| Abstract: | A simple model for calculating the fracture process for a single extended-chain molecule such as polyethylene is considered. The model consists of a chain of N coupled Morse oscillators. There exists a critical overall extension ΔLc below which the fracture is energetically unfavorable but above which fracture is favored both energetically and kinetically. This elongation ΔLc scales as N1/2. For the critically stretched chain, the activation energy for rupture increases with N. Long chains must be stretched beyond this critical value to fail within experimentally meaningful times. Chains of all lengths subjected to the same force will fail with the same activation energy, provided this force is large enough to stretch each chain to ΔL > ΔLc. Observed activation energies are less than 1/3De, where De is the bond energy. |
