Kinetics of Loop Formation in Polymer Chains

Details Kinetics of Loop Formation in Polymer Chains Kinetics of Loop Formation in Polymer Chains

2007-08-15

arxiv.org/abs/0708.2077v2

Physics

Condensed Matter

Soft Condensed Matter

30 pages, 9 figures. Revised version includes a new figure (8) and minor changes to the text

Scientific paper

We investigate the kinetics of loop formation in flexible ideal polymer chains (Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the time scale for cyclization is $\tau_c\sim \tau_0 N^2$ (where $\tau_0$ is a microscopic time scale and $N$ is the number of monomers), provided the coupling between the relaxation dynamics of the end-to-end vector and the looping dynamics is taken into account. The resulting analytic expression fits the simulation results accurately when $a$, the capture radius for contact formation, exceeds $b$, the average distance between two connected beads. Simulations also show that, when $a < b$, $\tau_c\sim N^{\alpha_\tau}$, where $1.5<{\alpha_\tau}\le 2$ in the range $7

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