Geometrical properties of interior segments of two-dimensional lattice polymer confined in a square box

We study two-dimensional lattice polymer fully confined in a square box by using exact enumeration, and examine the geometric properties of segments in the interior. We find that the scaling of geometric quantities closely resembles that of a full-length chain at θ-point. In particular, the interior segments are more swollen than random chains. This result is in contrast to that for the three dimensions, where such interior segments behave like random chains.