Theory of phase separation for a solution of tridisperse rod-like particles

Within the Onsager theory, we study solutions of polydisperse thin hard rods. An approximate method by Odijk is used numerically to determine the orientational distribution functions in the nematic phase in a straightforward way. Next, the coexistence relations are used in determining phase transitions. In coexisting nematic phases equality of osmotic pressure implies equal overall number density. A procedure is developed to locate equal chemical potentials between nematic phases of tridisperse systems. For length ratios larger than 3, we find phase diagrams showing nematic three-phase regions, critical points, critical end points and as a limit a tricritical point. The mechanism is not due to excluded-volume effects but to the interplay between orientational entropy and entropy of mixing. At higher concentrations the phase diagram is independent of concentration. Below a certain concentration, coexistence with an isotropic phase intervenes