The ferroelectric transition of dipolar hard spheres

We investigate by Monte Carlo simulation the size dependence of the variation of the polarization and the dielectric constant with temperature for dipolar hard spheres at the two densities rho sigma3=0.80 and 0.88. From the crossing of the fourth-order cumulant for different system sizes first more precise estimates of the ferroelectric transition temperatures are obtained. Theoretical approaches, when predicting an ordering transition, are shown to generally overestimate the critical temperature.     

Effect of attractions on the structure of polymer solutions confined between surfaces: a density functional approach

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials.     

Thermodynamic perturbation theory for fused sphere hard chain fluids using nonadditive interactions

A model is developed for the equation of state of fused chains based on Wertheim thermodynamic perturbation theory and nonadditive size interactions. The model also assumes that the structure (represented by the radial distribution function) of the fused chain fluid is the same as that of the touching hard sphere chain fluid. The model is completely based on spherical additive and nonadditive size interactions. The model has the advantage of offering good agreement with simulation data while at the same time being independent of fitted parameters. The model is most accurate for short chains, small values of Delta (slightly fused spheres) and at intermediate (liquidlike) densities.     

Scaled particle theory of mixtures of hard spheres with negatively non-additive diameters

The scaled particle theory is solved for mixtures of hard spheres with arbitrary negative non-additive diameters in three dimensions. The results obtained with the Gibbs—Duhem relation show excellent agreement with the Monte-Carlo calculations. The results from the virial relation for high densities and high non-additivity are less satisfactory.     

Effect of attractive interactions on the structure of polymer melts confined between surfaces: a density-functional approach

A density-functional theory is presented to study the structure of polymers, having attractive interactions, confined between attractive surfaces. The theory treats the ideal-gas free-energy functional exactly and uses weighted density approximation for the hard-chain contribution to the excess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained from generalized Flory equation of state and the attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions are found to be in quite good agreement with the Monte Carlo simulation results for varying densities, chain lengths, and different interaction potentials. The results confirm important implications of using different approximations for the hard-sphere and attractive interactions.     

Orientational order in high density dipolar hard sphere fluids

Taking advantage of recent estimates, by one of us, of the critical temperature of the isotropic-ferroelectric transition of high density dipolar hard spheres, we performed new Monte Carlo simulations in the close vicinity of these estimates and applied histogram reweighting methods to obtain refined values of the critical temperatures from the crossing of the fourth-order cumulant for different system sizes. The ferroelectric line is determined in the density range rho*=0.80-0.95, and the onset of columnar ordering is located.     

Equilibrium equation of state of a hard sphere binary mixture at very large densities using replica exchange Monte Carlo simulations

We use replica exchange Monte Carlo simulations to measure the equilibrium equation of state of the disordered fluid state for a binary hard sphere mixture up to very large densities where standard Monte Carlo simulations do not easily reach thermal equilibrium. For the moderate system sizes we use (up to N = 100), we find no sign of a pressure discontinuity near the location of dynamic glass singularities extrapolated using either algebraic or simple exponential divergences, suggesting they do not correspond to genuine thermodynamic glass transitions. Several scenarios are proposed for the fate of the fluid state in the thermodynamic limit.     

Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.     

The interfacial tension and phase diagram of the Widom-Rowlinson mixture via Monte Carlo simulations

Results of Monte Carlo simulations are reported for the interfacial tension between two fluid phases in a binary mixture of penetrable spheres in which molecular pairs of like species do not interact, while those of unlike species interact as hard spheres. Semigrand canonical ensemble Monte Carlo simulations in a cubic cell with periodic boundary conditions are used to obtain histograms for various system sizes at various densities. At a given density, the interfacial tension and compositions of coexisting phases for an infinite system are evaluated via histogram analysis combined with finite-size scaling. The density dependence of the interfacial tension and phase diagram for an infinite system are thus obtained. The simulated behavior of the interfacial tension close to the critical density corroborates previous suggestions that the model belongs to the three-dimensional Ising universality class.     

Field induced gradient simulations: a high throughput method for computing chemical potentials in multicomponent systems

We present a simulation method for direct computation of chemical potentials in multicomponent systems. The method involves application of a field to generate spatial gradients in the species number densities at equilibrium, from which the chemical potential of each species is theoretically estimated. A single simulation yields results over a range of thermodynamic states, as in high throughput experiments, and the method remains computationally efficient even at high number densities since it does not involve particle insertion at high densities. We illustrate the method by Monte Carlo simulations of binary hard sphere mixtures of particles with different sizes in a gravitational field. The results of the gradient Monte Carlo method are found to be in good agreement with chemical potentials computed using the classical Widom particle insertion method for spatially uniform systems.     

Depletion potentials in colloidal mixtures of hard spheres and rods

The depletion potential between a hard sphere and a planar hard wall, or two hard spheres, imposed by suspended rigid spherocylindrical rods is computed by the acceptance ratio method through the application of Monte Carlo simulation. The accurate results and ideal-gas approximation results of the depletion potential are determined with the acceptance ratio method in our simulations. For comparison, the depletion potentials are also studied by using both the density functional theory and Derjaguin approximations. The density profile as a function of positions and orientations of rods, used in the density functional theory, is calculated by Monte Carlo simulation. The potential obtained by the acceptance ratio method is in good agreement with that of density functional theory under the ideal-gas approximation. The comparison between our results and those of other theories suggests that the acceptance ratio method is the only efficient method used to compute the depletion potential induced by nonspherical colloids with the volume fraction beyond the ideal-gas approximation.     

A consistent integral equation theory for hard spheres

The standard integral equation approach is used to extract the bridge function and other correlation functions of hard spheres fluid. To achieve this, we first use a recent consistent closure relation proposed by Bomont et al. [J. Chem. Phys. 119, 2188 (2003)] that has already proven to be accurate to describe the Lennard-Jones fluid properties. Second, we take advantage of the coherent scheme derived by Bomont [J. Chem. Phys. 119, 11484 (2003)] to calculate the excess chemical potential, the entropy and some relative transport properties. Very good agreement is obtained for structural quantities and thermodynamic properties as compared to exact data at densities ranging from 0.1 to 0.9.     

改进压缩性近似并导出新的硬球微扰理论表达式

提出在Barker与Henderson的压缩性近似推导中,相邻壳层之间的分子数应该相关,导出了相关系数和改进的二级微扰项,提高了高级微扰项在较高密度区的准确性。对二级以上的高级微扰项采用Barker与Henderson的近似方法,得到一个简单的微扰理论表达式,以硬球势为参考势,方阱势为微扰势,用一新的级数形式的径向分布函数导出了自由能、内能、比热、压缩因子的级数表达式。其四项截断式的计算结果与MC、MD计算机模拟值符合较好。     

Thermodynamically consistent closure approximation for hard spheres systems

We present a new closure relation that is an extension of the Percus-Yevick approximation. In the proposed closure, we introduce an additional term and a mixing coefficient that can be determined by imposing a condition of thermodynamic self-consistency. Moreover, the mixing coefficient is calculated analytically within a linear approximation. In the case of a monodisperse system of hard spheres, we compare the results of our model to well-established thermodynamic expressions and also to the structural properties of fairly known closure approximations. In the second case, and using an equivalent scheme, the new closure relation is extended to the depletion potential between two large hard spheres immersed in a liquid of small hard spheres. In both cases, the results of our model are in good agreement with numerical simulations performed at intermediate concentrations.     

Phase diagram of hard snowman-shaped particles

We present the phase diagram of hard snowman-shaped particles calculated using Monte Carlo simulations and free energy calculations. The snowman particles consist of two hard spheres rigidly attached at their surfaces. We find a rich phase behavior with isotropic, plastic crystal, and aperiodic crystal phases. The crystalline phases found to be stable for a given sphere diameter ratio correspond mostly to the close packed structures predicted for equimolar binary hard-sphere mixtures of the same diameter ratio. However, our results also show several crystal-crystal phase transitions, with structures with a higher degree of degeneracy found to be stable at lower densities, while those with the best packing are found to be stable at higher densities.     

Shape factors in equations of state. Part II. Repulsion phenomena in multicomponent chain fluids

An equation of state for the multicomponent fluid phase of nonattracting rigid particles of arbitrary shape is presented. The equation is a generalization of a previously presented equation of state for pure fluids of rigid particles; the approach describes the volumetric properties of a pure fluid in terms of a shape factor, zeta, which can be back calculated by scaling the volumetric properties of pure fluids to that of a hard sphere. The performance of the proposed equation is tested against mixtures of chain fluids immersed in a "monomeric" solvent of hard spheres of equal and different sizes. Extensive new Monte Carlo simulation data are presented for 19 binary mixtures of hard homonuclear tangent freely-jointed hard sphere chains (pearl-necklace) of various lengths (three to five segments), with spheres of several size ratios and at various compositions. The performance of the proposed equation is compared to the hard-sphere SAFT approach and found to be of comparable accuracy. The equation proposed is further tested for mixtures of spheres with spherocylinders. In all cases, the equation proved to be accurate and simple to use.     

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.     

Diamagnetic orientation of a fluid of hard thin disks and anisotropy of the water diffusivity in the nematic phase of a suspension of clay platelets

Monte Carlo simulations of the diamagnetic orientation of a fluid of hard thin disks in a magnetic field are presented. The particle density and magnetic field dependences of the eigenvalues of the order parameter tensor are calculated in the presence of a wall which promotes nematic order in a definite direction. The existence of a paranematic region is confirmed, and the approach to the Langevin regime at low densities in the paranematic regime is examined. A relationship between the eigenvalues of the tensor and the anisotropy of water diffusivity in the nematic phase of a colloidal suspension is proposed. This permits a comparison between the Monte Carlo simulations and diffusion-weighted magnetic resonance imaging, which shows consistency with the experimental data.     

Polydisperse hard spheres at a hard wall

The structural properties of polydisperse hard spheres in the presence of a hard wall are investigated via Monte Carlo simulation and density functional theory (DFT). Attention is focused on the local density distribution rho(sigma,z), measuring the number density of particles of diameter sigma at a distance z from the wall. Estimates of rho(sigma,z) are obtained for bulk volume fractions eta(b)=0.2 and eta(b)=0.4, and for two choices of the bulk parent distribution: a top-hat form, which we study for degrees of polydispersity delta=11.5% and delta=40.4%, and a truncated Schulz form having delta=40.7%. Excellent overall agreement is found between the DFT and simulation results, particularly at eta(b)=0.2. A detailed analysis of rho(sigma,z) confirms the presence of oscillatory size segregation effects, as observed in a previous DFT study [I. Pagonabarraga, M. E. Cates, and G. J. Ackland, Phys. Rev. Lett. 84, 911 (2000)]. For large delta, the character of these oscillation is observed to depend strongly on the shape of the parent distribution. In the vicinity of the wall, attractive sigma-dependent depletion interactions are found to greatly enhance the density of the largest particles. The local degree of polydispersity delta(z) is suppressed in this region, while further from the wall it exhibits oscillations.     

Stability boundaries, percolation threshold, and two-phase coexistence for polydisperse fluids of adhesive colloidal particles

We study the polydisperse Baxter model of sticky hard spheres (SHS) in the modified mean spherical approximation (mMSA). This closure is known to be the zero-order approximation C0 of the Percus-Yevick closure in a density expansion. The simplicity of the closure allows a full analytical study of the model. In particular we study stability boundaries, the percolation threshold, and the gas-liquid coexistence curves. Various possible subcases of the model are treated in details. Although the detailed behavior depends upon the particularly chosen case, we find that, in general, polydispersity inhibits instabilities, increases the extent of the nonpercolating phase, and diminishes the size of the gas-liquid coexistence region. We also consider the first-order improvement of the mMSA (C0) closure (C1) and compare the percolation and gas-liquid boundaries for the one-component system with recent Monte Carlo simulations. Our results provide a qualitative understanding of the effect of polydispersity on SHS models and are expected to shed new light on the applicability of SHS models for colloidal mixtures.