Abstract
A variety of amphiphilic molecules reversibly and spontaneously self‐assemble in aqueous solution forming a polydisperse population of asymmetric aggregates. In binary water/surfactant systems, aggregates may be either oblate or prolate and form corresponding orientationally ordered phases. Such binary systems are modeled using a lattice statistics calculation of the configurational entropy of a polydisperse collection of hard rods and plates, combined with a phenomenological description of aggregate assembly. Using parameter values relevant to micellar surfactant systems, a series of phase diagrams and associated particle size distributions have been computed. Depending upon the competition between rod and plate growth, the concentration dependent transition sequences I→A, I→P, and I→A→P (where I≡isotropic micellar, A≡axial nematic, and P≡planar nematic) are seen. The A→P transition occurs when rod and plate growth are equally favorable and is discussed in detail. Qualitative comparisons are drawn between the calculated phase behavior and experimental results. No stable biaxial nematic phases are predicted for binary systems in the absence of positional order.