Topological constraints on polymer rings and critical indices

Abstract

Ring polymers in two and three dimensions have been simulated by closed Gaussian random walks. The effects of topological constraints is studied. In two dimensions, the non self crossing condition leads to an excluded volume effect and the critical index v so observed is in good agreement with the predictions of the renormalization group theory. In three dimensions, the condition of absence of knots should lead to new effects. However, it is observed that the probability of knot formation increases very slowly with the number of segments and consequently no comparable estimate could be made of any critical index