The Internal Energy Contribution to Rubber Elasticity

The simple treatment of rubber elasticity given above makes two assumptions, which require further consideration. First, it has been assumed that the internal energy contribution is negligible, which implies that different molecular conformations of the chains have identical internal energies. Secondly, the thermodynamic formulae that have been derived are, strictly, only applicable to measurements at constant volume, whereas most experimental results are obtained at a known pressure. These two assumptions are interrelated in the sense that the experimental work of Gee (see Section 4.2.1) based on the approximation 

More rigorous consideration suggests that this is not correct and that there is an anisotropic compressibility in the strained state. Gee s experimental result that the internal energy contribution is negligible, based on measurements of the change in stress with temperature at constant length, is therefore capable of another interpretation, which leads to the conclusion that the internal energy contribution may not be zero. 

The internal energy component of the tensile force/is given by 

The value fe can be expressed in terms of the tensile force-temperature relationship by the equation 

In addressing this problem, Flory, Ciferri and Hoeve [34] adopted a procedure based on the theory of the Gaussian network. They showed that if the rubber network obeys Gaussian statistics, the expression for measurement of simple extension at constant pressure is 

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