Intermolecular Obstruction in Rubber Elasticity Theory

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Abstract
The leading term of the equation of state of rubber relating elongation to stress may be obtained by treating the polymer chains in the rubber as independent and distributed according to the laws of Brownian motion. A great deal of theoretical work has been done on corrections to this simple picture, particularly in consideration of the finite extensibility of the chains and the network character of their connections. In this paper we attempt to take into account the fact that in the rubber there is a high density of chains which causes mutual obstruction among the chain Brownian motions. In the unstrained, symmetric state the obstruction is isotropic; however, when the rubber is stretched, the degree of obstruction will be different in different directions. An equation is obtained for the dependence of free energy on this anisotropic effect. The theoretically derived stress—strain equation is compared with experimental results.

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