Isotropic–nematic transition in micellized solutionsa)

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Abstract
We treat the isotropic‐to‐nematic transition in polydisperse suspensions of micellar rods. By generalizing an early theory of Onsager, we obtain a first‐order transition in which the ordered rods are significantly longer than those in the (coexisting) isotropic phase. We show that this ‘‘growth’’ is driven by the free energy term arising from loss of orientational entropy upon alignment. For large aggregates the product ρ̄L̄2D (where L̄ is a number‐averaged length, D the diameter of the rods, and ρ̄ the number density of aggregates) is roughly constant for each phase at coexistence. The transition value of the (nematic) order parameter (≂〈P2(cos θ)〉) first increases linearly with aggregation number s (for small rods) and approaches unity asymptotically (for large s). We compare our results to those of an earlier, monodisperse treatment of this system and interpret the nematic‐induced growth in terms of coupling between rod size and alignment in micellar solutions.