Rubber Elasticity

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Abstract
Rubberelasticity is treated in terms of a general randomnetwork bead‐spring model which expresses chain connectivity through Dirac delta functions. In contrast to the classical theory, the present starting point is the segmental distribution function, from which, besides elasticity, most polymerproperties are deducible, e.g., relaxation spectra, intrinsic viscosities, etc. The method is that developed by Fixman and by Imai. The salient results are: (a) macroscopic observables correspond to mean‐square vector quantities; (b) rubberelasticity is a function only of the strain invarient I 1 (not of I 2 ); in particular: (c) the C 2 term of the Mooney–Rivlin equation reflects effects of network connectivity (e.g., the functionality of cross links), not of I 2 ; (d) The new one‐parameter stress–strain equation here derived fits classical data on one‐ and two‐dimensional strain. The quantity corresponding to the “front factor” in the classical equation is ∼ 1.8, in reasonable agreement with measurements by Ferry et al.

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