Additive manufactured graphene composite Sierpinski gasket tetrahedral antenna for wideband multi-frequency applications

Journal Pre-proof Additive Manufactured Graphene Composite Sierpinski Gasket Tetrahedral Antenna for Wideband Multi-Frequency Applications William Clower (Conceptualization) (Methodology) (Software) (Writing - original draft) (Investigation) (Resources) (Data curation) (Writing - review and editing) (Visualization), Matthew J. Hartmann (Conceptualization) (Software) (Writing - original draft) (Investigation) (Data curation), Joshua B. Joffrion (Writing - original draft) (Validation) (Writing - review and editing), Chester G. Wilson (Conceptualization) (Supervision) (Project administration)

PII:

S2214-8604(19)31063-2

DOI:

https://doi.org/10.1016/j.addma.2019.101024

Reference:

ADDMA 101024

To appear in:

Additive Manufacturing

Received Date:

23 July 2019

Revised Date:

7 December 2019

Accepted Date:

27 December 2019

Please cite this article as: Clower W, Hartmann MJ, Joffrion JB, Wilson CG, Additive Manufactured Graphene Composite Sierpinski Gasket Tetrahedral Antenna for Wideband Multi-Frequency Applications, Additive Manufacturing (2020), doi: https://doi.org/10.1016/j.addma.2019.101024

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Additive Manufactured Graphene Composite Sierpinski Gasket Tetrahedral Antenna for Wideband Multi-Frequency Applications William Clower1, Matthew J. Hartmann2 Joshua B. Joffrion1 and Chester G. Wilson1 1 Institute for Micromanufacturing, Louisiana Tech University, 911 Hergot Ave, Ruston, LA 71272 2 Electrical Engineering Department, Louisiana Tech University, 600 Dan Reneau Dr, Ruston, LA 71272

Abstract

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Graphical abstract

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Here we report a pre-fractal antenna design based on the Sierpinski tetrahedron that has been developed with additive manufacturing. The Sierpinski tetrahedron-based antenna was simulated with finite element method (FEM) modeling and experimentally tested to highlight its potential for wideband communications. The Sierpinski tetrahedron-based antennas were fabricated by two methods, the first involves printing the antenna out of acrylonitrile butadiene styrene (ABS), followed by spin casting a coating of an ABS solution containing graphene flakes produced through electrochemical exfoliation, the second method involves 3D printing the antenna from graphene-impregnated polylactic acid (PLA) filament directly without any coating. Both fabrication methods yield a conductive medium to enable receiving EM signals in the low GHz frequency range with measured input return losses higher than 35 dB at resonance. These antennas incorporate the advantages of 3D printing which allows for rapid prototyping and the

development of devices with complex geometries. Due to these manufacturing advantages, selfsimilar antennas like the Sierpinski tetrahedron can be realized which provide increased gain and multi-band performance. 1. Introduction

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Pre-fractal iterative patterns are a widely researched method for developing complex geometry antennas for microwave applications. The self-similarity of the repeating pattern enables multiple distinct current modes to exist within the radiating element(s) of the antenna. This enables wideband multi-frequency response [1]. The geometric scaling used in the iterative fractal-generation process yields a reduction in size when compared to classical monopole antennas based on Euclidean geometries operating at similar frequencies [2]. These modifications to classic antenna architectures generate high-performance devices with increased bandwidth and reduced size which can be used in the miniaturization of space vehicles, drones, and UAVs as well as wireless energy harvesting and cellular telephony systems applications. Pre-fractal antennas have been demonstrated based on several designs starting with the Mandelbrot fractal boundary [3], the Sierpinski gasket [4–6], Sierpinski carpet [7,8], Koch curve [9], Koch snowflake [10,11] Hilbert curve [12], and Minkowski island [13] fractal patterns, with the Sierpinski gasket being the most widely explored due to its similarity with conventional triangular and bowtie antennas. Traditionally the Sierpinski gasket antennas have been developed as planar devices; problems associated with the Sierpinski planar antennas are that the devices have a narrow bandwidth and poor radiation patterns [14]. Figure 1 is of the Sierpinski gasket pre-fractal antenna pattern. Monopole antennas based on the Sierpinski gasket have been shown to exhibit multiband resonances corresponding to equivalently sized triangular radiating elements as shown in equation 1 where c is the speed of light in a vacuum, h is the height of the 0th-order triangular iteration, δ is the scaling factor between subsequent triangular iterations, and n is the iteration number [4]. 𝑓𝑛 = 0.26

𝑐 𝑛 𝛿 ℎ0

(1)

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While the electromagnetic properties of a Sierpinski gasket antenna structure have been investigated using both patch and monopole antenna configurations, little research has been presented which investigates the properties of the Sierpinski gasket antenna when realized in three dimensions [14-16]. Fabrication of the complex geometric structure of the threedimensional Sierpinski gasket antenna using conventional metal casting techniques is difficult and tedious work [14-16]. An accurate manufacturing process is required to ensure the antennas have the expected frequency response, and as the pre-fractal iteration is increased, the conventional metal casting techniques have a more difficult time to produce these 3D antennas. With the advent of additive manufacturing, devices that were previously difficult to construct can now be realized [17,18]. Fused filament fabrication employs embedding metal, metal oxide and carbon nanomaterials in numerous polymers with different elastic constants and melting temperatures. Electronic components and complete circuits have been realized with various filament components [19,20]. Fused filament fabrication has successfully been shown to create planar bow-tie antennas made from only conductive and non-conductive polymers [21].

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Figure 1. Sierpinski gasket pre-fractal pattern illustrating 3rd-order self-similarity with a scaling factor of δ = 2.

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Recent advances in additive manufacturing have enabled rapid prototyping of geometrically complex structures with high dimensional accuracy at low costs. This allows for quickly investigating various antenna structures that are based on variations of classical fractal geometries. Using fused-layer deposition 3D printing, the generation of higher-order complex pre-fractal structures for use as antenna radiating elements is possible. In this work, a Sierpinski tetrahedral radiating element is explored with two design approaches. The first design uses a conductive coating applied to the 3D printed antenna, and the second consists of 3D printing the antenna with a conductive filament. Figure 2 shows a monopole antenna based on a 3rd order prefractal Sierpinski gasket in three-dimensional form connected to a ground plane. The 3D design of these antennas further enhances the advantages found using planar fractal antennas [14]. The self-similarity of the pattern has been shown to yield multiband behavior when used as an antenna radiating element.

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Figure 2. Three-dimensional drawing of a monopole antenna based on a 3rd-order pre-fractal Sierpinski tetrahedron.

2. Materials and methods

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2.1 Materials and Reagents The pure ABS and PLA filament loaded with graphene were purchased from different vendors and used without modification. The graphene nanosheets used in the spin coated solution was synthesized via the electrochemical exfoliation method described in section 2.3. This fabrication process uses 99.995% pure graphite electrodes from Sigma Aldrich with lengths measuring 150 mm and diameters of 6 mm and 99% sodium dodecyl sulfate obtained from VWR.

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2.2 Antenna Characterization and DC Conductivity Testing The radiating elements were affixed to an Amphenol N-type RF connector with an attached copper ground plane to form a monopole antenna. The radiative properties of the 3Dprinted Sierpinski tetrahedral antennas were measured using an Agilent 4396B Network/Spectrum/Impedance analyzer in its vector network analyzer mode with an attached Agilent 87512A Transmission/Reflection Test Set. A Laird Technologies Phantom multi-band antenna was used as a reference transmitting antenna. The DC conductivity of the electrochemical exfoliated graphene sheets/ABS composites with varying concentration of graphene was measured by the four-point probe method using a Keithley 2400 source meter with an attached Signatone SP4 Four-Point Probe Head. The DC conductivity measurements of different graphene doping concentrations allows for understanding electrical percolation in the composites [22].

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2.3 Production of Graphene Sheets via Electrochemical Exfoliation The graphene sheets that are loaded into the ABS polymer solution were fabricated via electrochemical exfoliation [23]. The graphene lattice is composed of sp2 hybridized bonds; while graphite is composed of stacks of graphene sheets that are bonded together via van der Waals forces. Electrochemical exfoliation has two steps; the first is the oxidation reaction when the graphite electrode is intercalated with the liquid electrolyte (SDS), the second stage is the reduction reaction producing graphene sheets suspended in solution. Since the graphene lattice sp2 hybridized bonds are much stronger than the van der Waals forces, the graphene sheets can easily be removed through electrochemical synthesis. There are other methods to produce pristine graphene with higher electrical conductivity versus graphene produced through electrochemistry. Mechanical exfoliation and CVD processes are great at producing defect free monolayer graphene (highest electrical conductivity); however, these processes are associated with high costs making large scale production difficult [22]. Even though electrochemically exfoliated graphene will not be defect free, its electrical conductivity is acceptable for developing the graphene/ABS coating and can easily be scaled for batch production. At the frequency range used in this work, the electrical conduction does not require the use of defectfree graphene sheets due to the skin depth effect. For large-scale production of 3D printed Sierpinski antennas with a conductive coating, it is more economically viable to produce the graphene sheets through electrochemical exfoliation.

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2.4 Sierpinski Antenna Fabrication The Sierpinski tetrahedral antennas were fabricated using two distinctive fabrication methods. The first method involves printing the antennas from PLA filament that has been infused with graphene flakes creating a solid conductor. The second method involves creating the Sierpinski antenna structure from pure ABS polymer and then spin coating it with a mixture of graphene mixed in ABS dissolved in acetone. This spin coating method produces a layer of the graphene/ABS composite several ~10s of microns thick. For the pure ABS filament, the extruder temperature was maintained in the 230 to 250°C and for the PLA/graphene filament the extruder temperature range was kept at 190 to 200°C. The graphene/PLA composite must be in the specified temperature range due to its propensity to clog the printing system at lower temperatures and at higher temperatures the composite filaments will begin to degrade. The 3D printer used in this work has X and Y positioning precision of 12.5 µm, Z positioning precision 0.4 µm, and layer resolution of 20 to 400 µm. This system can print a wide range of materials with a good layer resolution for developing the Sierpinski tetrahedron structured antennas.

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In order to 3D print a structurally strong fractal antenna, the tetrahedrons were overlapped by 10%. If there were no overlap, the antenna would be to delicate to use for measuring the S-parameters. For the 10% overlap antenna the fabrication time using the conductive filament was 65 minutes. If a more robust antenna was needed, a 15% overlap could be 3D printed with only an additional 10 minutes. The conductive filament we utilized for the project costs ~$1/1g of material. Each antenna that we fabricated is roughly ~11.5g, with each one costing ~$11.50 in materials. The cost of producing the conductive carbon filament could be lowered by producing these materials in the laboratory with the initial large costs being the investment in an extruder. The carbon and polymer feedstock can be lowered extensively through wholesale.

3. Antenna Design and FEM (Finite Element Method) Analysis In this work, the modeled behavior (input return loss and radiation pattern) of Sierpinski tetrahedral antennas are compared with planar Sierpinski gasket antennas with equivalent geometrical parameters to illustrate the advantages in electrical performance of realizing the structure in three-dimensions. Due to the self-repeating patterns associated with fractals, these structures are great for producing multiple resonances. In order to model the complex Sierpinski tetrahedral antennas the finite element method was required.

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3.1 Antenna Design Realizing a Sierpinski gasket structure in three-dimensions requires the replacement of each triangle with a tetrahedron having the face dimensions of the replaced triangle. The resulting structure is a tetrahedron composed of smaller tetrahedral elements wherein each face forms a Sierpinski gasket. The dimensions of the antenna and the number of iterative patterns to include in the device architecture were chosen such that the first resonance of the antenna structure should occur at approximately 1.5 GHz, the middle of the L-band, with additional resonances occurring near the middle of the C- and S-frequency bands. Figure 3 illustrates a 3rdorder pre-fractal Sierpinski tetrahedron structure with the radiating element fed with a 50 Ω coaxial transmission line and placed on a circular finite ground plane with a radius of 90mm to form a monopole antenna. The radiating element is an equilateral tetrahedron with a face length of 128.0 mm and a height of 104.5 mm. This height corresponds to an h0 value of 110.8 mm for the Sierpinski gasket created on each tetrahedral face. To model EM wave propagation with an unbounded domain, a perfectly matched layer is required. The perfectly matched layer creates a perfect absorbing layer that absorbs all the outgoing EM waves without reflecting them back. This allows for proper modeling of signal propagation from the antenna in far-field conditions. To ensure adequate electrical connections between the tetrahedron structures, there is slight overlap. This also helps to improve the meshing required to eliminate extremely small points. The maximum element size of the mesh is proportional to the excitation frequency being simulated. The electrical resonance of a tetrahedral antenna should coincide with that of a planar antenna. The resonant frequency of a Sierpinski gasket planar monopole can be described by equations 2, 3, and 4 [21].

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𝑐 (0.15345 + 0.34𝜌𝑥) (𝜉 −1 )𝑛 𝑓𝑜𝑟 𝑛 = 0 ℎ𝑒 𝑓𝑟 = ̃{ 𝑐 𝑛 0.26 𝛿 𝑓𝑜𝑟 𝑛 > 0 ℎ𝑒 √3𝑠

𝑒 ℎ𝑒 = 2 𝑠𝑒 = 𝑠 + 𝑡(𝜀𝑟 )−0.5

(2)

(3) (4)

With he and se being the effective height and side-length, t is the thickness of the substrate, 𝜌 = 𝜉 − 0.230735, 𝜉 is 0.5, and 𝛿 is 2 [24].

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Figure 3. A finite element mesh for a 3rd-order Sierpinski tetrahedral monopole antennas with a finite ground plane and a coaxial feed line (Z0= 50 Ω).

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3.2 RF Modelling with Finite Element Method The FEM modeling of the antenna structure was performed using COMSOL’s RF Module over a frequency range of 0.1–6.75 GHz with a 50 MHz step-size in the frequency sweep. The simulations employed an adaptive mesh that limits the maximum element size to 20% of the wavelength of the excitation frequency being simulated. Modeling was carried out for 0th-, 1st-, 2nd-, and 3rd-order pre-fractal structures to analyze the changes in input return loss and radiation pattern as the structure becomes more complex. In addition, a planar Sierpinski gasket monopole antenna was also modeled over the same frequency range to enable comparisons between the electrical performance of the 2D and 3D structures. The radiating elements of each antenna structure were modeled as perfect electrical conductors to shorten computation time, and the simulation area was bounded by a perfectly matched layer to approximate far-field conditions. The Sierpinski antennas were solved with the COMSOL module “electromagnetic waves in frequency domain” (emw) for the RF spectrum for the electric field intensity at each node point generated by the mesh using equation 5, where μr and εr are the relative permeability and permittivity of the antenna medium, k0 is the wavenumber for free space (dependent on excitation frequency), and ε0 is the permittivity of free space. The mesh is limited to the minimum wavelength that is under simulation. ∇×

1 𝑗𝜎 (∇ × 𝐄) − 𝑘02 (𝜀𝑟 − )𝐄 = 0 𝜇𝑟 𝜔𝜀0

(5)

3.3 Simulation Results The simulation characterization began with comparing the input return loss of the Sierpinski tetrahedral to the Sierpinski gasket (i.e. the planar antenna). Figure 4 shows the simulated results when comparing the input return loss of a Sierpinski tetrahedral monopole

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antenna and a Sierpinski gasket monopole antenna for a frequency span from 100 MHz to 6.75 GHz. Both antennas have the same face dimensions discussed in section 3.1 for comparing resonance peaks. In the L-band the planar antenna has a slightly better resonance at 1.55 GHz. The tetrahedral antenna offers distinct advantages over conventional Sierpinski gasket antennas designed for S-band and C-band applications due to the stronger resonances. From the figure, the tetrahedral antenna has significantly better radiative properties than its planar counterpart at higher-order resonant modes with a minimum increase of 3.3 dB occurring at f3=6.3 GHz. The bandwidth of the tetrahedral antenna is also significantly increased at lower-order resonances. With these characteristics of the 3D Sierpinski antenna, it is possible to eliminate the need for multiple antennas in multiband communications systems.

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Figure 4. Comparison of the three-dimensional Sierpinski gasket antenna with the Sierpinski planar antenna.

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To determine the effectiveness of carbon-based and polymer materials for the radiating element of the 3D Sierpinski antennas, a variety of materials were simulated. Figure 5 shows the 3D 3rd-order Sierpinski antennas that were modeled with copper and graphite. The input return loss at the 1.55 GHz resonance frequency for copper was at -25.875 dB. The antenna modeled out of graphite had an input return loss at -24.927 dB. The skin depth (δ) can easily be calculated from equation 6, with the crucial factors being the material’s bulk resistivity (ρ), frequency (f), relative permeability (µR), and the permeability of free space (µ0=4π*10-7). 𝜌 𝜋𝑓𝜇𝑅 𝜇0

𝛿=√

(6)

At the GHz frequencies, copper slightly outperforms graphite (difference of 2.116 dB) which has a much lower electrical conductivity, but the skin depth of copper with a bulk resistivity of 1.724 µΩ*cm at 1.5 GHz is ~1.71 µm and for graphite with a bulk resistivity of 1429 µΩ*cm is ~49.1 µm. At GHz frequencies, the antennas are not required to be solid

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conductors but can still produce electromagnetic radiation with minimal change in radiation efficiency.

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Figure 5. 3D 3rd order Sierpinski antenna comparing the effects of a solid copper and solid graphite antenna.

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The next step in characterizing the Sierpinski tetrahedral antenna involves varying the pre-fractal iterations to analyze changes in the input return loss and radiation patterns as the structure becomes more complex. For these models, the 0th, 1st, 2nd, and 3rd-order pre-fractal structures of the Sierpinski tetrahedron were analyzed. Figure 6a shows the pre-fractal iteration patterns for the Sierpinski geometry from 0th to 3rd order. Figure 6b shows the input return loss of the simulated Sierpinski tetrahedral monopole antennas when varying the pre-fractal iteration numbers. Resonances are observed at 1.6, 3.0, 3.6, and 6.3 GHz, with each pre-fractal iteration generating an additional resonance as was observed in both simulated and practical Sierpinski gasket monopole antennas. The even-ordered resonances experience a slight frequency shift to the right as the number of iterations increase while odd-ordered resonances experience a similar shift to the left. The simulated antennas demonstrate high radiation efficiencies (S11 >20dB) at all resonances for 2nd and 3rd-order designs, showing potential for true multiband transmission of signals at these frequencies. The next characteristics modeled were the radiation patterns of 3rd order pre-fractal tetrahedral antenna at the different resonant frequencies: 1.55, 3.00, 3.70 and 6.25 GHz shown in figure 7. As the frequency increases, the changing electric field distribution causes the lobes of the radiation pattern to become less distinct and thus the directionality of the antenna decreases as a function of frequency. This is best illustrated by looking at the XY-plane radiation characteristics: as the excitation frequency increases the radiation direction alternates between the faces and edges of the tetrahedral structure with small perturbations occurring at 60° intervals between the directional lobes. At a frequency of 6.25 GHz, the antenna approaches omnidirectional radiation in the XY-plane as the magnitude of the perturbations is of similar scale to the directional lobes. Figure 8 shows the three-dimensional representation of the simulated radiation pattern data.

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Figure 6 a). 0th to 3rd order (clockwise from top left) Sierpinski pre-fractal pattern and b). simulated input return loss of pre-fractal Sierpinski tetrahedral antennas on a finite ground plane.

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Figure 7. Simulated radiation characteristics of a 3rd-order Sierpinski tetrahedral pre-fractal antenna.

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Figure 8. Simulated 3D radiation pattern data for a 3rd-order Sierpinski tetrahedral antenna at a) 1.55 GHz, b) 3.00 GHz, c) 3.7 GHz, and d) 6.25 GHz.

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Figure 9 shows the electric field distribution at each resonance of the 3rd-order pre-fractal tetrahedral antenna. At each frequency, the electric field distribution is effectively the same over each vertical face of the tetrahedral structure. As the frequency increases, different regions of the antenna activate, and the electric field is confined to a smaller area which causes the radiation pattern of the antenna to change drastically as a function of increasing frequency. The simulations presented here are the first to illustrate the performance potential of 3D printed antennas based on a 3rd-order Sierpinski fractal geometry. The extension of the Sierpinski gasket pre-fractal pattern into three-dimensions results in an increase of S11 response at higher-ordered resonant frequencies, demonstrating usefulness as a true multiband antenna. Expansion beyond the constraints of planar implementation into three dimensions increased efficiency, bandwidth, and directional gain -- characteristics which can be exploited for any application within the field of wireless communication -- as compared to a planar Sierpinski gasket antenna with equivalent face dimensions. The final parameter to simulate for the 3rd-order tetrahedral antenna is the efficiency which is shown in figure 10. At the operating frequencies of 1.55, 3.0, 3.7 and 6.25 GHz the antenna frequency is at 50%. The antenna frequency drops off by 10 to 25% for the simulated antenna. The 3rd-order Sierpinski antenna provides excellent wideband performance as shown with our FEM simulations.

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Figure 9. Electric field distribution on the surface of the antenna at (a) 1.55 GHz, (b) 3.00 GHz, (c) 3.70 GHz, and (d) 6.25 GHz.

Figure 10. Antenna Efficiency for 3rd-Order Sierpinski tetrahedral antenna from 1 GHz to 6.5 GHz.

4. Experimental Results and Discussions

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The radiating element for the antennas was fabricated utilizing two different methodologies. Both methodologies employed a fused-layer-deposition 3D printer to fabricate the 3rd-order Sierpinski tetrahedral antenna structure. The first method involved 3D printing the radiating element from natural unmodified ABS plastic filament that did not have any additional materials embedded. This is followed by a spin casting process to coat the entire radiating element with electrochemically exfoliated graphene sheets as shown in figure 11a. The graphene sheets are mixed with a solution consisting of acetone and ABS. The acetone/ABS solution provides the adhesion required to make a solid conductive layer on the ABS Sierpinski tetrahedron structure. These coatings form a thin electrically conducting layer (with the graphene sheets overlapping) on the surface of the Sierpinski antenna. The second method used to fabricate the 3rd-order Sierpinski tetrahedral radiating element involved 3D printing it from a carbon infused PLA filament shown in figure 11b. Morphological analysis of the graphene flakes before being embedded into ABS/acetone solution was conducted. Figure 12a is a SEM image of the graphene flakes before mixing showing flakes with lateral dimensions <10 microns. TEM analysis was conducted to confirm that the graphene flakes were monolayer to few-layer thick as shown in figure 12c. The detailed synthesis method for producing the graphene flakes is described in section 2.4. Carbon allotropes were chosen due to their electrical conductivity, being a lightweight material and easily 3D manufacturable. The coatings applied to the unmodified ABS filaments form a thin electrically conducting layer on the surface of the tetrahedral to create the radiating element for a monopole antenna. shown in figure 12b. Figure 12d is a conductive PLA filament that has been sliced in two pieces for determining the internal morphology. With the coating method only, the outside of the antenna structure is active, while building the antenna from a carbon infused filament makes the entire structure electrically conductive.

Figure 11. 3rd-order Sierpinski gasket 3D printed radiating element that has been a.) coated with a graphene/ABS solution and b.) printed from a conducting PLA filament.

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Figure 12. SEM images of a.) electrochemical exfoliated graphene flakes used as a dopant material, b.) 3D-printed graphene-embedded PLA filament for use in direct 3D printing of conductive structures, c.) TEM image of graphene nanosheet, and d.) SEM image of a sliced PLA filament.

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ABS is a non-conductive polymer requiring conductive particles in sufficient amount embedded in order to produce adequate electrical conductivity. Mixing conductive graphene sheets with the insulating ABS polymer follows percolation theory. Once the amount of graphene sheets reaches the percolation threshold, the overall polymer matrix will become electrically conductive. Before the percolation threshold, the polymer matrix acts more like an insulator not allowing any electrons to pass through it. As the matrix is further loaded with the graphene sheets, it moves closer to the percolation threshold where electrons will begin to tunnel from one graphene sheet to the next. Once the polymer matrix has enough graphene sheets, a conductive network forms allowing electrons to easily travel throughout. One key advantage of using graphene sheets is that they have large aspect ratios allowing them to have a reduced percolation threshold in any polymer matrix [22]. One issue to avoid is the agglomeration of the graphene sheets in the ABS matrix, which will cause selective localization. Selective localization occurs when conductive fillers are isolated in the polymer matrix without forming a conductive network throughout the insulating polymer [22]. The two ways to avoid this issue is proper mixing of the graphene sheets within the ABS matrix to ensure a homogeneous composite and to increase the amount of graphene sheets inside the polymer matrix thereby increasing the likelihood that a conductive structure is created. The electrical conductivity of the ABS-graphene polymer matrix was tested with loading percentages of graphene sheets to ABS from 5%wt to 25%wt shown in figure 13. Beyond 25%wt, the polymer becomes too brittle and will flake off after being deposited onto the ABS printed antenna structure. The 20%wt provides enough

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Figure 13. Electrical conductivity for graphene/ABS mixture.

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conductivity to build a functional antenna, and it does not have any mechanical issues with its structure due to flaking.

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The radiative properties of the 3D-printed Sierpinski tetrahedral antennas were measured using a vector network analyzer for testing reflection and transmission. A commercial multiband antenna was used as the reference transmitting antenna. S21 and S11 data was collected for each antenna over the operational bandwidth of the test set-up. As shown in Figure 14, the 3Dprinted antenna structures exhibit high S21 at a resonant frequency of f0 = ~1.4 GHz, indicating a high degree of signal reception at this frequency despite the use of non-metallic antenna structures. The measured input return losses are of similar magnitude to those simulated using copper, validating this process to fabricate otherwise unrealizable antenna geometries for specific frequency applications. The bandwidth of the antennas at the 1.4 GHz resonant frequency was tested and compared to a Sierpinski gasket planar antenna made from copper on a circuit board. The bandwidths were determined for each antenna using -30 dB as the reference for signal transmission. The Sierpinski planar copper antenna has a bandwidth of 15.8 MHz, the graphene/ABS coated antenna at 20%wt of electrochemical exfoliated graphene sheets has a bandwidth of 26.3 MHz, and the conductive filament antenna has a 20.1 MHz bandwidth. This observation validates the increased bandwidth observed when comparing the 2D and 3D Sierpinski antennas through FEM simulations. Further comparisons of the fabricated antennas with the FEM simulations by comparing the S11 parameter were performed. Figure 15 is measured data of both the conductive filament and graphene-coated 3D printed 3rd-order Sierpinski tetrahedral. When comparing the simulated S11 data to the simulations, we find the losses to be similar, with the main difference being that the simulated antenna has a larger bandwidth compared to both of the fabricated antennas.

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Figure 14. S21 for 3D printed Sierpinski tetrahedral radiating element made from PLA/Graphene and ABS coated with graphene nanosheet layer.

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Figure 15. S11 in dB measured for conductive filament and graphene coating 3rd-order Sierpinski tetrahedral radiating element.

5. Conclusions

This work demonstrates the performance potential of realizing complex geometrical antenna architectures via additive manufacturing techniques. These architectures were previously considered extremely difficult to produce through traditional methods. Third order Sierpinski tetrahedral antennas were modeled through FEM modeling and were fabricated from nanostructured carbon composites. These antennas were fabricated by coating a graphene

polymer matrix onto a non-conducting structure or 3D printed directly from a polymer filament with embedded conducting materials. The measured input return losses are of similar magnitude to those simulated using perfect electrical conductors, validating these processes as a means to fabricate otherwise unrealizable antenna geometries for specific frequency applications. While the electrical conductivity of the materials used will always be less than that of copper, the ability to use plastics as a structural material has many advantages that outweigh these limitations in applications requiring low weight, exposure to corrosion, or rapid fabrication. Author Statement

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William Clower: Conceptualization, Methodology, Software, Writing-Original Draft, Investigation, Resources, Data Curation, Writing-Review & Editing, Visualization Matthew J. Hartmann: Conceptualization, Software, Writing-Original Draft, Investigation, Data Curation

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Joshua B. Joffrion: Writing-Original Draft, Validation, Writing- Review &

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Editing Chester G. Wilson: Conceptualization, Supervision, Project

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Author Declaration

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administration

The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

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The manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property. We understand that the Corresponding Author is the sole contact for the Editorial process (including Editorial Manager and direct communications with the office). He is responsible for communicating with the other authors about progress, submissions of revisions and final

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approval of proofs. We confirm that we have provided a current, correct email address which is accessible by the Corresponding Author and which has been configured to accept email from: [email protected]

References

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