A high-resolution ac calorimetric technique has been employed to study the nematic–smectic-${\mathit{A}}_1$ (N–Sm-${\mathit{A}}_1$) phase transition in liquid-crystal binary mixtures of octyloxyphenyl-nitrobenzoyloxy benzoate (${\mathrm{DB}}_8$${\mathrm{ONO}}_2$) and decyloxyphenyl-nitrobenzoyloxy benzoate (${\mathrm{DB}}_{10}$${\mathrm{ONO}}_2$). The existence of a tricritical point on the N–Sm-${\mathit{A}}_1$ transition line has been reconfirmed in this study. This tricritical point occurs at mole percent X≃51 of the decyl homolog in the mixture. Heat-capacity measurements characterizing the N–Sm-${\mathit{A}}_1$ transition have been carried out for three samples in the vicinity of the tricritical point (X=47.0, 48.7, and 50.0) and for one sample with X=31.5. The results reveal a complete crossover behavior for the critical exponent α, which changes from the three-dimensional XY value (${\mathrm{\alpha }}_{\mathit{X}\mathit{Y}}$=-0.007) for X=31.5 to a value α=0.422 close to tricritical (${\mathrm{\alpha }}_{\mathit{t}}$=0.50) for x=50.0. The amplitude ratio ${\mathit{A}}^{\mathrm{-}}$/${\mathit{A}}^{+}$ for the X=31.5 sample conforms to that expected from the noninverted XY model. In addition, heat-capacity measurements on one sample with X=53.7 indicate that near the termination point of the Sm-${\mathit{A}}_{\mathit{d}}$–Sm-${\mathit{A}}_1$ transition line the phase sequence Sm-${\mathit{A}}_{\mathit{d}}$–${\mathit{N}}_{\mathit{d}}$–${\mathit{N}}_1$–Sm-${\mathit{A}}_1$ occurs, in accordance with theoretical predictions.

We report measurements of the critical behavior of an inverted micelle system. The two-component system consists of a nonionic surfactant n-decyl octaoxyethylene glycol monoether (${\mathrm{C}}_{10}$${\mathrm{E}}_8$) in a hydrocarbon, dodecane. The system has an upper critical consolute point at 30±2 wt. % ${\mathrm{C}}_{10}$${\mathrm{E}}_8$ at a temperature of T=28.05±0.03 °C. We demonstrate that both static and dynamic scaling are obeyed with universal three-dimensional Ising exponents describing the divergence of the osmotic compressibility and the static correlation length.

We present a systematic study of the wetting behavior of a one-component fluid at a wall and of interfacial wetting in binary liquid mixtures by taking into account all aspects of the long-range character of the van der Waals interactions between the particles. The corresponding effective interface potential is expressed in terms of those free interfacial profiles that emerge as a consequence of the wetting phenomena. This approach goes beyond previous ones, because we take into account the van der Waals tails of these interfaces, and in the one-component case the structure of the emerging wall-liquid interface. In addition, we discuss the distortion of the actual interface profile—compared with the corresponding free one—caused by a finite thickness of the wetting film. The analytic results allow us to draw conclusions about both the value of the wetting transition temperature for second-order wetting transitions and the size of the critical region for such a transition as well as about the onset of critical adsorption. We also present the exact expressions for the leading van der Waals tails of the liquid-gas, wall-liquid, and wall-gas interfaces in a one-component system as well as for interfaces in binary liquid mixtures. We find that at a critical wetting transition of the wall-gas interfaces, the wall-liquid interface profile undergoes a qualitative structural change.

We report on high-resolution synchrotron x-ray scattering studies of melts of a series of linear polyisoprenes with highly polar sulfozwitterion groups at one end. Studies were carried out for six different molecular weights between 2200 and 28 000. For low molecular weights between 2200 and 4650, we observe a lattice with the symmetry of a triangular array of cylinders. The lattice ordering is strong; the nominal domain size exceeds 5000 Å. A structural phase transition to a cubic (bcc) lattice with long-range order is observed to occur for melts with molecular weights between 4650 and 14 000. The lattice spacing increases over the molecular range between 83 Å (for ${\mathit{M}}_{\mathit{w}}$=2200) and 224 Å (for ${\mathit{M}}_{\mathit{w}}$=28 000). In contrast to usual block copolymers, for these copolymers the long-range order sets in at extremely small volume fraction of ionic species, less than 1%.

When a fluid composed of sufficiently asymmetric hard particles is compressed, purely entropic effects give rise to phases possessing long-range orientational and, in some cases, translational order. The various ordered phases observed in conventional lyotropic liquid-crystal systems are commonly described in terms of such a hard-particle model. Here we study the liquid-crystal phases observed in reversibly assembling lyotropics (i.e., systems in which amphiphilic monomers form asymmetric aggregates) within the framework of a hard-particle model. These self-assembling systems are complicated by a variable and polydisperse aggregate size distribution, which is both concentration and temperature dependent, and is coupled to the orientational and translational ordering of the system. Our approach employs a phenomenological description of aggregate assembly, in conjunction with a scaled particle treatment of fluid configurational entropy and a cell description of periodic columnar and smectic density modulations. Cases of rodlike and disklike aggregates are considered. The calculated phase diagram for the rodlike (disklike) system displays a low-temperature nematic phase intervening between a low-concentration isotropic phase and a high-concentration columnar (smectic) phase. With increasing temperature the region of nematic stability narrows and finally terminates at an isotropic-nematic-columnar (smectic) triple point above which there is a direct isotropic to columnar (smectic) transition. This general phase diagram is characteristic of a number of experimental systems in which the aggregates are restricted to either rod- or disklike geometries. The calculated concentration dependence of the aggregate size distribution, orientational order parameter, and periodic columnar and smectic spacings are also reported and compared with specific experimental results.

This paper describes an analytical and computer-simulation study of the way in which a system of droplets evolves during the condensation of a vapor onto a lyophobic substrate. The derivation of a system of first-order differential equations leads to a prediction for the spread of the distribution of the droplet sizes. The resulting equation was vindicated for a wide range of possible growth laws using the simulation. Furthermore, elimination of the time dependence of the differential equations produces a derivation of a previous empirical equation proposed by Vincent [Proc. R. Soc. London, Ser. A 321, 53 (1971)]. The equation directly relates the fraction of the substrate covered by the droplets to the number of droplets per unit of substrate area.

We have carried out extensive computer simulations of the Lebwohl-Lasher model of a nematic liquid crystal to determine the Frank elastic constant K for this system as a function of temperature. We use equilibrium, k-dependent, fluctuation expressions, valid at small wave vector k, and also measure the response to applied, spatially varying fields that couple to the k-dependent molecular orientation tensor. We find good agreement between these two methods. The ratio K/P¯ ${}_2{}^2{}_{}{}^{}$, where P${\mathrm{¯}}_2$ is the nematic order parameter, adopts its molecular-field value at low temperatures, but rises by over 20% on approaching the nematic-isotropic transition temperature ${\mathit{T}}_{\mathit{N}\mathrm{-}\mathit{I}}$. We note that this temperature dependence cannot be accounted for by molecular-field arguments. However, spin-wave theory correctly relates the k-dependent elastic constant with the order parameter at low temperatures, and is quite accurate up to T/${\mathit{T}}_{\mathit{N}\mathrm{-}\mathit{I}}$≊0.8. Finally, direct simulations of the Fréedericksz transition give results in reasonable agreement with the value of K as calculated by the other methods; however, we find that this is not a very efficient route to K.

Clustering and continuum percolation in dipolar fluids are studied through Monte Carlo simulation and connectedness theory with an emphasis on the effect of the dipole-dipole interactions on the size and shape of the clusters and on the threshold percolation density. Two simple models for the dipolar fluid are considered: (i) a system of hard spheres with an embedded point dipole and (ii) a related system of hard spheres in which the dipole-dipole forces are replaced by an angular-averaged dipolar potential. A first-order perturbation theory (for the first model) and the connectedness version of the Percus-Yevick integral equation (for the second one) are used to describe clustering and percolation, and their results are compared with the corresponding Monte Carlo data. Our results show that clusters become larger in size and acquire a stronger mean dipolar moment when the particles’ dipolar moments are increased. Far from the percolation transition, the clusters are nonspherical, the eccentricity being favored by the energetics of dipolar orientation. Furthermore, they reveal that larger dipolar strengths imply smaller percolation densities.

Static and dynamic behavior around the electrically driven Fréedericksz transition in a nematic liquid crystal [4-pentyl-4’-cyano-biphenyl, Merck K15 (5CB)] with large dielectric anisotropy has been studied experimentally as well as theoretically. Nematodynamic equations have been solved and numerical results for the homogeneous distortion and its dynamics have been compared with the experiment. The effect of the conductivity, that of the surface anchoring and a pretilt, as well as the influence of the magnitude of the dielectric anisotropy, has been treated and compared with the experiment. The surface anchoring constant has been determined. A two-dimensional fluctuating structure was detected, which becomes visible slightly below the transition and originates presumably from the thermal director fluctuations. In the dynamical regime a transient pattern also arises, consisting of a set of fairly regular stripes with a preferred direction parallel to the initial director alignment. The distribution and the time behavior of the light intensity of the patterns has been measured and growth rates have been determined.

A series of random growth models has been studied in which the growth probability at position r on the surface of the growing cluster is given by P(r)≃μ(r)${\mathit{l}}^{\mathrm{\phi }}$, where μ(r) is the harmonic measure at r and l is the distance from the seed or origin. The distance l can be either the Pythagorean distance or the minimum path distance measured on the growing cluster. The introduction of this scale-invariant perturbation of the usual diffusion-limited-aggregation (DLA) model (φ=0) introduces a distance-dependent correlation length, ξ=l/‖φ‖, that characterizes a geometrical crossover in the cluster structure. Although the structures generated by these models have an appearance that is quite different from that of DLA clusters (for ‖φ‖≫0), the growth of their radii of gyration and the internal density profile ρ(r) have simple power-law forms with the same exponents as those associated with DLA. The difference in scaling is manifest in the amplitudes of the power-law forms. These amplitudes exhibit a power-law dependence on the radial bias exponent φ.

For φ≫1 the clusters become self-affine structures with the same exponents as those associated with DLA on length scales r≪ξ. These clusters exhibit a crossover to self-affine wedgelike linearly growing structures at r≃${\mathit{scrR}}_{\mathit{x}}$≃φ. For φ≪-1 the growth probability is enhanced in the core of the clusters. These clusters exhibit a dense core having radius ${\mathit{scrR}}_{\mathit{x}}$∼‖φ‖. For r≃${\mathit{scrR}}_{\mathit{x}}$, the structure crosses over to a structure having the same scaling behavior as DLA. For growth from a line in a strip of width L, the density-density correlation function in the lateral direction can be represented by the scaling form ${\mathit{C}}_{\mathit{h}}$(x)∼${\xi }^{\mathrm{-}\mathrm{\alpha }}$g(x/${\xi }^{\mathrm{\alpha }/\nu }$), where h is the distance from the line substrate (height) and exponents α and ν have values of about 1/3 and 1/2, respectively. The scaling function g(x) has the form g(x)≃${\mathit{x}}^{\mathrm{-}\nu }$ for x≪1 and g(x)∼const for x≫1.

We study the dynamic behavior of the strongly coupled one-component classical plasmas by calculating a dynamic structure factor for various coupling strengths and momentum transfers in terms of the dynamically convergent calculation method recently developed. It is shown that the dynamically convergent calculation yields fast convergence, especially at large momentum transfer. We analyze the molecular-dynamics data for an intermediate momentum transfer at which the origin of the peak of power spectrum may be unclear, and show which elementary excitation is responsible for the peak. Our analysis also shows the disappearing process of plasma oscillation.

In the collisional-radiative model, the plasma parameters of a laser-produced Ge plasma were determined from the line-intensity ratio of He-like Al ions, which had been mixed into Ge targets as an impurity before laser irradiating. The plasma parameters were also determined from the line-intensity ratio of Ge ions themselves in the partial-local-thermodynamic-equilibrium model. Both are almost in agreement.

We present a method for calculating the total x-ray-scattering cross section as a function of angle for kilo-electron-volt x rays scattered by partially ionized hot dense plasma. The calculational procedure is based on determining the separate contributions of bound and free electrons to the scattering cross sections. Basic distributions needed for the calculation are obtained by solving the Thomas-Fermi model in the correlation sphere, where both electrons and ions are accounted for. The results indicate significant changes in the intensity and angular distribution of the scattering cross sections between different plasma conditions and between plasma and cold material.

The kinetic equation of a quantum plasma is derived by means of the Wigner distribution function and the Bogoliubov approach in a strong magnetic field. The equation includes correctional binary collisions, which account for the influence of a magnetic field on the collisions of particles and the effect of many-body effects.

A different relative diffusion coefficient for electrons interacting with coherent, localized Langmuir wave packets is proposed. It is shown that the coherent, localized wave packets can drive the formation of clumps in phase space, and only when the relative velocity is zero does the lifetime of clumps diverge logarithmically, with the relative positions of the constituents getting closer to one another.

We report the experimental study of the fine structure of bifurcation and hysteresis behaviors under two control parameters in a weakly ionized cylindrical rf magnetoplasma system that supports nonlinear ionization drift waves. With increasing rf power up to the onset of the quasiperiodic state, the system shows a cascade of hysteresis loops with an abrupt change of the collective mode for each subcritical bifurcation. Fine structures such as the embedded small hysteresis loops, which correspond to multistability, and the backward supercritical subharmonic and intermittent bifurcations were observed. The effects of changing pressure, for example, the conversion from subcritical to supercritical bifurcation through a tricritical point, are also presented and discussed.

The plasma physics of heavy-ion stopping in fully ionized matter is developed on the basis of the Vlasov-Poisson equations with particular emphasis on small ion velocities ${\mathit{v}}_{\mathit{p}}$, below the electron thermal velocity ${\mathit{v}}_{\mathrm{th}}$, and on solutions nonlinear in the coupling parameter scrZ=${\mathit{Z}}_{\mathrm{eff}}$/(${\mathit{n}}_0$${\lambda }_{\mathit{D}}^3$) between the heavy-ion projectile with effective charge ${\mathit{Z}}_{\mathrm{eff}}$ and the plasma with electron density ${\mathit{n}}_0$ and Debye length ${\lambda }_{\mathit{D}}$. Concerning the stopping power in the low-velocity regime relevant for the Bragg peak at the end of the ion range, results on the friction term dE/dx∝${\mathit{v}}_{\mathit{p}}$ are presented, and an improved dE/dx formula for plasma is derived in closed form and readily applicable for stopping-power calculations; it is identical to the standard result for ${\mathit{v}}_{\mathit{p}}$>${\mathit{v}}_{\mathrm{th}}$, but also describes the limit ${\mathit{v}}_{\mathit{p}}$→0 correctly.

For ${\mathit{v}}_{\mathit{p}}$<${\mathit{v}}_{\mathrm{th}}$, nonlinear results are found to contribute to the stopping power with terms ∝${\mathit{scrZ}}^{5/2}$ for positive ions and terms ∝${\mathit{scrZ}}^3$ for negative ions in addition to the basic ${\mathit{scrZ}}^2$ term; they are derived from a low-velocity expansion of a form-factor representation of dE/dx. Concerning high velocities ${\mathit{v}}_{\mathit{p}}$>${\mathit{v}}_{\mathrm{th}}$, the relevant coupling parameter is scrZ(${\mathit{v}}_{\mathrm{th}}$/${\mathit{v}}_{\mathit{p}}$${)}^3$, and nonlinear corrections to the stopping power ∝${\mathit{scrZ}}^3$/${\mathit{v}}_{\mathit{p}}^5$ are obtained by extending the work of Ashley, Ritchie, and Brandt [Phys. Rev. B 5, 2393 (1972)] to the plasma case. An interpolation between the low- and the high-velocity results is given; taking, e.g., parameters characteristic for heavy-ion beam inertial fusion the nonlinear corrections further enhance dE/dx up to 10% in the Bragg peak region. An application of the present results to heavy-ion energy loss in an electron-cooling line is also discussed. In the present paper, ${\mathit{Z}}_{\mathrm{eff}}$ is assumed to be constant; the physics determining ${\mathit{Z}}_{\mathrm{eff}}$ is treated in a subsequent article [Peter and Meyer-ter-Vehn, following paper, Phys. Rev. A 43, 2015 (1991)].

The effective charge ${\mathit{Z}}_{\mathrm{eff}}$ of fast heavy ions slowing down in hot dense matter is calculated simultaneously with the stopping power dE/dx. The various ionization and recombination processes determining ${\mathit{Z}}_{\mathrm{eff}}$ are discussed, and corresponding rate coefficients are given; particular attention is paid to dielectronic recombination which turns out to be the dominant capture mechanism in highly ionized target material. Important results are (1) the effective charge of heavy ions passing through matter is considerably higher for fully ionized plasma than for cold target matter; (2) in contrast to stopping in cold targets, where ${\mathit{Z}}_{\mathrm{eff}}$ runs through a series of equilibrium charge states essentially determined by the instantaneous projectile velocity, high nonequilibrium charge states of the projectile are found in strongly ionized targets due to reduced recombination and faster stopping; (3) this causes additional range shortening, in some cases by factors 2–7, in particular for relatively low projectile energies (${\mathit{E}}_{\mathrm{ion}}$<2 MeV/u) and target densities (n<${10}^{20}$ ${\mathrm{cm}}^{\mathrm{-}3}$). Typical results for ${\mathit{Z}}_{\mathrm{eff}}$ and dE/dx in this parameter region are presented. They are compared with recent experimental data; new experiments are proposed. Concerning applications to heavy-ion-driven inertial fusion, the described effects become relevant at the end of the range, and some illustrative cases are discussed.

The Lyapunov instability is studied numerically for a one-dimensional model of diatomic molecules with harmonic intramolecular and hard intermolecular interactions. Previous results are extended to characterize the equipartition regime in terms of the two parameters of the system, the number of molecules n and the vibrational frequency ω. When the system is in equipartition, we find the existence of a thermodynamic limit for the maximal Lyapunov exponent and a power-law behavior ${\mathrm{\omega }}^{\mathrm{\alpha }}$, in analogy with the Fermi-Pasta-Ulam model. The separation of trajectories in phase space, investigated by considering the time dependence of the distance of initially close trajectories and by averaging over the phase space, is related to the maximal Lyapunov exponent and shown to be an alternative way to compute it when n is not too large. Multiple-precision arithmetic analysis for the model and its link to Lyapunov instability are also discussed.

A pump-probe technique, x-ray inverse fluorescence allowed by molecular excitation (XIFAME), is proposed as a contrast mechanism for x-ray microscopy. The technique consists of using a laser to produce holes in the valence levels of selected molecules; these holes then permit inverse fluorescent absorption transitions to occur. The method would permit the selective mapping of simple molecular structures and oxidation states of light elements. Cross-section estimates are made, and it is argued that the technique is potentially more sensitive than imaging techniques based on the atomic absorption edge. It is also argued that XIFAME has advantages over the use of x-ray-absorption near-edge structure for spectroscopic measurements of very dilute molecular structures.