Stress softening of multigraft copolymers

The hysteresis behaviour of multigraft (MG) copolymers, with a polyisoprene backbone and polystyrene (PS) side chains, was investigated by applying a modified softening model proposed by Elías-Zúñiga, which uses an approach of Ogden and Roxburgh. The model was combined with the non-affine tube model of rubber elasticity of Kaliske and Heinrich. Four parameters are obtained: chemical and physical cross-link moduli (G_c, G_e), the number of statistical segments between two successive entanglements (n_e/T_e) and a softening parameter (b). The model was proven to be valid by a comparison with other methods evaluating hysteresis behaviour. The characterization of the multigraft copolymers revealed a branch point and molecular architecture dependence of the softening parameter. b was low for tetrafunctional MG copolymers with cylindrical microdomains, and it was further reduced for a spherical morphology and for more complex molecular architectures. The magnitude of b also depends on the PS arm molecular weight for hexa- and tetrafunctional multigraft copolymers.