The shapes of two-, four-, and five-dimensional linear and ring polymers

The shapes of two- , four- , and five-dimensional linear and ring polymers, with and without excluded volume, are investigated numerically via Brownian dynamics. It is found that the asphericity of nonexcluded volume linear polymers is in agreement with theoretical predictions in all dimensions. Agreement with available theoretical predictions is also obtained for two-dimensional nonexcluded volume ring polymers. Moreover, it is shown that excluded volume polymers become more ideal (i.e., closer to nonexcluded volume polymers) as the dimension is increased.