good agreement with luminescent lifetimes of ~50 ms reported for C60 in a frozen matrix solution [13.52], Very long triplet lifetimes have also been reported for C70 based on phosphorescent lifetime and time-resolved low-temperature (9 K) electron paramagnetic resonance (EPR) studies, yielding values of 53 ± 0.1 ms and 51 ± 2 ms, respectively [13.13], It is known that the presence of dioxygen rapidly relaxes the excited triplet state and that C60-C60 collisions in liquid solutions also relax the excited triplet state through triplet-triplet interactions. At present, the long triplet lifetimes for C70 appear to be well established especially by the phosphorescent lifetime studies, although more work may yet be needed to clarify the intrinsic magnitude of the triplet lifetime in C60, which has not yet been observed in phosphorescent lifetime studies.

Transient absorption spectra for C70 in toluene [Fig. 13.8(b)] show absorption peaks at 960 nm (1.29 eV) associated with triplet absorption and at 675 nm (1.84 eV) and 840 nm (1.48 eV) associated with singlet absorption. From the time response of the growth of the 960 nm peak and the decay of the peaks at 675 and 840 nm, a lifetime of 0.7±0.05 ns for the Sj singlet state was determined for C70, about a factor of 2 shorter than for C60 measured in a similar way [13.41], The molar absorption coefficient amol for C70 in both the singlet and triplet T, excited states is much lower than for the corresponding states in C60 (see Table 13.3), indicating lower excited state absorption for C70 relative to C60.

Because of the high efficiency of the intersystem crossing (see above), the long lifetime of the triplet state, and the low probability of the Tx S0 transition, it is possible to build up a population in the T{ triplet state. By populating this triplet 7, state, it is possible to enhance the absorption coefficient of C60 by making electric dipole-allowed transitions from the odd-parity Tt state to the appropriate higher-lying even-parity states satisfying the selection rule for such transitions. The practical application based on this excited state enhanced absorption is called "optical limiting" [13.5356], and this application exploits the increase in the absorption coefficient with increasing intensity of the incident light (see §20.1.1). The physical process supporting the optical limiting phenomenon is the enhanced absorption from the T, excited state to higher-lying triplet states as the photon intensity increases, and consequently the occupation of the state increases.

Optical power limiting processes in C60 (and also for C70) solutions have been measured in a double-pass geometry designed to produce high beam attenuation [13.57]. In the optical limiting process, an electron from a singlet ground state (S0) is excited to a singlet (5,) vibronic transition followed by an intersystem crossing to populate the metastable triplet states (7j) (see Fig. 13.4). Once the Tx triplet state is populated, its long lifetime allows optical excitations to excited triplet states (Tn for n > 1). Since the cross section for allowed optical transitions from the Tx state to higher-lying Tn states is high (an order of magnitude greater than the absorption from the ground state), strong absorption occurs in the visible and near-IR spectral regions. Experimentally it is found that during one single nanosecond pulse, each C60 molecule can absorb 200-300 eV of energy, or up to

100 photons per molecule. This magnitude of optical limiting requires that the intersystem crossing transfers the initial excitation to the triplet state within a few picoseconds. Because of the differences in the ground state and excited state absorption coefficients between C60 and C70 mentioned above, C60 is expected to be more suitable for optical limiting applications, in agreement with observations. Excited state absorption in fullerene films is further discussed in §13.7.

Values for some of the photophysical parameters in Table 13.3 show many similarities between C^ and C70, but also significant differences are found. The addition of ten atoms to the belt of CM to form the elongated, lower symmetry C70 molecule alters the photophysical properties with regard to the energies of the excited states, the relative intensities for excited state transitions, and their lifetimes. For both C60 and C70 the quantum efficiency <t>r for the intersystem crossing 5j Tx is very high: i>r ~ 1.0 for C60 and i>7 ~ 0.9 for C70. As for the case of C60, the triplet state lifetime for C70 in solution or in a frozen matrix is highly sensitive to 02 impurities, and for this reason wide variations for the triplet state lifetime appear in the literature for both C60 and C70 [13.30,58],

It is interesting to note that the exchange splitting between the 5, and Tx levels derived from optical measurements is small (~0.33 eV) because of the large diameter of the molecule and the small electron-electron repulsion energy [13.58]. The optical determination of the exchange splitting (Sj-Tj) in solution spectra is in good agreement with more accurate determination of Sx-T\ ~0.29 eV by electron energy loss spectroscopy in films (see §17.2.2).

13.2.4. Optically Detected Magnetic Resonance (ODMR) for Molecules

Optically detected magnetic resonance (ODMR) studies [13.59] are especially sensitive to the dynamics of spin-dependent recombination processes, thereby identifying photoexcitation processes associated with spin 0, 1/2, and 1 states and providing information about excited triplet states [13.6064], The 5 = 0 states are identified with singlet states, the 5 = 1 with triplet states, and the 5 = 1/2 with charged polarons [13.65], With the ODMR technique, pump laser excitation (e.g., at 488 nm, as supplied by an argon ion laser) induces a transition in the fullerene molecule from the ground state to an excited singlet state. Because of the highly efficient intersystem crossing (see Fig. 13.2), the C60 molecule reaches a metastable triplet Ty state (at ~1.6 eV) relative to the singlet ground state 50 (see Table 13.3). Microwave power at a fixed frequency (e.g., 9.35 GHz) is simultaneously introduced. When a magnetic field is then applied, the triplet (5 = 1) state splits into three levels corresponding to ms = 1,0,-1, with a splitting that is controlled by the magnetic field. There is, in addition, a small zero-field splitting due to the Jahn-Teller induced distortion of the molecule in the excited state, thereby giving rise to an angular dependence of the electronic wave function on the fullerene shells (see §16.2.3). Since all the singlet (5 = 0) exciton states are nondegenerate, the magnetic field does not introduce any magnetic field-dependent splitting of the singlet spin states. As the magnetic field is swept, a resonance condition is met when the separation between the adjacent ms levels is equal to the microwave frequency. Under the resonance condition, microwave power is resonantly absorbed, resulting in a change in population of the various ms levels and in a magnetic field-induced admixture of singlet and triplet state wave functions (the spin-orbit interaction could also cause such an admixture, but ^ffs_0 is too small in carbon-based systems to be effective). This admixture of singlet wave function to the triplet state increases the emission probability of the triplet excited state to the singlet ground state. Correspondingly, at resonance the probability of absorption from S0 to the Tx state by a probe optical beam is also increased. The ODMR technique is thus a magnetic resonance (MR) technique insofar as the magnetic field is swept to achieve resonant absorption of microwave power. However, optical detection (OD) techniques are used, including absorption (ADMR) and photoluminescence (PLDMR) of both the fluorescent or phosphorescent varieties. The pump and probe optical beams in the ODMR experiments need not be at the same frequency. The microwave absorption is usually modulated by a low frequency perturbation to permit phase-sensitive detection of small changes in transmission, absorption, or photoluminescence.

A number of ODMR studies of fullerenes in solution and in their crystalline phases have been carried out [13.61-63,66-70], Since ODMR spectra are usually taken at low temperatures, frozen solution samples are typically used for molecular spectroscopy, while films and single crystals are used for probing the solid state. Referring to Fig. 13.9 [13.63], we see typical ODMR spectra as a function of magnetic field for C60 and C70 in a frozen toluene/polystyrene solution at 10 K using 488 nm laser excitation and 9.35 GHz microwave excitation. For the case of C60, only a fluorescent emission signal is seen, whereas for C70 both fluorescent and phosphorescent (see §13.1.1) emission signals are observed. From the absence of a phosphorescent emission signal for C60, it was concluded that C70 has a longer lifetime in the triplet state [13.63]. The details of the ODMR spectra for C6(l and C70 are very different (Fig. 13.9), implying important differences for their triplet excited states. For the C60 frozen solution spectrum, the separation between the two strong peaks at ~120 G is attributed to a triplet exciton delocalized over the whole molecule, while the weaker and broader features separated by ~230 G in the C60 spectrum are attributed o

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