A Unified Spatiotemporal Failure Law for Polymer Chains

The prediction of the stochastic material failure governed by rare events, particularly at the nanoscale, represents a challenge of interdisciplinary convergence. By bridging the atomic-scale structures and interactions with macroscopic stochastic failure, we here derive an analytical spatiotemporal failure law for polymer chains that unifies the effects of time, length, loadings, and temperature. This law predicts that the survival probability (<i>S</i>) of polymer chains with a length (<i>l</i>) over a time (<i>t</i>) obeys a universal scaling as ln<i>S</i> = (ln<i>S</i>₀/<i>t</i>₀<i>l</i>₀)<i>tl</i>, where <i>t</i>₀, <i>l</i>₀, and <i>S</i>₀ are the elementary attempt time, bond length, and survival probability for a single bond, respectively. Extensive atomistic simulations across diverse potential forms, loadings, and scales validate this theory. This law reveals a fundamental spatiotemporal equivalence: spatial and temporal scales are interchangeable in governing failure statistics, and quantifies how common numerical artifacts can alter failure statistics. This work offers a universal physics-based framework for understanding and predicting material aging and failure from interatomic interactions for the nanotechnology community.