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Permittivity transition from positive to negative in acrylic polyurethane-aluminum composites
Composites Science and Technology 188 (2020) 107969
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Composites Science and Technology journal homepage: http://www.elsevier.com/locate/compscitech
Permittivity transition from positive to negative in acrylic polyurethane-aluminum composites Zhongyang Wang a, b, c, Kai Sun a, **, Peitao Xie b, Yao Liu b, Qilin Gu c, *, Runhua Fan a, *** a
College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai, 201306, China Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan, 250061, China c Department of Materials Science and Engineering, National University of Singapore, 117574, Singapore b
A R T I C L E I N F O
A B S T R A C T
Keywords: A-flexible composites A-polymer-matrix composites B-Electrical properties Negative permittivity
The insulator-conductor percolative composites have been mostly constructed to achieve high permittivity and negative permittivity. In this work, permittivity transition from positive to negative is investigated in acrylic polyurethane-aluminum (APu/Al) percolative composites at radio frequency. Both the high permittivity and negative permittivity are accompanied with low loss due to the self-passivated nature of aluminum. The reac tance and ac conductivity are studied to explain the dielectric properties, which provides an essential insight into the universal principles of high permittivity and negative permittivity behaviors in percolative composites. Meanwhile, when the conductive filler content exceeds the percolation threshold, a derived formula of permittivity has been put forward on the basis of the existing theoretical framework of percolation theory. Resourceful dielectric properties of APu/Al percolative composites will make them as potential alternatives for capacitors and metamaterials.
1. Introduction The insulator-conductor percolative composites not only involve a nonlinear conductivity transition with the increasing conductive fillers, but also possess a wide variety of functional properties, such as elasticity [1], thermal conductivity [2], magnetic permeability [3] as well as dielectric response [4]. In particular, the dielectric permittivity has been widely studied, both high permittivity and negative permittivity are achieved in the insulator-conductor percolative composites [5–8]. Spe cifically, the ones with high permittivity and low dielectric loss are widely used as capacitors in microelectronics and electrical energy storage devices [9–11]. In addition, negative permittivity materials have attracted considerable attention as so-called metamaterials in the recent years, which exhibit enticing electromagnetic properties in some mi crowave and optical devices [12,13]. For percolative composites, high permittivity can be obtained when the volume fraction of the conductive filler is slightly below the percolation threshold. In contrast, negative permittivity will occur when the volume fraction of the conductive filler exceeds the percolation threshold, and a large number of conductive pathways have been formed. Conductivity and permittivity of a
percolative system should obey power-law behaviors, as determined by the following equations [10],
σ ¼ σM ðf
fc Þt for f > fc
(1)
σ ¼ σD ðfc
f Þ q for f < fc
(2)
ε∝ðfc
f Þ q for f < fc
(3)
where f is the volume fraction of fillers, fc is the percolation threshold,
σ M and σ D are respectively the conductivities of the metallic and
dielectric components, q and t are critical exponents. Obviously, the traditional percolation theory is failed in predicating the permittivity when f >fc, so it is necessary to study the dielectric permittivity behavior when the conductive fillers content exceeds the percolation threshold, especially to evaluate the negative permittivity behavior. The percolative composites are mainly classified into ceramic-based and polymer-based composites. Usually, the ceramic-matrix composites are brittle and high-temperature processed, whereas, the polymer-based composites are flexible and easy to process. Therefore, great efforts have
* Corresponding author. ** Corresponding author. *** Corresponding author. E-mail addresses: [email protected] (K. Sun), [email protected] (Q. Gu), [email protected] (R. Fan). https://doi.org/10.1016/j.compscitech.2019.107969 Received 27 August 2019; Received in revised form 13 December 2019; Accepted 22 December 2019 Available online 24 December 2019 0266-3538/© 2019 Elsevier Ltd. All rights reserved.
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Composites Science and Technology 188 (2020) 107969
Fig. 1. Schematic illustration of the preparation process for the APu/Al composites.
been made to construct the polymer-based percolative composites for achieving high permittivity [14,15] and negative permittivity [16,17]. In general, high permittivity and low dielectric loss (tanδ) of percolative composite are rather difficult to achieve at the same time [18]. Thus, several feasible approaches have been developed to prevent conductive fillers connecting with each other directly, so as to reduce tanδ [19]. For example, Nan et al. [20] have coated the Ag cores with thin organic shells, which remarkably reduced the dielectric loss (less than 5%). Similarly, Yang et al. [21] have wrapped multiwall carbon nanotubes around polypyrrole to screen charge movement and decrease leakage current. Some self-passivation metal, such as aluminum (Al) is also promising to realize high permittivity and negative permittivity with low dielectric loss. For example, a high permittivity (εr~110) with low dielectric loss (about 0.02) was reported in Al/epoxy composites at 10 kHz [22]. Moreover, a permittivity as high as 100 was achieved in Al/polyethylene composites with a dielectric loss of about 0.26 at extremely low frequency (10 1 Hz) [23]. Yet as the development of miniaturization and high working frequency for electronics, to achieve high permittivity at high frequency is urgently pursued. The main challenge is that the permittivity decreases abruptly in the high fre quency region, which is widely known as relaxation phenomenon. For instance, a high permittivity of about 2700 was obtained in the poly (vinylidene fluoride)/graphite nanoplates nanocomposite at 100 Hz, but only 200 at 1 kHz [24]. It is rather difficult for the polymer matrix composites to possess a large permittivity (ε > 100) without raising dielectric loss (i.e. keep tanδ<5%) above 10 MHz [25]. Thus, herein we try to explore high permittivity behaviors in percolative composites at radio frequency. In this frequency band, negative permittivity materials are also significant in various communication devices, such as antennas [26], electromagnetic cloaks [27,28], capacitors [29] and transistors [30]. Therefore, the investigation of permittivity transition from posi tive to negative in percolative composites at megahertz is more practi cally meaningful. In this work, percolative composites consisting of commercial acrylic polyurethane and Al particles are well constructed. Acrylic polyurethane (APu) is widely used in coating industries because of its favorable properties, such as the stable adhesion to most substrates, high flexi bility and excellent abrasive resistance [31,32]. Therefore, APu/Al composites have potential applications in wearable devices and flexible invisibility cloaks, which requires the careful study on their dielectric properties, especially, the high permittivity and negative permittivity. In
Fig. 2. (a) XRD patterns of the APu/Al composites with different volume fractions of Al particles. The inset in (a) is the enlarged partial view of the XRD pattern of amorphous APu. (b) FTIR spectra of pure APu and the APu/Al composite with 86.41 vol% of Al. 2
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Composites Science and Technology 188 (2020) 107969
Fig. 3. The SEM image (a) and SAED pattern (b) of pure Al particles. The surface morphology (c, d) and cross-sectional SEM image (e) of the APu/Al composites. (f) The EDX spectra of the APu/Al composite with 57.23 vol% Al content. The inset in (f) shows the flexibility of the APu/Al composites.
addition, the reactance characteristics and ac conductivities of APu/Al composites are investigated to explain the permittivity transition pro cess from positive to negative. Finally, a derived formula is firstly put forward to describe the permittivity behaviors in excessively percolative composites.
APu matrix, the mixed slurries were transferred into the high-viscosity spray gun. Subsequently, the slurries were spray-coated onto a clean and smooth poly-tetrafluoroethylene substrate, and then dried at room temperature for 48 h. Finally, the APu/Al composites were obtained after carefully stripping from the substrate.
2. Experimental
2.2. Characterization and electrical measurement
2.1. Fabrication of the APu/Al composites
The phase structure of the composites was analyzed by X-ray diffraction (XRD, Tokyo, Japan). The morphology and microstructures of samples were observed by transmission electron microscope (TEM, JEM-3010, Questar, New Hope,USA)and field emission scanning elec tron microscopy (FESEM, SU-70, Hitachi, Tokyo, Japan) equipped with Energy Dispersive X-ray (EDX) Detector. The chemical components were examined by Fourier transform infrared spectra (FTIR, IRPrestige-21, Shimadzu, Japan). The dielectric property and ac conductivity were examined by Agilent E4991A RF Impedance Analyzer equipped with 16453A test fixture. The complex permittivity and ac conductivity were calculated from the following equations,
Untreated Al particles (Aladdin Co. Ltd, China) have a compact passivation layer to store themselves steady in case of high activity. Then, the Al particles were heated in air atmosphere at 180 � C for 2 h to form the reinforced passivation layer to block the conductive current in the composites. The precursor and curing agent of APu are commercial grade products (Marine Chemical Research Institute Co. Ltd, China) without any further treatment. The APu/Al composites with different volume fractions of Al particles were prepared by an in-situ polymeri zation process, and the detailed schematic is shown in Fig. 1. Firstly, Al particles and precursor of APu were dispersed in a beaker, and then the mixture was mechanically stirred and ultrasonically treated for 30 min to form a uniform suspension. After that, the curing agent was added into the beaker, followed by repeatedly stirring and ultrasonic treatment for another 30 min. After Al particles were uniformly dispersed into the
εr ’ ¼
3
Cd
ε0 A
(4)
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Composites Science and Technology 188 (2020) 107969
Fig. 4. Frequency dependence of the complex permittivity for the APu/Al composites. The real parts (a, b) and imaginary parts (c, d) of the permittivity. The dielectric loss tangent (tanδ) of the APu/Al composites (e, f). The red solid line in (b) is the fitting result based on Drude model. The red solid line in (d) demonstrates the linear relation between the imaginary permittivity and the reciprocal of frequency. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
εr } ¼
d RA2π f ε0
increases with the increase of Al content (shown in Fig. 2a). The inset shows the abroad peak located at 2θ ¼ 19.9� , indicating the amorphous nature of APu. In addition, Fig. 2b shows the FTIR spectra of pure APu and the APu/Al composite with 86.41 vol% of Al in the range of 1000–4000 cm 1. The two peaks located at 3373 and 1532 cm 1 are associated with N–H bonds [33]. Moreover, the absorption peaks at 1458, 1372, and 2863-2968 cm 1 are attributed to the C–H groups [34]. The characteristic peak at 1242 cm 1 is derived from the stretching vibration of C–O–C bond. The characteristic fingerprint bands in the range of 1701–1757 cm 1 are corresponding to C¼O bonds, and the feature peak at 1163 cm 1 belongs to the C–N bond. As demonstrated above, there is no chemical reaction between the Al and the matrix, confirming that the APu/Al composites have been successfully prepared.
(5)
where d is the sample thickness, C is the capacitance, A is the electrode plate area, ε0 is the vacuum dielectric constant (8.85 � 10 12 F m 1), R is the resistance, and f is the frequency of the electric field. 3. Results and discussion The phase composition and chemical structure of the APu/Al com posites are reflected by XRD patterns and FTIR spectra, respectively, as shown in Fig. 2. The diffraction peaks belonging to Al phase can be observed in the prepared samples, and the peak intensity gradually 4
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flexibility. The dielectric properties of the APu/Al composites are shown in Fig. 4. A high permittivity of about 315 is observed at 10 MHz in the APu/Al composite with 43.84 vol% Al content (Fig. 4a), accompanying with a high imaginary permittivity (Fig. 4c) and dielectric loss tangent of about 0.26 (Fig. 4e). Additionally, a permittivity as high as 158 with lower dielectric loss of 0.045 is obtained at 10 MHz in the composite with 57.23 vol% of Al content, which is favorable for radio frequency capacitors. Table 1 shows the comparison of the high permittivity in various polymer-based composites. Such a high permittivity with low dielectric loss achieved in this work is remarkable at megahertz. In principle, the permittivity drops when the content of conductive filler exceeds the percolation threshold. Thus, we assume that 57.23 vol% of Al content has exceeded the percolation threshold. The imaginary permittivity of the composites is also decreased when the Al content reaches 57.23 vol% and 75.07 vol%, but it is still much higher than that of the composites with lower Al content (Fig. 4c). This can be explained by the formation of conductive pathways, where the polarization loss is reduced while conductive loss is increased [38]. The dielectric loss of APu/Al composites with 57.23 vol% and 75.07 vol% of Al content keeps at low level on account of the high real permittivity and self-passivation layers that impede the leakage current (Fig. 4e). When Al content is further increased to 86.41 vol%, the negative permittivity behavior is observed (Fig. 4b), which is attributed to the low-frequency plasma oscillation of free electrons in continuous conductive pathway [46–48]. Theoretically, the negative permittivity versus frequency can be explained by Drude, as following [49],
Table 1 Comparison of high permittivity of typical polymer-based composites at high frequency reported in the recent literatures. Material systems
Permittivity
Dielectric loss
Fillers’ content (volume fraction: vol%, mass fraction: wt%)
Poly(vinylidene fluoride)graphene-BaTiO3 [39]
65 (@1 MHz)
0.35 (@1 MHz)
Poly(vinylidene fluoride)Ba0.95Ca0.05Zr0.15Ti0.85O3 [40] Polysulfone-multiwalled carbon nanotubes [41] Polyethylene-poly(vinylidene fluoride)-carbon nanotube [42] Poly(vinylidene fluoride)carbon black [43] Poly(vinylidene fluoride)graphene [44]
70 (@10 MHz)
0.18 (@10 MHz)
BaTiO3: 30 vol% graphene: 1.25 vol% 71 vol%
58 (@1 MHz) <50 (@1 MHz)
0.09 (@1 MHz) >0.1 (@1 MHz)
25 vol%
15 (@10 MHz) ~17 (@10 MHz)
7 wt%
Silicon elastomer-graphene nanoribbons [45]
6 (@10 MHz)
Acrylic PolyurethaneAluminum(this work)
158 (@10 MHz)
0.2 (@10 MHz) ~0.35 (@10 MHz) 0.008 (@10 MHz) 0.045 (@10 MHz)
8 vol%
16 wt% 0.5 wt% 57.23 vol%
ω2p
0
εr ðωÞ ¼ 1
ω þ ω2τ 2
sffiffiffiffiffiffiffiffiffiffiffi neff e2 ωp ¼ 2πfp ¼ meff ε0
(6)
(7)
where ω is angular frequency (ω ¼ 2πf), ωτ is the collisional frequency and inverse of relaxation time (ωτ ¼ 1/τ), ωp is the plasma frequency, neff is effective concentration of the free electrons, and meff is the effective mass of the electron. The Al particles embedded in APu matrix lead to the dilution of effective electron concentration and the increase of the effective electron mass. Therefore, a low-frequency plasmonic state is achieved. The experimental data are consistent well with the Drude model (the solid line in Fig. 4b), in which the fitting parameters ωp and ωτ are 8.51 GHz and 429.86 MHz, respectively. The imaginary permit tivity (Fig. 4d) shows a nearly linear relationship between ε" and 1/f at low frequency, demonstrating that the conductive loss dominates in the low-frequency region, and polarization loss takes it away from the linear relationship in the high-frequency region [8]. The dielectric loss tangent (Fig. 4f) shows a peak at 812 MHz, which is in accordance with zero cross point of permittivity in Fig. 4b. Dielectric loss in the most test frequency region is less than 3, which is relatively lower compared with the loss of negative permittivity materials reported previously [7,8]. Interestingly, the ε-near-zero region with a loss peak has perfect ab sorption effect in various communication equipment, arousing increasing interests recently [50–52]. The permittivity as a function of Al content is shown in the Fig. 5. With the increase of Al content, the permittivity goes up first (І), then it goes down (ІІ), and finally it becomes negative (Ш). Such a change trend should be universal in percolative composites. The experimental data in part I is fitted by Equation (3), and the fitting parameters fc and q are 47.05 vol% and 0.93, respectively. When the volume fraction of Al is slightly below the fc, a number of microcapacitors are formed, and thus the permittivity is gradually enhanced. When the volume fraction of Al is marginally above the fc, some Al particles will connect with each other to form the conductive pathways. As a result, a few microcapacitances are converted to inductances, and the permittivity goes down (parts II). When the Al content further increases to a higher level (86.41 vol%),
Fig. 5. Permittivity of the APu/Al composites with different Al content at 10 MHz. The resistances (R) of APu/Al composites always exist. The isolated Al particles and the APu matrix are responsible for the capacitors (C). The conductive loops formed by the interconnected Al networks are regarded as the inductors (L).
The morphological characteristics of pure Al particles and APu/Al composites are presented in Fig. 3. The average particle size of Al powders is about 1–4 μm, as shown in Fig. 3a. The SAED from the surface of Al particle is shown in Fig. 3b. The crystal planes (111) and (200) are belonging to the Al. The crystal planes (003) and (202) are assigned to the Al2O3 [35–37]. Therefore, the self-passivation layers have formed on the surface of Al particles. The surface morphology of the APu/Al composites is relatively smooth without any obvious bubbles and cracks, and the Al particles are distributed uniformly in the APu matrix (Fig. 3c and d). According to the cross-sectional SEM image (Fig. 3e) and the corresponding EDX results (Fig. 3f), we can see that some of ellipsoidal Al particles are connected in the APu/Al composite with 57.23 vol% of Al. It is worth noting that the composite with 57.23 vol% of Al content still can be folded (inset in Fig. 3f), demonstrating its excellent 5
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Composites Science and Technology 188 (2020) 107969
Fig. 6. Frequency dependence of the reactance of APu/Al composites with different Al content (a, b). Frequency dependence of ac conductivity (σac) of APu/Al composites (c, d). The red solid lines in (c) and (d) are the fitting results based on Jonscher power law and Drude model, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
more conductive pathways are formed and the inductance dominates over the capacitance, so the negative permittivity is achieved (parts III). The reactance (Z00 ) of the APu/Al composites with different Al con tent are shown in Fig. 6a and Fig. 6b. The reactance of the APu/Al composites is commonly expressed as the relationship: Z" ¼ ZLþZC, where ZC is the capacitive reactance (ZC ¼ 1/ωC, C is the capacitance) and ZL is the inductive reactance (ZL ¼ ωL, L is the inductance). For the APu/Al composites with lower Al content, the Z00 would be negative, which manifests a capacitive character (Fig. 6a). After the Al content exceeds the percolation threshold, the reactance will decrease yet remain negative, which is confirmed by the assumption in Fig. 5. With the increase of Al content, Z00 first increases due to the enhanced microcapacitors in APu/Al interfaces, and then decreases since some of microcapacitors change into inductors. For the APu/Al composite with 86.41 vol% of Al content (Fig. 6b), the conductive paths have been formed, and Z00 presents an inductive character. The reactance changes from positive to negative at high frequency, which is in sharp contrast with the transformation of the permittivity in Fig. 4b. In brief, the capacitive-inductive transition observed in APu/Al composites corre sponds to the permittivity change from positive to negative. Frequency dependence of ac conductivity (σac) for the APu/Al composites is shown in Fig. 6c and d. The ac conductivity goes up with the increasing Al content at low frequency. In addition, σac enhances with the increase of frequency, which follows the Jonscher power law: σ ac ¼ σdcþAωn [53], where σ dc is the direct current conductivity, A is the pre-exponential factor and n is the fractional exponent. The experi mental data matches well with the power law (red solid lines in Fig. 6c), indicating a hopping conduction behavior [54]. For the APu/Al com posite with 86.41 vol% of Al content, σ ac is decreased with the increase of frequency due to the skin effect, manifesting a metal-like conduction
behavior [55,56]. Usually, the ac conductivity of metal-like materials is also described as the Drude model [57],
σ ac ¼
σdc ω2τ ω2 þ ω2τ
(8)
where the fitting parameters σ dc is 0.076 S cm 1. As shown in Fig. 6d, the Equation (8) agrees well with the experimental data (red solid line). The permittivity transition in APu/Al composites has been qualita tive discussed above, while the quantitative prediction of dielectric behavior still needs to be further investigated, especially when the conductive fillers content is above the percolation threshold. In mega hertz frequency range, the particle size is much less than the wave length, and the quasi-static approximation can be used to describe the response of an individual particle. Given that Faraday’s law of in ductions is ignored, the electromagnetic response can be described in terms of the complex dielectric function: ε ¼ ε’þiε", and complex con ductivity: σ ¼ σ’þiσ "; these two parameters are related to the formula: ε ¼ 4πiσ/ω [58]. The σ0 of percolative composites is widely described by Equation (1) when f> fc, so:
ε’’ ¼
4πσM ðf
ω
fc Þt
for f > fc
(9)
Additionally, the real and imaginary permittivity should follow the Kramers-Kronig relation, which provides an approach to obtain the real permittivity from imaginary permittivity. The integral transformation of the Kramers-Kronig relation for the complex permittivity is shown as following [59]: Z 0 1 2 ∝ ω 1 0 (10) ¼1 þ dω 0 εr ðωÞ π 0 ω0 2 ω2 ε00r ðω0 Þ 6
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frequency plasma oscillation. Significantly, the universal change rules of permittivity in percolative composites are systematically demon strated. The impedance analysis shows that the capacitive-inductive transition corresponds to the permittivity changing from positive to negative. The ac conductivity of APu/Al composites shows hooping conduction when the Al content is lower, following the Jonscher power law. Meanwhile, a metal-like conductive behavior is observed when Al content is increased to 86.41 vol%, which can be fitted by Drude model. Finally, a derived model for predicting the permittivity is presented for the excessively percolative composites, which will supplement the existing theoretical framework of the percolation theory. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Zhongyang Wang: Investigation, Visualization, Writing - original draft. Kai Sun: Conceptualization, Data curation. Peitao Xie: Formal analysis. Yao Liu: Resources. Qilin Gu: Methodology, Writing - review & editing. Runhua Fan: Methodology, Supervision, Project administration. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51601105, No. 51871146 and No. 51803119), the Innovation Program of Shanghai Municipal Education Commission (Grant No. 2019-01-07-00-10-E00053) and Chenguang Program sup ported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (Grant No. 18CG56). Zhongyang Wang acknowledges the support from the China Scholarship Council.
Fig. 7. Comparison between the calculated and measured permittivity of APu/ Al composites when the Al content exceeds the percolation threshold.
With the combination of Equations (9) and (10), and taking σ ac as the approximation of σM when Al content is above percolation threshold, the permittivity can be described as following: Z 0 1 2 ∞ ω ω 0 (11) ¼1þ 0 t d ω for f > fc 0 02 εr ðωÞ π 0 ω ω2 4πσ ac ðω Þðf fc Þ
References [1] J. Xi, Y. Liu, Y. Wu, J. Hu, W. Gao, E. Zhou, H. Chen, Z. Chen, Y. Chen, C. Gao, Multifunctional bicontinuous composite foams with ultralow percolation thresholds, ACS Appl. Mater. Interfaces 10 (24) (2018) 20806–20815. [2] K. Sun, Z. Zhang, L. Qian, F. Dang, X. Zhang, R. Fan, Dual percolation behaviors of electrical and thermal conductivity in metal-ceramic composites, Appl. Phys. Lett. 108 (6) (2016), 061903. [3] L. Wang, Y. Bai, X. Lu, J.-L. Cao, L.-J. Qiao, Ultra-low percolation threshold in ferrite-metal cofired ceramics brings both high permeability and high permittivity, Sci. Rep. 5 (2015) 7580. [4] C.-W. Nan, Physics of inhomogeneous inorganic materials, Prog. Mater. Sci. 37 (1) (1993) 1–116. [5] J. Zhu, X. Ji, M. Yin, S. Guo, J. Shen, Poly (vinylidene fluoride) based percolative dielectrics with tunable coating of polydopamine on carbon nanotubes: toward high permittivity and low dielectric loss, Compos. Sci. Technol. 144 (2017) 79–88. [6] J. Shao, J.-W. Wang, D.-N. Liu, L. Wei, S.-Q. Wu, H. Ren, A novel high permittivity percolative composite with modified MXene, Polymer 174 (2019) 86–95. [7] C. Cheng, R. Fan, Y. Ren, T. Ding, L. Qian, J. Guo, X. Li, L. An, Y. Lei, Y. Yin, Radio frequency negative permittivity in random carbon nanotubes/alumina nanocomposites, Nanoscale 9 (18) (2017) 5779–5787. [8] Y. Sun, J. Wang, S. Qi, G. Tian, D. Wu, Permittivity transition from highly positive to negative: polyimide/carbon nanotube composite’s dielectric behavior around percolation threshold, Appl. Phys. Lett. 107 (1) (2015), 012905. [9] Z.M. Dang, J.K. Yuan, S.H. Yao, R.J. Liao, Flexible nanodielectric materials with high permittivity for power energy storage, Adv. Mater. 25 (44) (2013) 6334–6365. [10] Z.-M. Dang, J.-K. Yuan, J.-W. Zha, T. Zhou, S.-T. Li, G.-H. Hu, Fundamentals, processes and applications of high-permittivity polymer–matrix composites, Prog. Mater. Sci. 57 (4) (2012) 660–723. [11] F. Zhang, T. Li, Y. Luo, A new low moduli dielectric elastomer nano-structured composite with high permittivity exhibiting large actuation strain induced by low electric field, Compos. Sci. Technol. 156 (2018) 151–157. [12] Z. Wang, X. Fu, Z. Zhang, Y. Jiang, M. Waqar, P. Xie, K. Bi, Y. Liu, X. Yin, R. Fan, Paper based metasurface: turning waste-paper into a solution for electromagnetic pollution, J. Clean. Prod. 234 (2019) 588–596. [13] V.M. Shalaev, Optical negative-index metamaterials, Nat. Photonics 1 (1) (2007) 41.
The calculated results by Equation (11) are shown in Fig. 7. It is obvious that the calculated permittivity is close to the test results when the Al content exceeds fc, while the permittivity remains positive (Fig. 7a). However, Equation (11) fails to predict the negative permit tivity (Fig. 7b), mainly because the negative permittivity has high dispersion, and the integral interval is 10 MHz-1 GHz, rather than from 0 to infinity. Additionally, it is attributed to the fact that the conductive current dominates only in the low-frequency range(|ε’|≪ε"), and the displacement current dominates in the high frequency region(|ε’|≫ε") [60]. Thus, taking σ ac approximately equal to σM is not suitable at the high frequency. Although there is a deviation between the calculated results and the experimental data, it can be regarded as a supplement of the existing percolation theory, and a reliable prediction of the negative permittivity behavior still need to be explored in the future. It’s worth noting that Equation (11) is based on the Kramers-Kronig relation. Therefore, the derived formula is applicable only when the permittivity of materials remains a linear response, and at the same time the skin effect can be ignored. 4. Conclusions In summary, the permittivity transition of APu/Al composites from positive to negative is investigated. The high permittivity with low dielectric loss is obtained in the APu/Al composites with 57.23 vol% of Al. Moreover, a negative permittivity behavior is observed in the com posites with 86.41 vol% Al content, which can be explained by low7
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Composites Science and Technology 188 (2020) 107969 [38] K. Sun, P. Xie, Z. Wang, T. Su, Q. Shao, J. Ryu, X. Zhang, J. Guo, A. Shankar, J. Li, Flexible polydimethylsiloxane/multi-walled carbon nanotubes membranous metacomposites with negative permittivity, Polymer 125 (2017) 50–57. [39] D. Wang, T. Zhou, J.-W. Zha, J. Zhao, C.-Y. Shi, Z.-M. Dang, Functionalized graphene-BaTiO3/ferroelectric polymer nanodielectric composites with high permittivity, low dielectric loss, and low percolation threshold, J. Mater. Chem. 1 (20) (2013) 6162–6168. [40] B. Luo, X. Wang, Y. Wang, L. Li, Fabrication, characterization, properties and theoretical analysis of ceramic/PVDF composite flexible films with high dielectric constant and low dielectric loss, J. Mater. Chem. 2 (2) (2014) 510–519. [41] H. Liu, Y. Shen, Y. Song, C.W. Nan, Y. Lin, X. Yang, Carbon nanotube array/ polymer core/shell structured composites with high dielectric permittivity, low dielectric loss, and large energy density, Adv. Mater. 23 (43) (2011) 5104–5108. [42] J.-K. Yuan, S.-H. Yao, A. Sylvestre, J. Bai, Biphasic polymer blends containing carbon nanotubes: heterogeneous nanotube distribution and its influence on the dielectric properties, J. Phys. Chem. C 116 (2) (2012) 2051–2058. [43] J. Zhu, J. Shen, S. Guo, H.-J. Sue, Confined distribution of conductive particles in polyvinylidene fluoride-based multilayered dielectrics: toward high permittivity and breakdown strength, Carbon 84 (2015) 355–364. [44] B. Lin, Z.-T. Li, Y. Yang, Y. Li, J.-C. Lin, X.-M. Zheng, F.-A. He, K.-H. Lam, Enhanced dielectric permittivity in surface-modified graphene/PVDF composites prepared by an electrospinning-hot pressing method, Compos. Sci. Technol. 172 (2019) 58–65. [45] A. Dimiev, W. Lu, K. Zeller, B. Crowgey, L.C. Kempel, J.M. Tour, Low-loss, highpermittivity composites made from graphene nanoribbons, ACS Appl. Mater. Interfaces 3 (12) (2011) 4657–4661. [46] H. Gu, X. Xu, M. Dong, P. Xie, Q. Shao, R. Fan, C. Liu, S. Wu, R. Wei, Z. Guo, Carbon nanospheres induced high negative permittivity in nanosilverpolydopamine metacomposites, Carbon 147 (2019) 550–558. [47] H. Gu, J. Guo, Q. He, Y. Jiang, Y. Huang, N. Haldolaarachige, Z. Luo, D.P. Young, S. Wei, Z. Guo, Magnetoresistive polyaniline/multi-walled carbon nanotube nanocomposites with negative permittivity, Nanoscale 6 (1) (2014) 181–189. [48] H. Gu, J. Guo, M.A. Khan, D.P. Young, T. Shen, S. Wei, Z. Guo, Magnetoresistive polyaniline–silicon carbide metacomposites: plasma frequency determination and high magnetic field sensitivity, Phys. Chem. Chem. Phys. 18 (29) (2016) 19536–19543. [49] C. Cheng, R. Fan, G. Fan, H. Liu, J. Zhang, J. Shen, Q. Ma, R. Wei, Z. Guo, Tunable negative permittivity and magnetic performance of yttrium iron garnet/ polypyrrole metacomposites at the RF frequency, J. Mater. Chem. C 7 (11) (2019) 3160–3167. [50] S. Feng, K. Halterman, Coherent perfect absorption in epsilon-near-zero metamaterials, Phys. Rev. B 86 (16) (2012) 165103. [51] S. Feng, Loss-induced omnidirectional bending to the normal in ε-near-zero metamaterials, Phys. Rev. Lett. 108 (19) (2012) 193904. [52] T.S. Luk, S. Campione, I. Kim, S. Feng, Y.C. Jun, S. Liu, J.B. Wright, I. Brener, P. B. Catrysse, S. Fan, Directional perfect absorption using deep subwavelength lowpermittivity films, Phys. Rev. B 90 (8) (2014), 085411. [53] Y. Qu, G. Fan, D. Liu, Y. Gao, C. Xu, J. Zhong, P. Xie, Y. Liu, Y. Wu, R. Fan, Functional nano-units prepared by electrostatic self-assembly for three-dimension carbon networks hosted in CaCu3Ti4O12 ceramics towards radio-frequency negative permittivity, J. Alloy. Comp. 743 (2018) 618–625. [54] Z. Wang, K. Sun, P. Xie, Y. Liu, R. Fan, Generation mechanism of negative permittivity and Kramers–Kronig relations in BaTiO3/Y3Fe5O12 multiferroic composites, J. Phys. Condens. Matter 29 (36) (2017) 365703. [55] H. Wu, Y. Qi, Z. Wang, W. Zhao, X. Li, L. Qian, Low percolation threshold in flexible graphene/acrylic polyurethane composites with tunable negative permittivity, Compos. Sci. Technol. 151 (2017) 79–84. [56] R. Yin, X. Huang, L. Qian, Freeze-drying assisted fabrication of highly homogenized reduced graphene oxide/alumina metacomposites with negative permittivity, Ceram. Int. 45 (5) (2019) 5653–5659. [57] Z. Wang, P. Xie, C. Cheng, G. Fan, Z. Zhang, R. Fan, X. Yin, Regulation mechanism of negative permittivity in poly (p-phenylene sulfide)/multiwall carbon nanotubes composites, Synth. Met. 244 (2018) 15–19. [58] V.M. Shalaev, Electromagnetic properties of small-particle composites, Phys. Rep. 272 (2–3) (1996) 61–137. [59] H. Sadeghi, A. Zolanvar, H. Khalili, M. Goodarzi, J. Nezamdost, S. Nezamdost, Effective permittivity of metal–dielectric plasmonics nanostructures, Plasmonics 9 (2) (2014) 415–425. [60] J.S. Moya, S. Lopez-Esteban, C. Pecharrom� an, The challenge of ceramic/metal microcomposites and nanocomposites, Prog. Mater. Sci. 52 (7) (2007) 1017–1090.
[14] L. Wang, Z.-M. Dang, Carbon nanotube composites with high dielectric constant at low percolation threshold, Appl. Phys. Lett. 87 (4) (2005), 042903. [15] C. Huang, Q. Zhang, Enhanced dielectric and electromechanical responses in high dielectric constant all-polymer percolative composites, Adv. Funct. Mater. 14 (5) (2004) 501–506. [16] T. Tsutaoka, T. Kasagi, S. Yamamoto, K. Hatakeyama, Low frequency plasmonic state and negative permittivity spectra of coagulated Cu granular composite materials in the percolation threshold, Appl. Phys. Lett. 102 (18) (2013) 181904. [17] K. Sun, J. Dong, Z. Wang, Z. Wang, G. Fan, Q. Hou, L. An, M. Dong, R. Fan, Z. Guo, Tunable negative permittivity in flexible graphene/PDMS metacomposites, J. Phys. Chem. C 123 (38) (2019) 23635–23642. [18] Z.-H. Dai, T. Li, Y. Gao, J. Xu, J. He, Y. Weng, B.-H. Guo, Achieving high dielectric permittivity, high breakdown strength and high efficiency by cross-linking of poly (vinylidene fluoride)/BaTiO3 nanocomposites, Compos. Sci. Technol. 169 (2019) 142–150. [19] Y. Shen, Y. Lin, C.W. Nan, Interfacial effect on dielectric properties of polymer nanocomposites filled with core/shell-structured particles, Adv. Funct. Mater. 17 (14) (2007) 2405–2410. [20] Y. Shen, Y. Lin, M. Li, C.W. Nan, High dielectric performance of polymer composite films induced by a percolating interparticle barrier layer, Adv. Mater. 19 (10) (2007) 1418–1422. [21] C. Yang, Y. Lin, C. Nan, Modified carbon nanotube composites with high dielectric constant, low dielectric loss and large energy density, Carbon 47 (4) (2009) 1096–1101. [22] J. Xu, C. Wong, Low-loss percolative dielectric composite, Appl. Phys. Lett. 87 (8) (2005), 082907. [23] X. Huang, P. Jiang, C. Kim, Electrical properties of polyethylene/aluminum nanocomposites, J. Appl. Phys. 102 (12) (2007) 124103. [24] F. He, S. Lau, H.L. Chan, J. Fan, High dielectric permittivity and low percolation threshold in nanocomposites based on poly (vinylidene fluoride) and exfoliated graphite nanoplates, Adv. Mater. 21 (6) (2009) 710–715. [25] S. Luo, S. Yu, R. Sun, C.-P. Wong, Nano Ag-deposited BaTiO3 hybrid particles as fillers for polymeric dielectric composites: toward high dielectric constant and suppressed loss, ACS Appl. Mater. Interfaces 6 (1) (2013) 176–182. [26] N. Engheta, An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability, IEEE Anten. Wirel. Pr. 1 (2002) 10–13. [27] D. Schurig, J. Mock, B. Justice, S.A. Cummer, J.B. Pendry, A. Starr, D. Smith, Metamaterial electromagnetic cloak at microwave frequencies, Science 314 (5801) (2006) 977–980. [28] D. Estevez, F. Qin, Y. Luo, L. Quan, Y.-W. Mai, L. Panina, H.-X. Peng, Tunable negative permittivity in nano-carbon coated magnetic microwire polymer metacomposites, Compos. Sci. Technol. 171 (2019) 206–217. [29] J. Wang, Z. Shi, F. Mao, S. Chen, X. Wang, Bilayer polymer metacomposites containing negative permittivity layer for new high-k materials, ACS Appl. Mater. Interfaces 9 (2) (2017) 1793–1800. [30] Y.-F. Hou, W.-L. Li, T.-D. Zhang, Y. Yu, R.-L. Han, W.-D. Fei, Negative capacitance in BaTiO3/BiFeO3 bilayer capacitors, ACS Appl. Mater. Interfaces 8 (34) (2016) 22354–22360. [31] F. Xue, D. Jia, Y. Li, X. Jing, Facile preparation of a mechanically robust superhydrophobic acrylic polyurethane coating, J. Mater. Chem. 3 (26) (2015) 13856–13863. [32] R. Udagama, E. Degrandi-Contraires, C. Creton, C. Graillat, T.F. McKenna, E. Bourgeat-Lami, Synthesis of acrylic polyurethane hybrid latexes by miniemulsion polymerization and their pressure-sensitive adhesive applications, Macromolecules 44 (8) (2011) 2632–2642. [33] O. Pardini, J. Amalvy, FTIR, 1H-NMR spectra, and thermal characterization of water-based polyurethane/acrylic hybrids, J. Appl. Polym. Sci. 107 (2) (2008) 1207–1214. [34] Y. Zhu, J. Xiong, Y. Tang, Y. Zuo, EIS study on failure process of two polyurethane composite coatings, Prog. Org. Coat. 69 (1) (2010) 7–11. [35] G. Meng, L. Wei, T. Zhang, Y. Shao, F. Wang, C. Dong, X. Li, Effect of microcrystallization on pitting corrosion of pure aluminium, Corros. Sci. 51 (9) (2009) 2151–2157. [36] R. Jamaati, M.R. Toroghinejad, J. Dutkiewicz, J.A. Szpunar, Investigation of nanostructured Al/Al2O3 composite produced by accumulative roll bonding process, Mater. Des. 35 (2012) 37–42. [37] X. Nie, E. Meletis, J. Jiang, A. Leyland, A. Yerokhin, A. Matthews, Abrasive wear/ corrosion properties and TEM analysis of Al2O3 coatings fabricated using plasma electrolysis, Surf. Coat. Technol. 149 (2–3) (2002) 245–251.
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Contents lists available at ScienceDirect
Composites Science and Technology journal homepage: http://www.elsevier.com/locate/compscitech
Permittivity transition from positive to negative in acrylic polyurethane-aluminum composites Zhongyang Wang a, b, c, Kai Sun a, **, Peitao Xie b, Yao Liu b, Qilin Gu c, *, Runhua Fan a, *** a
College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai, 201306, China Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials (Ministry of Education), Shandong University, Jinan, 250061, China c Department of Materials Science and Engineering, National University of Singapore, 117574, Singapore b
A R T I C L E I N F O
A B S T R A C T
Keywords: A-flexible composites A-polymer-matrix composites B-Electrical properties Negative permittivity
The insulator-conductor percolative composites have been mostly constructed to achieve high permittivity and negative permittivity. In this work, permittivity transition from positive to negative is investigated in acrylic polyurethane-aluminum (APu/Al) percolative composites at radio frequency. Both the high permittivity and negative permittivity are accompanied with low loss due to the self-passivated nature of aluminum. The reac tance and ac conductivity are studied to explain the dielectric properties, which provides an essential insight into the universal principles of high permittivity and negative permittivity behaviors in percolative composites. Meanwhile, when the conductive filler content exceeds the percolation threshold, a derived formula of permittivity has been put forward on the basis of the existing theoretical framework of percolation theory. Resourceful dielectric properties of APu/Al percolative composites will make them as potential alternatives for capacitors and metamaterials.
1. Introduction The insulator-conductor percolative composites not only involve a nonlinear conductivity transition with the increasing conductive fillers, but also possess a wide variety of functional properties, such as elasticity [1], thermal conductivity [2], magnetic permeability [3] as well as dielectric response [4]. In particular, the dielectric permittivity has been widely studied, both high permittivity and negative permittivity are achieved in the insulator-conductor percolative composites [5–8]. Spe cifically, the ones with high permittivity and low dielectric loss are widely used as capacitors in microelectronics and electrical energy storage devices [9–11]. In addition, negative permittivity materials have attracted considerable attention as so-called metamaterials in the recent years, which exhibit enticing electromagnetic properties in some mi crowave and optical devices [12,13]. For percolative composites, high permittivity can be obtained when the volume fraction of the conductive filler is slightly below the percolation threshold. In contrast, negative permittivity will occur when the volume fraction of the conductive filler exceeds the percolation threshold, and a large number of conductive pathways have been formed. Conductivity and permittivity of a
percolative system should obey power-law behaviors, as determined by the following equations [10],
σ ¼ σM ðf
fc Þt for f > fc
(1)
σ ¼ σD ðfc
f Þ q for f < fc
(2)
ε∝ðfc
f Þ q for f < fc
(3)
where f is the volume fraction of fillers, fc is the percolation threshold,
σ M and σ D are respectively the conductivities of the metallic and
dielectric components, q and t are critical exponents. Obviously, the traditional percolation theory is failed in predicating the permittivity when f >fc, so it is necessary to study the dielectric permittivity behavior when the conductive fillers content exceeds the percolation threshold, especially to evaluate the negative permittivity behavior. The percolative composites are mainly classified into ceramic-based and polymer-based composites. Usually, the ceramic-matrix composites are brittle and high-temperature processed, whereas, the polymer-based composites are flexible and easy to process. Therefore, great efforts have
* Corresponding author. ** Corresponding author. *** Corresponding author. E-mail addresses: [email protected] (K. Sun), [email protected] (Q. Gu), [email protected] (R. Fan). https://doi.org/10.1016/j.compscitech.2019.107969 Received 27 August 2019; Received in revised form 13 December 2019; Accepted 22 December 2019 Available online 24 December 2019 0266-3538/© 2019 Elsevier Ltd. All rights reserved.
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Composites Science and Technology 188 (2020) 107969
Fig. 1. Schematic illustration of the preparation process for the APu/Al composites.
been made to construct the polymer-based percolative composites for achieving high permittivity [14,15] and negative permittivity [16,17]. In general, high permittivity and low dielectric loss (tanδ) of percolative composite are rather difficult to achieve at the same time [18]. Thus, several feasible approaches have been developed to prevent conductive fillers connecting with each other directly, so as to reduce tanδ [19]. For example, Nan et al. [20] have coated the Ag cores with thin organic shells, which remarkably reduced the dielectric loss (less than 5%). Similarly, Yang et al. [21] have wrapped multiwall carbon nanotubes around polypyrrole to screen charge movement and decrease leakage current. Some self-passivation metal, such as aluminum (Al) is also promising to realize high permittivity and negative permittivity with low dielectric loss. For example, a high permittivity (εr~110) with low dielectric loss (about 0.02) was reported in Al/epoxy composites at 10 kHz [22]. Moreover, a permittivity as high as 100 was achieved in Al/polyethylene composites with a dielectric loss of about 0.26 at extremely low frequency (10 1 Hz) [23]. Yet as the development of miniaturization and high working frequency for electronics, to achieve high permittivity at high frequency is urgently pursued. The main challenge is that the permittivity decreases abruptly in the high fre quency region, which is widely known as relaxation phenomenon. For instance, a high permittivity of about 2700 was obtained in the poly (vinylidene fluoride)/graphite nanoplates nanocomposite at 100 Hz, but only 200 at 1 kHz [24]. It is rather difficult for the polymer matrix composites to possess a large permittivity (ε > 100) without raising dielectric loss (i.e. keep tanδ<5%) above 10 MHz [25]. Thus, herein we try to explore high permittivity behaviors in percolative composites at radio frequency. In this frequency band, negative permittivity materials are also significant in various communication devices, such as antennas [26], electromagnetic cloaks [27,28], capacitors [29] and transistors [30]. Therefore, the investigation of permittivity transition from posi tive to negative in percolative composites at megahertz is more practi cally meaningful. In this work, percolative composites consisting of commercial acrylic polyurethane and Al particles are well constructed. Acrylic polyurethane (APu) is widely used in coating industries because of its favorable properties, such as the stable adhesion to most substrates, high flexi bility and excellent abrasive resistance [31,32]. Therefore, APu/Al composites have potential applications in wearable devices and flexible invisibility cloaks, which requires the careful study on their dielectric properties, especially, the high permittivity and negative permittivity. In
Fig. 2. (a) XRD patterns of the APu/Al composites with different volume fractions of Al particles. The inset in (a) is the enlarged partial view of the XRD pattern of amorphous APu. (b) FTIR spectra of pure APu and the APu/Al composite with 86.41 vol% of Al. 2
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Fig. 3. The SEM image (a) and SAED pattern (b) of pure Al particles. The surface morphology (c, d) and cross-sectional SEM image (e) of the APu/Al composites. (f) The EDX spectra of the APu/Al composite with 57.23 vol% Al content. The inset in (f) shows the flexibility of the APu/Al composites.
addition, the reactance characteristics and ac conductivities of APu/Al composites are investigated to explain the permittivity transition pro cess from positive to negative. Finally, a derived formula is firstly put forward to describe the permittivity behaviors in excessively percolative composites.
APu matrix, the mixed slurries were transferred into the high-viscosity spray gun. Subsequently, the slurries were spray-coated onto a clean and smooth poly-tetrafluoroethylene substrate, and then dried at room temperature for 48 h. Finally, the APu/Al composites were obtained after carefully stripping from the substrate.
2. Experimental
2.2. Characterization and electrical measurement
2.1. Fabrication of the APu/Al composites
The phase structure of the composites was analyzed by X-ray diffraction (XRD, Tokyo, Japan). The morphology and microstructures of samples were observed by transmission electron microscope (TEM, JEM-3010, Questar, New Hope,USA)and field emission scanning elec tron microscopy (FESEM, SU-70, Hitachi, Tokyo, Japan) equipped with Energy Dispersive X-ray (EDX) Detector. The chemical components were examined by Fourier transform infrared spectra (FTIR, IRPrestige-21, Shimadzu, Japan). The dielectric property and ac conductivity were examined by Agilent E4991A RF Impedance Analyzer equipped with 16453A test fixture. The complex permittivity and ac conductivity were calculated from the following equations,
Untreated Al particles (Aladdin Co. Ltd, China) have a compact passivation layer to store themselves steady in case of high activity. Then, the Al particles were heated in air atmosphere at 180 � C for 2 h to form the reinforced passivation layer to block the conductive current in the composites. The precursor and curing agent of APu are commercial grade products (Marine Chemical Research Institute Co. Ltd, China) without any further treatment. The APu/Al composites with different volume fractions of Al particles were prepared by an in-situ polymeri zation process, and the detailed schematic is shown in Fig. 1. Firstly, Al particles and precursor of APu were dispersed in a beaker, and then the mixture was mechanically stirred and ultrasonically treated for 30 min to form a uniform suspension. After that, the curing agent was added into the beaker, followed by repeatedly stirring and ultrasonic treatment for another 30 min. After Al particles were uniformly dispersed into the
εr ’ ¼
3
Cd
ε0 A
(4)
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Composites Science and Technology 188 (2020) 107969
Fig. 4. Frequency dependence of the complex permittivity for the APu/Al composites. The real parts (a, b) and imaginary parts (c, d) of the permittivity. The dielectric loss tangent (tanδ) of the APu/Al composites (e, f). The red solid line in (b) is the fitting result based on Drude model. The red solid line in (d) demonstrates the linear relation between the imaginary permittivity and the reciprocal of frequency. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
εr } ¼
d RA2π f ε0
increases with the increase of Al content (shown in Fig. 2a). The inset shows the abroad peak located at 2θ ¼ 19.9� , indicating the amorphous nature of APu. In addition, Fig. 2b shows the FTIR spectra of pure APu and the APu/Al composite with 86.41 vol% of Al in the range of 1000–4000 cm 1. The two peaks located at 3373 and 1532 cm 1 are associated with N–H bonds [33]. Moreover, the absorption peaks at 1458, 1372, and 2863-2968 cm 1 are attributed to the C–H groups [34]. The characteristic peak at 1242 cm 1 is derived from the stretching vibration of C–O–C bond. The characteristic fingerprint bands in the range of 1701–1757 cm 1 are corresponding to C¼O bonds, and the feature peak at 1163 cm 1 belongs to the C–N bond. As demonstrated above, there is no chemical reaction between the Al and the matrix, confirming that the APu/Al composites have been successfully prepared.
(5)
where d is the sample thickness, C is the capacitance, A is the electrode plate area, ε0 is the vacuum dielectric constant (8.85 � 10 12 F m 1), R is the resistance, and f is the frequency of the electric field. 3. Results and discussion The phase composition and chemical structure of the APu/Al com posites are reflected by XRD patterns and FTIR spectra, respectively, as shown in Fig. 2. The diffraction peaks belonging to Al phase can be observed in the prepared samples, and the peak intensity gradually 4
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flexibility. The dielectric properties of the APu/Al composites are shown in Fig. 4. A high permittivity of about 315 is observed at 10 MHz in the APu/Al composite with 43.84 vol% Al content (Fig. 4a), accompanying with a high imaginary permittivity (Fig. 4c) and dielectric loss tangent of about 0.26 (Fig. 4e). Additionally, a permittivity as high as 158 with lower dielectric loss of 0.045 is obtained at 10 MHz in the composite with 57.23 vol% of Al content, which is favorable for radio frequency capacitors. Table 1 shows the comparison of the high permittivity in various polymer-based composites. Such a high permittivity with low dielectric loss achieved in this work is remarkable at megahertz. In principle, the permittivity drops when the content of conductive filler exceeds the percolation threshold. Thus, we assume that 57.23 vol% of Al content has exceeded the percolation threshold. The imaginary permittivity of the composites is also decreased when the Al content reaches 57.23 vol% and 75.07 vol%, but it is still much higher than that of the composites with lower Al content (Fig. 4c). This can be explained by the formation of conductive pathways, where the polarization loss is reduced while conductive loss is increased [38]. The dielectric loss of APu/Al composites with 57.23 vol% and 75.07 vol% of Al content keeps at low level on account of the high real permittivity and self-passivation layers that impede the leakage current (Fig. 4e). When Al content is further increased to 86.41 vol%, the negative permittivity behavior is observed (Fig. 4b), which is attributed to the low-frequency plasma oscillation of free electrons in continuous conductive pathway [46–48]. Theoretically, the negative permittivity versus frequency can be explained by Drude, as following [49],
Table 1 Comparison of high permittivity of typical polymer-based composites at high frequency reported in the recent literatures. Material systems
Permittivity
Dielectric loss
Fillers’ content (volume fraction: vol%, mass fraction: wt%)
Poly(vinylidene fluoride)graphene-BaTiO3 [39]
65 (@1 MHz)
0.35 (@1 MHz)
Poly(vinylidene fluoride)Ba0.95Ca0.05Zr0.15Ti0.85O3 [40] Polysulfone-multiwalled carbon nanotubes [41] Polyethylene-poly(vinylidene fluoride)-carbon nanotube [42] Poly(vinylidene fluoride)carbon black [43] Poly(vinylidene fluoride)graphene [44]
70 (@10 MHz)
0.18 (@10 MHz)
BaTiO3: 30 vol% graphene: 1.25 vol% 71 vol%
58 (@1 MHz) <50 (@1 MHz)
0.09 (@1 MHz) >0.1 (@1 MHz)
25 vol%
15 (@10 MHz) ~17 (@10 MHz)
7 wt%
Silicon elastomer-graphene nanoribbons [45]
6 (@10 MHz)
Acrylic PolyurethaneAluminum(this work)
158 (@10 MHz)
0.2 (@10 MHz) ~0.35 (@10 MHz) 0.008 (@10 MHz) 0.045 (@10 MHz)
8 vol%
16 wt% 0.5 wt% 57.23 vol%
ω2p
0
εr ðωÞ ¼ 1
ω þ ω2τ 2
sffiffiffiffiffiffiffiffiffiffiffi neff e2 ωp ¼ 2πfp ¼ meff ε0
(6)
(7)
where ω is angular frequency (ω ¼ 2πf), ωτ is the collisional frequency and inverse of relaxation time (ωτ ¼ 1/τ), ωp is the plasma frequency, neff is effective concentration of the free electrons, and meff is the effective mass of the electron. The Al particles embedded in APu matrix lead to the dilution of effective electron concentration and the increase of the effective electron mass. Therefore, a low-frequency plasmonic state is achieved. The experimental data are consistent well with the Drude model (the solid line in Fig. 4b), in which the fitting parameters ωp and ωτ are 8.51 GHz and 429.86 MHz, respectively. The imaginary permit tivity (Fig. 4d) shows a nearly linear relationship between ε" and 1/f at low frequency, demonstrating that the conductive loss dominates in the low-frequency region, and polarization loss takes it away from the linear relationship in the high-frequency region [8]. The dielectric loss tangent (Fig. 4f) shows a peak at 812 MHz, which is in accordance with zero cross point of permittivity in Fig. 4b. Dielectric loss in the most test frequency region is less than 3, which is relatively lower compared with the loss of negative permittivity materials reported previously [7,8]. Interestingly, the ε-near-zero region with a loss peak has perfect ab sorption effect in various communication equipment, arousing increasing interests recently [50–52]. The permittivity as a function of Al content is shown in the Fig. 5. With the increase of Al content, the permittivity goes up first (І), then it goes down (ІІ), and finally it becomes negative (Ш). Such a change trend should be universal in percolative composites. The experimental data in part I is fitted by Equation (3), and the fitting parameters fc and q are 47.05 vol% and 0.93, respectively. When the volume fraction of Al is slightly below the fc, a number of microcapacitors are formed, and thus the permittivity is gradually enhanced. When the volume fraction of Al is marginally above the fc, some Al particles will connect with each other to form the conductive pathways. As a result, a few microcapacitances are converted to inductances, and the permittivity goes down (parts II). When the Al content further increases to a higher level (86.41 vol%),
Fig. 5. Permittivity of the APu/Al composites with different Al content at 10 MHz. The resistances (R) of APu/Al composites always exist. The isolated Al particles and the APu matrix are responsible for the capacitors (C). The conductive loops formed by the interconnected Al networks are regarded as the inductors (L).
The morphological characteristics of pure Al particles and APu/Al composites are presented in Fig. 3. The average particle size of Al powders is about 1–4 μm, as shown in Fig. 3a. The SAED from the surface of Al particle is shown in Fig. 3b. The crystal planes (111) and (200) are belonging to the Al. The crystal planes (003) and (202) are assigned to the Al2O3 [35–37]. Therefore, the self-passivation layers have formed on the surface of Al particles. The surface morphology of the APu/Al composites is relatively smooth without any obvious bubbles and cracks, and the Al particles are distributed uniformly in the APu matrix (Fig. 3c and d). According to the cross-sectional SEM image (Fig. 3e) and the corresponding EDX results (Fig. 3f), we can see that some of ellipsoidal Al particles are connected in the APu/Al composite with 57.23 vol% of Al. It is worth noting that the composite with 57.23 vol% of Al content still can be folded (inset in Fig. 3f), demonstrating its excellent 5
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Fig. 6. Frequency dependence of the reactance of APu/Al composites with different Al content (a, b). Frequency dependence of ac conductivity (σac) of APu/Al composites (c, d). The red solid lines in (c) and (d) are the fitting results based on Jonscher power law and Drude model, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
more conductive pathways are formed and the inductance dominates over the capacitance, so the negative permittivity is achieved (parts III). The reactance (Z00 ) of the APu/Al composites with different Al con tent are shown in Fig. 6a and Fig. 6b. The reactance of the APu/Al composites is commonly expressed as the relationship: Z" ¼ ZLþZC, where ZC is the capacitive reactance (ZC ¼ 1/ωC, C is the capacitance) and ZL is the inductive reactance (ZL ¼ ωL, L is the inductance). For the APu/Al composites with lower Al content, the Z00 would be negative, which manifests a capacitive character (Fig. 6a). After the Al content exceeds the percolation threshold, the reactance will decrease yet remain negative, which is confirmed by the assumption in Fig. 5. With the increase of Al content, Z00 first increases due to the enhanced microcapacitors in APu/Al interfaces, and then decreases since some of microcapacitors change into inductors. For the APu/Al composite with 86.41 vol% of Al content (Fig. 6b), the conductive paths have been formed, and Z00 presents an inductive character. The reactance changes from positive to negative at high frequency, which is in sharp contrast with the transformation of the permittivity in Fig. 4b. In brief, the capacitive-inductive transition observed in APu/Al composites corre sponds to the permittivity change from positive to negative. Frequency dependence of ac conductivity (σac) for the APu/Al composites is shown in Fig. 6c and d. The ac conductivity goes up with the increasing Al content at low frequency. In addition, σac enhances with the increase of frequency, which follows the Jonscher power law: σ ac ¼ σdcþAωn [53], where σ dc is the direct current conductivity, A is the pre-exponential factor and n is the fractional exponent. The experi mental data matches well with the power law (red solid lines in Fig. 6c), indicating a hopping conduction behavior [54]. For the APu/Al com posite with 86.41 vol% of Al content, σ ac is decreased with the increase of frequency due to the skin effect, manifesting a metal-like conduction
behavior [55,56]. Usually, the ac conductivity of metal-like materials is also described as the Drude model [57],
σ ac ¼
σdc ω2τ ω2 þ ω2τ
(8)
where the fitting parameters σ dc is 0.076 S cm 1. As shown in Fig. 6d, the Equation (8) agrees well with the experimental data (red solid line). The permittivity transition in APu/Al composites has been qualita tive discussed above, while the quantitative prediction of dielectric behavior still needs to be further investigated, especially when the conductive fillers content is above the percolation threshold. In mega hertz frequency range, the particle size is much less than the wave length, and the quasi-static approximation can be used to describe the response of an individual particle. Given that Faraday’s law of in ductions is ignored, the electromagnetic response can be described in terms of the complex dielectric function: ε ¼ ε’þiε", and complex con ductivity: σ ¼ σ’þiσ "; these two parameters are related to the formula: ε ¼ 4πiσ/ω [58]. The σ0 of percolative composites is widely described by Equation (1) when f> fc, so:
ε’’ ¼
4πσM ðf
ω
fc Þt
for f > fc
(9)
Additionally, the real and imaginary permittivity should follow the Kramers-Kronig relation, which provides an approach to obtain the real permittivity from imaginary permittivity. The integral transformation of the Kramers-Kronig relation for the complex permittivity is shown as following [59]: Z 0 1 2 ∝ ω 1 0 (10) ¼1 þ dω 0 εr ðωÞ π 0 ω0 2 ω2 ε00r ðω0 Þ 6
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frequency plasma oscillation. Significantly, the universal change rules of permittivity in percolative composites are systematically demon strated. The impedance analysis shows that the capacitive-inductive transition corresponds to the permittivity changing from positive to negative. The ac conductivity of APu/Al composites shows hooping conduction when the Al content is lower, following the Jonscher power law. Meanwhile, a metal-like conductive behavior is observed when Al content is increased to 86.41 vol%, which can be fitted by Drude model. Finally, a derived model for predicting the permittivity is presented for the excessively percolative composites, which will supplement the existing theoretical framework of the percolation theory. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Zhongyang Wang: Investigation, Visualization, Writing - original draft. Kai Sun: Conceptualization, Data curation. Peitao Xie: Formal analysis. Yao Liu: Resources. Qilin Gu: Methodology, Writing - review & editing. Runhua Fan: Methodology, Supervision, Project administration. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51601105, No. 51871146 and No. 51803119), the Innovation Program of Shanghai Municipal Education Commission (Grant No. 2019-01-07-00-10-E00053) and Chenguang Program sup ported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (Grant No. 18CG56). Zhongyang Wang acknowledges the support from the China Scholarship Council.
Fig. 7. Comparison between the calculated and measured permittivity of APu/ Al composites when the Al content exceeds the percolation threshold.
With the combination of Equations (9) and (10), and taking σ ac as the approximation of σM when Al content is above percolation threshold, the permittivity can be described as following: Z 0 1 2 ∞ ω ω 0 (11) ¼1þ 0 t d ω for f > fc 0 02 εr ðωÞ π 0 ω ω2 4πσ ac ðω Þðf fc Þ
References [1] J. Xi, Y. Liu, Y. Wu, J. Hu, W. Gao, E. Zhou, H. Chen, Z. Chen, Y. Chen, C. Gao, Multifunctional bicontinuous composite foams with ultralow percolation thresholds, ACS Appl. Mater. Interfaces 10 (24) (2018) 20806–20815. [2] K. Sun, Z. Zhang, L. Qian, F. Dang, X. Zhang, R. Fan, Dual percolation behaviors of electrical and thermal conductivity in metal-ceramic composites, Appl. Phys. Lett. 108 (6) (2016), 061903. [3] L. Wang, Y. Bai, X. Lu, J.-L. Cao, L.-J. Qiao, Ultra-low percolation threshold in ferrite-metal cofired ceramics brings both high permeability and high permittivity, Sci. Rep. 5 (2015) 7580. [4] C.-W. Nan, Physics of inhomogeneous inorganic materials, Prog. Mater. Sci. 37 (1) (1993) 1–116. [5] J. Zhu, X. Ji, M. Yin, S. Guo, J. Shen, Poly (vinylidene fluoride) based percolative dielectrics with tunable coating of polydopamine on carbon nanotubes: toward high permittivity and low dielectric loss, Compos. Sci. Technol. 144 (2017) 79–88. [6] J. Shao, J.-W. Wang, D.-N. Liu, L. Wei, S.-Q. Wu, H. Ren, A novel high permittivity percolative composite with modified MXene, Polymer 174 (2019) 86–95. [7] C. Cheng, R. Fan, Y. Ren, T. Ding, L. Qian, J. Guo, X. Li, L. An, Y. Lei, Y. Yin, Radio frequency negative permittivity in random carbon nanotubes/alumina nanocomposites, Nanoscale 9 (18) (2017) 5779–5787. [8] Y. Sun, J. Wang, S. Qi, G. Tian, D. Wu, Permittivity transition from highly positive to negative: polyimide/carbon nanotube composite’s dielectric behavior around percolation threshold, Appl. Phys. Lett. 107 (1) (2015), 012905. [9] Z.M. Dang, J.K. Yuan, S.H. Yao, R.J. Liao, Flexible nanodielectric materials with high permittivity for power energy storage, Adv. Mater. 25 (44) (2013) 6334–6365. [10] Z.-M. Dang, J.-K. Yuan, J.-W. Zha, T. Zhou, S.-T. Li, G.-H. Hu, Fundamentals, processes and applications of high-permittivity polymer–matrix composites, Prog. Mater. Sci. 57 (4) (2012) 660–723. [11] F. Zhang, T. Li, Y. Luo, A new low moduli dielectric elastomer nano-structured composite with high permittivity exhibiting large actuation strain induced by low electric field, Compos. Sci. Technol. 156 (2018) 151–157. [12] Z. Wang, X. Fu, Z. Zhang, Y. Jiang, M. Waqar, P. Xie, K. Bi, Y. Liu, X. Yin, R. Fan, Paper based metasurface: turning waste-paper into a solution for electromagnetic pollution, J. Clean. Prod. 234 (2019) 588–596. [13] V.M. Shalaev, Optical negative-index metamaterials, Nat. Photonics 1 (1) (2007) 41.
The calculated results by Equation (11) are shown in Fig. 7. It is obvious that the calculated permittivity is close to the test results when the Al content exceeds fc, while the permittivity remains positive (Fig. 7a). However, Equation (11) fails to predict the negative permit tivity (Fig. 7b), mainly because the negative permittivity has high dispersion, and the integral interval is 10 MHz-1 GHz, rather than from 0 to infinity. Additionally, it is attributed to the fact that the conductive current dominates only in the low-frequency range(|ε’|≪ε"), and the displacement current dominates in the high frequency region(|ε’|≫ε") [60]. Thus, taking σ ac approximately equal to σM is not suitable at the high frequency. Although there is a deviation between the calculated results and the experimental data, it can be regarded as a supplement of the existing percolation theory, and a reliable prediction of the negative permittivity behavior still need to be explored in the future. It’s worth noting that Equation (11) is based on the Kramers-Kronig relation. Therefore, the derived formula is applicable only when the permittivity of materials remains a linear response, and at the same time the skin effect can be ignored. 4. Conclusions In summary, the permittivity transition of APu/Al composites from positive to negative is investigated. The high permittivity with low dielectric loss is obtained in the APu/Al composites with 57.23 vol% of Al. Moreover, a negative permittivity behavior is observed in the com posites with 86.41 vol% Al content, which can be explained by low7
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Composites Science and Technology 188 (2020) 107969 [38] K. Sun, P. Xie, Z. Wang, T. Su, Q. Shao, J. Ryu, X. Zhang, J. Guo, A. Shankar, J. Li, Flexible polydimethylsiloxane/multi-walled carbon nanotubes membranous metacomposites with negative permittivity, Polymer 125 (2017) 50–57. [39] D. Wang, T. Zhou, J.-W. Zha, J. Zhao, C.-Y. Shi, Z.-M. Dang, Functionalized graphene-BaTiO3/ferroelectric polymer nanodielectric composites with high permittivity, low dielectric loss, and low percolation threshold, J. Mater. Chem. 1 (20) (2013) 6162–6168. [40] B. Luo, X. Wang, Y. Wang, L. Li, Fabrication, characterization, properties and theoretical analysis of ceramic/PVDF composite flexible films with high dielectric constant and low dielectric loss, J. Mater. Chem. 2 (2) (2014) 510–519. [41] H. Liu, Y. Shen, Y. Song, C.W. Nan, Y. Lin, X. Yang, Carbon nanotube array/ polymer core/shell structured composites with high dielectric permittivity, low dielectric loss, and large energy density, Adv. Mater. 23 (43) (2011) 5104–5108. [42] J.-K. Yuan, S.-H. Yao, A. Sylvestre, J. Bai, Biphasic polymer blends containing carbon nanotubes: heterogeneous nanotube distribution and its influence on the dielectric properties, J. Phys. Chem. C 116 (2) (2012) 2051–2058. [43] J. Zhu, J. Shen, S. Guo, H.-J. Sue, Confined distribution of conductive particles in polyvinylidene fluoride-based multilayered dielectrics: toward high permittivity and breakdown strength, Carbon 84 (2015) 355–364. [44] B. Lin, Z.-T. Li, Y. Yang, Y. Li, J.-C. Lin, X.-M. Zheng, F.-A. He, K.-H. Lam, Enhanced dielectric permittivity in surface-modified graphene/PVDF composites prepared by an electrospinning-hot pressing method, Compos. Sci. Technol. 172 (2019) 58–65. [45] A. Dimiev, W. Lu, K. Zeller, B. Crowgey, L.C. Kempel, J.M. Tour, Low-loss, highpermittivity composites made from graphene nanoribbons, ACS Appl. Mater. Interfaces 3 (12) (2011) 4657–4661. [46] H. Gu, X. Xu, M. Dong, P. Xie, Q. Shao, R. Fan, C. Liu, S. Wu, R. Wei, Z. Guo, Carbon nanospheres induced high negative permittivity in nanosilverpolydopamine metacomposites, Carbon 147 (2019) 550–558. [47] H. Gu, J. Guo, Q. He, Y. Jiang, Y. Huang, N. Haldolaarachige, Z. Luo, D.P. Young, S. Wei, Z. Guo, Magnetoresistive polyaniline/multi-walled carbon nanotube nanocomposites with negative permittivity, Nanoscale 6 (1) (2014) 181–189. [48] H. Gu, J. Guo, M.A. Khan, D.P. Young, T. Shen, S. Wei, Z. Guo, Magnetoresistive polyaniline–silicon carbide metacomposites: plasma frequency determination and high magnetic field sensitivity, Phys. Chem. Chem. Phys. 18 (29) (2016) 19536–19543. [49] C. Cheng, R. Fan, G. Fan, H. Liu, J. Zhang, J. Shen, Q. Ma, R. Wei, Z. Guo, Tunable negative permittivity and magnetic performance of yttrium iron garnet/ polypyrrole metacomposites at the RF frequency, J. Mater. Chem. C 7 (11) (2019) 3160–3167. [50] S. Feng, K. Halterman, Coherent perfect absorption in epsilon-near-zero metamaterials, Phys. Rev. B 86 (16) (2012) 165103. [51] S. Feng, Loss-induced omnidirectional bending to the normal in ε-near-zero metamaterials, Phys. Rev. Lett. 108 (19) (2012) 193904. [52] T.S. Luk, S. Campione, I. Kim, S. Feng, Y.C. Jun, S. Liu, J.B. Wright, I. Brener, P. B. Catrysse, S. Fan, Directional perfect absorption using deep subwavelength lowpermittivity films, Phys. Rev. B 90 (8) (2014), 085411. [53] Y. Qu, G. Fan, D. Liu, Y. Gao, C. Xu, J. Zhong, P. Xie, Y. Liu, Y. Wu, R. Fan, Functional nano-units prepared by electrostatic self-assembly for three-dimension carbon networks hosted in CaCu3Ti4O12 ceramics towards radio-frequency negative permittivity, J. Alloy. Comp. 743 (2018) 618–625. [54] Z. Wang, K. Sun, P. Xie, Y. Liu, R. Fan, Generation mechanism of negative permittivity and Kramers–Kronig relations in BaTiO3/Y3Fe5O12 multiferroic composites, J. Phys. Condens. Matter 29 (36) (2017) 365703. [55] H. Wu, Y. Qi, Z. Wang, W. Zhao, X. Li, L. Qian, Low percolation threshold in flexible graphene/acrylic polyurethane composites with tunable negative permittivity, Compos. Sci. Technol. 151 (2017) 79–84. [56] R. Yin, X. Huang, L. Qian, Freeze-drying assisted fabrication of highly homogenized reduced graphene oxide/alumina metacomposites with negative permittivity, Ceram. Int. 45 (5) (2019) 5653–5659. [57] Z. Wang, P. Xie, C. Cheng, G. Fan, Z. Zhang, R. Fan, X. Yin, Regulation mechanism of negative permittivity in poly (p-phenylene sulfide)/multiwall carbon nanotubes composites, Synth. Met. 244 (2018) 15–19. [58] V.M. Shalaev, Electromagnetic properties of small-particle composites, Phys. Rep. 272 (2–3) (1996) 61–137. [59] H. Sadeghi, A. Zolanvar, H. Khalili, M. Goodarzi, J. Nezamdost, S. Nezamdost, Effective permittivity of metal–dielectric plasmonics nanostructures, Plasmonics 9 (2) (2014) 415–425. [60] J.S. Moya, S. Lopez-Esteban, C. Pecharrom� an, The challenge of ceramic/metal microcomposites and nanocomposites, Prog. Mater. Sci. 52 (7) (2007) 1017–1090.
[14] L. Wang, Z.-M. Dang, Carbon nanotube composites with high dielectric constant at low percolation threshold, Appl. Phys. Lett. 87 (4) (2005), 042903. [15] C. Huang, Q. Zhang, Enhanced dielectric and electromechanical responses in high dielectric constant all-polymer percolative composites, Adv. Funct. Mater. 14 (5) (2004) 501–506. [16] T. Tsutaoka, T. Kasagi, S. Yamamoto, K. Hatakeyama, Low frequency plasmonic state and negative permittivity spectra of coagulated Cu granular composite materials in the percolation threshold, Appl. Phys. Lett. 102 (18) (2013) 181904. [17] K. Sun, J. Dong, Z. Wang, Z. Wang, G. Fan, Q. Hou, L. An, M. Dong, R. Fan, Z. Guo, Tunable negative permittivity in flexible graphene/PDMS metacomposites, J. Phys. Chem. C 123 (38) (2019) 23635–23642. [18] Z.-H. Dai, T. Li, Y. Gao, J. Xu, J. He, Y. Weng, B.-H. Guo, Achieving high dielectric permittivity, high breakdown strength and high efficiency by cross-linking of poly (vinylidene fluoride)/BaTiO3 nanocomposites, Compos. Sci. Technol. 169 (2019) 142–150. [19] Y. Shen, Y. Lin, C.W. Nan, Interfacial effect on dielectric properties of polymer nanocomposites filled with core/shell-structured particles, Adv. Funct. Mater. 17 (14) (2007) 2405–2410. [20] Y. Shen, Y. Lin, M. Li, C.W. Nan, High dielectric performance of polymer composite films induced by a percolating interparticle barrier layer, Adv. Mater. 19 (10) (2007) 1418–1422. [21] C. Yang, Y. Lin, C. Nan, Modified carbon nanotube composites with high dielectric constant, low dielectric loss and large energy density, Carbon 47 (4) (2009) 1096–1101. [22] J. Xu, C. Wong, Low-loss percolative dielectric composite, Appl. Phys. Lett. 87 (8) (2005), 082907. [23] X. Huang, P. Jiang, C. Kim, Electrical properties of polyethylene/aluminum nanocomposites, J. Appl. Phys. 102 (12) (2007) 124103. [24] F. He, S. Lau, H.L. Chan, J. Fan, High dielectric permittivity and low percolation threshold in nanocomposites based on poly (vinylidene fluoride) and exfoliated graphite nanoplates, Adv. Mater. 21 (6) (2009) 710–715. [25] S. Luo, S. Yu, R. Sun, C.-P. Wong, Nano Ag-deposited BaTiO3 hybrid particles as fillers for polymeric dielectric composites: toward high dielectric constant and suppressed loss, ACS Appl. Mater. Interfaces 6 (1) (2013) 176–182. [26] N. Engheta, An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability, IEEE Anten. Wirel. Pr. 1 (2002) 10–13. [27] D. Schurig, J. Mock, B. Justice, S.A. Cummer, J.B. Pendry, A. Starr, D. Smith, Metamaterial electromagnetic cloak at microwave frequencies, Science 314 (5801) (2006) 977–980. [28] D. Estevez, F. Qin, Y. Luo, L. Quan, Y.-W. Mai, L. Panina, H.-X. Peng, Tunable negative permittivity in nano-carbon coated magnetic microwire polymer metacomposites, Compos. Sci. Technol. 171 (2019) 206–217. [29] J. Wang, Z. Shi, F. Mao, S. Chen, X. Wang, Bilayer polymer metacomposites containing negative permittivity layer for new high-k materials, ACS Appl. Mater. Interfaces 9 (2) (2017) 1793–1800. [30] Y.-F. Hou, W.-L. Li, T.-D. Zhang, Y. Yu, R.-L. Han, W.-D. Fei, Negative capacitance in BaTiO3/BiFeO3 bilayer capacitors, ACS Appl. Mater. Interfaces 8 (34) (2016) 22354–22360. [31] F. Xue, D. Jia, Y. Li, X. Jing, Facile preparation of a mechanically robust superhydrophobic acrylic polyurethane coating, J. Mater. Chem. 3 (26) (2015) 13856–13863. [32] R. Udagama, E. Degrandi-Contraires, C. Creton, C. Graillat, T.F. McKenna, E. Bourgeat-Lami, Synthesis of acrylic polyurethane hybrid latexes by miniemulsion polymerization and their pressure-sensitive adhesive applications, Macromolecules 44 (8) (2011) 2632–2642. [33] O. Pardini, J. Amalvy, FTIR, 1H-NMR spectra, and thermal characterization of water-based polyurethane/acrylic hybrids, J. Appl. Polym. Sci. 107 (2) (2008) 1207–1214. [34] Y. Zhu, J. Xiong, Y. Tang, Y. Zuo, EIS study on failure process of two polyurethane composite coatings, Prog. Org. Coat. 69 (1) (2010) 7–11. [35] G. Meng, L. Wei, T. Zhang, Y. Shao, F. Wang, C. Dong, X. Li, Effect of microcrystallization on pitting corrosion of pure aluminium, Corros. Sci. 51 (9) (2009) 2151–2157. [36] R. Jamaati, M.R. Toroghinejad, J. Dutkiewicz, J.A. Szpunar, Investigation of nanostructured Al/Al2O3 composite produced by accumulative roll bonding process, Mater. Des. 35 (2012) 37–42. [37] X. Nie, E. Meletis, J. Jiang, A. Leyland, A. Yerokhin, A. Matthews, Abrasive wear/ corrosion properties and TEM analysis of Al2O3 coatings fabricated using plasma electrolysis, Surf. Coat. Technol. 149 (2–3) (2002) 245–251.
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