Authors used modelling of nanocomposites to find the thermal conductivity and compared it with the measured values. Some explanation is needed about modelling of nanocomposite.
Check the recent publications of Prof. Grmela, here is the link to his Msc student Thesis on this subject:
http://publications.polymtl.ca/921/
And his recent publications on modeling of thermal conductivity in particulate nanocomposites:
http://pubs.rsc.org/en/content/articlehtml/2014/ra/c4ra12368a
http://scitation.aip.org/content/aip/journal/apl/104/23/10.1063/1.4882279
Many empirical and semi-empirical equations based on simple rule of mixtures to complicated effective medium approaches can be used to 'model' experimental data.. but most of these so-called models are only applicable to below percolation limit.. above percolation, most of these models fail.
There are many review articles.
Please find attached two old articles of mine on dielectric mixture rules. The same equations can be used for permiitvity, ohmic conductivity and heat conductivity. Of course, these are only continuum models which do not take into account directly surface effects and agglomeration.
Article Comparison of electrical mixture rules for composites
Article Numerical analysis of complex dielectric mixture formulae
You could use the model of Nan and al. which take into account the size, the orientation of particles and also the thermal resistance between particle and matrix. This thermal resistance is a very important parameter. However, most of models work effectively without interaction between particles.
Check the recent publications of Prof. Grmela, here is the link to his Msc student Thesis on this subject:
http://publications.polymtl.ca/921/
And his recent publications on modeling of thermal conductivity in particulate nanocomposites:
http://pubs.rsc.org/en/content/articlehtml/2014/ra/c4ra12368a
http://scitation.aip.org/content/aip/journal/apl/104/23/10.1063/1.4882279
It depends on what nanocomposite you wish to model. The existing model e.g., Nan's model can predict the thermal conductivity of two-phase nanocomposite quite well, but it fails to predict the thermal conductivity of multiphase composites. Our group developed a mesoscopic model on multiphase composites and we achieved good agreement between the measured thermal conductivity and the predicted values. You can find out the details in the attached paper:
Feng Gong, Khoa Bui, Dimitrios V. Papavassiliou, Hai M. Duong, Thermal Transport Phenomena and Limitations in Heterogeneous Polymer Composites Containing Carbon Nanotubes and Inorganic Nanoparticles, Carbon 78 (2014) 305-316
202. E. Litovsky, V. Issoupov, S. Horodetsky, J. Kleiman, Express Methods for Determination of Apparent and True Thermophysical Properties of Materials within a Temperature Range of – 150 °C ... 1800 °C, Proceedings of the 31st International Thermal Conductivity Conference and the 19th International Thermal Expansion Symposium, May 2013, DEStech Pupbl.
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