Abstract In this paper the influence of a knot on the structure of a polymethylene (PM) strand in the tensile process is investigated by using the steered molecular dynamics (SMD) method. The gradual increasing of end-to-end distance, $R$, results in a tighter knot and a more stretched contour. That the break in a knotted rope almost invariably occurs at a point just outside the `entrance' to the knot, which has been shown in a good many experiments, is further theoretically verified in this paper through the calculation of some structural and thermodynamic parameters. Moreover, it is found that the analyses on bond length, torsion angle and strain energy can facilitate to the study of the localization and the size of a knot in the tensile process. The symmetries of torsion angles, bond lengths and bond angles in the knot result in the whole symmetry of the knot in microstructure, thereby adapting itself to the strain applied. Additionally, the statistical property of the force-dependent average knot size illuminates in detail the change in size of a knot with force $f$, and therefore the minimum size of the knot in the restriction of the potentials considered in this work for a PM chain is deduced. At the same time, the difference in response to uniaxial strain, between a knotted PM strand and an unknotted one is also investigated. The force-extension profile is easily obtained from the simulation. As expected, for a given $f$, the knotted chain has an $R$ significantly smaller than that of an unknotted polymer. However, the scaled difference becomes less pronounced for larger values of $N$, and the results for longer chains approach those of the unknotted chains.
Received: 11 July 2007
Revised: 21 November 2007
Accepted manuscript online:
(Elasticity and anelasticity, stress-strain relations)
Fund: Project supported by the National
Natural Science Foundation of China (Grant Nos 20274040, 20574052
and 20774066), the Program for New Century Excellent Talents in
University, China (Grant No NCET-05-0538) and the Natural Science
Foundation of Zhejiang Pr
Cite this article:
Shen Yu(沈瑜) and Zhang Lin-Xi(章林溪) A steered molecular dynamics study on the elastic behaviour of knotted polymer chains 2008 Chin. Phys. B 17 1480
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