We study the short-time and long-time self-diffusion coefficients for a system of interacting, spherical Brownian particles. To first order in the volume fraction occupied by particles, the coefficients are given by exact expressions, first derived by Batchelor [J. Fluid Mech. 83, 97 (1976); 131, 155 (1983); 137, 467 (1983)]. We show that the expression for the long-time self-diffusion coefficient may be cast in a different form by use of a dielectric analogy. The new expression turns out to be advantageous in practical calculations and in qualitative considerations.

Anchoring of nematic liquid crystals on silicon surfaces slightly tilted with respect to the (001), (110), or (111) crystollographic planes is studied. It is found that the silicon crystal and the terraced structure of these surfaces play different roles in the determination of the anchoring directions of the nematic liquid crystals. The first one determines the azimuthal orientation of the anchoring directions that are found to be that of the twofold axes of the silicon crystal parallel to the surface of the terraces. For [001] orientation, this leads to a bistable anchoring; for [111] orientation, the expected tristable anchoring is not observed and only one anchoring direction is induced. The terraced structure determines the tilt of the anchoring directions with respect to the mean surface of the substrate. The experimentally measured tilt is not the one expected if the nematic molecules simply lay parallel to the terraces composing such vicinal surfaces. It is shown that besides this contribution of the terraces, one must also take into account the contribution of the steps separating these terraces.

We numerically evaluate the inhomogeneous grand-potential functional for a planar interface separating coexisting isotropic and nematic phases of long, hard spherocylinders. This approach avoids the use of a second-order gradient expansion that could bias the theory’s predictions about the orientation of the interface relative to the bulk nematic phase. As in Onsager’s pioneering treatment of the bulk phases, we truncate the expansion of the nonideal free energy at second order in the density. For aspect ratios L/D (the length of the spherocylinders divided by their width) greater than about 10, the theory predicts that the nematic director should lie perpendicular to the interfacial normal in accord with a previous, square-gradient calculation. As the aspect ratio decreases, the interface broadens as does the range of the correlations between spherocylinders. For L/D<10, we observe a nontrivial tilt of the director compared to the interfacial normal. We compare our findings to recent experimental and theoretical calculations of isotropic-nematic interfacial properties and briefly discuss the effects that the second-order truncation of the free energy may have on our results.

The contact angle in a wall-fluid system can be obtained directly from a visual inspection of the liquid-vapor meniscus or it can be calculated from the solid-liquid, solid-vapor and liquid-vapor surface tensions. These routes were exploited in two previous simulations in which the wetting of a wall was studied. Both simulations showed the existence of a wetting and a drying transition with changing wall-fluid interaction, but the location of especially the drying transition was not consistent. It was suggested that the discrepancy was due to the use of a ‘‘live’’ wall, i.e., a wall in which the particles are not fixed at their lattice positions, in the measurements of the surface tensions. We have replaced the live wall by an inert wall and measured the surface tensions again, treating the wall as an external field now. The contact angles that are calculated from these measurements agree with the visual observations.

We derive the shape deformations, which occur as bifurcations from spherically symmetric vesicles, soap bubbles, and other nondissipative systems characterized by curvature elasticity (bending energy) only. A weakly nonlinear stability theory is used to obtain the lowest critical value of the control parameter (in the present case the radial pressure difference across the surface), for which nonspherical shapes can occur. The first bifurcation obtained can be of two different types, namely transcritical or subcritical, but never supercritical depending on the spontaneous curvature of the membrane, which forms the vesicle. It is shown that the well-known results of the linear stability theory are insufficient to describe the bifurcation: the actual threshold for nonspherical structures in the presence of finite-amplitude perturbations is always lower than that obtained by the linear theory; among the deformations corresponding to l=2 spherical harmonics only those with m=0 are possible; and, although these l=2, m=0 structures are the most likely ones to occur above threshold, higher harmonic structures (e.g., l=3) cannot be ruled out on the basis of a weakly nonlinear analysis.

The localization of a light particle (e.g., electron, positron, or positronium atom) in a fluid is known as self-trapping. In an earlier paper [B. N. Miller and T. L. Reese, Phys. Rev. A 39, 4735 (1989)] we showed that (1) the density-functional theories (DFT’s) of self-trapping could be derived from a mesoscopic model that employs a quantum-mechanical description of the light particle and a classical description of the fluid, and (2) the application of scaling to the simplest variant of DFT results in a universal model for all fluids that obey the principle of corresponding states. In this paper we apply the fully scaled theory to the pickoff annihilation of orthopositronium. Predictions of three different versions of the theory are compared with the experimental measurements of McNutt and Sharma on ethane [J. Chem. Phys. 68, 130 (1978)] and Tuomisaari, Rytsola, and Hautojarvi on argon [Phys. Lett. 112A, 279 (1988)]. Best agreement is obtained from a model that incorporates transitions between localized and extended states.

The interfacial surface tension of the liquid-vapor system is analyzed near the critical point in a manner similar to bulk thermodynamic critical-point analyses. This is accomplished by a critical-point analysis of the single-phase hard-wall surface tension. Both a Landau expansion and a scaling theory equation of state are investigated. Some general exponent relations are derived and, in addition, some thermodynamically defined correlation lengths are discussed.

The phase behavior near the nematic–smectic-A–smectic-${\mathit{C}}^{\mathrm{*}}$ (N–Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$) point has been studied with a high-resolution ac calorimetry technique in seven binary mixtures of two chiral compounds. The smectic-A (Sm-A)–smectic-${\mathit{C}}^{\mathrm{*}}$(Sm-${\mathit{C}}^{\mathrm{*}}$) phase transitions are continuous for all the mixtures studied. The Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$ specific-heat variations are well described by the extended Landau model, with the possible exception of the mixture closest to the N–Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$ composition. As the N–Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$ point is approached, the Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$ transition became more tricritical-like, indicating that the tricritical point (TCP) is located at or very near the N–Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$ point. These observations contradict a previous report that the Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$ TCP is displaced from the N–Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$ point in this system. Anomalous ${\mathit{C}}_{\mathit{p}}$ variations in the N range suggest a restructuring that might be associated with biaxial nematic fluctuations.

We study the roughening, the preroughening, and the orientational roughening transitions for interfaces between phases in the isotropic competing Ising Hamiltonian H=-J${\mathrm{\Sigma }}_{\mathit{nm}}$${\mathit{s}}_{\mathit{i}}$${\mathit{s}}_{\mathit{j}}$-2M ${\mathrm{\Sigma }}_{\mathit{lnnn}}$${\mathit{s}}_{\mathit{i}}$${\mathit{s}}_{\mathit{j}}$. The symbols, NN, DNN, and LNNN represent nearest-neighbor, diagonal-nearest-neighbor, and linear-next-nearest-neighbor pairs, respectively, with J>0 and -∞<M<∞. By performing low-temperature expansions in the three-dimensional cubic lattice, it is found that the roughening transition curve passes through the region in which paramagnetic, ferromagnetic, and modulated phases merge, and is parallel to the phase boundary of ferromagnetic and modulated phases. It is also found that crossover behavior occurs in the roughening transition from the surface tension dominant regime to the bending-energy dominant regime. We examine the preroughening transition for the case of the restricted solid-on-solid (RSOS) model. The preroughening transition line is found to be distinct from the roughening transition line. This confirms the recent prediction by den Nijs [Phys. Rev. Lett. 64, 435 (1990)]. Within the RSOS model, we find a multistate point for reconstructed surface structures. This is analogous to the multistate point in the bulk phase diagram. The orientational roughening transition is also examined. However, it was not possible to obtain the orientational roughening transition line at a temperature higher than that of the translational roughening transition, presumably due to the limited order of the low-temperature series. The results deduced from the low-temperature expansions are compared to the sine-Gordon renormalization-group calculations based on the SOS and RSOS models. Finally we discuss the implications of the surface structure, and the connections with bulk structure.

A detailed study of the hierarchical reference theory (HRT) of fluids is presented based on an Ornstein-Zernike closure, which can be considered a nontrivial extension of the optimized random-phase approximation. The resulting differential equations can be analyzed in the critical region following closely the spirit of the renormalization group. Universality of the critical behavior and scaling of thermodynamic quantities follow from such an analysis, which permits the explicit evaluation of the scaling function and critical exponents. At the same time, the short-range properties of the system can be described in a realistic way. Outside the critical region a detailed comparison with simulation results for thermodynamic and scattering quantities is presented for a Lennard-Jones potential and for hard spheres plus Lennard-Jones tail, showing that HRT is as successful as the best liquid-state theories. A comparison with experimental measurements is also presented and good agreement is found.

The implications of a self-consistent mode-coupling theory of dense fluids for the liquid-glass transition are considered. First, we show that when higher-order corrections are ignored from our model, there is a dynamic transition of the hard-sphere fluid at an intermediate density to an ideal glassy phase. This is in agreement with earlier theoretical works. Next, we demonstrate that in the present model there is a cutoff mechanism that rounds off the sharp transition. We compute the transport coefficients for the hard-sphere fluid, which show good agreement with computer-simulation results at supercooled densities. The viscosity follows a power-law increase for the intermediate densities with an exponent close to 2. For very high densities the sharp transition is cut off and the transport coefficient increases at a slower rate. We calculate how the density autocorrelation function in a Lennard-Jones fluid decays in time. This is done for different densities along an isotherm. Our results agree much better with the slow relaxation observed in molecular-dynamics simulations than earlier theories.

We formulate a computationally simple model for crystal growth, employing a lattice of coupled maps. This model allows us to study kinetic roughening and its effect on the surface tension. We demonstrate that the cusp in the Wulff plot, which via the usual construction gives rise to faceted crystals, disappears at sufficient undercooling. The implications of this for recent approaches to dendritic growth are briefly discussed.

This study is concerned with the linear stage of perturbation growth during the solidification from a pure supercooled liquid. The thermodiffusion model of crystal growth is directly integrated numerically from arbitrary initial conditions. The technique of the triad field formalism is introduced to overcome computational difficulties associated with a free-moving-boundary problem. The results of several approaches concerning the growth rates and the most unstable modes of morphological instabilities are summarized and compared. It is shown that morphological instabilities during free growth evolve according to a power law in agreement with WKB results and contrary to the exponential law found in a quasistationary approximation.

The nonlinear stage of free growth of a spherical solid nucleus from a pure supercooled liquid has been studied numerically in a fully time-dependent context. The emergence of a dominant mode from arbitrary initial conditions, including random perturbations, is found to correspond to the most unstable mode determined from linear stability analysis. The growth of instabilities, initiated by localized defects analogous to point and line defects in crystal lattices, is analyzed, and it is shown that the perturbations grow and spread in a wavelike manner, a phenomenon observed in experiments. The formation of a predendritic growth stage is characterized by establishment of constant values of tip radius and velocity.

An effective Hamiltonian approach is employed to evaluate the formation energy or binding energy of molecular clusters at 0 K. A generalized statistical-mechanical method to treat both homomolecular and heteromolecular clusters is then introduced in order to evaluate formation energies at finite temperatures. Computed results of formation energies and nucleation rates are found to be in agreement with measurements. It is shown that, in agreement with observation, there exists a simple propensity rule of a linearity between lnJ (J is the nucleation rate) and the inverse of temperature (1/T) for the molecular clusters of interest.

A Galerkin approximation scheme is proposed for voltage-driven, dissipative magnetohydrodynamics. The trial functions are exact eigenfunctions of the linearized continuum equations and represent helical deformations of the axisymmetric, zero-flow, driven steady state. In this paper, the lowest nontrivial truncation is explored: one axisymmetric trial function and one helical trial function each for the magnetic and velocity fields. The system resembles the Lorenz approximation to Bénard convection, but in the region of believed applicability its dynamical behavior is rather different, including relaxation to a helically deformed state similar to those that have emerged in the much higher resolution computations of Dahlburg et al. [Phys. Rev. Lett. 57, 428 (1986); J. Plasma Phys. 37, 299 (1987); 40, 39 (1988)]. In the region of applicability, the dynamical behavior is to seek out the steady state of lowest energy dissipation rate.

Hydrogenated amorphous-silicon (a-Si:H) film growth on glass fibers strung between discharge electrodes is used to measure the distribution of film-producing radicals in a silane dc discharge. The measured distribution, as well as film deposition rates on the electrodes, show that typically >80% of the depositing radicals are produced in the cathode sheath. Discharge models, confirmed by the spatial distribution of optical emission, rule out the possibility that this dissociation in the sheath is due to electron impact. Collisions of energetic ions and neutrals with silane are clearly implicated as the cause of this sheath dissociation. In contrast, due to much lower ion kinetic energies, almost all dissociation is due to electron collisions in the low-power rf discharges most commonly used for film production. In addition, the ratio of the number of Si atoms deposited on all surfaces to the total number of ions collected at the dc-discharge cathode is measured to be 30, demonstrating the dominance of neutral radical deposition in these discharges.

We present here a method for including the effects of neighboring atoms within the framework of the self-consistent average-atom method. The multiple-scattering theory developed for the study of liquid metals and amorphous materials is used to describe the effect of the adjacent scatterers in the dense plasma problem. The case of copper with its prominent d resonance at the natural density and at a temperature of 5 eV is treated. The resonance under the influence of the scatterers, which simulate the plasma environment, is observed to broaden significantly while the area under the broadened resonance is seen to decrease with respect to the single-scattering resonance, increasing the number of free electrons and thus the calculated pressure.

A model describing an arc plasma in argon is developed and predictions are compared with data from an ac cascade arc experiment. The model accounts for nonequilibrium effects such as ambipolar diffusion to the confining wall, differing species temperatures, and finite reaction rates. Dissociative recombination of electrons with the argon ionic dimer is accounted for, as well as multistep ionization and three-body recombination. The model contains no free parameters and is based on experimental data only at the level of collision cross-sections and reaction rates. The model successfully explains experimental features near current zero in the ac arc, where the ionic dimer plays an important role.

The confinement of high-temperature thermal radiation in x-ray-heated cavities was studied by relative measurements of the radiation temperature in ‘‘closed’’ and ‘‘open’’ cavities simultaneously heated by x rays generated in a common laser-heated cavity. The experimental observations provide direct evidence of radiation enhancement due to radiation confinement. We have developed a simple model based on the theory of the radiatively driven heat wave. The predictions of the model are in good agreement with the experimental results.