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

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Abstract

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.

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Acknowledgements

The author would like to thank Prof. F. J. Balta Calleja from the Instituto de Estructura de la Materia, CSIC, Madrid, Spain, for his stimulating discussions on the disclosed topic, as well as Prof. D. Rueda from the same Institute for reading the manuscript and for his valuable suggestions. Thanks are also due to Mag. Chem. M. Boyanova for her technical help during preparation of manuscript. The author acknowledges also the financial support of the Foundation for Reasearch, Science and Technology of New Zealand, making possible his stay at the Department of Mechanical Engineering and the Centre for Advanced Composite Materials of The University of Auckland, Auckland, New Zealand, where this study was finalized. The hospitality of The University of Auckland is also acknowledged.

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  1. Centre for Advanced Composite Materials and Department of Mechanical Engineering, The University of Auckland, 92019, Auckland, New Zealand

    S. Fakirov

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  1. S. Fakirov
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Correspondence to S. Fakirov.

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On leave from Laboratory on Polymers, University of Sofia, 1126 Sofia, Bulgaria.

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Fakirov, S. On the application of the “rule of mixture” to microhardness of complex polymer systems containing a soft component and/or phase. J Mater Sci 42, 1131–1148 (2007). https://doi.org/10.1007/s10853-006-1468-7

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