Thermal Conductivity of Composites with Carbon Nanotubes: Theory and Experiment
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Thermal Conductivity of Composites with Carbon Nanotubes: Theory and Experiment J. Ordonez-Miranda1, C. Vales-Pinzon1, J. J. Alvarado-Gil1 1 Department of Applied Physics, Cinvestav, Carretera Antigua a Progreso km. 6, A.P. 73 Cordemex, Merida, Yucatan, 97310, Mexico. E-mail: [email protected] ABSTRACT In this work, the thermal conductivity of composites made up of carbon nanotubes embedded in a polyester resin is investigated by comparing experimental data with theoretical predictions. The composite samples were prepared with a random and aligned distribution of carbon nanotubes. Its thermal conductivity is then measured by using the photothermal radiometry technique. The obtained experimental data is accurately described by the proposed theoretical model, which takes into account the size effects of the nanotubes. It is expected that the obtained results can provide useful insights on the thermal design of composites based on carbon nanotubes. Keywords: Composite, Nanostructure, Thermal conductivity. INTRODUCTION Over the past few decades, significant research efforts have been devoted to the study of the thermal properties of particulate composites, due to their many technological applications ranging from mechanical structures to electronics[1, 2]. Carbon materials, as carbon nanotubes, nanoplatelets, graphene oxide nanoparticles and graphene flakes; are among the most promising filler particles to maximize the enhancement of the usually low thermal conductivity of the matrix [1]. For instance, enhancements above 100% have been reported for a small concentration of 1% of carbon nanotubes or graphene loading,[1] which have a good coupling to the matrix materials and a geometry that favors the heat conduction through them. Despite their importance, the thermal performance of these smart materials is not well-understood to date, especially at high volume fractions of micro/nano-sized particles. In this work, the thermal conductivity of various composites with carbon nanotubes embedded in a polyester resin is measured by using the photothermal radiometry technique[3]. The composite samples were prepared with a random and aligned distribution of carbon nanotubes (CNT), which have a diameter ranging from 50nm to 80nm. The predictions of the proposed approach are in good agreement not only with the experimental data recorded in our laboratory, but also with the one reported in the literature [1]. It is expected that the obtained results can provide useful insights on the thermal design of composites based on carbon nanotubes. THEORY A suitable model to describe the thermal conductivity of composites made up with low concentrations of spheroidal particles embedded in a matrix has been proposed by Nan et al[4]. For cylindrical particles, this model reduces to
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k||
(1a) 1 K pm 1 f Km krandom 1 Bf (1b) 1 2 Af Km where K m and K p are the bulk thermal conductivities of the matrix and particles, respectively; K pm
K p Km , f is the volume fractions of the particles, and
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1 K pm 1 , 3 K pm 1
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