Thin hexatic

Free suspended films of smectic liquid crystals can show a change in the crystalline order from the quasi-two-dimensional to the three-dimensional one [11]. Very thin smectic B films (number of monolayers n < 10) are two dimensional with the hexatic in-plane order, and with (low temperatures) or without (higher temperatures) a tilt of molecules. With increasing n (n > 20) the transition to various three-dimensional crystalline structures is observed. 

The above developments had two major consequences. First, the identification of the various hexatic phases led to a detailed classification of the large variety of thermotropic liquid crystal phases. The essential structural details of these phases are illustrated in the Appendix8>9. Second, the diffraction patterns yield novel crossover critical phenomena. In three dimensions, this presented single experiments which yield a simultaneous measurement of many anisotropy crossover exponents, previously obtained from separate complex experiments. For very thin layers, the patterns allow detailed studies of the crossover from two to three dimensions, and provide new quantitative information on the two dimensional hexatic phase. 2 The present paper aims at a brief review of these developments. 

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