Kinetics of Ring Formation

Details Kinetics of Ring Formation Kinetics of Ring Formation

2011-02-25

arxiv.org/abs/1102.5348v1

Phys. Rev. E 83 061102 (2011)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 7 figures

Scientific paper

10.1103/PhysRevE.83.061102

We study reversible polymerization of rings. In this stochastic process, two monomers bond and as a consequence, two disjoint rings may merge into a compound ring, or, a single ring may split into two fragment rings. This aggregation-fragmentation process exhibits a percolation transition with a finite-ring phase in which all rings have microscopic length and a giant-ring phase where macroscopic rings account for a finite fraction of the entire mass. Interestingly, while the total mass of the giant rings is a deterministic quantity, their total number and their sizes are stochastic quantities. The size distribution of the macroscopic rings is universal, although the span of this distribution increases with time. Moreover, the average number of giant rings scales logarithmically with system size. We introduce a card-shuffling algorithm for efficient simulation of the ring formation process, and present numerical verification of the theoretical predictions.

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