Porous Low‐Loss Silica–PMMA Dielectric Nanocomposite for High‐Frequency Bullet Lens Applications

Several devices of the future generation wireless telecommunication technologies that use bands in THz frequencies for data transmission need low‐loss and low‐permittivity materials to enable ideal conditions for the propagation of electromagnetic waves. Herein, a lightweight dielectric bullet‐shaped lens operating in the frequency range of 110–170 GHz is demonstrated to collimate electromagnetic waves, thus increasing the intensity of the electric field. The material of the lens is based on a composite of silica nanoshells and poly(methylmethacrylate) made by the impregnation of the nanoshells with the polymer followed by hot pressing in a mold. As the polymer acts only as an adhesive between the hollow nanospheres without filling the inner cavity of the shells and their interparticle spaces, the composite is highly porous (67%) and has low dielectric permittivity and loss tangent (1.5 and 4 × 10−3, respectively, below 200 GHz). The size of the collimated beam and the increase of the corresponding field strength are measured to vary from 2.2 to 1.2 mm and from 17.2 to 8.98 dB depending on the frequency of the waves (110–170 GHz).


Introduction
Of the sixth generation (6G) telecommunication technologies, Internet of Things (IoT) is one of the most attractive features that allows fully automated human-free control and operation of connected devices, to create smart homes, institutes, factories, transportation, and cities. IoT may be assisted by artificial intelligence (AI) to increase the efficiency of the networks by providing complex problem-solving ability. Applications, which need real-time data processing, will be allowed by mobility-enhanced edge computing (MEEC) which is the modified version of cloud computing, bringing services closer to the end user, having quicker response time. The operation of battery-less smart devices will be ensured by wireless information and energy transfer (WIET) and unmanned aerial vehicles (UAV)/drones will be integrated into 6G to provide cellular connectivity and high data rate. Clearly, the implementation of these technologies requires enormous number of devices communicating wirelessly, thus high data transfer rate needs to be guaranteed. As the currently used frequency bands cannot transfer the amount of data demanded by these technologies, moving to bands of shorter wavelengths (0.1-10 THz) will increase the capacity by 1000 times in 6G in comparison to the fifth generation (5G) wireless telecommunication technology. Furthermore, applications with real-time response demand improved reliability (99.9%) and high data transmission rate (%1 TB s À1 ) with ultralow latency (1 ms), as expected in 6G. [1][2][3][4][5] As the path loss of electromagnetic (EM) waves increases with the frequency, antennas operating at THz frequency band need to have especially high gain and/or shall be equipped with lenses to ensure sufficiently high intensities. The operation of lenses is based on either diffraction (e.g., zone plate lenses) [6,7] or refraction of the EM waves. Of the latter, we may distinguish heterogeneous and homogeneous lenses depending on whether the refraction of the waves occurs within the bulk or on the surface of the dielectric lens. [8,9] Regardless of the type of the lens, the material it is made of is expected to have low loss (tan δ) to avoid signal attenuation. [10] Lens materials of high permittivity (ε r ) allow for relatively thin lens designs with small surface curvatures but necessitate the use of gradient structures in the proximity of the surface to minimize reflection losses. The production of such gradient structures is not trivial, thus making heterogeneous lenses less attractive than their homogeneous counterparts based on low-permittivity materials. [11] Among dielectrics, silica has good electromagnetic properties (ε r = 3.8 and tan δ = 0.005 at 300 GHz) and thus it is a popular choice of structural materials in high-frequency applications. Lowering ε r and tan δ of SiO 2 can be achieved by 1) partially replacing easy-to-polarize Si─O bonds with Si─F bonds (e.g., by F doping); [12,13] 2) introducing voids (e.g., pores filled DOI: 10.1002/adpr.202200208 Several devices of the future generation wireless telecommunication technologies that use bands in THz frequencies for data transmission need low-loss and lowpermittivity materials to enable ideal conditions for the propagation of electromagnetic waves. Herein, a lightweight dielectric bullet-shaped lens operating in the frequency range of 110-170 GHz is demonstrated to collimate electromagnetic waves, thus increasing the intensity of the electric field. The material of the lens is based on a composite of silica nanoshells and poly(methylmethacrylate) made by the impregnation of the nanoshells with the polymer followed by hot pressing in a mold. As the polymer acts only as an adhesive between the hollow nanospheres without filling the inner cavity of the shells and their interparticle spaces, the composite is highly porous (67%) and has low dielectric permittivity and loss tangent (1.5 and 4 Â 10 À3 , respectively, below 200 GHz). The size of the collimated beam and the increase of the corresponding field strength are measured to vary from 2.2 to 1.2 mm and from 17.2 to 8.98 dB depending on the frequency of the waves (110-170 GHz).
In this work, we build on the latter two strategies by applying hollow silica nanospheres (i.e., nanoshells) that we physically bind together with a low-permittivity and low-loss (ε r = 2.67 and tan δ = 0.027 at 500 GHz) [20] poly(methylmethacrylate) phase having a small volume fraction in the composite without forming a continuous matrix in the interparticle space. With this effort, not only the low permittivity and loss are ensured but also the mechanical integrity and option for postprocessing of the composite are achieved. To demonstrate the feasibility of the as-made material for high-frequency applications, the composite is hot-pressed in a mold to form a bullet-shaped lens operating at a central frequency of 140 GHz.

Synthesis of Silica Nanoshells
Hollow silica nanoshells were synthetized by template-assisted Stöber process, similar to that as reported earlier. [21] In short, first, polymer template spheres were synthetized by emulsion polymerization of styrene monomers using potassium persulfate as initiator. Next, the polymer spheres were covered with a thin layer of silica by polycondensation of tetraethyl orthosilicate in the presence of ammonium hydroxide. Finally, the polymer core of the coated particles was burned out resulting in the silica nanoshell product.

Preparation of the Porous Silica-PMMA Composite
Microspheres of PMMA were dissolved in 2-(2-butoxyethoxy) ethyl acetate (14 wt%), by stirring the mixture at 90°C for 3 h, and the solution was cooled down to room temperature. In the next step, silica nanoshells were mixed with acetone in 1:1 volume ratio and added to the polymer solution to obtain a mixture with a composition of V silica shells :V acetone :V PMMA solution = 1:1:0.7. This mixture was then poured into the cavity of a polyvinylideneflouide ring (12 mm in inner diameter and 2 mm in thickness) placed on a plate, which served as a mold for a producing a slab of the composite. The filled ring was then covered with a perforated release foil (silicon-coated polyethylene terephthalate film), a wipe (nonwoven polyester/cellulose), and then with a glass slide. The structure was placed in a box oven, to evaporate the solvents (50°C for 2 h followed by 110°C for overnight). After drying, a small aliquot (100-150 μL) of additional PMMA solution was dropped on the slabs and dried at 110°C for %12 h, which was repeated 8 times to provide sufficient amount of PMMA that binds the nanoshells together. The final composition of the composite was calculated to be 79.8 wt% PMMA and 20.2 wt% silica

Preparation of PMMA Reference Samples for Dielectric Measurements
PMMA reference samples were obtained by pouring 14 wt% polymer solution into a mold, similar to that of used for the composite preparation and placed into a box oven for overnight at 110°C to evaporate the solvent. Droplets of the polymer solution were added onto the slabs followed by evaporation, until the solid polymer filled the mold, completely.

Hot Pressing of the Dielectric Lens
To prepare the dielectric lens (Figure 1), 0.312 g of silica-PMMA composite was broken into small (%0.5 mm) pieces by a spatula and mixed with 0.2 mL of 2-(2-butoxyethoxy)ethyl acetate. The mixture was then transferred into a two-piece bullet-shaped mold and pressed (P/O/WEBER PW 20 HS Hotpress, 5 kPa, 200°C, 10 min). After releasing the pressure and cooling, the sample was placed in an oven to dry completely at 200°C for overnight.

Characterization
Field emission scanning electron microscopy (FESEM, Zeiss Ultra Plus) and transmission electron microscopy (TEM Jeol Table 1. Different silica-based materials and their relative dielectric permittivity.

Material
Synthesis method ε r References Silica -3.9-4.5 [12] Fluorosilicate glass F-doping 3.6-3.8 [12] Fluorosilicate glass F-doping 2.8 [13] Porous silica Template-assisted synthesis 1.9 [14] Porous silica CVD and thermal decomposition 2.2 [15] Fluorinated silica-PI composite Chemical decomposition and grafting 2.6 [16] Silica-PI composite Template-assisted synthesis and thermal polymerization 2.1 [17] Porous silica-PMMA composite Template-assisted synthesis and thermal polymerization 2.7 [18] PTFE-silica composite Sintering 1.9 [19] www.advancedsciencenews.com www.adpr-journal.com Jem-2200FS) were used to analyze the morphology and microstructure of the synthetized materials. To determine the size distribution of the obtained polymer template spheres, silica-coated polymer spheres, and hollow silica nanoshells, Fiji ImageJ software was used to analyze FESEM and TEM images of 100 particles of each. From dimension and weight measurements, the density and porosity of the composite slabs were calculated. The surface of the hot-pressed dielectric lens was characterized with an optical profilometer (Bruker Contour GT-K) to evaluate the surface roughness (root mean square height). Dielectric properties of the PMMA reference and silica-PMMA composite slabs were determined by THz spectroscopy (TeraPulse 4000) at frequency range of 0.1-1.5 THz, measuring air at the beginning for reference (90 dB dynamic range at the peak, 100 ps optical delay extent, 200 ps s À1 sweep speed, 50-fold averaging, high-resolution mode with 10 ps prescan extent). The real and imaginary parts of dielectric permittivity were calculated from the Fourier transformed amplitude-time data transmitted through the samples. The beam was limited by a metallic aperture of 11 mm in diameter. The effective permittivity of the porous composites was calculated by Maxwell-Garnett effective medium approximation model [22] where ε MG is the effective permittivity, ε h is the relative permittivity of the host medium, ε i is the relative permittivity of inclusions, and f is the volume filling factor. The bullet-shaped porous composite lens was mounted on a 3-axes transfer stage between two fixed frequency extenders (WR 6.5 (110-170 GHz), Virginia diodes, USA) and characterized using a network analyzer (N5242B PNA-X, Keysight, USA).

Results and Discussion
The spherical polystyrene templates (Figure 2a) synthetized by emulsion polymerization have an average diameter of   937 AE 284 nm. After the polycondensation reaction, the polymer spheres are covered with a thin silica layer, creating a core-shell structure with raspberry-like porous surface (Figure 2b) having an average diameter of 988 AE 62 nm. After the organic core is burned off at 550°C, hollow porous silica spheres (Figure 2c) with average diameter of 880 AE 141 nm are obtained. To prepare dielectric films (Figure 2f ) with sufficient mechanical stability, hollow silica nanospheres are mixed with acetone and dissolved PMMA, the mixture is poured into a mold, let dry at elevated temperature, and got additional droplets of PMMA solution to obtain a composition of 79.8 wt% PMMA and 20.2 wt% silica, having diameter and thickness of 12.0 and 1.7 mm, respectively. According to electron microscopy analysis (Figure 2d,e), the inner cavity of the hollow silica spheres remained to be unfilled with the polymer. In addition, the interparticle space is found to be mostly empty, i.e., the polymer phase of the composite acts only as a thin adhesive between the nanoshells, which explains the measured low density (0.44 g cm À3 ) and high porosity (67%) of the composite. The dielectric properties of silica-PMMA composite and PMMA polymer reference slabs are measured at frequency range of 0.1-1.5 THz using THz spectroscopy ( Figure 3). The composite has low relative part of permittivity, ε 0 r % 1.5 at the whole measured frequency range, in good agreement with the calculated effective permittivity (1.4). The loss factor, tanδ, is 4.0 Â 10 À3 at 140 GHz and increases with the frequency as it is expected. The improvements of dielectric properties of silica-PMMA samples compared to those of PMMA slabs are reasonable, considering the porosity of the composite samples. The lower tan δ of the composite is also a result of the presence of silica, having smaller loss than that of the polymer.
Although additional PMMA added to the composite would enhance the mechanical strength, it would result in porosity reduction and consequently increased dielectric permittivity. As calculated by the Maxwell-Garnett approximation, an increased concentration of PMMA by 5 and 10 wt% would decrease the porosity by 14% and 33%, resulting in higher effective permittivity values of 1.7 and 1.9, respectively.
As PMMA is a thermoplastic, it is anticipated that the silica-PMMA composite is feasible for further processing using molding, hot pressing, or other similar methods to create lens with, e.g., bullet shape. At mm-wave frequency bands, different commercial and noncommercial lens materials are applied such as polystyrene, polymethacrylate, acrylonitrile butadiene styrene, or polyetherimide, developed by different ways, having various dielectric properties ( Table 2). The dielectric properties, fabrication complexity, and size of porous silica-PMMA composite lens are better or comparable than those listed in Table 2.
To form bullet-shaped lens, we crashed the composite slabs into grains of %500 μm size and fused those again by hot pressing in a mold (Figure 4a). Dimension and weight measurements revealed that the hot pressing process had no effect on the porosity of the composite. The surface roughness (root mean square height) of the hot-pressed lens is %4.8 μm, according to measurement carried out by an optical profilometer (Figure 4b).  To assess the focusing behavior of the lens, the scattering parameter (S 21 ) of the transmitted beam was measured. The lens was placed on a 3-axes transfer stage, in the optimal position at the optical path (x direction) between the fixed transmitter and receiver, and was moved in y and z directions by 0.25 mm steps to map an area of 8 Â 7 mm of radiative field as shown in Figure 5a. The shape and the size of the measured focal spot slightly changed with frequency (Figure 5b,c). At 110 GHz, the spot is oval and has two sidelobes in the harmonic pattern, whereas at 140 and 170 GHz the focal spots are round and have  www.advancedsciencenews.com www.adpr-journal.com ring-shaped harmonics. Chromatic aberration (along with possible spherical aberration) as well as the frequency dependence of the loss factor can be reasons for the variation of the focal spot with the frequency. Furthermore, as the physical size of the lens is comparable to the wavelengths, even a small change of the frequency may result in different diffraction effects. [23] It is also important to note that the measurement was conducted in the Fresnel region, thus the frequency dependence of the field distribution and intensities can be significant. The measured maximum of S 21 had a mean variation of only 2.1 dB over the 110-170 GHz ( Figure S2, Supporting Information) with a maximum increase of the intensity of the E-field of 17.2 dB measured at 110 GHz (Figure 5d and S1, Supporting Information).

Conclusion
Porous composites of SiO 2 nanoshells and PMMA having low dielectric permittivity (ε 0 r = 1.5 at 140 GHz) and loss factor (tan δ = 4 Â 10 À3 at 140 GHz) were synthetized and hot-pressed to form a bullet-shaped lens for focusing electromagnetic waves above 100 GHz. According to the measurements of scattering parameter, up to 17.2 dB increase of the field maybe achieved with the lens, indicating that the structure may find use in radiating near-field and in short range communication. [24,25] The synthesis and postprocessing of the demonstrated porous composite is scalable and can be easily modified to tune not only the intrinsic dielectric material properties but also the size and geometry of lenses, [26][27][28] making those suitable for various antenna [29][30][31][32] and imaging [33][34][35] applications near to THz frequencies.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.