Energy dissipation resulting from chain extension

The Mullins effect, which can be considered as a hysteretic mechanism related to energy dissipated by the material during deformation, corresponds to a decrease in the number of elastically effective network chains. It results from chains that reach their limit of extensibility by strain amplification effects caused by the inclusion of undeformable filler particles [24,25]. Stress-softening in filled rubbers has been associated with the rupture properties and a quantitative relationship between total hysteresis (area between the first extension and the first release curves in the first extension cycle) and the enei-gy required for rupture has been derived [26,27]. 

In order to rationalize this result for PE, a simple calculation of the energy required for scission of main-chain bonds (E c c) the frictional dissipation between chains due to mechanical action was performed. The latter was calculated from the activation energy for viscosity of the monomer repeat unit, E, determined from a low-molar-mass analogue of polyethylene. This was then used to determine the number of repeat units, n, necessary to exceed the C-C bond energy of 349 kJ/mol. From the value of 4.22 kJ/mol for E, an estimate for n of 83 was made, which was considered a good approximation to the experimental result of 100 (Sohma, 1989b). However, such a simple approach is not amenable to extension to systems of structural complexity such as chain scission during the mastication of rubber. 

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