Rubber Elasticity

Abstract

Rubber elasticity is treated in terms of a general random network 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 polymer properties 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) rubber elasticity is a function only of the strain invarient I1 (not of I2); in particular: (c) the C2 term of the Mooney–Rivlin equation reflects effects of network connectivity (e.g., the functionality of cross links), not of I2; (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.