Effect of topology on dynamics of knots in polymers under tension

We use computer simulations to compare the dynamical behaviour of torus and even-twist knots in polymers under tension. The knots diffuse through a mechanism similar to reptation. Their friction coefficients grow linearly with average knot length for both knot types. For similar complexity, however, the torus knots diffuse faster than the even-twist knots. The knot length autocorrelation function exhibits a relaxation time that can be linked to a breathing mode. Its timescale depends on knot type, being typically longer for torus than for even-twist knots. These differences in dynamical behaviour are interpreted in terms of topological features of the knots.

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