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188   Principles and Methods

        Photosensitizers in the triplet state can also be quenched by oxygen
        (Eqs. 94 97) or by sensitizers in the ground state. Quenching by sen-
        sitizer in the ground state is known quite simply as self-quenching
        (Eq. 97). Finally, a sensitizer in the triplet state may also be quenched
        when a triplet collides with another triplet in a process known as triplet-
        triplet annihilation (Eq. 98). The summation of these processes is rep-
        resented in Eq. 99.

                                O 2
                                        1  ∗
                               k T
                      T 1 1 O 2 h S 0 1 O 2  (Type II reaction)       (94)
                               k O 2
                                        3
                                Td
                      T 1 O h S 1 O       2                           (95)
                                    0
                       1
                            2
                                O 2
                               k Tr
                      T 1 1 O 2 h product                             (96)
                               k S 0
                                SQ
                      T 1 S h 2S      0                               (97)
                            0
                       1
                               k T 1
                                AN                                    (98)
                      T 1 1 T 1 h S 0 1 T 1
                      k O 2  5 k O 2  1 k O 2  1 k O 2                (99)
                       TQ    T     Td    Tr
        Often the triplet state is more energetically stable than the singlet
        state, so the products of the above reactions are favored over those
        resulting from reactions with the singlet state in photosensitizing sys-
        tems. The triplet state is quenched by oxygen by three different path-
        ways; the fraction of triplet that participates in the Type II reaction to
        form singlet oxygen is represented by Eq. 100. Oxygen also competes
        with triplet-triplet annihilation and self-quenching as potential path-
        ways for triplet quenching. Consequently, the proportion of the triplet
        state quenched with oxygen can be calculated using Eq. 101. The quan-
        tum yield for singlet oxygen expresses how efficiently the photons are
        used to produce singlet oxygen (Eq. 102).
                                                                    (100)
                                          k O 2
                                     II
                                    f    5  T
                                          k O 2
                                           TQ
                O     ⎤
               k  2  O ⎡
          O     TQ ⎣  2 ⎦
         P  2                                                       (101)
          T              TD (  O               AN ⎣ ⎦)
                               2
                        k     k TQ ⎣ O ⎡  2 ⎦ ⎤   k SQ ⎣ ⎦    T 1  T ⎡ ⎤
                                      S 0 ⎡ ⎤  k
                                          S 0
                                                   1

                                     5   f   P

                                           II O 2
                                         T   T                      (102)
        The nonproductive pathways regarding ROS production such as triplet
        quenching by oxygen along with triplet-triplet annihilation and self-
        quenching represent inefficiencies in converting light energy to chemical
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