On the application of polymer renormalization group theory to polymer-like microemulsions

We report on the application of results from conformation space renormalization group theory for semi-dilute polymer solutions to “equilibrium polymers” such as worm-like micelles or microemulsions. We have tested this approach with data from an extensive static light scattering study of lecithin water-in-oil (w/o) microemulsions. We demonstrate that one can construct a universal curve $(M_{\rm w}/RT)(\partial\Pi/\partial c)$ versus a reduced concentration $X\sim c/c^{*}$, where $c^{*}$ is the overlap concentration, from the experimentally determined values of the osmotic compressibility if a power law of the form $M_{\rm w}\sim c^{\alpha}$ for the $c$-dependence of the average particle size is assumed. We show that one can thus obtain information from static light scattering experiments on the concentration dependence of both the micellar size distribution and the intermicellar interaction effects, i.e., on the weight average molecular weight $M_{\rm w}(c)$ and the static structure factor $S(0, c)$