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.     

Determination of the distance-dependent viscosity of mixtures in parallel slabs using non-equilibrium molecular dynamics

We generalize a technique for determination of the shear viscosity of mixtures in planar slabs using non-equilibrium computer simulations by applying an external force parallel to the surface generating Poiseuille flow. The distance-dependent viscosity of the mixture, given as a function of the distance from the surface, is determined by analysis of the resulting velocity profiles of all species. We present results for a highly non-ideal water + methanol mixture in the whole concentration range between rutile (TiO(2)) walls. The bulk results are compared to the existing equilibrium molecular dynamics and experimental data while the inhomogeneous viscosity profiles at the interface are interpreted using the structural data and information on hydrogen bonding.     

Effects of slip on the viscosity of polymer melts

We use existing scaling theories by de Gennes, Brochard, and Ajdari to calculate the apparent viscosity of multilayer blends with weakly entangled interfaces. The lowering of the apparent viscosity with respect to the bulk is a manifestation of interfacial slip. The theoretical predictions are compared with the recent experimental data of Zhao and Macosko. The theory is able to describe a continuous transition from a low-slip regime to a high-slip regime when the bulk rheology is still Newtonian, in agreement with experiments. However, the dependence of the apparent viscosity on the shear rate and layer thicknesses is much stronger than what is observed experimentally. The apparent viscosity is also calculated for dilute polymer emulsions. We modify a theory of Palierne, which is valid in the linear viscoelastic regime for the bulk, to include the effects of interfacial slip. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1888–1904, 2004     

Further test of third order + second-order perturbation DFT approach: hard core repulsive Yukawa fluid subjected to diverse external fields

Grand canonical Monte Carlo simulation is used to investigate density profiles of hard-core repulsive Yukawa (HCRY) model fluid under the influence of various external fields and radial distribution function (RDF) of the bulk HCRY system. The aim of these extensive simulations is to provide exact data for purely repulsive interaction potential against which the validity of a third order + second-order perturbation DFT approach can be tested. It is found that a semiempirical parametrized bridge function due to Malijevsky and Labik performs very well for the RDF of the bulk HCRY fluid. Incorporation of a bulk second-order direct correlation function (DCF) of the HCRY fluid based on the Malijevsky-Labik bridge function into the third order + second-order perturbation DFT approach yields the resulting theoretical predictions for the density profiles of inhomogeneous HCRY fluid that are in a very good agreement with the simulation data, an exception being somewhat larger deviations appearing for the structure of the fluid around the center of a hard spherical cavity. Both theory and simulation predict layering transition and gas-liquid coexistence phenomena occurring with the HCRY model fluid under confined conditions. For the case of an inverse sixth-power repulsive potential under the influence of a flat stationary wall defined by an inverse twelfth-power repulsive potential, the present third order + second-order perturbation DFT approach is found to be superior to several existing weighted density approximations (WDA) and partitioned WDA.     

Determining the bulk viscosity of rigid water models

We use equilibrium molecular dynamics methods to compute the shear and bulk viscosities of the pairwise additive and rigid SPC/E, TIP4P, and TIP4P/2005 water models. For the latter model it was found in a recent study (J. Chem. Phys. 2009, 131, 246101) an excellent agreement with experiment in the prediction of the shear viscosity over a range of different thermodynamic conditions. Here, we examine, for a wide range of temperatures, whether this remarkable accuracy of the TIP4P/2005 model remains in the prediction of the bulk viscosity. Moreover, we examine whether equilibrium molecular dynamics methods provide reasonable accuracy in the calculation of the bulk viscosity, as it was previously found for the shear viscosity (J. Chem. Phys. 2010, 132, 096101). We concluded that, by performing the appropriate data analysis, accurate estimates of the bulk viscosity can be obtained, while, compared to the other simple rigid/pairwise additive water models, the predictions of the TIP4P/2005 model for the bulk viscosity are significantly closer to the experiment.     

基于密度泛函理论研究二元排斥Yukawa流体的表面结构性质

基于自由能密度泛函理论(DFT)考察了二元排斥Yukawa (HCRY)流体在不同外场下的密度分布. 基于微扰理论, 体系的Helmholtz自由能泛函采用硬球排斥部分和长程色散部分贡献之和, 其中Kierlik和Rosinberg的加权密度近似(WDA)被用来计算硬球排斥部分, 而色散部分采用平均场理论(MFT)进行描述. 为了验证DFT计算结果的合理性, 研究中采用巨正则Monte Carlo(GCMC)模拟计算了在不同主体相密度、硬核直径和位能参数比的条件下二元HCRY混合流体的密度分布. 结果表明, 该DFT计算结果与GCMC模拟值吻合良好.     

Simulation of semidilute suspensions of non-Brownian fibers in shear flow

Particle-level simulations are performed to study semidilute suspensions of monodispersed non-Brownian fibers in shear flow, with a Newtonian fluid medium. The incompressible three-dimensional Navier-Stokes equations are used to describe the motion of the medium, while fibers are modeled as chains of fiber segments, interacting with the fluid through viscous drag forces. The two-way coupling between the solids and the fluid phase is taken into account by enforcing momentum conservation. The model includes long-range and short-range hydrodynamic fiber-fiber interactions, as well as mechanical interactions. The simulations rendered the time-dependent fiber orientation distribution, whose time average was found to agree with experimental data in the literature. The viscosity and first normal stress difference was calculated from the orientation distribution using the slender body theory of Batchelor [J. Fluid Mech. 46, 813 (1971)], with corrections for the finite fiber aspect ratios. The viscosity was also obtained from direct computation of the shear stresses of the suspension for comparison. These two types of predictions compared well in the semidilute regime. At higher concentrations, however, a discrepancy was seen, most likely due to mechanical interactions, which are only accounted for in the direct computation method. The simulated viscosity determined directly from shear stresses was in fair agreement with experimental data found in the literature. The first normal stress difference was found to be proportional to the square of the volume concentration of fibers in the semidilute regime. As concentrations approached the concentrated regime, the first normal stress difference became proportional to volume concentration. It was also found that the coefficient of friction has a strong influence on the tendency for flocculation as well as the apparent viscosity of the suspension in the semidilute regime.     

The rheology and microstructure of charged colloidal suspensions

The effects of electric charge interation and particle correlations on suspension rheology are examined. A one-component fluid analysis using a Smoluchowski equation for the equilibrium structure is applied to charged suspensions of spherical colloids under shear. The frequency dependent modulus and viscosity, predicted as functions of particle and added salt concentrations, are compared with published rheological measurements on model suspensions. Recent improvements in the statistical mechanical theories for the equilibrium microstructure, its nonequilibrium deformation, and the bulk shear stresses are included. The direct electrostatic interaction is found to drive the divergence in the shear viscosity near the liquid-solid phase transition. Extensions of the theory predict the elastic modulus of binary mixtures of charged colloids. Estimates of the primary electroviscous effect, hydrodynamic interactions, and errors in the Yukawa limiting form for the potential and applications of asymptotic theories are presented. Predictions for the rheology based on effective hard-sphere models are found to be reasonable when using a parameter fit from the equilibrium phase behavior. Mean-field mode coupling theories predict larger relaxation times than calculated from the Smoluchowski equation (=SE). A study of binary mixing effects on elasticity shows non-ideal behavior. It is noted that equilibrium structural information can be used to resolve discrepancies between the theoretical predictions and the measured rheology.     

Solvation effects for polymers at an interface: a hybrid self-consistent field-density functional theory approach

Using polyatomic density functional theory of Kierlik and Rosinberg, we show that Wertheim's thermodynamic perturbation theory (TPT) incorporates solvation effects in a systematic, although simplified form. We derive two approximate solvation potentials, which require the knowledge of the correlation function in the reference unbonded fluid only. The theoretical predictions are tested against many-chain Monte Carlo simulations for moderate chain lengths. The predictions of the end-to-end distance in the bulk are in a reasonable agreement with simulations for the TPT(M-1) approximation, while the simpler TPT2_e approximation leads to the solvation potential that is shorter ranged and considerably less accurate. The resulting conformations are used in the subsequent self-consistent field theory calculations of hard-sphere polymers at a hard wall. While the incorporation of the solvation effects has little impact on the density profiles, the predictions of the components of the end-to-end distance vector as a function of the distance to the wall are much improved.     

Reactivity indicators for degenerate states in the density-functional theoretic chemical reactivity theory

Density-functional-theory-based chemical reactivity indicators are formulated for degenerate and near-degenerate ground states. For degenerate states, the functional derivatives of the energy with respect to the external potential do not exist, and must be replaced by the weaker concept of functional variation. The resultant reactivity indicators depend on the specific perturbation. Because it is sometimes impractical to compute reactivity indicators for a specific perturbation, we consider two special cases: point-charge perturbations and Dirac delta function perturbations. The Dirac delta function perturbations provide upper bounds on the chemical reactivity. Reactivity indicators using the common used "average of degenerate states approximation" for degenerate states provide a lower bound on the chemical reactivity. Unfortunately, this lower bound is often extremely weak. Approximate formulas for the reactivity indicators within the frontier-molecular-orbital approximation and special cases (two or three degenerate spatial orbitals) are presented in the supplementary material. One remarkable feature that arises in the frontier molecular orbital approximation, and presumably also in the exact theory, is that removing electrons sometimes causes the electron density to increase at the location of a negative (attractive) Dirac delta function perturbation. That is, the energetic response to a reduction in the external potential can increase even when the number of electrons decreases.     

Slip flow in graphene nanochannels

We investigate the hydrodynamic boundary condition for simple nanofluidic systems such as argon and methane flowing in graphene nanochannels using equilibrium molecular dynamics simulations (EMD) in conjunction with our recently proposed method [J. S. Hansen, B. D. Todd, and P. J. Daivis, Phys. Rev. E 84, 016313 (2011)]. We first calculate the fluid-graphene interfacial friction coefficient, from which we can predict the slip length and the average velocity of the first fluid layer close to the wall (referred to as the slip velocity). Using direct nonequilibrium molecular dynamics simulations (NEMD) we then calculate the slip length and slip velocity from the streaming velocity profiles in Poiseuille and Couette flows. The slip lengths and slip velocities from the NEMD simulations are found to be in excellent agreement with our EMD predictions. Our EMD method therefore enables one to directly calculate this intrinsic friction coefficient between fluid and solid and the slip length for a given fluid and solid, which is otherwise tedious to calculate using direct NEMD simulations at low pressure gradients or shear rates. The advantages of the EMD method over the NEMD method to calculate the slip lengths/flow rates for nanofluidic systems are discussed, and we finally examine the dynamic behaviour of slip due to an externally applied field and shear rate.     

Electro-osmosis at inhomogeneous charged surfaces: hydrodynamic versus electric friction

Electrokinetic methods are efficient in probing the electrostatic surface properties of charged systems. However, anomalies observed in experiments indicate that the classical electrokinetic theory should be reconsidered. Using Green's function methods and hydrodynamic simulations, we investigate electro-osmosis driven by electric-field-induced ion motion near a charged planar substrate with smooth or rough boundary. First, a reformulation of electro-osmotic theory for planar charged surfaces employing Green's functions shows that the Helmholtz-Smoluchowski (HS) relation between electrostatic potential and solvent velocity is exact for smooth surfaces, even in the presence of ion correlations. Deviations from HS theory are caused by combined hydrodynamic and electric surface friction, as our hydrodynamic simulations of ions at smooth and corrugated charged surfaces in lateral electric fields demonstrate. Within the simulations, hydrodynamic interactions are treated in the continuum limit and the presence of a no-slip boundary condition at the surface is taken into account. While electrofriction is relevant in highly charged system and/or for multivalent ions, hydrodynamic friction is dominant in systems with moderate surface charge density and/or low ionic valency. We also derive the effective electrokinetic surface charge from the electro-osmotic solvent profiles, which is substantially reduced when compared with the bare value and shows qualitative agreement with the experimental tendency.     

Linear stability of a draining film squeezed between two approaching droplets

In the present paper we analyze the effect of infinitesimal non-axisymmetric perturbations in determining the critical gap thickness at which a draining, finite radius thin-film becomes unstable. The film is part of the suspending fluid trapped between two approaching deformable drops under the action of a flow field. We carry out a linear stability analysis in the context of a quasi-static approximation where the rate of growth of the disturbances is assumed to be much faster than the rate of film drainage. An analytical solution is derived for the model in the special case of a uniformly thick film, for two types of perturbation: fixed-end and free-end. It is shown, for this special case, when the hydrodynamic force pushing the drops together from the external flow is constant, that the four most unstable disturbances are of the free-end kind, associated with the lowest frequency modes of azimuthal variation in the film thickness. Higher modes are stabilized by surface tension. Our analysis also shows that adopting the unretarded form of the van der Waals disjoining pressure yields results similar to the analysis when electromagnetic retardation effects are included in the calculation. A second case is analyzed where the film is also of uniform thickness but its lateral extent and the gap thickness are both time-dependent. This case was included to extend the predictions to glancing drop-collisions where the external hydrodynamic force is time-dependent. We find that there is a maximum capillary number below which the film becomes unstable, and that there is range of angles in the trajectory where the film becomes unstable, but that outside this range the film is stable.     

Mesoscale constitutive modeling of magnetic dispersions: material functions for shear flows

We recently developed a constitutive model for magnetic dispersions by modeling the magnetic particles as rigid dumbbells dispersed in a solvent. The theory yielded a constitutive equation in which the stress tensor could be expressed as a function of the velocity gradient, an orientational order tensor, S, an average alignment vector, J, and any imposed external magnetic field, H. The constitutive equation is used here to predict material functions for steady shear flow (shear-rate dependent viscosity and first normal stress coefficient) as well as those for unsteady shear flows (stress growth upon inception of steady shear and small-amplitude oscillatory shear). The importance of effects of concentration, equilibrium nematic ordering in the dispersion, and anisotropy in the hydrodynamic drag are emphasized. Comparisons with available experimental data on viscosity for magnetic inks under steady shear flow and inception of steady shear flow show reasonably good agreement.     

Viscosity of concentrated suspensions: influence of cluster formation

Dispersed particles can form clusters even at low concentrations. Colloidal and hydrodynamic forces are responsible for this phenomenon and these forces determine both structure and size of clusters. We assume that the viscosity of a concentrated suspension is completely determined by cluster size distribution, regardless if clusters form under the action of colloidal, hydrodynamic interactions or applied shear rates. Based on this assumption an equation, which describes dependency of viscosity on a concentration of dispersed particles taking into account cluster formation, is deduced. Under special restrictions the deduced dependency coincides with the well-known Dougherty-Krieger's equation except for a clear physical meaning of parameters entered. Our consideration shows that Dougherty-Krieger's equation has deeper physical background than it has been supposed earlier. Experimental verification of the suggested model shows a good agreement with the theory predictions and proves a presence of clusters even at low concentrations of dispersed particles.     

Viscosity contribution of an arbitrary shape rigid aggregate to a dilute suspension

The study of rheological response of solid suspensions is essential in understanding the relationships governing their kinematics and dynamics. However the study is complicated mainly by the complex interplay between suspension rheology and hydrodynamic behavior of the suspended solids, which for most of the practically occurring situations have complex and arbitrary shapes, and exact equations accounting for their hydrodynamic contribution are not available. For this reason, using a recently developed methodology capable of computing the average rigid body resistance matrix of arbitrary shaped clusters made of uniform sized spheres, Brownian dynamic simulations under shear conditions are performed for clusters with different geometries with the objective of estimating their intrinsic viscosity. The population of clusters chosen encompassed a broad range of morphologies, such as fractals with a wide range of masses and fractal dimension values, dense clusters with spherical and spheroidal aspect ratios, similar to those produced during coagulation experiments of colloidal suspensions. It was found that fractal clusters with low fractal dimensions and spheroidal clusters have sufficient structural anisotropies to show deviations from Einstein's relationship, and display a moderate shear thinning behavior, as well as a non-negligible linear viscoelasticity. On the other hand, clusters with high fractal dimensions tend to behave progressively more like spheres as their fractal dimension increases. We also found that the intrinsic viscosity of all clusters, independent of their morphology, can be quantitatively predicted by means of an equivalent ellipsoid model, in which clusters are modeled as ellipsoids with the same principal moments of inertia.     

Local Transient Jamming in Stress Relaxation of Bulk Amorphous Polymers

Bulk amorphous polymers become stretched and parallel-aligned under loading stress, and their intermolecular cooperation slows down the subsequent stress relaxation process. By means of dynamic Monte Carlo simulations, we employed the linear viscoelastic Maxwell model for stress relaxation of single polymers and investigated their intermolecular cooperation in the stress relaxation process of stretched and parallel-aligned bulk amorphous polymers. We carried out thermal fluctuation analysis on t...     

Interfacial colloidal sedimentation equilibrium. I. Intensity based confocal microscopy

This paper reports confocal microscopy measurements of inhomogeneous colloidal sedimentation equilibrium profiles near planar wall surfaces for conditions when colloid dimensions are comparable to the characteristic gravitational length scale. The intensity based confocal method developed in this work enables real-space measurements of one-dimensional density profiles of Brownian colloids without identifying many single colloid centers in large imaging volumes. Measured sedimentation equilibrium profiles for single-phase interfacial fluids and for coexisting inhomogeneous fluid and solid phases are in agreement with a perturbation theory and Monte Carlo simulations within the local density approximation. Monte Carlo simulated colloid scale density profiles display some minor differences with confocal images in terms of microstructural transitions involving the onset of interfacial crystallization and the precise elevation of the fluid-solid interface. These discrepancies are attributed to polydispersity unaccounted for in the analyses, sensitivity of the perturbation theory to the effective hard sphere size, and the influence of ensemble, system size, and box shape in Monte Carlo simulations involving anisotropic/inhomogeneous solids. Successful demonstration of intensity based confocal microscopy provides a basis for future measurements of three-dimensional colloidal interactions, dynamics, and structure near surfaces.     

Global and critical test of the perturbation density-functional theory based on extensive simulation of Lennard-Jones fluid near an interface and in confined systems

The structure of a Lennard-Jones (LJ) fluid subjected to diverse external fields maintaining the equilibrium with the bulk LJ fluid is studied on the basis of the third-order+second-order perturbation density-functional approximation (DFA). The chosen density and potential parameters for the bulk fluid correspond to the conditions situated at "dangerous" regions of the phase diagram, i.e., near the critical temperature or close to the gas-liquid coexistence curve. The accuracy of DFA predictions is tested against the results of a grand canonical ensemble Monte Carlo simulation. It is found that the DFA theory presented in this work performs successfully for the nonuniform LJ fluid only on the condition of high accuracy of the required bulk second-order direct correlation function. The present report further indicates that the proposed perturbation DFA is efficient and suitable for both supercritical and subcritical temperatures.