Abstract
A Monte Carlo study of the mean-square radius of gyration and scattering function with k the magnitude of the scattering vector for semiflexible ring polymers of the trefoil knot was conducted by the use of the discrete version of the Kratky–Porod (KP) wormlike ring model. The behavior of and as functions of the reduced contour length , defined as the total contour length L divided by the stiffness parameter , is clarified. A comparison is made of the results for the KP ring of the trefoil knot with those for the KP ring of the trivial knot and for the phantom KP ring without the topological constraints.
Highlights
A vast amount of experimental, theoretical, and computational results have been reported for the dilute solution properties of flexible ring polymers, where a comparison was made of experimental and/or computational results with conventional Gaussian chain theories [1,2,3]
There, the behavior of these quantities as functions of the reduced contour length λL [5] has been clarified, λL being proportional to M and defined as the total contour length L measured in units of the stiffness parameter λ−1 [5], in the range of the crossover from the rigid-ring limit λL → 0 to the random-coil one λL → ∞
We examine the effects of chain stiffness on the dilute solution behavior of ring polymers of non-trivial knots
Summary
A vast amount of experimental, theoretical, and computational results have been reported for the dilute solution properties of flexible ring polymers, where a comparison was made of experimental and/or computational results with conventional Gaussian chain theories [1,2,3]. Considering the fact that for (semiflexible) circular DNA, the configurations of the trivial knot and of non-trivial knots are visualized by electron microscopy [4,13], and that liquid chromatography at critical condition makes it possible to separate the (flexible) ring a-PS of non-trivial knots from those of the trivial knot [14], it is necessary to investigate the dilute solution behavior of both semiflexible and flexible ring polymers of non-trivial knots for the fine characterization of ring polymers Such examination has been made theoretically and/or computationally only for flexible rings by the use of the Gaussian ring model or the corresponding models [15,16,17,18,19,20,21], as mentioned generally above. The most fundamental quantities Rg2 and P(k)—reflecting the repeat-unit distribution around the center of mass of a single polymer in solution, determined by light scattering or small-angle X-ray or neutron scattering measurements—in the field of polymer solution science are evaluated by the MC method using the ideal discrete KP ring of the trefoil knot, and their behavior is examined as functions of λL with comparison between the present results and the previous ones for the KP ring of the trivial knot and for the phantom KP ring
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