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

We present ab initio calculations of the internal C-C bond dissociation curve for single molecules of (cis 1,4) polyisoprene, polybutadiene, and polyethylene, all of comparable length. 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 well-defined though crude approximation, we find that rupture occurs at a tensile force of 6.8 nN for poly isoprene and 7.2 nN for polybutadiene. Their respective rupture strains are 45% and 42%. Our calculations show that the energy density vs. extension is not sensitive to the length of the molecule, i.e., it is essentially independent of the number of isoprene units contained. 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