Graphical representations of the Maier–Saupe mean field theory in nematic liquid crystals

ABSTRACT

We have developed the graphical representation to analyse the Maier–Saupe (MS) mean field theory in nematic molecular system. Based on the molecular field theory, the transcendental equations for the Helmholtz free energy and the orientational order parameter are derived and graphically represented for several physical parameters, from which the critical values of temperatures and order parameters are uniquely determined. The empirical formulae based on a four-parameter power law for temperature dependence of order parameter $S\left(\tau \right)$ are presented and compared with the MS theory, of which a modified Haller equation of the form $S\left(\tau \right)={\left(1-0.990\tau /{\tau }_{NI}\right)}^{0.21}$ yields the best result in a large portion of nematic range within ~0.5% deviation from the mean field theory. We also present the comparison of the MS theory with the Landau–de Gennes theory for universal ratios of the characteristic order parameters.

Graphical Abstract

KEYWORDS:

• Orientational order parameter
• nematic liquid crystal
• Maier–Saupe mean field theory
• nematic to isotropic phase transition
• Landau–de Gennes theory

Disclosure statement

No potential conflict of interest was reported by the authors.