Size distribution for aggregates of associating polymers. II. Linear packing

We study the micellization of associating polymers (hydrocarbon chains with dipolar head groups in hydrophobic solvents) for the case where the polar heads form a linear array. The head interaction is assumed to be short ranged and the chain conformation (free) energy is assumed to follow spherical scaling in the small aggregation number limit and to have cylindrical scaling in the large aggregation number limit. In the small aggregation number limit, the aggregation number is only weakly dependent on the chain length. Numerical solutions as well as analytical studies show that the size distribution displays features of both the spherical and cylindrical aggregates: namely the absence of a sharp CMC transition and a rather sharp distribution function with a width that increases slowly with the mean aggregation number. In the large aggregation limit, the aggregation number can be a strong function of the chain molecular weight. We discuss the importance of the ‘‘end cap’’ effect in determining the mean size as a function of the chain lengths.