Trapping in Self-Avoiding Walks with Nearest-Neighbor Attraction

Abstract

The statistics of self-avoiding random walks have been used to model polymer physics for decades. A self-avoiding walk that grows one step at a time on a lattice will eventually trap itself, which occurs after an average of 71 steps on a square lattice. Here, we consider the effect of nearest-neighbor attractive interactions on the growing self-avoiding walk, and examine the effect that self-attraction has both on the statistics of trapping as well as on chain statistics through the transition between expanded and collapsed walks at the theta point. We find the trapping length increases exponentially with the nearest-neighbor contact energy, but that there is a local minimum in trapping length for weakly self-attractive walks. While it has been controversial whether growing self-avoiding walks have the same asymptotic behavior as traditional self-avoiding walks, we find that the theta point is not at the same location for growing self-avoiding walks, and that the persistence length converges much more rapidly to a smaller value.

9 pages, 8 figures + 2 in appendix

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