Theoretical Characterization of Liquid Crystalline Mesophases: Analysis with Its Link to Phase Transition Temperature

Abstract

An estimation of category of liquid crystalline (LC) phase based on composite lattices using linear algebra and lattice parameters is proposed. The vector space in three dimensions [Formula: see text] is dissolved in the initial phase into two dimensions [Formula: see text], and one dimension [Formula: see text] subspace in a 3D crystal, respectively, rotate and/or slide between each other during thermal process. In linear algebra, this state is designated as [Formula: see text] composite subspaces of vector. As per linear algebraic approach, [Formula: see text] is not identical with 3D, and the mathematical sign ⊕ indicates addition directly. The phase is represented as [Formula: see text] lattice-based composite phase. Apart from the [Formula: see text] phase, two more mixed phases with [Formula: see text] and [Formula: see text] may also be theoretically studied using linear algebra. Finally, the category of phase is proposed to be analyzed with link to its transition temperature.