Fractal Brownian motion and polymers in external fields

Polymer behavior in external fields is modeled using fractal Brownian motion. The chain dimensions of polymer chains with and without excluded volume show a contour length dependence of N-v where v = h - 1. Chains with excluded volume have h = 3/5, chains without excluded volume, Gaussian chains have h = 1/2, and for chains in the collapsed state h = 1/3. This nonphysical result points to the distinction between fractals as models of the trajectory or path of a polymer that are self-similar on all length scales and real polymers that possess a lower and upper limit for self-similarity.