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The 500 MHz to 5.50 GHz complex permittivity spectra of single-wall carbon nanotube-loaded polymer composites
24 March 2000
Chemical Physics Letters 319 Ž2000. 460–464 www.elsevier.nlrlocatercplett
The 500 MHz to 5.50 GHz complex permittivity spectra of single-wall carbon nanotube-loaded polymer composites C.A. Grimes a
a,b,)
, C. Mungle a , D. Kouzoudis b, S. Fang c , P.C. Eklund
d
Department of Electrical Engineering, 453 Anderson Hall, The UniÕersity of Kentucky, Lexington, KY 40506, USA b Crale, 525 McCalls Mill Road, Lexington, KY 40515, USA c CarboLex, A064 ASTeCC Building, Lexington, KY 40506, USA d Department of Physics, PennsylÕania State UniÕersity, UniÕersity Park, PA 16803, USA Received 2 February 2000
Abstract The 500 MHz to 5.50 GHz complex permittivity spectra of a thick-film polymer loaded with 0–23 wt% single-wall carbon nanotubes is measured. At 500 MHz, as the weight percentage loading of the carbon nanotubes increases from 0 to 23% the real permittivity is found to increase by a factor of ; 35, and the imaginary permittivity by a factor of 1200. The spectral magnitudes decrease rapidly from the 500 MHz value over the measured frequency range. Experimental data are in qualitative agreement with values predicted using an effective medium theory for materials comprised of elongated cylindrical conductors wA.N. Lagarkov, A.K. Sarychev, Phy. Rev. B 53 Ž1996. 6318x. q 2000 Published by Elsevier Science B.V. All rights reserved.
1. Introduction Single-wall carbon nanotubes ŽSWNTs. have attracted much attention recently because of their small diameter, high aspect ratio, mechanical strength and flexibility, see e.g. Refs. w1–7x. Electronic band theory shows that 1r3 of carbon nanotubes are metallic, and the remaining 2r3 are semiconducting, with the semiconducting band gap decreasing to zero as Eg f 1rd, where d is the diameter of the individual nanotube. It has been known for some time that effective electromagnetic shielding materials can be fabricated by dispersing small, high aspect ratio con) Corresponding author. Fax: q1-606-257-3092; e-mail: [email protected]
ducting cylinders into dielectric hosts. We are therefore motivated to examine the rf permittivity spectra of single-wall carbon nanotube composite materials to see if they are suitable for use as microwave lenses, high-strength low weight electromagnetic interference ŽEMI. shielding materials, antennas, waveguides, etc. Earlier work has reported on the dielectric properties of nanotube composites at frequencies above 300 GHz w8,9x. In this Letter we report on measurement of the 500 MHz to 5.50 GHz complex permittivity spectra, ´ s ´ X y j ´ Y , of a composite material comprised of bundles of singlewall carbon nanotubes dispersed within a polymer matrix at 0–23 wt% nanotube loadings. The bundles of single-wall carbon nanotubes used in this work were made by the arc-discharge method, and are ; 1
0009-2614r00r$ - see front matter q 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 1 9 6 - 2
C.A. Grimes et al.r Chemical Physics Letters 319 (2000) 460–464
461
mm long, typically 10 nm in diameter, having aspect ratios of ; 100. Permittivity measurements are compared with theoretical predictions using an effective medium theory w10x developed for a dielectric material containing stick-like, elongated conducting cylinders of large aspect ratio.
2. Experimental details To fabricate the test samples, the monomer Žethyl methacrylate. in powder form and the bundles of carbon nanotubes were first mixed carefully together using a mortar and pestle. While stirring, liquid hardener was added to the solid suspension to polymerize the material. The nanotube polymer–composite paste was then immediately put into a mold with pressure applied to form a thin sheet ; 0.5 mm thick. The complex permittivity spectra of 2 = 5 = 0.5 mm test samples were measured using a stripline cavity w11–13x. The dc resistivity of the SWNT composites was measured in the van der Pauw geometry using four leads attached with silver paste made by Dupont. The SWNTs were obtained from Carbolex and contained ; 70 wt% nanotubes, with the balance of the carbon material in the form of carbon nanospheres ; 20 nm in diameter and carbon-coated Ni–Y catalyst, ; 5 wt%, also in the form of nanoparticles of similar diameter. An average nanotube bundle diameter of ; 10 nm was observed by high-resolution scanning electron microscopy.
3. Experimental results In Fig. 1 the room-temperature dc electrical resistivity of SWNT–polymer composite samples is plotted as a function of the weight percentage of nanotubes added to the monomer. Note that the log of the resistivity is plotted, and over the range of loading studied, to 23%, over nine orders of magnitude change in the SWNT–polymer composite resistivity is observed. The data in Fig. 1 fall on a smooth curve with a percolation threshold near ; 3 wt%. The fact that the resistivity data fall on a reasonably smooth curve indicates that the SWNT bundles were
Fig. 1. Measured dc conductivity of SWNT–polymer Žpoly-ethyl methacrylate. composites as a function of weight percentage loading.
well dispersed in the polymer host. Note that while data can be obtained for a sheet comprised of nanotubes, i.e. 100% loading, the material is brittle and susceptible to fracture which prevented useful highfrequency measurements. Fig. 2 shows the measured room-temperature complex permittivity spectra for different carbon nanotube-loading concentrations. Addition of the nanotubes to the polymer has a dramatic effect on the measured permittivity spectra. At 500 MHz the real permittivity increases by a factor of ; 35 as the nanotube concentration increases from p s 0 to 23%; at 5500 MHz this factor drops to ; 6. The imaginary permittivity shows a much higher dependence on p. At 500 MHz it increases by over three orders of magnitude from p s 0 to 23%, and at 5500 MHz the change is a factor of ; 200. Fig. 3 shows ´ Y of the polymer composite as a function of SWNT weight percentage loading. The data are obtained by linearly extrapolating the measured results to their approximate dc values. Similar to the dc conductivity data in Fig. 1, the data fall on a reasonably smooth curve, indicating the SWNT material is well dispersed within the polymer. However, the percolation threshold observed near 3 wt% in the dc conductivity is not observed in our 500 MHz ´ Y data.
4. Effective medium modeling Effective medium theories have long been used to calculate the frequency-dependent electromagnetic
462
C.A. Grimes et al.r Chemical Physics Letters 319 (2000) 460–464
X Y Fig. 2. Real Ž ´ . and imaginary Ž ´ . permittivity spectra of 0–23 wt% SWNT loaded polymer composites.
properties of composite materials w14–20x. Lagarkov and Sarychev w10x calculated the permittivity spectra of a composite material comprised of conducting ‘sticks’, i.e. conductive cylinders of large aspect ratio, inside a dielectric binder using a scale-dependent local-field dielectric constant. Their theory anticipates a percolation threshold that is linearly dependent upon the aspect ratio of the conducting stick. Using the low-frequency portion of the effective medium model w10x, experimental data for nanotubeloadings of p s 10% and 23% are numerically simulated, with results shown in Fig. 4. We assume that the nanotube bundles contain a blend of metallic and semi-conducting nanotubes. The dielectric response of the SWNT–polymer composite is most sensitive
Y
Fig. 3. ´ of the polymer composite as a function of SWNT weight percentage loading, linearly extrapolated from the measured 500 MHz values to dc.
C.A. Grimes et al.r Chemical Physics Letters 319 (2000) 460–464
463
Fig. 4. Comparison between theory w10x Žsolid line. and experiment Žsymbols. for the real and imaginary permittivity spectra of polymer containing at p s 10 and 23 wt% loading of single-wall carbon nanotubes.
to the electrical properties of the fraction of nanotubes that are metallic. The semi-conducting nanotubes in the composite can be viewed as effectively increasing the permittivity of the polymer-binder. Consequently, in our effective medium model the permittivity of the binder is adjusted upward from the 0% loading value, ´ s 2.6 y j0.1, to reflect the addition of semi-conducting nanotubes. The nanotube bundles are observed to have a diameter of ; 10 nm; their average length is not definitely known, but has been estimated to be in the range of 1–5 mm. The theoretical results shown in Fig. 4 are calculated assuming 30% of the nanotubes are metallic
and contribute to the composite permittivity, the nanotubes are assigned an aspect ratio of 1000. We further assume that in this frequency range: Ž1. the binder has a complex, frequency-independent form, i.e. ´ binder s 4.6 y j3.2; and Ž2. the effective dielectricresponse of the metallic SWNT bundle is given by s SW NT ´ SW NT s ´ XSWNT y j , Ž 1. v´ 0 where v is the radian frequency, and ´ 0 the permittivity of free space. The real part of the complex permittivity ´ XSW NT and the dc conductivity of the bundle s SW NT are also assumed constant. The usual
464
C.A. Grimes et al.r Chemical Physics Letters 319 (2000) 460–464
frequency dependence of the complex part of the permittivity of a metal has been used. For the results shown in Fig. 4, s SW NT s 885 Srm.
5. Conclusions The 500 MHz to 5.50 GHz complex permittivity spectra of poly-ethyl methacrylate polymer thickfilms containing single-wall nanotubes at 0–23 wt% loadings are presented. Small weight percentage additions of single-wall carbon nanotubes to the polymer are found to increase the magnitude of the permittivity spectra dramatically. Using an effective medium theory developed earlier to describe composite materials composed of stick-like conductors w10x, experimental data and theory are found to be in reasonable agreement.
Acknowledgements This work was supported in part by the Office of Naval Research SBIR contract N00014-99-M-0119, and by the National Science Foundation contract DMR-9809686. C.M. is supported through the NSF funded IGERT Integrated Sensing Architectures program.
References w1x M.S. Dresselhaus, Nature ŽLondon. 358 Ž1992. 195. w2x S. Ijima, Nature ŽLondon. 354 Ž1991. 56. w3x M. Dresselhaus, G. Dresselhaus, P. Eklund, R. Saito, Phys. World, Jan. Ž1998.. w4x T.W. Ebbesen, P.M. Ajayan, H. Hiura, K. Tanigaki, Nature ŽLondon. 367 Ž1994. 519. w5x R.F. Service, Science 281 Ž1998. 940. w6x M.M.J. Treacy, T.W. Ebbesen, J.M. Gibson, Nature ŽLondon. 381 Ž1996. 678. w7x J.W. Mintrime, B.I. Dunlap, C.T. White, Phys. Rev. Lett. 68 Ž1992. 631. w8x W.A. de Heer, W.S. Basca, A. Chetalein, T. Gerfin, R. Humphrey-Baker, L. Forro, D. Ugarte, Science 268 Ž1995. 845. w9x M.F. Lin, K.W.-K. Shung, Phys. Rev. B 50 Ž1994. 17744. w10x A.N. Lagarkov, A.K. Sarychev, Phys. Rev. B 53 Ž1996. 6318. w11x S.P. Maxwell, Marconi Rev., 1st Quarter Ž1964. 22. w12x S.P. Maxwell, Microwave J. Ž1966. 99. w13x R.A. Waldron, IEEE Trans. MTT Ž1964. 123. w14x J.C.M. Garnett, Philos. Trans. R. Soc. London 203 Ž1904. 385. w15x J.C.M. Garnett, Philos. Trans. R. Soc. London 205 Ž1906. 237. w16x D.A.G. Bruggeman, Ann. Phys. ŽLeipzig. 24 Ž1935. 636. w17x G.A. Niklasson, C.G. Granqvist, J. Appl. Phys. 55 Ž1984. 3382. w18x C.A. Grimes, IEEE Trans. Mag. 27 Ž1991. 4310. w19x C.A. Grimes, D.M. Grimes, Phys. Rev. B 43 Ž1991. 10780. w20x A. Lakhtakia, G.Y. Slepyan, S.A. Maksimenko, A.V. Gusakov, O.M. Yevtushenko, Carbon 36 Ž1998. 1833.
Chemical Physics Letters 319 Ž2000. 460–464 www.elsevier.nlrlocatercplett
The 500 MHz to 5.50 GHz complex permittivity spectra of single-wall carbon nanotube-loaded polymer composites C.A. Grimes a
a,b,)
, C. Mungle a , D. Kouzoudis b, S. Fang c , P.C. Eklund
d
Department of Electrical Engineering, 453 Anderson Hall, The UniÕersity of Kentucky, Lexington, KY 40506, USA b Crale, 525 McCalls Mill Road, Lexington, KY 40515, USA c CarboLex, A064 ASTeCC Building, Lexington, KY 40506, USA d Department of Physics, PennsylÕania State UniÕersity, UniÕersity Park, PA 16803, USA Received 2 February 2000
Abstract The 500 MHz to 5.50 GHz complex permittivity spectra of a thick-film polymer loaded with 0–23 wt% single-wall carbon nanotubes is measured. At 500 MHz, as the weight percentage loading of the carbon nanotubes increases from 0 to 23% the real permittivity is found to increase by a factor of ; 35, and the imaginary permittivity by a factor of 1200. The spectral magnitudes decrease rapidly from the 500 MHz value over the measured frequency range. Experimental data are in qualitative agreement with values predicted using an effective medium theory for materials comprised of elongated cylindrical conductors wA.N. Lagarkov, A.K. Sarychev, Phy. Rev. B 53 Ž1996. 6318x. q 2000 Published by Elsevier Science B.V. All rights reserved.
1. Introduction Single-wall carbon nanotubes ŽSWNTs. have attracted much attention recently because of their small diameter, high aspect ratio, mechanical strength and flexibility, see e.g. Refs. w1–7x. Electronic band theory shows that 1r3 of carbon nanotubes are metallic, and the remaining 2r3 are semiconducting, with the semiconducting band gap decreasing to zero as Eg f 1rd, where d is the diameter of the individual nanotube. It has been known for some time that effective electromagnetic shielding materials can be fabricated by dispersing small, high aspect ratio con) Corresponding author. Fax: q1-606-257-3092; e-mail: [email protected]
ducting cylinders into dielectric hosts. We are therefore motivated to examine the rf permittivity spectra of single-wall carbon nanotube composite materials to see if they are suitable for use as microwave lenses, high-strength low weight electromagnetic interference ŽEMI. shielding materials, antennas, waveguides, etc. Earlier work has reported on the dielectric properties of nanotube composites at frequencies above 300 GHz w8,9x. In this Letter we report on measurement of the 500 MHz to 5.50 GHz complex permittivity spectra, ´ s ´ X y j ´ Y , of a composite material comprised of bundles of singlewall carbon nanotubes dispersed within a polymer matrix at 0–23 wt% nanotube loadings. The bundles of single-wall carbon nanotubes used in this work were made by the arc-discharge method, and are ; 1
0009-2614r00r$ - see front matter q 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 1 9 6 - 2
C.A. Grimes et al.r Chemical Physics Letters 319 (2000) 460–464
461
mm long, typically 10 nm in diameter, having aspect ratios of ; 100. Permittivity measurements are compared with theoretical predictions using an effective medium theory w10x developed for a dielectric material containing stick-like, elongated conducting cylinders of large aspect ratio.
2. Experimental details To fabricate the test samples, the monomer Žethyl methacrylate. in powder form and the bundles of carbon nanotubes were first mixed carefully together using a mortar and pestle. While stirring, liquid hardener was added to the solid suspension to polymerize the material. The nanotube polymer–composite paste was then immediately put into a mold with pressure applied to form a thin sheet ; 0.5 mm thick. The complex permittivity spectra of 2 = 5 = 0.5 mm test samples were measured using a stripline cavity w11–13x. The dc resistivity of the SWNT composites was measured in the van der Pauw geometry using four leads attached with silver paste made by Dupont. The SWNTs were obtained from Carbolex and contained ; 70 wt% nanotubes, with the balance of the carbon material in the form of carbon nanospheres ; 20 nm in diameter and carbon-coated Ni–Y catalyst, ; 5 wt%, also in the form of nanoparticles of similar diameter. An average nanotube bundle diameter of ; 10 nm was observed by high-resolution scanning electron microscopy.
3. Experimental results In Fig. 1 the room-temperature dc electrical resistivity of SWNT–polymer composite samples is plotted as a function of the weight percentage of nanotubes added to the monomer. Note that the log of the resistivity is plotted, and over the range of loading studied, to 23%, over nine orders of magnitude change in the SWNT–polymer composite resistivity is observed. The data in Fig. 1 fall on a smooth curve with a percolation threshold near ; 3 wt%. The fact that the resistivity data fall on a reasonably smooth curve indicates that the SWNT bundles were
Fig. 1. Measured dc conductivity of SWNT–polymer Žpoly-ethyl methacrylate. composites as a function of weight percentage loading.
well dispersed in the polymer host. Note that while data can be obtained for a sheet comprised of nanotubes, i.e. 100% loading, the material is brittle and susceptible to fracture which prevented useful highfrequency measurements. Fig. 2 shows the measured room-temperature complex permittivity spectra for different carbon nanotube-loading concentrations. Addition of the nanotubes to the polymer has a dramatic effect on the measured permittivity spectra. At 500 MHz the real permittivity increases by a factor of ; 35 as the nanotube concentration increases from p s 0 to 23%; at 5500 MHz this factor drops to ; 6. The imaginary permittivity shows a much higher dependence on p. At 500 MHz it increases by over three orders of magnitude from p s 0 to 23%, and at 5500 MHz the change is a factor of ; 200. Fig. 3 shows ´ Y of the polymer composite as a function of SWNT weight percentage loading. The data are obtained by linearly extrapolating the measured results to their approximate dc values. Similar to the dc conductivity data in Fig. 1, the data fall on a reasonably smooth curve, indicating the SWNT material is well dispersed within the polymer. However, the percolation threshold observed near 3 wt% in the dc conductivity is not observed in our 500 MHz ´ Y data.
4. Effective medium modeling Effective medium theories have long been used to calculate the frequency-dependent electromagnetic
462
C.A. Grimes et al.r Chemical Physics Letters 319 (2000) 460–464
X Y Fig. 2. Real Ž ´ . and imaginary Ž ´ . permittivity spectra of 0–23 wt% SWNT loaded polymer composites.
properties of composite materials w14–20x. Lagarkov and Sarychev w10x calculated the permittivity spectra of a composite material comprised of conducting ‘sticks’, i.e. conductive cylinders of large aspect ratio, inside a dielectric binder using a scale-dependent local-field dielectric constant. Their theory anticipates a percolation threshold that is linearly dependent upon the aspect ratio of the conducting stick. Using the low-frequency portion of the effective medium model w10x, experimental data for nanotubeloadings of p s 10% and 23% are numerically simulated, with results shown in Fig. 4. We assume that the nanotube bundles contain a blend of metallic and semi-conducting nanotubes. The dielectric response of the SWNT–polymer composite is most sensitive
Y
Fig. 3. ´ of the polymer composite as a function of SWNT weight percentage loading, linearly extrapolated from the measured 500 MHz values to dc.
C.A. Grimes et al.r Chemical Physics Letters 319 (2000) 460–464
463
Fig. 4. Comparison between theory w10x Žsolid line. and experiment Žsymbols. for the real and imaginary permittivity spectra of polymer containing at p s 10 and 23 wt% loading of single-wall carbon nanotubes.
to the electrical properties of the fraction of nanotubes that are metallic. The semi-conducting nanotubes in the composite can be viewed as effectively increasing the permittivity of the polymer-binder. Consequently, in our effective medium model the permittivity of the binder is adjusted upward from the 0% loading value, ´ s 2.6 y j0.1, to reflect the addition of semi-conducting nanotubes. The nanotube bundles are observed to have a diameter of ; 10 nm; their average length is not definitely known, but has been estimated to be in the range of 1–5 mm. The theoretical results shown in Fig. 4 are calculated assuming 30% of the nanotubes are metallic
and contribute to the composite permittivity, the nanotubes are assigned an aspect ratio of 1000. We further assume that in this frequency range: Ž1. the binder has a complex, frequency-independent form, i.e. ´ binder s 4.6 y j3.2; and Ž2. the effective dielectricresponse of the metallic SWNT bundle is given by s SW NT ´ SW NT s ´ XSWNT y j , Ž 1. v´ 0 where v is the radian frequency, and ´ 0 the permittivity of free space. The real part of the complex permittivity ´ XSW NT and the dc conductivity of the bundle s SW NT are also assumed constant. The usual
464
C.A. Grimes et al.r Chemical Physics Letters 319 (2000) 460–464
frequency dependence of the complex part of the permittivity of a metal has been used. For the results shown in Fig. 4, s SW NT s 885 Srm.
5. Conclusions The 500 MHz to 5.50 GHz complex permittivity spectra of poly-ethyl methacrylate polymer thickfilms containing single-wall nanotubes at 0–23 wt% loadings are presented. Small weight percentage additions of single-wall carbon nanotubes to the polymer are found to increase the magnitude of the permittivity spectra dramatically. Using an effective medium theory developed earlier to describe composite materials composed of stick-like conductors w10x, experimental data and theory are found to be in reasonable agreement.
Acknowledgements This work was supported in part by the Office of Naval Research SBIR contract N00014-99-M-0119, and by the National Science Foundation contract DMR-9809686. C.M. is supported through the NSF funded IGERT Integrated Sensing Architectures program.
References w1x M.S. Dresselhaus, Nature ŽLondon. 358 Ž1992. 195. w2x S. Ijima, Nature ŽLondon. 354 Ž1991. 56. w3x M. Dresselhaus, G. Dresselhaus, P. Eklund, R. Saito, Phys. World, Jan. Ž1998.. w4x T.W. Ebbesen, P.M. Ajayan, H. Hiura, K. Tanigaki, Nature ŽLondon. 367 Ž1994. 519. w5x R.F. Service, Science 281 Ž1998. 940. w6x M.M.J. Treacy, T.W. Ebbesen, J.M. Gibson, Nature ŽLondon. 381 Ž1996. 678. w7x J.W. Mintrime, B.I. Dunlap, C.T. White, Phys. Rev. Lett. 68 Ž1992. 631. w8x W.A. de Heer, W.S. Basca, A. Chetalein, T. Gerfin, R. Humphrey-Baker, L. Forro, D. Ugarte, Science 268 Ž1995. 845. w9x M.F. Lin, K.W.-K. Shung, Phys. Rev. B 50 Ž1994. 17744. w10x A.N. Lagarkov, A.K. Sarychev, Phys. Rev. B 53 Ž1996. 6318. w11x S.P. Maxwell, Marconi Rev., 1st Quarter Ž1964. 22. w12x S.P. Maxwell, Microwave J. Ž1966. 99. w13x R.A. Waldron, IEEE Trans. MTT Ž1964. 123. w14x J.C.M. Garnett, Philos. Trans. R. Soc. London 203 Ž1904. 385. w15x J.C.M. Garnett, Philos. Trans. R. Soc. London 205 Ž1906. 237. w16x D.A.G. Bruggeman, Ann. Phys. ŽLeipzig. 24 Ž1935. 636. w17x G.A. Niklasson, C.G. Granqvist, J. Appl. Phys. 55 Ž1984. 3382. w18x C.A. Grimes, IEEE Trans. Mag. 27 Ž1991. 4310. w19x C.A. Grimes, D.M. Grimes, Phys. Rev. B 43 Ž1991. 10780. w20x A. Lakhtakia, G.Y. Slepyan, S.A. Maksimenko, A.V. Gusakov, O.M. Yevtushenko, Carbon 36 Ž1998. 1833.