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Journal of Nanomaterials
Volume 2015, Article ID 281308, 17 pages
Research Article

Investigation of Theoretical Models for the Elastic Stiffness of Nanoparticle-Modified Polymer Composites

1Norwegian Defence Research Establishment (FFI), P.O. Box 25, 2027 Kjeller, Norway
2Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo, Norway

Received 19 May 2015; Accepted 21 July 2015

Academic Editor: Abbas S. Milani

Copyright © 2015 T. Thorvaldsen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Mathematical models are investigated and suggested for the calculation of the elastic stiffness of polymer nanocomposites. Particular emphasis is placed on the effect on the elastic stiffness from agglomerates and the particle interphase properties. The multiphase Mori-Tanaka model and an interphase model are considered as two relevant models. These models only include and require the designation of a few system independent parameters with a clear physical meaning. Extensions of the models are also presented. The model calculations are compared to results from other models, as well as experimental data for different nanocomposites. For nanocomposites with spherical particles and with fiber-like particles, the suggested models are found to be the most flexible ones and are applicable to estimate the stiffness increase of nanocomposites for both low and high particle volume fractions. The suggested theoretical models can hence be considered as a general multiscale “model toolbox” for analysis of various nanocomposites.