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

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 (3D) is dissolved in the initial phase into two dimensions (2D), and one dimension (1D) subspace in a 3D crystal, respectively, rotate and/or slide between each other during thermal process. In linear algebra, this state is designated as [2D circle plus 1D] composite subspaces of vector. As per linear algebraic approach, [2D circle plus 1D] is not identical with 3D, and the mathematical sign circle plus indicates addition directly. The phase is represented as [2D circle plus 1D] lattice-based composite phase. Apart from the [2D circle plus 1D] phase, two more mixed phases with [1D circle plus 1D] and [1D circle plus 1D circle plus 1D] may also be theoretically studied using linear algebra. Finally, the category of phase is proposed to be analyzed with link to its transition temperature.