Shape of polymer chains confined in spheres

A self-avoiding polymer chain confined in a sphere is generated by Monte Carlo technique on a simple cubic lattice. The dependence of shape of polymer chain on concentration C of polymer solution is studied. The shape of polymer chain is denoted as [L-1(2)]:[L-2(2)]:[L-3(2)], where L-1 less than or equal to L-2 less than or equal to L-3 are orthogonal components in the system of principal axes of gyration. Al low concentration (C less than or equal to 0.001), [L-2(2)]/[L-1(2)] and [L-3(2)]/[L-1(2)] remain approximately unchanged with the concentration. Then, with increase of the concentration, [L-2(2)]/[L-1(2)] and [L-3(2)]/[L-1(2)] decrease, and [L-3(2)]/[L-1(2)] decreases more rapidly than [L-2(2)]/[L-1(2)]. Asymptotically, [L-2(2)]/[L-1(2)] and [L-3(2)]/[L-1(2)] become 1.0 at a concentration C=1.0.