Thermotropic liquid crystals Onsager theory

In contrast to the Onsager and Flory theories, the Maier-Saupe theory no longer takes into account molecular steric effects as the basic interaction but instead proposes that the van der Waals interactions between molecules are the basis for forming a liquid crystal phase. The van der Waals interaction depends on molecular orientations. The Maier-Saupe theory adopts a rather simple mathematical treatment and can easily take into account the relationship of system properties to temperature. This theory has been successfully applied to a thermotropic system of small molecular mass liquid crystal. 

The results of several molecular theories that describe the smectic ordering in a system of hard spherocylinders enable us to conclude that the contribution from hardcore repulsion can be described by the smoothed-density approximation. On the other hand, a realistic theory of thermotropic smectics can only be developed if the intermolecular attraction is taken into account, The interplay between hard-core repulsion and attraction in smectic A liquid crystals has been considered by Kloczkow-ski and Stecki [17] using a very simple model of hard spherocylinders with an ad-ditonal attractive r potential. Using the Onsager approximation, the authors have obtained equations for the order parameters that are very similar to the ones found in the McMillan theory but with explicit expressions for the model parameters. The more general analysis has been performed by Me-deros and Sullivan [76] who have treated the anisotropic attraction interaction by the mean-field approximation while the hardcore repulsion has been taken into account using the nonlocal density functional approach proposed by Somoza and Tarazona. 

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