The Effect of the Magnitude of the Disordered Phase Temperature Range on the Given Phase Transition in Liquid Crystals

Abstract

The difference between phases separated by a given phase transition can be characterized by one particular physical property called the order parameter. For example, the order parameter for distinguishing a ferromagnetic phase from a paramagnetic phase is the magnetization. Consequently, the order parameter (ψ) is zero for the disordered phase (T>T_C) and nonzero for the ordered phase (T < T_C). Here T is the transition temperature. Depending on the way ψ approaches zero at T = T_C, we have two types of phase transitions. The one with ψ asymptotically approaching zero as T approach T ⁻_C is a continuous transition; otherwise, the transition is a first order one. For a continuous transition, the divergence of the order parameter-order parameter correlation length at T = T_C results in anomalous behavior in many physical properties, e.g., heat capacity (C), susceptibility (χ), etc. For example, in the limit where the reduced temperature t = ((T-T_C)/T_C) approaches zero, the critical exponent γ related to the diverging behavior of the susceptibility (χ) is defined as

$$ \gamma \equiv - \mathop{{\lim }}\limits_{{t \to 0}} \,{\text{en}}\,x{\text{/en}}\,{\text{t}} $$

. Consequently, in the temperature range sufficiently close to T_C, the susceptibility can be expressed as

$$\chi {\text{ = D}}{{{\text{t}}}^{{ - \gamma }}}$$

.