The application of blending law on linear viscoelastic properties of linear–star and star–star polymer blends

A quadratic binary blending law of the terminal relaxation spectra is used to predict the viscoelastic properties of star–star and linear–star polymer blends. The results are compared with the experimental data reported by Struglinski et al. Star polymers with long arms are assumed to dominate the relaxation behavior of the star–star polymer blends. In the linear–star polymer blends, star polymers are assumed to dominate the relaxation behavior. The ‘iso-relaxation time’ approach is proposed to represent the linear chain by an equivalent star chain for the linear–star polymer blends. The predicted viscoelastic properties agrees with the experimental observation very well. Also, the well known relation, Jeob∝1/v2 (v2 is the volume fraction of long-arm star chains), can be deduced from the binary blending law for the concentrated long-arm star chains entangled with much shorter chains. Furthermore, it also predicts that it would systematically depart from the relation, Jeob∝1/v2, when the molecular weight of shorter chain becomes closer to the molecular weight of long-arm chain. In the limit, M1/M2=1, the relation is switched to Jeob∝v2.