Monte Carlo simulation studies of the size and shape of ring polymers

The present work gives a comparison between the properties of athermal ring polymers and those of linear chains. Based on bond fluctuation (BE) and pivot algorithm (PIV) for the construction of molecules, a new algorithm was developed, which proved most efficient due to large acceptance fractions and small (integral) auto-correlation rimes of global properties, in addition having the advantage of a large set of different bond vectors. While the topological stare of ring polymers remains unchanged by exclusive use of BF, knotted structures (which were identified with the help of Alexander polynomials) can by formed and removed by the use of PN. In accordance with previous work, it turned out that the probability of unknotted rings tin principle) exponentially decreases with an increasing number of segments, however, so slowly that the appearance of knotted structures (ca, 0.1% for N = 512) is a rare event in the range of chain-lengths evaluated (N = 32 - 8192). The chain-length dependence of global quantities of ring polymers are described by the use of scaling relations with proper short chain corrections, in analogy to linear chains. The instantaneous shape of ring polymers is more symmetric than that of linear chains. Local quantities, i.e., mean squared bond lengths and mean bond angles are the same for both systems, at least in the limit of an infinite number of segments.