Contributions of repulsive and attractive interactions to nematic order

ABSTRACT

Both repulsive and attractive molecular interactions can be used to explain the onset of nematic order. The object of this paper is to combine these two nematogenic molecular interactions in a unified theory. This attempt is not unprecedented; what is perhaps new is the focus on the understanding of nematics in the high density limit. There, the orientational probability distribution is shown to exhibit a unique feature: it has compact support on configuration space. As attractive interactions are turned on, the behaviour changes, and at a critical attractive interaction strength, thermotropic behaviour of the Maier-Saupe type is attained.

Graphical Abstract

KEYWORDS:

• Dense nematic liquid crystals
• mean-field theories
• nematic order
• compressibility of nematics

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The reader is referred to the closing Section 6 for a short discussion on pre-existing models; here, it would disrupt the flow of our presentation and overshadow the novelty of our approach.

2. Which might better be thought of as phenomenological function of the number density ${\rho }_0$ introduced shortly below, in (19).

3. We study $f$ only for $0\le x\le 1$, as it is clearly even in $-1\le x\le 1$.