Shape anisotropy of polymers in disordered environment

We study the influence of structural obstacles in a disordered environment on the size and shape characteristics of long flexible polymer macromolecules. We use the model of self-avoiding random walks on diluted regular lattices at the percolation threshold in space dimensions $d=2$ and $d=3$⁠. Applying the pruned-enriched Rosenbluth method, we numerically estimate rotationally invariant universal quantities such as the averaged asphericity $⟨Ad⟩$ and prolateness $⟨S⟩$ of polymer chain configurations. Our results quantitatively reveal the extent of anisotropy of macromolecules due to the presence of structural defects.