Linear aggregation revisited: Rods, rings and worms

Abstract

The problem of ring formation in solutions of cylindrical micelles is reinvestigated theoretically, taking into account a finite bending rigidity of the self-assembled linear objects. Transitions between three regimes are found when the scission energy is sufficiently large. At very low densities only spherical and very short, rod-like micelles form. Beyond a critical density, mainly rings but also worm-like chains appear in (virtually) fixed relative amounts. Above a second transition both the length of the linear chains and the relative amount of material taken up by them increase rapidly with increasing concentration. The mass accumulated into long, semi-flexible worms then overwhelms that in rings. The ring-dominated regime is very narrow for semi-flexible chains, confirming that the presence of rings may be difficult to observe in many micellar systems, and indeed disappears completely for sufficiently low scission energy and/or large persistence length.

A simple and general approach for reversible condensation polymerization with cyclization

“…Semiflexibility has also been a topic of the work related to the n-vector model, in particular regarding the formation of giant micelles as one of the best studied model systems of self-assembly [71]. Here, ring formation becomes unimportant for micelle formation at sufficiently large persistence lengths [74], which has been argued also in a related simulation work [75].…”