Novel results of extremely thin substrate-free liquid-crystal films obtained from calorimetric and computer simulation studies

Experimental results from extremely thin free-standing liquid-crystal films have been found to exhibit divergent heat-capacity anomalies in the vicinity of the smectic-A-hexatic-B (SmA-HexB) transition. In fact, the data can be successfully fit to a power-law expression yielding the critical exponent α=0.30±0.04. The results clearly indicate that the transition cannot be described solely in terms of hexatic order and that some additional molecular order must be created in the SmA-HexB transition in these liquid crystals. This transition is therefore not the simple liquid-hexatic transition as had been suggested previously. In light of x-ray diffraction studies indicating the existence of herringbone order in some liquid-crystal samples, Bruinsma and Aeppli formulated a coupled XY hamiltonian as a possible explanation for the anomalous experimental data obtained on the SmA-HexB transition in three dimensions (i.e. bulk samples). Based on our novel calorimetric and optical reflectivity results from thin liquid-crystal films, we have conducted extensive Monte Carlo simulations to explore this model in two-dimensional lattices. These studies have resulted in a number of novel discoveries that reveal important aspects of both the SmA-HexB transition in thin liquid-crystal films and two-dimensional melting phenomena in general.