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We investigate by means of a number of different dynamical Monte Carlosimulation methods the self-assembly of equilibrium polymers in dilute,semidilute and concentrated solutions under good-solvent conditions. In oursimulations, both linear chains and closed loops compete for the monomers,expanding on earlier work in which loop formation was disallowed. Our findingsshow that the conformational properties of the linear chains, as well as theshape of their size distribution function, are not altered by the formation ofrings. Rings only seem to deplete material from the solution available to thelinear chains. In agreement with scaling theory, the rings obey an algebraicsize distribution, whereas the linear chains conform to a Schultz--Zimm type ofdistribution in dilute solution, and to an exponentional distribution insemidilute and concentrated solution. A diagram presenting different states ofaggregation, including monomer-, ring- and chain-dominated regimes, is given.

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