Theory of size distribution of associating polymer aggregates. I. Spherical aggregates

We examine the stability of spherical, micellelike aggregates composed of long-chain, polymeric surfactants in dilute solution. The associating polymers consist of long, unbranched hydrophobic chains with one polar end-group per chain and are in a good solvent for the chains. Although the head groups prefer to aggregate in the nonpolar solvent and thus stabilize the spherical structure, the energy associated with the chain repulsions tends to destabilize the aggregates as the chain length increases. For a liquid-drop model of the head interactions, the average aggregation number evolves smoothly towards zero as the chain length increases. An alternate model of the head region, which assumes a preferred head-packing geometry, results in the ultimate destabilization of the spherical aggregate as the chain length is increased beyond a certain threshold. Both models yield a critical micelle concentration (CMC) at low values of the polymer concentration.