| Polarized-video-microscopy has been used to study the layer-by-layer surface freezing transitions found in four liquid crystal materials: 90.4, 40.7, 70.7 and {dollar}overline{lcub}14{rcub}{dollar}S5. The functional form for the growth of the frozen surface layer thickness versus temperature, l(t), depends on the dominant intermolecular forces in the system. Examples of surface freezing, with long-range van der Waals forces and with short-range exponential forces, have been found for the first ten surface freezing transitions in {dollar}L approx{dollar} 64 layer thick films. For the surface freezing of 90.4, the appearance of the first ten surface layers is described very well by the simple power-law form predicted for a system with long-range van der Waals forces. The surface freezing of 40.7 and 70.7 is described by the simple logarithmic form predicted for surface freezing in a system with short-range exponential forces. The surface freezing of {dollar}overline{lcub}14{rcub}{dollar}S5 is described equally well by either long-range van der Waals or short-range exponential force models. After the first ten transitions, there is a systematic slowdown in the appearance of subsequent surface freezing transitions and l(t) deviates from the initial power-law or logarithmic divergence. To study this slowdown, we have measured the influence of film thickness on the surface freezing in two LC materials, 40.7 and 70.7, for film thicknesses ranging from 17 about a thousand layers. A remarkable variation with film thickness has been observed which can be explained with a single effective interfacial potential. From this model-independent effective interfacial potential, the shape of the repulsive potential responsible for the finite-size effects can be deduced.; A new method is described to make model-independent determinations of the interlayer density profile of freely suspended liquid crystal films by directly inverting grazing incidence x-ray scattering data. Although, in general, the measured scattering intensities determine only the magnitude of the scattering amplitudes, in the special case of one-dimensional centrosymmetric freely suspended films, the phases can be determined by inspection. The direct inversion analysis is a completely new method for solving the phase problem that does not depend on intensity relationships between different Bragg peaks used by direct methods, but instead uses the directly measured zeros of the primary and subsidiary maxima of the structure factor to determine the phase of each "Bragg peak" (primary maximum) and of each subsidiary maximum. An experimental demonstration of this method is presented for the evolution of smectic ordering in smectic-G and smectic-I/C films of 70.7 for thicknesses from three to 15 molecular layers. |
