Unusual thickness-dependent heat-capacity anomaly in free-standing hexatic liquid-crystal films

High-resolution heat-capacity and optical-reflectivity measurements have been conducted near the smectic-A to hexatic-B transition in thin free-standing films of the liquid-crystal compound 64COOBC. We find an unexpected dependence on film thickness of the integrated magnitude of the heat-capacity anomalies as the films undergo layer-by-layer transitions. We measure the penetration depths of the ordering from the surface and next-to-surface layers which are pertinent to the highly correlated thermal behavior.