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

Significance Statement

One of the common ways to optimize material characteristics and performance is to blend two materials with varying mechanical attributes in a bid to come up with a composite blend with the best characteristics of both components. The resulting morphology of the multi-phase component such as shape and size of the phase separated minority component, appears to be a critical aspect in controlling the mechanical attributes and counts on several factors. These factors include the proportion of the two constituents as well as their relative viscosity in the melt.

Many researchers have shown that a rubber separated structure, on a micron scale length, impacts performance by imparting energy-absorbing mechanisms, for example, shear yielding, and craze. The design and fabrication of new blend materials has been much facilitated by the development of modeling, which allows researchers to analyze an array of variables without necessarily manufacturing every material.

An analytical model without any unknown or fitting parameters, is considered a good option when compared to a finite element approach, as it allows the modeler to get fast solutions. This therefore, allows the materials designer to explore an array of parameters and so optimize the final material combination. In view of previous findings, researchers led by Professor Andrei Gusev at the ETH Zurich, Department of Materials investigated the accuracy of a number of analytical micromechanics models for analyzing viscoelastic attributes, which included loss tangent and storage modulus, starting with the generalized self-consistent Christensen and Lo model. They then compared the experimental measurements and predictions. Their research work is published in Composites Science and Technology.

The authors prepared blends of polystyrene (PS) and a polystyrene/polyisoprene/polystyrene (SIS) triblock rubber in blend fractions of 97/3, 90/10, and 80/20. The resulting blends were white. This was opposed to pure polystyrene that was transparent suggesting phase separated structures in the materials of the order of light wavelength, later confirmed by scanning electron microscopy (SEM).

The authors explored in their paper the use of a rational two-phase micromechanics analytical model to predict the viscoelastic attributes of the phase separated polystyrene/SIS blends containing micron-sized rubber particles. They observed that the model, comprising an all rubber spherical inclusion particle, could yield superior predictions of the loss tangent and storage modulus for rubber assemblages of up to 10% of the SIS fraction.

Above a 10% SIS fraction, the predictions of this simple model were less successful, with the model suggesting a higher plateau modulus and narrower loss tangent peak than was measured. At first sight, this was assumed to be due to the SIS rubber particles agglomerating at higher fractions; but numerical modeling indicated that this would not explain the measured results. However, it was observed that experimental results could be predicted more efficiently by the presence of a polystyrene core in some of the rubber particles, which was seen in the samples using the SEM.

The outcomes of the study indicated a great opportunity for using the rational micromechanics analytical models to analyze the capacity to investigate how the blend morphologies affect the measured properties, using unaltered bulk attributes of the constituent phases. This makes the models attractive to designers, and offers the opportunity to explore numerous combinations of phase characteristics and microstructures in a bid to search for novel combinations which could have unexpected and unusual viscoelastic performance.

The accuracy of the validated models is valuable in paving the way for looking for new materials with unique viscoelastic performance.

 Predicting visco-elastic properties of polystyrene/SIS composite blends-Advances in Engineering

This SEM image shows the complicated multiscale microstructure of the PS/SIS composite blends. The dark particles are the phase separated SIS rubber component dispersed in the PS matrix. The particles can be seen to range in size from 100 nm up to a few microns, and are seen to have a range of aspect ratios up to 3:1. It is also possible to make out a fine structure within the rubber zones, which is due to the arrangement of the SIS co-polymer molecules (as was studied with TEM). Finally, it is also possible to see some pure PS zones within the phase separated rubber regions.


A.P. Unwin, P.J. Hine, I.M. Ward, O.A. Guseva, T. Schweizer, M. Fujita, E. Tanaka and A.A. Gusev. Predicting the visco-elastic properties of polystyrene/SIS composite blends using simple analytical micromechanics models. Composites Science and Technology, volume 142 (2017), pages 302-310.

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