Mechanical String Model for Liquid Crystal Ensemble: A Comprehensive Model for Polymorphism

Abstract

A mechanical string model is proposed for liquid crystal phase behaviour to comprehensively interpret the polymorphism phenomenon. In the proposed mechanical string model, the strings consist of many molecules existing among many layers in a smectic phase stretched perpendicular to the layers. The string itself induces self-excitation, a resonance between the string's vibrational mode and local molecular vibration or rotational motion, which in turn induces a phase transition from one phase to another phase at these resonance points. We propose a possible procedure for extracting and assigning a set of two parameters that represent the string's eigenvalue (energy term) and freedom of motion (entropy term) from the existing experimental data. The set of parameters or the code is a representation of the phase sequence or polymorphism of each liquid crystal. It is directed that such a code assignment of the ratios with rational numbers be originated in the mechanics of the string. The characteristic representations of the rational number sets for various liquid crystals are correlated to the molecular structures and their mechanical and dynamical characteristics.