Theoretical Foundation of Some Properties of Chain Ordering in Liquid Crystals

Abstract

Nuclear magnetic resonance splittings $\delta {\nu }_i\mathrm{}\left(T\right)\mathrm{}$ from deuterated molecules in liquid crystals are assimilated to vectors in a "space of molecular conformations," $\mathcal{E}\mathrm{}\left(T\right)\mathrm{}$, defined at each temperature $T$. The orientational parameters form a basis of $\mathcal{E}\mathrm{}\left(T\right)\mathrm{}$. An equivalence is established between temperature changes $T\to T^{\prime }$ and linear mappings $\mathcal{E}\mathrm{}\left(T\right)\mathrm{}\to {\mathcal{E}}^{\prime }\left(T^{\prime }\right)$, and used to explain a number of observations concerning the conformation of flexible molecules in liquid crystals. As an example, the invariance of certain "conformation coefficients" with temperature and phase transitions is theoretically demonstrated for the first time.