Predicting the visco-elastic properties of polystyrene/SIS composite blends using simple analytical micromechanics models

This paper is concerned with the prediction of the viscoelastic properties of rubber filled polymer blends. The question asked was as follows. Can the temperature dependent viscoelastic properties of phase separated polymer blends be adequately predicted using only a rational two phase micromechanics based analytical model with no empirical fitting parameters? In particular using only a knowledge of the individual bulk phase properties and the blend microstructure, but without any further detailed polymer physics knowledge such as the presence of an interphase region or any additional nanoscale structures within the separated rubber phase with the properties different from those of the two bulk phases? Blends of a polystyrene matrix and phase separated rubber inclusions (a polystyrene-polyisoprene-polystyrene triblock polymer (SIS)) were manufactured in a range of blend fractions (up to 20 vol % of the triblock co-polymer). Experimental measurements, for the storage modulus G′ and the loss tangent tanδ, of both the individual phases and the blends, were made using dynamic mechanical tests over a range of temperatures from −50 to +70 °C. Numerical predictions, of the same parameters, were first obtained using the generalised self-consistent Christensen and Lo model which uses a simple representative volume element (RVE) of an isolated sphere of the minority rubber component in a surrounding sheath of polystyrene matrix embedded in a homogeneous effective medium. The agreement between the Christensen and Lo model and the experimental measurements, for G′ and tanδ, was found to be excellent for rubber contents up to 10%. For a 20% rubber content, an improved prediction was obtained by altering the RVE to include the observed effect of having a polystyrene central core in a number of the dispersed rubber zones at this rubber fraction, using the Herve and Zaoui generalization of the Christensen and Lo model. Although conjoined (and therefore non-spherical) zones became more prevalent at the highest rubber content, use of the Tandon and Weng model showed that this shape anisotropy would not be expected to affect the viscoelastic properties.