Triplet mini-excitons

In Chap. 6, we discussed low-energy optical excitation states, the singlet and triplet excitons and energy transfer. The primary experimental method applied there was optical spectroscopy in the visible, in the near IR and in the UV spectral ranges. In the present chapter, we treat the structure and the dynamics of localised triplet states, of triplet mini-excitons, and of triplet excitons in molecular crystals. The primary experimental method for the investigation of the lowest-energy triplet level Ti is electron-spin resonance (ESR) (Fig. 7.1). 

The simple dimer model as in Fig. 6.7 can be called a mini-exciton. It shows how intermolecular interactions can lead to shifts and spUttings in the spectra. An example is shown on the right-hand side of Fig. 6.7. D and D are based to first order on the molecular polarisability in the ground and excited states, and the resonance energy In in the singlet state is due to the resonance interaction between molecule 1 in an excited state and molecule 2 in its ground state or vice versa. In the triplet state, lu is determined in the main by the overlap of the orbitals of the two molecules, one of which is excited. 

Along the path from isolated, oriented molecules to excitons in non-doped crystals, we next take up the triplet states of oriented dimers, which we called mini-excitons in Sect. 6.4. Mini-triplet-excitons are excitations of triplet states which are spatially distributed over exactly two molecules, for example the two A and B molecules in the unit cell of Fig. 7.11, and they are localised there. In principle, mini-excitons can also be localised on a pair of molecules with the same orientation in crystals with a dimeric structure, e.g. in the a-perylene crystal (Fig. 2.12). We will however restrict ourselves in this section to the treatment of A - B mini-excitons. 

Fig. 7.14 Schematic portion of the term diagram of the triplet states of the molecules A and B and the mini-excitons M in the naphthalene crystal for a selected orientation of the applied magnetic field Bq. 8B is the difference in the fine structure of the two ms = + ms = 0 ESR transitions A+ and B+ of the molecules A and B. The magnitude of 5B is independent of the magnitude Bol, if...

In non-doped anthracene crystals, as in non-doped naphthalene crystals at T = 300 K, two sharp Lorentzian ESR lines from excitons are observed (Figs. 7.18 and 7.21). They have, in complete analogy to the M lines of mini-excitons, a large and anisotropic fine structure (Fig. 7.19). The fine-structure constants of the triplet excitons in the anthracene crystal are D /he = -0.00575 cm and B /he = -1-0.0330 cm . The choice of axes is here the same as for the mini-excitons (cf. Fig. 7.11) z = b. From the measurements, the angle Z(x, a) = 27.25° is determined. VBth the methods treated in Sect. 7.4, this yields the fine-structure constants of the isolated anthracene molecule at room temperature, D/he = -1-0.0694 cm and E/hc = -0.00836 cm . (The small deviations from the values obtained for isolated anthracene molecules in a single-crystal matrix (see... 

The large mean squared displacement can by the way explain the small residual linewidth of the triplet ESR lines in a natural way (for small A - B spacing) this was also observed for the triplet excitons in naphthalene crystals (Eig. 7.21). It is due to the complete averaging-out of the hyperfine structure, because the number N of molecules over which the average is carried out is not 2, as for the mini-excitons, but rather is very large (N 1). The second moment is then not reduced by the factor V2, as for the mini-excitons, but instead by the factor 1/N. The exciton ESR linewidth is therefore narrowed in relation to the linewidths of the isolated... 

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