How short-range attractions impact the structural order, self-diffusivity, and viscosity of a fluid

We present molecular simulation data for viscosity, self-diffusivity, and the local structural ordering of (i) a hard-sphere fluid and (ii) a square-well fluid with short-range attractions. The latter fluid exhibits a region of dynamic anomalies in its phase diagram, where its mobility increases upon isochoric cooling, which is found to be a subset of a larger region of structural anomalies, in which its pair correlations strengthen upon isochoric heating. This "cascade of anomalies" qualitatively resembles that found in recent simulations of liquid water. The results for the hard-sphere and square-well systems also show that the breakdown of the Stokes-Einstein relation upon supercooling occurs for conditions where viscosity and self-diffusivity develop different couplings to the degree of pairwise structural ordering of the liquid. We discuss how these couplings reflect dynamic heterogeneities. Finally, we note that the simulation data suggest how repulsive and attractive glasses may generally be characterized by two distinct levels of short-range structural order.     

Model for the free-volume distributions of equilibrium fluids

We introduce and test via molecular simulation a simple model for predicting the manner in which interparticle interactions and thermodynamic conditions impact the single-particle free-volume distributions of equilibrium fluids. The model suggests a scaling relationship for the density-dependent behavior of the hard-sphere system. It also predicts how the second virial coefficients of fluids with short-range attractions affect their free-volume distributions.     

Magnetophoresis, sedimentation, and diffusion of particles in concentrated magnetic fluids

A dynamic mass transfer equation for describing magnetophoresis, sedimentation, and gradient diffusion of colloidal particles in concentrated magnetic fluids has been derived. This equation takes into account steric, magnetodipole, and hydrodynamic interparticle interactions. Steric interactions have been investigated using the Carnahan-Starling approximation for a hard-sphere system. In order to study the effective interparticle attraction, the free energy of the dipolar hard-sphere system is represented as a virial expansion with accuracy to the terms quadratic in particle concentration. The virial expansion gives an interpolation formula that fits well the results of computer simulation in a wide range of particle concentrations and interparticle interaction energies. The diffusion coefficient of colloidal particles is written with regard to steric, magnetodipole and hydrodynamic interactions. We thereby laid the foundation for the formulation of boundary-value problems and for calculation of concentration and magnetic fields in the devices (for example, magnetic fluid seals and acceleration sensors), which use a concentrated magnetic fluid as a working fluid. The Monte-Carlo methods and the analytical approach are employed to study the magnetic fluid stratification generated by the gravitational field in a cylinder of finite height. The coefficient of concentration stratification of the magnetic fluid is calculated in relation to the average concentration of particles and the dipolar coupling constant. It is shown that the effective particle attraction causes a many-fold increase in the concentration inhomogeneity of the fluid if the average volume fraction of particles does not exceed 30%. At high volume concentrations steric interactions play a crucial role.     

Structure, dynamics, and optical properties of concentrated milk suspensions: an analogy to hard-sphere liquids

A systematic study of the effects of volume fraction increment on the optical properties, the structure, and the dynamics of the casein micelles and fat droplets in milk was performed using diffusing wave spectroscopy. Four types of milk were investigated, NIDO full fat milk, fat-free milk, whey and fat-free milk, and finally lactose and fat-free milk. Independent measurements to calculate the dependence of the viscosity and the index of refraction of the milk serum and casein micelles as a function of the volume fraction were also performed. We compare the experimentally determined quantities photon transport mean free path (l*) and self-diffusion coefficient D(s) with the predictions from theoretical calculations using classical colloidal models such as a hard-sphere fluid. We demonstrate that all types of milk with and without fat content behave, structurally, like colloidal hard-sphere systems up to volume fractions well over 45%. In the case of dynamic measurements, both lactose- and fat-free and whey- and fat-free milk behave also like hard-sphere systems whereas fat-free milk and fat-containing NIDO milk deviate slightly at volume fractions over 35%. Finally, a comparative measurement and theoretical calculation of the casein micelle's size was performed.     

Voronoi neighbor statistics of hard-disks and hard-spheres

The neighbor distribution in hard-sphere and hard-disk fluids is analyzed using Voronoi tessellation. The statistical measures analyzed are the nth neighbor coordination number (Cn), the nth neighbor distance distribution [fn(r)], and the distribution of the number of Voronoi faces (Pn). These statistics are sensitive indicators of microstructure, and they distinguish thermodynamic and annealed structures. A sharp rise in the hexagon population marks the onset of hard-disk freezing transition, and Cn decreases sharply to the hexagonal lattice values. In hard-disk random structures the pentagon and heptagon populations remain significant even at high volume fraction. In dense hard-sphere (three-dimensional) structures at the freezing transition, C1 is close to 14, instead of the value of 12 expected for a face-centered-cubic lattice. This is found to be because of a topological instability, where a slight perturbation of the positions in the centers of a pair of particles transforms a vertex in the Voronoi polyhedron into a Voronoi surface. We demonstrate that the pair distribution function and the equation-of-state obtained from Voronoi tessellation are equal to those obtained from thermodynamic calculations. In hard-sphere random structures, the dodecahedron population decreases with increasing density. To demonstrate the utility of the neighbor analysis, we estimate the effective hard-sphere diameter of the Lennard-Jones fluid by identifying the diameter of the spheres in the hard-sphere fluid which has C1 equal to that for the Lennard-Jones fluid. The estimates are within 2% deviation from the theoretical results of Barker-Henderson and Weeks-Chandler-Andersen.     

Rheology of polystyrene latexes with adsorbed and free gelatin

The rheology of monodisperse polystyrene latex particles of two different particle radii (26 and 67 nm) has been studied with a range of concentrations of the polyampholyte gelatin. Gelatin contributes to the rheology by adsorption to the particles and by thickening the continuous phase. High viscosities and strong shear thinning are measured for low volume fractions of latex. A procedure is presented to deconvolute the effects of free and bound gelatin by applying simple hard-sphere models. This procedure allows us to estimate the effective size of the gelatin-covered particles as well as the continuous-phase gelatin concentration and viscosity. The layer thicknesses from rheology agree well with those from PCS. The effect of varying particle volume fraction, ionic strength, pH and gelatin and surfactant concentration on the rheology of these suspensions is presented. For the smaller latex, the adsorbed layer occupies a greater fraction of the effective volume. Increasing free polymer concentration reduces the adsorbed-layer thickness. The reduced critical shear stress increases with the suspension viscosity for suspensions of the 26 nm latex but is constant for the 67 nm latex. At very high shear (>2000 s⁻¹), the suspensions show excess shear thinning over that expected from a hard-sphere model. This excess thinning is attributed to deformation of the adsorbed gelatin layer under high shear stress and interpreted in terms of an empirical interparticle potential.     

Voronoi cell volume distribution and configurational entropy of hard-spheres

The Voronoi cell volume distributions for hard-disk and hard-sphere fluids have been studied. The distribution of the Voronoi free volume vf, which is the difference between the actual cell volume and the minimal cell volume at close packing, is well described by a two-parameter (2gamma) or a three-parameter (3gamma) gamma distribution. The free parameter m in both the 2gamma and 3gamma models is identified as the "regularity factor." The regularity factor is the ratio of the square of the mean and the variance of the free volume distribution, and it increases as the cell volume distribution becomes narrower. For the thermodynamic structures, the regularity factor increases with increasing density and it increases sharply across the freezing transition, in response to the onset of order. The regularity factor also distinguishes between the dense thermodynamic structures and the dense random or quenched structures. The maximum information entropy (max-ent) formalism, when applied to the gamma distributions, shows that structures of maximum information entropy have an exponential distribution of vf. Simulations carried out using a swelling algorithm indicate that the dense random-packed states approach the distribution predicted by the max-ent formalism, though the limiting case could not be realized in simulations due to the structural inhomogeneities introduced by the dense random-packing algorithm. Using the gamma representations of the cell volume distribution, we check the numerical validity of the Cohen-Grest expression [M. H. Cohen and G. S. Grest, Phys. Rev. B 20, 1077 (1979)] for the cellular (free volume) entropy, which is a part of the configurational entropy. The expression is exact for the hard-rod system, and a correction factor equal to the dimension of the system, D, is found necessary for the hard-disk and hard-sphere systems. Thus, for the hard-disk and hard-sphere systems, the present analysis establishes a relationship between the precisely defined Voronoi free volume (information) entropy and the thermodynamic entropy. This analysis also shows that the max-ent formalism, when applied to the free volume entropy, predicts an exponential distribution which is approached by disordered states generated by a swelling algorithm in the dense random-packing limit.     

A small-angle X-ray scattering study of the interactions in concentrated silica colloidal dispersions

The structure factors of colloidal silica dispersions at rather high volume fractions (from 0.055 to 0.22) were measured by small-angle X-ray scattering and fitted with both the equivalent hard-sphere potential model (EHS) and the Hayter-Penfold/Yukawa potential model (HPY). Both of these models described the interactions in these dispersions successfully, and the results were in reasonable agreement. The strength and range of the interaction potentials decreased with increasing particle volume fractions, which suggests shrinkage of the electrical double layer arising from an increase in the counterion concentration in the bulk solution. However, the interactions at the average interparticle separation increased as the volume fraction increased. The interaction ranges (delta) determined by the two models were very similar. Structure factors were also used to determine the size and volume fraction of the particles. The values of the size obtained from the structure factors were slightly larger than those obtained from the form factors; this difference is ascribed to the nonspherical shape and polydispersity of the colloidal particles. The volume fractions measured by these two methods were very similar and are both in good agreement with the independently measured results.     

Entropic interfaces in hard-core model amphiphilic mixtures

We investigate bulk and interfacial properties of a recently proposed hard-body model for a ternary mixture of amphiphilic particles, spheres and needles using density functional theory. The simple model amphiphiles are formed by bonding a vanishingly thin needle tail radially to a hard-sphere head group. Such particles provide a natural amphiphile when added to a binary mixture of spheres and needles. As all interactions are hard, we seek to find whether amphiphilic effects can be driven by entropy without the need to invoke attractive interactions. In order to assess the amphiphilic character of the model we first examine the spatial and orientational distribution of the amphiphiles at the free interface between demixed needle-rich and amphiphile-rich fluid phases of the binary amphiphile-needle subsystem. We then consider the free interface between sphere-rich and needle-rich phases upon adding amphiphiles with low concentration to the demixed system. In both cases the orientational distribution of the particles in the interface provides strong evidence that amphiphilic properties can arise purely from geometrical packing effects.     

A novel method to describe the interaction pressure between charged plates with application of the weighted correlation approach

Based on the Euler-Lagrange equation for ion density distribution in an inhomogeneous, charged, and hard-sphere fluid, a novel method is proposed to determine the interaction pressure between charged plates. The resulting expression is a sum of distinct physical contributions to the pressure, which involves different contributions to the single-particle direct correlation function. It can, therefore, be conveniently used in any density functional approach to facilitate analysis of the pressure components. In this study, the so-called fundamental measure theory (FMT)∕weighted correlation approach (WCA) approach is applied to estimate both the hard-sphere and the electric residual contributions to the single-particle direct correlation function, upon the calculation of the ionic density profiles between charged plates. The results, against the Monte Carlo simulations, show that the FMT∕WCA approach is superior to the typical FMT∕mean spherical approximation approach of the density functional theory in predicting the interaction pressure between charged plates immersed in an electrolyte solution upon various conditions in the primitive model. The FMT∕WCA approach can well capture the fine features of the pressure-separation dependence, to reproduce not only the shoulder shape and the weak attractions in monovalent electrolytes but also the strongly oscillatory behavior of pressure in divalent electrolytes where pronounced attractions are observed. In addition, it is found that the FMT∕WCA approach even has an advantage over the anisotropic, hyper-netted chain approach in that it agrees with the Monte Carlo results to a very good extent with, however, much less computational effort.     

A corresponding states principle for the equation of state of hard body fluid mixtures

A theoretically based corresponding-states principle is developed for athermal mixtures consisting of hard molecules. The principle states that when scaled appropriately, the excess compressibility factor for such mixtures reduces to a universal function of the effective packing fraction of the mixture. The latter represents the number density reduced by means of the effective molecular volume, which is defined as the volume a molecule excludes to any point of another molecule and depends on the geometry of both molecules. The scaling factor is related to a sort of effective nonsphericity parameter for the mixture that depends on composition as well as the nonsphericity parameters of the molecules which form the mixture and their effective molecular volumes. The universal function represents the excess compressibility factor of a pure hard-sphere fluid. Results are in good agreement with available simulation data.     

The decay of pair correlations in quantum hard-sphere fluids

A study of the asymptotic decay of the pair radial correlations in the bare quantum hard-sphere (QHS) fluid and in the quantum hard-sphere Yukawa (QHSY) fluid is presented. The conditions explored are far from quantum exchange and are contained within the region (0.1相似文献   

Structures and correlation functions of multicomponent and polydisperse hard-sphere mixtures from a density functional theory

The structures of nonuniform binary hard-sphere mixtures and the correlation functions of uniform ternary hard-sphere mixtures were studied using a modified fundamental-measure theory based on the weight functions of Rosenfeld [Rosenfeld, Phys. Rev. Lett. 63, 980 (1989)] and Boublik-Mansoori-Carnahan-Starling-Leland equation of state [Boublik, J. Chem. Phys. 53, 471 (1970); Mansoori et al., J. Chem. Phys. 54, 1523 (1971)]. The theoretical predictions agreed very well with the molecular simulations for the overall density profiles, the local compositions, and the radial distribution functions of uniform as well as inhomogeneous hard-sphere mixtures. The density functional theory was further extended to represent the structure of a polydisperse hard-sphere fluid near a hard wall. Excellent agreement was also achieved between theory and Monte Carlo simulations. The density functional theory predicted oscillatory size segregations near a hard wall for a polydisperse hard-sphere fluid of a uniform size distribution.     

Hard structured particles: suspension synthesis, characterization, and compressibility

Hard interactions are developed on three grades of fumed silica by eliminating interparticle forces and sterically stabilizing the particles by attaching an organic coating to the surface of the particles, suspending them in an index-matching solvent and screening the electrostatics. These hard-structured particles are studied to understand the effects of the particle's microstructure on suspension properties without the influence of interparticle forces other than volume exclusion, Brownian, and hydrodynamic interactions. Light and X-ray scattering studies of low-volume-fraction suspensions suggest that the fumed silicas consist of primary particle of radius of gyration R(g1) approximately equals 16 nm and aggregate size R(g2) approximately 50 nm and mass fractal dimension D(f) approximately equals 2.2. Osmotic compressibilities of these suspensions are measured as a function of particle concentration exploring the packing mechanism of fumed silica. While there is minimal detectable change in the primary particle size, R(g2) varies by approximately 15%, providing insight into how suspension properties are related to particle size. As expected of hard particles with the same microstructure, the concentration dependence on the osmotic pressure superimposes with volume fraction of solids. The comparison of fumed-silica-suspension measurements to the known behavior of hard-sphere suspensions demonstrates the effects of particle geometry on suspension properties with indications of interpenetration of the fumed silica due to their open geometry.     

Phase coexistence in polydisperse multi-Yukawa hard-sphere fluid: high temperature approximation

High temperature approximation (HTA) is used to describe the phase behavior of polydisperse multi-Yukawa hard-sphere fluid mixtures. It is demonstrated that in the frames of the HTA the model belongs to the class of "truncatable free energy models," i.e., the models with thermodynamical properties (Helmholtz free energy, chemical potential, and pressure) defined by the finite number of generalized moments. Using this property we were able to calculate the complete phase diagram (i.e., cloud and shadow curves as well as binodals) and size distribution functions of the coexisting phases of several different models of polydisperse fluids. In particular, we consider polydisperse one-Yukawa hard-sphere mixture with factorizable Yukawa coefficients and polydisperse Lennard-Jones (LJ) mixture with interaction energy parameter and/or size polydispersity. To validate the accuracy of the HTA we compare theoretical results with previously published results of more advanced mean spherical approximation (MSA) for the one-Yukawa model and with the Monte Carlo (MC) computer simulation results of [Wilding et al. J. Chem. Phys. 121, 6887 (2004); Phys. Rev. Lett. 95, 155701 (2005)] for the LJ model. We find that overall predictions of the HTA are in reasonable agreement with predictions of the MSA and MC, with the accuracy range from semiquantitative (for the phase diagram) to quantitative (for the size distribution functions).     

Distinguishing between dynamic yielding and wall slip in a weakly flocculated colloidal dispersion

Silica spheres coated with grafted poly(butyl methacrylate) chains and dispersed in a poor solvent at low to moderate volume fractions display high elastic and loss moduli, together with viscosities that diverge at a dynamic yield stress and decrease by several orders of magnitude with increasing stress. The elastic modulus and dynamic yield stress increase rapidly with volume fraction, but remain in constant ratio. Longer grafted chains produce stronger interparticle attractions, resulting in a smaller yield strain and larger elastic modulus. An apparent Newtonian plateau at extremely low shear rates in creep experiments is argued to result from slip at the wall. Thus, attractions between these grafted layers in a poor solvent generate a pseudo plastic solid, a metastable state that persists indefinitely and demonstrates little affinity for the walls of the rheometer, hence the slip. In contrast, depletion flocculated dispersions with higher volume fractions but weaker attractions produce very similar rheology but with a true Newtonian viscosity and adhesion to the wall.     

Structure and thermodynamics of hard-core Yukawa fluids: thermodynamic perturbation approaches

The thermodynamic perturbation theories, which are based on the power series of a coupling constant (λ-expansion), have been proposed for studying the structural and thermodynamic properties of a hard-core Yukawa (HCY) fluid: one (A1-approximation) is the perturbation theory based on the hard-sphere repulsion as a reference system. The other (A2-approximation) is the perturbation theory based on the reference system which incorporates both the repulsive and short-range attractive interactions. The first-order mean-spherical approximation (FMSA) provided by Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] has been employed for investigating the thermodynamic properties of a HCY fluid using the alternative method via the direct correlation function. The calculated results show that (i) the A1 and A2 approximations are in excellent agreements with previous computer simulation results in the literature and compare with the semi-empirical works of Shukla including the higher-order free energy terms, (ii) the A1 and A2 approximations are better than the FMSA and the mean-spherical approximation, (iii) the A2-approximation compares with the A1-approximation, even though the perturbation effect of an A2-approximation is much smaller than that of an A1-approximation, and that (iv) the FMSA study is particularly of advantage in providing the structure and thermodynamics in a simple and analytic manner.