Abstract
Reversibly self-assembling systems, such as micelle-forming surfactants, polymerizing proteins, and linearly aggregating polyaromatic molecules, form a variety of ordered mesophases in solution. The liq- uid crystalline phases observed in these inherently polydisperse systems are often characterized by trans- lational, as well as orientational, order. For example, in the relatively simple case of linear aggregation, both nematic and columnar phases are found. In this paper, we model the linearly aggregating system,
taking into account polydispersity and the coupling between the variable aggregate size, orientation, and position distributions. The model utilizes a single-parameter phenomenological description of aggre- gate assembly in conjunction with a scaled particle calculation of the configurational entropy of the polydisperse system. Translational order in the columnar phase is treated by using an extension of our recent cell theory. The phase behavior exhibited by the model system reproduces many of the features characteristic of the experimental systems. The concentration and temperature dependence of the aggregate size distribution, orientational order parameter, and columnar spacing are also reported.