Isotropic-nematic phase behavior of length polydisperse hard rods

TL;DR

This paper investigates the phase separation behavior of length-polydisperse hard rods using a numerical Onsager model, revealing strong fractionation effects, triphasic equilibria, and the influence of polydispersity on phase stability.

Contribution

It provides a detailed numerical analysis of isotropic-nematic phase behavior in polydisperse rods, including triphasic equilibria and fractionation effects, for arbitrary length distributions.

Findings

Strong fractionation for polydispersities >50%

Prediction of triphasic isotropic-nematic-nematic phases

Phase stability region closes at a critical polydispersity

Abstract

The isotropic-nematic phase behavior of length polydisperse hard rods with arbitrary length distributions is calculated. Within a numerical treatment of the polydisperse Onsager model using the Gaussian trial function Ansatz we determine the onset of isotropic-nematic phase separation, coming from a dilute isotropic phase and a dense nematic phase. We focus on parent systems whose lengths can be described by either a Schulz or a `fat-tailed' log-normal distribution with appropriate lower and upper cutoff lengths. In both cases, very strong fractionation effects are observed for parent polydispersities larger than roughly 50 %. In these regimes, the isotropic and nematic phases are completely dominated by respectively the shortest and the longest rods in the system. Moreover, for the log-normal case, we predict triphasic isotropic-nematic-nematic equilibria to occur above a certain threshold polydispersity. By investigating the properties of the coexisting phases across the coexistence region for a particular set of cutoff lengths we explicitly show that the region of stable triphasic equilibria does not extend up to very large parent polydispersities but closes off at a consolute point located not far above the threshold polydispersity. The experimental relevance of the phenomenon is discussed.