Anisotropic elasticity of composite molecular networks formed from non‐gaussian chains

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Abstract
The theory of composite networks by Berry, Scanlan, and Watson was generalized so as to include the case in which the elasticity of the chains is described by non‐Gaussian statistics. For this purpose, existing theories of non‐Gaussian networks had to be critically reviewed and a new simple treatment is presented here. This new treatment yields substantially the same results as that obtained from the more complex theory of Wang and Guth. Results obtained from the simple three‐chain model for the network, as described by Treloar, were also shown to be in satisfactory agreement with both the new treatment and that of Wang and Guth. The generalized theory of composite networks predicts anisotropic elastic behavior; the tensile force at a given strain should be generally higher for elongation in the direction parallel to orientation than in the direction perpendicular to it. However, depending upon details pertaining to the preparation of the networks (ratio of first and second stage crosslinks and elongation at which the latter are introduced), the tensile force required for elongation in the direction perpendicular to orientation may be higher. It appears that the isotropic elastic behavior, predicted by previous theories of composite networks, is merely a consequence of the use of the Gaussian approximation.