Linear aggregation revisited: Rods, rings and worms

The problem of ring formation in solutions of cylindrical micelles is reinv estigated theoretically, taking into account a finite bending rigidity of t he self-assembled linear objects. Transitions between three regimes are fou nd when the scission energy is sufficiently large. At very low densities on ly spherical and very short, rod-like micelles form. Beyond a critical dens ity, mainly rings but also worm-like chains appear in (virtually) fixed rel ative amounts. Above a second transition both the length of the linear chai ns and the relative amount of material taken up by them increase rapidly wi th increasing concentration. The mass accumulated into long, semi-flexible worms then overwhelms that in rings. The ring-dominated regime is very narr ow for semi-flexible chains, confirming that the presence of rings may be d ifficult to observe in many micellar systems, and indeed disappears complet ely for sufficiently low scission energy and/or large persistence length.