| We present an algorithm which returns a number of entanglements for a given configuration of a polymeric system in 2 or 3 dimensions. Rubinstein and Helfand, and later Everaers et al. introduced a concept to extract primitive paths for dense polymeric melts made of linear chains (a multiple disconnected path), where each primitive path is defined as a path connecting the (space-fixed) ends of a polymer under the constraint of excluded volume between primitive paths of different chains, such that the multiple disconnected path fulfills a minimization criterion. The present algorithm uses geometrical operations and does not only provide a -- model independent -- efficient approximate solution to this hard problem, but releases several shortcomings of alternate approaches. In particular, primitive paths are treated as 'infinitely' thin (optionally: thick), and tensionless lines rather than multibead chains, excluded volume is taken into account without a force law. The present implementation allows to construct a shortest multiple disconnected path (SP) for 2D systems (polymeric chain within spherical obstacles) and an optimal SP for 3D systems (collection of polymeric chains). The number of entanglements is then simply obtained from the SP as either the number of kinks, or from the average length of a line segment. Further, information about structure (and potentially also the dynamics) of entanglements is immediatly available from the SP.
for LaTeX users @article{MKroger2005-168,
author = {M. Kr\"oger},
title = {Shortest multiple disconnected path for the analysis of entanglements in two- and three-dimensional polymeric systems},
journal = {Comput. Phys. Commun.},
volume = {168},
pages = {209-232},
year = {2005}
}
\bibitem{MKroger2005-168} M. Kr\"oger,
Shortest multiple disconnected path for the analysis of entanglements in two- and three-dimensional polymeric systems,
Comput. Phys. Commun. {\bf 168} (2005) 209-232.MKroger2005-168
M. Kr\"oger
Shortest multiple disconnected path for the analysis of entanglements in two- and three-dimensional polymeric systems
Comput. Phys. Commun.,168,2005,209-232 |
mk@mat.ethz.ch
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