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

• Published in: Journal of materials science Vol. 42; no. 4; pp. 1131 - 1148
• Main Author: FAKIROV, S
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.02.2007; Springer Nature B.V
• Subjects: Accounting; Applied sciences; Blends; Block copolymers; Deformation effects; Deformation mechanisms; Deviation; Exact sciences and technology; Extreme values; Indentation; Materials science; Mathematical analysis; Mechanical properties; Melting; Microhardness; Organic polymers; Physicochemistry of polymers; Plastic deformation; Polymers; Properties and characterization; Experimental test; Polymer blends; Property composition relationship; Theoretical study; Mechanical properties; Mixture theory; Semicrystalline polymer; Microhardness; Modeling; Heterogeneous mixture; Amorphous polymer; Homogeneous mixtures; Block copolymer
• ISSN: 0022-2461; 1573-4803
• DOI: 10.1007/s10853-006-1468-7

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, Tg, or melting, Tm, temperatures below room temperature) component and/or phase. According to the common practice, the contribution to H of the soft component and/or phase, Hs, is considered as Hs = 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 Tg−571. Using the reported data on H and Tg 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 Tg; its application results in much smaller differences between the measured and calculated H values.