DERIVATION OF FLORY'S THERMODYNAMIC RELATIONS FROM A PHENOMENOLOGICAL THEORY OF RUBBER ELASTICITY

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Abstract
It is shown that the thermodynamic formulae relating to simple elongation of a highly elastic material, first obtained by Flory (1) by appeal to the statistical mechanics of a Gaussian network, can be derived, without approximation, from a refined form of a phenomenological model of rubberlike thermoelasticity proposed by Chadwick (2). The modification consists of including in the Helmholtz free energy a second distortional response function which implies an energetic contribution to the retractive force f in a stretched strip. Flory's formulae are recovered when neo-Hookean forms of the two distortional response functions are chosen, and corresponding results for non-Gaussian functions are readily drawn from the general analysis given here. As an example, the connection between the isometric temperature derivatives of f at constant pressure and at constant volume found by Flory (1) is generalized to the case in which the first distortional response function is analogous to Mooney's strain-energy function.

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