Conformation of a polymer chain at the theta’ point: Connection to the external perimeter of a percolation cluster

Abstract

We present an argument that the statistics of polymer rings at the theta point in two dimensions is exactly given by the statistics of the external perimeter (‘‘hull’’) of a percolation cluster. As a consequence, the fractal dimension $d_f$(theta) of a polymer chain at the theta point coincides with that of the hull of the percolating cluster, $d_f$(theta)=$d_H$. Here theta’ is the coil-globule transition point for a special interaction parameter. We also discuss conditions under which the theta’ point may be related to the conventional theta point.