Kinetics of Loop Formation in Polymer Chains
| dc.creator | Toan, Ngo Minh | |
| dc.creator | Morrison, Greg | |
| dc.creator | Hyeon, Changbong | |
| dc.creator | Thirumalai, D. | |
| dc.date | 2007-08-15 | |
| dc.date | 2007-11-13 | |
| dc.date.accessioned | 2026-07-07T08:42:11Z | |
| dc.date.available | 2026-07-07T08:42:11Z | |
| dc.description | 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 $τ_c\sim τ_0 N^2$ (where $τ_0$ 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 $a < b$, $τ_c\sim N^{α_τ}$, where $1.5<{α_τ}\le 2$ in the range $7<N<200$ used in the simulations. By using a diffusion coefficient that is dependent on the length scales $a$ and $b$ (with $a<b$), which captures the two-stage mechanism by which looping occurs when $a < b$, we obtain an analytic expression for $τ_c$ that fits the simulation results well. The kinetics of contact formation between the ends of the chain are profoundly affected when interactions between monomers are taken into account. Remarkably, for $N < 100$ the values of $τ_c$ decrease by more than two orders of magnitude when the solvent quality changes from good to poor. Fits of the simulation data for $τ_c$ to a power law in $N$ ($τ_c\sim N^{α_τ}$) show that $α_τ$ varies from about 2.4 in a good solvent to about 1.0 in poor solvents. Loop formation in poor solvents, in which the polymer adopts dense, compact globular conformations, occurs by a reptation-like mechanism of the ends of the chain. | |
| dc.description | 30 pages, 9 figures. Revised version includes a new figure (8) and minor changes to the text | |
| dc.identifier | https://arxiv.org/abs/0708.2077 | |
| dc.identifier | http://arxiv.org/abs/0708.2077 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141874 | |
| dc.subject | Soft Condensed Matter | |
| dc.title | Kinetics of Loop Formation in Polymer Chains | |
| dc.type | text |