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Kinetics of ring formation

E. Ben-Naim and P. L. Krapivsky
Phys. Rev. E 83, 061102 – Published 2 June 2011
Physics logo See Synopsis: Laws of the rings

Abstract

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 we present numerical verification of the theoretical predictions.

    • Received 25 February 2011

    DOI:https://doi.org/10.1103/PhysRevE.83.061102

    ©2011 American Physical Society

    Synopsis

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    Laws of the rings

    Published 2 June 2011

    Ring formation in polymerization offers new insight into the formation of giant polymer clusters.

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    Authors & Affiliations

    E. Ben-Naim1 and P. L. Krapivsky2

    • 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
    • 2Department of Physics, Boston University, Boston, Massachusetts 02215, USA

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    Issue

    Vol. 83, Iss. 6 — June 2011

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