Simple model for the fracture of a polymer chain: Single-bond potential of mean force and tension-based rate constants for chain rupture

Abstract

A linear chain of N particles connected by Morse bonds with periodic boundaries in a Brownian bath is considered as a model for polymer fracture. The potential of mean force (pomf) with respect to the length of a bond and its energy and entropic components are computed via Langevin Dynamics simulations at various chain elongations λ > 1. A narrow range of λ values is identified over which equilibrium is established between an intact (i) and a fractured (f) state over a pomf barrier. While the barrier and (f) regions of the pomf are well described by a well-known (N − 1)-bond adiabatic approximation, the shape of the (i) region departs from it, exhibiting a bimodal character. A new, 1-bond adiabatic approximation is proposed to explain this. The lower envelope of the two adiabatic approximations provides an excellent description of the pomf. The relationship between (f) states for individual bonds and for the entire chain is elucidated. A new approach, based on analysis of equilibrium tension autocorrelation functions, is developed to extract rate constants for the fracture and reformation of the chain in dependence of λ. Results from it agree with tension relaxation during nonequilibrium simulations initiated at equispaced configurations of the particles. Rate constants for chain fracture conform to a Boltzmann–Arrhenius–Zhurkov dependence on the tension averaged over the intact state of the chain, the activation length being higher than estimated from pomf extrema. These findings constitute a step toward a predictive multiscale simulation scheme for fracture in polymeric materials.