Understanding Strain and Failure of a Knot in Polyethylene Using Molecular Dynamics with Machine-Learned Potentials

A neural network potential (NNP) has been developed by fitting to ab initio electronic structure data on hydrocarbons and is used to study failure of linear and knotted polyethylene (PE) chains. A linear PE chain must be highly strained before breaking as the stress is equally distributed across the chain. In contrast, the stress in a PE chain with a 3₁ or overhand knot, accumulates at the knot's entrance/exit. We find the strain energy is greatest when the bond length and angle are strained simultaneously, and that the knot weakens the chain by increasing the variance of the C-C-C angle, thereby allowing rupture at lower bond strains. We extend our analysis to both 5₁ and 5₂ knots and find that both break at the entrance/exit of a loop. Notably, molecular scale PE knots exhibit many of the same characteristics as knots in a macroscopic rope, with stick-slip phenomena upon tightening and similar points of failure.