Free-space reconstruction of the electrical properties of carbon nanotube based composites in the Q-band range Ahmed M. Hassan 1 , Jan Obrzut 2 , Edward J. Garboczi 3 . 1 Engineering Laboratory, Materials and Structural Systems Division 2 Material Measurement Laboratory, Materials Science and Engineering Division National Institute of Standards and Technology, Gaithersburg, MD 20899 3 Material Measurement Laboratory, Applied Chemicals and Materials Division National Institute of Standards and Technology, Boulder, CO 80305 Abstract — A free-space transmission-reflection measurement method for the non-destructive electrical characterization of carbon nanotube based composites was developed. Specifically, this versatile method measures the dielectric properties of the sample in the Q-band, corresponding to a frequency range of 30 GHz to 50 GHz, and can be used with specimens that are either thinner or thicker than the radiation penetration depth. This method also involves an error correction model in order to accurately reconstruct the constitutive dielectric properties of the composites from the measured scattering parameters. In order to perform the error-correction only two reference scattering parameters measurements are required: one from a metal plate of known reflection coefficient and the other from air with no specimen. The simplicity of our error-correction model makes the method attractive for research, development, and for quality control in the manufacturing environment. Index Terms — Free space measurement; microwave error- correction model; nanocarbon composites; non-destructive testing I. INTRODUCTION Carbon nanotubes (CNTs) composites have been incorporated in a wide range of applications, especially in the aerospace and automotive industries [1-3]. The mechanical, thermal, and electrical properties of these composites are predominantly determined by the properties of the CNTs and their dispersion in the embedding polymer matrix [2-3]. A technique to evaluate the properties of these composites is based on quantifying the free-space microwave scattering parameters. However, free-space microwave characterization is plagued by the mismatch between the two antennas and free space, the multiple reflections between the antennas and the material under test (MUT), and the diffraction of the waves in free space. Therefore, free space systems require elaborate procedures to extract the electrical properties of the MUT. These procedures can involve the movement of the antennas, the movement of the MUT, and the measurement of the scattering parameters from multiple references [4-5]. One of the standard calibration techniques is the Thru- Reflect-Line (TRL) calibration technique [4-5]. However, the main challenge in this calibration is the need to move the antennas disturbing the alignment/coupling between them. The Line-Network-Network (LNN) procedure is another calibration technique that does not require a reflect standard [5]. Instead, this methodology corrects the measurement using four measurements: one thru and three MUT locations separated by an equal distance Δx [5]. However, it is difficult to implement the multiple shifting of the MUT in the quality control of high-thru-put unrolling thin film materials in a manufacturing line. In this paper, we present a free-space Q-band experimental system for non-destructive non-contact characterization of CNT composites. For this system, we have devised a simple and accurate error correction model that mitigates the limitations of the previous calibration techniques. Only two reference scattering parameters measurements are required: one from a metal plate of known reflection coefficient and the other from air with no specimen. The use of microwaves in the Q-band, defined to be between 30 GHz and 50 GHz, is a broadband technique that is capable of providing both the real and imaginary parts of the complex dielectric permittivity constant, which can be related to the dispersion of the CNTs in the polymer matrix. The technique is relatively simple and, therefore, attractive for non-destructive quality control in the manufacturing environment. II. EXPERIMENTAL SETUP Our Q-band non-contact microwave measurement system utilizes two horn antennas connected to a vector network analyzer. The distance between the antennas was 225 mm and the beam radius at the MUT plane in the middle between the antennas was roughly 52.5 mm. A holder, with an aperture in its center larger than the beam width, was utilized and U.S. Government work not protected by U.S. copyright