Isotropic-nematic phase equilibria of polydisperse hard rods: The effect of fat tails in the length distribution

TL;DR

This paper investigates how fat-tailed length distributions in polydisperse hard rods influence phase behavior, revealing unique phenomena like kinked cloud curves and three-phase coexistence, supported by theoretical and numerical analysis.

Contribution

It provides a detailed theoretical and numerical analysis of phase behavior in polydisperse hard rods with fat-tailed length distributions, highlighting novel phase coexistence features.

Findings

Kink in the isotropic cloud curve due to long rods

Existence of a narrow three-phase coexistence region

Theoretical derivation of cloud and shadow curves in the large cutoff limit

Abstract

We study the phase behaviour of hard rods with length polydispersity, treated within a simplified version of the Onsager model. We give a detailed description of the unusual phase behaviour of the system when the rod length distribution has a "fat" (e.g. log-normal) tail up to some finite cutoff. The relatively large number of long rods in the system strongly influences the phase behaviour: the isotropic cloud curve, which defines the where a nematic phase first occurs as density is increased, exhibits a kink; at this point the properties of the coexisting nematic shadow phase change discontinuously. A narrow three-phase isotropic-nematic-nematic coexistence region exists near the kink in the cloud curve, even though the length distribution is unimodal. A theoretical derivation of the isotropic cloud curve and nematic shadow curve, in the limit of large cutoff, is also given. The two curves are shown to collapse onto each other in the limit. The coexisting isotropic and nematic phases are essentially identical, the only difference being that the nematic contains a larger number of the longest rods; the longer rods are also the only ones that show any significant nematic ordering. Numerical results for finite but large cutoff support the theoretical predictions for the asymptotic scaling of all quantities with the cutoff length.