{'fraction_non_alphanumeric': 0.03348115299334811, 'fraction_numerical': 0.014356984478935698, 'mean_word_length': 4.77312, 'pattern_counts': {'":': 0, '<': 5, '<?xml version=': 0, '>': 2, 'https://': 0, 'lorem ipsum': 0, 'www.': 1, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 3, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Characterization of microwave absorption in carbon nanotubes using resonance aperture transmission method

A new method to characterize microwave electromagnetic absorption of a bulk carbon nanotube material is proposed and experimentally evaluated in this paper. The method is based on the measurement of microwave transmission through a capacitive-resonator aperture in a conductive screen loaded with a CNT sample under test. This method allows to measure microwave permittivity and absorption of thin samples, several atomic layers to few micrometers thick, with linear dimensions much smaller than the wavelength of radiation in free space. This minimal sample requirement restricts the application of conventional microwave characterization methods such as free-space or waveguide permittivity characterization. It is demonstrated that the resonance E-field enhancement inside the CRA leads to strong EM interaction of the microwave E-field with the CNT sample under test thus enabling high sensitivity and dynamic range of the measurement procedure. Another advantage of the proposed technique over conventional non-resonance characterization methods is that in the resonance transmission band, the CRA operation is reflection-less which leads to a relatively simple qualitative algebraic de-embedding procedure of the material parameters based on the principle of energy conservation. The experimental microwave absorption data of the multiwall CNT samples are presented in the S frequency band (2-4GHz), demonstrating microwave absorption properties of the multiwall CNT ribbons.


I. INTRODUCTION
Development of advanced composite and nanomaterials requires a range of measurement techniques to characterize the electrical, electronic, mechanical and thermal properties of the material. One important class of materials is represented by thin films and selfstanding nano-materials with sample thickness varying from mono-atomic layers to few micrometers with relatively large, macroscopic area dimensions. An example of such a material is CNT ribbons which exhibit very unique mechanical, electric and electronic properties 1 .
CNTs have a wide range of unique applications in nano-and microelectronics, radiation detection, chemical and bio-sensing, composite materials, etc 2,3 . In this letter, a new method to characterize EM properties of a bulk CNT material in the microwave range is proposed. The method is based on the reflection-less resonance transmission of microwave radiation through the CRAs with and without a CNT sample. From the measurement data, real and imaginary parts of the CNT complex permittivity can be extracted using differential material parameters de-embedding 4,5 . Permittivity of the pure CNT can be further employed to design EM absorbers and EM interference shielding based on the composite materials formed by the CNT material inclusions inside a host medium, e.g. epoxy or resins 6,7 . These composite materials can be promising for advanced aerospace applications 3,6-8 and future wireless communications, especially, for the design of the intelligent EM-controlled metasurfaces 8 , due to mechanical and chemical stability and very low weight density of the CNTs.
The existing EM material characterization methods [10][11][12][13][14] can be divided into several groups including free-space, waveguide, resonating cavity, 3D resonator, transmission line, open coaxial, evanescent probe and a parallel-plate capacitor method. The discussion of the application range, advantages and drawbacks of these methods can be found elsewhere [10][11][12][13][14] . As a rule, most of the abovementioned methods require sufficiently large CNT samples covering the area of at least 0.25λx0.5λ, where λ is a wavelength of radiation in free space. Also, the measurement of thin samples (thickness of few micrometers or less) represents significant challenge for free-space or waveguide methods in microwave range (λ is in the range of 0.1cm-30cm) due to low sensitivity and numerical errors in permittivity de-embedding algorithm in the thin sample permittivity reconstruction scenario 14 .
Resonance CRA transmission method discussed here offers a number of distinctive advantages: high sensitivity and dynamic range of the method is due to EM field enhancement inside the CRA leading to strong EM interaction between the testing microwave and even very thin samples. Electrically small size of the CRA allows to use "minimal" thin CNT samples with characteristic 2D dimensions significantly smaller than the radiation wavelength.

II. GEOMETRY OF THE MEASUREMENT SETUP
The measurement setup geometry is shown in Fig.  1. The setup consists of a pair of dipole antennas and a CRA in the conductive screen loaded with a thin CNT material sample. The transmit (TX) and receive (RX) microwave signals are generated and received by the vector network analyzer (VNA). This material characterization method is based on differential measurements, when the transmission data through the loaded and unloaded aperture are required along with the measurement of the free-space transmission link between the RX and TX antennas, in order to de-embed antenna characteristics and freespace propagation link properties from the overall measurement system transmission.

III. ELECTROMAGNETIC MODEL OF THE CRA MICROWAVE TRANSMISSION
Microwave transmission through the CRA aperture can be described 10,12,15 by the system of equations (1)-(2): where -is a TX microwave E-field through the unloaded (in the air) CRA, ( ) is a TX E-field through the CRA loaded with a CNT sample, is a radius-vector of observation point in the z>0 half-space, is a radius-vector of observation point across the CRA aperture, in the plane z=0, Fig.1(b). ̂i s a secondrank (3x3) tensor operator describing microwave TX properties of the CRA.
is the incident EM field generated by a TX antenna with the center located at z=-z d . To derive the transmission equations in terms of the measurable RX power, the TX antenna is characterized by its radiation gain ( , ), where is a radius-vector of the TX antenna center. The dipole RX antenna can be characterized by its effective vector length, , relating RX voltage across the RX antenna terminal and the E-field acting on the antenna. Assuming that the input impedances of the RX and TX antennas are the same (50 ohm), it is straightforward to derive the transmission equation in terms of the TX and RX power and EM transmission tensor ̂ of the CRA, Differential measurement procedure is based on the normalization of the transmitted power through the CNT-loaded CRA, , , by the transmitted power through the unloaded CRA, , for the same input power P TX , , where T(ε CNT ) and T(ε 0 ) are the EM transfer functions of the loaded and unloaded CRA for the vertically ypolarized E-field. Differential measurement method allows to eliminate RX and TX antenna characteristics from the CNT permittivity de-embedding procedure which employs normalized transmitted power function (4). The microwave transmission function of the CRA appeared in (1), (2) is an integral-differential tensor operator, whose form can be established using the EM field potential equations. For the monochromatic, (− ), time dependence the EM field transmitted through the material-loaded aperture can be written in the form 16,17 In (5) μ is a magnetic permeability of free space, index n defines the material, n = CNT or n = free space or air, = √ ⁄ , c is a speed of light in vacuum, and A and F are the EM vector-potentials 17 , In (6) the integration is carried out over the volume occupied by the CNT material, Fig.1(b), and involves the electric polarization current density where = ′ + ′′ is a complex-valued relative permittivity of CNT, ( ) is an E-field inside the CNT volume. In (7), the area integration is carried out inside the CRA area -L a /2<x< L a /2, -H a /2<y< H a /2, free from the CNT or conductor, at the plane z= t c , and involves magnetic current density Finally, the scalar Green's function in (6), (7) is given by a relation The explicit form of the transfer function T in (1), (2) can be established by using permittivity in (5) -(10) and calculating the E-field ( )inside the CRA from the boundary conditions and equations (6), (7). It should also be noted that the real ′ and imaginary ″ parts of the CNT permittivity appear in the transmission equation (4) in a coupled form, thus permittivity de-embedding requires the inverse problem solution of (1)-(10) based on the full-wave numerical computation. Below, an analytical solution based on the energy conservation principle is proposed which can also serve as an initial approximation in the full-wave numerical solution to (1)-(10).

IV. ANALYTICAL SOLUTION FOR THE CNT PERMITTIVITY DE-EMBEDDING
To obtain an approximate analytical solution to the permittivity of the CNT sample under test, unloaded and loaded CRAs can be represented as equivalent circuits 18  In these circuits, source V in models TX antenna, R FS stands for the free-space characteristic impedance, R rad is CRA radiation resistance, L IND is a CRA equivalent inductance and C 0 and C L is unloaded and loaded equivalent capacitance. R loss models the microwave loss due to conductivity (imaginary part of the permittivity) of the CNT sample, while loaded capacitance C L is a real-valued function of CRA geometry and real part of the CNT permittivity. Since the CNT material studied in this work is a lossy nonmagnetic or weakly-magnetic dielectric, equivalent inductance of the loaded and unloaded aperture is approximately the same. The exact form of the equivalent circuit lump parameters can be established using surface currents and charge density 16,17 across the CRA, however this is not required for the analytical model described below. Using resonance circuit models in Fig.2, it can be seen that CRA loading with a CNT sample results in the microwave transmission resonance frequency shift, where 0 and are the resonance frequencies of the unloaded and loaded CRA respectively. Due to the high-quality resonance of the CRAs used in this work (measured Q-factor typically exceeds 10), resonance frequency pulling 19 , , = 0 √1 − 1 4 2 ⁄ due to microwave loss caused by the CNT absorption is small (less than 5%), and therefore the real part of CNT permittivity plays a dominant role in the CRA transmission resonance frequency change. To derive analytical expressions for the resonance frequency shift as a function of the CNT permittivity real part, CNTloaded and unloaded capacitance of a CRA can be evaluated using a quasi-static approximation (please refer to Appendix A for details) where the constant 0 = ( (1 + ⁄ )) ⁄ depends on the CRA capacitive resonator gap to width of the plate's ratio. Formula (12)

A. Sample preparation
CNTs were made in an axial tubular high temperature furnace at 1290 °C known as a floating catalyst chemical vapor deposition (FC-CVD) in background hydrogen (1350 sccm). The precursors used for the CNT production, are ferrocene for the catalyst's nanoparticles, thiophene to supply sulfur as a growth limiter of the CNT diameter and methane as a carbon precursor. Both ferrocene and thiophene are introduced via bubblers with hydrogen flow at 130 sccm and 90 sccm, respectively. The bubbler with thiophene was kept at 25°C. The decomposition of the ferrocene precursor leads to nucleation and growth of iron nanoparticles with incorporation of sulfur, which has been shown to play an important role in these mechanisms 20,21 . Methane flow was set at 160 sccm. During the synthesis process, an aerogel forms at the exit of the chamber and this is collected and pulled out from the furnace by the help of a rod. This process allows the formation of macroscopic assemblies of multiwall CNTs that can be adapted in different morphologies. In this case, CNTs have been mechanically compacted and cut in length to produce CNT ribbons of a few centimeters and a thickness with the range of 1-4 μm.
The CRAs have been fabricated using thin aluminum foil of approximately 10 µm thickness. The CNT samples were positioned on the Rohacell 5mmthick substrate IG51 (permittivity 1.071, tan δ =0.0031) and affixed with Scotch tape (permittivity 1.9, tan δ =0.006). Four CRAs were fabricated with the dimensions summarized in Table I. In all CRAs w s =w a , <g s > is an average value of gap g s .

B. Microwave measurement data and analysis
Two sets of dipole antennas were used to provide optimal matching in the bands 1.7-2.5GHz and 2.4-3.2GHz. The return loss |S 11 | characteristics of the antennas in measurement setup are provided in Appendix C. This choice of the frequency range is chosen due to practical interest in the WiFi band CNT characteristics and ease of the measurements at lower frequency range. However, the design can be straightforwardly scaled for higher frequency range.  Table II summarizes the measured parameters: resonance frequency, Q-factors, RX power and de-embedded CNT permittivity using an approximate model (13)- (14). The dipole antennas are fed with -10dBm power (at the VNA output).
FIG.4. demonstrate very high dynamic range and sensitivity of the CRA to the CNT sample loading, the resonance frequency shift in all cases is around 11% -14%, RX power variation between unloaded and loaded CRA |S 21 | is approximately 2-10dB which is due to field enhancement inside the CRA (please see more detail in the Appendix D). The permittivity data calculated in Table II are consistent with the previous measurements carried out by other authors [22][23][24][25][26] , it is believed that the major absorption mechanism in the studied CNT ribbons is due to CNT conductivity losses 26 . No. CRA It should be noted that additional measurements not presented here for the brevity sake demonstrate the CRA transmission sensitivity to the gap g s between the CNT sample and the CRA plates. This gap leads to the lower values of permittivity as can be understood from the effective medium approximation 27 , therefore the gap g s should be as minimal as possible for accurate permittivity characterization. The major drawback of the proposed method in its present form is a requirement for broadband dipole antennas matched in the wide frequency band. This drawback can be eliminated by using printed resonators fed by broadband printed strip lines and incorporating printed array of the CRA resonators on a single printed circuit board.

VI. CONCLUSIONS
A new method to characterize permittivity of the CNT samples using resonance, reflection-less CRA transmission is proposed. Initial experimental data demonstrate high sensitivity and dynamic range of the proposed method, which is practically important for the EM characterization of thin "minimal" samples of the CNT material. Approximate analytical procedure of the permittivity de-embedding from the measurement data is proposed, reconstructed permittivity values are consistent with the previous measurements. This method can be easily scaled in the frequency range (from microwave to THz) thus providing an accurate EM characterization tool in addition to existing methods.

APPENDIX A. CRA CAPACITANCE CALCULATION
Quasi-static capacitance of the unloaded and loaded CRAs can be evaluated considering the geometry of the CRA resonator, Fig.S1. FIG. 5. Capacitance between the capacitive resonator conductive faces of the CRA The quasi-static part of the capacitance between the CRA plates 1 and 2 corresponds to the first term in the E-field representation through the scalar potential 16 , where ( ′ ) is a charge surface density across the surface of 1 and 2, and the field is calculated inside the gap g a . Neglecting other terms except for the quasistatic part of the CRA equivalent capacitance is an accurate approximation when | − ′ | ≤ 1 4 ⁄ , i.e. when the CRA is electrically small. Since the charge and potential distribution across the surface of the CRA plates is non-uniform in the high-frequency case, average capacitance per unit area needs to be used in derivation of (12). The total CRA capacitance per unit area is a sum of capacitance per unit area between the parallel faces Cp and capacitance per unit area between the coplanar faces Cc, Fig. 5 Taking this into account, the C L /C 0 can be written as follows where the capacitance between the parallel faces is given by and capacitance between the coplanar faces 28 is . Equation (12) follows directly from (16).

APPENDIX B. POWER BALANCE EQUATION
The imaginary part of the CNT sample defines power dissipation; therefore, the power conservation principle can be employed to derive an equation for the imaginary part of the permittivity. The balance of microwave power delivered to the CRA from the TX antenna and radiated (transmitted), stored (in the reactive near field) and dissipated due to CNT material loss can be written as Equations (17), (18) In (19), coefficient R characterizes matching of the RX antenna at frequency f, ( ) = |1 − 22 ( )| −1 . The stored power can be expressed through the Qfactors of the loaded ( ) and unloaded ( 0 ) CRAs, radiated power and dissipated power due to CNT microwave absorption 18 , ( 0 ) = 0 ( 0 ), Taking into account that = ″ ′ ⁄ it is possible, using (17)- (20) to derive expression (13) for the imaginary part of the CNT permittivity based on the measured RX power, microwave Q factors of the CRA and S parameters of the RX and TX antennas.

APPENDIX C. MEASURED |S11| PARAMETERS OF THE TX DIPOLE ANTENNAS
The measured |S 11 | data demonstrate that the reflected power from the CNT-loaded and unloaded CRAs is the same in the resonance transmission band.

APPENDIX D. EM FIELD ENHANCEMENT INSIDE THE CRA
EM field enhancement inside the CRA gap is shown, as an example, for the CRA 2 using full-wave simulation data (obtained with FEKO solver, www.feko.info). Simulations presented in FIG.7 show that the E-field is enhanced mode than 36 times (31dB) inside the CRA as compared to the counterpart rectangular aperture (26mmx18mm).