A simple model for polysoaps' thread-like aggregates

The equilibrium polymerization, a model for one-dimensional reversible aggregates is used under conditions of theta and bad solvent to describe thread-like aggregates of polysoaps. In two dimensions, the aggregate size distribution decreases always more slowly than an exponential distribution and the dependence of the mean aggregate size L on the density φ and end-cap energy E of the polysoap cylindrical micelle is of the form L[φexp(E/KT)]^δ with δ<1/2. On the other hand, in three dimensions in the bad solvent regime, the dependence of L on φ becomes exponential explaining the high φ dependence of the viscosity in experimental results.