J. CHEM. SOC. FARADAY TRANS., 1994, 90(21), 3323-3330 Time-resolved Microwave Conductivity Part 2.-Quantum-sized TiO, and the Effect of Adsorbates and Light Intensity on Charge-carrier Dynamics Scot T. Martin, Hartmut Herrmannt and Michael R. Hoffmann' W. M. Keck Laboratories, California Institute of Technology, Pasadena, CA 91 125,USA Charge-carrier recombination dynamics after a pulsed laser excitation are investigated by time-resolved micro- wave conductivity (TRMC) for quantum-sized (Q-) TiO, and P25, a bulk-phase TiO, . Adsorbed scavengers such as HNO, , HCI, HCIO, , isopropyl alcohol, trans-decalin, tetranitromethane, and methyl viologen dichloride result in different charge-carrier recombination dynamics for Q-TiO, and P25. The differences include a current doub- ling with isopropyl alcohol for which electron injection into Q-TiO, is much slower than into P25 and relaxation of the selection rules of an indirect-bandgap semiconductor due to size quantization.However, the faster inter- facial charge transfer predicted for Q-TiO, due to a 0.2 eV gain in redox overpotentials is not observed. The effect of light intensity is also investigated. Above a critical injection level, fast recombination channels are opened, which may be a major factor resulting in the dependence of the steady-state photolysis quantum yields on /-'',. The fast recombination channels are opened at lower injection levels for P25 than for Q-TiO,, and a model incorporating the heterogeneity of surface-hole traps is presented.When the radius of a colloidal semiconductor particle falls below the exciton radius (1-10 nm), size-quantization effects appear.'-6 Colloidal TiO, can be prepared in the size-quantized regime by sol-gel synthesis methods7-' Over the last several years, we have been investigating the feasibility of using size-quantized TiO, as a strategy to improve the quantum efficiencies of redox transformations. lo-', In partic- ular, ultra-bandgap illumination (A < 388 nm) of a suspen- sion of TiO, particles results in the stoichiometric oxidation of many chlorinated hydrocarbons to CO, and HCl.'5-20 A generalized photoelectrochemical mechanism involving the major processes can be written as follow^:^ '-', photogeneration: TiO, + hv -+e-+ h+ carrier trapping : >Ti4+-02-H + e-t)>Ti3+-02-H >Ti4+ -02-H + h+ + >Ti4+-0'-H recombination : e-+ >Ti4+ -0O-H + >Ti4+-02-H substrate oxidation : >Ti4+-0'-H + R -+ >Ti4+-02-H + R" substrate hydroxylation : >Ti4+-0'-H + R --r >Ti4+ + +'ROZ-H >Ti4+ + H+02-H-+ >Ti4+-02-H + H+ electron deactivation : >Ti3+-02-H + 0,+ >Ti4+-02-H + 0,' 0,'-+ H+ -+ HO,' Critical steps of the photoelectrochemical mechanism of eqn.(1)-(9) have been investigated by the transient absorp- tion spectra obtained following laser flash photolysis of trans- parent colloidal TiO, .24-31 Most investigators have assumed that conclusions reached regarding colloidal TiO, are applic- able to larger bulk-phase TiO, particles.In the present study, t Present address : Institut fur Physikalische und Theoretische Chemie der Universitat, GH Essen, Germany. the basis of this assumption is investigated by using TRMC measurements, which do not discriminate by crystallite size,10,32-39 to compare the photoelectrochemical mecha- nisms of quantum-sized TiO, and bulk-phase TiO, (Degussa p25).l7--20,40-63 We have recently reported that the relative steady-state quantum efficiencies obtained with these two dif- ferent forms of TiO, depend upon the specific reaction mechanisms involving the electron donors (e.g. direct hole transfer or hydroxyl radical attack).lo Flash photolysis-TRMC experiments are used to compare the charge-carrier dynamics of Q-TiO, and P25 TiO, as functions of the acid used in the sol-gel synthesis, of the charge-carrier scavengers present at the particle interfaces and of light intensity.Experimental Preparation and Characterization Powders of Q-sized TiO, particles were synthesized by the controlled hydrolysis of titanium@) tetraisopropoxide in the presence of HCl, HNO,, or HClO, according to procedures described previously. 7~1 The sol-gel suspension from HClO, was neutralized with NaOH to pH 3.0 in order to obtain a powder. A powder containing methyl viologen (MV) dichlo- ride hydrate (Aldrich) was obtained by rotary evaporation of a resuspension of Ti0,-HNO, mixed with MV. Dry powders of P25 were obtained by the rotary evaporation of suspen- sions (1.44 g 1-', pH 1.5) in HNO,, HCl, HClO, or MV.P25 and Q-TiO, were supported with several drops of trans-decalin (T) except for the preparations containing isopropyl alcohol (ISP) and tetranitromethane (TM), which were pre- pared at the time of measurement by adding several drops to the powders. The Q-TiO, particles were characterized as described pre- viously.' high-resolution transmission electron microscopy (HRTEM) lattice spacing images and X-ray diffraction (XRD) Scherrer line broadening showed the size distribution of the particles was between 2 and 4 nm. The electron diffraction (ED) and XRD patterns of the TiO, particles were character- istic of anatase. A blue shift of the absorption onset to 345 nm (3.6 eV) was observed. The absorption coefficient at 308 nm was 2.9 x lo4 cm-'.Degussa P25 particles, which were composed of 30 nm crystallites consisting of 80% anatase and 20% rutile, aggregated to form 1 pm particle^.^'.^' J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 TRMC Measurements The TRMC apparatus is described in the previous paper." In a typical TRMC experiment separated charge-carriers, which are generated by a laser pulse, lead to a perturbation of the initial microwave absorbance. The temporal decay of the conductivity signal (i.e. microwave absorbance) reflects the lifetime of the photogenerated carriers and is given by the following equation I II I I 1 I I 2800 3200 3600 field/G Fig. 1 EPR spectra obtained at 77 K for sol-gel preparations of size-quantized TiO, in (a) HNO, ,(6)HCl and (c) HClO, where a is the conductivity, eT- is a trapped electron, hT+ is a trapped hole, ecb- is a conduction-band electron, and hvbt is a valence-band hole.The hole terms in eqn. (I) are negli- EPR Measurements gible on the timescales of Fig. 1-4 (later) due to fast hole An E-line Century X-band Spectrometer (Varian, Palo Alto, trapping at immobile surface hydroxy group^.'^ In this case, CA) was used to record the first-derivative EPR spectra at the conductivity is due to the two-electron terms in eqn. (12), 77 K. CuSO, was used as a calibration standard. The TiO, and the conductivity decay corresponds to the recombination samples were prepared as gels (ca. 10 g 1-I) for the EPR [eqn. (4)] or emission of electrons to substrate [eqn.(10)-analysis. (13~ I I I I 112.0 I I I I I 1 8.01 10.0 A > 8.0 Ef 6.0 & 4.0.-v, 2.0 0.0 -2.0 ' I I I I I -2.0' I I I I I -400 0 400 800 1200 1600 -2.0 0.0 2.0 4.0 6.0 8.0 ti me/ns time/ps 4.0I I I I I I 2.0 3.0 1.5 >E 2.0 1.0 ---. cp 2-& 1.0 2 0.5.-fn .-0) 0.0 * 0.0 -0.5' 1-1 .O1-20 0 20 40 60 80I I I I-200 0 200 400 600 800 ti me/ps time/ms Fig. 2 Effect of (a) HNO, ,(6) HCl and (c) HClO, on the conductivity decays of Degussa P25 supported in T. A, 200 ns div- ' timebase; B, 2 ps div-'timebase; C, 200 ps div-'timebase; D, 10 ms div- 'timebase. Table 1 Relative initial carrier concentrations and conductivity decay half-lives relative initial carrier concentration half-life adsorbate P25 Q-TiO, P25 Q-TiO, HC10, 11.2 2.1 750 ns 25 ps 1.6 ms 1.6 ps 800 ps 11 ms HNO, 3.6 3.0 8.0 ps 4.3 ms 2.8 ms 6.3 ms HCl 1.4 1.7 35 ps 8.7 ms 2.8 ps 110 ps 8.3 ms T 4.3 3.0 7.9 ps 5.9 ms 2.8 ms ISP 6.8 1.1 3.5 ps 650 ps 8.7 ms 19 ms TM 4.3 n/a 230 ns 2.2 ps 51 ps n/aMV 5.0 0.9 95 ns 1.1 ps 13 ms J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 3325 3.0 2.5 --2.5 2.0 2.0 -0.5 I -0.5'I I I I 1 I I 1 -400 0 400 800 1200 1600 -2.0 0.0 2.0 4.0 6.0 8.0 t ime/ns ti me/p 1.5 I I I I 4 > 1.o 1.51 I E1-0.5 C .-0 a 0.0 (4 I I-0.5 L I II I I -200 0 200 400 600 800 time/ps IFig. 3 Effect of (a)HNO,, (b) HC1 and (c) HC10, on the conductivity ns div-timebase. B, 2 ps div-' timebase.C, 200 ps div-' timebase; D, 10 ms div-' timebase. interfacial electron transfer from the conduction-band: The recombination channel [eqn. (4)] is exhausted for t S-10 ns because all the holes have escaped the particle [eqn. (5) substrate reduction : e-+ Ox +0'-(10) and (6)]." The conductivity decay is then due solely to inter-facial electron transfer to the adsorbed substrate [eqn. (10)-short circuit : e-+ Red'+ -+Red (11) (13)], and the microwave conductivity at 100 ns is due to the interfacial electron transfer mediated by a surface trap: fraction of charge pairs that have not recombined [eqn. (4)] or transferred immobile sites [eqn. (3) and (5)-(13)].'* substrate reduction : >Ti3+-02-H + Ox -+ >Ti4+-02-H + Ox'-(12) Results The EPR spectra of Q-TiO, prepared in HNO, , HClO,, orshort-circuit : HCl are shown in Fig.1. The effects of adsorbed HNO,, >Ti3+-02-H + Red" >Ti4+-02-H + Red (13) HCIO,, and HCl on the conductivity decays of P25 and Q-7.0 7.0 6.0 6.0 5.0 5.0 > 4.05 3.0 & 2.0 4.0 E 3.0 > 1-2 2.0 3 1.0 .g 1.0 0.0 0.0 -1 .o' -400 I 0 I 400 I 800 I 1 1200 1600 -1 -2.0.o I0.0 I2.0 I4.0 I6.0 8.0 time/ns time/p 3.0 2.0 2.5 1.5 2.0 >E 1.5 1----. z 1.0 0.5ul v)Z 0.5 .-0.00.0 I I I I I-0.5 -1.0 -0.5 ' -200 0 200 400 600 800 -20 0 20 40 60 80 time/ps time/ms Fig. 4 Effect of (a) ISP, (6) T, (c) TM and (6)MV on the conductivity decays of Degussa P25. A, 200 ns div-' timebase; B, 2 ps div-' timebase; C, 200 ps div-' timebase; D, 10 ms div-' timebase.J. CHEM. SOC. FARADAY TRANS., 1994,VOL. 90 3.0"3:;j 2.5 2.5 2.0 2.0 >E 1.52 1.5 1-2 1.0 .-g 1.0 0.5 fA 0:5 0.0 0.0 1 -0.5' II I I I I I I I-0.5 I -400 0 400 800 1200 1600 -2.0 0.0 2.0 4.0 6.0 8.0 ti rne/ns ti rne/ps 2.5 -1.51I I I I I I I I 1 2.0 -(4 C 1.o >5 0.5 .G0, 0.0 0.0 I I I I I I I 1-0.5 ' I -0.5 (d) -200 0 200 400 600 800 -20 0 20 40 60 80 tirne/ps ti me/ms Fig. 5 Effect of (a) ISP, (b) T and (d) MV (supported in T) on the conductivity decays of Q-TiO, prepared in HNO, .A, 200 ns div-' timebase; B, 2 ps div-' timebase; C, 200 ps div-' timebase; D, 10ms div-' timebase. 3.0-I 2.5--> 2.0 E 100%21.5 -C c El,'5 1.0-.cr, 2.0 -0.5 0.0-4 2* 0% 1.4% I I I I I I I-0.5' I 0.0-5.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 0.0 10.0 20.0 30.0 40.0 ti me/p pulse energy/mJ Fig.6 Effect of the incident laser pulse energy (100%= 4.9 mJ Fig. 8 Effect of the incident laser pulse energy on the initial (0,100 pulse-') on the conductivity decays of Degussa P25 supported in ns) and the residual (m, 15 ps) conductivity of Q-TiO, prepared in trans-decalin on the 2 ps div-' timebase NaClO, and T 0.0 0.0 10.0 20.0 30.0 40.0I pulse energy/mJ pulse energy/mJ Fig. 7 Effect of the incident laser pulse energy on the initial (0,100 Fig. 9 Effect of the incident laser pulse energy on the initial (0,100 ns) and the residual (m, 15 ps) conductivity of Degussa P25 prepared ns) and the residual (m, 15 ps) conductivity of Degussa P25 prepared in NaClO, and T in HNO, and T J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 TiO, are shown in Fig. 2 and 3 while the corresponding con- ductivity decays of P25 and Q-TiO, in the presence of T, ISP, TM and MV2+ are shown in Fig. 4 and 5. The relative initial charge-carrier concentrations (Table l), which are determined at 100 ns, are proportional to the conductivity signal strengths observed in Fig. 2(a)-S(a). The time-resolved conductivity signals of P25 supported in T were found to be a function of the incident pulse energy, as shown in Fig. 6. Similar results were obtained for different adsorbate systems (i.e. ClO,-, and Cl- in T), as shown in Fig.(7)-(9) in which the initial charge-carrier concentrations at 100 ns and 15 ps are plotted as functions of the laser pulse energy (i.e. the charge-carrier injection level). For P25 pre-pared in NaClO, and T (Fig. 7) the carrier concentrations at 100 ns and 15 ps appear to have a lower rate of increase above 4 mJ for a similar increase in injection level. In the presence of NaClO, and T (Fig. 8), the critical injection level for Q-TiO, shifts to ca. 10 mJ, and a second critical level at 25 mJ is also apparent. Samples of P25 prepared in HNO, and T (Fig. 9) appear to have critical injection levels at 5 mJ and lower saturation levels than similar samples prepared in NaClO, (Fig. 7). Discussion Char ge-carrier recombination The fate of the majority of photoexcited charge-carrier pairs in undoped ultra-small particulate semiconductor particles is rapid recombination2' since the instantaneous charge-carrier concentrations from the laser pulse are of the order of 1021 At these concentrations, the higher energy states of the energy bands are populated and symmetry-allowed (i.e.direct) bandgap recombination in TiO, is facilitated. Fast recombination also occurs between free holes and trapped electrons [eqn. (4)].1'*24 Both these channels are exhausted within the time-resolution of our experiment. When the residual carrier-level concentration falls to 10l8 ~m-~, the Fermi level is moved out of degeneracy and the residual con- ductivity is detected by our measurement system.A carrier concentration of ca. 10l8 cm-3 should be representative of the steady-state concentrations of accumulated charge car- riers in CW photolysis experiment^.^, Fast charge-pair recombination rates are further enhanced in size-quantized semiconductor particles owing to the mixing of states that relaxes the selection rules for an indirect This latter effect of size quantization is clearly illustrated in the data summarized in Table 1. For all sorbates (electron acceptors and electron donors) the concen- tration of charge-carriers is lower in Q-TiO, than in P25 after 100 ns. These experiments suggest that indirect-bandgap semiconductors in the Q-sized domain are less photoefficient redox catalysts owing to inherently faster rates of charge-carrier recombination.This photophysical effect offsets the predicted gains associated with higher thermodynamic driving forces for interfacial electron transfer. Surface Structures The EPR spectra shown in Fig. 1 suggest the formation of radical species on the surface of the TiO, particles. The species may include >Ti"'-Cl, >Ti'"-ONO, , >Tirv-C1' and >TilV-ONO,'. However, the radicals present in the sample constitute only 1% of the atoms, as indicated by a comparison of the integrated intensity of the EPR signals to the CuSO, standard. The observed radicals suggest that the acid anions interact with the surface of the particle and that the bulk of the anions speciate as >TiW-Cl, >TitV-0NO, and >Tirv-OC1O,.Fluctuating energy Level Model The observed differences as a function of added acids (Fig. 2 and 3) suggest that photogenerated charge carriers undergo interfacial charge transfer to the acid anions on the surface of the TiO, particles. The kinetics of the interfacial charge transfer can be understood in terms of the fluctuating-energy model proposed by Gerischer. 70 The one-electron oxidation potentials of the acid adsorbates under standard conditions are as follow^:^' C1-*--) C1' + e-; E" = -2.6 V (14) NO,--NO,' + e-; E" = -2.3 V (15) OH-*--)'OH + e-; E" = -1.9 V (16) Although the one-electron oxidation potential for perchlorate is not known, we assume that the value lies between 2.0 and 3.0 eV based upon comparison with eqn.(14) and (15). The oxidation potential of the surface-bound hydroxide anion [ie. eqn. (3)] can be estimated also from eqn. (17); it has been reported to be -1.5 V." Thus, the oxidation of the adsorbed acids can take place only from direct valence-band hole transfer since the E:,.. (*OH-acid anion) value <O (i.e. AGO 9 0). The corresponding two-electron reduction potentials for nitrate and perchlorate are as follows:72 NO3-+ 2e-+ 3H+++HN02+ H,O; E" = +0.9 V (17) C10,-+ 2e-+ 2H+++ClO,-+ H,O; E" = +1.2 V (18) Within f0.2 V, a conduction-band electron has a reduction potential of -0.3 V [eqn. (10) and (ll)] and a valence-band hole has a reduction potential of 2.9 V [eqn. (3)J at pH 0. In these calculations, we used the constraints that the conduction-band edge for TiO, is 0.1-0.2 V negative of the flatband potential and that the bandgap of anatase is 3.2 eV.The flatband potential has been determined to be -0.127 and -0.2 V7, us. NHE at pH 0 for colloidal TiO,. The size- quantization effects in Q-TiO, increase the bandgap by 0.4 eV.' This increase corresponds to a shift in the reduction potential of the conduction-band electron to -0.5 V and of the valence-band hole to +3.1 eV for Q-TiO, at pH 0. Since Degussa P25 is predominantly anata~e,~' its band edges are at -0.3 and 2.9 V at pH 0. The apparent reduction potentials of trapped charge car-riers are difficult to estimate. In the case of a trapped elec- tron, Ti"' is 0.2-0.5 eV negative of the conduction-band edge at zero surface charge, E&, of r~tile.~,-'~ Using EEb = -0.3 V us.NHE and pH,,, = 5.8,77 the reduction potential of a trapped electron [eqn. (8), (12) and (13)] is ca. -0.25 V us. NHE. Because the trapped electron is localized, the reduction potential is the same for both Q- and P25 TiO, . The trap is 50 mV below E,, of P25, in agreement with other sugges- tion~,~~and is 250 mV below E,, of Q-TiO,. The reduction potential of a trapped hole [eqn. (6) and (7)] is +1.5 V, as discussed for eqn. (16). The acid anions (Cl-, NO3- and C104-) are chemisorbed onto the surface of TiO, by ligand substitution of surface hydroxy groups and by electrostatic attraction at pH < 6.8. The one-electron oxidation potentials [eqn.(14)-( 16)] indi- cate that the acid anions at the TiO, surface are thermody- namically less capable of hole capture than surface hydroxide but may still serve as good hole traps [eqn. (3)] owing to the high overlap between the energy levels of the acid anions and the valence-band hole for 0.5 < A/eV < 1.0 where A is the reorganization en erg^.^',^^ Although OH- and C1- cannot be further reduced, NO, -and ClO,- undergo multi-electron reductions [eqn. (17)and (18)]and thus may serve as effective electron traps. Inorganic Donors and Acceptors Interfacial charge transfers to the acid anion adsorbates occur on the ps and short ns timescales and compete with interfacial recombination processes. This effect is clearly seen in Table 1, in which the initial charge-carrier concentrations appear to be unique for each adsorbate.In the case of HCl, the chemisorbed C1- anion directly scavenges valence-band holes [eqn. (19)] within 10 ns in direct competition with surface OH- [eqn. (3)]:26 >Ti4+-C1-+ h+ + >Ti4+-C1' (19) After formation, the surface chloride radical may open a second channel for charge-carrier recombination as follows : e-+ >Ti4+-C1* + >Ti4+-C1-(20) The relatively low carrier concentrations observed at 100 ns indicate that the cross-section for electron capture by a surface chloride radical [eqn. (20)]is greater than that for a surface hydroxy group [eqn. (4)J This observation could be explained, in part, by the relative differences in electronega- tivity for OH- and C1-.Since nitrate and perchlorate serve as both potential electron scavengers and hole scavengers, three scenarios are possible to explain their effects: (a) >Ti'V-ONO, and > Ti'V-OC1O, could act as fast hole scavengers; (b)they could act primarily as fast electron scavengers or (c) they could act equally with respect to the trapping of both charge types. In case (a)fast hole trapping exhausts the reservoir of electron- accepting species and the conductivity signal is proportional to the concentration of electrons. Case (b)is the opposite of case (a), i.e. the conductivity signal is due to free holes. In case (c) electrons and holes are equally separated on the surface of the semiconductor particle while the charge carriers remain- ing within the particle recombine rapidly and thus no residual conductivity is observed at 100 ns.As shown in Fig. 2, case (c) does not appear to occur. Thus, preferential trap- ping of one carrier type as in (a) or (b)appears to take place. Although processes (a) and (b)are not directly distinguishable in our experiment, we will attempt to show that interfacial electron transfer does not occur significantly within the time- resolution of the experiment (tide infra). In this case, the con- ductivity signal should be due to electrons as in (a). The relatively high electron-charge-carrier concentrations shown in Fig. 3(a)for P25 in the presence of HClO, suggest that the cross-sections for hole capture by >Ti'V-OC1O, or >TirV-0H are comparable while >Ti'V-OC103' has a lower cross-section for electron capture than >Ti"-OH'.In the case of Q-TiO,, the electron concentration in the pres- ence of HClO, shows that the cross-section for electron capture by >Ti'V-CIO,' increases relative to P25. The lower charge-carrier concentrations observed in the presence of HCl for P25 as compared with Q-TiO, indicate that valence-band hole-capture rates of >TiIV-C1 [eqn. (19)]are greater for P25 than for Q-TiO,. In this case, more carriers are short-circuited by conduction-band electron transfer to >Ti'V-CI' [eqn. (20)]for P25 than for Q-TiO,, and thus the residual charge-carrier concentration at 100 ns is greater for Q-TiO, than for P25 (Table 1).Organic Donors and Acceptors TM and MV2+ are known to serve readily as electron scav- engers in TD, system^',^^,^^ while T, a saturated bicyclic hydrocarbon, and ISP serve as surface hole scavenger^.^.^^*^^ J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 The measured charge-carrier concentrations at 100 ns in P25 are comparable in the presence of MV2+, TNM, ISP and T. If fast interfacial electron transfer were taking place to TM and MV2+, then the carrier concentrations at 100 ns would be expected to be reduced. The first half-lives for the charge carriers in the presence of MV2+, TNM, ISP and T are 95 ns, 230 ns, 3.5 ps and 7.9 ps, respectively. Thus, we conclude that, even in the presence of fast electron acceptors, interfacial elec- tron transfer takes place primarily at timescales 2 100 ns.In the presence of electron acceptors (TNM and MV2+), the conductivity decays flatten on the ms timescale, as shown in Fig. 4(b) and (c) and Fig. 5(b) and (c); this effect suggests that electron transfer does not take place on this timescale. Electron transfer to TNM and MVZ+ takes place during the first 500 ns, as shown in Fig 4(a) and 5(a).After that time, the surface substrate is exhausted and further electrons do not escape the particle until fresh substrate diffuses to the surface, as shown in Fig. 4(d) and 5(4.''The increasing charge-carrier concentrations seen in Fig. 5(a)and (b)suggest that back electron injection from ISP into Q-TiO, takes place. The current-doubling effect occurs when a one-electron oxidant such as ISP produces a radical that can inject an electron into the conduction band of TiO, as follows:7 h+PH PH CH,-C-CH, -CH,-C-CH,-H+IH 0-CH,-C-CH, II -e-,H+ This effect is absent in Fig.4(a) and (b)for P25.However, the highest initial conductivity signal for P25 is observed when ISP is the electron donor, which supports the argument that back electron injection takes place much more quickly than in Q-TiO,. A slower rate for Q-TiO, may be due to the 0.2eV shift to the negative of the conduction-band edge of Q-TiO, , which should slow electron injection. Slower elec- tron injection rates into Q-TiO, may also arise from a drop in the electron-transfer probability due to a higher surface density of hydroxy groups that sterically hinder surface Ti", which is the likely site for electron injection into the conduc- tion band.The sol-gel preparation method is expected to result in higher surface densities of hydroxy groups for Q- TiO, than for P25,which is prepared by flame hydrolysis. Light Intensity Effects The observed decay rates from 100 ns to 35 ps (Fig. 6)follow apparent first-order kinetics ;this observation implies that the charge carriers act independently of one another at t d 35 ps. However, the charge-carrier concentrations at 100 ns are not directly proportional to the initial charge-carrier injection levels because fast recombination is a second-order process. The observed carrier concentrations at 100 ns give us a measure of the extent of charge-carrier recombination at t < 100ns.The charge-carrier injection level can be determined from the number of photons injected into the penetration depth of Q-TiO, at 308 nm: I (~m-~) I (mJ) a (cm-') = 2.3 x 1017hv (eV) A (mm2) (23) where I (cm-,) is the injection level, I (mJ) is the pulse energy, a is the absorption coefficient, A is the cross-sectional J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 area, and hv is the photon energy. In our flash photolysis system, a 4.5 mJ pulse results in ca. 10,' carriers ern-,. The slopes of the lines in Fig. 7-9 can be defined as response factors. The response factor is the relative change in the carrier concentration at a time, t, produced by a change in the injection level.In the absence of higher order (i.e. fast) recombination processes, the response factor should be high while the response factor is zero at saturation. The injection level at which the response factor changes is defined as the cross-ouer threshold. These thresholds (Table 2) are the injec- tion levels at which new higher order deactivation channels are opened and they appear as discontinuities in the lines in Fig. 7-9. The response factors in Table 2 decrease as the injection level increases, which indicates that higher injection levels result in larger quantum yields for fast recombination. In a typical CW experiment, higher light intensities are expected to raise the quantum yields for fast recombination and thus to reduce the net quantum yields for substrate oxidation and reduction.This conclusion provides evidence for our hypoth- esis that the quantum efficiencies for oxidation and reduction in CW photolysis fall as the square-root of absorbed light intensity (acc I-'I2) owing to rapid recombination at higher light intensitie~.'~ The apparent discontinuities at the cross-over thresholds in Fig. 7-9 may be explained in terms of a mechanism involving two chemically distinct hole-trapping sites, S, and S,, in TiO, that have hole-trapping cross-sections CT, and 0, .21 S, is most likely OH,' formed on a surface TiIV site and S, is OH,' formed on a surface p-0 site. We propose that crl $ 6, due to a potentially unfavourable charge balance on p-0.The concentrations of S, and S, following an injection level of [So] are subject to the following constraints: where [S,] and [S,] are the concentration of occupied hole traps. At the time of injection, [S,](O) + [S2](0) = [So]. Due to stoichiometric annihilation, [C](t) = [S,](t) + [S,](t) for t -g qhtwhere qhtis the time for interfacial hole transfer and [C](t) is the concentration of electrons. The time-dependent decay of [S,] and [S,] may be model-led as follows : where kl, ,are the cross-sections for charge-carrier recom- bination [eqn. (4)] and the response factors, m,,,, are exp[ -kl, ,(lo0 ns)]. A plot of the conductivity signal [C](lOo ns) us. the injection level, [So], under the conditions set out in eqn.(11) results in two straight lines with a discontinuity at the cross-over threshold where [So] = S,. The higher surface area and surface hydroxylation of Q-TiO, results in cross-over thresholds at an injection level five to ten times higher than P25, as shown in Table 1. The effect of HNO, and HCIO, on the surface states of Degussa P25 is shown by the difference in cross-over thresholds and response factors. Saturation of the response factor for HNO, indicates that k, is fast. Q-TiO, has a second cross-over threshold, which indicates a third possible site for trapped holes. Conclusions We have shown that the charge-carrier dynamics of Q-TiO, and P25 respond differently with respect to added electron donors and acceptors and to absorbed light intensity. These effects suggest significant differences in the photoelec-trochemical mechanisms for Q-TiO, and P25.Anions such as C1-affect the charge-carrier recombination processes by introducing surface states through specific adsorption as follows: >Ti-OH + C1-+ Hf >Ti-Cl + H,O (27) Hence, the photoreactivity of Q-TiO, could be enhanced by deactivation of fast surface recombination processes. Wide bandgap quantum-sized semiconductors such as ZnO and TiO, should be moving further into the Marcus inverted with respect to the net driving force for oxidation. However, when quantum efficiencies are limited by the rate of reduction, size quantization has been shown to yield high quantum yields for H,O, production on ZnO" or alkene reduction on Ti0,.82 In the case of pollutant oxida- tion on TiO,, quantum efficiencies may be limited primarily by the effective rate of interfacial reducti~n.~~*~~ However, the mixing of states in the size-quantization regime appears to enhance direct electron-hole pair recombination in indirect-bandgap semiconductors (i.e.TiO,). In the size-quantization regime of TiO, ,faster electron-hole pair recom- bination may offset the increased driving force for interfacial reduction. We are indebted to Prof. Nathan S. Lewis for the loan of microwave components and to Prof. Geoffrey A. Blake for the use of the excimer laser. We are grateful to ARPA and ONR {NAV 5 HFMN N0001492J1901) for financial support. S.M. is supported by a National Defence Science and Engineering Graduate Fellowship.H.H. wishes to thank NATO/DAAD for financing a research visit at the California Institute of Technology. Wonyong Choi, Dr. Amy Hoffman, Nicole Peill and Dr. Andreas Termin provided valuable support and stimulating discussion. Table 2 injection level cross-over threshold /lo-,' cm-, system 100 ns 15 ps P25 in NaClO, < 3.6 < 3.6 and T > 3.6 > 3.6 sol-gel Q-TiO, in NaClO, and T -= 14 <25 <8.6 <25 >25 > 25 P25 in HNO, < 6.0 < 6.0 and T >6.0 >6.0 Injection level cross-over thresholds and response factors Ainjection level 100 ns 15 ps 2.4 0.7 0.6 0.2 0.24 0.13 0.12 0.05 0.03 0.003 0.40 0.23 0.03 0.01 response factor Acarrier concentration 3330 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 References 44 C. Y. Hsiao, C. L. Lee and D. F. Ollis, J. Catal., 1983,82,418. 45 M. Barbeni, E. Pramauro, E. Pelizzetti, E. Brogarello, M. 1 D. W. Bahnemann, Zsr. J. Chem., 1993,33,115. Gratzel and N. Serpone, Nouu. J. 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