Transition-state analysis for fracture nucleation in polymers: The Lennard-Jones chain

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Abstract
We present here a microscopic theory for fracture nucleation in finite chains, which may account for results found in simulations and in some experimental situations. We obtain the characteristic breaking time for an ensemble of one-dimensional Lennard-Jones chains, which is mainly a large prefactor times an Arrhenius rate. We show that the expression scales well and that the activation energy agrees with the analytical results. We show that the delay in the fragmentation is a consequence of the long-range time correlation in the relative motion of two adjacent particles. This correlation is responsible for the origin of a self-organized memory as well as the large elongation necessary for irreversible break to occur. We discuss the possibility of using this simple theory to understand the main characteristic of fragmentation in more complex and realistic systems.

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