X-ray studies of tilted hexatic phases in thin liquid-crystal films

Kosterlitz-Thouless physics: a review of key issues

This article reviews, from a very personal point of view, the origins and the early work on transitions driven by topological defects such as vortices in the two dimensional planar rotor model and in (4)Helium films and dislocations and disclinations in 2D crystals. I cover the early papers with David Thouless and describe the important insights but also the errors and oversights since corrected by other workers. I then describe some of the experimental verifications of the theory and some numerical simulations. Finally applications to superconducting arrays of Josephson junctions and to recent cold atom experiments are described.

Disjoining pressure in free-standing smectic-A films and its effect on their reflectivity

The results of calculations of a disjoining pressure and smectic layer spacings in free-standing smectic-A films (FSSAF's) heated above the temperature of disappearance of the smectic order in bulk liquid crystal samples are presented. An effect of the disjoining pressure on the optical reflectivity of FSSAF's having a different number of the smectic layers is investigated. The results of calculations are in agreement with results of experimental optical-reflectivity investigations of FSSAF's.

Structural study of the smectic-I to smectic-F transition in freely suspended films

The smectic-I (S(I)) to smectic-F (S(F)) phase transition in terephthal-bis-(4n)-decylaniline (TB10A) has been examined for a possible continuous transition via the intermediate smectic-L (S(L)) phase. X-ray diffraction measurements of thick, single-domain, freely suspended films are used to classify the phases and to determine the hexatic order parameter C6 and its harmonics. Instead of the continuous transition suggested in the literature we find a first-order S(I)-->S(F) transition with a discontinuous change in the direction of the bond-orientational order relative to the molecular tilt. The tilt of the molecular form factor in the hexatic phases is inconsistent with the tilt estimated from published layer spacing measurements, suggesting that the hexatic phases of TB10A must have the molecular cores oriented at an angle relative to the tails. This result taken together with published results on the S(C) phase suggests that the S(C)-->S(I)-->S(F) transitions are driven by changes in the conformation of the hydrocarbon tails. Examination of the harmonic scaling relation between the hexatic order parameters shows mean-field behavior in the S(I) phase. This result will make binary mixtures of TB10A with other materials a practical system for the study of the crossover from mean field to the XY behavior seen in other hexatic systems.

Thermal fluctuations and x-ray scattering from free-standing smectic-A films

The present paper is devoted to theoretical investigation of thermal fluctuations and correlations between them in free-standing smectic-A films (FSSAF's) formed of liquid crystal compounds with bulk smectic-A-isotropic (SmA-I) and SmA-nematic (SmA-N) phase transitions, as well as small angle x-ray scattering from these FSSAF's. The study took into account the dependence of the bending elastic constant K and the smectic layer compressibility B on the distance from the boundary free surfaces of the films. The results of calculation are compared with those obtained in the framework of the Holyst model [Phys. Rev. Lett. 65, 2153 (1990); Phys. Rev. A. 44, 3692 (1991)] for spatially uniform FSSAF's. It has been found that, well below the temperature at which the smectic order in the bulk liquid crystal disappears, taking into account the profiles of the elastic moduli K and B does not produce noticeable differences from this model. However, at maximum temperatures of existence of FSSAF's, our results are considerably different from the predictions of the Holyst model. The results obtained are applied to calculation of specular and diffuse x-ray reflectivities of FSSAF's in the whole temperature interval of their existence. Displacement of the molecular centers within the film layers along those normal to them and the deviation of the local orientational order in FSSAF's from the ideal are also taken into account. The results of calculation are in agreement with experiments on the small angle x-ray scattering from FSSAF's.