How far can a rubber molecule stretch before breaking? Ab initio study of tensile elasticity and failure in single-molecule polyisoprene and polybutadiene

Abstract

We present ab initio calculations of the internal C-C bond dissociation curve for single molecules of (cis-1,4) polyisoprene and polybutadiene. We define "bond rupture" as that point on the reaction coordinate where the unrestricted Kohn-Sham, or diradical, solution falls below the restricted, or closed-shell, solution. Using this definition, we find that rupture occurs at a tensile force of 6.8 nN for polyisoprene and 7.2 nN for polybutadiene. Their respective rupture strains are 45% and 42%. Our calculations show that the energy density versus extension is not sensitive to the number of isoprene units contained in the molecule, i.e., it is essentially independent of the chain length. These relatively large rupture strains have important implications for understanding the failure mechanism in rubber, and imply that purely enthalpic chain stretching must commence well before tensile failure occurs.

The molecular kink paradigm for rubber elasticity: Numerical simulations of explicit polyisoprene networks at low to moderate tensile strains

“…It is based on previous ab initio and MD studies of polyisoprene molecules that have established that: (1) local molecular kinks, composed of a few isoprene units, can act as entropic springs 19 and (2) that there is a purely enthalpic elastic force associated with stretching a chain beyond its nominal contour length. 18 We presented two new chain force extension models to treat low and moderate strains along the chain contour (entropic regimes Ia and Ib) and combined them with the enthalpic force extension model, regime II. Both the low and moderate strain models assume that the network chains are constrained by tubes in the surrounding melt and that the intra-node forces are a consequence of the tensions along the connected chain contours.…”

“…Our ansatz is that the force extension curve for polyisoprene molecules mimics this behavior; i.e., there are also three distinct extension regions for chain stretching. For two of these regions, MD and ab initio simulations 18,19 have provided quantitative predictions for the relevant chain forces, albeit for isolated chains. The simulations showed that isoprene units have 18 unique rotameric states and those with shorter end-to-end distances tend to be ∼1 kcal/mole higher in energy than the more extended conformations.…”

“…1.Chain extension beyond the nominal contour length, up to and including bond rupture, has been studied with ab initio simulations. 18,20 At failure, the material experiences the rupture of covalent bonds across the entire network, along a nearly straight line, normal to the strain axis. Simulations have shown that a large, purely enthalpic restoring force arises from bond length and angle distortions as an isoprene chain is extended beyond its nominal contour length.…”

“…Force extension curves for cis-polyisoprene and cis-polybutadiene chains, beyond their nominal contour length, were determined using quantum chemistry methods. 18 The force required to rupture an isoprene bond was found to be about 6.8 nN and the corresponding strain surprisingly large, greater than 40%. Ab initio and MD studies 19 have also established that entropic forces are inherent in local molecular kinks, comprised of a few isoprene units.…”

“…Depending on the number of isoprene units in a kink, the values of the entropic spring constants was found to be in the range of 0.06 to 0.6 nN/strain. Numerical simulations, using the chain force extension model found from ab initio simulations, 18 have been reported for threedimensional random polyisoprene networks undergoing moderate to high tensile strains. 20 In these studies, non-affine node motion was allowed, to equilibrate chain forces at a node.…”