of intrachain origin.     

Tracer diffusion in colloidal suspensions under dilute and crowded conditions with hydrodynamic interactions

We consider tracer diffusion in colloidal suspensions under solid loading conditions, where hydrodynamic interactions play an important role. To this end, we carry out computer simulations based on the hybrid stochastic rotation dynamics-molecular dynamics (SRD-MD) technique. Many details of the simulation method are discussed in detail. In particular, our choices for the SRD-MD parameters and for the different scales are adapted to simulating colloidal suspensions under realistic conditions. Our simulation data are compared with published theoretical, experimental and numerical results and compared to Brownian dynamics simulation data. We demonstrate that our SRD-MD simulations reproduce many features of the hydrodynamics in colloidal fluids under finite loading. In particular, finite-size effects and the diffusive behavior of colloids for a range of volume fractions of the suspension show that hydrodynamic interactions are correctly included within the SRD-MD technique.