It has been suggested that ferroelectric smectic phases may be formed by ‘‘fraternal-twin’’ liquid-crystal molecules, consisting of two very different mesogens bonded together by an appropriate spacer [R. G. Petschek and K. M. Wiefling, Phys. Rev. Lett. 59, 343 (1987)]. We discuss the range in which these ferroelectric phases appear in a Monte Carlo simulation of a simple computer model for such mesogens. The mesogens consist of two identical flexible segments that are bonded to two rigid segments with very different lengths which, in turn, are bonded together by a flexible segment. In the computer model these monomers can move freely in one direction, but are constrained to lie on a hexagonal lattice of rods in the other two directions, roughly the packing expected in a smectic-B crystal. The flexible segments are modeled by springs, and there is an energy cost for the overlap of flexible and rigid segments on neighboring lattice rods. The region in which polar (flexible, short rigid, flexible, long rigid, flexible) smectic layers form will be discussed.

The phase diagram of a tethered-ring model for vesicles in two dimensions is investigated. Each element on the vesicle’s perimeter is subject to attraction to other elements, and the vesicle as a whole is under pressure. Four different phases, characterized by their scaling exponents, are found to be present in this range of parameter space: inflated, dense, self-avoiding-walk, and branched phases. An approximate phase diagram at small pressure is determined.

We apply the technique of optical second-harmonic generation to study homogeneously aligned liquid-crystal cells. The surface dipole sensitivity of the technique made it possible to study the monolayer in the absence and presence of a bulk of liquid crystal. By comparing the monolayer orientational distribution functions of three surface treatments (rubbed polymer-coated substrates, rubbed surfactant-coated substrates, and substrates made from oblique evaporation of ${\mathrm{SiO}}_{\mathit{x}}$ film), we find that two different surface-originated mechanisms are effective in aligning liquid-crystal films. For rubbed polymer samples, it is shown that a short-range molecular interaction is responsible for alignment of the first monolayer, which then aligns the bulk via an epitaxylike interaction. Results on polymers with various structures and compositions and rubbed with a variety of rubbing strengths are presented. For the other surface treatments, the first monolayer is isotropically distributed, indicating that a bulk elastic interaction is responsible for the bulk alignment.

Entropic elastic constants of lamellar tethered membrane phases are considered both in the vicinity of and at temperatures well below the membrane-crumpling-transition critical point. We calculate entropic forces acting on boundaries of these systems. Various predictions of the statistical physics of tethered membranes, such as the breakdown of the classical membrane elasticity theory at low temperatures or the existence of the crumpling transition, can be tested experimentally by using our results.

The adhesion of vesicles in two dimensions is studied by solving the shape equations that determine the state of lowest energy. Two ensembles are considered where for a fixed circumference of the vesicle either a pressure difference between the exterior and the interior is applied or the enclosed area is prescribed. First, a short discussion of the shape of free vesicles is given. Then, vesicles confined to a wall by an attractive potential are considered for two cases: (i) For a contact potential, a universal boundary condition determines the contact curvature as a function of the potential strength and the bending rigidity. Bound shapes are calculated, and an adhesion transition between bound and free states is found, which arises from the competition between bending and adhesion energy. (ii) For adhesion in a potential with finite range, the crossover from the long-ranged to the short-ranged case is studied. For a short-ranged potential, a decrease in the strength of the potential can lead to a shape transition between a bound state and a ‘‘pinned’’ state, where the vesicle acquires its free shape but remains pinned by the potential. In such a potential, fluctuations lead to unbinding for which two different cases are found. Small vesicles unbind via fluctuations of their position, while large vesicles unbind via shape fluctuations.

We have used x-ray specular reflection to study the structure of the air–liquid-crystal interface of the lyotropic liquid crystal formed from binary mixtures of cesium perfluoro-octanoate (CsPFO) and water. In the isotropic phase the surface is coated with a monolayer of CsPFO separated by layers of water from one or more smectic bilayers of CsPFO. As for the case of thermotropic liquid crystals, the isotropic-to-nematic phase transition has no effect on the surface structure, and as the temperature is lowered towards the nematic–to–smectic-A transition temperature, the number of surface-induced smectic layers increases dramatically (e.g., approximately 100 layers were observed). Theoretical modeling of the reflectivity excludes the possibility that the surface bilayers are arrays of micelles. X-ray scattering from critical smectic short-range order in the bulk, studied by tuning the spectrometer away from the specular condition, indicates that the scattering is fundamentally different from short-range smectic order in thermotropic systems.

Analogous to the theory of cholesteric liquid crystal, a theory for tilted chiral lipid bilayers (TCLB) [briefly reported in Phys. Rev. Lett. 65, 1679 (1990)] is developed. The tilt equation and the surface-shape-equilibrium equation have been derived. Application of the theory shows that on a cylindrical surface, the field of tilt directions of TCLB molecules forms a right-handed helix with a 45° gradient angle for ${\mathit{k}}_2$>0 or a left-handed helix with -45° gradient angle for ${\mathit{k}}_2$<0, where ${\mathit{k}}_2$ is the chiral curvature modulus of the cholesteric liquid crystal. In addition, there exists another type of helical structure that looks like twisted strips or helicoids. It is also shown that on a spherical surface, the tilt field has at least two singular points. Based on these results, the succession of transitions from a vesicular dispersion to a phase involving helical structures and then to tubes observed in several laboratories can be reasonably explained. The general formula that explains the aggregation of narrow and prolate ribbon structures is derived. By including more terms of elasticity free energy into the theory, the size of the helical structure is obtained and is shown to agree with experimental observations.

We apply a density-functional formalism to a system of hard spherocylinders and obtain a phase diagram including the isotropic, nematic, and smectic-A phases. The nematic–smectic-A transition can be of either first or second order, and the tricritical point is located at a length-to-diameter ratio L/D=5.9. The coexistence of all three phases (i.e., the triple point) occurs at L/D=3.2 and for L/D<3.2 we find a first-order isotropic–smectic-A transition.

According to a model introduced by Helfrich [Z. Naturforsch. 28c, 693 (1973)], the shape of a closed lipid vesicle is determined by minimization of the total bending energy at fixed surface area and enclosed volume. We show that, in the appropriate regime, this model predicts both budding (the eruption of a satellite connected to the parent volume via a neck) and vesiculation (the special case when the neck radius goes to zero). Vesiculation occurs when the minimum is located at a boundary in the space of configurations. Successive vesiculations produce multiplets, in which the minimum-energy configuration consists of several bodies coexisting through infinitesimal necks. We study the sequence of shapes and shape transitions followed by a spherical vesicle of radius ${\mathit{R}}_{\mathit{V}}$, large on the scale ${\mathit{R}}_0$ set by the spontaneous curvature, as its area A increases at constant volume V=4π${\mathit{R}}_{\mathit{V}}^3$/3. Such a vesicle periodically sheds excess area into a set of smaller spheres with radii comparable to ${\mathit{R}}_0$. We map out this (shape) phase diagram at large volume. In this region the phase diagram is dominated by multiplets and reflects the details of the shedding process. The overall effect of successive vesiculations is to reduce the energy from a quantity of order ${\mathit{R}}_{\mathit{V}}^2$ down to zero or near zero when the area reaches 3V/${\mathit{R}}_0$; however, the decrease is not uniform and the energy E(A,V) is not convex.

This paper discusses the static and dynamic properties for ‘‘reasonable’’ charged polyelectrolyte chains (f<1, where f is the degree of ionization) in semidilute solution (φ>${\mathrm{\phi }}^{\mathrm{*}}$, where ${\mathrm{\phi }}^{\mathrm{*}}$ is the ‘‘overlap’’ concentration) with and without added salt on the basis of the Edwards-Hamiltonian formalism. In this formalism the hydrodynamical effects are neglected. Expressions for the free energy F, the osmotic pressure Π, the structure factors ${\mathit{S}}_{\mathit{i}\mathit{j}}$(q), the charge fluctuations ${\mathit{S}}_{\mathrm{CF}}$(q), the screened potentials ${\mathit{U}}_{\mathrm{scr}}$(q) for polyions and counterions, and the radius of gyration ${\mathit{R}}_{\mathit{g}}$ are derived. As for the dynamics of such systems, two relaxation modes characterize the intermediate scattering function S(q,t). The first mode represents the standard diffusion and is identified as being the cooperative diffusion frequency. It increases with the polyelectrolyte concentration φ and with the degree of ionization f [${\mathit{D}}_{\mathit{c}}$(f)>${\mathit{D}}_{\mathit{c}}$(f=0)] and is independent of the Debye screening parameter ${\mathrm{\kappa }}^2$. The second process presents a nonzero frequency at ‖q‖=0 and is called the ‘‘plasmon’’ mode. The variation with polyelectrolyte concentration φ, degree of ionization f, counterion concentration ${\mathrm{\phi }}_{\mathit{i}}$, and wave vector q is presented in a systematic way for all measurable quantities. We also present some remarks regarding the statics and dynamics of neutral and polyelectrolyte mixtures in solution.

Equilibrium axial-radial director fields of a nematic liquid crystal confined to micrometer cylindrical cavities are examined in the approximation of one elastic constant K and spatially homogeneous nematic order parameter. It is shown that, in the strong-anchoring regime with homeotropic boundary conditions, a metastable partially escaped domain structure with an array of alternating radial and hyperbolic point defects is locked in. It can be unstable for very small domain sizes (length less than or approximately equal to 0.25 times the radius), where the two adjacent defects annihilate and thus increase the domain size. Furthermore, it is unstable for larger domain sizes (length greater than or approximately equal to R) if the surface anchoring strength is weaker (${\mathit{w}}_0$≲5K/R). Here, the radial defects disappear and transform into axial domain walls while the hyperbolic defects remain unchanged. The corresponding phase diagram is presented.

The decay rate of critical fluctuations in a nonionic micellar solution of tetraethylene glycol n-decylether (${\mathrm{C}}_{10}$${\mathrm{E}}_4$) in water has been investigated very close to its critical point of mixing from the time-dependent correlation function of scattered light. We find the scaled decay rate ${\mathrm{\Gamma }}_{\mathit{c}}^{\mathrm{*}}$ (=[6πη(T)/${\mathit{k}}_{\mathit{B}}$T](Γ-${\mathrm{\Gamma }}_{\mathit{B}}$)/${\mathit{k}}^3$) for ${\mathrm{C}}_{10}$${\mathrm{E}}_4$ in water obeys a universal function over the range from a scaled variable of kξ≃0.3–26, where ${\mathrm{\Gamma }}_{\mathit{B}}$ is the noncritical background contribution. Our experimental findings suggest that the micellar solution of ${\mathrm{C}}_{10}$${\mathrm{E}}_4$ in water should belong to the static and the dynamical universality class as a fluid, in conjunction with our previous works [K. Hamano et al., Phys. Lett. A 150, 405 (1990); J. Chem. Phys. 94, 2172 (1991).

Deuterium-NMR spectra and relaxation measurements for selectively deuterated acrylamide units in polyacrylamide (PA) gels exhibiting collapse transitions are presented. The main aim of the present study is to investigate the microscopic dynamics of the segmental units of the polymer network while the entire gel is approaching the collapse transition accompanied by the critical long-wavelength diffusivelike excitations. The D nucleus, with the electric quadrupole interaction, is directly sensitive to the chain dynamics because of the random modulations of the electric-field-gradient components in the frame of reference of the external field, induced by the motion of the monomer axes. From the analysis of the spectra and of the relaxation rates, it is shown how, while the macroscopic motions exhibit critical slowing down, the dynamics of the segmental units is described by practically isotropic local modes, weakly coupled to the density fluctuations of the PA network. Quantitative estimates of the effective correlation times are given.

Small-angle neutron scattering has been performed on lysozyme solutions at different concentrations, both at the Intense Spallation Impulsed Source (ISIS), Rutherford-Appleton Laboratory) and at Orphée (Laboratoire Leon Brillouin). The results show that, in addition to the large-scale structural properties revealed by light-scattering experiments elsewhere, there is also partial ordering on a molecular scale, with features similar to the large-scale ones, provided a suitable scaling of the spatial length is made. We obtained a careful evaluation of the shape and size of the lysozyme molecule that compares favorably with existing data, and achieved a quantitative description of the intracluster structural properties in terms of a preferred distance among macromolecules. In addition, comparison with results obtained for solutions in different chemical and physical conditions allows for some insight concerning the kinds of interactions responsible for the structure.

Static structure factors S(q) were measured by laser light scattering for very concentrated systems of spherical, near-monosized, sterically stabilized particles dispersed in nonpolar liquids. A range of systems with particle concentrations beyond that corresponding to the disorder to order transition configurations were found to have amorphous structures. As the particles were stabilized by means of very short chain polymers, these systems were thought to closely approximate the fundamentally important amorphous, hard-sphere system. Subsequent analysis of S(q) carried out by means of data generated by the molecular-dynamics method for very concentrated, amorphous states of the hard-sphere system confirmed this interpretation. Thus we were able, by a combination of experiment and simulation, to give an extensive analysis and description of the structure of the amorphous state of a system of hard spheres. This study complements past work on the thermodynamic and transport properties of metastable, amorphous states of a system of hard spheres.

We have studied the growth of electrodeposits from solutions of copper sulfate in thin cells, and focused our attention on the spectacular morphological transitions that occur in almost every experimental condition. We give experimental evidence and numerical and theoretical results showing that these transitions are due to the propagation of charged impurities leaving the dissolving anode at the beginning of the growth and hitting the deposit at later times. The arrival of the impurity front against the growing deposit modifies the growing conditions, thus leaving on the deposit the trace of an almost homothetical ‘‘ghost’’ image of the anode.

A diffusion-controlled recombination, A+A→O/ and/or A+A→A, is investigated on the basis of a field theory where initial conditions are explicitly taken into account. The renormalization is performed exactly to all orders in perturbation and a complete scaling form of Green (correlation) functions is derived. The asymptotic decay of a reactant density ρ, ρ(t)∝${\mathit{t}}^{\mathrm{-}\mathit{d}/2\mathrm{}}$, is confirmed. In addition, it becomes evident that ρ exhibits mean-field reaction rate dependence and is in inverse proportion to a reaction rate k, ρ∝${\mathit{k}}^{\mathrm{-}1}$. An explicit universal form of ρ is calculated perturbatively in two different ways, i.e., to first order of ε=${\mathit{d}}_{\mathit{c}}$-d=2-d and to first order of a scaling field X∼${\mathit{kt}}^{\mathit{d}/2\mathrm{}}$. Logarithmic corrections at d=${\mathit{d}}_{\mathit{c}}$=2 are also discussed.

The front dynamics during directional solidification of a dilute binary mixture with noninstantaneous interface kinetic attachment is investigated in the weakly and highly nonlinear regimes. In the linear regime we find that, even for small enough kinetic coefficient, the most unstable mode is appreciably modified. With the help of multiscale analysis, we derive the amplitude equation that governs the front dynamics close to criticality. It is found that, for the case of a constant miscibility gap, studied here, the supercritical nature of the bifurcation remains unaltered. However, the computation of the Landau coefficient shows that the interface excursion is reduced by kinetics. Moreover, the analysis of the Mullins-Sekerka spectrum close to the instability threshold indicates that higher harmonics should be activated by interface kinetics. This is confirmed numerically. We study the transition from cells to dendrites by adopting a recent code to the present situation. We find scaling laws that confirm those obtained in the free-growth situation [Brener and Mel’nikov (unpublished)]. The interface structure is ‘‘angular,’’ and side branches are much less pronounced, even when the Péclet number exceeds a few unities, than those obtained in the free-kinetics case [Saito, Misbah, and Müller-Krumbhaar, Phys. Rev. Lett. 63, 2377 (1989)]. Our findings agree well with experiments [P. Kurowski, C. Guthmann, and S. de Cheveigné (unpublished)] on impure ${\mathrm{CBr}}_4$. We speculate that dendrites in this system are selected by kinetic anisotropy rather than by surface-tension anisotropy.

It is shown that the nonlinear dynamics of the radiation field in a free-electron laser can be modeled by the Ginzburg-Landau equation. The refractive index of the electron beam in the nonlinear regime and the saturation intensity of the radiation field are obtained from WKB theory. Although the Ginzburg-Landau equation does not permit soliton solutions, it is shown that certain types of solitary-wave solutions have a strong resemblance to spikes observed in simulations and experiments.

The time-space behavior of ions and electrons, whose density and temperature are typical of laser multiphoton-ionization experiments, is analyzed from the point of view of the fluid approximation, taking into account all nonlinear terms. The analytic methods of solution, already presented, are applied to describe the three-dimensional coupled motion of both ions and electrons, including also the energy exchange with the laser field and electron-ion collisions. It is shown that the plasma interacts with the laser field to produce a complex spectrum of odd harmonics of incident radiation whose features depend on experimental parameters, such as type and density of gas, laser pulse duration, frequency, and focusing conditions. The influence of collective electron motion on the phase-matching factor is also discussed. It is demonstrated that, under a suitable choice of involved parameters, a large number of harmonics is generated in a coherent process.