Effective Medium Calculations of the Electromagnetic Behavior of Single Walled Carbon Nanotube Composites
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Effective Medium Calculations of the Electromagnetic Behavior of Single Walled Carbon Nanotube Composites John W. Schultz, Rick L. Moore Georgia Tech Research Institute Atlanta, GA 30332-0824, U.S.A. ABSTRACT Dielectric properties of single walled carbon nanotube assemblies were calculated with an effective medium approximation at frequencies from 200 MHz to 200 GHz. The model treats the carbon nanotubes as layered cylinders, each with a core, a graphene layer and an outer layer, to investigate the dielectric properties of coated and filled nanotubes. The graphene and metal layer properties were modeled with a Drude approximation based on literature data. A generalized Bruggeman model was then used to determine the macroscopic behavior of the modified carbon nanotubes in a composite structure as a function of volume fraction, frequency, and aspect ratio. The depolarization factors in this model were scaled by the normalized effective permittivity to better account for percolation behavior. The model showed a wide variety of frequency dependent dielectric properties. Uncoated tubes were calculated to form highly conductive materials at volume fractions of just a few percent and metal-coated tubes enhanced the conductivity by an order of magnitude. Calculations of nanotubes with insulating coatings showed that high dielectric constants with moderate to low dielectric loss were possible. INTRODUCTION With their unique electrical and mechanical properties, single wall carbon nanotubes (SWNT) are under intense study for a wide variety of potential applications. The high aspect ratio and unique conductive behavior of carbon nanotubes provide opportunities for new composite materials with useful RF and microwave properties. Coating or filling carbon nanotubes with insulating or metallic materials can provide further enhancements to their electromagnetic properties. Some applications in EMI and telecommunications require lightweight conductive materials while other applications call for low loss substrate materials with high dielectric constants. By dictating the appropriate SWNT nano-structure, the materials designer can choose a conducting or semiconducting phase while using the same lightweight, strong, thermally stable chemistry. Thus, SWNT composites may be used to achieve controlled electromagnetic permittivity and conductivity in composite materials. However, there is limited understanding of how SWNTs can be effectively and practically manipulated to obtain the enhanced composite properties. Towards this end, an electromagnetic dispersion model was developed that predicts macroscopic permittivity for carbon nanotubes in a dielectric matrix. This SWNT model includes the capability to model ‘decorated nanotubes’, which include dielectric and metallic substances coating the exterior and/or filling the interior of the SWNT. NANOTUBE MODEL DESCRIPTION The composite SWNT model for frequency dispersive permittivity consists of four physical scales, and thus represents a ‘multi-scale effective medium’ model. At eac
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