Solution printable multifunctional polymer-based composites for smart electromagnetic interference shielding with tunable frequency and on–off selectivities

The advances in modern intelligent electronic systems have a pressing need for smart electromagnetic interference (EMI) shielding capabilities in a frequency-selective manner to choose which electromagnetic waves in a certain range to be blocked. Herein, we present multilayered EMI shielding composites that can provide selective on–off characteristics for specific frequency ranges across a broad spectrum. The composites are composed of outermost dielectric layers and conductive interlayers fabricated via solution printing, wherein hexagonal boron nitride (BN) and silver-coated BN particles are embedded, respectively. The EMI shielding frequency range and on–off selectivity are controllable by varying the configuration of the composite structure in terms of the BN content and the number of composite layers, providing different interstitial spaces between the fillers and interfacial dielectric properties. Furthermore, the optimal combination of these layers permits excellent combinatorial properties of EMI shielding effectiveness (32–62 dB), thermal conductivity (7.61 W/m·K), and electrical insulation (4.03 kV/mm) in the through-plane direction. The developed composites and their synthetic pathways have enormous potential for tailored material design and flexible system integration in next-generation EMI shielding technologies.


Introduction
As electronic components are miniaturized and highly integrated with the rapid development of high-performance electronics, electromagnetic interference (EMI) shielding has been highlighted in modern electronic devices, equipment, and systems. Both irradiated and radiated electromagnetic (EM) waves can lead to device malfunction and may have detrimental effects on living organisms [1][2][3]. In particular, next-generation EMI shielding materials are needed to provide smart frequency-selective capabilities, which can selectively shield or transmit incident EM waves in specified frequency ranges [4,5]. For example, the exterior surface of the installed part and assembled devices of the core control system, sensors, navigation, communication, etc. can be coated directly onsite using EMI shielding materials, which selectively block unwanted interfering EM waves and transmit them in telecommunication frequency ranges. To achieve this, the EMI shielding effectiveness (SE) of materials must be adjusted with frequency to exhibit both low/ moderate and high SE in different frequency ranges with high on-off selectivity.
Unfortunately, these unique properties of EMI shielding have rarely been reported because the EMI SE of the vast majority of materials is frequency independent. Pioneering studies have demonstrated that multilayered, segregated, and Mina Seol and Uiseok Hwang have contributed equally to this work. core-shell structures of materials can provide frequencyselective EMI shielding capability with resonance characteristics [4][5][6][7]. However, the sophisticated control of shielding frequency and high on-off selectivity is a considerably complicated challenge, as the mechanisms of these frequency-selective characteristics, such as peak shift, peak wide/narrowness, and shielding mechanism across different frequency ranges, are still obscure and require elucidation in conjunction with multiple influencing factors. Recently, we found fundamental principles of a novel composite system that could shield the selective ranges of EM wave frequency, which was ensured by the utilization of a collective combination of core-shell spheres functionalized for EM wave-absorbing and -reflecting capabilities [4,8]. The frequency-selective capability could be maximized by a specific assembly of these two types of materials, where the resonance of EM waves of a specific wavelength is triggered. In this vein, if core-shell structured fillers are incorporated in multilayered composites consisting of different types of layers, the frequency-selective properties of the resulting materials may be modified by varying the filler content and altering the combination of different composite layers. The design of fillers and the resonances of EM waves across the composite layers in the through-plane directions can allow for the selective blocking of EM waves within a given frequency range.
Due to the dense packing of the electronic components and exposure to hostile temperature cycles (e.g., 0-150 °C), thermal management has also become one of the key issues in modern electronic devices owing to the accumulation of high heat fluxes, which accelerate the aging and degradation of the material, causing device malfunction and reducing the operational lifetime [9]. The absorption of EM waves worsens the issue because these waves are dispersed as heat, which raises the temperature of the equipment [10]. Furthermore, electrical insulation is often required to prevent electrical shock or electronic crosstalk by isolating the components [11][12][13]. However, it should be noted that materials used for EMI shielding or thermal dissipation are electrically conductive (> 1 S/m) [14,15]. Consequently, it is essential to develop a novel multifunctional material system possessing excellent EMI shielding and heat dissipation properties with an electrically nonconductive nature.
Polymer-based composites containing electrically and thermally conductive fillers have been intensively researched in recent years for applications in EMI shielding and heat dissipation. These composites offer lightweight, excellent processability, low cost, and design versatility [16][17][18][19]. In this regard, metallic particles, MXene, graphene, and carbon nanotubes have gained attention for attenuating incident EM waves by reflection and absorption with their charge carriers [19][20][21][22][23], but it should be mentioned that they are not often considered dielectric in nature. In contrast, dielectric ceramic fillers, such as aluminum oxide, aluminum nitride, boron nitride, and silicon nitride, exhibit excellent heat dissipation properties, i.e., high thermal conductivities, but little EMI shielding capability [16]. Although many types of fillers with distinct properties exist, imposing multiple functionalities on a single material system remains a challenge.
In fabrication and utilization of a composite system, as the device's parts must be installed in a highly integrated manner, sometimes within a restricted space, solutionbased printing of composite inks can be quite advantageous for developing functional coatings with ease on any shape of three-dimensional complex surfaces that are printed directly onsite. Nonetheless, when polymeric materials (90-220 ppm/°C) are in contact with other materials having different thermal expansion coefficients (CTE), such as metals (4-25 ppm/°C), residual peel-off stress analysis and prediction must be performed to design the material system. This anisotropic CTE mismatch could cause severe issues such as mechanical delamination and permanent deformation. It is reasonable to consider that adjusting the content of various types of fillers would provide the CTE controllability of composite materials combined with different functionalities originating from the fillers. However, there is no exhaustive combinatorial experimental report on this issue.
In this study, we investigated a multilayered composite system providing excellent combinatorial properties of tunable frequency-selective EMI shielding, thermal dissipation, and electrical insulation. The composite layers were fabricated using a facile solution-printing method, followed by thermal treatment and compression to produce the multilayered composites, wherein plate-shaped hexagonal boron nitride (BN) and silver-coated BN particles (Ag@BN) were incorporated as fillers as they were considered to provide optimal rheological properties of composite inks and to realize multifunctionality with given dielectric properties. The EMI SE and on-off selectivity could be controlled as a function of frequency by regulating the BN content and configuration of the composite layers, which were interpreted in terms of the dielectric properties and composite structures in a combined manner. Furthermore, the thermomechanical stability, through-plane thermal conductivity, and breakdown strength of the multilayered composites were investigated thoroughly.

Preparation of Ag@BN particles
Electroless plating of silver nanoparticles (Ag NPs) onto BN particles was performed to produce Ag@BN particles. Silver nitrate (0.8 g) was dissolved in 20 mL of deionized water, followed by the addition of BN powder (2.0 g). The dispersion was then stirred at room temperature for 20 min. A reduction bath was prepared by mixing glucose (1.6 g), tartaric acid (1.0 g), ethanol (10 mL), and deionized water (70 mL). Sodium hydroxide (1.0 g) was then added, followed by the dropwise addition of ammonium hydroxide solution (10 mL). The resulting BN dispersion was added dropwise to a reduction bath under vigorous stirring. After 50 min of reaction at room temperature, the product was collected in the form of a wet cake by filtration. The cake was washed repeatedly with deionized water till neutral pH was achieved, and then dried at 40 °C for 12 h.

Preparation of BN and Ag@BN composite inks
As a binder for the BN and Ag@BN inks, an NMP/PEI solution (15 wt.% PEI) was utilized. Typically, PEI pellets (35.18 g) and NMP (200 g) were charged in a 500 mL fournecked reaction vessel equipped with a mechanical stirrer, thermometer, reflux condenser, and nitrogen inlet. The mixture was heated to 90 °C and gently stirred for 4 h until the PEI pellets were entirely dissolved. Then, the BN and Ag@ BN particles were dispersed into the NMP/PEI solution in various volume fractions using a paste mixer three times for 1 min each, yielding BN and Ag@BN inks, which were labeled BN00 ink and Ag80 ink, respectively (00 = 60-80, corresponding to the volume fractions of the BN and Ag@ BN particles in the resulting composites, respectively).

Fabrication of Ag@BN/BN/PEI multilayered composites
The inks were printed using a 3-axis dispensing system (E2V, Nordson EFD, USA), wherein each ink was extruded under pneumatic pressure. The pressure was controlled using an Ultimus IV pressure box (Nordson EFD, USA). The inks were printed at the optimal nozzle speed on glass substrates with a line spacing of 1 mm and a nozzle inner diameter of 0.41 mm. After printing, the samples were dried at 60 °C for 20 h, followed by 150 °C for 6 h to evaporate the NMP solvent, and then detached from the glass substrates [24]. The single-layered composites containing BN and Ag@BN particles were labeled BN00 and Ag80, respectively (00 = 60-80, corresponding to the volume fractions of the BN and Ag@BN particles in the composites, respectively). Typically, to fabricate the Ag@BN/BN/PEI multilayered composites, the single-layered composites were alternately stacked in the order of BN00, Ag80, and BN00, followed by compression in a hydraulic press at 3 MPa and 160 °C for 30 min. The composites with several layers were designated as xL-AgBN00, where "x" represents the number of stacked layers. For instance, 5L-AgBN60 indicates that the composite was fabricated by stacking the single-layered composites in the order of BN60, Ag80, BN60, Ag80, and BN60.

Characterization
The size, structure, and elemental composition of the samples were analyzed using field-emission scanning electron microscopy (FE-SEM) (JSM 7401F, JEOL, Japan). The crystal structures of the BN and Ag@BN particles were analyzed using X-ray diffraction (XRD) (D8 ADVANCE, Bruker, Germany) in the 2θ range of 10-80°, at a scanning speed of 3°/min. The chemical components and surface properties of the particles were analyzed using X-ray photoelectron spectroscopy (XPS) (ESCALAB 250, Thermo Fisher Scientific, USA). The rheological properties of the inks were determined at room temperature using a rheometer (ARES-G2, TA Instruments, USA) with coneand-plate geometry (gap: 500 μm, disk diameter: 50 mm, cone angle: 0.04 rad). The flow sweep experiments were conducted at shear rates of 10 0 -10 3 s −1 . Thermogravimetric analysis (TGA) (Q50, TA Instruments, USA) was performed under nitrogen from room temperature up to 450 °C (heating rate = 10 °C/min). The CTE of the composites was determined at temperature ranging from ambient temperature to 275 °C (heating rate = 5 °C/min) using a thermomechanical analyzer (TMA) (TMA6100, Seiko, Japan) in accordance with ASTM E831. Using a Precision LCR Meter (E4980A, Agilent, USA), the dielectric properties of composites were measured as a function of frequency from 100 Hz to 1 MHz. The electrical resistivities of the composites were measured using a fourpoint probe instrument (CMT-SR2000N, AIT Co., Ltd., Korea). The EMI SE of each composite was calculated from the S-parameter measured in the frequency range of 8.2-12.4 GHz (X-band) using a vector network analyzer (E5071C, Keysight Technologies, UK). The thermal diffusivities of the composites were measured using the laser flash technique (LFA 447, Netzsch, Germany) and used to calculate the thermal conductivities. The zeta potentials of the BN particles were measured by laser Doppler electrophoresis using a Zetasizer Nano-ZS (Malvern, UK).

Results and discussion
Ceramic fillers impart high thermal conductivity and electrical insulation to composites, whereas metallic fillers provide shielding from the incident EM waves. To integrate these properties, BN and Ag@BN particles were strategically selected as fillers for the electrically insulating and conducting composite layers, respectively, which were then combined to form multilayered composites to provide frequency-selective EMI shielding. Figure 1 depicts the fabrication process of the Ag@BN/BN/PEI multilayered composites, including the function of each composite layer. The Ag@BN particles were initially prepared via the electroless plating of Ag NPs onto BN particles (Fig. 1a). When BN particles were dispersed in a silver nitrate solution, Ag + ions were adsorbed on the negatively charged BN particle surface by electrostatic attraction (as confirmed by zeta potential analysis, Fig. S1). Then, Ag NPs were generated on the surface owing to reduction by glucose.
Different volume fractions of BN and Ag@BN particles were dispersed into NMP/PEI solutions to produce homogenous composite inks with varying viscosities (BN00 inks and Ag80 ink, respectively) (Fig. 1b). After printing, the samples were thermally treated to eliminate the solvent and produce single-layered composites (BN00 and Ag80) [24]. The fabricated composites were easily detachable from the substrate. The BN00 and Ag80 composites were then alternately stacked and compressed to yield 3-layered and 5-layered Ag@BN/BN/PEI composites (denoted as 3L-AgBN00 and 5L-AgBN00, respectively). The crosssectional digital images of the composites with varying numbers of layers are shown in Fig. 1b. For the EMI SE measurements, all single-layered composites had identical dimensions (40 mm × 40 mm × 0.5 mm) to accommodate within the specimen container (Fig. S2). The thickness of the 3-and 5-layered composites, after stacking and compression, was ~ 1.4 and ~ 2.3 mm, respectively.
In the through-plane direction, the outermost layers comprising BN particles (white hexagons) were insulating layers, isolating the conductive Ag@BN particles (white hexagons with green dots) containing an electrically conductive interlayer. All layers exhibited high thermal conductivity in the through-plane direction (red arrows), and the alternately stacked layers with different electrical conductivities and dielectric properties exhibited unique Fig. 1 Schematic of the fabrication process of (a) Ag@BN particles and (b) Ag@BN/BN/PEI multilayered composites having multifunctionality of frequency-selective EMI shielding, electrical insulation, and heat dissipation frequency-selective EMI shielding properties resulting from the structural resonances of core-shell-structured Ag@BN particles and multilayer-structured composites [4][5][6][7]. Owing to the existence of ether units, the PEI matrix was also considered to possess great thermal and mechanical stability and superior processability [24][25][26].
The formation of the Ag NPs was further confirmed by XPS analysis (Fig. 2b). The B1s and N1s binding energies of BN and Ag@BN particles were 190.1 and 398.1 eV, respectively. In addition to the characteristic peaks of BN, the Ag@BN XPS spectrum revealed the Ag3d 5/2 and Ag3d 3/2 peaks at 368.5 and 374.5 eV, respectively (inset of Fig. 2b). Both peaks changed to higher binding energies (by 0.6 eV) compared to the reported values of Ag3d 5/2 (367.9 eV) and Ag3d 3/2 (373.9 eV), demonstrating interactions between Ag and BN [28].
To determine the effect of plating time, the tap densities of Ag@BN samples with varied plating times were evaluated (Fig. 2c). The tap density increased from 1.78 to 2.28 g/ cm 3 as the plating time increased from 0 to 40 min due to the high density of silver (10.49 g/cm 3 ) and remained constant thereafter. This indicates that the BN particles were completely coated with Ag NPs within the critical plating time of 40 min. Therefore, 50 min-plated Ag@BN particles were utilized since they were considered to have a continuous silver coating and thus could facilitate to form electrically conductive channels when applied to composites [19]. Based on the tap densities, the silver weight fraction in Ag@BN particles was 26.4 wt.% Figure 2d-g display FE-SEM images of BN and Ag@ BN particles with plating durations of 0, 10, 30, and 50 min at different magnifications, respectively. The BN particles possessed flat and layered structures with a smooth surface (Fig. 2d), but the surface of Ag@BN particles became increasingly rough as plating time increased, indicating the formation of Ag NPs (Fig. 2e-g). Compared to shorter plating times of 10 and 30 min (Fig. 2e, f, respectively), it was discovered that the plating time for 50 min produced a uniform and continuous silver coating (Fig. 2g) [29]. With increasing plating time, Ag NPs between 50 and 200 nm in size were gradually generated and fused to create a continuous silver coating on the surface of BN particles [30]. The presence of silver caused the white BN powder (Fig. S3a) to turn brown (Fig. S3b) following silver plating. Figures 3a and S4 compare the digital images of the NMP/PEI solution and BN00 inks extruded from the nozzle under different pneumatic pressures. Because the ink viscosity increased with increasing BN content, requiring a relatively high pressure, various pressures were chosen Fig. 3 a Digital images of BN00 inks printed under pneumatic pressures and b digital images of the corresponding contact angles. c Viscosities and d shear stresses of NMP/PEI solution, BN00 inks, and Ag80 ink as a function of shear rate. e Yield stresses of NMP/PEI solution, BN00 inks, and Ag80 ink as a function of particle content. f TGA curves of BN80 ink and BN80 composite. g Dimensional change of PEI, BN80, and Ag80 films as a function of temperature for optimal printing circumstances. The NMP/PEI solution (Fig. S4a) and BN60, BN70, and BN80 inks (Fig. 3a) were printed continuously and consistently at pressures of 60, 80, 100, and 150 kPa, respectively, whereas the inks exhibited distinct behaviors for their respective viscosities. Specifically, the NMP/PEI solution, BN60 ink, and BN70 ink were spread and compacted by gravity after printing, whereas the BN80 ink displayed two distinct phases: a liquid-like condition within the nozzle and a solid-like state after printing in the stacked feature [31]. When the pressure was too high (BN60 ink at 100 kPa), the ink spilled dropwise (Fig. S4b), and at a very low pressure (BN80 ink at 100 kPa), the ink could not be printed consistently by agglomeration at the end of the ink stream (Fig. S4c). The contact angles of each ink on glass substrates are illustrated in Figs. S5 and 3b. The NMP/PEI solution exhibited a low contact angle of 16.6° (Fig. S5), which can be compared to the contact angles of BN60 ink (22.3°), BN70 ink (35.0°), and BN80 ink (58.1°) (Fig. 3b). The increasing contact angle of the ink with increasing BN content was attributed to the supporting ability provided by the BN fillers, which may lead to an increase in ink viscosity [24].
Notably, ink viscosity is a critical component in determining printability and printing conditions throughout the printing process to fabricate single-layered composites. Particularly, the flow rate of ink, which is greatly influenced by its viscosity, should be regulated because the volume of the extruded ink at a given pressure might vary for different flow rates and viscosities [32]. As shown in Fig. 3c, d, the viscosity and shear stress of NMP/PEI solution, BN00 inks, and Ag80 ink were measured by varying the shear rate from 10 0 to 10 3 s −1 . The NMP/PEI solution displayed normal Newtonian fluid behavior with a shear rate-independent viscosity of 0.6 Pa·s (Fig. 3c). However, the addition of dispersed particles significantly altered the rheological properties of the NMP/PEI solution. The viscosity of composite inks increased linearly with particle loading, which was attributed to decreased interparticle distances, causing agglomeration and making the ink difficult to flow [33,34]. BN60 ink and BN70 ink displayed Newtonian fluid-like behavior, exhibiting relatively shear rate-independent viscosities ranging between 1.8-1.2 and 4.3-2.3, respectively. The viscosities of BN80 ink and Ag80 ink decreased with increasing shear rate in the ranges of 25.8-2.7 and 32.2-3.5 Pa·s, respectively, exhibiting the characteristic shear-thinning behavior of a non-Newtonian fluid [35]. Under equilibrium conditions, random collisions between particles in inks may make them inherently resistant to flow, resulting in a high viscosity. However, as the shear rate increased, the anisotropic particles were arranged and self-organized into a streamlined configuration with the flow, resulting in a low viscosity [36]. Thus, the BN80 ink and Ag80 ink were easily dispensed under pressure and immediately regained their high viscosity when the force was withdrawn, making them suitable for printing and subsequently permitting selfstanding on the substrate to maintain the shapes (see BN80 ink in Fig. 3a) [37].
On plotting the shear stress of the inks as a function of shear rate (Fig. 3d), the NMP/PEI solution, BN60 ink, and BN70 ink exhibited linear graphs with very low yield stresses of < 5 Pa. However, the slopes of the BN80 ink and Ag80 ink curves declined with increasing shear rate, and the inks exhibited relatively high yield stresses of 25.7 and 30.7 Pa, respectively, indicating their nature as Herschel-Bulkley fluids with typical yield stress fluid behavior. As depicted in Fig. 3e, the distinct fluid behaviors of the inks were originated from their distinct particle contents; the weight and volume compositions of the inks are listed in Table S1. It is remarkable that the yield stress of the ink drastically increased with a filler content of > 25 vol.%. This change in the fluid behavior of the inks can be attributed to the fact that at a high filler content over the critical point, some of the randomly dispersed plate-shaped BN particles were in mutual contact in the NMP/PEI solution, hence necessitating high forces for the ink to begin to flow. As evidenced by the FE-SEM images (Fig. 2d, g), the higher yield stress of the Ag80 ink compared to that of the BN80 ink was attributed to the rougher surface of the Ag@BN particles than that of the BN particles, making it more difficult for them to slide with each other.
If the ink viscosity is too low, it will readily fall and spread out owing to its lack of support, making it difficult to regulate the shape of the printed specimen. In contrast, excessive viscosity can cause particle agglomeration at the end of the ink stream, which would entail a high extrusion pneumatic pressure. It can be concluded that the ink system was tuned for a solution-based dispensing method with suitable viscosity and shear-thinning qualities particularly for BN80 ink and Ag80 ink. As demonstrated in Fig. S6, this method is advantageous because a variety of composite shapes can be precisely developed.
TGA was performed to confirm the effect of thermal treatment and compare the thermal properties of the composite inks and as-prepared composites (Fig. 3f). The BN80 ink exhibited rapid weight loss up to 150 °C, primarily owing to solvent evaporation. The remaining PEI and BN particles accounted for 48.3% of the residual weight. In contrast, the BN80 composite was stable up to 450 °C with only a 0.6% weight loss indicating that the NMP solvent in the composite ink was almost entirely evaporated by thermal treatment [24]. These results confirmed that the thermal treatment produced thermally stable single-layered composites. Figure 3g depicts the TMA curves of heat-treated PEI, BN80, and Ag80 films as a function of temperature, where the slope of the dimensional changes represents the CTE. PEI, BN80, and Ag80 were thermally stable up to ~ 175 °C, exhibiting linear curves with CTEs of 51.4, 15.2, and 8.34 ppm/°C, respectively, measured in the range of 50-175 °C. The composite inks exhibited CTEs comparable to those of metals such as aluminum (23.6 ppm/°C) and copper (16.6 ppm/°C), indicating that they can be applied onto the metallic substrates with minor variances in CTE values. BN80 and Ag80 exhibited glass-transition temperatures (T g ) of 208.1 and 190.7 °C, respectively, which were lower than that of PEI (215.2 °C). This was because the fillers disrupted the stacking of PEI molecules, generating free volumes or voids inside the composite structures. Interestingly, both the BN80 and Ag80 composites exhibited plateau regions above their T g (blue and orange arrows, respectively) that were not detected in pristine PEI, indicating that the composites were in rigid states at these temperatures. This result can be attributed to the friction between the fillers and the van der Waals forces between the filler-PEI molecules, which inhibited the thermal expansion of the materials. Ag80 exhibited a lower CTE than BN80 in the plateau region because the highly rough surfaces of the Ag@BN particles (Fig. 2g) showed high inter-filler adhesion forces with micromechanical interlockings, which further reduced the molecular chain mobilities, whereas the plate-shaped BN particles with smooth surfaces (Fig. 2d) allowed some slippage between them. Figure 4a, b depict polished cross-sectional FE-SEM images of 3L-and 5L-AgBN80 composites, respectively. The interfaces between the BN80 and Ag80 layers, which possessed thicknesses of approximately 490 and 360 nm, respectively, corroborated the multilayered architectures of the Ag@BN/BN/PEI composites. As the composites were compressed under high-pressure and high-temperature conditions, the combined thickness of each layer decreased slightly. Magnified polished cross-sectional FE-SEM and corresponding EDS elemental mapping images of the interface between the BN80 and Ag80 layers are shown in Fig. 4c, d, respectively. By pressing the alternately stacked single-layered composites at 160 °C and applying an optimal pressure, close contact was obtained between the layers,  (Fig. 4c). Plate-shaped BN particles were observed in both composite layers (white dashed lines). The BN particle sizes are in good agreement with the FE-SEM images in Fig. 2d-g (< 20 μm). Moreover, the elemental maps of B, N, Ag, and C (Fig. 4d) are in excellent agreement with the FE-SEM image in Fig. 4c, clearly demonstrating the formation of a multilayered structure in Ag@BN/BN/ PEI composites. Particularly in the Ag80 layer, a silver coating with a homogeneous elemental distribution of Ag in the form of core-shell structures was observed surrounding the BN particles. Additional elemental analyses of BN80 and Ag80 composites presented in Figs. S7 and S8, respectively, clearly comparing the structural differences between them and further confirming the well-defined core-shell structures of Ag@BN fillers.
The EMI shielding performance of materials is mainly determined by their electrical conductivities and complex permittivities. Due to the insulating outermost BN00 layers, the Ag@BN/BN/PEI multilayered composites exhibited low electrical conductivity in the through-plane direction (< 0.0005 S/m), whereas the Ag80 composite exhibited a moderate electrical conductivity of 0.0963 S/m with continuous silver coatings on BN particles. Because multilayered composites had numerous interfaces between the different materials of silver, BN, and PEI in the composite structures, they may exhibit strong interfacial polarization, which can be expressed as a function of the complex permittivity of the material consisting of the real part (ε′) and the imaginary part (ε″). Each permittivity value represents the EM energy stored and dissipated in the material. Figure 4e shows the permittivity curves of various composites as a function of frequency ranging of 100 kHz-1 MHz. The ε′ curves showed frequency-independent behavior, and a negligible decrease in ε′ was observed with increasing frequency. The average ε′ values of the composite increased from 3.70 (BN60) to 14.03 (5L-AgBN80) with increasing filler content and number of composite layers, which resulted in more interfaces between the different phases, subsequently causing an interfacial polarization process. In contrast, it is noteworthy that the ε″ values of the composites differ significantly at different frequencies, i.e., the embedded BN and Ag@BN fillers affected the dielectric loss in the PEI matrices, and the extent of energy loss was highly frequency dependent, indicating the typical dielectric resonances of the materials. As ε″ is contributed from both polarization and electrical conduction loss, the incorporation of the electrically conductive Ag@BN particles further increased the ε″ values of the composites, where the ε″ curves of the 5L-AgBN00 and Ag80 composites were located on the upper side of those of the 3L-AgBN00 and BN00 composites, respectively, indicating that the energy dissipation from the composites was significantly influenced by the conductive fillers.
Based on the permittivities (i.e., ε′ and ε″), the dielectric loss tangent (tan δ) was calculated using the formula: tan δ = ε″/ε′, which was used to estimate the EM wave absorption capability of the composites. As shown in Fig. 4f, the shape and tendency of the tan δ curves were remarkably similar to those of the ε″ curves, indicating that the frequency dependency of tan δ mainly resulted from the dielectric loss of the composites. Specifically, the tan δ values of BN60, BN80, 3L-AgBN60, and 5L-AgBN60 decreased with increasing frequency, but those of Ag80, 3L-AgBN80, and 5L-AgBN80 increased. To specify and visualize the frequency-selective properties of tan δ exerted by the composites, the tan δ selectivity of the materials was defined as follows: where tan δ max and tan δ min are the maximum and minimum values of tan δ, respectively, in the measured frequency range. As illustrated in Fig. 4g, the average tan δ value and tan δ selectivity were observed to be dependent on the type of multilayered composites. The tan δ selectivities of the 3L-AgBN60, 3L-AgBN80, 5L-AgBN60, and 5L-AgBN80 composites were 1.06, 1.30, 1.15, and 2.20, respectively, in the measured frequency range. It is noteworthy that the tan δ selectivity increased with the BN filler content and number of composite layers, which could possibly result in frequency-dependent variations in dielectric resonance characteristics.
The total EMI SE (SE T ) of BN00 and Ag80 singlelayered composites with a thickness of 0.5 mm was first measured in the X-band to evaluate the ability of BN and Ag@BN particles to block EM waves. As shown in Fig. 5a, wave-shaped curves were observed when the SE T of the BN00 composites was plotted as a function of frequency. Two characteristic peaks at 11.1 and 12.1 GHz can be observed, indicating that more incident EM waves were blocked at these frequencies than at the other frequencies.
Although the SE T of the BN00 composites improved marginally with increasing BN content, which may result from the enhanced dielectric loss tangent (Fig. 4f), the values were still quite low (< 4 dB), transmitting over 40% of the incident EM waves. Note that increasing the BN content had no effect on the location of the peaks, indicating that the filler level had no bearing on the frequency-selective features of the BN00 composites. In the studied frequency range, the SE T of the Ag80 composite was significantly higher than that of the BN00 composites, with an average value of 25.0 dB, which satisfies the commercial EMI shielding requirements (> 20 dB) [38]. This indicates that the Ag80 composite could block ~ 99.7% of the incident EM waves while transmitting only 0.3%. This exceptional EMI shielding ability was primarily attributed to the (1) tan selectivity = tan max tan min well-defined Ag@BN particles and their electrically conductive routes within the composite structure. Figure 5b depicts the shielding mechanism (i.e., transmission, absorption, and reflection) of the BN00 and Ag80 composites as a function of frequency. The reflection fraction curves of BN00 composites exhibited a similar shape and trend as the respective SE T curves, with two characteristic reflection peaks at 11.1 and 12.1 GHz, indicating that the frequency selectivity of BN00 composites was predominantly derived from wave reflection. The average ratios of transmission, Fig. 5 a EMI SE T and b shielding mechanism of BN00 and Ag80 single-layered composites as a function of frequency. SE T of c 3L-AgBN00 and d 5L-AgBN00 multilayered composites as a function of frequency. e f s and Φ of different multilayered composites. f Com-parison of SE T , SE A , and SE R of different multilayered composites at f s . g Suggested EMI shielding effects from phase shift of EM waves and h different aperture sizes and number of interfaces absorption, and reflection for the BN60, BN70, and BN80 composites were 81:12:7, 59:24:17, and 50:31:19, respectively, indicating electrically nonconductive absorption-dominated shielding. In the Ag80 composite, 89.9% of the incident EM waves were reflected on the surface of the highly electrically conductive Ag NPs, exhibiting the reflection-dominant shielding characteristic of typical metallic materials.
Using the 3L-AgBN00 and 5L-AgBN00 composites, the influence of multilayered structures on EMI shielding was then examined (Fig. 5c, d, respectively). The EMI shielding performance of the 3L-AgBN00 and 5L-AgBN00 composites exceeded 20 and 30 dB, respectively, across the full X-band frequency range. The relatively high SE T of 5L-AgBN00 composites may be attributed to the incorporation of two Ag80 layers into the composite structures, causing multiple internal reflections between their electrically conductive surfaces [39]. This multiple internal reflection effect allows EM waves to travel a longer path in the materials in the through-plane direction, hence increasing the probability of attenuation. Remarkably, the multilayered composites exhibited frequency selectivity, as evidenced by the presence of sharp peaks at different frequencies (f s ) of the highest SE T value, shielding more EM waves than at other frequency ranges, which was not observed in single-layered composites and the majority of conventional EMI shielding materials. By altering the number of composite layers and BN content in the BN00 layer, the frequency-selective EMI shielding performance may be adjusted. Specifically, as BN content increased, the peak shifted to a lower frequency and a higher SE T . For example, the f s of the 3L-AgBN60 composite was 11.6 GHz with a SE T of 35.6 dB, whereas that of the 3L-AgBN80 composite was 10.8 GHz with a SE T of 56.6 dB (Fig. 5c). Moreover, increasing the number of composite layers shifted f s toward lower frequency regions. Compared to the 3L-AgBN80 composite, the 5L-AgBN80 composite exhibited a much lower f s of 8.6 GHz (Fig. 5d).
As the multilayered composites exhibited various f s and selectivities for SE T , an EMI shielding on-off selectivity parameter (Φ) was utilized to specify and highlight the unique features: where T min and T max are the minimum and maximum transmission coefficient values in the measured frequency range of the samples corresponding to SE T,max and SE T,min , which are the maximum and minimum values of SE T , respectively. Figure 5e summarizes the f s and Φ values of the composites, demonstrating that this composite system may be utilized as a frequency-selective EMI shielding material with tunable properties, where the shielding frequency range and selectivity are governed by the composite structure and composition. These significantly different Φ values suggest that the materials exhibited distinct transmission/shielding selectivities. It is quite intriguing that the Φ curves exhibited a similar tendency to those of tan δ selectivity, in that both the Φ and tan δ selectivities rose with increasing BN content and number of composite layers. For example, the 3L-AgBN80 composite had the highest Φ (3071) among all multilayered composites, suggesting that it transmitted 3071 times fewer incoming EM waves at 10.8 GHz (f s ) than at the point of greatest transmission (12.2 GHz) in the X-band frequency range. With a low Φ value of 19, the 3L-AgBN60 composite was relatively frequency independent. Figure 5f compares the EMI shielding mechanism of the composites by depicting the SE T and SE values induced by absorption (SE A ) and reflection (SE R ) for different multilayered composites at f s . Increasing the amount of BN and the number of composite layers led to a rise in SE A ; however, no such trend in the SE R was observed. When the absorption and reflection fraction curves of the multilayered composites were plotted as a function of frequency (Fig. S9), the transmission fractions were nearly zero (< 1%), corresponding to the SE T values (> 20 dB) [40]. The curves indicated some frequency dependence with wave forms, but there was no propensity for absorption and reflection at f s . Furthermore, no correlation was observed between the absorption:reflection ratio and the type of multilayered composites. This indicates that the frequency selectivity of multilayered composites may be the result of numerous mechanisms changing the ratio of absorption to reflection in a complex manner.
As frequency-selective characteristics were not exhibited by the Ag80 composite and could not be controlled by the filler content in the BN00 composites, the tunability of these phenomena in the multilayered composites was primarily due to the presence of interfaces between the various types of layers, as depicted schematically in Fig. 5g. The majority of incident EM waves passed thorough the outermost BN00 layer, partially reflected or absorbed in the medium until encountering the Ag80 layer. Consequently, the EM waves that reached on the surface of the electrically conductive Ag80 were mostly reflected owing to the high number of free electrons in the Ag NPs. At this time, the difference in the dielectric permittivities at the interfaces of the two composite layers triggered changes in the phase of residual EM waves in terms of wavelength and velocity, which may interfere with other EM waves, resulting in frequency selectivity in dielectric loss and EMI shielding efficiency. The increasing number of composite layers decreased f s because more interfaces existed between the composite layers, which increased the likelihood of EM waves interfering with one another.
Increasing the BN concentration considerably increased this difference in dielectric characteristics between the composite layers, resulting in a decrease in f s (Fig. 5h). In other words, EM waves with shorter wavelengths (λ short ) were tended to be shielded at lower filler concentration, while those with longer wavelengths (λ long ) were shielded at higher concentration. Additionally, it should be noted that each multilayered composite exhibited a unique breadth and thickness of respective SE T peaks at f s (Fig. 5c, d). This phenomenon can be explained by the size of "aperture," which is determined by the interstitial space between the fillers [4,8,5]. At a low BN content, the BN particles were randomly scattered in the PEI matrix, which provided varied aperture widths within a single material, resulting in a change in the shielding frequency, hence broadening the SE T peak at f s . With increased BN content, the particles tended to be in densely packed states with minute aperture size differences, allowing incident EM waves to be insulated only at f s as opposed to other frequency ranges, resulting in a highly sharp peak with a high SE T value. In conclusion, the homogeneous dispersion of fillers and their identical aperture sizes in composites can offer a very narrow peak of SE T and high on-off selectivity in EMI shielding.
When EMI shielding materials block incident EM waves, some EM waves are absorbed and converted to heat, hence increasing the temperature. Consequently, ideal multifunctional materials should conduct heat away. The through-plane thermal conductivities (k) and thermal diffusivities (α) of various composites were evaluated to determine their heat dissipation capacity (Fig. 6a). Using thermal diffusivities of the samples, the thermal conductivities were determined as follows: where ρ and C p are density and specific heat, respectively. Thermal conductivities and diffusivities of the composites increased with increasing BN content, indicating that thermally conductive fillers can improve the heat dissipation ability of the polymer matrix via phonon scattering using a thermally conductive BN network in the composites. The thermal conductivity of BN60 was 1.48 W/m·K, which linearly increased to 2.33 W/m·K for BN80. In the case of multilayered composites, the thermal conductivity increased significantly with the number of layers, indicating that the interfacial bonding between the composite layers was excellent, thereby reducing the contact thermal resistance. The Ag@BN-containing Ag80 interlayers were highly advantageous for thermal dissipation as well; the thermal conductivities of 3L-AgBN80 and 5L-AgBN80 composites were 5.42 and 7.61 W/m·K, respectively. In the Ag80 layers, heat may be dissipated synergistically by Ag NPs and BN particles using free electrons and phonons as heat carriers, generating thermal pathways in the composites [14].
In addition, it is noteworthy that the thermal conductivities of the multilayered composites grew dramatically and remained constant as the BN content increased, as a result of the corresponding thermal diffusivities. This was attributed to the fillers' percolation behavior over the percolation threshold. In other words, the plate-shaped BN particles were densely packed in interstitial areas, providing a large physical contact area.
To characterize the electrical insulating qualities, the breakdown strengths of the composites were determined (Fig. 6b). In BN00 composites, the breakdown strength decreased from 15.22 to 9.04 kV/mm as the BN concentration increased from 60 to 80 vol.%, indicating that the electrically insulating ability of BN particles was inferior to than that of PEI matrix. Due to the existence of electrically conducting Ag80 interlayers, it was discovered that increasing the number of layers negatively affected the electrical insulation performance. Nonetheless, the breakdown strength of all composites exhibited high breakdown voltage of > 4 kV/mm, with 5L-AgBN80, the composite with the highest thermal conductivity, reaching 4.03 kV/mm. The topmost electrically insulating BN00 layers ensured overall electrical insulation of the multilayered composites by separating the electrically conducting Ag80 interlayers in the through-plane direction.
The frequency-selective EMI shielding capability and strong thermal conductivity of the Ag@BN/BN/PEI multilayered composites may enhance the device's endurance. Figure 7 depicts a complete comparison of the multifunctionality of the composites with previously reported multifunctional polymer-based composite materials (details are provided in Table S2). Typically, a trade-off exists between the electrical insulation and EMI shielding capabilities. For example, the BN foam/BN/PDMS composite had a high breakdown voltage of 21.8 kV/mm but exhibited a poor EMI SE (1-1.5 dB). Although the GO/BN/SEBS composite displayed strong EMI SE (36-38 dB) and thermal conductivity (< 6 W/m•K) owing to the synergistic effects of graphene oxide and BN hybrid fillers, its electrical insulation (1.52 kV/mm) was comparatively poor. In contrast, the 5L-AgBN80 composite demonstrated an excellent performance in terms of EMI SE (32-62 dB) with tunable frequency selectivity, electrical insulation (4.03 kV/mm), excellent through-plane thermal conductivity (7.61 W/m·K), and shape controllability via a sophisticated solution-printing method. Notably, among the multifunctional polymer composites, the Ag@BN/ BN/PEI multilayered composites had one of the greatest performances, suggesting enormous potential as nextgeneration EMI shielding materials.

Conclusion
Multifunctional Ag@BN/BN/PEI composites consisting of BN particle-containing outermost dielectric layers and Ag@ BN particle-containing conductive interlayers were generated using solution printing. By deliberately mixing composite layers with different electrical and dielectric properties, it was demonstrated that the composites may simultaneously provide multifunctionality, including frequency-selective EMI shielding, through-plane thermal dissipation, and electrical insulation. Particularly, the frequency selectivity in EMI shielding can be carefully manipulated in the X-band region by modifying the filler and composite layer design. Combined with their sophisticated and facile solution-printing methodology, thermal stability, and tunability, the composites are promising candidates for multifunctional coatings on a variety of metallic surfaces, hence expanding their application windows.

Author contribution
The manuscript was written through contributions of all authors.
Funding This work was supported by the project from the U.S. Air Force Office of Scientific Research/AOARD (grant number: FA2386-22-1-0041), which was efficiently facilitated and technically advised by Dr. Tony Kim, the project's PO. We also appreciate the instrumental and financial support from the Technology Innovation Program (KEIT-20013794, MOTIE).

Fig. 7
Radar plot showing a comparison of comprehensive performance between Ag@BN/ BN/PEI multilayered composites and previously reported multifunctional polymer composites, covering EMI shielding with frequency selectivity, thermal conductivity, electrical insulation, and shape controllability