We study a system of hard spherocylinders with rotational freedom in which the length-to-diameter ratio of the spherocylinder L/D is large. The asymptotic expressions for the one-particle distribution function and the free-energy functional in the limit L/D→∞ are found. The virial expansion of the free energy is used to study the nematic to smectic-A transition by means of a bifurcation analysis and the third-order term of the expansion is taken into account. Then the bifurcation analysis is extended to the next order to determine the order of the transition. We also compare our results with computer simulations and other density-functional theories.

A combination of static and quasielastic light scattering and the theory of scaling solutions to Smoluchowski's equation was used to determine the absolute coagulation rate K0′ and kernel homogeneity λ of a coagulating liquid-drop aerosol. Droplet sizes ranged from 0.23 to 0.42 μm, implying Knudsen numbers in the range 0.26 and 0.14. The temporal evolution of the number concentration M0 and the modal radius rM of an assumed zeroth-order log-normal distribution showed near-power-law behavior similar to that predicted by the scaling theory. From the temporal scaling behavior of M0(t) and rM(t), the absolute coagulation rate was calculated. The coagulation rates from each method were in good agreement. The rate also agreed well with theory that corrected the Brownian rate, good for the continuum regime, by the average Cunningham correction factor. In addition, the time dependence of the moments M0 and rM, hence the determination of K0′, was in good agreement with a real-time numerical solution of Smoluchowski's equation for initial conditions analogous to our experimental ones.

A nonlinear theory of transient patterns in the electrically induced splay Fréedericksz transition in nematic liquid crystals is presented. Growth conditions for periodic perturbations with a wave vector perpendicular to the initial director alignment, superposed on the homogeneous realignment process, have ben investigated. The decisive effect leading to this type of pattern formation arises from the field distortion resulting from the electric anisotropies. The nonlinear analysis with rigid boundary conditions delivers the onset of the pattern-forming instability at a critical value of the control parameter ${\mathrm{\epsilon }}_{\mathit{c}}$, which appears to be too large.

We report a computer-simulation study of a system of ‘‘hard cut spheres,’’ oblate particles that are obtained by slicing off the top and bottom caps of a sphere at a distance L/2 from the equatorial plane. This system serves as a model for a disklike mesogen. The phase behavior of this system is found to be strongly dependent on the length-to-width ratio (L/D) of the particles. In addition to isotropic and solid phases, we find nematic and columnar phases for L/D=0.1. For L/D=0.2 we find a columnar phase, and a phase with cubic orientational order but no translational order. For L/D=0.3, only the isotropic fluid and the solid are stable. Where possible, we have located the phase transitions.

Simulations are performed for a fluid whose atoms interact with the Lennard-Jones pair potential and the Axilrod-Teller three-body potential, and results are tabulated for the internal energy and for the virial pressure. The triple dipole potential is effectively repulsive, as is well known, making the internal energy less negative and the pressure more positive than for the underlying Lennard-Jones fluid. For the relatively low polarizabilities examined, ν/3ε${\mathrm{\sigma }}^9$≊0.03, the perturbation approximation of Barker, Fisher, and Watts [Mol. Phys. 21, 657 (1971)] is shown to be essentially exact, and the hypernetted-chain approximation of Attard [Phys. Rev. A 45, 3659 (1992)] is quantitatively accurate at low densities, but only qualitatively correct for the liquid state.

The structural-mapping approximation introduced by Lutsko and Baus [Phys. Rev. A 41, 6647 (1990)] in the generalized effective-liquid approximation is extended to include a local thermodynamic mapping based on a spatially dependent effective density for approximating the solid phase in terms of the uniform liquid. This latter approximation, called the local generalized effective-liquid approximation (LGELA) yields excellent predictions for the free energy of hard-sphere solids and for the conditions of coexistence of a hard-sphere fcc solid with a liquid. Moreover, the predicted free energy remains single valued for calculations with more loosely packed crystalline structures, such as the diamond lattice. The spatial dependence of the weighted density makes the LGELA useful in the study of inhomogeneous solids.

We study the hydrodynamics of colloidal crystals in a thin-film cell using dynamic-light-scattering techniques. The measured time dependence of the fluctuating scattered light intensity reflects the characteristic frequencies of crystal modes. At variance with the theory of hydrodynamic interactions in colloidal crystals, photon-correlation functions of light scattered by longitudinal modes are nonexponential. In the long-wavelength limit, transverse modes acquire a finite damping due to the finite sample thickness. We systematically investigate this effect as a function of cell separation.

We observed a spontaneous transition from a vertical chevron texture to a striped texture (striped ‘‘bookshelf’’ texture) in a surface-stabilized film of ferroelectric liquid crystal mixture (ZLI 4237-000, from E. Merck). The transition takes place gradually, at temperatures more than 20 °C below the smectic-A–smectic-${\mathit{C}}^{\mathrm{*}}$ transition. The layers in the stripe texture are perpendicular to the plate, but in successive stripes, the orientation of the layer normal alternates by ±23°. The polarization is perpendicular to the film and alternates between up and down, while the director orientation is in plane and alternates by ±5°. The width of the stripes was typically 50 μm for samples of about 5 μm thickness. The area of the kink interfaces between the stripes is accordingly an order of magnitude smaller than in chevron textures, which energetically favors the stripe texture. The formation of this texture is slow because it requires sliding of the layers along the surface. The observed transition can be of importance for display technology because it may enable one to obtain a uniform bookshelf texture.

We consider three approximate expressions for the entropy of a single-particle fluid that require as input only the pair-correlation function g(r). By evaluating numerically these entropy estimates, for several model interparticle interactions of varying range, we examine the accuracy of these expressions compared to the ‘‘exact’’ entropy determined from computer simulation. With the exception of the one-component plasma at very low densities, the entropy of all systems studied can be approximated within 10% of the exact value for fluid densities up to 95% of the freezing density, with the agreement improving for the shorter-ranged potentials. For hard spheres, a preliminary extension to third-order terms is presented.

An alternative method is proposed to estimate particle coordination number in a random packing of spheres. It is based on the correlation between random dense packing and random dense parking, where random dense parking is defined as the random placement of equal-size disks (or spheres) on a surface such that none overlap. Assuming that the limit for random dense parking (fraction of area covered by the projected area of particles) is independent of surface curvature, an analytical expression of the coordination number for spheres surrounding a central sphere of equal or different size is obtained. A similar analysis is achieved for a sphere touching a flat wall. Both expressions are tested through numerical simulations of bimodal, spherical particle systems.

The dynamics of immiscible-fluid displacement is studied in the simple geometry of a capillary tube. Here the interesting physics lies in the breakdown of the no-slip boundary condition near the contact line, defined as the intersection of the fluid-fluid interface with the solid wall. Through numerical hydrodynamic calculations, we link macroscopic-flow behavior to the microscopic parameters governing the contact-line region. It is shown that the moving contact line generates two types of frictional forces. One, the viscous stress, is responsible for the observed deformation of the fluid-fluid interface as the flow velocity U increases. Our calculation is in excellent agreement with prior analytic works on this aspect. In particular, our results reproduce Hoffman’s scaling relation as well as the logarithmic dependence of the viscous friction on slipping length. Identical macroscopic-flow behaviors are also found to result from three different slipping models provided that their slipping lengths are each renormalized by a model-dependent constant. Besides the viscous stress, however, comparison with experiments revealed a second frictional force that varies as ${\mathit{U}}^{\mathit{x}}$, with 0<x≤0.5, which is dominant at capillary numbers <${10}^{\mathrm{-}3}$. We propose that the source of this new friction is the excitation of damped capillary waves at the fluid-fluid interface due to contact-line motion over wall roughness. Consideration of this mechanism yields not only the correct range of x values, but also good agreement with the measured magnitude of the second frictional force. The paper concludes with an analysis of the frequency-dependent pressure response to an imposed ac velocity perturbation. An expression is derived for the critical frequency that separates the low-frequency behavior from that of the high-frequency regime.

The coherent dynamic structure factor S(Q,ω) of liquid Cs has been measured by inelastic neutron scattering near the melting point at 308 K. Using triple-axis spectrometers at the Institut Laue-Langevin in Grenoble and at the Forschungs-Reaktor München the scattering law was determined for energy transfers ħω from -2 to 10 meV and for momentum transfers ħQ between 0.2 and 2.55 A${\mathrm{̊}}^{\mathrm{-}1}$. The measurement has been corrected for all significant effects, including multiple and incoherent scattering as well as resolution broadening. In this paper we present mainly experimental results including a table of the measured scattering law. The analysis of the dispersion relation and the full width at half maximum of the longitudinal current correlation function ${\mathit{J}}_1$(Q,ω) reveals an anomalous dispersion due to shear relaxation in the liquid. In the vicinity of the structure-factor maximum the measured half-width of the coherent central peak of S(Q,ω) confirms recent theoretical assumptions of a collective-diffusion-like structural relaxation process in dense liquids near the melting point.

An exactly solvable discrete reptation model applicable to polyelectrolytes is extended to include large fluctuations in tube length. Unlike the original constant-tube model, here coiling of the chain in discrete steps leads to large length changes of the confining tube and, correspondingly, a multitude of chain-tube states which are linked by transitions driven by Brownian and electric-field forces. For the steady-state mobility, it is found that a minimum found previously in the curve of mobility versus inverse chain size is suppressed. In constant applied fields, probability distributions of chain size show that the migrating molecule alternates between fully extended and collapsed configurations.

Percolation theory for supercooled water predicts an enhanced intensity in the low-q range of the spectrum. In small-angle x-ray measurements on water in the ‖q‖ range 0.4–1.8 ${\mathrm{nm}}^{\mathrm{-}1}$ and the temperature range 273–253 K, no enhanced intensity could be measured. The spectra just follow the normal equilibrium thermodynamic behavior. A nonequilibrium enhanced intensity is observed in the spectra of supercooled water in vertically mounted capillaries in the ‖q‖ range below 0.3 ${\mathrm{nm}}^{\mathrm{-}1}$. This intensity is due to convection in the capillaries.

Lipid-monolayer isotherms often show a kink that changes to a flat section and back to a kink within a narrow temperature range. In heneicosanoic acid monolayers, along a high-pressure isobar, we have observed a slightly distorted ‘‘rotator-I’’ phase between the known distorted hexagonal and hexagonal phases. Isotherms show a flat section only where this new phase occurs. The diffraction peaks are broader in this phase than in the adjacent phases; this reentrant behavior occurs in the same region of the phase diagram where the viscosity shows anomalous trends (first reported, we believe, by Copeland, Harkins, and Boyd [J. Chem. Phys. 10, 357 (1942)] and thought to indicate a ‘‘superliquid’’ phase).

Quasielastic-light-scattering measurements are reported for a dialkoxyphenylbenzoate monomer and its dimer in their respective nematic phases. The splay and twist elastic moduli of the dimer are found to be nearly independent of molecular length. The dimer’s bend modulus, however, shows an anomalous increase with decreasing temperature well below the nematic-isotropic phase transition. Monomer viscosities are consistent with typical literature values, although ${\gamma }_1$/${\mathrm{\eta }}_{\mathrm{splay}}$ and ${\mathrm{\eta }}_{\mathrm{bend}}$ seem to be larger than expected for the dimer, where ${\gamma }_1$ is the twist viscosity. The results are discussed in terms of viscoelastic properties of semiflexible rods. The elastic properties in particular are in good agreement with a recent model by Terentjev and Petschek (unpublished).

Dynamic wetting of nematic liquid crystals on substrates inducing a tilted anchoring is unstable for a given range of wetting velocities. This unstable regime is studied and an instability mechanism is given, based on the two characteristics of wetting in nematic liquid crystals: the coupling of the director and velocity fields and the selection of anchoring directions at the substrate surface by the wetting conditions. The dependence of the velocity range of the instability on the wetting geometry is also studied, which is shown to give some information about the behavior of the wetting nematic-liquid-crystal wedge close to the contact line.

Using a microscopic density-functional theory for inhomogeneous van der Waals fluids, we derive the equation for the shape of the interface between a liquidlike adsorbed film and the vapor phase in the bulk exposed to a long-range potential of a wedge-shaped substrate. This is a nonlinear and nonlocal integral equation associated with the line tension of the system. Within certain approximations it reduces to that equation which follows from the common phenomenological approach for bent interfaces between fluid phases. The asymptotic lateral behavior of the interfacial profile far away from the center of the wedge displays the presence of van der Waals tails; they are calculated analytically for the cases of complete and critical wetting. The full solutions of the integral equation are obtained numerically. They allow us to predict a scaling behavior of the excess coverage as a function of the thickness of the wetting layer far away from the center of the wedge.

A simple reinterpretation of the lattice Boltzmann equation is presented that allows it to track passive scalar dynamics in grossly irregular geometries without adding any new ingredient to the basic hydrodynamic algorithm. The scheme is numerically demonstrated for two representative test cases: diffusion in two-dimensional fractal media and Taylor hydrodynamic dispersion.

An anomalously large flexoelectric effect is predicted in the nematic phase of thermotropic main-chain polymers, which have a defined orientation of subsequent monomers bonded on the chain. We identify two different ranges of order parameters. When the persistence length of the chain in the direction parallel to the order parameters is larger than a monomer length but not too long (small order parameter), the longitudinal flexoelectric coefficient ${\mathit{f}}_{\mathrm{\parallel }}$ is proportional to this exponentially large persistence length, assuming that the polymers are many persistence lengths long. This result corresponds to the simple estimation that relates flexoelectric coefficients to the Frank elastic constants: ${\mathit{f}}_{\mathrm{\parallel }}$∼${\mathit{K}}_{\mathit{s}}$. When the nematic ordering approaches its saturation (strongly extended chains), the flexoelectric effect is essentially independent of the persistence length and is either determined by a competition between this effect and the tendency of the chain segments to align antiparallel, or the system is ferroelectric in the absence of deformations.