Molecular field treatment of nematic liquid crystals

Abstract

The Maier-Saupe theory of the nematic mesophase is extended to rod-like molecules interacting with a perfectly general anisotropic potential. The resulting series expansion for the pseudopotential accounts quantitatively for the observed temperature dependence of the orientational order, even when the expansion is restricted to just the first two terms. However, the agreement can only be obtained if the expansion coefficients are assumed to depend on the inverse fourth power of the molar volume. The orientational molar enthalpy of transition calculated with the parameters determined by fitting the orientational order is qualitatively correct, although rather too large. The theory is also modified to allow for deviations from a spherically symmetric distribution of the intermolecular vector in the mesophase. A comparison of this new expression for the pseudo-potential with that derived by Chandrasekhar and Madhusudana reveals that certain of their assumptions are invalid. Finally, calculations made with the new pseudo-potential indicate that a modification of the Maier-Saupe theory based solely on deviations from a spherically symmetric distribution cannot yield quantitative agreement with theory.

Understanding and Describing the Liquid-Crystalline States of Polypeptide Solutions: A Coarse-Grained Model of PBLG in DMF

“…However, these theories involve a complicated mathematical treatment which make them difficult to apply to realistic LC models. The more commonly employed mean-field approaches for anisotropic phases such as the MaierSaupe 61,62 and the related molecular-field theories [63][64][65][66][67] (which are based the assumption that orientationally dependent attractive interactions are the molecular feature that give rise to liquid-crystalline order) are not appropriate for the description of lyotropic systems such as solutions of PBLG. This is because the LC phases exhibited by these polypeptides are governed principally by the repulsive interactions between the highly anisometric rod-like macromolecules.…”

A generalisation of the Onsager trial-function approach: describing nematic liquid crystals with an algebraic equation of state

“…In their mean-field treatment, Maier and Saupe [22][23][24] also make the assumption that orientationally dependent attractive interactions are the molecular feature that give rise to liquid crystalline order. The MaierSaupe approach and its extensions [1,6,[25][26][27][28], now represent a very popular mean-field treatment of anisotropic phases. The analytical description of the order parameter (but not the free energy) within the Maier-Saupe theory means that this has been the method of choice for comparison/correlation with experiment.…”

Liquid Crystal Observables: Static and Dynamic Properties

“…This is because the g 0 (r 12 ) are mainly structured at short range, and at short range liquid crystals are just like normal liquids. The set of quantities g + L (r 12 ) associated to the intermolecular vector correlation function represent a sort of order parameters [29,30] g + L (r 12 ) = 1 2 g 0 (r 12 ) dβ r 12 sin β r 12 g(r 12 , β r 12 )P L (cos β r 12 ) (78) = P L (cos β r 12 ) r 12 .…”

“…More generally it is useful to define distributions along different orientations ω r 12 of the intermolecular vector relative to the director [29,30,18]:…”