Influence of the surface on the elastic properties of liquid crystals

A statistical approach including direct correlation functions is applied to study the influence of the surface confining the nematic liquid phase on the Franck elastic coefficients. Specific calculations are made for a model system composed of ellipsoidal molecules interacting by means of the Gay-Berne potential near the interacting surface. Fiz. Tverd. Tela (St. Petersburg) 40, 1356–1359 (July 1998)     

Anomalous light diffusion in ferroelectrics having a diffuse phase transition

It has been shown by using the statistical approach that the angular dependence of intensity I(θ) in multiple small-angle light scattering can be described by Lévy’s universal distribution functions. The fundamental property of the stability of these distributions permits one to extract information on the characteristics of fractal media as complete as it is possible in the simple single-scattering case. In particular, an analysis of the polarization characteristics of I(θ) in disordered PST reveals that the surface fractals observed in these crystals are of the heterophase rather than domain origin. Fiz. Tverd. Tela (St. Petersburg) 40, 1537–1541 (August 1998)     

Two Theorems of Hardy-Bennett-Type

The factorization of inequalities, introduced by G. Bennett, is a new and very effective method providing the best possible version of several classical and latest inequalities. Here two theorems of G. Bennett are extended into factorized forms up to the exact values of the constants. In the proofs we construct appropriate sequence spaces and utilize one of our recent theorems.     

Underdoped manganites: Canted antiferromagnetic ordering or two-phase ferro-antiferromagnetic state?

We calculate the energy of charge-carrier-induced canted ordering in conducting layered antiferromagnetic systems with double exchange. The quantum approach to the d-spins is used. In the jellium model the energy of the canted state is lower than the energies of both collinear ferro-and antiferromagnetic states over a certain range of charge carrier densities, beginning with arbitrarily small densities. Nevertheless, the canted state cannot be realized, because it is unstable against charge-carrier density fluctuations. The two-phase ferro-antiferromagnetic state can play the role of an alternative to canting. The case of an intermediate electronic-impurity phase separation is investigated. Zh. éksp. Teor. Fiz. 114, 2225–2237 (December 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

A shape model for the twisting power of chiral solutes in nematics

The twisting power of chiral probes in nematics is interpreted in terms of a shape model, in which the surface elements of the solute molecules tend to align with the local director. The theoretical treatment is based on a previous approach, suitable for relating order parameters in nematics to molecular shape, and leads to the definition of a molecular pseudo-tensor whose orientational average determines the pitch and handedness of the helical macrostructures. Results of numerical calculations performed for distorted biphenyl and binaphthyl molecules are in agreement with the experimental results.     

Orientational ordering of liquid crystals containing a difluoro-substituted phenyl ring

The orientational ordering of several liquid crystals containing a difluorosubstituted phenyl ring has been studied through the use of C-13 NMR. The fluorinated phenyl ring of these liquid crystals have C_s symmetry, so three order parameters are required to completely describe the ordering of this ring. All three of these order parameters have been calculated from carbon-fluorine dipolar coupling constants obtained from the carbon-fluorine splittings in the C-13 NMR spectra. Because of the complexity of the fluorine-coupled spectra, variable angle spinning (VAS) was used to resolve the carbon-fluorine splittings. In order to study the orientational ordering over wide ranges of temperature, we have developed an empirical correlation between the order parameter and the value of a carbon-fluorine dipolar coupling constant. This enabled us to study the change in the order parameter with temperature. The results of applying this method to several structurally similar liquid crystals containing the same type of difluorinated phenyl ring are presented. A comparison is made to a similar mono-fluorinated liquid crystal.     

A partial differential equation which describes an interatomic surface

In this work we present a first-order partial differential equationwhich defines the topology of single ‘atomic entities’in multiatomic systems. Such an equation, obtained by R. F.W. Bader, is here analysed and discussed from a general mathematicalpoint of view; a method is then proposed for defining the initialor boundary condition. With this contribution we would liketo promote and stimulate a more detailed analysis which goesbeyond practical purposes and basic mathematical analysis inorder to have a deeper understanding of the theory behind theequation and its consequences for practical applications.