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The statistics of self-avoiding random walks have been used to model polymerphysics for decades. A self-avoiding walk that grows one step at a time on alattice will eventually trap itself, which occurs after an average of 71 stepson a square lattice. Here, we consider the effect of nearest-neighborattractive interactions on the growing self-avoiding walk, and examine theeffect that self-attraction has both on the statistics of trapping as well ason chain statistics through the transition between expanded and collapsed walksat the theta point. We find the trapping length increases exponentially withthe nearest-neighbor contact energy, but that there is a local minimum intrapping length for weakly self-attractive walks. While it has beencontroversial whether growing self-avoiding walks have the same asymptoticbehavior as traditional self-avoiding walks, we find that the theta point isnot at the same location for growing self-avoiding walks, and that thepersistence length converges much more rapidly to a smaller value.

Trapping in Self-Avoiding Walks with Nearest-Neighbor Attraction