Theoretical Models for Liquid Crystals

The general rules that emerge from analysis of the factors that influence the formation of a liquid crystalline phase are that  

Theoretical interest over the last thirty years in the modelling of the properties of liquid crystals has been driven by their application in displays. A variety of theoretical approaches have been applied to the description of the physical properties of liquid crystals. The statistical models developed are intuitively closer to our molecular understanding of these materials and will be considered initially. The more continuum approach, which allows visualization of macroscopic effects, will be considered later. 

If the liquid crystalline molecule is considered as a rod, then as the liquid is cooled and the density increases, the molecules will attempt to align and crystallize. To stop the molecules crystallizing it is necessary for the aligmnent of individual pairs of molecules to be inhibited. A molecule in the isotropic liquid phase has three degrees of freedom two degrees of freedom in terms of rotation about the major and minor axes and one in terms of translation. Loss of these elements of freedom describes the liquid crystal phase transitions discussed above. 

Starting from the isotropic phase, where the molecules have all three degrees of freedom, cooling will increase the density and rotation about the long axis becomes restricted. Series of models have been developed that consider the density of liquid in terms of the restriction of the order.These theories identify a critical density at which the isotropic to nematic transition would be predicted. Constraint of the molecule in terms of its rotation about the long axis defines the nematic phase. If now the translational freedom is restricted and layered alignment is imposed on the molecules, then smectic order is created. The smectic phase can still retain disorder in rotational freedom about the short axis. Loss of this final degree of freedom will lead to the creation of a erystalline ordered structure. This simple approach provides a description for the isotropic nematic smectic crystalline transitions. 

Many molecules exhibiting liquid crystal properties have either a terminal alkyl or alkyl ether group. The terminal chains exhibit a number of different conformations, as in (31)  

---