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Under-knotted and Over-knotted Polymers: Unrestricted Loops | | N.T. Moore
; R. Lua
; A.Y. Grosberg
; | | Date: |
18 Mar 2004 | | Subject: | Soft Condensed Matter | cond-mat.soft | | Affiliation: | Department of Physics, University of Minnesota | | Abstract: | We present computer simulations to examine probability distributions of gyration radius for the no-thickness closed polymers of N straight segments of equal length. We are particularly interested in the conditional distributions when the topology of the loop is quenched to be a certain knot, K. The dependence of probability distribution on length, N, as well as topological state K are the primary parameters of interest. Our results confirm that the mean square average gyration radius for trivial knots scales with N in the same way as for self-avoiding walks, where the cross-over length to this "under-knotted" regime is the same as the characteristic length of random knotting, N_0. Probability distributions of gyration radii are somewhat more narrow for topologically restricted under-knotted loops compared to phantom loops, meaning knots are entropically more rigid than phantom polymers. We also found evidence that probability distributions approach a universal shape at N>N_0 for all simple knots. | | Source: | arXiv, cond-mat/0403457 | | Services: | Forum | Review | PDF | Favorites | |
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