A simple model for polysoapsʹ 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.