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Pulling Knotted Polymers

Oded Farago·Yacov Kantor·Mehran Kardar
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Abstract

We compare Monte Carlo simulations of knotted and unknotted polymers whose ends are connected to two parallel walls. The force $f$ exerted on the polymer is measured as a function of the separation $R$ between the walls. For unknotted polymers of several monomer numbers $N$, the product $fN^ν$ is a simple function of $R/N^ν$, where $ν\simeq 0.59$. By contrast, knotted polymers exhibit strong finite size effects which can be interpreted in terms of a new length scale related to the size of the knot. Based on this interpretation, we conclude that the number of monomers forming the knot scales as $N^t$, with $t=0.4\pm 0.1$.

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Oded Farago, Yacov Kantor, Mehran Kardar. 2002-05-06. Pulling Knotted Polymers. https://doi.org/10.1209/epl%2Fi2002-00317-0

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