Fabrication of low dielectric constant composite filaments for use in fused filament fabrication 3D printing

Journal Pre-proof Fabrication of Low Dielectric Constant Composite Filaments for use in Fused Filament Fabrication 3D Printing Paul Parsons, Zachary Larimore, Faheem Muhammed, Mark Mirotznik

PII:

S2214-8604(19)30797-3

DOI:

https://doi.org/10.1016/j.addma.2019.100888

Reference:

ADDMA 100888

To appear in:

Additive Manufacturing

Received Date:

21 June 2019

Revised Date:

26 September 2019

Accepted Date:

26 September 2019

Please cite this article as: Parsons P, Larimore Z, Muhammed F, Mirotznik M, Fabrication of Low Dielectric Constant Composite Filaments for use in Fused Filament Fabrication 3D Printing, Additive Manufacturing (2019), doi: https://doi.org/10.1016/j.addma.2019.100888

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Fabrication of Low Dielectric Constant Composite Filaments for use in Fused Filament Fabrication 3D Printing

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Paul Parsons*, Zachary Larimore, Faheem Muhammed and Mark Mirotznik

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Electrical and Computer Engineering Department, University of Delaware, Newark, DE 19716 USA

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emails: [email protected], [email protected] and [email protected]

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* Denotes Corresponding Author

Abstract

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In this paper we describe a method for creating flexible composite filaments with dielectric constants below 2.0 over a wide frequency band (i.e. 18 - 40 GHz). We demonstrate that a low dielectric constant composite filament, useful for FFF printing, can be manufactured by combining a base thermoplastic polymer with hollow microspheres and a plasticizer. Experimental results are provided for filaments made from two different base polymers (i.e. ABS and HDPE) and varying volume fractions of hollow microspheres. We also describe an effective media model to predict the dielectric properties of the composite filaments as a function of the properties of the constituent materials (e.g. base polymer, hollow microspheres) and their relative volume fractions within the composite filament. Experimental test samples were printed using the new low-K filaments and experimental characterization results are provided that validate this approach.

1. Introduction

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While still at an early stage, the application of additive manufacturing (AM) for fabrication of electronic and electromagnetic devices is rapidly evolving. For example, engineers are experimenting with AM for use in printed sensors [1, 2], conformal electronics [3, 4, 5, 6], stretchable electronics [7] and radiofrequency (RF) devices [8 - 17]. In the case of RF and microwave devices and systems, further progress will require exploring innovative design methods, new materials and novel manufacturing approaches to realize cost-effective, customizable and conformal RF systems that do not rely on standard commercial off-the-shelf technologies. While the current AM market has been growing rapidly, it is still built primarily around single material based systems. These systems are capable of fabricating complicated 3D parts out of a single material (e.g., polymers, metals or ceramics) selected primarily based only on mechanical properties. Thus the applicability of these systems to RF applications is often quite limited. Over the last few years we have seen an increase in commercially available multi-material AM systems that are much more material agnostic. These systems allow users to print a wide range of commercial or custom made materials via micro-dispensing, material jetting or fused filament fabrication (FFF). Additionally, some systems allow multiple materials to be printed without ever moving the part by integrating an array of print heads. This opens up the possibility of fabricating a complete RF system (e.g., substrates, connectors, transmission lines, apertures) using a single machine.

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While good progress has been made on the development of general multi-material AM printers, less progress has been made on the development of materials tailored for use in RF applications. In many cases the lack of suitable materials is the principal bottleneck preventing this technology from having a larger impact on real-world applications. Current material development needs include high conductivity inks and pastes with RF conductivities that approach bulk metal and dielectrics with tailorable permittivities that extend both above and below the range of most commercially available polymers used in AM. In Figure 1 the dielectric constant and loss tangent of some of the more popular polymers used in AM are shown. While many of these materials have attractive loss tangents (<0.01) their dielectric constants cover a relatively narrow range between 2.25 and 3.25. To achieve dielectric constants higher than 3.25 several investigators have developed composite materials that combine high dielectric constant powders with base polymers [18, 19, 20]. Using these approaches, composite materials have approached relative permittivities up to 11.0 with corresponding dielectric loss tangents of ~0.03 at microwave frequencies. However, for some applications it is desirable to print materials with dielectric constants less than 2.25. For example, the use of low dielectric constant substrates has been found to improve the radiation efficiency and reduce surface waves for microstrip antennas of a given substrate thickness [21]. This is particularly important for AM printed antennas in which the conductivity of the printed metallic structures is often an order of magnitude lower than bulk metal properties. High-speed RF electronic circuits can also benefit from a low dielectric constant substrate that reduces parasitic capacitive effects [22]. One method for achieving this is a macro-scale approach where a base polymer is 3D printed with intentional air voids so that its effective dielectric constant can be controlled by the local volume fraction of polymer to air (see Figure 2). As long as the length scale of the inhomogeneities are small compared to the electromagnetic wavelength then effective media theory (EMT) can be used to predict the effective dielectric properties of the composite. While useful for some applications there is still one major drawback with this approach. Namely, the low fill density results in a relatively rough surface profile. If this structure is

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subsequently used as the dielectric substrate for a printed metallic antenna or transmission line the rough surface often results in undesirable electromagnetic losses (see Figure 3). While there are more elegant solutions of introducing voids into the substrate, such as space-filling curves [23], the aforementioned issue is still problematic, particularly when printing dielectric structures that have properties which closely resemble air (e.g., very low fill fraction). Additionally, as the local fill fraction of polymer during a print is reduced, the mechanical properties of the finished part can become compromised. This is especially true for fill fractions that are close to the properties of air.

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Figure 1 – Generalized dielectric RF properties of typically used polymers on additive manufacturing platforms for electromagnetic applications.

Figure 2 – Macro-scale approach to reducing the dielectric constant of structures by patterning voids within the substrate, where (a) is densely packed, and (b) is loosely packed.

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Figure 3 – Macro-scale approach to reducing the dielectric constant of structures by patterning voids within the substrate with a conductive element residing on the loosely packed surface (left), and inset showing undulation of conductive layer increasing the electrical path length (right).

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To avoid this issue, it is advantageous to explore other approaches to achieve low dielectric properties at nearly 100% fill densities. Previously, investigators have reported the development of low-K dielectric PTFE/PI core-shell nanoparticles for additive manufacturing applications, with dielectric constants as low as 2.2 at 7.2 GHz [24]. These nanoparticles were suspended into a solution, and then aerosol sprayed into 2 μm layers onto sodium borosilicate glass slides. In this paper we describe a scalable method for creating flexible composite filaments with dielectric constants below 2.0 over a wide band of frequencies (i.e. 18 to 40 GHz.) We demonstrate that a low dielectric constant composite filament, useful for FFF printing, can be manufactured by combining a base thermoplastic polymer with hollow microspheres and a plasticizer. Experimental results are provided for filaments made from two different base polymers (i.e. ABS and HDPE) and varying volume fractions of hollow microspheres. We also describe an effective media model to predict the dielectric properties of the composite filaments as a function of the properties of the constituent materials (e.g. base polymer, hollow microspheres) and their relative volume fractions within the composite filament.

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This paper is organized as follows. In section 2 we describe the materials and processing methods used to fabricate flexible low-dielectric constant filaments. In section 3 we describe the effective media models used to describe the dielectric properties of the hollow glasses spheres and the composite filaments. In section 4 we provide results that includes electromagnetic characterization of printed samples, microscopy and measured viscoelastic properties.

2 Materials and Methods 2.1 Materials

The low dielectric constant (i.e. low-K) composite filaments combined three constituent materials; (1) a base thermoplastic polymer, (2) hollow glass microspheres (HGS) and (3) a plasticizer. Two classes of HGS, procured from 3M, were investigated. These were, S22, with an isostatic crush strength of 400 psi, and iM16K, with an isostatic crush strength of 16,000 psi. According to the vendor literature, the average particle size for the HGS are 35µm and 20µm for the S22 and iM16K particles, respectively.

For the thermoplastic binding matrix, we tested both acrylonitrile butadiene styrene (ABS) pellets (MFI 28, Filabot), and high-density polyethylene (HDPE) powders (Microthene FA7 series, Lyondell Bassell). Dibutyl phthalate (DBP, C18H22O4) was used as a plasticizer for the ABS system and was purchased from Sigma Aldrich. 2.2 ABS/HGS Filament Compounding and Extrusion

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ABS/HGS composite filaments were prepared using the method described in [19] without the addition of a surfactant. Commercially available ABS pellets (Filabot) were dissolved in acetone until complete dissolution. After dissolution, DBP (Sigma Aldrich), a plasticizer, was loaded into the solution at 5% by mass of the polymer and homogenized for 12 hours. Plasticizer was used to reduce the viscosity of the composite material matrix, enabling a higher volumetric loading of hollow glass microsphere additives, while retaining desired filament flexibility. It should be noted that if too much plasticizer is added to the composite, the resulting material becomes very elastic and difficult to print using FFF platforms. HGS microparticles were then added to the system in varying volume percentages between 10 – 40% for iM16K particles and 10 – 30% for S22 particles. After incorporating the HGS the composite suspension was spread out onto a tray covered in chemically resistant release film and allowed to dry. The dried composite slab was cut into pieces and placed into a 70°C oven for 12 hours, allowing the acetone to fully migrate out of the composite. Lastly, the dried pieces were ground into mm-size pellets using a granulator (Shr3d It, 3Devo). These pellets were used as feedstock for the single screw extruder system (Filabot EX1 Filament Extruder, FilaBot) equipped with a 2.0mm diameter die orifice and filament spooler/tensioner (Filabot Spooler, Filabot). Using this system, the composite material consisting of ABS/iM16K/DBP and ABS/S22/DBP was extruded at 190°C with tension being applied from the spooler to produce continuous filaments of approximately 1.75mm in diameter.

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2.3 HDPE/HGS Filament Compounding and Extrusion

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HDPE-HGS composite filaments were prepared through a twin-screw compounding process without the addition of plasticizer. Base HDPE is naturally very elastic and flexible, thus the introduction of a plasticizer could potentially make the resulting composite very difficult to print and is unnecessary under our loading conditions. Commercially available HDPE powders (Lyondell Bassell) were compounded only with iM16K HGS. S22 particles, as described later, have very thin walls are unlikely to survive the processing conditions using a twin-screw compounder (Process 11, Thermo Scientific). This compounder/extruder was equipped with a standard screw profile consisting of conveying and kneading elements, with temperatures set at 180 – 200°C between the feeding and extrusion ports. HDPE powder was introduced in varying volume (30% – 50%) at the cooled feed inlet, with iM16K HGS introduced downstream in the polymer melt using a gravimetric feeder (MiniTwin MT0, Thermo Scientific). Tension was applied to the extrudate using the Filabot Spooler after the compounded material was cooled in a water bath, producing continuous filaments of approximately 1.75mm in diameter. At 50% volume loading of HGS into HDPE, the filaments remained very flexible even without the addition of plasticizer as shown in Figure 4.

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Figure 4 – HDPE/iM16K composite filaments with 30% volume loading of HGS particles (left), 40% volume loading (center), and 50% volume loading (right).

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2.4 Samples for Dielectric Characterization of Composite Filaments at Radio and Microwave Frequencies

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To characterize the microwave dielectric properties of the composite filaments, flat plate test samples (nsamples = 2), 125 mm × 125 mm × 1-1.5 mm in size, were printed using FFF platforms, such as the nScrypt 3Dn-300 multi-material printer. Prints were completed using an overlapping fill pattern to minimize printing defects, such as internal voids, while maximizing printed fill fraction. This is important, because as the loading of HGS increases, the composite materials become stiffer and more difficult to print, potentially leading to defects when using standard printing profiles. For the ABS-HGS system, extrusion was performed at 240 °C at a print bed temperature of 110°C using a thin ABS-adhesive layer. Deposition occurred at 50 mm/s with a layer thickness of 0.1 mm. Images of a finished plate and confocal laser measurements of surface roughness, which were validated using a Keyence VK-X200 3D Color Laser Scanning Microscope, are shown in Figure 5. For the HDPE-HGS system, extrusion was performed at 170°C at a print bed temperature of 100°C using an HDPE-tape adhesive layer. For these samples the print speed was similar to the ABS-HGS system. During the printing of HDPE, all external cooling fans were disabled to keep HDPE in a molten state during print head extrusion to promote adhesion between layers.

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Figure 5 – Printed low-dielectric composite material plate used for RF and microwave characterization (a), with laser scanned image of surface (b) and corresponding height map (c). Average surface roughness of this ABS composite sample, loaded at 30% by volume, was measured to be Ra = 12 µm.

2.5 Radio and Microwave Frequency Dielectric Characterization Setup

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To experimentally characterize the microwave dielectric properties of the low-K composite filaments, a custom built free-space focused beam system, illustrated in Figure 6, was used. This system measures the dielectric properties of each sample across the frequency range of 18 – 40GHz. Our system employs a pair of lensed antennas to focus a Gaussian beam onto the test sample. An Agilent vector network analyzer (VNA, model E8364B) is used to measure the phase and amplitude of the transmitted microwave signal (S12) and reflected microwave signal (S11) across the entire frequency band. Data post processing, using standard material measurement algorithms [25], is used to calculate the dielectric constant and loss tangent of the sample based on the complex transmission data.

Figure 6 – Printed low-dielectric composite material plates placed within the free-space beam path for RF characterization.

2.6 Determination of Dielectric Properties for Hollow Glass Spheres To determine the distribution of HGS particle geometries both S22 and iM16K particles were characterized using a laser diffraction particle size analyzer (LS-13-320, Beckman Coulter). Additionally, a field emission scanning electron microscope (JSM-7400f, JEOL) was used to

characterize the cross sections of HGS particles to determine average wall thickness. From these measurements the volume fraction of gas-to-glass can be determined. This data was input into effective media models to predict the permittivity of HGS particles and the resulting polymer-HGS composite. 2.7 HGS Analysis for Verification of Effective Medium Approximations

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Figure 7 – Particle Size Distribution of HGS with the mean particle diameter being 16 µm for iM16K (grey), and 33 µm for S22 (red) particles. All measurements showed particle sizes that are < 70 µm in diameter.

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An illustration of the relative difference in size of these particles is shown in Figure 8, where the iM16K HGS shows a smaller particle with thicker walls (~0.55 μm), and the S22 HGS shows a larger particle with thinner walls (~0.3 μm). This data was used to infer the volume loading of gas for the S22 and iM16K particles as approximately 95% and 80%, respectively and are summarized in Table 1. With these parameters known, we can then estimate the complex relative permittivity of the HGS and polymer-HGS composite systems.

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The size distribution for both HGS series particles are shown in Figure 7. The measured mean diameters are 16 µm for iM16K (with a standard deviation of 8 μm), and 33 µm for S22 (with a standard deviation of 11 μm). The average wall thickness of the HGS particles was measured using HGS cross sections and SEM analysis to be approximately 0.55 µm for the iM16K, and 0.3 µm for the S22 particles, respectively.

Figure 8 – Relative sizes of HGS particles with iM16K (left) having a mean diameter of 16 µm and average wall thickness of 0.55 µm, and S22 (right) having a mean diameter of 33 µm and average wall thickness of 0.3 µm.

It should be noted that while the iM16K HGS are more suitable for the harsh extrusion process (due to a higher isostatic crush strength), there is still a relatively large volume that is occupied by very small particles (< 10 μm). These smaller particles actively contribute to a higher effective permittivity since the gas volume in these particles is much lower than those of larger particles (i.e. 10 μm diameter spheres correspond to a gas volume of 70%, 5 μm diameter spheres correspond to a gas volume of 47.5%, etc.). To reduce the permittivity further, smaller particles should be separated and removed prior to compounding. Table 1. HGS Physical Properties to verify EMA Relative Permittivity Mean diameter (m)

Mean wall thickness (m)

Isostatic Crush Strength (psi)

Density (g∙cm-3)

Gas Volume Fraction (%)

iM16K

16

0.55

16,000

0.46

80

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33

0.30

400

0.22

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2.7 Viscoelastic Behavior of ABS and HDPE Composites

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Rheological measurements were performed to gauge the influence of the incorporated micronsized particles and the effect of the plasticizer on the resulting composites. This information is necessary when defining the upper particle volume threshold for “printability” using FFF. The viscoelastic properties of the samples were measured by a Discover HR-2 Hybrid Rheometer parallel plate rheometer using 25 mm aluminum plates. Measurements were performed from 180oC to 240oC for the ABS composites and 120oC to 170oC for the HDPE composites at 10oC intervals. Oscillatory shear rates ranging from 0.01 to 100 rad/s were performed at 1% strain. These rates were selected as they resemble the shear rate on the extrudate as it passes through the heated print head [26, 27]. Data was collected at 25 points/decade with a 3 second sampling time. Prior to measurements, the samples were annealed for 1 hour in a block heater at 77oC (ABS) and 45oC (HDPE) to remove excess moisture. After temperature equilibration a further 120 second soak was employed at each 10o increment. The gap size was force controlled to maintain a 5 N axial force. All presented viscoelastic measurement data is represented as the average data.

3. Modeling

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In this section we describe an effective media model used to predict the dielectric properties of the HGS inclusions and fabricated composite filaments as a function of the individual material permittivities, particle geometry and relative volume fractions. Our approach, described in more detail below, combines two different effective media approximations. The first model predicts the effective dielectric properties of the individual HGS particles as a function of their average diameter, wall thickness and material properties. For this model we employed the Bruggeman symmetric mixture formulas [28]. This model was chosen due to its known accuracy for highly loaded systems (i.e. volumetric loading greater than 50%). The results from the Bruggeman model were then applied to a second effective media model used to calculate the effective dielectric properties of the HGS loaded polymer filaments. For this second model we used the MaxwellGarnett equations. Maxwell-Garnett has been shown by numerous investigators to provide accurate results for volumetric loading between 0% and 50% [28, 29]. 3.1 Effective Medium Approximations for HGS particles Using the Bruggeman effective medium approximation [28] the effective permittivity of the HGS particles, εHGS eff , are determined using

1  f

air

 glass   effHGS  air   effHGS air  f 0  glass  2 effHGS  air  2 effHGS

(1)

where f air represents the volume fill fraction of the HGS’s air core and εglass and εair denotes the permittivity of the glass wall and air core respectively. The volume fill fraction, f air, is easily calculated using Eq. (2) as a function of the average diameter of the hollow glass spheres, d, and their average wall thickness, w. f

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 d  2w   1    d 

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(2)

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In Figure 9 the predicted effective complex permittivity of a HGS particle is plotted compared to the volume fraction of the air core. For these calculations we measured the complex permittivity of sodium borosilicate glass plates (the glass component of the HGS), with values of Glass = 4.60 and tanGlass= 0.016 between 18 – 40 GHz. These values are similar to values of other borosilicate glasses, where r = 4.6 with a loss tangent of tan= 0.024, measured at 13.4 GHz by other research groups [30]. Not surprisingly, to achieve a very low dielectric constant requires the wall thickness of the sphere to be quite thin compared to the sphere’s diameter. However, as shown later in this manuscript, if the glass wall is too thin the particles do not survive the extrusion process. Thus, it is important to find HGS particles that have the highest possible volume fraction of air while maintaining a high enough isostatic crush strength to survive processing (compounding and extrusion) conditions.

Figure 9 – Effective medium approximations using Bruggeman relations for HGS. The boundary conditions used are εhost = 4.6 − 𝑗0.0736 (sodium borosilicate glass) and εinc = 1.00059 – j0.00 (air).

In Table 2 we provide the mean geometrical parameters, density, and predicted effective permittivity, using Eq. (1), for the iM16K and S22 hollow glass microspheres. It should be noted that while the S22 particles have a much lower effective permittivity than the iM16K particles their isostatic crush strength is also much lower.

Particle iM16K S22

Gas Volume Fraction (%) 80 95

Table 2. Bruggeman EMA for HGS Mean wall Mean diameter 𝜺𝑯𝑮𝑺 𝒆𝒇𝒇 thickness (m) (Bruggeman) (m) 16 0.55 1.4 33 0.30 1.1

Loss tangent (Bruggeman) 0.005 0.001

3.2 Effective Medium Approximations for Polymer/HGS Composites

𝑐𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑒 𝜀𝑒𝑓𝑓

= 𝜀𝑝𝑜𝑙𝑦𝑚𝑒𝑟 + 3𝑓

𝐻𝐺𝑆

𝐻𝐺𝑆 𝜀𝑒𝑓𝑓 − 𝜀𝑝𝑜𝑙𝑦𝑚𝑒𝑟

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Using a Maxwell-Garnett mixture formula for spherical inclusions [29] the effective permittivity of the low-K composite filament is determined using 𝐻𝐺𝑆 𝐻𝐺𝑆 𝜀𝑒𝑓𝑓 + 2𝜀𝑝𝑜𝑙𝑦𝑚𝑒𝑟 − 𝑓𝐻𝐺𝑆 (𝜀𝑒𝑓𝑓 − 𝜀𝑝𝑜𝑙𝑦𝑚𝑒𝑟 )

(3)

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where f HGS represents the volume fill fraction of the HGS’s particles, εpolymer is the permittivity of 𝐻𝐺𝑆 the base polymer and 𝜀𝑒𝑓𝑓 denotes the effective permittivity of the HGS particles calculated using Eq. (1).

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In Figure 10 we plot the predicted effective permittivity of composite filaments using two different base polymers (i.e. ABS and HDPE) loaded with two different HGS particles (i.e. iM16K and S22). We expect the relative permittivity for the composite materials to decrease as the loading of HGS increases. For these calculations we measured the relative permittivity of the host materials, such as ABS with 5% mass loading of DBP and HDPE with corresponding values of εABS-DBP = 2.68 and εHDPE = 2.36 with loss tangents of tanABS-DBP = 0.003, and tanHDPE < 0.001 at the frequencies of interest (up to 40 GHz). These values coincide with published results found in previous works [18, 31] but also show that small additions of DBP in ABS have negligible effect on the complex dielectric properties in this frequency range. Investigators acknowledge that not all ABS polymer contains the same relative compositions, and that frequency-dependent electromagnetic properties can vary between grades and manufacturers.

Figure 10 – Effective medium approximations using Maxwell-Garnett relations for Polymer/HGS composites, where the solid lines represent composites using iM16K HGS and dashed lines represent composites using S22 HGS.

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At very low-volume loadings there is little difference between the iM16K and S22 composite systems as the properties are dominated by the base polymer. However, as the volume loading increases the properties for different HGS particles begin to dominate. We wish to note that we assumed an upper volume loading of HGS particles of 50%. Using the methods described in this work, an upper limit of 50% was observed for HGS particle loadings in ABS. Volume loadings greater than 50% became increasingly brittle even with the addition of more plasticizer, and as such were unsuitable for FFF printing. However, the upper limit for HGS loading in a flexible, printable HDPE-composite has yet to be determined. Tables 3 and 4 provide a more quantitative comparison of the predicted dielectric properties for composites at various volume loadings.

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Table 3. Predicted Effective Permittivity for Polymer/HGS Composites Effective Permittivity Composite Volume Loading 0% 10% 20% 30% 40% 50% ABS/iM16K 2.68 2.53 2.39 2.25 2.12 1.99 ABS/S22 2.68 2.49 2.30 2.13 1.96 1.80 HDPE/iM16K 2.36 2.26 2.15 2.05 1.95 1.85 HDPE/S22 2.36 2.22 2.07 1.93 1.79 1.67

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Table 4. Predicted Effective Loss Tangent for Polymer/HGS Composites Effective Loss Tangent Composite Volume 0% 10% 20% 30% 40% 50% Loading ABS/iM16K 0.0035 0.0036 0.0036 0.0036 0.0037 0.0034 ABS/S22 0.0033 0.0031 0.0030 0.0028 0.0026 HDPE/iM16K 0.0004 0.0007 0.0010 0.0014 0.0018 >0.0001 HDPE/S22 0.0001 0.0002 0.0003 0.0003 0.0004

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As the volume loading of iM16K HGS increases in the ABS-composite system, we predict that the loss tangent should marginally increase at high loading. In the S22-ABS composite system, we predict that the loss tangent should slightly decrease at high loading. These changes should be relatively small, as the predicted loss tangents for the HGS particles are similar to measured values for ABS-DBP at these frequencies. It should be noted that for the HDPE-composite system, as the volume fraction of HGS increases, the loss tangent is expected to slightly increase for both HGScomposite systems. This is due to the very small loss tangent of the base HDPE polymer (<0.001) compared to the HGS particles.

4. Results and Discussion In this section we provide experimental characterization results of low-K printed samples including microscopy, rheology and electromagnetic measurements.

4.1 Microscopy

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Using a scanning electron microscope images, presented in Figure 11, were taken of ABS/iM16K filament cross sections. In these images, both low-loading (left, 10% vol.) and high-loading (right, 40% vol.) are shown with mostly intact spheres between 10 – 30 μm.

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Figure 11 – SEM images of the ABS/iM16K composite filament showing mostly intact HGS in both a 10% volume loading system (left) and a 40% volume loading system (right) with a corresponding scale bar of 50 µm.

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Images for the ABS/S22 filament cross sections are shown in Figure 12. These images showing both low particle loading (left, 10% vol.) and high particle loading (right, 30% vol.). Unlike the iM16K HGS, the S22 composite images reveal mostly broken spheres. In these images, it is very difficult to even determine the diameters of intact spheres.

Figure 12 – SEM images of the ABS/S22 composite filament showing mostly broken HGS in both a 10% volume loading system (left) and a 20% volume loading system (right) with a corresponding scale bar of 50 µm.

Lastly, SEM images of the HDPE/iM16K filament cross sections are shown in Figure 13. In these images, relatively high-loadings (right, 30% vol., and left, 50% vol.) are shown. Similarly, to the ABS/iM16K composite, there is a high degree of intact HGS.

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Figure 13 – SEM images of the HDPE/iM16K composite filament showing mostly intact HGS in both a 30% volume loading system (left) and a 50% volume loading system (right) with a corresponding scale bar of 50 µm.

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These results are a clear indication that the thin walled S22 particles, while attractive from an electromagnetic perspective, do not have enough mechanical rigidity to survive the extrusion process.

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4.2 Rheology of Composite Samples

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Rheological measurements were performed to gauge the influence of the incorporated micronsized particles and the plasticizer on the flexibility of the resulting composite filaments. This information was critical in defining the upper particle volume threshold for 3D printing applications. In Figure 14 the effect of increased particle loading on the storage modulus (Gʹ) of ABS is shown. As plasticizer is introduced into the system, the storage modulus of the composite decreases as the shear rate increases, indicating more fluid-like behavior. However, with increasing particle loading there is an increase in the Gʹ. An increase in the Gʹ indicates a higher mechanical rigidity, or solid-like behavior, of the composite system.

Figure 14 – Storage modulus of ABS and ABS-composites. There is a steep increase in G’ when going from the 30 to 40 vol% sample, indicating solid-like behavior that makes printing more difficult.

This behavior is apparent in the trend shown in Figure 15 where the complex viscosity (η*) increases with increasing particle volume fraction. Shear thinning behavior is noted as η* decreases with increasing angular frequency. Through application of the Cox-Merz rule (Eq. 4) [32] this complex viscosity trend can be related to the steady state shear viscosity. By relating the steady state shear viscosity to the complex viscosity the material’s response to shear (print speed) can be anticipated during the extrusion process. 𝜂(𝛾)̇ = 𝜂(𝜔)

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Figure 15 – Complex viscosity of the ABS system. With the introduction of plasticizer, the viscosity of the composite drops below that of the base ABS. Even modest loadings (HGS up to 20% vol.) match the viscosity of base ABS. Loading above 20% leads to increased viscosity, with a large jump between the 30% and 40% vol. composite. This phenomena may be a result of the lack of G’/G’’ crossover in the 40 vol% sample indicating that the sample would relax, or exhibit fluid like behavior, only over very long time scales.

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As noted previously, a plasticizer was added in preparing the ABS-composite system to aid in the printability and to increase the maximum particle loading. Generally, plasticizers are lowmolecular weight polymers that increases the spacing between polymer chains. This effectively increases the flexibility of the composite by lowering the steric hindrance and interactions between polymer chains. This is demonstrated by the lower volume fraction samples (10% and 20% vol.) possessing a lower viscosity than the pure ABS system at elevated angular frequencies that resemble printing conditions. For the HDPE-composite system without plasticizer, we observe in Figure 16 a lower complex viscosity than all cases using the ABS-composite system. This is an indication that the upper limit of HGS loading into HDPE has not yet been achieved.

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Figure 16 – Complex viscosity of the HDPE system. The viscosity of the composite increases with introduction of HGS. At the highest loading, 50% vol., this material exhibits a lower storage modulus than the ABS-composite, indicating that the upper limit of HGS loading into HDPE has not been achieved.

4.3 Radio Frequency (K-Ka Band) Evaluation of Printed Composite Materials

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To measure the dielectric properties of the printed plate samples the complex transmission coefficient (S21) was measured using a free-space focused beam system between 18 – 40 GHz. The relative permittivity of the samples was then calculated from the complex transmission data using rigorous coupled wave analysis methods with results for the ABS-iM16K system shown in Figure 17.

Figure 17 – Relative permittivity of printed ABS-iM16K composite plates between 18 – 40 GHz with HGS volume loading between 0 – 40%. Also included are error bars denoting minimum and maximum measured values of multiple samples at corresponding frequency.

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We also note that the permittivity of the samples did not vary much with frequency over the band of the measurement, nor did the permittivity vary much between samples within the same sample set. The measured mean relative permittivity and effective medium approximations using Maxwell-Garnett for the respective composite systems are shown in Figure 18 as points and lines, respectively. These values are further summarized in Tables 5 and 6 for the ABS-DBP and HDPE systems, respectively.

Figure 18 – Mean relative permittivity of printed polymer/HGS composite plates (points) between 18 – 40 GHz compared to the associated effective medium approximations of each composite (solid lines).

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The iM16K particles as filler reduce the permittivity for ABS or HDPE as the host matrix for all volume loadings. The S22 particles, on the other hand, initially reduce the permittivity, but as the volume loading increases, the permittivity begins to also increase. This deviation from the effective medium prediction is attributed to the fragile microspheres breaking during the compounding and printing processes. As the spheres break, the number of sodium borosilicate glass-rich sites increase, effectively increasing the permittivity of the composite. As the volume loading of S22 HGS increases, so too does the likelihood of particle-particle interaction between S22 HGS, resulting in more broken spheres. Table 5. Measured Mean Dielectric Properties of Printed ABS-HGS Samples between 18 – 40 GHz Composite

Relative Permittivity Loss Tangent Relative Permittivity Loss Tangent

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ABS/iM16K ABS/S22

0% 2.68 ± 0.04 0.003 2.68 ± 0.04 0.003

Volume Loading of HGS (%) 10% 20% 30% 2.55 ± 0.02 2.41 ± 0.01 2.29 ± 0.03 0.004 0.003 0.004 2.46 ± 0.02 2.46 ± 0.03 2.57 ± 0.03 0.003 0.003 0.003

40% 2.14 ± 0.03 0.005 N/A

Table 6. Measured Mean Dielectric Properties of Printed HDPE-HGS Samples between 18 – 40 GHz Volume Loading of HGS (%) 0% 30% 40% 50% Relative Permittivity 2.36 ±0.02 2.05 ±0.02 1.96 ±0.01 1.89 ±0.03 HDPE/iM16K Composite

Loss Tangent

<0.001

0.003

0.005

0.005

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In comparing the measured permittivity and loss tangents against the values predicted using our effective media models we note that for the ABS/iM16K system, while close to the effective medium predictions, are slightly higher. While we are not entirely certain why this deviation occurs we believe it can be attributed to the contribution of very small, higher-permittivity HGS as denoted by laser diffraction particle size analysis. The HDPE/iM16K composite showed similar behavior with a slightly higher permittivity and loss tangents than predicted. These dielectric properties can likely be further reduced by separating out these much smaller, higher-permittivity particles from the additives prior to compounding. Additionally, while the iM16K particles have a very high isostatic crush strength, there is the possibility of some broken spheres within the composite, although at a much lower rate than the S22 HGS. The dielectric properties of these composite materials may be further reduced by utilizing an intermediate grade HGS between S22 and iM16K that contains both desirable electromagnetic properties and structural qualities that can survive processing conditions.

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5. Discussion and Conclusions

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Low-permittivity and low dielectric loss tangent composite materials have been designed as flexible feedstock for use in FFF printing. The introduction of low permittivity hollow glass spheres into a polymer medium effectively reduces the permittivity of the composite. This permittivity can be predicted using effective medium approximations such as Maxwell-Garnett and Bruggeman relations. These materials were compounded and extruded into flexible filament feedstock for 3D printers, with samples printed to characterize the complex permittivity between 18 – 40 GHz. In the ABS-iM16k system, the lowest ideal permittivity achieved was close to 2.14 with dielectric loss tangents ≤ 0.005. Dielectric constants as low as 1.89 and loss tangents ≤ 0.005 were achieved using an HDPE-iM16K composite material. Rheological measurements show that the volume loading of HDPE can still be increased beyond 50%, as it does not exhibit as strong solid-like behavior as the ABS-composite. It was determined that the lowest permittivity for these materials has yet to be achieved for several reasons: 1) the loading of HGS into HDPE can be increased, 2) sieving of HGS to remove very small particles (i.e. particle diameter < 10μm) with high permittivity, and 3) the inclusion of HGS with optimal electromagnetic properties between S22 and iM16K with mechanical properties to survive processing conditions can be used. All of these actions should produce a flexible filament material suitable for FFF printing with dielectric constants well below 2.0 with low dielectric loss tangents at RF and microwave frequencies.

6. Acknowledgement

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This work was supported by the Office of Naval Research.

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