Isotropic–nematic phase behavior of length-polydisperse hard rods

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 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.