Living polymers and polymer solutions: a misleading analogy

Experimental results from colloidal suspensions of worm-like micelles are currently interpreted in terms of close analogies between this kind of systems and polymeric solutions. In particular, it was hypothesized that the viscoelastic properties of dense systems of giant flexible cylindrical micelles can be rationalized in terms of an entangled network of worm-like aggregates, very similar to a neutral random polymeric network. Such an idea is strongly supported by theoretical results that, in a mean-field approximation, suggests for an unlimited growth process of the micellar contour length with concentration. The mean-held theory indicates for an exponentially shaped length distribution function, with mean [L] depending on concentration, phi, in agreement with a scaling law [L] proportional to phi(alpha) (alpha = 0.5 in the simpler approach). A number of experimental results seem to be successfully interpretable within this framework. Aim of this work is to show that the agreement between theory and experiment is just an accident, being the mean-field approach, in principle, inadequate in describing systems dense enough to show a concentration dependence of the mean micellar size. It will be unambiguously shown that there is no way to describe semi-diluted micellar solutions through a mean-field approximation and that there does not exist any scaling law of the kind [L] proportional to phi(alpha). Furthermore, it will be shown that the shape of the size distribution function is markedly different from the exponential one. The basis for a more realistic approach for the growth process of micellar aggregates is also presented and some preliminary indications are successfully compared with experimental results.