Equilibrium polymerization of chains and rings: A bicritical phenomenon

Dynamical Monte Carlo study of equilibrium polymers. II. The role of rings

“…11, using the directly measured end-to-end distance Ϸ0.1 for the constant of proportionality ͑Fig. 9͒, similar to the one estimated by Pfeuty and co-workers 6 in their analysis of self-assembled chains. While the scaling relation Eq.…”

“…In other types of equilibrium polymer, such as liquid sulfur, the presence of rings is on the other hand thought to be all-important. 6 It is believed that rings are suppressed in those self-assembled polymeric systems that are sufficiently rigid on the scale of the individual monomers. [3][4][5] A useful model describing the self-assembly of giant micelles is what we call the Restricted Model of equilibrium polymers, where by definition ring closure and branching of chains are disallowed, and only linear chains form.…”

Ring-driven shear thickening in wormlike micelles?

“…Micellar rings are expected theoretically [14]: their apparent absence in most experiments has been mysterious [15]. In the limit of a high end-cap energy E/2 for the micelles, the physics near φ * is, according to theory, completely dominated by rings.…”

Microstructure and macroscopic properties of polydisperse systems of hard spheres

“…There are, however, other constraints in the system (the number of primary, small constituents, for instance), and these may induce new kinds of transitions characterized by the appearance of one or a few macroscopic aggregates. Such are phenomena as the appearance of lamellar and columnar phases in surfactant solutions [45], emulsification failure in micro-emulsions [46], or long chain formation in polymer solutions [47].…”

“…Therefore, we also study this size distribution of sphere radii, which has the form [222]: where a 0 is a reference radius setting the length scale: 47) and σ is the dimensionless geometric standard deviation: Figure 3.12: Jamming density plotted against σ for systems with log-normal (LN) radii distribution and for their tridisperse maximal equivalents (TLN), using N = 16384. In the inset, the behavior of the fitting equations beyond the range of data is shown for larger values of σ, using the same axis and symbols.…”