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The distribution of end‐to‐end distances of the weakly bending rod model
Author(s) -
Schurr J. Michael,
Fujimoto Bryant S.
Publication year - 2000
Publication title -
biopolymers
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.556
H-Index - 125
eISSN - 1097-0282
pISSN - 0006-3525
DOI - 10.1002/1097-0282(200012)54:7<561::aid-bip80>3.0.co;2-m
Subject(s) - bending , chain (unit) , monte carlo method , persistence length , chemistry , range (aeronautics) , limit (mathematics) , domain (mathematical analysis) , distribution (mathematics) , physics , statistical physics , mathematical analysis , thermodynamics , mathematics , materials science , statistics , quantum mechanics , polymer , organic chemistry , composite material
The weakly bending rod model is an approximation to a wormlike chain in the limit where the ratio L 0 / P of the contour length L 0 to the persistence length P is not too large. The range of validity of the weakly bending rod model is investigated by deriving analytical expressions for its distribution of end‐to‐end distances P ( L ) and its moments 〈 L m 〉 and numerically comparing the results with corresponding values for the wormlike chain model. No general, closed form analytical expression for either P ( L ) or the average length 〈 L 〉 of a wormlike chain exists, so those quantities are obtained by Monte Carlo simulations. Exact analytical expressions for 〈 L 2 〉 and 〈 L 4 〉 for the wormlike chain are employed in the comparison of the computed moments. Moments calculated for the approximate distributions of Daniels and Yamakawa and Stockmayer are also compared with the others. In addition, P ( L ) and its moments for the alternative model of Winkler et al. are compared with the others. The weakly bending rod model gives a reasonably good account of both P ( L ) and 〈 L m 〉, m = 1,2,4, over the range L 0 / P ≤ 0.6, but deviates significantly for L 0 / P ≥ 1.0. In contrast, the alternative model of Winkler et al. yields rather poor results in the rodlike domain. © 2000 John Wiley & Sons, Inc. Biopoly 54: 561–571, 2000