Polysoaps within the p-cluster model:: Solutions and brushes

The p-cluster model, proposed by de Gennes for PEO, is applied to polysoaps and hydrophobically modified water soluble polymers incorporating numerous "stickers" joined by long spacer chains. The phase behavior is determined by three parameters, the critical micelle concentration of the unpolymerized amphiphiles, phi(cmc), their aggregation number, p(o), and the length of the spacer chains, n. The phase behavior of free chains is discussed in the limit of infinite polymerization degree, N --> infinity, which is applicable to polymer brushes of any N. When n is high enough, a layering, vertical phase separation may occur in brushes of associating polymers.