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1, with the maximum extensibility varying between 500 and 1000 per cent, depending on the extent of cross-linking. The behaviour is Hookean, with a linear relationship between stress and strain only at strains of the order of 1 per cent of so. At larger strains the force–extension relation is non-linear, and we will show that its form is determined essentially by changes in configurational entropy rather than internal energy. 1 200 400 600 800 extension (%) The force developed in uniaxial extension of a typical lightly cross-linked rubber High extension results in a greatly reduced entropy, so that retraction is a consequence of the necessity for entropy to be maximized.

3 above. 12 Plot of ln[r(r)] vs. r 2 at 298 K for polydimethyl siloxane chains of 40 bonds compared with Gaussian and Langevin treatments of the freely jointed chain. (Reproduced with permission from Stepto and Taylor, J. Chem. Soc. 18) above) and the Langevin function (Equation above) show clear differences. In particular, the molecular structurebased Monte-Carlo p(r) reflects clearly the limited extensibility of chains in the true network. 4 above but there is a new factor s, which is a function of º and quantitatively accounts for the Mooney–Rivlin softening.

E. for zero strain. A further requirement is that for small strains we should obtain Hooke’s law for simple tension and the equivalent equation for simple shear. e. there is no change in volume on deformation, which is true to a good approximation. For example, consider extension under a tensile force f in the x direction. This gives º1 ¼ º and º2 ¼ º3 ¼ ºÀ1=2 (2:4) where we have used the incompressibility assumption º1 º2 º3 ¼ 1. 1) we have   @U 1 ¼ 2C1 º À 2 f ¼ @º º (2:6) This familiar equation is more usually represented as a consequence of the molecular theories of a rubber network.