Energy Barriers for Reversible Chain Scission and Healing under Tension with Displacement Control
Polymer chain scission is a key mechanism for fracture of soft materials. It is well known from single-molecule force spectroscopy experiments that the critical condition for chain scission depends on the loading rate and other environmental effects (e.g., temperature and solvent). Common approaches to describing the kinetics of chain scission often assume force-controlled conditions, that is, when a polymer chain is stretched by a prescribed force. As a result of this assumption, chain scission is irreversible, excluding the possibility of healing. In many soft materials, however, self-healing has been observed after fracture, suggesting possibly reversible chain scission. Here, we show that reversible chain scission is possible under displacement-controlled conditions, that is, when a polymer chain is stretched with a prescribed end-to-end distance. We present a breakable freely-jointed chain model, assuming that a polymer chain breaks when one of its links breaks while the other links remain nearly rigid. At a prescribed end-to-end distance, the free energy of the chain has two local minima and a local maximum (the transition state), giving rise to energy barriers for chain scission and healing. As the prescribed displacement increases, the energy barrier decreases for scission but increases for healing, depending on the chain length (number of links) and the potential energy of the link. With the energy barriers, we adopt a kinetic approach to predict the statistics and kinetics of a single polymer chain under tension, first by integrating the rate equation and then by kinetic Monte Carlo simulations. Notably, the present model predicts rate-dependent chain scission, with a lower bound for the rupture force that could be several orders of magnitude lower than the upper bound (which is close to the theoretical strength of the covalent bonds).