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Reactive Oxygen Species Generation on Nanoparticulate Material  187

        (Eqs. 81 83). Intersystem crossing is a spontaneous nonradiative
        transition from the singlet to the triplet electronic state.

                                     k F
                                 S 1 h S 0 1 hv F                     (81)
                                     k ic
                                 S h S    0                           (82)
                                  1
                                     k isc
                                 S 1 h T 1                            (83)
          The rate of singlet decay is taken as the sum of these rates of singlet
                  , (Eq. 84) and the quantum yield,   , is defined by the frac-
        decay, k SD                                T
        tion of the singlet state that decays to the triplet state (Eq. 85).
                                                   1
                           k SD  5 k 1 k 1 k isc  5                   (84)
                                   F
                                        ic
                                                   sS d
                                                     1
                                          k isc
                                      5                               (85)
                                      T
                                          k SD
        The singlet form of a photosensitizer can also be quenched by oxygen to
        form the triplet state of the sensitizer, generating either singlet oxygen
        (Eq. 86) or ground-state oxygen (Eq. 87). It can also be quenched to the
        ground state (Eq. 88) or the sensitizer may be altered through a reac-
        tion to form a new product (Eq. 89).
                                     k O 2
                                      S       1  ∗
                                          1
                                  2
                             1
                            S 1 O h T 1 O 2                           (86)
                                      O 2
                                     k isc
                                              3
                            S 1 1 O 2 h T 1 1 O 2                     (87)
                                     k O 2
                                      Sd      3
                            S 1 O 2 h S 0 1 O 2                       (88)
                             1
                                      O 2
                                     k Sr
                            S 1 O h reaction product                  (89)
                                  2
                             1
                            k O 2  5 k O 2  1 k O 2  1 k O 2  1 k O 2  (90)
                             SQ    S     isc   Sd    Sr
          The triplet state in turn decays by phosphorescence (Eq. 91) or inter-
        system crossing (Eq. 92). Phosphorescence releases light energy as elec-
        trons fall to a lower energy level, and internal conversion involves the
        same drop in energy without the associated energy release. The rate of
        triplet decay is the sum of these processes (Eq. 93).
                                  k Tp
                              T h S 1 hv      p                       (91)
                                1
                                        0
                                  k Td
                              T h S     0                             (92)
                                1
                                                  1
                                  5 k   1 k   5                       (93)
                              k TD    Tp    Td
                                                  sT d
                                                    1
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