Differential Geometry of Polymer Models: Worm-like Chains, Ribbons and Fourier Knots

Details Differential Geometry of Polymer Models: Worm-like Chains, Ribbons and Fourier Knots Differential Geometry of Polymer Models: Worm-like Chains, Ribbons and Fourier Knots

2007-02-08

arxiv.org/abs/cond-mat/0702203v1

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

10.1088/1751-8113/40/17/003

We analyze several continuum models of polymers: worm-like chains, ribbons and Fourier knots. We show that the torsion of worm-like chains diverges and conclude that such chains can not be described by the Frenet-Serret (FS) equation of space curves. While the same holds for ribbons as well, their rate of twist is finite and, therefore, they can be described by the generalized FS equation of stripes. Finally, Fourier knots have finite curvature and torsion and, therefore, are sufficiently smooth to be described by the FS equation of space curves.

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