Dynamics in dense suspensions of charge-stabilized colloidal particles

The dynamic behavior of charge-stabilized colloidal particles in suspension was studied by photon correlation spectroscopy with coherent X-rays (XPCS). The short-time diffusion coefficient, D(Q) , was measured for volume concentrations φ ⩽ 0.18 and compared to the free particle diffusion constant D₀ and the static structure factor S(Q) . The data show that indirect, hydrodynamic interactions are relevant for the system and hydrodynamic functions were derived. The results are in striking contrast to the predictions of the PA (pairwise-additive approximation) model, but show features typical for a hard-sphere system. The observed mobility is however considerably smaller than the one of a respective hard-sphere system. The hydrodynamic functions can be modelled quantitatively if one allows for an increased effective viscosity relative to the hard-sphere case.     

Thermodynamics of pure and multicomponent dipolar hard-sphere fluids

The thermodynamics of two recent models of hard-sphere polar fluids is investigated. The two models are the Onsager model developed by Nienhuis and Deutch and the mean spherical approximation results obtained by Wertheim. The equation of state, vapour pressure curve, and other pertinent thermodynamic properties are determined. These results for the pure hard-sphere polar fluid complement the results recently reported by Rushbrooke, Stell and Høye. The thermodynamics of simple multicomponent hard-sphere polar mixtures is examined for the case of equal hard-sphere radii. Results for the multicomponent MSM are based on the exact solution of this model by Adelman and Deutch. The Onsager model is generalized to the case of many components. For both multicomponent models it is demonstrated that a variety of regions of instability exist for the one-phase fluid. Finally a discussion is included of how well these models agree with experiment.     

Universal cubic equation of state and contact values of the radial distribution functions for multi-component additive hard-sphere mixtures

A universal cubic equation of state (UC EOS) is proposed based on a modification of the virial Percus-Yevick (PY) integral equation EOS for hard-sphere fluid. The UC EOS is extended to multi-component hard-sphere mixtures based on a modification of Lebowitz solution of PY equation for hard-sphere mixtures. And expressions of the radial distribution functions at contact (RDFC) are improved with the form as simple as the original one. The numerical results for the compressibility factor and RDFC are in good agreement with the simulation results. The average errors of the compressibility factor relative to MC data are 3.40%, 1.84% and 0.92% for CP3P, BMCSL equations and UC EOS, respectively. The UC EOS is a unique cubic one with satisfactory precision among many EOSs in the literature both for pure and mixture fluids of hard spheres.     

Absence of re-entrant phase transition of the antiferromagnetic Ising model on the simple cubic lattice: Monte Carlo study of the hard-sphere lattice gas

We perform Monte Carlo simulations of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion. The critical activity is estimated, z_c = 1.0588 ± 0.0003. Using a relation between the hard-sphere lattice gas and the antiferromagnetic Ising model in an external magnetic field, we conclude that there is no re-entrant phase transition of the latter on the simple cubic lattice.     

带电粒子形成胶体晶体的有效硬球模型判据的计算机模拟验证

在对胶体晶体的研究中,带电粒子胶体晶体的形成机理比硬球胶体晶体更加复杂,对其形成条件目前还缺少有效的判断依据. 有效硬球模型判据提出以有效直径作为判断参数. 为了验证该判据的有效性,利用布朗动力学模拟研究了不同有效直径下带电粒子胶体晶体的特性. 为了更加定量地研究单因素对带电胶体晶体形成的影响,取有效直径为2.8至0.8,并对一定的有效直径,研究了粒子几何直径和排斥力不同情况下的结晶行为. 在布朗动力学模拟过程中,采用径向分布函数和键序参数方法检测体系的结构变化,并分析所形成的晶体结构. 结果表明,在判断带电粒子胶体体系能否形成有序结构方面,有效硬球模型判据有一定的合理性. 但是,并不能将有效直径作为唯一的判别参数,而是需要综合其他参数的影响,这显示出该判据的片面性. 关键词： 布朗动力学模拟 带电胶体晶体 有效硬球模型     

Is the percolation transition of hard spheres a thermodynamic phase transition?

In hard-sphere systems, there is a fluid-solid transition, but no gas-liquid transition. In the fluid region, however, one can find a purely geometric percolation transition, which is studied in detail. The van der Waals model of hard spheres is treated. In this model, a uniform negative background potential is added. This modification does not change the structure, but induces a gas-liquid transition. In fact, percolation and the gas-liquid transition can be related to each other.     

Thermodynamic properties of liquid metals,temperature dependent hard-sphere model

An analytic solution of the Percus-Yevick equation for the hard-sphere model of a liquid is used to investigate the thermodynamic properties of liquid metals near the triple point. The temperature dependence of the packing fraction (or hard-sphere diameter) is introduced by the phenomenological method using the compressibility equation. Agreement between theory and experiment is improved for both the thermal pressure coefficient and specific heat.     

Stationary extended kinetic theory for a gas of hard spheres

Summary Analytical and numerical results for the stationary, spatially homogeneous distribution function of a gas of ?hard-sphere? particles are reported. Both removal and scattering effects are accounted for. In the case of only removal, comparison is also made with results obtained in the frame of alternative models proposed for approximating the exact ?hard-sphere? model.     

Hard-sphere-like dynamics in a non-hard-sphere liquid

The collective dynamics of liquid gallium close to the melting point has been studied using inelastic x-ray scattering to probe length scales smaller than the size of the first coordination shell. Although the structural properties of this partially covalent liquid strongly deviate from a simple hard-sphere model, the dynamics, as reflected in the quasielastic scattering, are beautifully described within the framework of the extended heat mode approximation of Enskog's kinetic theory, analytically derived for a hard-sphere system. The present work demonstrates, therefore, the applicability of Enskog's theory beyond simple liquids.     

Selective-pivot sampling of radial distribution functions in asymmetric liquid mixtures

We present a new method for selectively sampling radial distribution functions and effective interaction potentials in asymmetric liquid mixtures using a Monte Carlo simulation. We demonstrate its efficiency for hard-sphere mixtures, and for model systems with more general interactions, and compare our simulations with several analytical approximations. For interaction potentials containing a hard-sphere contribution, the algorithm yields the contact value of the radial distribution function.     

An equation of state for the isotropic phase of linear,partially flexible and fully flexible tangent hard-sphere chain fluids

A new equation of state is developed that accurately describes the isotropic phase behaviour of linear, partially flexible and fully flexible tangent hard-sphere chain fluids and their mixtures. The equation of state is based on the equation of state of Liu and Hu [H. Liu and Y. Hu, Fluid Phase Equilibr. 122, 75 (1996)] for fully flexible chain fluids. The effect of molecular flexibility is described by a pure-component parameter that is introduced in the theory at the level of the cavity correlation function of next-to-nearest neighbour segments in a chain molecule. The equation of state contains a total of three adjustable model constants. The extension to partially flexible- and linear chain fluids is based on a refitting of the first model constant to numerical data of the second virial coefficient of partially flexible and linear tangent hard-sphere chain fluids. The numerical data were obtained from an analytical approximation for the pair-excluded volume. The other two parameters were adjusted to molecular simulation data for the pressure of linear tangent hard-sphere chain fluids. For both, pure component systems and mixtures of chains of variable flexibility, the pressure and second virial coefficient obtained from the equation of state, are in excellent agreement with the results from Monte Carlo simulations. A significant improvement to TPT1, TPT2, generalised Flory-dimer theory and scaled particle theory is observed.     

Quasihard-sphere model in simulation of the processes of particle scattering

A model of interatomic potentials of interaction is suggested for static simulation of the processes of elastic scattering of atomic particles by atoms of gas, plasma, and solid. In the developed model, the atomic particle radii, whose magnitude depends on the energy of their relative motion, are internal parameters. The suggested quasihard-sphere model enables one to simulate elastic processes of scattering of atomic particles, using different interatomic potentials of interaction with relatively high rates of statistical simulation characteristic of simulation within the hard-sphere model. The Born-Mayer potential is selected as the interatomic potential of interaction and modified for a wide class of partners in atomic collisions. It is demonstrated that the suggested mathematical model of quasihard spheres describes fairly correctly the processes of elastic scattering of atoms in a gas medium and of displaced atoms in a solid with an almost constant rate of static simulation.     

Microscopic theory of intrinsic shear and bulk viscosities

A microscopic theory of intrinsic shear and bulk viscosities of solutions is given for a model of particles that interact with hard-sphere cores and weak longrange attraction. The approximation considered (the velocity chaos assumption of the Enskog theory) can be expected to yield quantitatively useful values for viscosities of the model solute-solvent system when the solute particles are not much larger than the solvent particles. Under solute-solvent mixing conditions of constant pressure and temperature we find that the intrinsic viscosities of a hard-sphere solute in a hard-sphere solvent can be positive or negative, depending upon size and mass ratios; for solute and solvent particles whose mass ratio equals their volume ratio, the intrinsic shear and bulk viscosities are always positive for solute particles larger than solvent particles: in the opposite case, the intrinsic shear viscosity is always negative while the intrinsic bulk viscosity is for the most part negative, becoming positive again when the solute particle is sufficiently small. For solute particles smaller than solvent particles, this result is sensitive to change in mass ratio. The addition of solvent-solvent attraction is found to lower the intrinsic viscosities substantially; the addition of solute-solvent attraction raises it. Detailed quantitative analysis of these effects is given.     

Stochastic hard-sphere dynamics for hydrodynamics of nonideal fluids

A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard-sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.     

Weighted-density approaches for polymer structure at solid–polymer interfaces

Weighted-density approximations (WDAs), which are based on the weighting function for the second-order direct correlation functions (DCFs) of the uniform polymeric fluids, have been developed to investigate the structural and thermodynamic properties of polymer melts at interfaces. The advantage is the simplicity of calculation of the weighting functions and their accuracies in the applications. They were applied to study the local density distributions and adsorption isotherms of the freely jointed tangent hard-sphere chain, Yukawa chain, and hard-sphere chain mixture in slit pores. The polymer reference interaction model (PRISM) integral equation with the Percus–Yevick (PY) closure has been used to calculate the second-order DCF of the polymeric fluids required as inputs. The mean-field approximation (MFA) has been used to calculate the weighting function for the attractive contribution of a freely jointed tangent Yukawa chain fluid, having attraction among the beads. The calculated results show that (i) for the freely jointed tangent hard-sphere chain, the present theory is in excellent agreement with the computer simulations over a wide range of chain lengths and bulk densities, (ii) the WDA approach for the attraction provides an accurate method for the local density distributions of a freely jointed tangent Yukawa chain fluid, and that (iii) the present theory also yields a reasonably good result for the structural properties of the freely jointed hard-sphere chain mixtures composed of the chain and monomer.     

Generalized hydrodynamic equations in the hard-spheres model

Generalized linearized hydrodynamic equations in the hard-sphere model are considered on the basis of N.N. Bogolubov’s approximate approach to the analysis of collective interactions. The generalized matrix of transfer coefficients is shown not to be self-adjoint when the finiteness of the two-particle interaction region is taken into account.     

Quantum perturbations to the radial distribution function of a hard-sphere fluid

Expressions derived in the previous paper for quantum corrections to the radial distribution function of a fluid are applied to the hard-sphere fluid. It is found that the perturbation theory given in the paper is valid only at very high values of temperatures when applied to calculate the correction to the distribution function of the hard-sphere fluid and is not valid at the temperatures at which Gibson and others have obtained numerical results for a given value of ?a³, where ? is the number density and a the hard-sphere diameter.     

Disappearance of the gas-liquid phase transition for highly charged colloids

We calculate the full phase diagram of spherical charged colloidal particles using Monte Carlo free energy calculations. The system is described using the primitive model, consisting of explicit hard-sphere colloids and point counterions in a uniform dielectric continuum. We show that the gas-liquid critical point becomes metastable with respect to a gas-solid phase separation at colloid charges Q > or =20 times the counterion charge. Approximate free energy calculations with only one and four particles in the fluid and solid phases, respectively, are used to determine the critical line for highly charged colloids up to Q=2000. We propose the scaling law T*(c) approximately Q(1/2) for this critical temperature.