Fractal Brownian motion and polymers in external fields

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Abstract
Polymer behavior in external fields is modeled using fractalBrownian 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.

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