Energy Barriers for Reversible Chain Scission and Healing under Tension with Displacement Control

Abstract

Polymer chain scission is a key mechanism for fracture of soft materials such as elastomers and
hydrogels. 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 usually
assume force-controlled conditions, that is, when the 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 with healing is
possible under displacement-controlled conditions, that is, when the 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 the kinetic approach to predict the statistics and kinetics
of a single polymer chain under tension, first by integrating the rate equation for the survival
probability of the chain and then by kinetic Monte Carlo simulations. Notably, the present model
predicts rate-dependent chain scission, with a lower bound for the critical force that could be
several orders of magnitude lower than the upper bound (which is close to the theoretical strength
of the covalent bonds in the backbone).