Elastic anharmonic chain

Direct experimental verifications of the temperature dependences of the elastic moduli of perfect crystals of polyethylene in the chain-extended form, as represented in Table 4.3, present great difficulties, first because they relate to a perfect crystalline material and second because they are based on the anharmonic atomic interactions in such perfect material. Polymeric solids, even those that are highly crystalline, incorporate a variety of crystal imperfections that permit thermally assisted relaxations under stress. These dramatically attenuate the elastic properties that, at all but the lowest cryogenic temperatures, mask the temperature dependence of elastic interactions of the perfect crystal, particularly the stiffest intra-molecular interactions along the C—C backbone. In the vast majority of cases the elastic moduli of polymers reflect the soft intermolecular interactions, and the temperature dependence of these overwhelmingly dominates the intramolecular variety at all but the lowest temperatures. 

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