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J. Phys. Chem. B 1999, 103, 2614-2619
Photon Energy and Photon Intermittence Effects on the Quantum Efficiency of Photoinduced Oxidations in Crystalline and Metastable TiO2 Colloidal Nanoparticles M. A. Grela and A. J. Colussi* National Research Council of Argentina and Department of Chemistry, UniVersity of Mar del Plata, PO Box 422, Mar del Plata, 7600-Argentina ReceiVed: July 10, 1998; In Final Form: January 30, 1999
We report quantum yields φ-NP for the photocatalytic oxidation of 3-nitrophenol (NP) in clear, aerated, aqueous colloids of crystalline or metastable TiO2 nanoparticles as a function of photon wavelength (254 e λ/nm e 366) and photon absorption intermittence Iap (0.002 e Iap/photons particle-1 s-1 e 2). φ-NP’s vary as φ-NP ∝ Iap-0.21(0.05 at all λ’s in metastable TiO2 sols and are ∼20 times smaller than the Iap-independent φ-NP’s determined in crystalline suspensions. Higher energy photons are always more efficient. We infer that (1) hyperthermal holes are able to capture electrons from NP while being deactivated in both types of particles, (2) thermalized electrons and holes are trapped in metastable particles within nanoseconds and persist as such for minutes, and (3) shallower traps become populated at larger Iap’s. The similar action spectra of φ-NP and φ-S for nonchelating NP and bidentate salicylate (S) [E0(NP/NP+•) ≈ E0(S-/S•) ≈ 2.8 V vs NHE], in the presence or absence of phosphate as a competing ligand, are evidence that hot carrier effects are indeed associated with outer-sphere interfacial redox reactions. Our data support kSC,max g 6 × 105 cm s-1 for h + NP f NP.+, which is close to the adiabatic coupling limit.
Introduction Kinetic factors determine the energy efficiency of photocatalytic or photosynthetic devices based on illuminated semiconductor/solution interfaces.1-20 Ultimately, the conversion of radiant energy into chemical potential is maximized if surface redox reactions leading to products occur early and fast.1b Nanometer-sized domains seem essential because their large surface/volume ratios make possible the timely utilization of photogenerated carriers in interfacial processes.2,5,12 The specific rates of the dissipative and reactive channels involved depend on particle size and surface characteristics.13-17 Carrier recombination is enhanced in the constrained environments of smaller particles. In addition, the redox potentials of both carriers may be magnified by the inverse dependence of band gap energy EBG on particle radius R.21 Less predictable is the influence of the chemical nature of particle surfaces on the rates of redox processes.17,18,22,23 Orbital overlap and nuclear relaxation dynamics may be affected by impurities or intervening layers.1a The existence of surface traps within the band gap that depend on preparation and conditioning can critically modify photocatalytic efficiency.10,13-15,23,24 We recently showed that the kinetic analysis of events taking place in nanoparticles exposed to cw illumination must deal with few carriers, with the discontinuous nature of these processes, and with a finite number of traps.20 It is immediately apparent that if both carriers are removed by chemical reaction before a second photon strikes the particle (1) the recombination of the single carrier pair follows first-order kinetics and (2) it is the faster (rather than the slower) redox process that determines the fraction of carriers escaping recombination.20 Thus, less than unitary chemical quantum yields can be actually independent of photon flux.20,25 On the other hand, the decline in photochemical efficiency at sufficiently larger photon fluxes implies carrier buildup and the onset of variable (g1) recombination kinetic orders.20,22 The less reactive carriers will
accumulate if the intermittence of photon absorption exceeds the frequency of the slower redox reaction. Multiple carrier pairs can be simultaneously present if the rates of anodic, cathodic, and recombination processes cannot keep up with photon absorption. The outcome expected from the latter conjunction of events is very low quantum yields that are adversely affected by increasing photon flux even at very low levels. The nonmonotonic dependence of interfacial electron-transfer rates on the redox potentials of the donor and acceptor relative to the semiconductor band system brings additional kinetic features.12,26 Thermalized carriers at band edge energies can be more reactive than those trapped within the band gap but less reactive than hot carriers generated at photon wavelengths shorter than the absorption threshold.1,2,4,12 For example, the increasingly larger quantum yields for the photocatalytic oxidation of salicylate and NP in nanocrystalline TiO2 sols at shorter wavelengths indicate that electron transfer can effectively compete with hot carrier relaxation in the subnanosecond time scale and that optimal exoergicity is reached at valence band energies.12 We now report the results of a quantitative study on the photocatalytic oxidation of 3-nitrophenol in TiO2 sols of different origin as a function of photon flux and wavelength. We use commercial pyrolytic TiO2 powders and TiO2 sols prepared by arrested polymerization in the acid hydrolysis of titanium tetraisopropoxide,10c,24 as representative of crystalline and metastable materials, respectively.27 Their similar optical properties that correspond to a fully developed semiconductor band structure in both cases21a,28 betray the relative photochemical inertness of metastable TiO2 colloidal nanoparticles.13-15 The trapping of holes and electrons in the discrete sets of surface defects present in the latter is the dominant feature underlying decreased chemical potentials and lower reactivities.16,23,24,29 The analysis of experimental φ-NP’s as a function of R, Iap, and λ on the basis of the preceding considerations shows that the
10.1021/jp9829492 CCC: $18.00 © 1999 American Chemical Society Published on Web 03/19/1999
Quantum Yields for Photocatalytic Oxidations
J. Phys. Chem. B, Vol. 103, No. 14, 1999 2615 TABLE 1: Experimental Conditions Involving Metastable TiO2 Colloids λ/nm
[TiO2]/mM
absorbance (l ) 1 cm)
particle number density × 10-14/cm-3
254 303 330 350 366
0.078 0.21 1.6 8.9 13.0
0.40 0.30 0.25 0.20 0.20
1.8 4.8 35 200 290
Figure 1. Normalized absorption spectrum of metastable (a) and polycrystalline (b) TiO2 sols, obtained with an integrating sphere accessory.
photoreactivity of colloidal materials is not uniquely determined by particle size or band gap energy. It is also apparent that the extremely wide dynamic range of the processes controlling overall quantum yields covers about 15 decades and cannot be fully explored by any single technique spanning a (inevitably) limited time window. Experimental Section Visually clear nanocrystalline TiO2 sols were prepared by exhaustive ultracentrifugation (20 min at 9770g) of previously sonicated (15 min at 35 kHz, 100 W) 2 g/L TiO2 (Fredriks Research Products, 76% anatase-24% rutile) slurries in 1 mM PO4H2Na (pH ≈ 4.5). The UV absorption spectra of the stable sols thus obtained, recorded with an integrating sphere accessory (Hitachi U-3210 model; 60 mm sphere diameter; opening ratio, 7.8%), are shown in Figure 1. Atomic force microscopy (PSI) of sol samples dried on mica holders reveals the presence of fine particles (〈R〉 e 3 nm), interspersed with a few larger (R ≈ 15 nm) aggregates.12,19,30 Metastable TiO2 was prepared by dropwise addition of Ti[OCH(CH3)2]4 (Aldrich) solutions in 2-propanol to aqueous HCl (pH ) 1.5) maintained at 1 °C.10c,24 After a 20 h aging period in the dark, these solutions were rotaevaporated to dryness at 35 °C. The resulting solids were dispersed in water at pH ) 2.5, sonicated 5 min, and then ultracentrifuged. The spectra of these sols (Figure 1), which are blue-shifted by about 20 nm (0.19 ( 0.1 eV) relative to polycrystalline TiO2, are consistent with the presence of 〈R〉 ≈ 1.3 ( 0.2 nm particles.21 The use of TiCl4 as starting material led to very similar results.10b Air saturated sols (3 cm3, absorbance ) 0.2-0.4, [O2] ) 0.3 mM) contained in square prismatic silica cells were fully illuminated with monochromatic radiation (from a Kratos-Schoeffel monochromator, 10 nm bandwidth) at several wavelengths in the presence of variable concentrations of 3-nitrophenol (Aldrich). The spectra of these colloidal suspensions proved to be linear superpositions (within 2%) of separate TiO2 and NP spectra, thereby ruling out the formation of charge-transfer complexes under present conditions even in the absence of competing ligands.12,31,32 Constant (up to 50% conversion) NP decay rates R-NP were determined by HPLC [Spherisorb (Sigma) ODS-2, 5µm, methanol/water 4:10 by volume as eluent]. The combined yields of nitrodihydroxybenzenes NDHB’s, the identifiable reaction products, amount to (49 ( 4)%. The remainder of NP losses is ascribed to the formation of (CO2 + H2O + NH3), concurring with previous
Figure 2. Quantum yields of 3-nitrophenol photocatalyzed oxidation in polycrystalline TiO2 sols vs absorbed photon intensity Ia, at λ/nm: 366 (b), 254 (9).
reports.33 We verified that this stoichiometry is independent of λ or [NP], and that the extent of NP photodecomposition in TiO2-free solutions is negligible. We adopt the frequency of photon absorption per particle Iap (rather than per unit volume of solution, Ia, as usual) as the light intensity variable appropriate to colloidal photochemistry (see below). Iap was calculated from incident photon fluxes Io, 4 × 1013 e I0 (photons cm-2 s-1) e 4 × 1015, as determined in situ using the phenylglyoxylic acid actinometer,12,19 experimentally determined TiO2 absorbances (that are consistent with an extinction coefficient of ) 5100 M-1 cm-1 at 254 nm), and the number density Np of TiO2 particles calculated assuming monodisperse sols of spherical particles of radius 〈R〉 and density 3.84 g cm-3, as in anatase. The weights of dry TiO2 recovered from crystalline and metastable sols indicate that crystalline ≈ 0.63 metastable at 254 nm, implying that the amorphous TiO2 matrix either absorbs light as efficiently as the embedded crystals or that its dry weight is negligible, or both. Notice that similar absorbances of ca. 0.3 at all wavelengths lead to increasingly larger NP values, and to correspondingly smaller Iap’s, toward the red end of the spectral range Table 1 (cf. Figure 1). Results and Discussion Quantum Yields. Crystalline TiO2. Quantum yields for the photocatalytic oxidation of NP, calculated as φ-NP ) R-NP/Iap were determined in both types of TiO2 colloids in the ranges 2 e [NP]/µM e 10, 0.016 e Ia/µM s-1 e 1.35, 254 e λ/nm e 366. By analogy with previous results for salicylic acid as a substrate in crystalline TiO2 sols,12 we found that (1) R-NP is a linear function of Ia, i.e., φ-NP is independent of Ia (or Iap for that matter) (Figure 2) and (2) φ-NP is an increasing function of photon energy and varies between 1 and 3% at [NP] ) 10 µM (Figure 3). Considering that most (98%) of the excess
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Figure 3. Quantum yields of 3-nitrophenol photocatalyzed oxidation in polycrystalline TiO2 sols vs excess photon energy. Excess photon energy calculated as E* ) hc(λ-1 - λBG-1): circles, data in [NP] ) 10.5 µM; solid lines, calculated with a 20-level master equation model of electron transfer/excited hole deactivation as described in text.
Figure 4. Quantum yields of 3-nitrophenol photocatalyzed oxidation in metastable TiO2 sols vs absorbed light intensity Ia at various wavelengths, λ/nm: 366 (9), 330 (b), 303 (2), and 254 (1). The solid line is a second-order polynomial fit.
photon energy above the band gap goes to the lighter charge carrier21 (i.e., the hole in the case of TiO2; mh/me e 0.02),34 the excitation wavelength dependence of φ-NP (Figure 3) implies that (1) supraband gap radiation generates excited holes at energies approaching the optimal exoergicity for electron donation by NP6,26,35,36 and (2) that their excitation persists long enough to affect electron-transfer rates.4,12 The following scheme encodes the above findings on crystalline TiO2:
hν f eCB + hVB*
(1)
hVB* + NP f X
(2)
βhVB* + X f (NDHB’s + CO2 + H2O, etc.)
(2′)
hVB* f hVB
(3)
hVB, hVB* (+ eCB) f recombination
(4)
(eCB + O2 f O2-)
(5)
where hVB* and hVB stand for hot and thermalized valence band holes, respectively, and X for reactive surface intermediates; β is the average number of holes consumed in the oxidation of X. Thermalized electrons eCB are assumed to be slowly scavenged by O2. This mechanism leads to φ-NP-1 ) (1 + β) + 〈(k3 + k4)/k2〉[NP]-1. Considering that about 50% of NP ends up as CO2 according to the following stoichiometry (that amounts to a 20 electron oxidation process):33
C6H4(OH)NO2 + 5O2 w 6CO2 + H2O + NH3
(6)
it is possible to evaluate the primary quantum yield as φ2 ) φ-NP /(1 - 10φ-NP). Present results are very similar to those previously obtained for salicylate under identical conditions. Metastable TiO2. Quantum yields measured in metastable TiO2 sols behave very differently. They are considerably smaller than those in crystalline TiO2 (cf. Figure 3) and decrease with absorbed light intensity Ia (in Einstein L-1 s-1 ≡ M s-1) along a common curve for all wavelengths (Figure 4). On this basis, one could reasonably, but incorrectly, infer the absence of hot carrier effects in metastable TiO2 colloids. However, the same
Figure 5. Quantum yields of 3-nitrophenol photocatalyzed oxidation in metastable TiO2 sols vs the frequency of photon absorption Iap at various wavelengths, λ/nm: 350 (2), 330 (9), 303 ([), and 254 (b). Solid lines have slopes of -0.21 ( 0.05.
φ-NP data split into distinct sets when plotted as function of Iap (in photons particle-1 s-1) (Figure 5). Remarkably, we obtain linear log φ-NP vs log Iap plots of slope -0.21 ( 0.05 over a 1000-fold variation of photon intermittence.22 Quantum yields evaluated at the same photon intermittence (e.g., at Iap ) 0.03 photons particle-1 s-1) increase at shorter λ’s (Figure 6) in a fashion similar to that found in crystalline TiO2 sols (cf. Figure 3). The lower φ-NP values reveal that the removal of hyperthermal holes via trapping and/or recombination in metastable TiO2 is faster than in crystalline nanoparticles. Furthermore, the inverse Iap dependence of measured quantum yields is direct evidence of the accumulation of extremely unreactive carriers in metastable nanoparticles. Given the relatively long intervals between the absorption of successive photons by a single particle at the lowest Iap’s, at least some of such carriers must linger for minutes. This purely phenomenological observation, which is obviously independent of any mechanistic considerations, is at variance with expectations based on previous flash photolysis
Quantum Yields for Photocatalytic Oxidations
Figure 6. Quantum yields of 3-nitrophenol photocatalyzed oxidation in metastable TiO2 sols vs excess photon energy, measured at Iap ) 0.03 photons particle-1 s-1.
studies of hydrolytic TiO2 coloids in the microsecond range (see below).10 Clearly, carriers undergo a series of processes across many time scales before becoming inert in metastable TiO2. The last stages of such a series of events necessarily involve trapping. Kinetic Analysis. Crystalline TiO2. The wavelength dependence of quantum yields in Figure 3 can be rationalized in terms of the above scheme (reactions 1-5). Irradiation with supraband gap photons carrying excess energy E* ) Eλ - EBG generates electrons at the conduction band edge and excited holes with sizable energies E* below, i.e., at energies more positive than the valence band edge (EVB ≈ +3 V). Excited holes are assumed to undergo stepwise deactivation, whose combined effect is lumped into step 3, with rate constants kjfj-1 ) k1f0 Ej*,4 while electron transfer is taking place with rate constants that obey the classical Marcus equation, i.e., k2j ) A2[NP] exp{-(Ej* E0 - λR)2/4λRkBT}, Ej* ) E* + EVB.12,26 Integration of the set of master equations: {dnj/dt ) ri + kj+1fjnj+1 - [k2j + kjfj-1 + k4]nj} for a 56-level manifold leads to the solid curve in Figure 3; ri is the rate of formation of the specific level populated by the monochromatic light used in a particular experiment. The best fit is obtained with a reorganization energy λR ) 0.575 eV, A2/k1f0 ) 1.8 × 102 M-1 eV, A2/k4 ) 2.1 × 107 M-1, EVB (pH ) 5) ) 2.93 eV (vs NHE), and E0 ) 2.75 V, the oxidation potential of NP. The latter value coincides with the reversible oxidation potential of the (NP/ NP+•) couple estimated using the ionization potential IP(NP) ) 9.0 eV in Eberson’s relationship: E0(V) ) 0.78IP - 4.26.37 Assuming that k4 ≈ 1.3 × 107 s-1 as in ref 10d, we obtain A2 ) 4.5 × 10-7 cm3 s-1, and k1f0 ) 1.5 × 1012 s-1 eV-1. The derived k1f0 value leads to relaxation times in the picosecond range for a hole excited at Ej* ) 1 eV. Further details on similar calculations for salicylate were reported recently.12 Basic considerations suggest that A2 values for outer-sphere electron transfer from NP into a hole of effective radius rh ) 7.0 × 10-7 cm confined to the particle surface can be estimated as35,36 A2 ) 4πR2 rh κ νN ) 4π (2.5 × 10-7)2(7.0 × 10-7)κνN ) (5.5 × 10-19)κνN cm3 s-1. Hence, our data actually support a value of κνN ) 8.3 × 1011 s-1 for the product of the transmission coefficient κ times the nuclear frequency factor νN. On the other hand, the experimental A2 value, in conjunction with the area of the average particle, Ap ) 7.8 × 10-13 cm2,
J. Phys. Chem. B, Vol. 103, No. 14, 1999 2617 leads to an interfacial electron-transfer velocity of kSC ) A2/Ap ) 6 × 105 cm s-1, which corresponds to a redox process in the strong electronic coupling limit.1 Since salicylate, which can potentially chelate Ti4+, and 3-nitrophenol, which cannot, are oxidized with similar kSC values, we infer that prior chemical bonding with the semiconductor surface is not a requisite for strong electronic coupling. A similar conclusion was recently derived from a study of ferrocenium reduction on GaAs surface quantum wells.38 Metastable TiO2. Sols prepared by room-temperature hydrolysis of suitable precursors are known to consist of R ≈ 1.5 nm TiO2 clusters consisting of anatase islands embedded in an amorphous mass.10,16 The wider band gap of these aggregates translates into a valence band shift to more oxidizing potentials.21,34 On the basis of the preceding arguments, a more positive EVB potential should have enhanced the rate of NP oxidation in metastable TiO2 nanoparticles relative to their crystalline counterparts and led to larger φ-NP’s. In practice, however, metastable sols are about 20-fold less reactive than expected, revealing that unidentified adverse factors override favorable free energy effects. The φ-NP vs Iap dependences of Figures 5 and 6 show that any enhancement of excitation pumping rates, even at the very low radiation levels of present experiments, noticeably decreases quantum yields in metastable TiO2 particles.22 The obserVed effect means that particles do not recoVer their pristine condition within ∼500 s, the average interval between successive photons at the lowest radiant fluxes. We suggest that it is trapped carrier pairs rather than trapped electrons that give rise to this phenomenon. This is so because if carriers recombined within microseconds to the extent required by the very low measured quantum yields, hardly any electrons would remain by the time the next photon strikes on the average particle. We reason that it is incongruous to ascribe very low quantum yields φ-NP to extensive recombination within microseconds and simultaneously invoke a significant presence of electrons after 500 s! The uniform slopes over the entire Iap range further indicate that the steady-state concentration of such unreactive carrier pairs does not sensibly increase with Iap. In fact, stochastic calculations show that an average of 2-3 pairs/particle will account for the experimental φ-NP ∝ Iap-0.21 law.20 To put these findings in perspective, notice that the rate constant k5 ) 7.6 × 107 M-1 s-1 recently derived for the decay of trapped electrons absorbing at λ g 650 nm10a,c in the flash photolysis of similarly prepared TiO2 colloids would lead to lifetimes of the order of 30 µs in air-saturated media! The same study reports single electron/hole recombination lifetimes of the order of 50 ns.10b,c The inescapable conclusion, which will hold regardless of mechanistic details, is that rate data obtained in the nanoseconds to millisecond window are marginally relevant to the analysis of quantum yields measured in weakly irradiated, metastable Q-sized TiO2 colloids, i.e., under typical conditions.10e,22 A realistic picture of photocatalytic action in metastable TiO2 colloids must then deal with the existence of (1) hot carrier effects even at very low quantum yields and (2) a φ-NP vs Iap-n dependence with n being approximately constant over extremely wide Iap ranges. Assuming that hot carrier relaxation indeed takes place within picoseconds,4 and considering that the recombination of some trapped carriers extends for minutes, present experimental observations certainly preclude a single value for the carrier recombination rate constant. They further suggest a strong dependence of reactivity on the chemical potential of the variously trapped carriers. The fact that only a few, distinct traps are available on any single particle implies that higher
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energy traps can be readily populated yielding increasingly reactive species at modest photon fluxes. As a result, the average number of carrier pairs may not significantly increase with Iap. Dramatic evidence of the protracted recovery of irradiated TiO2 surfaces has been recently obtained by Fujishima et al. Photoinduced surface amphiphilicity, which has been ascribed to the generation of Ti3+ sites, i.e., electrons trapped at surface Ti4+, may last up to 2 months in the dark.39 Accordingly, we propose that the results in metastable TiO2 colloids can be rationalized in terms of steps 1-5, plus the following reactions:
hVB, hVB* f hTR
(7)
eCB f eTR
(7′)
hTR + NP f X
(8)
βhTR + X f (NDHB’s + CO2 + H2O, etc.)
(8′)
eTR + hTR f recombination
(9)
eTR + O2 f O2-•
(10)
where hTR and eTR represent trapped carriers. Notice that in addition to recombination, step 4, excited holes are also trapped via step 7. We deal with Iap-dependent recombination rates by assuming that the first-order rate constant k4 is an implicit function of Iap. Actually, the set of parameters EVB (pH ) 2.5) ) 3.3 V, λR ) 0.73 eV, A2 ) 1.0 × 10-10 cm3 s-1, k1f0 ) 1.1 × 1010 eV-1 s-1, k4(Iap ) ) 3.0 × 107 s-1, k7 ) 1.0 × 108 s-1, k8 [NP]/k9 ) 6.9 × 10-4 within an expanded master equation scheme (see above) can account for the λ dependence of φ-NP at Iap ) 0.01 photons particle-1 s-1. Modeling similar experiments at Iap ) 1 photon particle-1 s-1 just requires that k4(Iap ) ) 4.3 × 108 s-1 In all cases, only a very small fraction of excited holes is able to accept electrons from NP. However, since reactions 8/8′ compete unfavorably with step 9, that fraction still contributes significantly to overall quantum yields. Our calculations also suggest that both electron transfer and energy relaxation may be considerably slower in metastable as compared with crystalline TiO2 nanoparticles (cf. the A2 and k1f0 values for both materials derived above). Assuming that k10 ) (2/3)πre3κνNκN ) (2.8 × 10-21) κνNκN cm3, where re ) 1.1 × 10-7 cm is the electron effective radius, κ and νN have the same meaning as before, and κN ) exp{-(E0 - ECB - ∆TR - λR′)2/(4λR′kBT)},35,36 we estimate lifetimes of the order of 500 s, as observed, for electrons trapped at ∆TR ) 0.67 eV below the conduction band edge of R ) 1.3 nm particles suspended in air-saturated media ([O2] ) 0.3 mM). Nuclear relaxation factors, κN ≈ 2.75 × 10-12, were calculated from E0(O2/HO2) ) -0.046 V,40 ECB ) -0.05 V (both at pH ) 2.5),41 and νNκN ) 1012 s-1 for λR′ ) 0.6 or 1.0 eV.32 Therefore, low quantum yields require that hole trapping, step 7, be fast enough to compete with reactions 2/2′, and that reactions 8/8′ be slower than recombination, step 9. In addition, recombination of trapped carriers, step 9, must be sufficiently slow to maintain a significant number of carriers at low photon intermittence. It is apparent that all reaction pathways open to trapped carriers are extremely slow. The mechanism of recombination between trapped carriers probably involves long-range electron transfer rather than random hopping.21a,42 Further discussion is unwarranted at present. The contrasting photochemical behaviors of polycrystalline and metastable TiO2 nanoparticles having similar S/V ratios must
be specifically ascribed to the presence of deep traps in the incompletely relaxed crystal structure of the latter.16,21 Regarding the nature of such traps, it is relevant to point out that very recent photoelectron spectroscopy measurements and calculations on (TiO2)n- clusters reveal HOMO-LUMO gaps of about 2 eV up to n ) 4, i.e., considerably smaller than the band gap of bulk TiO2 in any of its crystalline forms.43 The tentative explanation advanced to account for the apparent anomaly is that while Ti4+ is hexacoordinated in bulk TiO2, its coordination number drops to 3 or 4 in small clusters. Since the LUMO and HOMO levels have Ti 3d and O 2p character, respectively, the lower coordination numbers imply a weaker interaction and, hence, a smaller HOMO-LUMO gap. We suggest a similar rationale for the chemical nature of deep electron traps in metastable TiO2 particles. Such low-lying excited states are apparently inaccessible through allowed vertical dipolar transitions and play a similar role to triplet states in molecular photochemistry. Equally relevant is the finding that holes can be actually injected into midgap holes of Q-sized TiO2 particles by strong oxidants such as SO4-•[E0(SO4-•/SO42-) ) 2.4 V], OH and Ti2+.16 It should be emphasized that, although metastable TiO2 colloids are very inefficient as photocatalysts in the oxidation of donors with E0’s close to +3 V, trapped holes will favorably drive less endoergic processes, such as the oxidation of I-.10b Conclusions A quantitative photochemical study of the photocatalytic oxidation of 3-nitrophenol in polycrystalline and metastable TiO2 nanoparticles reveals that (1) quantum yields sensibly increase with photon energy on both materials, (2) such an effect does not require prior chemical binding between the substrate and dark particle surfaces, (3) quantum yields on metastable TiO2 are dominated by carrier trapping, (4) the rates of the pseudoelementary processes actually determining quantum yields in metastable TiO2 are much slower than those derived from optical transients in the submicrosecond time scale. Acknowledgment. This work was financially supported by the National Research Council of Argentina (CONICET). Ignacio Gil Torro´ (University of Valencia, Spain) collaborated with this project as a fellow of the Instituto de Cooperacio´n Iberoamericano. References and Notes (1) (a) Miller, D. J. R.; McLendon, G. L.; Nozik, A. J.; Schmickler, W.; Willig, F. Surface Electron-Transfer Processes; VCH Publishers: New York, 1995; Chapter 4. (b) Meisel, D. In Semiconductor Nanoclusters; Kamat, P. V., Meisel, D., Eds.; Surface Science and Catalysis, Vol. 103, 1996; pp 79-97. (2) Nozik, A. J.; Memming, R. J. Phys. Chem. 1996, 100, 1306. (3) (a) Wang, Y. AdV. Photochem. 1995, 19, 179. (b) Weller, H.; Eychmu¨ller, A. AdV. Photochem. 1995, 20, 165. (c) Fox, M. A.; Dulay, M. T. J. Photochem. Photobiol. A 1996, 98, 91. (d) Zhang, J. Z. Acc. Chem. Res. 1997, 30, 423. (e) Hagfelt, A.; Gra¨tzel, M. Chem. ReV. 1995, 95, 49. (4) Nozik, A. J.; Turner, J. A.; Peterson, M. W. J. Phys. Chem. 1988, 92, 2493. (5) Nozik, A. J. Photocatalytic Purification and Treatment of Water and Air; Ollis, D. F., Al-Ekabi, H., Eds.; Elsevier Science Publishers: Amsterdam, 1993; p 39. (6) Gra¨tzel, M. Heterogeneous Photochemical Electron Transfer; CRC Press: Boca Raton, 1989. (7) Bahnemann, D.; Cunningham, J.; Fox, M. A.; Pelizzetti, E.; Pichat, P.; Serpone, N. In Aquatic and Surface Photochemistry; Helz, G. R., Zepp, R. G., Crosby, D. G., Eds.; Lewis Publishers: Boca Raton, 1994; Chapter 21.
Quantum Yields for Photocatalytic Oxidations (8) Rehm, J. M.; McLendon, G. L.; Nagasawa, Y.; Yoshihara, K.; Moser, J.; Gra¨tzel, M. J. Phys. Chem. 1996, 100, 9577. (9) Tributsch, H.; Pohlmann, L. Science 1997, 279, 1891. (10) (a) Bahnemann, D. W.; Hilgendorff, M.; Memming, R. J. Phys. Chem. 1997, 101, 4265. (b) Kormann, C.; Bahnemann, D. W.; Hoffmann, M. R. J. Phys. Chem. 1988, 92, 5196. (c) Bahnemann, D. W.; Henglein, A.; Lillie, J.; Spanhel, L. J. Phys. Chem. 1984, 88, 709. (d) Rothenberger, G.; Moser, J.; Gra¨tzel, M.; Serpone, N.; Sharma, D. K. J. Am. Chem. Soc. 1985, 107, 8054. (e) Hoffmann, M. R.; Martin, S. T.; Choi, W.; Bahnemann, D. W. Chem. ReV. 1995, 95, 69. (11) Moser, J. E.; Gra¨tzel, M. Chimia 1998, 52, 160. (12) Grela, M. A.; Brusa, M. A.; Colussi, A. J. J. Phys. Chem. 1997, 101, 10986. (13) Herrmann, H.; Martin, S. T.; Hoffmann, M. R. J. Phys. Chem. 1995, 99, 16641. (14) Martin, S. T.; Herrmann, H.; Hoffmann, M. R. J. Chem. Soc. 1994, 90, 3323. (15) Martin, S. T.; Herrmann, H.; Choi, W.; Hoffmann, M. R. J. Chem. Soc. 1994, 90, 3315. (16) Micic, O. I.; Rajh, T.; Nedeljkovic, J. M.; Comor, M. I. Israel J. Chem. 1993, 33, 59. (17) Wang, C.-C.; Zhang, Z.; Ying, J. Y. Nanostruct. Mater. 1997, 9, 583. (18) Rivera, A. P.; Tanaka, K.; Hisanaga, T. Appl. Catal. B: EnVironm. 1993, 3, 37. (19) Grela, M. A.; Coronel, M. E. J.; Colussi, A. J. J. Phys. Chem. 1996, 100, 16940. (20) Grela, M. A.; Colussi, A. J. J. Phys. Chem. 1996, 100, 18214 and references therein. (21) (a) Brus, L. E. J. Phys. Chem. 1986, 90, 2555. (b) Brus, L. E. J. Chem. Phys. 1983, 79, 5566. Application of Brus’ theory to TiO2 leads to a blue shift (eV) ) (0.23/R2) - (0.0135/R). Since in this case the hole is the lighter carrier (mh/me ) 0.02), the blue-shift translates into a shift of the valence band edge to more positive energies. (22) Choi, W.; Termin, A.; Hoffmann, M. R. J. Phys. Chem. 1994, 98, 13669. (23) Cerrato, G.; Marchese, L.; Morterra, C. Appl. Surf. Sci. 1993, 70, 200. (24) Blanchard, J.; Barboux-Doeuff, S.; Maquet, J.; Sanchez, C. New J. Chem. 1995, 19, 929. (25) Schwarz, P. F.; Turro, N. J.; Bossmann, S. H.; Braun, A. M.; Wahab, A. A.; Du¨rr, H. J. Phys. Chem. B 1997, 101, 7127.
J. Phys. Chem. B, Vol. 103, No. 14, 1999 2619 (26) (a) Marcus, R. A. Angew. Chem., Int. Ed. Engl. 1993, 32, 1111. (b) Marcus, R. A. J. Chem. Phys. 1965, 43, 679. (c) Marcus, R. A. J. Phys. Chem. 1990, 94, 1050. (27) Alivisatos, A. P. Ber. Bunsen-Ges. Phys. Chem. 1997, 101, 1573. (28) Sze, S. M. Physics of Semiconductor DeVices; Wiley: New York, 1981; Chapter 1. (29) Kittaka, S.; Matsuno, K.; Takahara, S. J. Solid State Chem. 1997, 132, 447. (30) Lepore, G. P.; Langford, C. H.; Vichova, J.; Vlcek, A. J. Photochem. Photobiol. A 1993, 75, 67. (31) Tunesi, S.; Anderson, M. J. Phys. Chem. 1991, 95, 3399. (32) Moser, J.; Punchihewa, S.; Infelta, P. P.; Gra¨tzel, M. Langmuir 1991, 7, 3012. Salicylate markedly red-shifts the absorption spectra of hydrolytic TiO2 colloids in the absence of competing ligands. (33) (a) Tanaka, K.; Luesaiwong, W.; Hisanaga, T. J. Mol. Catal. A: Chem. 1997, 122, 67. (b) Minero, E.; Pellizetti, W.; Piccini, P.; Vincenti, M. Chemosphere 1994, 28, 1229. (34) (a) Enright, B.; Fitzmaurice, D. J. Phys. Chem. 1996, 100, 1027. (b) Effective carrier radii were estimated as de Broglie’s lengths rh,(e)/cm ) 1.88 × 10-20mh,(e)1/2. The resulting values at 300 K are rh ) 7 × 10-7 cm and re ) 1.1 × 10-7 cm. (35) (a) Lewis, N. S. Annu. ReV. Phys. Chem. 1991, 42, 543. (b) Lewis, N. S. J. Phys. Chem. B 1998, 102, 4843. (36) Gerischer, H. Photocatalytic Purification and Treatment of Water and Air; Ollis, D. F., Al-Ekabi, H., Eds.; Elsevier Science Publishers: Amsterdam, 1993; p 1. (37) (a) Eberson, L. AdV. Phys. Org. Chem. 1982, 18, 79. (b) Eberson, L. Electron-Transfer Reactions in Organic Chemistry; Springer-Verlag: New York, 1987. (38) Diol, S. J.; Poles, E.; Rosenwaks, Y.; Miller, R. J. D. J. Phys. Chem. B 1998, 102, 6193. (39) Sakai, N.; Wang, R.; Fujishima, A.; Watanabe, T.; Hashimoto, K. Langmuir 1998, 14, 5918. (40) Hoare, J. P. In Standard Potentials in Aqueous Solution; Bard, A. J., Parsons, R., Jordan, J., Eds.; Marcel Dekker: New York, 1987; Chapter 4. (41) (a) Matsumoto, Y. J. Solid State Chem. 1996, 126, 227. (b) Foster, N. S.; Brown, G. N.; Noble, R. D.; Koval, C. A. In Photocatalytic Purification and Treatment of Water and Air; Ollis, D. F., Al-Ekabi, H., Eds.; Elsevier Science Publishers: Amsterdam, 1993; p 365. (42) Copyn, M.; Gelinck, G. H.; Schouten, P. G.; Warman, J. M. J. Phys. Chem. 1995, 99, 11780. (43) Wu, H. B.; Wang, L. S. J. Chem. Phys. 1997, 107, 8221.
