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Magnetic Field (kG)

Fig. 13.9. Experimental ODMR spectra of CM and C70 in frozen toluene/polystyrene solution at 10 K observed through photoluminescence (PLDMR) using 488 nm laser excitation and 9.35 MHz microwave excitation. The excited triplet state is observed for: (a) triplet Cm fluorescence, (b) triplet C,0 fluorescence, and (c) triplet C,0 phosphorescence [13.63], to a triplet exciton state localized over a pentagon or hexagon face. A third type of triplet exciton with peaks separated by only 37 G is attributed to a triplet exciton delocalized over several coupled C60 molecules (as discussed below) and is most clearly seen in the solid state [13.63].

In contrast, the ODMR spectra for C70 show a strong signal and an asymmetric lineshape. The triplet exciton delocalized over the whole molecule is identified with the pair of structures separated by ~200 G, and a strong asymmetric phosphorescent structure is observed for the triplet C70 exciton [13.63]. The linewidth of the ODMR lines for the delocalized triplet exciton in C70 is narrower than in triplet C60 because of the larger size of the C70 molecule. The ODMR spectra are strongly temperature dependent, reflecting the temperature dependence of the excited state lifetimes. The temperature dependence of the ODMR features is used to identify the physical origins of the ODMR spectral features. For example, the delocal-

ized triplet features are more rapidly quenched for both C60 and C70 by increasing the temperature than is the localized exciton [13.63], Variation of the modulation frequency for the magnetic resonance features is used to provide information on lifetimes associated with various ODMR structures.

The ODMR spectra associated with films show some features that are present in the frozen solution ODMR spectra, and other features which are different. The ODMR spectra associated with spin 1 are closely related to the solution spectra and show two features at 1.1 and 1.8 eV in the absorption ADMR spectra, and they are associated with long-lived neutral triplet excitons excited to higher-lying triplet exciton states, in good agreement with induced photoabsorption measurements (see §13.7.1) [13.64].

In the solid state, an additional sharp feature, not present in the solution ODMR spectra, is observed for both C60 and C70 and is attributed to a long-lived polaron with spin 1/2 and g = 2.0017 for C60 and g = 2.0029 for C70 [13.63], Excited isolated molecules decay rapidly to an excitonic state, thereby accounting for the absence of the polaron feature in solution ODMR spectra. In films, the electrons and holes can separate in a charge transfer process between adjacent fullerenes, thereby stabilizing polarons. Evidence for polarons is also found in EPR spectra (see §16.2.3) and in photoconductivity spectra (see §14.7). This sharp feature identified with polaron formation is observed both in the photoluminescence (PLDMR) spectrum [13.63] and in the absorption ADMR spectra [13.61,64]. The spin 1/2 ADMR spectrum contains three features (at 0.8, 2.0, and 2.4 eV), in good agreement with the induced photoabsorption spectrum (see §13.2.3) that was measured independently [13.64] and with the optical spectra of doped C60 films (see §13.4) [13.71,72].

Photopolymerization of the C60 film greatly reduces the intensity of the features in the ODMR spectrum associated with the localized triplet exciton state and strongly enhances the features associated with the triplet exciton (with 37 G separation) that is delocalized over more than one fullerene [13.63].

13.3. Optical Properties of Solid C60

Since the absorption and luminescence spectra of solid C60 resemble to a considerable degree the corresponding spectra observed for C60 in solution, it is believed that molecular states should be a good starting point for the description of the electronic bands in solid C60.

Thus the discussion of the optical properties of solid C60, as in solution, concerns both forbidden transitions near the absorption edge and dipole-allowed transitions at higher photon energies. In solution, the forbidden electronic transitions are described by weak phonon-assisted excitonic tran sitions, while conventional, one-electron molecular calculations are more successful in accounting for the allowed transitions at higher photon energies. In §13.3.1 we present an overview of the optical properties of solid C60, which is followed in §13.3.2 by a discussion of both the forbidden transitions near the absorption edge and the allowed transitions at higher energies. In §13.3.3 the low-frequency dielectric response of is briefly summarized. Finally, in §13.3.4 the optical properties of phototransformed films are summarized.

13.3.1. Overview

Many of the observed optical properties of solids are expressed in terms of the complex optical dielectric function e(w) = e^w) + ie2(w), so that e(w) provides a convenient framework for discussing the optical properties over a broad frequency range. It is also convenient to express e(oj) in terms of the complex refractive index N(a)) = [n(w) + ik(w)]:

e(a>) = 6,(cu) + ie2(a>) = [JV(w)]2 = [«(a») + ik(o>)]2 (13.8)

where n and k are the frequency-dependent optical constants and are, respectively, the refractive index and extinction coefficient, while et and e2 are the real and imaginary parts of the dielectric function. The optical absorption coefficient a is then defined by a = 2 (u/c)k(o>), (13.9)

and the intensity of a plane electromagnetic wave is attenuated exponentially according to e~az, where z is distance in the medium along the line of wave propagation (Beer's law).

In Fig. 13.10 is shown the frequency dependence of the dispersive part [£](&>); upper panel] and the absorptive part [e2(a>); lower panel] of e(at) for solid C60 films at room temperature, as obtained from a variety of optical experiments, as discussed below [13.1]. The data are plotted on a semilog scale and cover the frequency range from the IR to the ultraviolet (~0.05 to 5.5 eV). Above 7 eV e,(<w) obtained from electron energy loss spectroscopy (EELS) studies is included. We now discuss e(w) for various frequency ranges. The behavior at very low frequencies (below 0.05 eV) has special properties that are singled out and discussed in §13.3.3.

Using the experimental results for e(w), the molecular polarizability aM(o)) can be calculated from the Clausius-Mossotti relation

""<•>-dbiij (1310) where pN = 4/a3 is the number density of C60 molecules in the face-centered cubic (fee) unit cell with a lattice constant a — 14.17 A. The real

0.1eV 1eV 10eV

0.1eV 1eV 10eV

excitation frequency (Hz)

Fig. 13.10. Summary of real e,(tu) and imaginary e2(w) parts of the dielectric function for Qq vacuum-sublimed solid films at room temperature over a wide frequency range. The data between 0.05 and 0.5 eV (mid- to near-infrared) were collected using the Fourier transform infrared (FTIR) transmission technique [13.1]. The visible-UV range was investigated by variable angle spectroscopic ellipsometry (VASE) [13.73] and near-normal-incidence reflection and transmission experiments [13.74], UV data above ~7 eV were obtained using electron energy loss spectroscopy (EELS) [13.75] by Kramers-Kronig analysis of the EELS loss function (inset). The arrow at the left axis points to e, = 4.4, the low-frequency value of the dielectric constant determined by capacitance measurements [13.76].

excitation frequency (Hz)

Fig. 13.10. Summary of real e,(tu) and imaginary e2(w) parts of the dielectric function for Qq vacuum-sublimed solid films at room temperature over a wide frequency range. The data between 0.05 and 0.5 eV (mid- to near-infrared) were collected using the Fourier transform infrared (FTIR) transmission technique [13.1]. The visible-UV range was investigated by variable angle spectroscopic ellipsometry (VASE) [13.73] and near-normal-incidence reflection and transmission experiments [13.74], UV data above ~7 eV were obtained using electron energy loss spectroscopy (EELS) [13.75] by Kramers-Kronig analysis of the EELS loss function (inset). The arrow at the left axis points to e, = 4.4, the low-frequency value of the dielectric constant determined by capacitance measurements [13.76].

part of the resulting molecular polarizability aM(a>) up to 5 eV is shown in Fig. 13.11 on a semilog plot [13.24,77], The application of Eq. (13.10) assumes minimal intermolecular interaction, which is strictly valid for an ideal molecular solid. The contributions to the low-frequency aM(w) from vibrational and electronic processes are estimated to be ~2 and ~83 A3, respectively, as shown in Fig. 13.11, leading to a value of aM ~ 85 A3 [13.24], This value for aM compares well with some other determinations of the low-frequency polarizability [13.78-80] and not as well with others [13.22,81,82],

Between 0.05 and 0.5 eV (1 eV = 8066 cm-1), the experimental data of Fig. 13.10 (solid curves) were collected by measuring the optical transmission through an ~6000 A thick film of C60 on a KBr substrate. To obtain quantitative values for e,(w) and e2(w) in the infrared region of the spectrum, the contributions to the reflectance and transmission from multiple internal reflections within the film were taken into account.

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