2 research outputs found
Diffusion of a ring polymer in good solution via the Brownian dynamics
Diffusion constants D_{R} and D_{L} of ring and linear polymers of the same
molecular weight in a good solvent, respectively, have been evaluated through
the Brownian dynamics with hydrodynamic interaction. The ratio ,
which should be universal in the context of the renormalization group, has been
estimated as for the large-N limit. It should be consistent
with that of synthetic polymers, while it is smaller than that of DNAs such as
. Furthermore, the probability of the ring polymer being a
nontrivial knot is found to be very small, while bond crossings may occur at
almost all time steps in the present simulation that realizes the good solvent
conditions.Comment: 11 pages, 4 figure
On the size of knots in ring polymers
We give two different, statistically consistent definitions of the length l
of a prime knot tied into a polymer ring. In the good solvent regime the
polymer is modelled by a self avoiding polygon of N steps on cubic lattice and
l is the number of steps over which the knot ``spreads'' in a given
configuration. An analysis of extensive Monte Carlo data in equilibrium shows
that the probability distribution of l as a function of N obeys a scaling of
the form p(l,N) ~ l^(-c) f(l/N^D), with c ~ 1.25 and D ~ 1. Both D and c could
be independent of knot type. As a consequence, the knot is weakly localized,
i.e. ~ N^t, with t=2-c ~ 0.75. For a ring with fixed knot type, weak
localization implies the existence of a peculiar characteristic length l^(nu) ~
N^(t nu). In the scaling ~ N^(nu) (nu ~0.58) of the radius of gyration of the
whole ring, this length determines a leading power law correction which is much
stronger than that found in the case of unrestricted topology. The existence of
such correction is confirmed by an analysis of extensive Monte Carlo data for
the radius of gyration. The collapsed regime is studied by introducing in the
model sufficiently strong attractive interactions for nearest neighbor sites
visited by the self-avoiding polygon. In this regime knot length determinations
can be based on the entropic competition between two knotted loops separated by
a slip link. These measurements enable us to conclude that each knot is
delocalized (t ~ 1).Comment: 29 pages, 14 figure