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.     

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered matrix of hard spheres: attractive wall-hard sphere interaction

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered hard sphere matrix is studied using the inhomogeneous Ornstein-Zernike equation with hypernetted chain closure. In contrast to previous studies, an attractive wall-hard sphere interaction is considered. The adsorption is affected by the attractive interaction both directly by the fluid-wall interaction and indirectly by the change in the structure of the matrix. Density profiles and pair distribution functions are reported. For comparison, grand canonical Monte Carlo simulation data are obtained. The agreement of the theoretical and simulation results is satisfactory but somewhat less pleasing than for the purely repulsive case.     

Dynamics of a hard sphere granular impurity

An impurity particle coupling to its host fluid via inelastic hard sphere collisions is considered. It is shown that the exact equation for its distribution function can be mapped onto that for an impurity with elastic collisions and an effective mass. The application of this result to the Enskog-Lorentz kinetic equation leads to several conclusions: (1) every solution in the elastic case is equivalent to a class of solutions in the granular case; (2) for an equilibrium host fluid the granular impurity approaches equilibrium at a different temperature, with a dominant diffusive mode at long times; (3) for a granular host fluid in its scaling state, the granular impurity approaches the corresponding scaling solution.     

Computer simulations of a rough sphere fluid I

A molecular dynamics simulation of a rough sphere fluid with variable roughness is presented from which the intermediate scattering function, orientational correlation functions and velocity autocorrelation functions are calculated for several values of the density, roughness and wave number. The dependence of these correlation functions on the parameters is discussed and a comparison with a neutron scattering experiment on neopentane [C(CH₃)₄] is made, which gives good agreement between the two experiments.     

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．     

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.     

Heterogeneous shear in hard sphere glasses

There is growing evidence that the flow of driven amorphous solids is not homogeneous, even if the macroscopic stress is constant across the system. Via event-driven molecular dynamics simulations of a hard sphere glass, we provide the first direct evidence for a correlation between the fluctuations of the local volume fraction and the fluctuations of the local shear rate. Higher shear rates do preferentially occur at regions of lower density and vice versa. The temporal behavior of fluctuations is governed by a characteristic time scale, which, when measured in units of strain, is independent of shear rate in the investigated range. Interestingly, the correlation volume is also roughly constant for the same range of shear rates. A possible connection between these two observations is discussed.     

大口径粗糙球面的检测

 为了解决大口径光学元件在精磨阶段的检测问题,基于电磁场散射理论,分析了在红外干涉仪测量粗糙表面过程中,所产生干涉条纹的对比度与粗糙表面粗糙度之间的关系,并通过测量不同粗糙表面对这一结果进行了实验验证。利用红外干涉仪测量了280#精磨粗糙球面（Φ=1130mm,R=3600mm）的面形,讲述了测量大型粗糙球面时干涉仪的调整方法。从测量结果可以看出,此粗糙球面具有比较明显的球差,面形峰谷（PV）值为0.526λ(λ=10.6μm),均方根（RMS）值为0.117λ(λ=10.6μm)。     

Structure factors in a two-dimensional binary colloidal hard sphere system

ABSTRACT

Hard disks are one of the simplest interacting many-body model system in two dimensions (2D). Here, we present a comprehensive set of measurements of the static structure factors for quasi-2D monodisperse fluids and two different binary colloidal hard sphere mixtures: a small size ratio (SSR) system with a negligibly small negative non-additivity and a large size ratio system with a significantly larger non-additivity. We compare the experimental results for the monodisperse and SSR systems to those calculated using density functional theory (DFT) for additive mixtures. Furthermore, we determine the zero-wavevector limits of the static structure factors for the monodisperse and binary hard sphere fluids directly from an analysis of number and concentration fluctuations. For the monodisperse case, this leads to the isothermal compressibility, which agrees very well with DFT, and is consistent with the scaled particle theory equation of state for hard disks. For the binary fluids, the partial static structure factors are used to calculate the Bhatia–Thornton structure factors, and we find qualitative agreement with DFT for the SSR mixture. Finally, the zero-wavevector limits of the Bhatia–Thornton structure factors are determined and directly related to the thermodynamic factor, the dilatation factor and the isothermal compressibility.     

Settling statistics of hard sphere particles

Direct imaging of settling, non-Brownian, hard sphere, particles allows measurement of particle occupancy statistics as a function of time and sampling volume dimension. Initially random relative particle number fluctuations, (2)>/ = 1, become suppressed, anisotropic, and dependent. Fitting to a simple Gaussian pair correlation model suggests a minute long ranged correlation leads to strong if not complete suppression of number fluctuations. Calflisch and Luke predict a divergence in velocity fluctuations with increasing sample volume size based on random (Poisson) statistics. Our results suggest this is not a valid assumption for settling particles.     

Crystallization mechanism of hard sphere glasses

In supercooled liquids, vitrification generally suppresses crystallization. Yet some glasses can still crystallize despite the arrest of diffusive motion. This ill-understood process may limit the stability of glasses, but its microscopic mechanism is not yet known. Here we present extensive computer simulations addressing the crystallization of monodisperse hard-sphere glasses at constant volume (as in a colloid experiment). Multiple crystalline patches appear without particles having to diffuse more than one diameter. As these patches grow, the mobility in neighboring areas is enhanced, creating dynamic heterogeneity with positive feedback. The future crystallization pattern cannot be predicted from the coordinates alone: Crystallization proceeds by a sequence of stochastic micronucleation events, correlated in space by emergent dynamic heterogeneity.     

Structure of the hard sphere solid

We show that near densest packing the perturbations of the hexagonal close packed (hcp) structure yield higher entropy than perturbations of any other densest packing. The difference between the various structures shows up in the correlations between motions of nearest neighbors. In the hcp structure random motion of each sphere impinges slightly less on the motion of its nearest neighbors than in the other structures.     

Transport coefficients of hard sphere fluids

New calculations have been made of the self-diffusion coefficient D, the shear viscosity η_s, the bulk viscosity η_b and thermal conductivity λ of the hard sphere fluid, using molecular dynamics (MD) computer simulation. A newly developed hard sphere MD scheme was used to model the hard sphere fluid over a wide range up to the glass transition (～0.57 packing fraction). System sizes of up to 32 000 hard spheres were considered. This set of transport coefficient data was combined with others taken from the literature to test a number of previously proposed analytical formulae for these quantities together with some new ones given here. Only the self-diffusion coefficient showed any substantial N dependence for N < 500 at equilibrium fluid densities (ε 0.494). D increased with N, especially at intermediate densities in the range ε ～ 0.3–0.35. The expression for the packing fraction dependence of D proposed by Speedy, R. J., 1987, Molec. Phys., 62, 509 was shown to fit these data well for N ～ 500 particle systems. We found that the packing fraction ε dependence of the two viscosities and thermal conductivity, generically denoted by X, were represented well by the simple formula X/X ₀ = 1/[1 ? (ε/ε₁)]^m within the equilibrium fluid range 0 > ε > 0.493. This formula has two disposable parameters, ε and m, and X ₀ is the value of the property X in the limit of zero density. This expression has the same form as the Krieger-Dougherty formula (Kreiger, I. M., 1972, Adv. Colloid. Interface Sci., 3, 111) which is used widely in the colloid literature to represent the packing fraction dependence of the Newtonian shear viscosity of monodisperse colloidal near-hard spheres. Of course, in the present case, X _o was the dilute gas transport coefficient of the pure liquid rather than the solvent viscosity. It was not possible to fit the transport coefficient normalized by their Enskog values with such a simple expression because these ratios are typically of order unity until quite high packing fractions and then diverge rapidly at higher values over a relatively narrow density range. At the maximum equilibrium fluid packing fraction ε = 0.494 for both the hard sphere fluid and the corresponding colloidal case a very similar value was found for η_s/η_o ?30–40, suggesting that the ‘crowding’ effects and their consequences for the dynamics in this region of the phase diagram in the two types of liquid have much in common. For the hard sphere by MD, D_o/D ～ 11 at the same packing fraction, possibly indicating the contribution from ‘hydrodynamic enhancement’ of this transport coefficient, which is largely absent for the shear viscosity. Interestingly the comparable ratio for hard sphere colloids is the same.     

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.     

Crystal nucleation in the hard sphere system

The structure and growth of crystal nuclei that spontaneously form during computer simulations of the simplest nontrivial model of a liquid, the hard sphere system, is described in this work. Compact crystal nuclei are observed to form at densities within the coexistence region of the phase diagram. The nuclei possess a range of morphologies with a predominance of multiply twinned particles possessing in some cases a significant decahedral character. However the multiply twinned particles do not form from an initial decahedral core but appear to nucleate as blocks of a face-centered cubic crystal partially bounded by stacking faults.     

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.     

Structure factor of a system with shouldered hard sphere potential

The structure factor of a system of particles interacting through a shouldered hard sphere potential is computed from a Monte Carlo simulation. The result pleads for a similar effective two-body potential in liquid metals like bismuth and confirms previous conclusions of Silbert and Young.