Pulling Knotted Polymers

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 $f{N}^{\nu }$ is a simple function of $R/N^{\nu }$, where $\nu \simeq 0.59$. 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 $t=0.4\pm 0.1$.

5 pages, 3 figures

References in corpus (2)

• Equilibrium shapes of flat knots
• Tightness of slip-linked polymer chains

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