Polymer shapes in two, four, and five dimensions

The average asymmetry of two-, four-, and five-dimensional linear and ring polymers, with and without excluded volume, is investigated numerically via Brownian dynamics. It is found that the average asymmetry of nonexcluded volume chains is in good agreement with theoretical predictions in all dimensions studied. The distribution of the average asymmetry is also determined. This distribution indicates that two-dimensional ring chains are likely to be nearly symmetrical. Moreover, the distribution of the maximum eigenvalues of the tensor of the moment of inertia is also in agreement with the theoretical predictions.