Intrinsic curvature governs entanglement of elastic tumbled rods

The spontaneous entanglement of filaments is a pervasive phenomenon across length scales, from DNA and proteins to wired headphones, climbing ropes, and engineering cables. Despite this ubiquity of filament entanglement, its characterization, predictive description of the underlying mechanisms, and prevention remain poorly understood. In this study, we examine the knotting and locking of tumbled elastic rods using a combination of precision desktop experiments, and imaging with X-Ray micro-computed tomography. Our objective is to quantify the knotting and locking probability and entanglement complexity of elastic rods subjected to bi-directional rotation in a cylindrical container, at constant tumbling velocity and test duration. We consider both straight and helical rods and systematically vary their total arc-length and natural curvature. We conduct a statistical analysis of a large ensemble of experiments, finding that the knotting probability of elastic rods decreases non-monotonically with increasing natural curvature and decreasing length of the rod. Moreover, we find that overall locking complexity is reduced for rods with increasing natural curvature. These results indicate the existence of an optimal range of rod geometric parameters that can inhibit self-entanglement. Even if we focus exclusively on the macroscale, our findings suggest that similar mechanisms may be relevant to filamentary microscopic systems such as DNA.