Equilibrium shapes of flat knots

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localized on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.     

Transition from smectic-A to crystalline phase in the mean field approximation

We present here a smectic-A to crystalline phase transition curve for liquid crystals, in addition to the phase diagram previously reported which includes the isotropic, nematic, and smectic-A phases calculated in the mean field approximation.     

Equilibrium shapes of crystals attached to walls

We discuss equilibrium shapes of crystals attached to walls. Optimal shapes for different configurations of walls are found and the minimality of the overall surface tension is proven with the help of a simple geometrical argument based on the isoperimetric inequality and monotonicity. Stability results in the form of Bonnesen inequalities are obtained in the two-dimensional case.     

On the possibility of a smectic-A phase in paraffins

It is proposed that for paraffins (CH₂)_N and N not too large melting may not lead immediately to an isotropic fluid but first to a layered liquid state with smectic-A properties.     

Surface ordering transitions at a liquid crystal-solid interface above the isotropic smectic-A transition

The degree of orientational order induced by confining cylindrical surfaces is monitored via deuteron nuclear magnetic resonance linesplitting and linewidth above the smectic-A to isotropic phase transition. The orientational order strongly depends on the length of the surfactant coupling molecule, on the surface coverage, and on the liquid crystal. Continuous and stepwise growth of orientational order and surface-induced orientational order transitions found in the isotropic phase are explained in terms of a simplified model of surface-induced layering and molecular self-diffusion.     

Low-frequency electrodynamic instability in the smectic-A phase of a liquid crystal

An instability, induced by constant and alternating electric fields, is observed and studied in the planar texture of the smectic-A phase of a liquid crystal. The effect of the parameters of the applied field and of the material on the characteristics of the instability is studied. The mechanism for the appearance of the instability is linked to the nonuniform distribution of the electric field over the thickness of the liquid crystal.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 82–86, October, 1985In conclusion, the authors thank V. G. Chigrinov for useful discussion and interest in this work.     

X-ray scattering from freely suspended smectic-A films

This work is devoted to a theoretical analysis of specular reflection and diffuse scattering of x-rays from a freely suspended smectic-A film, taking into account its spatial inhomogeneity and deviations of orientational and position ordering in smectic layers from ideal ordering. The results of the calculations are compared with the experimental data on small-angle scattering of x-rays from freely suspended films of 7 AB liquid crystals. It is found that the theoretical results agree with the experimental data.     

Bend-induced melting of the smectic-A phase: analogy to a type-I superconductor

Using an atomic force microscope to nanopattern a substrate for liquid crystal alignment, a bend distortion is imposed on a liquid crystal. In regions of large bend the smectic-A phase melts into the nematic phase, and the width of the melted region is measured as a function of temperature. The results are consistent with type-I superconducting (nematic-smectic-A) behavior, wherein a large magnetic field (bend or twist distortion) induces an order to disorder transition. A model that accounts for non-mean-field behavior is presented.     

Dynamic critical scattering near the smectic-A—nematic phase transition in CBOOA

High resolution neutron quasielastic scattering has been applied to a study on the critical dynamics near the smectic-A—nematic phase transition in CBOOA. A line narrowing is observed for a certain value of the momentum transfer. We interpret this narrowing as a critical slowing down of the smectic order parameter fluctuations near the transition temperature T_SN. The relaxation times vary between 10^-8 and 10^-7 sec for a temperature interval of 2 K below T_SN.     

Surface morphologies of anthracene single crystals grown from vapor phase

The morphologies and lattice structures of anthracene single crystals grown from the vapor phase were investigated using optical microscopy, phase contrast microscopy, atomic force microscopy (AFM), and X-ray diffraction analysis. Common morphologies with hexagonal large planes were observed irrespective of crystal size. The observation of certain surface morphologies with a phase contrast microscopy revealed that the spiral steps originated from screw dislocations present on the (0 0 1) planes. Moreover, the center and edge of the (0 0 1) planes had large curvatures, similar to hills. Resultantly, quarter-monolayer (ML) steps were observed on the large and flat planes between both hills.     

Gel phase vesicles buckle into specific shapes

Osmotic deflation of giant vesicles in the rippled gel phase P(β') gives rise to a large variety of novel faceted shapes. These shapes are also found from a numerical approach by using an elastic surface model. A shape diagram is proposed based on the model that accounts for the vesicle size and ratios of three mechanical constants: in-plane shear elasticity and compressibility (usually neglected) and out-of-plane bending of the membrane. The comparison between experimental and simulated vesicle morphologies reveals that they are governed by a typical elasticity length, of the order of 1 μm, and must be described with a large Poisson's ratio.     

Some physical properties of ZnS crystals grown from the vapour phase

Wurtzite-type crystals with wide regions of high purity and good optical properties have been grown in a few hours by an improved flow method. Dislocations have been found to be mainly arranged inside isolated striation regions where a weak green fluorescence and phosphorescence has been observed. Under bending deformation the crystals show a plastic behaviour that is not directly correlated to the mean dislocation density of the samples. Rupture has been found at about 10³ kg/cm².The microwave method for the detection of crystal deflection has been suggested by Prof. A. Gozzini. His helpful advice and interest in this research has been deeply appreciated. Many thanks are also due to the Physical Institute of SAV in Prague, for the possibility to work on their crystals of ZnS. Finally we wish to thank Mr. Coli and Mr. Montanari for design and construction of the mechanical equipment and the furnace quartz assembly.     

Incorporation of Sn into epitaxial GaAs grown from the liquid phase

The incorporation of Sn into LPE GaAs was studied as a function of the atomic fractionx _Sn ^l of Sn in the liquid (1.6×10⁻⁴≤x _Sn ^l ≤0.54), the growth temperatureT _K and the cooling rate α. The diffusion coefficient of As in Ga for moderate Sn-doping was deduced from the growth velocities to beD _As (760° C)=(3.3±1.0)×10⁻⁵ cm²/s. The epitaxial layers were analyzed after van der Pauw with special emphasis on the sources of experimental error. With the aid of current mobility theories the concentrations of the ionized donors and acceptors were derived. From their dependence onx _Sn ^l , on α and onT _K combined with the Schottky-barrier model of Sn incorporation it can be concluded that the melt and the growing crystal surface were in thermal equilibrium. The diffusion coefficient of Sn in GaAs is about 8×10⁻¹⁴ cm²/s at 760° C. The distribution coefficient for Sn increases from 4.4×10⁻⁵ to 12.3×10⁻⁵ in the temperature range from 690 to 800° C. The total Sn incorporationx _Sn ^s was measured using the atomic absorption spectroscopy for the first time down tox _Sn ^s =10¹⁷/cm³. From these data it can be concluded that up tox _Sn ^l =0.54 the dopant Sn is incorporated as donor and as acceptor only and that within the experimental scatter there is no indication of incorporation as a neutral species.     

Structural phase transitions in isotropic magnetic elastomers

Magnetic elastomers represent a new type of materials that are “soft” matrices with “hard” magnetic granules embedded in them. The elastic forces of the matrix and the magnetic forces acting between granules are comparable in magnitude even under small deformations. As a result, these materials acquire a number of new properties; in particular, their mechanical and/or magnetic characteristics can depend strongly on the polymer matrix filling with magnetic particles and can change under the action of an external magnetic field, pressure, and temperature. To describe the properties of elastomers, we use a model in which the interaction of magnetic granules randomly arranged in space with one another is described in the dipole approximation by the distribution function of dipole fields, while their interaction with the matrix is described phenomenologically. A multitude of deformation, magnetic-field, and temperature effects that are described in this paper and are quite accessible to experimental observation arise within this model.     

Equilibrium topology of the intermediate state in type-I superconductors of different shapes

A high-resolution magneto-optical technique was used to analyze flux patterns in the intermediate state of bulk Pb samples of various shapes - cones, hemispheres, and discs. Combined with the measurements of macroscopic magnetization, these results allowed studying the effect of bulk pinning and geometric barrier on the equilibrium structure of the intermediate state. Zero-bulk pinning discs and slabs show hysteretic behavior due to topological hysteresis - flux tubes on penetration and lamellae on flux exit. (Hemi)spheres and cones do not have a geometric barrier and show no hysteresis with flux tubes dominating the intermediate field region in both regimes. It is concluded that flux tubes represent the equilibrium topology of the intermediate state. Real-time video is available in the EPAPS Document No. E-PRLTAO-98-024726..