Nanoscale Positional Order Correlations: Swarms, Cybotactic Groups, Clusters, and Pretransitional Fluctuations in Liquid Crystals

Short-range molecular associations in organic liquids were first described as ``cybotactic'' groups [1] followed by the development of the swarm theory [2] to explain the structure, strong light scattering, and flow behavior of the nematic (N) liquid crystal phase. However, these ideas became inconsequential with the advent of the Oseen-Frank's continuum theory [3]. In 1970, de Vries reinvoked \textit{cybotactic} groups for the N phase of bis-(4'-n-octyloxybenzal)-2-chloro-l,4-phenylenediamine. These were eventually understood to be SmC pretransitional fluctuations, i.e., small correlated regions of the lower symmetry phase near the transition. Thermotropic biaxial mesophases have resurrected the faith in \textit{cybotacticity} in the guise of a new word - ``clusters''. Previous x-ray studies of normal organic fluids, and calamitic, lyotropic, and bent-core mesogens show that these clusters fall into three groups depending on the relative contributions of normal liquid structure and pretransitional fluctuations. A comparison with other organic and inorganic fluids will also be made.\\[4pt] [1] G.W. Stewart, Phys. Rev. \textbf{35}, 726 (1930).\\[0pt] [2] L.S. Ornestein and W. Kast, Trans. Farad. Soc. \textbf{29}, 931 (1933).\\[0pt] [3] FC Frank, Discuss. Faraday Soc. \textbf{25}, 19 (1958); W. Oseen, Ark. Mat., Astron. Fys. \textbf{19}, 1 (1925).