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.