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180   Principles and Methods

                 18
        O 2 , with  O verified that H 2 O 2 was produced directly by the reduction
        of adsorbed oxygen by conduction band electrons. Quantum yields were
        as high as 30 percent for H 2 O 2 production at low photon fluxes. At the
        same time, the quantum yield was shown to vary with the inverse
        square root of absorbed light intensity [i.e., f~s!I abs d 21 ], with the wave-
        length of excitation f~sld 21 , and with the diameter of the Q-sized col-
        loids (i.e., f~D 21 ). For example, d[H 2 O ]/dt  is 100 to 1000 times faster
                      p
                                            2
        on Q-sized ZnO particles (D p   2   4 nm) than with bulk-phase ZnO par-
        ticles (D p   100 nm).
          Hydrogen peroxide production proceeds, after initial photoactivation,
        by electron transfer from the conduction band to dioxygen adsorbed on
        the surface of the excited-state metal oxide as follows:

                                  2
                                                2.
                               2[e cb 1 O 2 h O 2 ]                   (41)
                                            4.8
                                        pK a
                                              →
                                      ⎯⎯⎯⎯⎯

                               .
                                              ⎯
                            O    H    ←⎯⎯⎯⎯      HO . 2               (42)
                              2
                                   .
                              2HO 2 h H O 1 O     2                   (43)
                                             2
                                           2
          Hoffmann and coworkers [25, 36, 37] observed a tenfold increase in
        the measure quantum yield for H 2 O 2 production upon reduction of the
        mean particle diameter from 40 to 23 nm for ZnO, where O 2 was the elec-
        tron acceptor and small molecular organic compounds (e.g., carboxylic
        acids and alcohol) the electron donor. Similar effects were reported by
        Hoffmann and coworkers [35, 38, 39] for photo-polymerization reac-
        tions catalyzed by Q-sized CdS, Q-ZnO, and Q-TiO 2 and for SO 2 oxida-
        tion in the aqueous phase.
          In addition to ROS generated from surface hydroxyl species and from
        adsorbed O 2 , there are other oxygen-containing free radical species
        that are generated on the surface of photoactivated semiconductors. For
                                                             2
                                       ⋅ H O]   [HSO ]   [SO ]) is readily
        example, S(IV) ( [S(IV)] # [SO 2  2         3        3
        photooxidized [28] in the presence of colloidal suspensions of nanopar-
        ticulate  -Fe O .
                    2
                      3
                                     hn#520 nm
                                2
                                                    22

                        1 2 HSO 3   h2 SO 4 1 2H           1
                     O 2                                              (44)
                                        -Fe 2 O 3
        Quantum yields ranged from 0.08 to 0.3 with a maximum yield found
        at pH 5.7. The primary initiation pathway involved irradiation at wave-
        lengths equal to or less than the nominal bandgap of hematite, which
        is 2.2 eV or 560 nm. Upon bandgap illumination, conduction-band electrons
        and valence-band holes are separated; the trapped electrons are trans-
        ferred either to surface-bound dioxygen or to Fe(III) sites on or near the
        surface, while the trapped holes accept electrons from adsorbed SO 2   to
                                                                     3
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