An expression for the stress tensor of a dilute polymer solution under shear has been derived via renormalization-group theory. It is valid to first order in ε(=4-d, where d is the spatial dimensionality) to arbitrary flow rates. The polymeric contribution to the viscosity exhibits shear thinning for intermediate values of the shear. This thinning depends sensitively on the solvent quality (amount of excluded volume): for good solvents, the thinning is greatly enhanced, as is observed experimentally. The first and second normal stresses are also calculated. The ratio of the second to first normal stress for low shear is found to be a small negative quantity, approximately -0.03, nearly independent of solvent quality. This is in reasonable agreement with the sparse experimental results. A discussion of the Fokker-Planck operator and steady-state correlation functions for the Rouse theory is provided.

The results of Monte Carlo simulations on a two-dimensional fluid of particles interacting via anisotropic van der Waals forces are reported. This nonseparable potential exhibits a nematic phase in which the ordering in the molecular director induces an ordering of the nearest-neighbor bond orientations with rectangular symmetry. To make comparison with this behavior, we have studied a separable system that also exhibits a nematic phase. Unlike the nonseparable case, we find that the separable system exhibits only short-range order in the correlations of the nearest-neighbor bond orientations. The phenomenological couplings between molecular and bond orientations present in Landau theories of liquid crystals play an important role in explaining the phase transitions observed in smectic-liquid-crystal films. Our results lead us to conclude that these couplings take their microscopic origin in the nonseparability of the intermolecular pair potential.

We present an expression providing an accurate representation, for all densities, of Monte Carlo–molecular-dynamics (MCMD) equation-of-state data for the fluid phase of hard D-dimensional hyperspheres (D-spheres), with D=2–5. This expression incorporates the exact values of the virial coefficients ${\mathit{B}}_2$,${\mathit{B}}_3$, ${\mathrm{B}}_4$, and two constants determined from the MCMD data.

Compressible artifical dielectrics, such as bubbly fluids, have sufficiently large acousto-optical coefficients that they can be utilized as nonlinear media for acoustical-optical four-wave-mixing processes in which two of the input beams are sound waves and the other two are electromagnetic waves. We examine frequency shifting and acoustic-beam deflection at visible wavelengths as well as acoustically pumped optical phase conjugation at microwave frequencies in these media.

Macroscopic equations of motion describing the coupled dynamics and fluctuations of a dilute colloidal crystal and the underlying fluid in the presence of shear are analyzed for plane Couette flow. The system becomes unstable through a transverse acoustic resonance mechanism at a critical shear rate ${\mathrm{\omega }}_{\mathrm{cr}}$. For large system size L, ${\mathrm{\omega }}_{\mathrm{cr}}$∼[L ln(L)${]}^{\mathrm{-}1}$. The lattice displacement fluctuations excited by thermal motion only diverge logarithmically as the instability is approached, but cause the Debye-Waller factors to become periodic functions of time. The theory is discussed in terms of recent scattering experiments and other theoretical work.

We report on molecular-dynamics simulations of Lennard-Jones liquids sheared between two solid walls. The velocity fields, flow boundary conditions, and fluid structure were studied for a variety of wall and fluid properties. A broad spectrum of boundary conditions was observed including slip, no-slip, and locking. We show that the degree of slip is directly related to the amount of structure induced in the fluid by the periodic potential from the solid walls. For weak wall-fluid interactions there is little ordering and slip was observed. At large interactions, substantial epitaxial ordering was induced and the first one or two fluid layers became locked to the wall. This epitaxial ordering was enhanced when the wall and fluid densities were equal. For unequal densities, high-order commensurate structures formed in the first fluid layer creating slip within the fluid.

We report experiments on the low-temperature adsorption of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films on the surface of graphite fibers. We contrast the adsorption on two kinds of fibers, one with a positive radius of curvature, and one for which part of the surface has a negative curvature. The curvature has a dramatic effect on the limiting thickness of the film. For the fiber with positive curvature, the limiting film thickness is less than 200 Å, while for the fiber with negative curvature it can reach over 10 000 Å. The data agree very well with the universal form of the Dzyaloshinskii, Lifshitz, and Pitaevskii [Adv. Phys. 10, 165 (1961)] theory as worked out by Cheng and Cole [Phys. Rev. B. 38, 987 (1988)]. This agreement, though, may perhaps be fortuitous as the convoluted surface of the fiber gives rise to an adsorption process that is more complex than what this theory describes.

Self-avoiding trails (SAT’s) are paths on regular lattices that may revisit sites but not bonds. If each twice-visited site in a SAT is assigned an energy -ɛ, a collapse transition will occur at sufficiently low temperatures. Shapir and Oono [J. Phys. A: Math. Gen. 17, L39 (1984)] have suggested that the collapse transition of a self-attracting SAT may be in a different universality class than the θ point of the self-avoiding walk (SAW). We present the results of a small-cell real-space renormalization-group study on a model that includes self-attracting SAW’s and SAT’s as special cases. We find distinct fixed points for the SAW and SAT collapse transitions, and so conclude that these transitions are indeed in different universality classes. We also find a tetracritical point characterizing the crossover between the two kinds of tricritical scaling behavior.

A general dynamical model for the first-order optical Fréedericksz transition incorporating spatial transverse inhomogeneities and hydrodynamic effects is discussed in the framework of a time-dependent Ginzburg-Landau model. The motion of an interface between two coexisting states with different director orientations is considered. A uniformly translating front solution of the dynamical equations for the motion of that interface is described.

We report high-resolution ac-mirocalorimetry and birefringence measurements near the nematic–smectic-A (N–Sm-A) transition in a weakly polar very wide nematic range (${\mathit{T}}_{\mathit{N}–\mathrm{Sm}\mathrm{-}}$A/${\mathit{T}}_{\mathit{N}\mathrm{-}\mathit{I}}$=0.768) liquid-crystal compound 4-n-pentyl-cyclohexyl-4-n-butyl-cyclohexyl benzoate (Merck S-1223). The data show a very weak anomaly at the transition with α=${\mathrm{\alpha }}_{\mathit{e}\mathit{f}\mathit{f}}$∼0.2. The very wide nematic range notwithstanding, birefringence data show coupling between the nematic and sematic-A order parameters, which can explain ${\mathrm{\alpha }}_{\mathit{e}\mathit{f}\mathit{f}}$>0. However, the presence of an underlying discontinuity in ${\mathit{C}}_{\mathit{p}}$ at ${\mathit{T}}_{\mathit{c}}$ suggests that ${\mathrm{\alpha }}_{\mathit{e}\mathit{f}\mathit{f}}$>0 may alternatively be due to evolution from classical mean-field behavior with Gaussian fluctuation corrections to asymptotic critical behavior, a scenario that is shown to be consistent with the Ginzburg criterion.

The wetting behavior of argon at the solid ${\mathrm{CO}}_2$ surface has been studied with a constant-temperature molecular-dynamics technique. In order to obtain results as accurately as possible, except from the minimum image convention, no additional cutoff of the intermolecular potential was used in the calculations that were all performed with vectorized codes on the Cyber 205 supercomputer. First, the orthobaric densities are determined consistently by simulating the free-liquid surface at three temperatures. Then the density profiles of the adsorbed gas are presented for bulk-gas densities approaching the dew density. With some caution, the results seem to confirm the existence of the thin-film to thick-film transition found by recent density-functional theories. The wetting temperature of that specific system is located to be between 0.95 and 1.00 in units of the reduced temperature.

We present a density-functional theory, based on the smoothed density approximation, to study systems of hard rods with full translational and orientational freedom. For hard spherocylinders, we find both the nematic-isotropic and the nematic–smectic-A transition in a wide range of length-to-width ratios (L+D)/D. We locate the tricritical point for the nematic–smectic-A transition and also make some predictions about the nematic–smectic-A–smectic-B point. Finally, we calculate the nematic elastic constants. The predictions of our theory are compared with the results of computer simulations and other theories. We also make some comments about application of the theory to systems of hard ellipsoids of revolution and hard cylinders.

The geometry of diffusion-limited aggregation clusters is mapped into single-valued functions by tracing the surface of the aggregate and recording the X (or Y) coordinate of the position of a walker moving along the perimeter of the cluster as a function of the arc length. Our numerical results and scaling arguments show that the related plots can be considered as self-affine functions whose scaling behavior is determined by the exponent H=1/D, where D is the fractal dimension of the aggregates.

Measurements are reported of the evolution of foam structures in monolayers of pentadecanoic acid at the air-water interface. The foams are observed by fluorescence microscopy. Various statistical properties of this random two-dimensional cellular structure have been determined: the second moment of the cell-side distribution is constant with time, the characteristic size grows according to a power law with an exponent ≊0.4, Aboav’s law is obeyed, and the average cell perimeter is proportional to the number of sides. Comparisons are made with experiments on soap foams, metal grains, and simulations.

We present a study of the temporal evolution of a two-dimensional bubble pattern in the liquid-gas coexistence region of monolayers. Using fluorescence microscopy of pentadecanoic acid or dipalmitoyl phosphotidylcholine on the surface of water, we study the coarsening of the pattern for several days. Two different regimes appear, depending on the percentage of gas phase observed on the surface. At high gas coverage (∼75%), we observe ‘‘polygonal’’ gas bubbles separated by thin liquid lines like a two-dimensional soap froth. We confirm the results of Glazier and co-workers [J. A. Glazier, S. P. Gross, and J. Stavans, Phys. Rev. A 36, 306 (1987); J. Stavans and J. A. Glazier, Phys. Rev. Lett. 62, 1318 (1989)] on the nature of the asymptotic scaling states, but find a growth exponent α≊1.0 for the time evolution of the mean area. At intermediate gas coverage (∼50%), we observe weakly interacting ‘‘circular’’ gas bubbles, which grow at a slower rate with an exponent α≊0.6. This state does not reach a scaling regime: The probability distribution for bubble areas broadens continuously and develops a power law at late-stage. The pattern itself evolves toward a critical object. Also, secondary nucleation of tiny liquid droplets in the gas bubbles is observed. The relevance of long-range dipolar interactions is discussed.

We have studied by ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ NMR the complete condensation kinetics in the conditions of rapid hydrolysis (acidic medium, water in excess) of three silicon alkoxides. The gelation of the tetravalent tetraethoxysilane (TEOS) takes several weeks, whereas the trivalent methyltriethoxysilane (MTEOS) and vinyltriethoxysilane (VTEOS) do not form gels. From a quantitative analysis of the data, we deduce that the first steps of the condensation proceed by progressive assembling of small organized units. This accounts for the very slow kinetics (logarithmic function of time), the occurrence of highly condensed agglomerates, and the absence of gelation in trivalent systems. For the tetravalent TEOS, this is followed by an aggregation phase, which has been studied both by NMR and small-angle x-ray scattering. The fractal dimension D=1.9 and the growing kinetics (cluster size increasing as a linear function of time) are consistent with reaction-limited cluster-cluster aggregation with preferential reactivity at the external cluster sites. Finally, we suggest that the progressive transformation of the sol phase into the gel phase after the gel time can be observed by comparing static and magic-angle-spinning NMR spectra.

We study the temporal evolution of a planar interface that separates two coexisting phases, after it becomes morphologically unstable. We solve numerically the interface equation of motion of the one-sided model in two dimensions. Evidence is presented for the appearance of a regime of self-similar growth in which the evolving pattern is characterized by a single, time-dependent length scale, R(t), in agreement with earlier similar studies in the two-sided symmetric model. We have implemented a renormalization procedure to obtain the asymptotic time dependence of R(t). We find R(t)∼t at sufficiently long times. We also show that the asymptotic scaling behavior is determined by the driving term in the equations of motion. This term is proportional to the flux externally imposed ahead of the moving interface. The stabilizing contribution, which is proportional to the capillary length, is shown to be irrelevant for the large-scale behavior. We finally study the effects introduced by anisotropic surface tension and show that the asymptotic behavior of the system remains unchanged.

We describe the testing of a non-muffin-tin extension to the scattered-wave method (due to Natoli, Benfatto, and Doniach Phys. Rev. A 34 4682 1986 for the calculation of one-electron energy eigenvalues and photoionization cross sections of molecules. For bound states the hydrogen molecular ion is used, and for continuum photoionization an ionized lithium pseudocluster is used, these being excellent tests because the analytic results are also known. Comparison of the results shows that the theory is correct and that the computational approach is feasible.

The electron collision shift of the ${\mathrm{He}}^{+}$ Lyman-α line emitted from a low-density plasma has been calculated in the distorted-wave approximation with the inclusion of second-order corrections to the diagonal elements of the scattering matrix. The effects of exchange, inelastic collisions, interference term, and second-order contributions to the line shift are compared. The present results are also compared with the semiclassical calculations, the Coulomb-Born approximation, the results based on the R-matrix method, and the line shifts derived from the electrostatic interaction of the radiator with the surrounding plasma.

Basis invariant characterizations of bound states and bound fraction of a partially ionized hydrogen plasma are given in terms of properties of the spectrum of eigenvalues and eigenfunctions of the equilibrium quantum statistical one-proton–one-electron reduced density matrix. It is suggested that these can be used to place theories of a proposed plasma-ionization phase transition on a firm foundation. This general approach may be relevant to cosmological questions such as the quark deconfinement-confinement transition.