The triplet distribution function in a fluid of hard spheres

The distribution functions of a fluid can be expressed as a series in powers, of the density. The coefficient of the fourth power of the density in the expansion of the triplet distribution function is obtained as a function of the separations of the molecules for a fluid of hard spheres. The coefficient is negative. It is used to estimate the amount by which the true triplet distribution function is less than the value attributed to it by the superposition approximation.     

Static structure factor for a fluid with interaction of hard spheres plus two Yukawa tails

We determine the static structure factor S(k) for a fluid of hard spheres with two-Yukawa interactions through the application of the mean spherical approximation (MSA) to a multi-component system composed of hard-spheres plus double Yukawa interactions (HSDY). This S(k) depends on scaling parameters Γ_n that satisfy a system of nonlinear equations. We report explicit results for a mono-dispersed HSDY fluid and show that the hard-sphere contributions control the main peak of the S(k),while for wave vectors approaching zero, we predict a cluster peak which could be identified with that of recent experimental results of Liu et al. [Y. Liu, W.-R. Chen, S.H. Chen, J. Chem. Phys. 122 (2005) 044507-1].     

Knudsen diffusivity of a hard sphere in a rough slit pore

An analytic theory for the Knudsen self-diffusivity D(s) of hard spheres in an atomically rough slit-shaped pore is presented which quantitatively matches simulation results. The theory assumes that, due to chaotic molecular trajectories caused by surface morphology, collisions of gas molecules with the wall are partly diffuse and partly specular, the relative magnitude of each depending upon the magnitude of the tangential momentum accommodation coefficient f. The theory thus represents a universal Knudsen fluctuation-dissipation correlation between longitudinal momentum loss and diffusivity that can simplify efforts to estimate D(s). It is also found that D(s) computed using Maxwell's theory of slip, in which collisions with the walls are assumed to be purely diffuse or specular, overpredicts the simulated D(s) by a large margin.     

Electron spectral density in a disordered system of hard sphere scatterers

The spectral density of an electron propagating in a disordered system of hard sphere scatterers is studied by use of a self-consistent approximation for the self-energy. The spectral density at fixed wavenumber is found to be a single-peaked function of energy. The approximation yields a sharp wavenumber-dependent band edge. For large wavenumbers the spectral density is well approximated by a Lorentzian, but for small wavenumbers it is dominated by a characteristic square root singularity at the band edge.     

The pressure of a hard sphere fluid on a curved surface

Utilizing the integral equation approach to the hard sphere fluid system developed in the preceding paper, the hard sphere-hard wall interaction is studied. For the case of a flat wall, perturbation solutions of the integral equation valid to second and third order in the packing fraction,y, are derived. For a surface of arbitrary curvature, an equation of state valid to second order in the packing fraction is also derived. When applied to very small cavities, it is found that the pressure at high densities is significantly higher than it would be for a flat wall.     

Computer simulation of cavity pair distribution functions of hard spheres in a hard slit pore

We describe efficient Monte Carlo computer simulation techniques to calculate conditional distribution functions for pairs of hard-sphere (HS) cavities in a hard slit pore of width L, n* (z ₁,z ₂,r), and use these as an efficient route to calculating the corresponding dimensionless excess chemical potentials μ ^e (z ₁,z ₂,r). z_i is the distance of an HS centre from a (specified) wall and r is the distance between the cavity centres. This is the first calculation of such functions, which are of interest in their own right and provide data for the testing of theories, in addition to providing data for a simple model for the infinite dilution behaviour of a polyatomic solute in a simple molecularly confined solvent. Results are presented for special cases for the cavity functions n* (z ₁,z ₂,r) which occur when the spheres are in the same plane, when the line of sphere centres is perpendicular to the walls, and when the spheres are in contact. We compare results obtained using the Kirkwood superposition approximation in conjunction with results obtained from the computer simulation data using the first member of the BGY integral equation hierarchy. The approximation is found to be exact in certain limiting geometrical situations, but in general is quantitatively poor.     

Extended hydrodynamic modes in a dense hard sphere fluid

A computer simulation experiment of a dense hard sphere fluid of 256 particles shows that the intermediate scattering function and the longitudinal velocity correlation function can be described by three extended hydrodynamic modes, the properties of which agree well with those predicted by the revised Enskog theory.     

Structure and phase transitions in a network-forming associating Lennard-Jones fluid in a slit-like pore: a density functional approach

A study is reported of adsorption of an associating Lennard-Jones fluid with four associative sites per molecule in a slit-like pore. The density distribution of particles in the pore and thermodynamics properties are evaluated by using a density functional method. It is found that at low temperatures the fluid exhibits a set of layering transitions, followed by capillary condensation. Transitions are localized by analysing the grand canonical potential. The density profiles of particles and the distribution of unbound and differently bonded particles demonstrate changes in the structure of the fluid in the pore along the phase coexistence. The critical temperature is lower for a confined fluid, compared with the bulk counterpart. However, an increase in the energy of association increases the critical temperature. The envelope of the capillary condensation is narrower than the bulk liquid-vapour phase diagram. The dependence of the solvation force on the energy of association and on the bulk density is discussed.     

The second dielectric virial coefficient of a dipolar sticky hard sphere fluid

We calculate the second dielectric virial coefficient, B _?, of a fluid whose molecules are sticky hard spheres with embedded central point dipoles. The effect of stickiness is to increases B _? markedly.     

The orientational pair correlation functions in a dense hard sphere fluid at long times

The two-particle contribution to the potential part of the stress tensor autocorrelation function of a dense hard sphere fluid is studied. It is shown that the long-time decay is given as the solution of a diffusion equation for the relative particle in a potential of mean force. The diffusion constant needed in order to accurately reproduce molecular dynamics results is found to be somewhat lower than the self-diffusion constant.     

Density fluctuations and the structure of a nonuniform hard sphere fluid

We derive an exact equation for density changes induced by a general external field that corrects the hydrostatic approximation where the local value of the field is adsorbed into a modified chemical potential. Using linear response theory to relate density changes self-consistently in different regions of space, we arrive at an integral equation for a hard sphere fluid that is exact in the limit of a slowly varying field or at low density and reduces to the accurate Percus-Yevick equation for a hard core field. This and related equations give accurate results for a wide variety of fields.     

Liquid-glass transition of a fluid confined in a disordered porous matrix: a mode-coupling theory

We derive an extension of the mode-coupling theory for the liquid-glass transition to a class of models of confined fluids, where the fluid particles evolve in a disordered array of interaction sites. We find that the corresponding equations are similar to those describing the bulk, implying that the methods of investigation which were developed there are directly transferable to this new domain of application. We then compute the dynamical phase diagram of a simple model system and show that new and nontrivial transition scenarios, including reentrant glass transitions and higher-order singularities, can be predicted from the proposed theory.     

Competition of percolation and phase separation in a fluid of adhesive hard spheres

Using a combination of Monte Carlo techniques, we locate the liquid-vapor critical point of adhesive hard spheres. We find that the critical point lies deep inside the gel region of the phase diagram. The (reduced) critical temperature and density are tau(c)=0.1133+/-0.0005 and rho(c)=0.508+/-0.01. We compare these results with the available theoretical predictions. Using a finite-size scaling analysis, we verify that the critical behavior of the adhesive hard sphere model is consistent with that of the 3D Ising universality class, the default for systems with short-range attractive forces.     

Analytical expressions for the correlation function of a hard sphere dimer fluid

A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids.     

Monte Carlo data of dilute solutions of large spheres in binary hard sphere mixtures

Monte Carlo (MC) simulation data for additive binary hard sphere mixtures are reported for dilute concentrations of the large sphere. Using a single occupancy linked cell method, binary hard sphere solutions with a size ratio of 5 are simulated at high reduced density and low concentration of the large sphere. Data for the solute-solvent pair distribution function show that at the lowest concentrations of the large sphere simulated, the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation underestimates the contact value; whereas the recently proposed Henderson-Chan (HC) equation gives a good prediction. For the solute-solute contact value at the colloidal limit, the MC data lie between the two predictions. The BMCSL equation underestimates, while the HC equation overestimates, the correct solute-solute contact value.     

一个简单硬球碰撞问题中的混沌

对于一个在铅垂线上的两个硬球及刚性地面组成的硬球碰撞体系,计算了它的Lyapunov指数．因为该Lyapunov指数的正定性,所以该体系是一个混沌体系．