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Reactive Oxygen Species Generation on Nanoparticulate Material  179

          The photochemistry and photophysics of quantum-sized nanoparticles
        [16, 22, 24, 35] (1 nm   D   10 nm) in contrast with the larger, bulk-phase
                              p
        particles (D < 100 nm), can be quite different. Many nanoparticulate semi-
                  p
        conductors, which are often described as “quantum-sized particles” or
        “quantum dots” depending on their applications, exhibit a characteristic
        blue shift in the UV or visible absorption spectrum. Along with the blue
        shift in the absorption spectrum, there is a corresponding increase in the
        bandgap energy,  E which can be described in terms of a simple solution
                          g
        to the Schrödinger equation with an appropriate Hamiltonian.
                                         2
                                      2
                                     p  h   1   1.8 e 2               (39)
                                            b 2
                              E g  . a  2
                                     2R          εR
        where R is the particle radius and µ is the reduced mass of the exciton
        or the electron-hole pair.
                                1      1      1                       (40)
                                m  5 a  ∗  1  ∗  b
                                      m e 2  m h 1
                ∗                                        ∗
        where  m e 2  is the effective mass of the electron and m h 1  is the effective
                                                              h
        mass of the hole, and ε is the dielectric constant of TiO 2 , and  is Planck’s
        constant.
          According to Eq. 39, as R decreases the bandgap energy,   E  , increases
                                                               g
        (i.e., RT 5  E g c ). As an example, Kormann et al. [24] prepared Q-sized
        TiO 2 with a characteristic blue shift from the bulk state bandgap of 385
        nm for anatase TiO 2 down to 350 nm (i.e.,  E    3.2 to 3.35 eV). The steady-
                                               g
        state particle size ranged from 2.0 nm to 2.5 nm depending on the prepa-
        ration conditions and the Ti(IV) reagent used in the synthesis (e.g., TiCl 4
        or Ti(IV)-isopropoxide). The corresponding cluster size (oligomer) for the
        nanoparticles ranged from 120 to 220 monomers. In an earlier study,
        Bahnemann et al. [16] reported that Q-ZnO exhibited bandgap increases
                                      4.2 eV).
        as large as 1 eV or  E g, Q2ZnO
          An increase in  E g often enhances the reactivity of the photocatalyst
        by increasing its reduction/oxidation potential and thus the driving
        force for electron transfer in the normal Marcus regime; thereby ROS
        (reactive oxygen species) should also be a function of particle size.
          In a subsequent study, Hoffman et al. [36] investigated the photo-
        chemical production of H 2 O 2 on irradiated Q-ZnO over the wavelength
        range of 320      370 nm in the presence of carboxylic acids and
        oxygen. Steady-state concentrations up to 2 mM H 2 O 2 were formed.
        Maximum H 2 O 2 concentrations were obtained only with added electron
        donors (i.e., hole scavengers). The order of photochemical efficiency for

        H 2 O 2 production with carboxylic acids as electron donors was HCO 2
            2
        C 2 O 4 	 CH 3 CO 2 	 citrate. Isotopic labeling of the electron acceptor,
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