The small wavenumber region of the static structure factor, S(k), for monodisperse systems and the compressibility factor, θ(k), for bidisperse mixtures, are investigated for jammed packings of frictionless spheres. Both S(k) and θ(k) exhibit a linear dependence on wavenumber k at small values of k that is not only independent of force model, but also persists away from the jamming transition. The zero-wavenumber intercepts, S(k = 0) and θ(k = 0), are constant above jamming and retain a finite value in the limit of zero pressure as the jamming transition is approached. We also present results for zero-temperature, Lennard-Jones glasses, which similarly exhibit a finite, zero-k intercept that depends weakly on the density of the glass.

The structural properties of static, jammed packings of monodisperse spheres in the vicinity of the jamming transition are investigated using large-scale computer simulations. At small wave number k , we argue that the anomalous behavior in the static structure factor, S(k) approximately k , is consequential of an excess of low-frequency, collective excitations seen in the vibrational spectrum. This anomalous feature becomes more pronounced closest to the jamming transition, such that S(0)-->0 at the transition point. We introduce an appropriate dispersion relation that accounts for these phenomena that leads us to relate these structural features to characteristic length scales associated with the low-frequency vibrational modes of these systems. When the particles are frictional, this anomalous behavior is suppressed providing yet more evidence that the jamming transitions for frictional spheres lie at lower packing fractions than for frictionless spheres. These results suggest that the mechanical properties of jammed and glassy media may therefore be inferred from measurements of both the static and dynamical structure factors.

The relation between thermodynamic properties and the long-wavelength limit of the structure factors for mixtures of two simple molten salts with a common ion is derived. While the long-wavelength limit of the partial structure factors for binary ionic systems is directly related to the isothermal compressibility, for ternary ionic systems it is shown that it is also related to the mean square thermal fluctuation in the relative concentration of the non-common ions. This result leads to a generalization of the Bhatia–Thornton formalism. From the local fluctuations in the total number-density, charge-density, and relative concentration, six static structure factors, and the corresponding spatial correlation functions, are defined. By introducing three complementary structure factors, it is possible to describe either these mixtures as a system of cations and anions irrespective of the species of the non-common ions, or solely the binary subsystem of the non-common ions. The generalized structure factors and their long-wavelength limits are illustrated by molecular dynamics simulation results of the molten mixture Ag(Br0.7I0.3). The mixture retains the charge order characteristic of pure molten monovalent salts and the topological order observed in monovalent ionic melts in which the cations are smaller than the anions, while the main trends of the anionic chemical order are those of simple binary alloys. The long-wavelength fluctuations in the local relative concentration are found to be very sensitive to the choice of the short-range interactions between the non-common ions.

We present neutron diffraction measurements of the total structure factor of the molten salt mixture Ag(I0.3Br0.7) at 650°C, measured by using the high intensity total scattering time-of-flight spectrometer, HIT-II, at the spallation neutron source of the Neutron Science Laboratory in the High Energy Accelerator Research Organization of Japan. We have compared the experimental data with molecular dynamics simulations using Vashishta–Rahman type potentials. Within the known constraints of pairwise rigid ion potentials, the results of the simulations are in fair agreement with experiment. We also present results using a linear combination of the experimental and molecular dynamics simulations of the structure factors of the AgI and AgBr melts. The latter are in somewhat better agreement with experiment.

The structure factors of the ionic liquid mixture Ag(Br0.7I0.3) at three temperatures, 723, 923, and 1023K, as well as of the pure molten AgI at 923K and the pure molten AgBr at 773 and 923K, were studied experimentally and by means of molecular dynamics simulations. The experiments were carried out using the high intensity total scattering time-of-flight spectrometer, HIT-II, at the KENS spallation neutron source in Japan. The experimental data are very reliable, with the possible exception of the small momentum transfer region, whose accessibility is limited by neutron energy and detector positions. The simulations made use of the semiempirical rigid ion potentials of the Vashishta-Rahman [Phys. Rev. Lett. 40, 1337 (1978)] type using a new set of parameters appropriate for the mixture. Within the known constraints of the pairwise rigid ion potentials, the simulated structure factors are in fair agreement with experiment. The results for the pair distribution functions suggest that the molten mixture retains the superionic character found in previous calculations of both the AgI and AgBr melts. This suggestion is confirmed by the results for the self-diffusion coefficients. Values obtained for the ionic conductivities are also presented.

We present the analytical solution of the Percus-Yevick equation for the sticky sphere model in odd D dimensions. Explicit expressions for the direct correlation function c(r) are given for D = 1, 3 and 5. For D = 1 our solution does not agree with the one previously obtained by Tago, Y. and Katsura, S., 1975, Can. J. Phys., 53, 2587, whereas for D = 3 we recover the results of Baxter, R. J., 1968, J. chem. Phys., 49, 2770.

The equation of state of a quasi one-dimensional model lipid monolayer is obtained in analytic form. The method used is the Laplace transform approach leading to a homogeneous Fredholm integral equation. Two cases are studied. The first considers a purely short range repulsive potential, when we recover the results previously obtained by Gianotti et al. (J. Phys. A.: Math. Gen.25:2889 (1992)). The second incorporates the long range attractive Kac potential, and the equation of state is calculated in the van der Waals limit. This extends the approach originally developed by Kac et al. (J. Math. Phys.4:216 (1963)).

Three sets of molecular dynamics simulations have been carried out to study the static structure and transport properties of molten AgCl at 1073 K. The first uses the Vashishta-Rahman rigid-ion potential (R-VR). The other two are polarizable ion potentials, which consist of the Vashishta-Rahman (P-VR) or the Born-Mayer (P-BM) rigid-ion potentials to which the anion-induced dipole polarization contributions are added. Both polarized model potentials reproduce well the main features of the structure of molten AgCl, including the characteristic three-peak feature present in the experimental broad principal peak of its total structure factor; this is not present in the R-VR simulations. The two polarized model potentials differ significantly in the way they account for the transport properties of the melt, by the mean square displacements, the velocity correlation functions, self-diffusion coefficients, or the ionic conductivity. In the case of the latter, the experimental result (sigma = 4.7 (Omega.cm)(-1)) is bracketed between the R-VR (sigma = 5.8 (Omega.cm)(-1)) and the P-VR (sigma = 4.0 (Omega.cm)(-1)) values, with the P-BM value (sigma = 1.3 (Omega.cm)(-1)) significantly lower.

We have studied the total structure of molten AgCl at 1073 K by means of two polarizable ion models via molecular dynamics simulations. The model potentials consisted of either the Vashishta–Rahman (VR) or the Born–Mayer rigid-ion potentials to which the anion-induced polarization contribution is added. Both model potentials reproduce well the main features of the structure of molten AgCl with that using the VR model potential giving marginally better results.

We present the results of calculations of the static structure factor S(k) and the pair distribution function g(r) of the tetrahedral amorphous semiconductors germanium, silicon and carbon using the structural diffusion model (SDM).The results obtained with the SDM for S(k) and g(r) are of comparable quality with those obtained by the unconstrained Reverse Monte Carlo simulations and existing ab initio molecular dynamics simulations for these systems. We have found that g(r) exhibits a small peak, or shoulder, a weak remnant of the prominent third neighbour peak present in the crystalline phase of these systems. This feature has been experimentally found to be present in recently reported high energy X-ray experiments of amorphous silicon (Phys. Rev. B 60 (1999) 13520), as well as in the previous X-ray diffraction of as-evaporated amorphous germanium (Phys. Rev. B 50 (1994) 539). (C) 2002 Elsevier Science B.V. All rights reserved.

We have used experimental values of the entropies, near melting, of molten salts to calculate their effective charges by using a charge alpha spheres model in the Mean Spherical Approximation (MSA).We compare the values of the effective charges with the electronegativity differences for a number of 1:1 molten salts. We find a reasonable good correlation for the alkali halides, but no for the copper, silver and thallium halides, and we offer an explanation for these results.

Calculations are presented on the phase behaviour of quasi-two-dimensional Lennard-Jones fluid binary mixtures. The results obtained show a Type III phase equilibria diagram similar to that observed in three-dimensional binary mixtures. A transition is found from a Type III to a Type I phase equilibria diagram. The study uses a mean field theory similar to that applied to a binary mixture of hard spheres with immersed point dipoles that showed that the transition was from Type III to Type IV instead. Consequently we suggest that, within mean field theories, a Type IV phase diagram is only obtained if the interactions are angle-dependent.

The bridge functions of molten NaCl and AgI near melting were obtained by using the model potentials of Born–Huggins–Mayer for NaCl and Vashishta–Rahman for AgI. The calculations of the bridge functions involved molecular dynamics simulations, the extension of the procedure originally proposed by Poll et al. [Phys. Rev. A 37, 1672 (1988)] and the numerical solution of the Ornstein–Zernike equations. The calculated bridge functions do not conform with the universality ansatz. They also differ from the bridge functions obtained for model electrolytes. Following the results obtained for electrolytes and those of this work for molten salts, it is conjectured that the universality ansatz for the bridge functions does not apply for systems whose attractive interactions play a decisive role in their structural ordering.

The total structure factors of eleven 3:1 molten salts and the partial structure factors of molten YCl3 have been calculated using rigid ion model potentials with the functional form originally proposed by Vashishta and Rahman (VR) /18/. The calculations were performed by solving numerically the hypernetted chain approximate theory of liquids.The results of these calculations were compared with neutron diffraction data and those obtained by using the rigid ion potentials proposed by Tatlipinar et al. /16/ (TAPT).The results obtained by using the VR potentials follow the main features of the experimental total structure factors better than those obtained using the TAPT potentials.

The induced polarization contributions to the effective interionic potentials are derived for liquid metals, liquid alloys and charge stabilized colloidal dispersions. These contributions have been obtained within a perturbative scheme that includes up to three-body terms. The formalism is illustrated by calculating the static structure factor S(k) of liquid Ga near melting. It is found that the main effects due to the induced polarization in S(k) are first lowering the height of the principal diffraction peak, and second sharpening the subsidiary peak present in liquid Ga.

Sterically stabilized colloidal dispersions, such as PMMA, have long been regarded as archetypal realizations of hard spheres and hard-sphere mixtures. Indeed, this is precisely what is found in studies of these systems as a function of the volume fraction, at constant temperature. However, a much richer behaviour-which goes beyond what is expected from just hard spheres-is found as a function of both volume fraction and temperature T. For instance, sterically stabilized colloids are known to exhibit both upper (high-T) and lower (low-T) two-phase behaviour, such that the former is temperature sensitive but the latter is not.We review model calculations based on a double Yukawa potential that exhibits some of the rich phase behaviour found experimentally, and predicting other behaviour which has not yet been found by experiment. Both the former and latter show a degree of similarity to the phase behaviour of polymer solutions. We also present preliminary results for the phase behaviour of bidisperse model sterically stabilized colloids.

The critical behaviour of two-dimensional Lennard-Jones fluid binary mixtures is investigated by using thermodynamic perturbation theory. Preliminary results show that the critical curves for the two-dimensional mixtures exhibit the same behaviour as that found in the corresponding three-dimensional fluid binary mixtures, with similar shortcomings as those found in mean field theories.

Orbital free ab initio molecular dynamics is applied to study the static structure and some dynamic properties of liquid Cs at several states along the liquid–vapour coexistence line. Two different kinetic energy functionals are used, namely, the Thomas–Fermi–von Weizsäcker functional and a simplified average density one, and the comparison with experimental data favours the latter, especially at high temperatures. We also show that the approximation of the electron density by a superposition of pseudatomic densities is poor at high temperatures, while acceptable near the triple point. However, the pseudoatom density predicted by linear response theory appears to be too diffuse even close to the triple point.

The gas-liquid coexistence curve of a two-dimensional Lennard-Jones system has been calculated using three different thermodynamic perturbation theories: Zwanzig (to second order), Gibbs-Bogoliubov variational method, and Weeks-Chandler-Andersen. The results of recent approximate expressions for the Helmholtz free energy and equation of state of the underlying hard disc reference system were compared also. Agreement between Gibbs ensemble Monte Carlo simulations and our calculations are fair only over a narrow range of thermodynamic states, both in the liquid and gas phases.