Bilayer Polymer Metacomposites Containing Negative Permittivity

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Bilayer polymer metacomposites containing negative permittivity layer for new high-k materials Jing Wang, Zhi-cheng Shi, Fan Mao, Shougang Chen, and Xin Wang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b12786 • Publication Date (Web): 22 Dec 2016 Downloaded from http://pubs.acs.org on December 27, 2016

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ACS Applied Materials & Interfaces

Bilayer polymer metacomposites containing negative permittivity layer for new high-k materials Jing Wang, Zhicheng Shi*, Fan Mao, Shougang Chen, and Xin Wang* Institute of Material Science and Engineering, Ocean University of China Qingdao 266100, China E-mail: [email protected]; [email protected]

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ACS Paragon Plus Environment


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ABSTRACT Polymer matrix high-k composites are of considerable interest in various electronic devices, such as capacitors, antennas and actuators, etc. However, how to enhance the permittivity without elevating the loss remains a challenge for us. Here we present a novel design of bilayer high-k metacomposites consisting of two stacked single-layers with positive permittivity and negative permittivity. Interestingly, the bilayer system shows an obvious permittivity boost effect with a permittivity improved by 40-fold increases compared with the polymer matrix, while maintaining the loss tangent as low as 0.06. Further calculation results indicate that the permittivity of the bilayer composites could be enhanced by 4000-fold or even greater increase as compared with the polymer matrix via balancing the dielectric properties of single layers. Insights into how the thickness ratios and dielectric properties of single-layers interfere with the dielectric performances of bilayer composites were discussed. This study provides a new route for the design of high-k materials, and it will have great significance on the development of dielectric materials. Hopefully, multilayer high-k metacomposites with fascinating dielectric performances could be achieved via balancing the dielectric properties of single-layers.

KEYWORDS: High-k material; Negative permittivity; Metamaterial; Dielectric property; Multi-layer composite.

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1. INTRODUCTION High permittivity (high-k) materials are widely used in organic field-effect transistors (OFETs),1-3 actuators,4-6 antennas,7 and energy storage devices,8-10 etc. Especially, polymer-based high-k materials have attracted increasing attention in recent years owing to their flexibility, easy processibility, and tailorable dielectric properties. To date, two technical routes have been developed to obtain high-k polymer

composites:

percolative

conductor/polymer

composites11-13

and

ceramic/polymer composites.14-16 For conductor/polymer composites, significantly enhanced permittivity, compared with the polymer matrix, could be achieved. Unfortunately, the high permittivity in percolative composites is often accompanied by quite high losses due to the delocalization of charges on a macroscopic scale near percolation as a result of tunnelling or ohmic conduction. Although the loss of ceramic/polymer composite is low, the permittivity is usually no more than 50 even with a high ceramic loading.17-19 That is to say, although significant advances have been made, the balance of permittivity and loss remains a challenging task. And scientists were urged to find new ways to achieve high performance high-k materials. Recently, there is a fast growing interest in multi-layer high-k composites owing to the fact that there exist charge accumulations and polarizations on the interfaces between adjacent layers, which will contribute to the extra enhancement of permittivity.20-23 Theoretically, a bilayer composite is equivalent to a capacitor consisting of two series connected capacitors, where each single-layer is equivalent to a capacitor. And the capacitance of the bilayer composite Cs can be expressed as 3



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Cs=1/(1/C1+1/C2), where C1 and C2 are the capacitances of the two single-layers. Generally speaking, C1 and C2 are both positive values, thus Cs will be smaller than anyone of C 1 and C2. Interestingly, if C1 becomes negative while C2 remains positive, an enhanced Cs will be obtained. Especially, once the absolute value of C1 and C2 are comparable to each other, the value of Cs could be infinite (Figure 1a). As we know, the relationship between the capacitance (C) and permittivity (ε) of a material can be described by C = Aε0ε/t, where A the area of the electrode, ε0 is the absolute permittivity of free space, t is the thickness of material. Thus, the permittivity of a bilayer composite (εs) can be expressed as:

εs =

( N + 1) × ε 1 × ε 2 Nε 1 + ε 2

(1)

where N is the thickness ratio of two single-layers, ε1 and ε2 are the permittivities of single-layers. Accordingly, bilayer materials consisting of series connected negative-k layer and positive-k layer could be promising candidates for new high-k materials with excellent dielectric performances. And the dielectric performances of the bilayer composites are tailorable via adjusting the thickness ratios and dielectric properties of single-layers. In order to realize the aforementioned bilayer high-k composites, both positive-k and negative-k materials are required. There are numerous positive-k materials, such as insulating polymers, ferroelectric ceramics, and composites, etc.24-27 However, negative-k material is rare in the nature. In recent years, metamaterials with negative-k have drawn extensive attention. In metamaterials, negative-k is usually obtained in artificial medium of periodic structures composed of metals, graphene, 4


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and superconductors, etc.28 However, the absolute values of negative permittivities for these materials (>108 @1 kHz) are much larger than traditional positive-k materials (< 104 @1 kHz).29-32 Therefore, they are not appropriate candidates for negative-k layers in bilayer high-k composites. Fortunately, our previous work showed that suppressed negative-k could be obtained in percolative composites consisting of conductive fillers dispersed in insulating matrix.33-36 In addition, negative-k phenomena were also reported

in

ferroelectrics,

metal-oxide-semiconductor

devices,

and

ferroelectric-dielectric superlattice heterostructures, etc.37-41 In our current work, graphite/polyvinylidene difluoride (PVDF) composites consisting of isolated graphite particles distributed in PVDF host is designed as the positive-k layer (top layer, Figure 1b), while the negative-k layer is percolative graphite/PVDF composites with partially interconnected graphite particles (bottom layer, Figure 1b). As will be shown in this work, the introduction of negative-k layer in bilayer composites dramatically enhanced the permittivity, while the low loss is still comparable to that of pure polymer matrix. Furthermore, the influences of layer thickness ratio and dielectric property of single-layers on the dielectric performance of bilayer composites were investigated in detail.

2. EXPERIMENTAL SECTION 2.1 Sample Preparation. Preparation of graphite-PVDF mixture. Graphite powders (200 mesh, AR) and Polyvinylidene difluoride (PVDF) powders (Arkema) were mixed via ball-milling 5



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(300 r/min) for 30 min in absolute ethyl alcohol. The as ball-milled mixture was dried in an oven at 70 °C for 6h, and ground in an agate mortar for 20 min to obtain graphite-PVDF mixture. Preparation of graphite/PVDF composites. The graphite-PVDF mixture was hot pressed under a pressure of 10 MPa at 180 °C for 5 min and then cooled down to room temperature to obtain single-layer graphite/PVDF composites. Single-layer composites with graphite volume fractions ranging from 1.7 vol% to 46.0 vol% were prepared, and the single-layer composite with α vol% graphite is reported as S-α (e.g., S-8.6 represents the single-layer composite containing 8.6 vol% graphite). For the fabrication of bilayer graphite/PVDF composites with two single-layers containing α vol% and β vol% graphite, three steps were performed (Supplementary Scheme S1): (1) Graphite-PVDF mixture with α vol% graphite was put into the die, and cold-pressed with a pressure of 1 MPa at room temperature to form the α-layer; (2) Graphite-PVDF mixture with β vol% graphite was put onto the surface of the α-layer and cold-pressed to form the β-layer; (3) The two cold-pressed layers were heated to 180 °C and maintained under a pressure of 10 MPa at 180 °C for 5 min, and cooled down to room temperature to obtain the bilayer polymer composite which is reported as B-α-β (e.g., B-8.6-29.6 represents the bilayer composite with two single-layers containing 8.6 vol% and 29.6 vol% graphite, respectively). The diameter of the samples was 20 mm, and the thicknesses of the samples range from 1.0 mm to 2.0 mm.

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2.2 Structural Characterizations. The morphologies of the composites were observed by scanning electron microscopy (SEM, S-4800, Hitachi, Ltd.). The compositions of the composites were analyzed by X-ray Diffractometer (XRD, D8 Advance, Bruker, Ltd.).

2.3 Dielectric and Breakdown Strength Measurements. For the dielectric measurements, gold electrodes were sputtered on both sides of the sample disks. One side was entirely sputtered with gold electrode, while the other side was sputtered using an annular shadow mask with internal and external diameters of 6.4 mm and 10 mm, respectively. The dielectric measurements were carried out under AC voltage 100 mV at room temperature in the frequency ranging from 100 Hz to 1 MHz using Agilent E4980A Precision LCR Analyzer with Electrode-D of 16451B dielectric test fixture. Meanwhile, open and short compensation were performed before dielectric properties test. The permittivity was calculated by εr=tCp/Aε0, where t is the thickness of the sample, A the area of the electrode, Cp is the parallel capacitance, f the electric field frequency, ε0 is the absolute permittivity of free space (8.85×10-12F/m). The DC breakdown strength (BDS) measurements were carried out using a breakdown voltage instrument (CS2674AX, Nanjing Changsheng Instrument Co. Ltd., China) at room temperature. Ten breakdown tests were performed on each sample.

3. RESULTS AND DISCUSSION 7



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Morphologies and compositions. Figure 1c and d show the cross-section SEM morphologies of bilayer composites. Clearly, the composites are composed of two layers with different morphologies, and further enlarged SEM images suggest that the two layers are merged into a whole (Supplementary Figure S1b). The composition and thickness ratio of the two layers can be easily adjusted during the fabrication process. The XRD patterns in Figure 1e indicate that the composites are composed of PVDF and graphite, no additional phase appears. The SEM and XRD analyses suggest that graphite/PVDF composites with different graphite contents have been prepared. So we next explored the dielectric performances of single-layer and bilayer graphite/PVDF composites, respectively. Dielectric performances of single-layer composites. As shown in Figure 2a, for the single-layer composites with graphite content below 14.9 vol%, the permittivity increases with graphite content, which is ascribed to the interfacial polarization as a result of the conductivity contrast between the conducting graphite and insulating PVDF. Especially, an obvious increase of permittivity from 20 to 160 was observed when the graphite content increases from 13.1 vol% to 14.9 vol%, and a sharp increase of loss tangent takes place (Figure 2c). Meanwhile, an abrupt enhancement of conductivity from ~ 10-4 S/cm to ~ 2.12 S/cm occurs (Supplementary Figure S2a and S3a). This phenomenon indicates the formation of conductive networks near percolation threshold which results in the great enlargement of graphite-PVDF interface areas and the elevation of leakage conductive loss. Fitted results using the power law suggest that the main conduction mechanism of these 8


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composites is hopping conduction (Supplementary Figure S3b). Further increasing the graphite content to 20.3 vol% brings about the appearance of negative permittivity

Figure 1. (a, b) Schematic illustration of bilayer polymer composites consisting of positive-k and negative-k layers. Positive-k and negative-k are provided by graphite/PVDF composites with different volume fractions of graphite. (c, d) Cross-section SEM morphologies of bilayer composites. (e) XRD patterns of single-layer graphite/PVDF composites. 9



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(Figure 2b) and severely enhanced loss tangent (Figure 2d). Correspondingly, significantly enhanced conductivity is observed and the main conduction mechanism turns into metal-like conduction (Supplementary Figure S3b). Theoretically, the plasma-like negative permittivity behavior can be described by lossy Drude model, which gives a frequency dependence of permittivity for delocalized electrons42:

ε r′ (ω ) = 1 − ωΡ =

ωΡ2 ω 2 + ωτ 2

(2)

neff e 2 meff ε 0

(3)

where ωp (ωp=2πfp) is the plasma frequency, ω is frequency of electric field, ωτ is

Figure 2. Frequency dependences of permittivity (a, b) and loss tangent (c, d) for single-layer graphite/PVDF composites with different graphite contents. Fitted results by Drude model for composites with graphite contents of 31.4 vol%, 36.2 vol% and 46.0 vol% are shown as the solid line in Figure 2b. 10


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damping parameter, ε0 is permittivity of vacuum (8.85×10-12 F/m), neff is effective concentration of delocalized electrons, meff is effective weight of electron, and e is electron charge (1.6×10-19 C). As shown in Figure 2b, the fitted results (solid line) show that the experimental results agree well with lossy Drude model, and the fitted plasma frequencies of the composites (~ 108 Hz) are much lower than that of pure metals (~ 1015 Hz).42 Besides, the absolute value of negative permittivity increases along with increasing graphite content, which could be attributed to the elevated effective electron concentrations as described by lossy Drude model. As discussed above, positive-k layer and negative-k layer with tunable dielectric performances have been prepared. Thus we next set out to determine how the dielectric properties of single layers affect the dielectric performance of bilayer composites. Dielectric performances of bilayer composites. Systematic investigations were carried out to explore how the thickness ratios and dielectric properties of single-layers influence the dielectric performances of bilayer composites. To clarify the impact of thickness ratios on the dielectric performances of bilayer composites, a series of graphite/PVDF bilayer composites with different thickness ratios were assessed. In these composites, the positive-k layer contains 8.6 vol% graphite (S-8.6), while the negative-k layer contains 29.6 vol% graphite (S-29.6). The thickness ratios of S-8.6 layer to S-29.6 layer range from 1:0.5 to 1:20. The experimental results (dot line) in Figure 3a show that the permittivity increases as the thickness ratio decreases. When the thickness ratio reaches 1:20, the permittivity becomes as high as 400 @10 kHz, which is improved by 40-fold increase as compared with the polymer matrix 11



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(~10 @10 kHz, Figure 2a). Interestingly, although the permittivity is greatly enhanced, the loss tangent of the bilayer composite still keeps at a lower level (~ 0.06 @10 kHz, Figure 3b) which is comparable to that of the polymer matrix. What is more important is that the calculated results derived from the series capacitance model (solid lines, Figure 3a) agree well with experimental results. That is to say, we experimentally demonstrated the feasibility of our novel design. Furthermore, we calculated the dielectric spectra of bilayer composites with much smaller thickness ratios, and it is

Figure 3. Frequency dependences of permittivity (a) and loss tangent (b) for bilayer composites with different layer thickness ratios. The graphite contents of positive-k layer and negative-k layer are 8.6 vol% and 29.6 vol%, respectively. The thickness ratios of S-8.6 layer to S-29.6 layer vary from 1:0.5 to 1:20. Calculated results are shown as the solid line. 12


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indicated that the permittivity could be as high as 30000 @10 kHz when the thickness ratio decreases to 1:100 (Supplementary Figure S4a). However, when the thickness ratio decreases to below 1:115, negative permittivities, along with dielectric resonances, appear (Supplementary Figure S4b), indicating that the contribution of negative-k layer has overwhelmed the positive-k layer. Thus, at current time, our experimental and theoretical results have demonstrated that the introduction of negative permittivity layer into bilayer composites can result in greatly enhanced permittivity, while maintaining low loss. What is more important is that the dielectric properties of the bilayer composites could be feasibly adjusted by varying thickness ratios of the two single-layers. Apart from the thickness ratio, the permittivities of single layers also play vital roles in the dielectric performances of the bilayer composites. Figure 4 presents the impacts of positive-k layers on the dielectric properties of bilayer composites. Figure 4a and c show that the experimental results (dot lines) are in accordance with the calculated results (solid lines). To provide a more intuitive comparison of the bilayer composites with different positive-k layers, the variations of permittivity (@10 kHz) with thickness ratio are shown in Figure 4c. Clearly, for the bilayer composites with a certain thickness ratio, the permittivity increases as the graphite content of the positive-k layer gets higher. Furthermore, we calculated the dielectric spectra of bilayer composites containing positive-k layers with permittivities vary from 3 times to 20 times of the permittivity of S-8.6 composite (~ 20 @10 kHz). As shown in Figure 4d, when the positive-k layer possess a permittivity of 5 times of S-8.6 13



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composite, which is ~ 100 @10 kHz, the permittivity of the bilayer composite exceeds 500 @10 kHz. Furthermore, when the permittivity of the positive-k layer reaches 20 times of S-8.6 composite, which is ~ 400 @10 kHz, the permittivity of the

Figure 4. Frequency dependences of permittivity for bilayer composites with different positive-k layers (a: pure PVDF, b: S-13.1 composite). Calculated results are shown as the solid lines. (c) The variation of permittivity (@10 kHz) with thickness ratio for bilayer composites with different positive-k layers; (d) Calculated dielectric spectra of bilayer composites with the permittivity of positive-k layer varying from 3 times to 20 times of the permittivity of S-8.6 composite, the corresponding negative-k layer is S-29.6 composite and the thickness ratio of positive-k layer to negative-k layer is 1:5 in the calculation. The symbol X of B-X-29.6 represents the graphite volume fraction of positive-k layer. 14


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bilayer composite could be as high as 2700 @10 kHz. Further increasing the permittivity of positive-k layer to 100 times of S-8.6 composite, which is ~ 2000 @10 kHz, the bilayer composite could possess a very high permittivity of ~ 40000 @10 kHz (Supplementary Figure S6a). Therefore, if we choose high-k materials, such as barium titanate whose permittivity could be as high as 104 @10 kHz, as the positive-k layers, bilayer composites with fascinating dielectric properties may be achieved. However, when the permittivity of positive-k layer reaches some critical value, dielectric resonances along with negative permittivities appear (Supplementary Figure S6b), indicating that the contribution of negative-k layer has overwhelmed the positive-k layer. As described by equation (1), to achieve ultra-high permittivity, the key point lies in the balance of negative-k and positive-k. So we next discussed the effect of negative-k layers on the dielectric properties of bilayer composites. Figure 5 shows the impacts of negative-k layers on the dielectric properties of bilayer composites. As shown in Figure 5a and b, the experimental results (dot lines) agree well with calculated results (solid lines), which demonstrated the feasibility of our strategy once again. The variation of permittivity (@10 kHz) with thickness ratio for bilayer composites with different negative-k layers is shown in Figure 5c. We can see that, for the bilayer composites with a certain thickness ratio, the permittivity increases as the graphite content of the negative-k layer gets higher. To further reveal how the negative-k layer influence the bilayer composites, we calculated the dielectric spectra of bilayer composites containing negative-k layers with permittivities vary from 1/10 times to 1/107 times of the permittivity of S-29.6 composite (~ -14000 15



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@80kHz, Figure 2b). It is shown that when the negative-k layer possess permittivities of 1/70 and 1/107 times of 29.6 vol% graphite/PVDF composite, which are about -200 @80kHz and -131 @80kHz, the permittivity of the bilayer composite exceeds

Figure 5. (a, b) Frequency dependences of permittivity for bilayer composites with different negative-k layers (a: S-20.3 composite, b: S-46 composite). Calculated results are shown as the solid lines; (c) The variation of permittivity (@10 kHz) with thickness ratio for bilayer composites with different negative-k layers; (d) Calculated dielectric spectra of bilayer composites with the permittivity of negative-k layer varying from 1/10 times to 1/107 times of the permittivity of S-29.6 composite, the positive-k layer is S-8.6 composite and the thickness ratio of positive-k layer to negative-k layer is 1:5 in the calculation. The symbol X of B-8.6-X represents the graphite volume fraction of negative-k layer. 16


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200 @80 kHz and 300 @80 kHz, respectively (Figure 5d.). Further decreasing the permittivity of negative-k layer results in the appearances of negative permittivity (Supplementary Figure S8.) in some frequency regions, indicating the dominating contribution of negative-k layer in the bilayer composites. Breakdown strengths of bilayer composites The dielectric breakdown strength (BDS) of a material is defined as the maximum electric field that a dielectric material can withstand without losing its insulating properties. Generally, the dielectric breakdown strength of a material could be analyzed using the two-parameter Weibull distribution43:   E β  P( E ) = 1 − exp−      α  

(4)

Where P is the cumulative failure probability, E is the experimentally tested breakdown electric field, α is the electric field for which there is a 63.2 % probability for sample to breakdown (Weibull breakdown strength), β is a shape parameter indicating the scatter of tested breakdown strengths. When the β value is 3, the tested data follows Gaussian distribution, and a higher value of β represents higher level of reliability. The Weibull distribution curves of breakdown strength and corresponding Weibull breakdown strengths and β value for bilayer composites were illustrated in Figure 6. In our present work, the β values of the composites range from 41.91 to 140.55, indicating a high reliability of the tested results in all the composites. As shown in Figure 6, the breakdown strength has a slight decrease as the graphite content of the negative-k layer gets higher, while an obvious decrease was observed with increasing thickness of negative-k layer. The breakdown strength of the bilayer 17



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composites need to be further improved in view of applications, and there are several approaches which can achieve that purpose. For example, the thickness of negative-k layer could be effectively reduced by matching the permittivity of positive-k layer with that of negative-k layer. In addition, positive-k layers with improved BDS could be prepared by replacing conductive fillers with high BDS ceramic fillers (e.g. SiO2, BN, TiO2) or surface modified fillers. Hopefully, bilayer composites with simultaneous high permittivity and breakdown strength could be realized via the aforementioned or other routes.

Figure 6. Weibull plots of the breakdown strength (a), and characteristic breakdown strength (BDS) (b) for bilayer composites with different positive-k layer, negative-k layer and relative thickness ratio (1:0.5, 1:1.0 and 1:1.5).

4. CONCLUSIONS In this paper, negative permittivity layer was incorporated into bilayer composites, forming a new design of high-k metamaterials. Insights into how the dielectric properties and thickness ratios of single layers interfere with the dielectric performances of bilayer metacomposites were discussed in detail. Interestingly, 18


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experimental results show that the bilayer metacomposites manifest an obvious permittivity boost effect with a permittivity improved by 40-fold increase as compared with the polymer matrix, while maintaining a loss tangent that comparable to pure polymer matrix. Further calculation results indicate that the permittivity of the bilayer composites could be enhanced by over 4000-fold increase as compared with the polymer matrix via balancing the dielectric properties of negative permittivity and positive permittivity single layers. This study opens a new way for the design of high-k materials with tailored dielectric performances, and it will have great significance on the development of dielectric materials. Hopefully, numerous bilayer high-k metacomposites with fascinating dielectric performances will be proposed in the near future.

ASSOCIATED CONTENT Supporting Information The supporting information includes scheme for the preparation process of bilayer composites and cross-section SEM images of the bilayer composites, as well as the frequency dependences of conductivity, reactance, loss tangent and calculated dielectric constant for bilayer composites. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Authors 19



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E-mail: [email protected]; [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work was supported by National Natural Science Foundation of China (51402271), Foundation for Outstanding Young Scientist in Shandong Province (BS2014CL003),

Qingdao

Science

and

Technology

Plan

(14-2-4-118-jch),

Fundamental Research Funds for the Central Universities (201413001), Projects Funded by Shandong and Qingdao Postdoctoral Science Foundation.

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TOC Figure

27


Bilayer Polymer Metacomposites Containing Negative Permittivity

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