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Quadrupolar light scattering by fullerene
3 March 1995
CHEMICAL PHYSICS LETTERS
ELSEVIER
Chemical Physics Letters 234 (1995) 265-268
Quadrupolar light scattering by fullerene 0leg A. Nerushev, Sergei A. Novopashin, Alexander L. Perepelkin Thermophysics Institute of the Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russian Federation Received 4 October 1994
Abstract
On the basis of the theory of molecular polarizability and measurements of the intensity and the depolarization ratio of scattered light, the symmetric and antisymmetric parts of the scattering tensor have been estimated. The value of the scalar part was taken from theoretical calculations. The result is that the symmetric (quadrupolar) part of the scattering tensor makes the major contribution to the light scattering.
1. Introduction
The knowledge of the properties of fullerene molecules is basic to our understanding of the nature of fullerene-containing substances including semiand super-conductors and optical nonlinear films and solutions. A property which contributes to many physical phenomena is the molecular polarizability tensor. In previous work [1] we have reported the anomalous value of the light scattering intensity on fullerene in the gas phase. A number of theoretical works were devoted to calculations of the molecular polarizability by different methods [2-5]. They are all in good mutual agreement but cannot explain the observed intensity of light scattering. At the same time the calculated value of the polarizability is in fair agreement with the experimental results on the refraction index of the fullerene films [6]. We should note here that the well-known Lorenz-Lorentz equation relates the refractive index with the mean molecular polarizability and corresponds to the coherent part of scattered light with zero frequency shift [7,8]. The intensity, angle distribution and polarization Elsevier Science B.V.
SSDI 0 0 0 9 - 2 6 1 4 ( 9 5 ) 0 0 0 1 3 - 5
of scattered light on free molecules are associated with the polarizability tensor which may be calculated with the use of the second-order quantum perturbation theory. The validity of this theory is based on the assumption that the energy of photons is far from the energy of the allowed transitions of the tested molecules. According to Refs. [8,10] we assume this condition is fulfilled for the wavelength used (540 nm). The differential cross section of scattering by free oriented molecules may be written in the form [7,8]
dtr/do=(ww'3/c4)[Gole'*el 2 +~Gs(l + le'el 2-2~le'*el 2)
+~Ga(1- le'el2)],
(1)
where w and w' are the incident and scattered light frequences, c is the speed of light, e' and e are the complex polarization vectors of incident and scattered light, and G o, Q and G a are real, positive quantities, corresponding to the scalar, symmetric and antisymmetric parts of the polarizability tensor of the tested molecules, respectively.
O.A. Nerushev et al. / Chemical Physics Letters 234 (1995) 265-268
266
G O is connected with the coherent part of the scattered light with zero-shifted frequency and fullsymmetric vibrational Raman lines (Q branches). Gs corresponds to rotational-vibrational Raman lines and scattering on orientational anisotropy of media. The antisymmetric part Ga corresponds to the absorption processes (it is defined by the imaginary part of the polarizability tensor). G 0, Gs and Ga may be calculated from the molecular polarizability tensor aik,
Fig. 1. E x p e r i m e n t a l setup: C C -
K n u d s e n cell, V C - v a c u u m
c h a m b e r , P L - p u l s e laser, L - lens, 01, 0 2 - o b j e c t i v e s , P M p h o t o m u l t i p l i e r s , F O - f i b e r optics, C D C - c h a r g e - d i g i t a l converter, P D - p h o t o d i o d e , A n - G l a n p r i s m
G s = ( Sik Si*k >,
(2)
G a =
1
where °10 = ~c~ii, sik = -~(ai~ + aki) - Ceo6ik, aik = ½(c~ik - crki). The brackets ( ) correspond to averaging over orientations and initial quantum states of the target molecules and summing over all final quantum states. The first term in the right part of expression (1) is largest for scattering of nonresonant photons by most of the molecules. To define experimentally all terms of expression (1) it is nesessary to measure the absolute value of scattered light, depolarization ratio and inversion of circulary polarized light. In present Letter, we report results of depolarization ratio measurements. On the basis of these data, and using previous results of measurements of the absolute value of scattered light [1] and the theoretical calculation of the molecular polarizability [2-5], we have estimated the symmetric and antisymmetric parts of the scattering tensor for a wavelength of 540 nm.
2. Experimental Fullerene was prepared by the well-known plasma arc technology [11] and soxhlet extraction without separation of C6o and C70. Solvents were eliminated under vacuum, at 10 -2 Pa, at 280-300°C during 2 h. The experimental setup is close to the one described in Ref. [1]. The schematic diagram of the experimental setup is shown in Fig. 1. The fullerene microcrystalline powder was loaded into a copper cell (CC) (inner diameter 40 mm, height 30 mm),
with an orifice (3 mm) for gas-phase fullerene outflow. The cell was placed in a vacuum chamber (VC) with a background pressure of 10 -2 Pa. The temperature of the cell might be varied in the range of 300-1000 K. The pulse laser PL beam (wavelength 540 nm, pulse duration 20 ns, pulse energy 20 n J, linewidth 0.25 cm -1) crossed the flow at 6.5 mm from the orifice. It was focused by a lens L (focus length 400 mm) at flow axis to a spot with a diameter of about 0.1 mm. The scattered light was observed at an angle of 90 ° to the incident beam and polarization vector. It was collected by the objectives 01 and 02 and transmitted onto the photomultipliers PM1 and PM2 through fiber optics FO. An analyser (An) (Glan prism) was positioned behind the objective 01. It was oriented for transmission of line polarized light with the polarization vector parallel to that for the incident laser beam. Thus the signal on PM2 corresponded to the total scattering intensity while that on PM1 was related only to the polarized component. The incident beam intensity was measured by a photodiode (PD). The signals from the photomultipliers and the photodiode were registred by a charge-digital converter (CDC) (the sensitivity of the CDC is 2.5 × 10 -13 C per count) synchronized with the laser pulse. The low pulse repetition rate (1-5 Hz), the small duration (100 ns) of charge integrating and statistical data handling allow us to measure small optical signals by noncooled photomultipliers in the current regime. Calibration of the relative optical transmission of channels 0 1 - A n - P M 1 and 02-PM2 was made by measuring the scattering of light on nitrogen. The
O.A. Nerushec et al. / Chemical Physics Letters 234 (1995) 265-268
experimental value of the depolarization ratio was obtained by averaging over 100 laser pulses.
3. Results and discussion The measured ratio of the intensity 11 of the scattered light polarized parallel to the polarization vector of the incident light to the total scattered intensity 12 is 0.6 _ 0.04 for a cell temperature range of 750-850 K (this corresponds to the depolarization ratio of 0.56-0.78). The experimentally defined ratio of the intensities, the absolute value of the scattering intensity and the calculated mean polarizability were used to estimate G 0, Gs and Ga from Eq. (1). The intensity of the polarized component 11 for experimental conditions is proportional to G O+ 430G s, the total scatter1 ing intensity 12 is proportional to G O+ 7 G s + gGa). Putting G O equal to the square of the calculated molecular polarizability (the validity of this value is confirmed by the measurements of the refractive index of the thin fullerene films [6]) we can obtain the following estimations for the values: G O= 6 × 10 -45 c m 6, Gs = 4.5 X 10 -42 c m 6,
267
determined by vibrational-rotational Raman scattering. The scalar part of the polarizability lies considerably above the quadrupolar one for most if not all of the molecules. So the fact that the quadrupolar part of the scattered light on fullerene is greater than the scalar part is a new unique property of fullerene. Note that the quadrupolar part should be equal to zero for fullerene in the ground state due to highorder symmetry. What may be the reason for this phenomenon? It should be noted that the experiments were carried out at a temperature range of 750-850 K and the fullerene molecules were vibrationally excited under these conditions. The excitation can break the symmetry of fullerene and affects the electron level structure. Another important fact is that the light absorption on this frequency may appear due to Herzberg-Teller vibronic interactions or other mechanisms considered in more detail in Ref. [10]. The frequency of the incident light corresponds to the band of light absorption in hexane solution of C60 observed in the work of Ref. [10]. It corresponds to a number of orbital-forbidden singlet-singlet transitions. At the same time the observed scattering cannot be identified as resonance phosphorescence because no time delay was observed in scattered light as was reported earlier [1].
G a = 0 _ 1 0 -43 c m 6.
The value of G O is somewhat underestimated due to ignoring the contribution of Raman scattering on fully symmetric vibrations, but it is obvious that Gs >> G O and the inclusion of these terms will not change the above relations significantly. The accuracy of the measurement of the depolarization ratio does not allow one to determine Ga more definitely. The best way to measure it is to measure the polarization inversion of circularly polarized light for some angle (not equal 90 °) of scattering light [7]. The angle distribution of scattering intensity for symmetric and anti-symmetric parts is strictly different. However, the present results show unambiguously that the main part of the scattered light corresponds to the symmetric (quadrupolar) part of the polarizability tensor. The quadrupolar part of the scattering light is determined by two factors. The first one is an anisotropy of molecular polarizability. The second is
Acknowledgement The authors are indebted to V.A. Maltsev and Dr. B.A. Selivanov for help in fullerene preparing and extraction. The research described in this Letter was made possible in part by Grant N PRN000 from the International Science Foundation and was supported, in part, by a Meyer Foundation Grant awarded by the American Physical Society.
References [1] V.A. Maltsev, O.A. Nerushev, S.A. Novopashin and B.A. Selivanov, Chem. Phys. Letters 212 (1993) 480. [2] P.W. Fowler, P. Lazaretti and R. Zanasi, Chem. Phys. Letters 165 (1991) 79. [3] N. Matsuzawa and D.A. Dixon, J. Phys. Chem. 96 (1992) 6872. [4] F. William and L.M. Falicov, J. Chem. Phys. 98 (1993) 6369.
268
0.,4. Nerushev et al. / Chemical Physics Letters 234 (1995) 265-268
[5] H. Weiss, R. Alrich and M. Haser, J. Chem. Phys. 99 (1993) 1262. [6] S.L. Ren, Y. Wang, A.M. Rao, E. McRae, J.M. Holden, T. Hager, K.A. Wang, W.-T. Lee, H.F. Ni, C. Selegue and P.C. Eklund, Appl. Phys. Letters 59 (1991) 2678. [7] G. Placzek, Rayleigh and Raman scattering, US Atomic Energy Commission, UCRL-Trans-526(L) (1962) p. 175 (translated from E. Marx, ed., Handbuch der Radiologie, Vol. 6, part II, 2nd Ed. (Akademische Verlagsgesellschaft, Leipzig, 1934) pp. 205-374.
[8] V.B. Berestetskij, E.M. Lifshic and L.P. Pitaevskij, Quantum electrodynamics (Moskva, 1989) 728 S (in Russian). [9] W. Kr~itschmer, L.D. Lamb, K. Fostiropoulos and D.R. Huffman, Nature 347 (1990) 354. [10] S. Larsson, A. Volosov and A. Rosen, Chem. Phys. Letters 137 (1987) 501. [11] S. Leach, M. Vervolet, A. Despres, E. Brehert, J.P. Hare, T.J. Dennis, H.W. Kroto, R. Taylor and D.R.M. Walton, Chem. Phys. 160 (1992) 451.
CHEMICAL PHYSICS LETTERS
ELSEVIER
Chemical Physics Letters 234 (1995) 265-268
Quadrupolar light scattering by fullerene 0leg A. Nerushev, Sergei A. Novopashin, Alexander L. Perepelkin Thermophysics Institute of the Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russian Federation Received 4 October 1994
Abstract
On the basis of the theory of molecular polarizability and measurements of the intensity and the depolarization ratio of scattered light, the symmetric and antisymmetric parts of the scattering tensor have been estimated. The value of the scalar part was taken from theoretical calculations. The result is that the symmetric (quadrupolar) part of the scattering tensor makes the major contribution to the light scattering.
1. Introduction
The knowledge of the properties of fullerene molecules is basic to our understanding of the nature of fullerene-containing substances including semiand super-conductors and optical nonlinear films and solutions. A property which contributes to many physical phenomena is the molecular polarizability tensor. In previous work [1] we have reported the anomalous value of the light scattering intensity on fullerene in the gas phase. A number of theoretical works were devoted to calculations of the molecular polarizability by different methods [2-5]. They are all in good mutual agreement but cannot explain the observed intensity of light scattering. At the same time the calculated value of the polarizability is in fair agreement with the experimental results on the refraction index of the fullerene films [6]. We should note here that the well-known Lorenz-Lorentz equation relates the refractive index with the mean molecular polarizability and corresponds to the coherent part of scattered light with zero frequency shift [7,8]. The intensity, angle distribution and polarization Elsevier Science B.V.
SSDI 0 0 0 9 - 2 6 1 4 ( 9 5 ) 0 0 0 1 3 - 5
of scattered light on free molecules are associated with the polarizability tensor which may be calculated with the use of the second-order quantum perturbation theory. The validity of this theory is based on the assumption that the energy of photons is far from the energy of the allowed transitions of the tested molecules. According to Refs. [8,10] we assume this condition is fulfilled for the wavelength used (540 nm). The differential cross section of scattering by free oriented molecules may be written in the form [7,8]
dtr/do=(ww'3/c4)[Gole'*el 2 +~Gs(l + le'el 2-2~le'*el 2)
+~Ga(1- le'el2)],
(1)
where w and w' are the incident and scattered light frequences, c is the speed of light, e' and e are the complex polarization vectors of incident and scattered light, and G o, Q and G a are real, positive quantities, corresponding to the scalar, symmetric and antisymmetric parts of the polarizability tensor of the tested molecules, respectively.
O.A. Nerushev et al. / Chemical Physics Letters 234 (1995) 265-268
266
G O is connected with the coherent part of the scattered light with zero-shifted frequency and fullsymmetric vibrational Raman lines (Q branches). Gs corresponds to rotational-vibrational Raman lines and scattering on orientational anisotropy of media. The antisymmetric part Ga corresponds to the absorption processes (it is defined by the imaginary part of the polarizability tensor). G 0, Gs and Ga may be calculated from the molecular polarizability tensor aik,
Fig. 1. E x p e r i m e n t a l setup: C C -
K n u d s e n cell, V C - v a c u u m
c h a m b e r , P L - p u l s e laser, L - lens, 01, 0 2 - o b j e c t i v e s , P M p h o t o m u l t i p l i e r s , F O - f i b e r optics, C D C - c h a r g e - d i g i t a l converter, P D - p h o t o d i o d e , A n - G l a n p r i s m
G s = ( Sik Si*k >,
(2)
G a =
1
where °10 = ~c~ii, sik = -~(ai~ + aki) - Ceo6ik, aik = ½(c~ik - crki). The brackets ( ) correspond to averaging over orientations and initial quantum states of the target molecules and summing over all final quantum states. The first term in the right part of expression (1) is largest for scattering of nonresonant photons by most of the molecules. To define experimentally all terms of expression (1) it is nesessary to measure the absolute value of scattered light, depolarization ratio and inversion of circulary polarized light. In present Letter, we report results of depolarization ratio measurements. On the basis of these data, and using previous results of measurements of the absolute value of scattered light [1] and the theoretical calculation of the molecular polarizability [2-5], we have estimated the symmetric and antisymmetric parts of the scattering tensor for a wavelength of 540 nm.
2. Experimental Fullerene was prepared by the well-known plasma arc technology [11] and soxhlet extraction without separation of C6o and C70. Solvents were eliminated under vacuum, at 10 -2 Pa, at 280-300°C during 2 h. The experimental setup is close to the one described in Ref. [1]. The schematic diagram of the experimental setup is shown in Fig. 1. The fullerene microcrystalline powder was loaded into a copper cell (CC) (inner diameter 40 mm, height 30 mm),
with an orifice (3 mm) for gas-phase fullerene outflow. The cell was placed in a vacuum chamber (VC) with a background pressure of 10 -2 Pa. The temperature of the cell might be varied in the range of 300-1000 K. The pulse laser PL beam (wavelength 540 nm, pulse duration 20 ns, pulse energy 20 n J, linewidth 0.25 cm -1) crossed the flow at 6.5 mm from the orifice. It was focused by a lens L (focus length 400 mm) at flow axis to a spot with a diameter of about 0.1 mm. The scattered light was observed at an angle of 90 ° to the incident beam and polarization vector. It was collected by the objectives 01 and 02 and transmitted onto the photomultipliers PM1 and PM2 through fiber optics FO. An analyser (An) (Glan prism) was positioned behind the objective 01. It was oriented for transmission of line polarized light with the polarization vector parallel to that for the incident laser beam. Thus the signal on PM2 corresponded to the total scattering intensity while that on PM1 was related only to the polarized component. The incident beam intensity was measured by a photodiode (PD). The signals from the photomultipliers and the photodiode were registred by a charge-digital converter (CDC) (the sensitivity of the CDC is 2.5 × 10 -13 C per count) synchronized with the laser pulse. The low pulse repetition rate (1-5 Hz), the small duration (100 ns) of charge integrating and statistical data handling allow us to measure small optical signals by noncooled photomultipliers in the current regime. Calibration of the relative optical transmission of channels 0 1 - A n - P M 1 and 02-PM2 was made by measuring the scattering of light on nitrogen. The
O.A. Nerushec et al. / Chemical Physics Letters 234 (1995) 265-268
experimental value of the depolarization ratio was obtained by averaging over 100 laser pulses.
3. Results and discussion The measured ratio of the intensity 11 of the scattered light polarized parallel to the polarization vector of the incident light to the total scattered intensity 12 is 0.6 _ 0.04 for a cell temperature range of 750-850 K (this corresponds to the depolarization ratio of 0.56-0.78). The experimentally defined ratio of the intensities, the absolute value of the scattering intensity and the calculated mean polarizability were used to estimate G 0, Gs and Ga from Eq. (1). The intensity of the polarized component 11 for experimental conditions is proportional to G O+ 430G s, the total scatter1 ing intensity 12 is proportional to G O+ 7 G s + gGa). Putting G O equal to the square of the calculated molecular polarizability (the validity of this value is confirmed by the measurements of the refractive index of the thin fullerene films [6]) we can obtain the following estimations for the values: G O= 6 × 10 -45 c m 6, Gs = 4.5 X 10 -42 c m 6,
267
determined by vibrational-rotational Raman scattering. The scalar part of the polarizability lies considerably above the quadrupolar one for most if not all of the molecules. So the fact that the quadrupolar part of the scattered light on fullerene is greater than the scalar part is a new unique property of fullerene. Note that the quadrupolar part should be equal to zero for fullerene in the ground state due to highorder symmetry. What may be the reason for this phenomenon? It should be noted that the experiments were carried out at a temperature range of 750-850 K and the fullerene molecules were vibrationally excited under these conditions. The excitation can break the symmetry of fullerene and affects the electron level structure. Another important fact is that the light absorption on this frequency may appear due to Herzberg-Teller vibronic interactions or other mechanisms considered in more detail in Ref. [10]. The frequency of the incident light corresponds to the band of light absorption in hexane solution of C60 observed in the work of Ref. [10]. It corresponds to a number of orbital-forbidden singlet-singlet transitions. At the same time the observed scattering cannot be identified as resonance phosphorescence because no time delay was observed in scattered light as was reported earlier [1].
G a = 0 _ 1 0 -43 c m 6.
The value of G O is somewhat underestimated due to ignoring the contribution of Raman scattering on fully symmetric vibrations, but it is obvious that Gs >> G O and the inclusion of these terms will not change the above relations significantly. The accuracy of the measurement of the depolarization ratio does not allow one to determine Ga more definitely. The best way to measure it is to measure the polarization inversion of circularly polarized light for some angle (not equal 90 °) of scattering light [7]. The angle distribution of scattering intensity for symmetric and anti-symmetric parts is strictly different. However, the present results show unambiguously that the main part of the scattered light corresponds to the symmetric (quadrupolar) part of the polarizability tensor. The quadrupolar part of the scattering light is determined by two factors. The first one is an anisotropy of molecular polarizability. The second is
Acknowledgement The authors are indebted to V.A. Maltsev and Dr. B.A. Selivanov for help in fullerene preparing and extraction. The research described in this Letter was made possible in part by Grant N PRN000 from the International Science Foundation and was supported, in part, by a Meyer Foundation Grant awarded by the American Physical Society.
References [1] V.A. Maltsev, O.A. Nerushev, S.A. Novopashin and B.A. Selivanov, Chem. Phys. Letters 212 (1993) 480. [2] P.W. Fowler, P. Lazaretti and R. Zanasi, Chem. Phys. Letters 165 (1991) 79. [3] N. Matsuzawa and D.A. Dixon, J. Phys. Chem. 96 (1992) 6872. [4] F. William and L.M. Falicov, J. Chem. Phys. 98 (1993) 6369.
268
0.,4. Nerushev et al. / Chemical Physics Letters 234 (1995) 265-268
[5] H. Weiss, R. Alrich and M. Haser, J. Chem. Phys. 99 (1993) 1262. [6] S.L. Ren, Y. Wang, A.M. Rao, E. McRae, J.M. Holden, T. Hager, K.A. Wang, W.-T. Lee, H.F. Ni, C. Selegue and P.C. Eklund, Appl. Phys. Letters 59 (1991) 2678. [7] G. Placzek, Rayleigh and Raman scattering, US Atomic Energy Commission, UCRL-Trans-526(L) (1962) p. 175 (translated from E. Marx, ed., Handbuch der Radiologie, Vol. 6, part II, 2nd Ed. (Akademische Verlagsgesellschaft, Leipzig, 1934) pp. 205-374.
[8] V.B. Berestetskij, E.M. Lifshic and L.P. Pitaevskij, Quantum electrodynamics (Moskva, 1989) 728 S (in Russian). [9] W. Kr~itschmer, L.D. Lamb, K. Fostiropoulos and D.R. Huffman, Nature 347 (1990) 354. [10] S. Larsson, A. Volosov and A. Rosen, Chem. Phys. Letters 137 (1987) 501. [11] S. Leach, M. Vervolet, A. Despres, E. Brehert, J.P. Hare, T.J. Dennis, H.W. Kroto, R. Taylor and D.R.M. Walton, Chem. Phys. 160 (1992) 451.