Tunable negative permittivity behavior of random carbon/alumina composites in the radio frequency band

Abstract

A random metamaterial, carbon/alumina (C/Al₂O₃) composite, was prepared using a precursor infiltration and pyrolysis method, which has potential applications in novel antennas, microwave absorbing and shielding. The microstructures, radio-frequency dielectric property and conductivity behavior of the composites with different carbon contents were investigated in detail. It was found that the carbon membrane spread out on the pore walls of the alumina matrix. As the carbon content increased, the composites underwent a percolation phenomenon, and the conductive mechanism changed from hopping conduction to metal-like conduction due to the formation of conductive carbon networks. A negative permittivity behavior was observed in the composites above the percolation threshold, and this was ascribed to the low frequency plasmonic state produced by the carbon networks. The frequency dispersion of such negative permittivity efficiently agreed with the Drude model. The negative magnitude of permittivity in the testing frequency was small, ranging from −370 to −28, which originated from the lower carrier concentration in the conducting carbon networks. This work will greatly facilitate the practical application of random metamaterials with tunable electrical properties, and has great significance for the development of metamaterials.

---

1. Introduction

Recently, substantial effort has gone into the development of metamaterials with negative permittivity or/and permeability.^1–4 While most of the conventional electromagnetic media have positive permittivity and permeability, the metamaterials offer unprecedented electromagnetic properties, and are very promising for applications in the field of invisibility, imaging, antennas, and microwave absorbing and shielding, among others.^5–9 When negative permittivity and permeability are mentioned, patterened metamaterials composed of periodic unit cells usually come to mind. For this metamaterial, the negative electromagnetic parameters mainly originate from the arrangement of ordered structures, and are closely associated with shape, size and spacing of periodic structures, rather than the chemical composition and microstructure of the material.¹⁰ In the recent study, some materials without obvious periodic arrays have been prepared by typical processing of material and also possessed negative parameters in various frequency ranges.^11–14 It is clear that the negative parameters of these materials depended on their composition and microstructure. These materials, so-called random metamaterials, have greatly expanded the scope of metamaterials.

A variety of random metamaterials consisting of conductive, magnetic or dielectric component have been fabricated to achieve tunable negative parameters by controlling their compositions and microstructures.^15–21 However, in those researches, the major concern is tuning the frequency band of negative parameters and reducing dissipative losses, and there is almost no attention to adjusting the magnitude of negative parameters. In fact, it is of great theoretical significance to adjust the magnitude of negative parameters, and is needed for some practical applications. For instance, if the permittivity is tuned close to the permeability, the metamaterials will possess good impedance matching (Z_im = Z₀(ε/μ)^1/2, where Z₀ is the impedance of free space, ε is the permittivity, and μ is the permeability), and the incident electromagnetic wave can enter these materials, which is essential requirement for application in wave-transparent and absorbing fields.^22–24

Because metals possess negative permittivity below their plasma frequencies (the visible or near ultraviolet band), most of studies have been devoted to achieve tunable negative parameters in the metal composites.^15,17 Although the plasma frequency of these composites was in the radio frequency band, which is much lower than that of bulk metal, the magnitude of negative permittivity increased sharply with decreasing frequency, leading to the enormous negative value at the frequency lower than its plasma frequency, as with bulk metal.^11,15 The giant negative value of permittivity results in the mismatching between permittivity and permeability, because the negative value of permeability is generally small (∼−100).^16,25,26 This mismatching hampers many of their practical applications, such as solar energy harvesting, super absorbers and microwave attenuator.^8,27 Hence, the search for weakly negative permittivity behavior with small permittivity negative value in wide frequency band is required.

It is well known that the formation of conductive network and carrier concentration in such network plays a key role in generating the negative permittivity.^28,29 The moderate carrier concentration is desired to provide a weakly negative permittivity behavior; otherwise, the larger negative values would be obtained with further increases in carrier concentration.³⁰ As the metals have high electron densities in the range 10²² to 10²³ cm⁻³, it is very difficult to control the metal filler loading to achieve moderate carrier concentration in the metal composites.³¹ It is believed that conductive materials with relatively low carrier concentration are viable alternatives for metals in these composites, and are more beneficial to achieve the weakly negative permittivity behavior in a wide frequency range.^14,32–34 The conductive carbon materials, such as carbon nanotube, carbon fiber and graphene, have much lower carrier concentration than that of metal.^35–37 So carbon materials can be regarded as a good candidate for realizing weakly negative permittivity behavior.

The amorphous carbon materials generally were prepared from pyrolysis of organic precursors, and their electrical properties and microstructures can be easily tuned by adjusting heat treatment conditions.^38,39 Thus, in this work, the amorphous carbon derived from commercial sucrose was incorporated into the porous Al₂O₃ matrices using an infiltration–pyrolysis process. A percolation phenomenon appeared in the C/Al₂O₃ composites with the increase of carbon content. When the carbon content reached the percolation threshold, the composites undergone a capacitive–inductive transition, and changed from an ordinary dielectric medium to a metamaterial. A weakly negative permittivity behavior with lower frequency dispersion was obtained in the composites above percolation threshold, and the generation mechanism of such unique behavior is also explored.

2. Experimental

2.1 Sample preparation

The porous alumina with a porosity of ∼45% was fabricated by pressureless sintering, using activated carbon powder as pore-forming agent. Firstly, the mixtures of alumina powder (Sinopharm Chemical Reagent Co., Ltd., China), 15 wt% activated carbon powder (Tianjin Damao Chemical Reagent Factory, China) and 2 wt% titania powder (Sinopharm Chemical Reagent Co., Ltd. China) were milled for 1.5 h using agate grinding media. Then, the resulting mixtures were molded into aquare discs (22 mm × 10 mm × 2 mm). Finally, all the green bodies were sintered at 1300 °C for 1 h.

The obtained Al₂O₃ discs were dipped into the 2.1, 1.0 or 0.5 g ml⁻¹ sucrose aqueous solutions (sucrose powder was purchased from Sinopharm Chemical Reagent Co.,Ltd.), and vacuumized for 12 h to “press” the sucrose solution into porous Al₂O₃ discs. The discs were then removed from the sucrose solution and dried in a ventilated oven at 80 °C for 12 h. Afterwards, the preforms were pyrolyzed at 800 °C for 1 h in N₂ atmosphere to obtain the C/Al₂O₃ composites. After repeating impregnation–pyrolysis process, the composites with carbon content of 3 wt% (2.9 vol%), 5 wt% (5.5 vol%), 9.8 wt% (11.6 vol%), 11.2 wt% (13.2 vol%), 13.7 wt% (16.6 vol%) and 14.3 wt% (17.4 vol%) were prepared.

2.2. Characterization

The phase composition of composites was measured by X-ray diffractometer (XRD, Rigaku Dmax-rc, Tokyo, Japan) with CuKa radiation at room temperature. X-ray photoelectron spectroscopy (XPS, Perkin-Elmer, PHI-5400, USA) were carried out in order to obtain information about composites and amorphous carbon. The morphology and microstructure of the composites were observed using a field emission scanning electron microscope (FESEM, Hitachi SU-70, Tokyo, Japan) and energy dispersive X-ray spectroscopy (EDX) attached with the SEM system. The conductivity and permittivity of the C/Al₂O₃ composites were determined using Agilent E4991A Precision Impedance Analyzer with 16453A dielectric test fixture under AC voltage 100 mV at room temperature. The impedance (Z′, Z′′), capacitance (C) and resistance (R_p) data of the sample were tested by the impedance analyzer in the frequency range from 30 MHz to 1 GHz. The complex permittivity (ε′, ε′′) and the real part of alternating current (ac) conductivity (σ_ac) were calculated by εʹ = Cd/ε₀S, ε′′ = d/2πfε₀SR_p and σ_ac = d/RS respectively, where d is the sample thickness, S the electrode plate area, C the capacitance, R_p is parallel resistance, R is real part of impedance (R = Z′), ε₀ is the permittivity of vacuum (8.85 × 10⁻¹² F m⁻¹), and f is the frequency.

3. Results and discussion

3.1 Microstructure and composition

Fig. 1a shows XRD patterns of pyrolytic carbon and C/Al₂O₃ composites with different carbon contents. Two strong and wide peaks appear at around 23° and 43°, which are the characteristic XRD peaks for amorphous carbon.⁴⁰ It indicates that the carbon from pyrolysis of sucrose is amorphous. The main diffraction peaks of the composites are Al₂O₃ phases, and the amorphous carbon peaks cannot be clearly identified in the XRD patterns, which may result from that the intensity of amorphous carbon peaks is much lower in comparison with that of Al₂O₃ peaks. In order to further analyze the chemical composition of composites, XPS analysis was employed. Fig. 1b verified that carbon is hosted in porous alumina. XPS spectra of C1s regions for the composites with carbon content of 3 wt% and 9.8 wt% are shown in Fig. 1c. The deconvolution of the C1s spectra yield four peaks, C–C/C=C, C–O–C, C=O and O–C=O, corresponding to binding energies of 284.6 eV, 286.1 eV, 287.6 eV, and 288.9 eV, respectively.^39,41 These result shows that a small amounts of oxygen remained in the amorphous carbon. Fig. 2 shows the FESEM images and EDX results of the C/Al₂O₃ composites with different carbon contents. The EDX analysis (Fig. 2e and f) further corroborates that carbon is embedded in the porous matrixes. Fig. 2d demonstrates the magnified SEM image of the composite with carbon content of 14.3 wt%, and the carbon layer spreading out on the hole wall of matrixes can be clearly observed. As shown in Fig. 2a–c, the carbon layer is more obvious in the composites with high carbon content.

Fig. 1 (a) XRD patterns of pyrolytic carbon and C/Al₂O₃ composites with different carbon contents; (b) XPS spectra of the composites with carbon contents of 3 wt% and 9.8 wt%; (c) deconvolved C1s XPS spectra of the composites with carbon contents of 3 wt% and 9.8 wt%.

Fig. 2 FESEM images and EDX analysis of the C/Al₂O₃ composites with different carbon contents. (a) The composite with carbon content of 3 wt%, (b) the composite with carbon content of 9.8 wt%; (c) and (d) the composites with carbon content of 14.3 wt%; (e) EDX result corresponding to elliptic region in picture (b); (f) EDX result corresponding to elliptic region in picture (d).

3.2 Conductivity behavior

Fig. 3 shows the frequency dispersions of ac conductivity (σ_ac) for composites with different carbon contents. We can see that σ_ac increases as the carbon content increases. For the composites with carbon content of 13.7 wt% and 14.3 wt%, the variation trend of σ_ac depending on frequency is different from the other samples', indicating that a percolation phenomenon appears, and the percolation threshold is between 11.2 wt% (13.2 vol%) and 13.7 wt% (16.6 vol%). For the composites below the percolation threshold, the σ_ac–f relationship obeys the formula σ_ac = σ_dc + A(2πf)ⁿ, where σ_dc is the direct current (dc) conductivity, f is the frequency, A is the pre-exponential factor, and n is the fractional exponent. This frequency dispersion characteristic manifests that the composites show a hopping conduction behavior.⁴² For the composites above the percolation threshold, the formation of carbon pathways for facilitating electron transfer results in the conductive mechanism changing from hopping conduction to metal-like conduction, and the σ_ac decreases with increasing the frequency due to skin effects.¹⁷ According to the above analysis, the microstructural evolution schematic of the composites with increasing carbon content is shown in Fig. 4. When the carbon content reaches percolation threshold, the carbon networks are formed in the composites.

Fig. 3 Frequency dispersions of ac conductivity for the C/Al₂O₃ composites with different carbon contents.

Fig. 4 The schematic preparation process of C/Al₂O₃ composites. As the carbon content increases, the continuous carbon networks are formed, and possible electrical current paths are schematically indicated.

Fig. 5 depicts frequency dispersions of reactance (Z′′) and impedance (|Z|) for the composites with different carbon contents. As shown in Fig. 5a, there is a shift for Z′′ from negative to positive in the composites near the percolation threshold. It indicates that an capacitive–inductive transition appear in the composites with the increase of carbon content.²¹ It was known that Z′′ = Z_L − Z_C, where Z_L is inductive reactance, and Z_C is capacitive reactance. As Z′′ < 0, the capacitive reactance is larger than inductive reactance, indicating a lag of the voltage behind that of the current. Hence the composites below the percolation threshold can be regarded as a capacitor with leakage current, manifesting a capacitive behavior. Correspondingly, when Z′′ > 0, the composites above the percolation threshold manifest an inductive behavior. The formation of current loops, which are induced in the conductive carbon network under the action of high frequency electric field, leads to the inductive character. In order to further analyze the electrical properties of composites, the equivalent circuit analysis was performed. The results obtained through the equivalent circuit models are shown in Fig. 5b and are in a rather good agreement with the experimental data. The composites below the percolation threshold are equivalent to circuit model consisting of resistor R and capacitor C, while shunt inductors L are introduced into the equivalent circuit models for the composites with the carbon content more than 9.8 wt%. The impedance module |Z| of the composites with low carbon content decreases with increasing frequency, and |Z| increases with the increase of frequency in the composites beyond the percolation threshold. As discussed later, a negative permittivity behavior is obtained in the composites with inductive character. Moreover, in many other metamaterials, negative permittivity was also observed and usually provided by shunt inductances.^11,18,28,43 Hence, there's reason to believe that the inductive character is a characteristic of negative permittivity behavior.

Fig. 5 Frequency dispersions of reactance (a) and impedance (b) for the C/Al₂O₃ composites with different carbon contents. The equivalent circuit models are also shown in (b).

3.3 Dielectric behavior

Fig. 6 depicts the dependence of permittivity (ε′ and ε′′) and dielectric loss tangent (tan δ, where tan δ = ε′′/|ε′|) on frequency for composites with various contents of carbon. It can be seen that the permittivity of composites closely related with the frequency and carbon content. For the composites with low carbon content (≤11.2 wt%), the ε′ obviously decreases with the increase of frequency due to the enhanced leakage conductance at high frequency, and the carbon/alumina interface areas increase with the increase of carbon content, leading to the higher ε′ in the composites (Fig. 6a). Further increase in content of carbon could switch permittivity to negative (Fig. 6b), which is because conductive networks are formed in the composites beyond percolation threshold. The variation of ε′ as a function of frequency was herein analyzed by the Drude model:³¹where ω_p (ω_p = 2πf_p) is the angular plasma frequency, ω (ω = 2πf) is the angular frequency of the electric field, ω_τ (ω_τ = 2πf_τ) is the damping parameter, ε₀ is the permittivity of a vacuum (8.85 × 10⁻¹² F m⁻¹), n_eff is the effective concentration of delocalized electrons, m_eff is the effective weight of an electron, and e is the electron charge (1.6 × 10⁻¹⁹ C). The fitted ε′–f curves (solid line in Fig. 6b) of the composites above percolation threshold satisfies the experimental data very well, which indicated their plasma frequency f_p is 3.7 GHz and 4.01 GHz, respectively. As compared with metal composites, the carbon composites show weakly negative permittivity behavior with lower frequency dispersion,^11,17,18 and the values range from −370 to −28 in the testing frequency band. The lower carrier concentration of the conductive network results in the weakly negative permittivity behavior in the carbon composites.³⁰

Fig. 6 Frequency dependence of the permittivity (a, b and c) and dielectric loss tangent (d) for the C/Al₂O₃ composites with different carbons.

With regard to a percolating composite system, the dielectric loss mainly includes the polarization loss and conduction loss.^44,45 Generally, the polarization loss results from dipolar orientation and interfacial polarization, and the conductivity loss is caused by the flow of charge in the composites and depends on the electric conductivity.⁴⁶ As shown in Fig. 6c, ε′′ descends with increasing frequency. For samples with high carbon content (≥9.8 wt%), the plots of ε′′ versus f show strict linear relationships, and this can be expressed by:⁴⁶

where ε₀ is a constant, σ_dc is the direct current conductivity, and f is the frequency. Thereby, the conduction loss plays a dominant role in the dielectric loss in these composites. The ε′′ spectrums of the samples with carbon content of 3 wt% to 5 wt% have a plateau in the high frequency region. The reason could be that the contribution from the polarization loss becomes more evident at the high frequency, while the conductivity loss decreases as the frequency increases. The frequency-dependent tan δ of the composites is given in Fig. 6d. A high tan δ ranging from 0.8 to 40 is observed within the measured frequency range. The higher carbon loading leads to the increase of tan δ, which is ascribed to the high conductivity. Such a high tan δ suggests their potential applications as novel lossy materials, although it must be noted that the magnitude of permittivity was still high.

4. Conclusions

In this paper, the C/Al₂O₃ composites consisting of amorphous carbon embedded in porous alumina were fabricated by an infiltration–pyrolysis process. The conductive mechanism changes from hopping conduction to metal-like conduction in the composite with the increase of carbon content. A weakly negative permittivity behavior appeared in the composites above the percolation threshold, which was analyzed using Drude model. It was found that the plasma oscillation of conduction electrons in carbon networks resulted in such negative permittivity characteristic. The low carrier concentration in conducting carbon networks lead to the small magnitude of negative permittivity in the testing frequency. The high dielectric loss was detected for the composites and dominated by the conductivity loss. The obtained C/Al₂O₃ composites with tunable electrical properties can be regarded as a promising candidate for a random metamaterial to realize the weakly negative permittivity behavior.

Acknowledgements

The authors acknowledge the supports of National Basic Research Program of China (973 Program, No. 2014CB643306) and National Natural Science Foundation of China (Grant No. 51172131, No. 51402170).

Notes and references

1. X. He, Q. Zhang, G. Lu, G. Ying, F. Wu and J. Jiang, RSC Adv., 2016, 6, 52212–52218.
2. T. Cao, S. Wang and W. Jiang, RSC Adv., 2013, 3, 19474–19480.
3. Z. Shi, F. Mao, J. Wang, R. Fan and X. Wang, RSC Adv., 2015, 5, 107307–107312.
4. Z. Zhang, R. Fan, Z. Shi, K. Yan, Z. Zhang, X. Wang and S. Dou, RSC Adv., 2013, 3, 26110–26115.
5. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry and M. Wegener, Science, 2010, 328, 337–339.
6. M. Wiltshire, J. Pendry, I. Young, D. Larkman, D. Gilderdale and J. Hajnal, Science, 2001, 291, 849–851.
7. R. W. Ziolkowski and A. Erentok, IEEE Trans. Antennas Propag., 2006, 54, 2113–2130.
8. X. He, S. Yan, G. Lu, Q. Zhang, F. Wu and J. Jiang, RSC Adv., 2015, 5, 61955–61959.
9. K. Sun, Z. Zhang, R. Fan, M. Chen, C. Cheng, Q. Hou, X. Zhang and Y. Liu, RSC Adv., 2015, 5, 61155–61160.
10. H. Chen, J. Mater. Chem. C, 2011, 21, 6452–6463.
11. Z. C. Shi, R. H. Fan, Z. D. Zhang, L. Qian, M. Gao, M. Zhang, L. T. Zheng, X. H. Zhang and L. W. Yin, Adv. Mater., 2012, 24, 2349–2352.
12. T. Tsutaoka, K. Fukuyama, H. Kinoshita, T. Kasagi, S. Yamamoto and K. Hatakeyama, Appl. Phys. Lett., 2013, 103, 261906.
13. J. Zhu, X. Zhang, N. Haldolaarachchige, Q. Wang, Z. Luo, J. Ryu, D. P. Young, S. Wei and Z. Guo, J. Mater. Chem., 2012, 22, 4996–5005.
14. B. Li, G. Sui and W. H. Zhong, Adv. Mater., 2009, 21, 4176–4180.
15. T. Tsutaoka, T. Kasagi, S. Yamamoto and K. Hatakeyama, Appl. Phys. Lett., 2013, 102, 181904.
16. Z. C. Shi, S. G. Chen, K. Sun, X. Wang, R. H. Fan and X. A. Wang, Appl. Phys. Lett., 2014, 104, 252908.
17. Z. C. Shi, R. H. Fan, K. L. Yan, K. Sun, M. Zhang, C. G. Wang, X. F. Liu and X. H. Zhang, Adv. Funct. Mater., 2013, 23, 4123–4132.
18. Z. C. Shi, R. H. Fan, Z. D. Zhang, K. L. Yan, X. H. Zhang, K. Sun, X. F. Liu and C. G. Wang, J. Mater. Chem. C, 2013, 1, 1633–1637.
19. B. Qiu, J. Guo, Y. Wang, X. Wei, Q. Wang, D. Sun, M. A. Khan, D. P. Young, R. O'Connor and X. Huang, J. Mater. Chem. C, 2015, 3, 3989–3998.
20. J. Zhu, Z. Luo, S. Wu, N. Haldolaarachchige, D. P. Young, S. Wei and Z. Guo, J. Mater. Chem., 2012, 22, 835–844.
21. X. Yao, X. Kou, J. Qiu and M. Moloney, RSC Adv., 2016, 6, 35378–35386.
22. X. Yin, L. Kong, L. Zhang, L. Cheng, N. Travitzky and P. Greil, Int. Mater. Rev., 2014, 59, 326–355.
23. M. Han, X. Yin, L. Kong, M. Li, W. Duan, L. Zhang and L. Cheng, J. Mater. Chem. A, 2014, 2, 16403–16409.
24. W. Duan, X. Yin, F. Ye, Q. Li, M. Han, X. Liu and Y. Cai, J. Mater. Chem. C, 2016, 4, 5962–5969.
25. H. Zhao, J. Zhou, Q. Zhao, B. Li, L. Kang and Y. Bai, Appl. Phys. Lett., 2007, 91, 131107.
26. Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li and Y. Meng, Appl. Phys. Lett., 2008, 92, 051106.
27. V. Yannopapas and I. E. Psarobas, J. Phys. Chem. C, 2012, 116, 15599–15603.
28. K. L. Yan, R. H. Fan, Z. C. Shi, M. Chen, L. Qian, Y. L. Wei, K. Sun and J. Li, J. Mater. Chem. C, 2014, 2, 1028–1033.
29. Q. Hou, K. Yan, R. Fan, Z. Zhang, M. Chen, K. Sun and C. Cheng, RSC Adv., 2015, 5, 9472–9475.
30. A. Boltasseva and H. A. Atwater, Science, 2011, 331, 290–291.
31. J. M. Luther, P. K. Jain, T. Ewers and A. P. Alivisatos, Nat. Mater., 2011, 10, 361–366.
32. L. Qian, L. Lu and R. H. Fan, RSC Adv., 2015, 5, 16618–16621.
33. H. Gu, Y. Huang, X. Zhang, Q. Wang, J. Zhu, L. Shao, N. Haldolaarachchige, D. P. Young, S. Wei and Z. Guo, Polymer, 2012, 53, 801–809.
34. V. Prigodin and A. Epstein, Synth. Met., 2001, 125, 43–53.
35. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, Science, 2004, 306, 666–669.
36. S. Bhattacharyya and S. R. P. Silva, Thin Solid Films, 2004, 482, 94–98.
37. M. Jablan, H. Buljan and M. Soljačić, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 308–310.
38. M. Chen, L. L. Shao, X. Qian, T. Z. Ren and Z. Y. Yuan, J. Mater. Chem. C, 2014, 2, 10312–10321.
39. Y. R. Rhim, D. Zhang, D. H. Fairbrother, K. A. Wepasnick, K. J. Livi, R. J. Bodnar and D. C. Nagle, Carbon, 2010, 48, 1012–1024.
40. M. Xie, J. Yang, J. Liang, X. Guo and W. Ding, Carbon, 2014, 77, 215–225.
41. J. H. Zhou, Z. J. Sui, J. Zhu, P. Li, D. Chen, Y. C. Dai and W. K. Yuan, Carbon, 2007, 45, 785–796.
42. J. C. Dyre and T. B. Schrøder, Rev. Mod. Phys., 2000, 72, 873.
43. T. Crépin, J. Lampin, T. Decoopman, X. Mélique, L. Desplanque and D. Lippens, Appl. Phys. Lett., 2005, 87, 104105.
44. J. Wang, Z. Shi, F. Mao, X. Wang, K. Zhang and J. Shi, RSC Adv., 2016, 6, 43429–43435.
45. Y. Yang, H. Sun, D. Yin, Z. Lu, J. Wei, R. Xiong, J. Shi, Z. Wang, Z. Liu and Q. Lei, J. Mater. Chem. A, 2015, 3, 4916–4921.
46. K. Ahmad, W. Pan and H. Wu, RSC Adv., 2015, 5, 33607–33614.

---