Alignment characterization of single-wall carbon nanotubes by Raman scattering

Physics Letters A 313 (2003) 302 306 www.elsevier.com/locate/pla Alignment characterization of single-wall carbon nanotubes by Raman scattering Pijun Liu, Liyue Liu, Yafei Zhang Key Laboratory for Thin Film and Microfabrication of Ministry of Education, Research Institute of Micro/Nanometer Science and Technology, Shanghai Jiao Tong University, Shanghai 200030, PR China Received 24 March 2003; accepted 9 May 2003 Communicated by R. Wu Abstract A novel method for identifying the Raman modes of single-wall carbon nanotubes (SWNT) based on the symmetry of the vibration modes has been studied. The Raman intensity of each vibration mode varies with polarization direction, and the relationship can be expressed as analytical functions. This method avoids troublesome numerical calculation and easily gives clear relations between Raman intensity and polarization direction. In this way, one can distinguish each Raman-active mode of SWNT through the polarized Raman spectrum. 2003 Elsevier B.V. All rights reserved. PACS: 71.20.Tx; 61.48.+c; 81.05.Tp Keywords: SWNT; Raman scattering; Raman-active modes; Polarizability tensor 1. Introduction Single-wall carbon nanotubes (SWNT) with their well-defined atomic structure, chemical stability, small diameter, and high aspect ratio, constitute wonderful one-dimensional (1D) molecules [1. This characteristic aroused the interest of both academic research and industry. Recently, with the successful synthesis of large numbers of high quality SWNTs, the manipulation of SWNTs is becoming a hot research topic [2. The polarization effects of the Raman scattering are commonly observed in low-dimensional materials. * Corresponding author. E-mail address: yfzhang@sjtu.edu.cn (Y. Zhang). Since the SWNT is a kind of one-dimension material, the use of light that is polarized parallel or perpendicular to the tube axis will show the low dimensionality of the nanotubes. Raman spectra analysis has proven to provide a unique characterization tool for SWNTs [3 5, as well as other carbon materials [6. Rao et al. [3 showed that Raman signals from (m, n) SWNTs not only consist of the graphite-oriented E 2g mode, which occurs around 1550 1600 cm 1, but also contain a strong low frequency A 1g -active mode, known as a radial breathing mode. Satio et al. [7 presents a detailed calculation on the Raman intensity of a SWNT as a function of the polarization of light and the chirality of the carbon nanotube using non-resonant bondpolarization theory [8. Unfortunately, the Raman intensity of each vibration mode as a function of the 0375-9601/03/$ see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/s0375-9601(03)00764-3

P. Liu et al. / Physics Letters A 313 (2003) 302 306 303 SWNT sample orientation was not in analytic from. In the present work, a simple method to give each curve an analytical function is developed. This method avoids burdensome numerical calculation and gives analytical functions based on the symmetry of SWNTs vibration modes. Using these functions, one can easily verify the orientation of the SWNT through polarized Raman spectra [2. This method provides a useful way of evaluating the manipulation of SWNTs. 2. Theory outline According to the symmetries of Raman-active modes [9 for the armchair carbon nanotube with the chair vector (n, n), the point group for this kind nanotube belongs to D nh when n is even and its Raman-active modes are denoted by 4A 1g + 4E 1g + 8E 2g.Inthis Letter we mainly considered two Raman-active A 1g modes and two high frequency E g modes, E 1g (ω = 1585 cm 1 ) and E 2g (ω = 1591 cm 1 ). Satio et al. [7 pointed out that the low frequency A 1g mode (ω = 165 cm 1 ) is a radial breathing mode. According to the discussion of Ref. [7, the lattice of SWNT can be split into two sublattices consisting of A and B atoms. In the low frequency A 1g mode, the A and B atoms move in the same direction in the unit cell, while in the high frequency A 1g mode, these atoms move in opposite directions. Compared with other vibration modes, the higher A 1g mode corresponds to the folded vibration of the higher frequency E 2g mode. Based on the analysis of the vibration symmetries [9 of these Raman-active modes, the matrix of the polarizability tensor of Raman scattering a for each mode is: a(a 1g ) = a(e 1g ) = a(e 2g ) = [ a 0 0 0 a 0 0 0 a/2 [ 0 0 c c 0 0 [ d 0 0 0 d 0,. and [ a 0 0 0 a 0, 0 0 2a (1) Here the matrices of A 1g represent the low frequency and higher mode, respectively, and a, c and d are constants. We assigned three Cartesian coordinates axes x, y and z to the SWNTs with the long axis of the tube along z. The coordinate system x, y and z, is taken as the fixed axes. To start, the two z axes overlapped and the polarization vectors were chosen to lie along the z or x axes, respectively, for two polarization directions V and H. Rotating the nanotube axis about the x and y axes yields the rotation angles θ 1 and θ 2,respectively. θ 3 corresponds to rotation of the nanotube about the z axis. The detailed configurations are illustrated in Fig. 1. The fixed and active coordinate system are related by, r = T r,wheret is a transformation matrix. The matrix of each polarizability tensor of Raman scattering under the two coordinates systems can Fig. 1. The aligned carbon nanotubes which were fixed in the (z y ) plane were rotated round y axis with the VV (a) and VH (b) configurations used in polarized Raman spectrum measurement, θ corresponds to the rotation angle θ 1.

304 P. Liu et al. / Physics Letters A 313 (2003) 302 306 then be obtained by [10 [α=t[α T 1. (2) The Raman intensities of carbon nanotubes with nonresonant bond-polarization theory [8 are founded to be I ηη η α η β α 2 αβ. (3) αβ Here η and η denote the unit vectors along the incident and scattered polarization directions, α and β are Cartesian coordinates, and α αβ is the element of the polarizability tensor matrix. 3. Result and discussion We now consider the two possible geometries for the polarization of light showed in Fig. 1. In the VV configuration, the incident and the scattered polarizations are parallel to each other, i.e., both along the z direction. In the VH configuration they are perpendicular to each other. The intensity, Eq. (3), can then be simplified to α zz 2 for the VV configuration and α zx 2 for the VH configuration. According to the analysis mentioned above, these two elements of the polarization tensor matrix can be calculated with Eq. (2). Therefore, the Raman intensities as a function of rotation angle can be obtained. The basic form of these Raman-active modes in the two configurations for (10, 10) armchair SWNTs have been listed in Tables 1 and 2. They clearly show the Raman intensity dependence on the orientation of the nanotube and fit well with the numerical calculation results in Ref. [7. However, in our results the Raman intensity of the E 2g (ω = 1591 cm 1 ) mode is zero at θ 2 with the VH configuration. For a given polarization tensor matrix with E 2g symmetry, the matrix of D 6h has two forms [10: [ c 0 0 0 c 0 and [ 0 c 0 c 0 0. By rotating the nanotube axis about x axis, the transformation matrix T has the form [ 1 0 0 T = 0 cosθ sin θ. 0 sin θ cos θ Table 1 The basic functions of Raman-active modes for the (10, 10) armchair SWNT in the VV configuration. θ 1 and θ 2 are angles of the nanotube axis from z axis to the x axis and y axis, respectively. θ 3 is the angle of the nanotube axis around the z axis from x axis to y axis ω(cm 1 ) Raman intensity θ 1 θ 2 θ 3 A 1g 165 a 2 4 [ 2 + cos2 (θ 1 ) 2 a2 4 [ 2 + cos2 (θ 2 ) 2 a2 4 1587 a 2 [3cos 2 (θ 1 ) 1 2 a 2 [3cos 2 (θ 2 ) 1 2 4a 2 E 1g 1585 c 2 sin 2 (2θ 1 ) 0 0 E 2g 1591 d 2 [cos 2 (θ 1 ) 1 2 d 2 [cos 2 (θ 2 ) 1 2 0 Table 2 The basic functions of Raman-active modes for the (10, 10) armchair SWNT in the VH configuration ω(cm 1 ) Raman intensity θ 1 θ 2 θ 3 A 1g 165 a 2 16 sin2 (2θ 1 ) 0 0 1587 9a 2 4 sin2 (2θ 1 ) 0 0 E 1g 1585 c 2 [2cos 2 (θ 1 ) 1 2 c 2 cos 2 (θ 2 ) c 2 cos 2 (θ 3 ) E 2g 1591 d 2 4 sin2 (2θ 1 ) 0 0 By using Eq. (2), the transformed tensor matrices are [ c 0 0 0 c cos 2 θ ccos θ sin θ 0 c cos θ sin θ ( 1 + cos 2 θ)c [ 0 c cos θ c sin θ and c cos θ 0 0. c sin θ 0 0 This calculation obviously shows that the α xz and α zz elements in each above E 2g matrix are not equal, while similar curves are shown in the middle figures of Ref. [7 for the E 2g (ω = 1591 cm 1 ) mode. The present result is then in disagreement with Ref. [7. The reason may originate from the fact that the calculation [7 were performed within nonresonant theory and neglecting the depolarization effect predicted by Ajiki and Ando [11. Another reason is due to the reliable assignment of the mode with the frequency ω = 1591 cm 1, which is assigned to the different irreducible representation A(A 1g ) + E 1 (E 1g ) [12, while it is simply assigned to E 2g here. Anyway, these aspects will be considered within more accurate calculation. In this article a simple way was deduced to evaluate

P. Liu et al. / Physics Letters A 313 (2003) 302 306 305 Fig. 2. The Raman intensity measured at 1590 cm 1 changes with the rotation angle (circle dots), the real line shows the basic function of higher A 1g mode in VV configuration. the polarization and sample orientation dependence of the Raman intensity. Using these two groups of basic functions of Raman-active modes for VV and VH polarization configurations, one can easily plan the experiment configuration to distinguish them. Recently, we successfully manipulated SWNTs into aligned molecular layers by the Langmuir Blodgett (LB) method. The SWNT samples were prepared using a hydrogen and argon electric arc method [13. Purification and solubilization of SWNTs were carried out according to the reported procedure using SWNT-containing raw soot as a starting material [14. The detailed experiment of manipulation of SWNTs described in Ref. [2. The orientation of SWNTs in the LB film was investigated by means of polarized Raman spectroscopy [2. The backscattering Raman spectra were performed at 300 K using a laser Raman spectrophotometer (LabRam-010) with the 15 mw 514.5 nm (2.1 ev) excitation from an Ar + gas laser. In the experiment configuration we consider the y direction as the light propagation, and the z direction as the nanotube axis direction, i.e., the SWNT oriented direction. Fig. 2 shows the Raman intensity measured from the SWNT LB film in the VV(Y (ZZ) Y) configuration (dots) and the corresponding theoretical function (solid). The peak intensities varied with the measured angle θ 1, and the experimental data fit well with the basic function, a 2 [3cos 2 (θ 1 ) 1 2,of the A 1g mode. In Fig. 2 it is clear that the measured Raman mode shows the same behavior as that of the higher A 1g mode. However, this Raman mode is measured at 1590 cm 1 and is higher than the value of 1587 cm 1 calculated by Satio [7. The similar Raman intensity dependence for the G-band has already been demonstrated in multiwalled carbon nanotubes [15. Generally, there are many chiralities in the SWNT sample, but the reason why the total nanotubes orientation dependence in the experiment fits well with what that of (10, 10) armchair theory predicts is still not exactly known. Maybe the polarization effect for (10, 10) SWNT, can be treated as a first approximation for explaining experiments [15. The 514.5 nm laser excitation was used to resonantly select semiconducting SWNTs [3,16, and 647.1 nm laser excitation was used to probe the metallic SWNTs [3, in the further work the experiment-theory comparison for metallic SWNTs will be performed. 4. Conclusion In summary, two groups of basic functions of Raman-active modes in (10, 10) armchair SWNTs were deduced by analysis of their structure and vibration symmetries. This method avoids numerical calculation and gives a clear function of polarization direction for each vibration mode. For the sample orientation dependence of the Raman intensity of E 2g mode, I(E 2g ) vs. θ 2, the disagreement with those in Ref. [7 may originate from the presuppositions used in Ref. [7 or the inexplicit frequency assignment for this mode. One can employ these functions to arrange the experimental configuration and verify each mode. The functions can be used as a probe to characterize the orientation of carbon nanotubes. In the end, the Raman intensity of the higher frequency A 1g mode measured with polarization Raman spectroscopy was compared with the theoretical function and good agreement was found. Acknowledgement This work was supported by National Natural Science Foundation of China, key program No. 50272039.

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