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High-temperature microwave absorption and evolutionary behavior of multiwalled carbon nanotube nanocomposite
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Scripta Materialia 61 (2009) 201–204 www.elsevier.com/locate/scriptamat
High-temperature microwave absorption and evolutionary behavior of multiwalled carbon nanotube nanocomposite Wei-li Song,a Mao-sheng Cao,a,* Zhi-ling Hou,a Jie Yuanb and Xiao-yong Fanga a
School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China b School of Information Engineering, Central University for Nationality, Beijing 100081, China Received 20 December 2008; revised 21 March 2009; accepted 24 March 2009 Available online 29 March 2009
The high-temperature dielectric property and evolutionary behavior of multiwalled carbon nanotube/silica nanocomposite from 30 to 600 °C in the range 8.2–12.4 GHz were investigated. Both increasing temperature and elevated multiwalled carbon nanotube concentration are found to enhance complex permittivity, and a mechanism for this enhancement is also proposed. The calculated attenuation suggests that multiwalled carbon nanotube/silica a good candidate for high-temperature microwave-absorbing materials, and this could help in material designs with matching conditions. Crown Copyright Ó 2009 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. Keywords: Carbon nanotube; High-temperature; Microwave absorption; Dielectric property
Carbon nanotubes (CNTs) have attracted extensive interest from a number of groups from various fields, such as physics, materials, chemistry and biology, and much effort has been devoted to fabricating these materials and investigating their properties. The unique electrical, thermal and mechanical properties of CNTs, which cannot be matched by conventional materials, make CNTs good candidates for use in practical applications, e.g. field emission devices, transparent conductive films, light sources, energy storage devices and biosensors [1–6]. In recent years, a significant amount of research has successfully been focused on electromagnetic interference (EMI) shielding or microwave absorption for the purpose of protecting the workspace and the environment from the radiation emitted by telecommunication apparatus [7]. Meanwhile, CNTs are prime candidates in the development of potentially revolutionary EMI shielding materials due to their light weight, resistance to corrosion, flexibility and processing advantages [8–11]. Very recently, the high-temperature microwaveabsorbing properties of carbon materials [12], MnO2 nanorods [13], ZnO [14], etc. [15], have been widely explored. However, the high-temperature microwaveabsorbing property of CNTs has not been intensively
* Corresponding author. Tel.: +86 01068914062; e-mail: caomaosheng@ bit.edu.cn
studied to date, even though it is believed that these materials could be potential candidates for a wide range of EMI shielding materials for use in severe environment. In this paper, the complex permittivity of a multiwalled carbon nanotube/silica nanocomposite (MWNT/SiO2) at temperatures from 30 to 600 °C in the 8.2–12.4 GHz (X-band) was studied experimentally. Both dielectric constant and dielectric loss depend on the temperature, frequency and MWNT concentration. In order to predict the high-temperature EMI shielding property, an attenuation calculation was employed based on the measured data in this study, which suggests that MWNT/SiO2 is good high-temperature microwave-absorbing material. MWNT/SiO2 samples with different MWNT concentrations were prepared by the conventional ceramic method, wherein SiO2 xerogel nanopowder was fabricated by the sol–gel method. MWNTs, purchased from Shenzhen Nanotech Port Co. Ltd. (China), were fabricated by the catalytic decomposition of CH4, with diameters ranging from 20 to 40 nm and lengths ranging from 5 to 15 lm. The samples were synthesized from mixtures of SiO2 nanopowder with different amounts of MWNTs (MWNT concentration: 2, 5 and 10 wt.%). These mixtures were then blended in an ethanol solution. Ultrasonic treatment was employed to disperse the mixture solution for 40 min. After the slurry was dried, crushed in an agate mortar and pestle, and sieved (150 lm), the fine powder was then compacted into sheet (22.5 10 2.5 mm) under a pressure of 60 MPa. The green
1359-6462/$ - see front matter Crown Copyright Ó 2009 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. doi:10.1016/j.scriptamat.2009.03.048
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W. Song et al. / Scripta Materialia 61 (2009) 201–204
compact was sintered at a temperature of 500 °C for 2 h for annealing treatment. Before dielectric measurement, the sample was dried at 200 °C for 24 h. A vector network analyzer (Anritsu 37269D) was used to determine the values of the relative complex permittivity, dielectric constant (e0 ) and dielectric loss (e00 ) of MWNT/SiO2 by the wave-guide method in the X-band. The complex permittivity of MWNT/SiO2 was determined at 12 temperatures covering the temperature range from 30 to 600 °C. MWNT/SiO2 was put in the test apparatus and heated by an internal heater at 20 °C min1. In order to ensure the accuracy of the test data, a period of 25 min was required for the system to stabilize, once each set-point temperature was achieved, and a set of duplicate measurements was then obtained. This process went on until data covering the whole temperature range were obtained. Scanning electron microscopy (SEM) gives an overview of the fractured surface of MWNT/SiO2 with different amounts of MWNTs (2, 5 and 10 wt.%) dispersed in silica, as shown in Figure 1a–c, respectively. The transmission electron microscopy (TEM) image in Figure 1d shows the original MWNT pieces used in this work. Figure 1e illustrates the MWNT cluster feature. This clustering, caused by the aggregation of MWNTs owing to the difficulty of dispersion, will simultaneously confer stiffness, toughness and strength on the composite. Apparently, more MWNTs clusters are observed in the sample with 10 wt.% MWNTs shown in Figure 1c and the sample with 2 wt.% MWNTs has the fewest clusters, as shown in Figure 1a. Figure 2 illustrates the complex permittivity of MWNT/SiO2 (10 wt.% MWNTs), which represents the typical dielectric property of the samples investigated in this work. Both e0 and e00 apparently decrease with increasing frequency, as shown in the insets of Figure 2a and b,
Figure 1. (a–c) SEM images of MWNT (2, 5 and 10 wt.%, respectively) dispersion in MWNT/SiO2. (d) TEM image of MWNTs used in this work. (e) SEM image of a MWNT cluster.
Figure 2. Complex permittivity of MWNT/SiO2 (10 wt.% MWNTs). (a) The profile of dielectric constant (e0 ) vs. temperature and frequency (inset). (b) The profile of dielectric loss (e00 ) vs. temperature and frequency (inset).
respectively. These decreases imply that the complex permittivity has a weakening response to increasing frequency. It is proposed that the molecules and electrons have enough time to polarize at low-frequency. Nevertheless, at high-frequency, the polarization of molecules and electrons could not have enough time to catch up with the change in electromagnetic field frequency. Additionally, a very good monotonic relationship between complex permittivity and temperature is exhibited over the experimental temperature range according to Figure 2a and b. Both e0 and e00 increase smoothly at each frequency (9, 10, 11 and 12 GHz) with rising temperature. This temperature-dependent dielectric property will now be discussed in more detail. Firstly, e0 is mainly related to electron polarization. As electrons are very light, they respond rapidly to an alternating electromagnetic field and their relaxation time is associated with a change of temperature. The Eyring formalism is suitable for describing this relationship for MWNT/SiO2 [16]: h DH DS exp exp ; ð1Þ sðT Þ ¼ kT RT R where h and k are the Planck constant and the Boltzmann constant, respectively, and DH and DS are the enthalpy and entropy of activation, respectively. It is proposed that the migrating electrons in MWNT/SiO2 respond faster to the alternating electromagnetic field when the temperature is rising, which causes a shorter relaxation time during the polarization. Meanwhile, the relationship between e0 and relaxation time can be expressed in terms of the Debye theory:
W. Song et al. / Scripta Materialia 61 (2009) 201–204
e0 ¼ e1 þ
es e1 1 þ x2 sðT Þ
2
;
ð2Þ
where es is the static permittivity, e1 is the relative dielectric permittivity at the high-frequency limit, x is the angular frequency and sðT Þ is the temperaturedependent relaxation time. Based on Eqs. (1) and (2), we could deduce that a shorter relaxation time leads an increasing dielectric constant in MWNT/SiO2 with elevated temperature in the temperature range from 30 to 600 °C. On the other hand, e00 can be also expressed in terms of dielectric physics theory: e00
rðT Þ ; e0 x
ð3Þ
where rðT Þ is the temperature-dependent electrical conductivity and e0 is the dielectric constant in vacuum. As shown in Eq. (3), the electrical conductivity of the composite plays a dominating role in dielectric loss. For individual MWNTs, the ballistic transport property [17] and the current in the outer shell [18] suggest that MWNTs are good conductors. Furthermore, the electrical conductivity of individual MWNTs will be increased due to the increase in the concentration of migrating electrons in conductive MWNT tubes at elevated temperature. In addition, the electrical conductivity of MWNT bulk material also possesses this characteristic [19] due to the temperature-dependent electrical conductivity of individual MWNTs. According to the above analysis, at elevated temperatures, the increasing electrical conductivity enhances the dielectric loss of MWNT/SiO2. Furthermore, the concentration-dependent dielectric property of MWNT/SiO2 has also been investigated. Compared with the complex permittivity at three temperatures (100, 300 and 500 °C), both e0 and e00 increase with an increase in MWNT concentration (from 2 to 10 wt.%), as illustrated in Figure 3. According to the effective medium theory [20], the dielectric constant increases with elevated concentration of MWNTs. Moreover, the increase in the number of continuous conductive networks of MWNTs [9,21,22], which leads to elevated electrical conductivity, contributes to the enhanced dielectric loss as the concentration of MWNTs rises.
Figure 3. Complex permittivity of MWNT/SiO2 with different MWNT content (2, 5 and 10 wt.%) at various temperatures (100, 300 and 500 °C) vs. frequency.
203
For further investigation of the high-temperature microwave absorption, the high-temperature reflection loss of MWNT/SiO2 (10 wt.%) was calculated. The normalized input impedance Z in of the MWNT/SiO2 microwave-absorbing layer is described by [23,24]: rffiffiffiffiffi lr 2p pffiffiffiffiffiffiffiffi Z in ¼ tanh j lr er fd ; ð4Þ er c where lr and er represent the relative permeability and permittivity of the composite medium, respectively, c is the velocity of light, f is the microwave frequency, and d is the thickness of the absorber. The reflection loss (R) is related to Zin as: R ¼ 20 log
jZ in 1j : jZ in þ 1j
ð5Þ
Figure 4a shows the calculated attenuation vs. frequency for each temperature by using the actual measured values of e and l, where l is taken as 1 due to MWNT/SiO2 being extremely weakly magnetic. All the calculated values were predicted based on a constant thickness d = 2.5 mm. The maximum attenuations at each temperature vary little with changing frequency and the points are around 10.1 GHz, which indicates that the reflection loss peak point of the composite is insensitive to temperature in the X-band. The relationship of reflection loss and temperature is demonstrated in Figure 4b. It is apparent that the strongest calculated attenuation occurs at around 30 °C at each frequency. The minimum attenuation point in this present temperature range remains at about 8.2 GHz. More importantly, the attenuation behavior is significantly dependent upon the tem-
Figure 4. High-temperature microwave absorption of MWNT/SiO2 (10 wt.% MWNTs). (a) Calculated reflection loss vs. frequency. (b) Calculated reflection loss vs. temperature.
204
W. Song et al. / Scripta Materialia 61 (2009) 201–204
perature. A monotonic decrease in calculated attenuation is observed in the range from 100 to 600 °C when the temperature increases. According to the experimental data and calculated reflection loss, the relationship between decreasing calculated attenuation and increasing temperature can be explained in terms of matching conditions. In order to investigate the evolutionary behavior and analyze the optimum design for ideal microwave-absorbing materials, the corresponding conditions and related parameters are discussed. To obtain resonant absorption of a single-layer absorber, the thickness and wavelength should obey the following relationship [25]: d ¼ ki =4;
ð6Þ
where d is the thickness and ki is the wavelength of incident wave. As indicated by Eq. (6), the response of the material to electromagnetic microwaves is close to resonant absorption, which leads to formation of a standing wave in the material, resulting in optimum microwave attenuation. Unfortunately, actual materials generally deviate from this resonant condition, since the optimum thickness varies with frequency. On the other hand, to meet the requirement of A(dB) attenuation, the corresponding electromagnetic parameters, frequency and thickness should follow the conditions [25]: p 1 10A=20 pc e0 ¼ ð7Þ cot h tgd 2dx 2 1 þ 10A=20 e00 ¼ e0 tgd ð8Þ where d is thickness, c is the velocity of light and x presents angular frequency. For this case, the calculated attenuation of MWNT/SiO2 exhibits good absorbing property at room temperature, where the reflection loss peak is close to 20 dB and the minimum attenuation is below 16 dB at 8.2 GHz, as shown in Figure 4a. However, when the temperature is rising, the impedance matching condition between air and the absorbing medium is disturbed. According to the Eqs. (7) and (8), the main reason for this is the variation in electromagnetic parameters (e0 , e00 ) with changing temperature. As exhibited in the calculated results, the microwave-absorbing property of MWNT/SiO2 decreases at elevated temperature, though this nanocomposite can still be considered as a good candidate for high-temperature absorbing materials, owing to the high-reflection loss (<10 dB) even at high-temperature. Therefore, attention should be paid to adjusting the electromagnetic parameters, thickness and related parameters in order to obtain high-performance microwave-absorbing materials. In summary, the high-temperature complex permittivity and the evolutionary behavior of MWNT/SiO2 over the temperature range 30–600 °C in the X-band were studied. When temperature rises, the increase in dielectric constant is attributed to the reduction of relaxation time and the increasing dielectric loss is due to the increase in electrical conductivity. With increasing MWNT concentration, the increase in continuous conductive networks can contribute to enhancing the dielec-
tric loss. The calculated reflection loss based on the parameters from measurement demonstrated that the attenuations were all below 10 dB in the temperature range in X-band, which indicates that MWNT/SiO2 could be a good candidate for high-temperature microwave-absorbing materials. The experimental data, as well as the matching conditions discussed, should help in further designs of EMI shielding materials for numerous applications. The authors thank the National Nature Science Foundation (Grant No. 50572010 and 50872159), the National Defense Funds (Grant No. A2220061080) and the Scientific Research Foundation of Graduate School of BIT (Grant No. AA200802). [1] M. Zhang, S.L. Fang, A.A. Zakhidov, S.B. Lee, A.E. Aliev, C.D. Williams, K.R. Atkinson, R.H. Baughman, Science 309 (2005) 1215. [2] K. Yu, Y.S. Zhang, F. Xu, Q. Li, Z.Q. Zhu, Q. Wan, Appl. Phys. Lett. 88 (2006) 153123. [3] H. Pan, T.H. Lin, D.P. Yu, Phys. Rev. B 70 (2004) 245412. [4] R.C. Che, L.M. Peng, X.F. Duan, Q. Chen, X.L. Liang, Adv. Mater. (Weinheim, Ger.) 16 (2004) 401. [5] S.C. Tjong, G.D. Liang, S.P. Bao, Scr. Mater. 57 (2007) 461. [6] Q. Wan, T.H. Wang, C.L. Lin, Chin. Phys. Lett. 20 (2003) 301. [7] D.D.L. Chung, Carbon 39 (2001) 279. [8] H.J. Choi, G.B. Kwon, G.Y. Lee, D.H. Bae, Scr. Mater. 59 (2008) 360. [9] L. Wang, Z.M. Dang, Appl. Phys. Lett. 87 (2005) 042903. [10] C.P.P. Watts, W.K. Hsu, A. Barnes, B. Chambers, Adv. Mater. 15 (2003) 7. [11] M.S. Cao, Z.J. Gao, J. Zhu, J. Mater. Eng. 2 (2003) 34 (in Chinese). [12] J.E. Atwater, R.R. Wheeler, Carbon 41 (2003) 1801. [13] X.L. Shi, M.S. Cao, X.Y. Fang, J. Yuan, Y.Q. Kang, W.L. Song, Appl. Phys. Lett. 93 (2008) 223112. [14] T.A. Baeraky, Egypt. J. Solids 30 (2007) 1. [15] Z.L. Hou, L. Zhang, J. Yuan, W.L. Song, M.S. Cao, Chin. Phys. Lett. 25 (2008) 2249. [16] N.T. Correia, J.J.M. Ramos, Phys. Chem. Chem. Phys. 2 (2000) 5712. [17] A.P. Garrido, A. Urbina, Carbon 40 (2002) 1227. [18] P.G. Collins, M.S. Arnold, P. Avouris, Science 292 (2001) 706. [19] H.L. Zhang, J.F. Li, B.P. Zhang, K.F. Yao, W.S. Liu, H. Wang, Phys. Rev. B 75 (2007) 205407. [20] J.V. Mantese, A.L. Micheli, D.F. Dungan, R.G. Geyer, J.B. Jarvis, J. Grosvenor, J. Appl. Phys. 79 (1996) 1655. [21] M.S. Cao, X.L. Shi, X.Y. Fang, H.B. Jin, Z.L. Hou, W. Zhou, Y.J. Chen, Appl. Phys. Lett. 91 (2007) 203110. [22] X.Y. Fang, X.L. Shi, M.S. Cao, J. Yuan, J. Appl. Phys. 104 (2008) 096101. [23] S.S. Kim, S.B. Jo, K.K. Choi, J.M. Kim, K.S. Churn, IEEE Trans. Magn. Mag. 27 (1991) 5462. [24] P. Singh, V.K. Babbar, A. Razdan, R.K. Puri, T.C. Goel, J. Appl. Phys. 87 (2000) 4362. [25] M.S. Cao, R.R. Qin, C. Qiu, J. Zhu, Mater. Design 24 (2003) 391.
Scripta Materialia 61 (2009) 201–204 www.elsevier.com/locate/scriptamat
High-temperature microwave absorption and evolutionary behavior of multiwalled carbon nanotube nanocomposite Wei-li Song,a Mao-sheng Cao,a,* Zhi-ling Hou,a Jie Yuanb and Xiao-yong Fanga a
School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China b School of Information Engineering, Central University for Nationality, Beijing 100081, China Received 20 December 2008; revised 21 March 2009; accepted 24 March 2009 Available online 29 March 2009
The high-temperature dielectric property and evolutionary behavior of multiwalled carbon nanotube/silica nanocomposite from 30 to 600 °C in the range 8.2–12.4 GHz were investigated. Both increasing temperature and elevated multiwalled carbon nanotube concentration are found to enhance complex permittivity, and a mechanism for this enhancement is also proposed. The calculated attenuation suggests that multiwalled carbon nanotube/silica a good candidate for high-temperature microwave-absorbing materials, and this could help in material designs with matching conditions. Crown Copyright Ó 2009 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. Keywords: Carbon nanotube; High-temperature; Microwave absorption; Dielectric property
Carbon nanotubes (CNTs) have attracted extensive interest from a number of groups from various fields, such as physics, materials, chemistry and biology, and much effort has been devoted to fabricating these materials and investigating their properties. The unique electrical, thermal and mechanical properties of CNTs, which cannot be matched by conventional materials, make CNTs good candidates for use in practical applications, e.g. field emission devices, transparent conductive films, light sources, energy storage devices and biosensors [1–6]. In recent years, a significant amount of research has successfully been focused on electromagnetic interference (EMI) shielding or microwave absorption for the purpose of protecting the workspace and the environment from the radiation emitted by telecommunication apparatus [7]. Meanwhile, CNTs are prime candidates in the development of potentially revolutionary EMI shielding materials due to their light weight, resistance to corrosion, flexibility and processing advantages [8–11]. Very recently, the high-temperature microwaveabsorbing properties of carbon materials [12], MnO2 nanorods [13], ZnO [14], etc. [15], have been widely explored. However, the high-temperature microwaveabsorbing property of CNTs has not been intensively
* Corresponding author. Tel.: +86 01068914062; e-mail: caomaosheng@ bit.edu.cn
studied to date, even though it is believed that these materials could be potential candidates for a wide range of EMI shielding materials for use in severe environment. In this paper, the complex permittivity of a multiwalled carbon nanotube/silica nanocomposite (MWNT/SiO2) at temperatures from 30 to 600 °C in the 8.2–12.4 GHz (X-band) was studied experimentally. Both dielectric constant and dielectric loss depend on the temperature, frequency and MWNT concentration. In order to predict the high-temperature EMI shielding property, an attenuation calculation was employed based on the measured data in this study, which suggests that MWNT/SiO2 is good high-temperature microwave-absorbing material. MWNT/SiO2 samples with different MWNT concentrations were prepared by the conventional ceramic method, wherein SiO2 xerogel nanopowder was fabricated by the sol–gel method. MWNTs, purchased from Shenzhen Nanotech Port Co. Ltd. (China), were fabricated by the catalytic decomposition of CH4, with diameters ranging from 20 to 40 nm and lengths ranging from 5 to 15 lm. The samples were synthesized from mixtures of SiO2 nanopowder with different amounts of MWNTs (MWNT concentration: 2, 5 and 10 wt.%). These mixtures were then blended in an ethanol solution. Ultrasonic treatment was employed to disperse the mixture solution for 40 min. After the slurry was dried, crushed in an agate mortar and pestle, and sieved (150 lm), the fine powder was then compacted into sheet (22.5 10 2.5 mm) under a pressure of 60 MPa. The green
1359-6462/$ - see front matter Crown Copyright Ó 2009 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. doi:10.1016/j.scriptamat.2009.03.048
202
W. Song et al. / Scripta Materialia 61 (2009) 201–204
compact was sintered at a temperature of 500 °C for 2 h for annealing treatment. Before dielectric measurement, the sample was dried at 200 °C for 24 h. A vector network analyzer (Anritsu 37269D) was used to determine the values of the relative complex permittivity, dielectric constant (e0 ) and dielectric loss (e00 ) of MWNT/SiO2 by the wave-guide method in the X-band. The complex permittivity of MWNT/SiO2 was determined at 12 temperatures covering the temperature range from 30 to 600 °C. MWNT/SiO2 was put in the test apparatus and heated by an internal heater at 20 °C min1. In order to ensure the accuracy of the test data, a period of 25 min was required for the system to stabilize, once each set-point temperature was achieved, and a set of duplicate measurements was then obtained. This process went on until data covering the whole temperature range were obtained. Scanning electron microscopy (SEM) gives an overview of the fractured surface of MWNT/SiO2 with different amounts of MWNTs (2, 5 and 10 wt.%) dispersed in silica, as shown in Figure 1a–c, respectively. The transmission electron microscopy (TEM) image in Figure 1d shows the original MWNT pieces used in this work. Figure 1e illustrates the MWNT cluster feature. This clustering, caused by the aggregation of MWNTs owing to the difficulty of dispersion, will simultaneously confer stiffness, toughness and strength on the composite. Apparently, more MWNTs clusters are observed in the sample with 10 wt.% MWNTs shown in Figure 1c and the sample with 2 wt.% MWNTs has the fewest clusters, as shown in Figure 1a. Figure 2 illustrates the complex permittivity of MWNT/SiO2 (10 wt.% MWNTs), which represents the typical dielectric property of the samples investigated in this work. Both e0 and e00 apparently decrease with increasing frequency, as shown in the insets of Figure 2a and b,
Figure 1. (a–c) SEM images of MWNT (2, 5 and 10 wt.%, respectively) dispersion in MWNT/SiO2. (d) TEM image of MWNTs used in this work. (e) SEM image of a MWNT cluster.
Figure 2. Complex permittivity of MWNT/SiO2 (10 wt.% MWNTs). (a) The profile of dielectric constant (e0 ) vs. temperature and frequency (inset). (b) The profile of dielectric loss (e00 ) vs. temperature and frequency (inset).
respectively. These decreases imply that the complex permittivity has a weakening response to increasing frequency. It is proposed that the molecules and electrons have enough time to polarize at low-frequency. Nevertheless, at high-frequency, the polarization of molecules and electrons could not have enough time to catch up with the change in electromagnetic field frequency. Additionally, a very good monotonic relationship between complex permittivity and temperature is exhibited over the experimental temperature range according to Figure 2a and b. Both e0 and e00 increase smoothly at each frequency (9, 10, 11 and 12 GHz) with rising temperature. This temperature-dependent dielectric property will now be discussed in more detail. Firstly, e0 is mainly related to electron polarization. As electrons are very light, they respond rapidly to an alternating electromagnetic field and their relaxation time is associated with a change of temperature. The Eyring formalism is suitable for describing this relationship for MWNT/SiO2 [16]: h DH DS exp exp ; ð1Þ sðT Þ ¼ kT RT R where h and k are the Planck constant and the Boltzmann constant, respectively, and DH and DS are the enthalpy and entropy of activation, respectively. It is proposed that the migrating electrons in MWNT/SiO2 respond faster to the alternating electromagnetic field when the temperature is rising, which causes a shorter relaxation time during the polarization. Meanwhile, the relationship between e0 and relaxation time can be expressed in terms of the Debye theory:
W. Song et al. / Scripta Materialia 61 (2009) 201–204
e0 ¼ e1 þ
es e1 1 þ x2 sðT Þ
2
;
ð2Þ
where es is the static permittivity, e1 is the relative dielectric permittivity at the high-frequency limit, x is the angular frequency and sðT Þ is the temperaturedependent relaxation time. Based on Eqs. (1) and (2), we could deduce that a shorter relaxation time leads an increasing dielectric constant in MWNT/SiO2 with elevated temperature in the temperature range from 30 to 600 °C. On the other hand, e00 can be also expressed in terms of dielectric physics theory: e00
rðT Þ ; e0 x
ð3Þ
where rðT Þ is the temperature-dependent electrical conductivity and e0 is the dielectric constant in vacuum. As shown in Eq. (3), the electrical conductivity of the composite plays a dominating role in dielectric loss. For individual MWNTs, the ballistic transport property [17] and the current in the outer shell [18] suggest that MWNTs are good conductors. Furthermore, the electrical conductivity of individual MWNTs will be increased due to the increase in the concentration of migrating electrons in conductive MWNT tubes at elevated temperature. In addition, the electrical conductivity of MWNT bulk material also possesses this characteristic [19] due to the temperature-dependent electrical conductivity of individual MWNTs. According to the above analysis, at elevated temperatures, the increasing electrical conductivity enhances the dielectric loss of MWNT/SiO2. Furthermore, the concentration-dependent dielectric property of MWNT/SiO2 has also been investigated. Compared with the complex permittivity at three temperatures (100, 300 and 500 °C), both e0 and e00 increase with an increase in MWNT concentration (from 2 to 10 wt.%), as illustrated in Figure 3. According to the effective medium theory [20], the dielectric constant increases with elevated concentration of MWNTs. Moreover, the increase in the number of continuous conductive networks of MWNTs [9,21,22], which leads to elevated electrical conductivity, contributes to the enhanced dielectric loss as the concentration of MWNTs rises.
Figure 3. Complex permittivity of MWNT/SiO2 with different MWNT content (2, 5 and 10 wt.%) at various temperatures (100, 300 and 500 °C) vs. frequency.
203
For further investigation of the high-temperature microwave absorption, the high-temperature reflection loss of MWNT/SiO2 (10 wt.%) was calculated. The normalized input impedance Z in of the MWNT/SiO2 microwave-absorbing layer is described by [23,24]: rffiffiffiffiffi lr 2p pffiffiffiffiffiffiffiffi Z in ¼ tanh j lr er fd ; ð4Þ er c where lr and er represent the relative permeability and permittivity of the composite medium, respectively, c is the velocity of light, f is the microwave frequency, and d is the thickness of the absorber. The reflection loss (R) is related to Zin as: R ¼ 20 log
jZ in 1j : jZ in þ 1j
ð5Þ
Figure 4a shows the calculated attenuation vs. frequency for each temperature by using the actual measured values of e and l, where l is taken as 1 due to MWNT/SiO2 being extremely weakly magnetic. All the calculated values were predicted based on a constant thickness d = 2.5 mm. The maximum attenuations at each temperature vary little with changing frequency and the points are around 10.1 GHz, which indicates that the reflection loss peak point of the composite is insensitive to temperature in the X-band. The relationship of reflection loss and temperature is demonstrated in Figure 4b. It is apparent that the strongest calculated attenuation occurs at around 30 °C at each frequency. The minimum attenuation point in this present temperature range remains at about 8.2 GHz. More importantly, the attenuation behavior is significantly dependent upon the tem-
Figure 4. High-temperature microwave absorption of MWNT/SiO2 (10 wt.% MWNTs). (a) Calculated reflection loss vs. frequency. (b) Calculated reflection loss vs. temperature.
204
W. Song et al. / Scripta Materialia 61 (2009) 201–204
perature. A monotonic decrease in calculated attenuation is observed in the range from 100 to 600 °C when the temperature increases. According to the experimental data and calculated reflection loss, the relationship between decreasing calculated attenuation and increasing temperature can be explained in terms of matching conditions. In order to investigate the evolutionary behavior and analyze the optimum design for ideal microwave-absorbing materials, the corresponding conditions and related parameters are discussed. To obtain resonant absorption of a single-layer absorber, the thickness and wavelength should obey the following relationship [25]: d ¼ ki =4;
ð6Þ
where d is the thickness and ki is the wavelength of incident wave. As indicated by Eq. (6), the response of the material to electromagnetic microwaves is close to resonant absorption, which leads to formation of a standing wave in the material, resulting in optimum microwave attenuation. Unfortunately, actual materials generally deviate from this resonant condition, since the optimum thickness varies with frequency. On the other hand, to meet the requirement of A(dB) attenuation, the corresponding electromagnetic parameters, frequency and thickness should follow the conditions [25]: p 1 10A=20 pc e0 ¼ ð7Þ cot h tgd 2dx 2 1 þ 10A=20 e00 ¼ e0 tgd ð8Þ where d is thickness, c is the velocity of light and x presents angular frequency. For this case, the calculated attenuation of MWNT/SiO2 exhibits good absorbing property at room temperature, where the reflection loss peak is close to 20 dB and the minimum attenuation is below 16 dB at 8.2 GHz, as shown in Figure 4a. However, when the temperature is rising, the impedance matching condition between air and the absorbing medium is disturbed. According to the Eqs. (7) and (8), the main reason for this is the variation in electromagnetic parameters (e0 , e00 ) with changing temperature. As exhibited in the calculated results, the microwave-absorbing property of MWNT/SiO2 decreases at elevated temperature, though this nanocomposite can still be considered as a good candidate for high-temperature absorbing materials, owing to the high-reflection loss (<10 dB) even at high-temperature. Therefore, attention should be paid to adjusting the electromagnetic parameters, thickness and related parameters in order to obtain high-performance microwave-absorbing materials. In summary, the high-temperature complex permittivity and the evolutionary behavior of MWNT/SiO2 over the temperature range 30–600 °C in the X-band were studied. When temperature rises, the increase in dielectric constant is attributed to the reduction of relaxation time and the increasing dielectric loss is due to the increase in electrical conductivity. With increasing MWNT concentration, the increase in continuous conductive networks can contribute to enhancing the dielec-
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