The effects on rubber elasticity of the addition and scission of cross-links under strain

Abstract Edwards’s equilibrium theory of rubber elasticity is used to study the effect on the network elasticity of the consecutive addition and removal of cross-links under different strains. The treatment is compared with those of Flory, Scanlan and others based on classical rubber elasticity theory. For a composite network made by first introducing (v1 + v01) links in an isotropic state, then adding v2 at deformation λ, and finally removing v01 of the original group, the strain-dependent free energy at some subsequent deformation ξ (relative to the initial unstrained state) is shown under certain conditions to be F(ξ) = ½kT[(v1 + фv2) Ʃi ξ2i + (v2 - фv2) Ʃi (ξi/λi)2], where ф = ф{v1, v01, v2). A similar equation has been obtained by Flory. When v01 = 0, ф = 0, confirming the familar ‘two -network’ theory for this case. The ‘memory’ effects which occur when v01 is non-zero are discussed.