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Research Papers

# A Micromechanics Model for the Thermal Conductivity of Nanotube-Polymer Nanocomposites

[+] Author and Article Information
Gary D. Seidel

Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141

Dimitris C. Lagoudas1

Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141lagoudas@aero.tamu.edu

In Ref. 33, the rotation matrix corresponds to a 3-1-3 set of Euler angles with the 1-rotation specified to be $π∕2$, and is an equivalent change of basis, but different parametrization.

Upon closer inspection of the theory behind the MG-EMA (see, for example, Ref. 37), it is found that the MG-EMA and Mori–Tanaka methods are rooted in the same philosophy of using single inclusions embedded in an infinite matrix material subject to a perturbation in the thermal gradient to obtain effective thermal conductivities and that both methods account for random orientations of inclusions in exactly the same manner. For aspect ratios of 200 or greater, it can be shown that the geometrical factors in Ref. 37 are equal to the Eshelby tensor components of the Mori–Tanaka method for circular cylinders.

Nan et al.  use a $5nm$ radius and aspect ratio of 2000 corresponding to a $20μm$ long CNT.

1

Corresponding author.

J. Appl. Mech 75(4), 041025 (May 20, 2008) (9 pages) doi:10.1115/1.2871265 History: Received August 09, 2007; Revised November 07, 2007; Published May 20, 2008

## Abstract

A micromechanics approach for assessing the impact of an interfacial thermal resistance, also known as the Kapitza resistance, on the effective thermal conductivity of carbon nanotube-polymer nanocomposites is applied, which includes both the effects of the presence of the hollow region of the carbon nanotube (CNT) and the effects of the interactions amongst the various orientations of CNTs in a random distribution. The interfacial thermal resistance is a nanoscale effect introduced in the form of an interphase layer between the CNT and the polymer matrix in a nanoscale composite cylinder representative volume element to account for the thermal resistance in the radial direction along the length of the nanotube. The end effects of the interfacial thermal resistance are accounted for in a similar manner through the use of an interphase layer between the polymer and the CNT ends. Resulting micromechanics predictions for the effective thermal conductivity of polymer nanocomposites with randomly oriented CNTs, which incorporate input from molecular dynamics for the interfacial thermal resistance, demonstrate the importance of including the hollow region in addition to the interfacial thermal resistance, and compare well with experimental data.

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## Figures

Figure 1

Schematic representation of CNT-polymer nanocomposite consisting randomly oriented high aspect ratio composite cylinder assemblages

Figure 2

Initial comparison of micromechanics modeling approaches with the measured data from Choi (25), Bryning (12), and Guthy (13)

Figure 3

Schematic representation of how the Kapitza layer conductivity is used to introduce anisotropy into the nanotube conductivity

Figure 4

Comparison of two-step CCM/MT effective thermal conductivities that include the effects of the interface thermal resistance with EMA effective thermal conductivities and with measured data from Choi (25), Bryning (12), and Guthy (13) for values of the Kapitza conductivity parameter β obtained from MD studies (19)

Figure 5

Schematic representation of the difference between the rule of mixtures approach employed by Nan (16) to account for the Kaptiza resistance and the composite cylinder model approach applied herein

Figure 6

Parametric study on the influence of the Kapitza resistance using the two-step CCM/MT effective thermal conductivities in comparison with measured data from Choi (25), Bryning (12), and Guthy (13) for a range of values of the Kapitza conductivity parameter β obtained from MD studies (19-20)

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