Quantum mechanical calculation of the longitudinal elastic modulus and of deviations from Hooke’s law in polyethylene

Abstract

The microscopic longitudinal elastic modulus, deviations from Hooke’s law, the maximum of the retractive force and tensile strength are calculated for single infinite polyethylene chains using a first principle crystal orbital method and including electron correlation effects by perturbation theory. The best theoretical value of the modulus is 334 GPa at the single-particle level and 276 GPa including correlation. Significant deviations from Hooke’s law start at small deformations and amount to 30%–40% at ε=0.10–0.15. The maximum of the retractive force is f=0.814 mdyn at ε=0.38 and f=0.631 mdyn at ε=0.31, using restricted or unrestricted Hartree–Fock states as zeroth-order wave functions for perturbation theory, respectively. The corresponding maxima of the microscopic tensile strength are at 44.6 and 34.2 GPa, respectively.