Long-range order in liquid crystals

One often encounters the statement that ordinary isotropic liquids are disordered, something which is not entirely true. The average distance to the nearest neighbor of each molecule (or other constituent of the phase) is actually quite well defined, a fact that distinguishes this least ordered condensed phase from the gaseous state, which is truly disordered. However, the distance to the next nearest neighbor is much less defined and over longer distances the correlation between molecule position is very poor. We say that the correlation length is short or that the liquid is only short-range ordered.

The key characteristic of liquid crystals is that they exhibit long-range order in at least orientation, while largely maintaining the molecular mobility of isotropic liquids (at least for the nematic phase which has no long-range positional order and where the molecules thus have very large translational freedom). Nematics are the least ordered liquid crystals, as the orientational order is their only type of long-range order. Smectics in addition have 1D positional order as the molecules order up into layers. Two-dimensional positional order occurs in columnar phases, frequent for instance in case of disc-shaped molecules or rod-like micelles forming liquid crystal phases. The different types of long-range order and the resulting macroscopic anisotropic properties, in combination with the ease in rearranging the molecules/micelles, give liquid crystals unique properties and responsiveness, which are at the core of their applications in technology as well as nature.

In our research the varying types and degree of liquid crystalline long-range order play key roles. For instance, in smectic liquid crystals exhibiting a de Vries-type SmA-SmC transition, a characteristic seems to be unusually high positional order along the layer normal coupled with unusually low orientational order. Another example is the case of nanoparticle organization in lyotropic liquid crystal templates, where the degree of ordering imposed on the nanoparticles, as well as the possible disturbance of liquid crystalline long-range order by the presence of the nanoparticles are important issues to investigate.

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