Topological effect in ring polymers investigated with Monte Carlo simulation.

We studied equilibrium conformations of ring polymers in the melt over the wide range of segment number up to 1000 by the Monte Carlo simulations and the bond fluctuation model, and estimated Flory's scaling exponent nu. The radial distribution function of segments for the ring polymers in the melt is obtained. We have found that nu for ring polymers is decreased with increasing segment number N, and nu goes down to 0.365 when N reaches 1000, whose value is apparently smaller than the theoretically predicted one, i.e., 25. Those values are in contrast to the well established nu value of 0.5 for linear polymers in the melt. This is because ring polymer chains in the melt are squeezed both by their own topological effect and the compression effect by the neighboring ring polymer coils which are also squeezed at bulk state. The difference in our result and the theory may be due to the fact that the estimation of topological entropy loss was ignored in the theoretical prediction, while it has been taken into consideration in the present study. If polymer coils repel each other in melt at N --> infinity, we have the limiting nu value of 13, so we conclude that nu is in the range of 13 < or = nu << 0.365 when the molecular weight of a ring polymer is high enough.