Structure of hard sphere packings near Bernal density

The structural features of packings of similar hard spheres in the vicinity of Bernal density corresponding to space occupancy ∼0.64 have been studied. This is maximum density for disordered packings, which give way to crystallization at higher densities. The structure was analyzed using Delaunay simplices. Aggregates of simplices approximating a regular tetrahedron (polytetrahedra) in form have been studied. They have a high local density and various morphologies, but are incompatible with translation symmetry. Percolation analysis of these clusters was carried out. The “critical” nature of structural transformations at Bernal density is related with the appearance of percolation through tetrahedra. The closest disordered packings really have no significant nucleating seeds of crystal structures, as shown by a sensitive seed detection procedure. Their appearance and fast growth are observed after passing through Bernal density. The total fraction of the crystal phase increases monotonically with the density; the fcc and hcp structures appear in different proportions in the packings.     

Equation of state of the hard sphere liquid

Using the results of Monte Carlo simulation, equations of state of hard sphere liquids are calculated for 106 values of the fill factor η= 0.005–0.530 (step of 0.005). In the region of liquid phase stability the absolute accuracy of about 0.00001–0.00008 is reached. Correctness of the accuracy estimate is discussed. The results obtained are compared with reported equations of state of the hard sphere liquid.     

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.     

Dielectric properties of a dipolar hard sphere liquid: Association equilibria theory

The hindered rotation model is used to generalize the association equilibria theory for the case of a dense dipolar hard sphere (DHS) liquid. The derived expressions for the orientation constant of association and the Kirkwood factor of a DHS liquid are well consistent with machine experiments in the high temperature region.     

The temperature dependence of the hard sphere diameter

The temperature dependence of the equivalent hard sphere diameter is analyzed using statistical mechanics. The analysis shows that algebraic equations for the hard sphere diameter which were developed by previous workers are not consistent with the statistical mechanics at high temperature. An algebraic equation which is consistent with the statistical mechanics is developed.     

Viscosity of hard sphere suspensions

A simple functional representation of the concentration dependence of the low-shear viscosity eta of hard sphere suspensions is proposed. The representation, which agrees with published literature at all volume fractions phi, has a hitherto-unremarked transition in its functional form at phi approximately 0.42 identical with phi(t). phi(t) is definitely less than the volume fraction 0.49 of the hard sphere melting transition.     

Two-dimensional crystallization of hard sphere particles at a liquid–liquid interface

A method for studying crystallization of hard sphere like particles in two dimensions is presented. The method involves trapping the particles at the interface between two immiscible liquids. Particles at the interface undergo 2D Brownian motion, and at sufficiently high densities crystallization is observed. The pseudo hard sphere nature of the particle interactions under these conditions is maintained, as demonstrated by the area density at which crystallization occurs. In contrast to established techniques for studying crystallization in pseudo 2D hard spheres, the particles trapped at the interface undergo no vertical motion, so the system is in principle closer to a true 2D system. The method is therefore amenable to the study of the effects of polydispersity on crystallization behaviour. The advantages and disadvantages of the method are discussed.     

Thermodynamics of dipolar hard sphere mixtures

The thermodynamic properties of mixtures of hard spheres with imbedded point dipoles are investigated by an extension of the perturbation theory used by Rushbrooke et al. for pure fluids. Equations are presented for the general multicomponent mixture in which all the hard spheres have the same diameter. Numerical calculations are presented of the phase behaviour and excess thermodynamic mixing functions for the special case of the binary mixture in which only one species is polar. A brief discussion is given of the relationship of this model to experimental results for real fluid mixtures and of possible extensions of this work.     

The effect of gravity on the drainage of a thin liquid film between a solid sphere and a liquid/fluid interface

A study has been made of the influence of gravitational forces on the thinning of the liquid film which forms as a solid sphere comes to rest on a liquid/fluid interface. It is found that rates of drainage can be dramatically affected by the ratio of gravity to surface tension forces within the film. At long times a secondary film can possibly be formed which spreads out radially from the apex of the sphere.     

Evaluating the accuracy of a density functional theory of polymer solutions with additive hard sphere diameters

We assess the accuracy of a density functional theory for athermal polymer solutions, consisting of solvent particles with a smaller radius than that of the monomers. The monomer and solvent density profiles in a slit bound by hard, flat, and inert surfaces are compared with those obtained by a Metropolis Monte Carlo simulation. At the relatively high density at which the comparison is performed, there are considerable packing effects at the walls. The density functional theory introduces a simple weight function to describe nonlocal correlations in the fluid. A recent study of surface forces in polymer solutions used a different weighting scheme to that proposed in this article, leading to less accurate results. The implications of the conclusions of that study are discussed.     

How to extend hard sphere density functional approximation to nonuniform nonhard sphere fluids: applicable to both subcritical and supercritical temperature regions

A methodology for the formulation of density functional approximation (DFA) for nonuniform nonhard sphere fluids is proposed by following the spirit of a partitioned density functional approximation [Zhou, Phys. Rev. E 68, 061201 (2003)] and mapping the hard core part onto an effective hard sphere whose high order part of the functional perturbation expansion is treated by existing hard sphere DFAs. The resultant density functional theory (DFT) formalism only needs a second order direct correlation function and pressure of the corresponding coexistence bulk fluid as inputs and therefore can be applicable to both supercritical and subcritical temperature cases. As an example, an adjustable parameter-free version of a recently proposed Lagrangian theorem-based DFA is imported into the present methodology; the resultant DFA is applied to Lennard-Jones fluid under the influence of external fields due to a single hard wall, two hard walls separated by a small distance, a large hard sphere, and a spherical cavity with a hard wall. By comparing theoretical predictions with previous simulation data and those recently supplied for coexistence bulk fluid situated at "dangerous" regions, it was found that the present DFA can predict subtle structure change of the density profile and therefore is the most accurate among all existing DFT approaches. A detailed discussion is given as to why so excellent DFA for nonhard sphere fluids can be drawn forth from the present methodology and how the present methodology differs from previous ones. The methodology can be universal, i.e., it can be combined with any other hard sphere DFAs to construct DFA for other nonhard sphere fluids with a repulsive core.     

Equation of state and jamming density for equivalent bi- and polydisperse, smooth, hard sphere systems

We study bi- and polydisperse mixtures of hard sphere fluids with extreme size ratios up to 100. Simulation results are compared with previously found analytical equations of state by looking at the compressibility factor, Z, and agreement is found with much better than 1% deviation in the fluid regime. A slightly improved empirical correction to Z is proposed. When the density is further increased, excluded volume becomes important, but there is still a close relationship between many-component mixtures and their binary, two-component equivalents (which are defined on basis of the first three moments of the size distribution). Furthermore, we determine the size ratios for which the liquid-solid transition exhibits crystalline, amorphous or mixed system structure. Near the jamming density, Z is independent of the size distribution and follows a -1 power law as function of the difference from the jamming density (Z → ∞). In this limit, Z depends only on one free parameter, the jamming density itself, as reported for several different size distributions with a wide range of widths.     

Probability of fluctuations of the number of nearest neighbors in a hard sphere liquid: Asymptotic decomposition

Fluctuations of the number of nearest neighbors M _λ inside the coordination sphere of a given radius λ, in a hard sphere liquid (M _λ is the total number of neighbors for all N particles of the system) are analyzed. For the probability density distribution of this random value, an exact asymptotic decomposition over the number of particles N in the system has been derived, and the decomposition coefficients were recorded in terms of the semi-invariants of the random value of Mλ The result coincides completely with the asymptotic decomposition in the central limiting theorem of the probability theory. Due to this, the number of nearest neighbors in a liquid of N hard spheres can be represented as the sum of N independent random values with equal distributions. The hard sphere liquid of N particles was simulated by the Monte Carlo method in the canonical Gibbs ensemble over a wide range of densities (N= 864, periodic boundary conditions, occupancy pg from 0.005 to 0.500). The theoretical equations are in good agreement with the results of simulation.     

Collapse of a two-state sticky hard sphere chain

The collapse of a homopolymer gaussian chain into a globule is represented as a transition between two states, viz., extended and collapsed. Appropriately, this model has been labeled as the all-or-none view of chain collapse. In the collapsed state, the single polymer partition function is expressed by a single Mayer diagram with the maximum number of f-bonds arising from nonbonded square well interactions. Our target is the dependence of the transition temperature on chain length and the interaction range of the square well, as indicated through the behavior of the radius of gyration and the constant volume heat capacity. Properties of the collapse transition are calculated exactly for chains with three to six backbone atoms and heuristically for long chains using arguments derived from the small chains and from conditions of integrability. Comparison with simulation studies is made.     

Transport properties of the rough hard sphere fluid

Results are presented of a systematic study of the transport properties of the rough hard sphere fluid. The rough hard sphere fluid is a simple model consisting of spherical particles that exchange linear and angular momenta, and energy upon collision. This allows a study of the sole effect of particle rotation upon fluid properties. Molecular dynamics simulations have been used to conduct extensive benchmark calculations of self-diffusion, shear and bulk viscosity, and thermal conductivity coefficients. As well, the validity of several kinetic theory equations have been examined at various levels of approximation as a function of density and translational-rotational coupling. In particular, expressions from Enskog theory using different numbers of basis sets in the representation of the distribution function were tested. Generally Enskog theory performs well at low density but deviates at larger densities, as expected. The dependence of these expressions upon translational-rotational coupling was also examined. Interestingly, even at low densities, the agreement with simulation results was sometimes not even qualitatively correct. Compared with smooth hard sphere behaviour, the transport coefficients can change significantly due to translational-rotational coupling and this effect becomes stronger the greater the coupling. Overall, the rough hard sphere fluid provides an excellent model for understanding the effects of translational-rotational coupling upon transport coefficients.     

Phase diagram of the adhesive hard sphere fluid

The phase behavior of the Baxter adhesive hard sphere fluid has been determined using specialized Monte Carlo simulations. We give a detailed account of the techniques used and present data for the fluid-fluid coexistence curve as well as parametrized fits for the supercritical equation of state and the percolation threshold. These properties are compared with the existing results of Percus-Yevick theory for this system.     

Isostructural solid-solid transitions in binary asymmetrical hard sphere system: based on solvent-mediated potential

Size dependence is imparted onto a modified bridge functional, adopted for a recently proposed semi-analytical hard sphere reference system theory for calculation of solvent-mediated potential (SMP). The SMP for two large hard sphere particles immersed in a small hard sphere solvent bath predicted by the present improved version is in satisfactory agreement with the prediction from a theoretically based fitting formula. Isostructural solid-solid transitions in the binary asymmetrical hard sphere system are investigated based on a single-component macrofluid approximation combined with the improved version. It is found that the isostructural solid-solid transition appears when size asymmetry increases. The limiting asymmetry size ratio is near 1/8. As the size asymmetry increases, critical density for both large and small hard sphere components for the fcc isostructural solid-solid transition increases and decreases, respectively.     

An exact formula for the contact value of the density profile of a system of charged hard spheres near a charged wall

An exact formula for the contact value of the density of a system of charged hard spheres near a charged hard wall is obtained by means of a general statistical mechanical argument. In addition, a formula for the contact value of the charge profile in the limit of large field is obtained. Comparison with the corresponding expressions in the Poisson-Boltzmann theory of Gouy and Chapman shows that these latter expressions become exact for large fields, independent of the density of the hard spheres.