On the application of the “rule of mixture” to microhardness of complex polymer systems containing a soft component and/or phase

The main goal of this work is to find a reasonable explanation for the frequently reported drastic deviations from the “rule of mixture” applied for calculation of the overall microhardness, H, of complex polymer systems comprising a soft, (with a glass transition, T _g, or melting, T _m, temperatures below room temperature) component and/or phase. According to the common practice, the contribution to H of the soft component and/or phase, H ^s, is considered as H ^s = 0, which results in extremely large differences between the measured and calculated H values for systems comprising more than 20–25 wt% soft component and/or phase. For such systems a different deformation mechanism during indentation process is postulated, namely “floating” of the solid particles in the soft component and/or phase, in addition to their plastic deformation. The contribution of the “floating effect” to the overall H is accounted for by the empirically derived relationship H = 1.97 T _g−571. Using the reported data on H and T _g for homopolymers, blockcopolymers and blends, the H values are recalculated and a good agreement with the experimentally measured values is found. A modified additivity law is suggested, which contains a term accounting for the contribution of the soft component and/or phase to the overall microhardness via the relationship between H and T _g; its application results in much smaller differences between the measured and calculated H values.