Linear Aggregation Revisited: Rods, Rings and Worms

TL;DR

This paper theoretically investigates ring formation in cylindrical micelles, revealing how finite bending rigidity influences transitions between spherical, rod-like, ring, and worm-like micelles at different densities.

Contribution

It introduces a theoretical model accounting for finite bending rigidity, elucidating the conditions under which rings and worms form and dominate in micellar solutions.

Findings

At low densities, only spherical and short rod-like micelles form.

Increasing density leads to a transition where rings and rods coexist.

Long worms dominate at high concentration, overshadowing rings.

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 rod-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.