Langmuir 1991, 7, 1091-1096
1091
Pulsed-Laser-InducedCharge-Transfer Reactions in Aqueous Ti02 Colloids. A Study of the Dependence of Transient Formation on Photon Fluence Gottfried Grabner* and Ruth M. Quint Institut fur Theoretische Chemie und Strahlenchemie, Wahringerstrasse 38, A-1090 Wien, Austria Received September 20,1990. In Final Form: December 5, 1990 The formation of charge-transfer transients in the reduction of methyl viologen and the oxidation of halides in aqueous unprotected Ti02colloids has been studied as a function of the photon fluence (pulse energy) of 10-ns 355-nm laser pulses. Nonlinearityof the observed dependence is interpreted by a model based on depletion of surface-adsorbed reactants at high photon fluences. It is shown that this model is able to give a consistent explanation of data obtained at various concentrationsof reactant and semiconductor. Results of model calculationsinclude adsorption properties of reactants and information concerning the factorsthat influence quantum yields of transient formation. The alternative model introducedby Nosaka and Fox is also applied to the data; it is shown that depletion of adsorbed reactants is a consequence of this model also as long as the assumption of reactant adsorption is retained.
Introduction Investigations of photoinduced charge-transfer processes in finely dispersed semiconductors are of growing interest.lI2 Among these, colloidal semiconductors are of particular importance: first because a high specificsurface is available for reactions due to the small size of the particles; second, the colloidsdisperse light to such a small degree that time-resolvedstudies by transient spectroscopy are possible. This approach has been widely applied during the last decade. Upon absorption of photons of energy exceeding the semiconductor band gap, conduction-band electrons (e:b) and valence-band holes (h+,b) are separated and can react with suitable acceptors or donors at the particle surface. A substantial number of studies of this process by timeresolved transient spectroscopy has been carried out on two systems, namely oxidation of halides or pseudohalides, X-,by h+,b mainly in colloidal Ti02,- on the one hand, and reduction of methyl viologen,MV2+,in colloidal Ti02 or CdS,6~~1*~2 on the other. These systems have the advantage of yielding transient radical species, X2*- and MV'+, which are easy to observe by absorption spectrosCOPY. One of the relevant questions when using pulsed lasers for excitation is to what extent high photon fluences can influence photoinduced processes. This applies, in particular, to electron-hole recombination, which might be expected to be favored over carrier transfer and trapping if light-induced carrier densities are high. This is precisely what has been found in studies of intensity-dependent charge collectionquantum yields in pulsed-laser-irradiated (1) Henglein, A. Chem. Rev. 1989, 89, 1861. (2) Henglein, A. Top. Curr. Chem. 1988,143, 113. ( 3 ) Henglein, A. Ber. Bumen-Ges. Phys. Chem. 1982,86, 241. (4) Moser, J.; Gritzel, M. Helu. Chim. Acta 1982, 65, 1436. (5) Duonghong, D.; Ramsden, J.; Gritzel, M. J. Am. Chem. SOC.1982, 104,2977. (6) Rossetti, R.; Beck, S.M.; Brus, L. E. J. Am. Chem. SOC.1982,104, 7322. (7) Bahnemann, D.; Henglein, A.; Spanhel,L. Faraday Discuss. Chem. SOC.1984, 78, 151. (8) Kamat, P. V. Langmuir 1985, I , 608. (9) Nosaka, Y.; Fox, M. A. J. Phys. Chem. 1988,92, 1893. (10) Moser, J.; Gritzel, M. J. Am. Chem. SOC.1983, 105, 6547. (11) Serpone, N.; Sharma, D. K.; Jamieson, M. A.; Gritzel, M.; Ramsden, J. J. Chem. Phys. Lett. 1986, 115,473. (12) Nosaka, Y.; Fox, M. A. Langmuir 1987,3, 1147.
0743-7463/91/2407-1091$02.50/0
Si photodiodes13 and polycrystalline as well as singlecrystal Ti02 e1e~trodes.l~ There have been few studies of photon fluence dependence in colloidal semiconductor systems. Nonlinear dependence of 12'- formation in aqueous Ti02 on pulse energy, suggesting saturation at higher energies, was already noted by Henglein.3 Later, the decrease of the quantum yield of the reduction of MV2+in aqueous CdS and Ti02 with increasing pulse energy was treated quantitatively by Nosaka and Fox9 in a model based on competition between charge-transfer a t the interface and e,b-h+,b recombination. It thus seems straightforward to assume that enhanced carrier recombination at high photon fluences is able to provide a consistent explanation of quantum yield decrease in bulk semiconductors as well as in small colloidal particles. There are, however, arguments that speak against such a simple picture. In the bulk case, the measured quantity is the photogenerated current, whereas in colloid studies the yields of the products of chemical reactions are determined, which will be influenced by other factors besides recombination. Among these, adsorption of reactants may be of particular importance. Many experimental results provide indirect evidence for the assumption that redox reactants must be adsorbed onto semiconductor particles in order to enable charge transfer. These include prompt appearance of transient signals after 10-ns laser pulses314and Langmuir adsorption isotherm behavior of quantum yield@ and reaction ratesl"l7 on bulk reactant concentrations. The present work is an attempt to assess the importance of adsorptive and kinetic parameters for transient formation in pulsed laser experiments. This has been done by taking a fresh look on oxidation of X-and reduction of MV2+in nonprotected aqueous Ti02 sols. In both cases, saturation of transient absorbance with increasing photon fluence is observed. We will argue that this behavior can (13) Neumann-Spallart, M.; Schwarz, A.; Grabner, G. Appl. Phys. A 1988, 46, 9. (14) Neumann-Spallart, M.; Schwan, A.; Grabner, G. J. Phys. Chem. 1989, 93, 1984. (15) Herrmann, J. M.; Pichat, P. J . Chem. SOC., Faraday Tram 1 1980, 76, 1138. (16) Al-Ekabi, H.; Serpone, N. J. Phys. Chem. 1988,92, 5276. (17) Maldotti, A.; Amadelli, R.; Carassiti, V. Can. J. Chem. 1988,66, 76.
0 1991 American Chemical Society
1092 Langmuir, Vol. 7, No. 6, 1991
Grabner a n d Quint
be due to depletion of surface-adsorbed reactants and show that experimental data can be quantitatively interpreted by using a model based on this effect. If valid, this model can be used to extract information about the adsorption behavior of reactants, as well as provide additional insight into the factors that limit product quantum yields.
Experimental Section Small-particle Ti02 has been prepared by hydrolysis of titanium(1V) tetraisopropylate according to the method of Bahnemann et al.18 with some slight modifications. In particular, 0.1 M HNOswas used instead of 0.03 M HC1as the hydrolysis medium in an effort to avoid presence of C1-on the particle surface, which could interfere in the study of halide oxidation. For the same reasons,we have refrained from using Tic&as starting compound, since colloids prepared from it may also contain substantial amounts of Cl-.19 According to literature data? the colloid particles can be assumed to have an average diameter of 40 nm. From their absorption spectra, applying the method discussed by Kormann et aI.,m we find band gap values of 3.16 eV (at In a = 6.5, a being the absorption coefficient) at pH 11 and 3.22 eV at pH 1, in agreement with the results of these authors. These values show that the optical properties of the colloid are close to that of bulk anatase. Solutions containing between 0.27 and 1.6 g/L Ti02 were used for measurements. Water was triply distilled, and HClO, or NaOH used to adjust the final pH. No protecting agents were added. All chemicals (supplied by Merck, Darmstadt, or Aldrich, Steinheim) were used as received. The third harmonic (A = 355 nm) of a Q-switched Nd:YAG laser (Quanta-Ray DCR-1, pulse duration 10 ne) was used for excitation. The samples were presaturated with argon and then transferred to a flow-through cell with a right-angle geometry for excitation and analysis. For quantum yield measurements, the reaction volume was defined by rectangular apertures (0.32 X 0.13cmforexcitation,0.17X 0.13cmforanalysis) andthenumber of photons in the laser pulse was measured at the location of the cell with a ballistic calorimeter (Raycon-WEC 730). Analysisof dependence of transient absorbance on pulse energy according to the method of partial saturationz1was performed by taking spatial nonhomogeneity of photon distribution into account.= The procedure was tested by ameasurement of triplettriplet extinction coefficient and intersystem crossing quantum = 266 nm, yielding yield of benzophenone in n-hexane at bo = 1.02 and e K = 6980 M-l cm-1, in good agreement with literature values.21Bza Transient absorption was measured by using a 450-W Xe arc as analyzing light source, a Schoeffel Kratos monochromator, a Hamamatsu R955 photomultiplier, and a Tektronix 7912 digitizer. Averages over up to 64 individual pulses were taken for each measurement of transient absorbance.
Results Measurement of Laser-Induced Transients. On irradiation of alkaline colloidal solutions of Ti02 (0.270.8 g/L, pH 9-12) containing methyl viologen (10" to 5 X 10-4 M) with 10-ns pulses at X = 355 nm, prompt formation of methyl viologen radical cations, M V + (1" = 606 nm, em = 14 500 M-' cm-' 24) is observed. No increase in absorption of M V + is seen after pulse end, and partial decay of photoinduced absorbance occurs over (18) Bahnemann, D.; Henglein, A.; Lilie, J.; Spanhel, L. J. Phys. Chem. 1984,88,709. (19) Davidson, R. S.; Morrison, C. L.; Abraham, J.J.Photochem. 1984, 24, 27.
(20)Kormann, C.; Bahnemann, D. W.; Hoffmann, M. R. J.Phys. Chem. 1988,92, 5196. (21) Carmichael, I.; Hug, G. L. J. Phys. Chem. Ref. Data 1986,15, 1. (22) Grabner, G. Roc.-ZUPAC Symp. Photochem., 12th 1988,410. (23) Carmichael, I.; Helman, W. P.; Hug, G. L. J. Phys. Chem. Ref. Data 1987, 16,239. (24) Solar,S.;Solar,W.;Getoff,N.;Holcman,J.;Sehested,K.J. Chem. Sac., Faraday Trans 1 1984,80, 2929.
B
0
0.1
Figure 1. Dependence of transient absorbance at pulse end, measured at 606 nm, on laser pulse energy, for the system Ti02 (0.8 g/L)/MVZ+ at pH 1 0 (A) 1 X lo-' M MV+; (B) 2 X 1O-aM MV2+.
a time scale of about 100 ps. No reduction of MV2+was observed in unirradiated solutions. Similarly, irradiation of acid colloidal solutions of Ti02 (0.4-1.6 g/L, pH 1-3) containing halides (X- = I-, Br-, C1-, 5 X 10-3 to 0.15 M) leads to prompt formation of X$radical anions, with the observation wavelengths and extinction coefficients as follows:25I,*-, X = 385 nm, €385 = 9400 M-1 cm-1; Br2*-, X = 390 nm, €390 = 7000 M-l cm-l; Clz*-, X = 370 nm, €370 = 6600 M-' cm-l. X2'- absorbance is found to decay over a period of 10-50 ps, the initial part of the decay being formally of second order with 2k = 8 X l o 9 M-l s- for I,*-, 2k = 2 X 1Olo M-l s-l for Brz*-, and 2k = 3 X 1O1O M-' s-l for Clz'-. In agreement with previous studies,2+JO the overall processes involved in transient production can be described as follows: hv
TiO,
-+
ecb, h+,b
-t h+,b
+
+ x- x' +
(2)
MV"
-
(3)
&*-
(4)
-
e-cb MV2+ h+,b
TiO,
X-
In this scheme, the detailed fate of the photoproduced eb; and h+"b is not taken into account. In particular, trapping of electrons and holes and the various possibilities of recombination (between free and trapped species) are not differentiated. In our experiments, we have focused on the determination of the dependence of the laser-induced absorbance in the systems TiOz/MV2+ and TiOZ/X- on photon fluence, i.e., on the energy of the laser pulse. Typical results of such measurements are shown in Figures 1 and 2. Strongly nonlinear behavior is obtained in all cases. The same observation was made for all systems studied in this work. Modeling of Dependence on Pulse Energy. How can the nonlinear behavior apparent in the data of Figures 1 and 2 be understood? Analogous results for the reduction of MV2+ in CdS and Ti02 sols have previously been analyzed by Nosaka and Fox9 in the framework of a model based on competition between reactions 2 and 3. We shall (25) Hug, G. L., Ed. Optical Spectra of Nonmetallic Inorganic Transient Species in Aqueous Solution; NSRDS-NBS 6% Government Printing Office: Washington, D.C., 1981.
Charge Transfer Reactions in Ti02 Colloids
Langmuir, Vol. 7, No. 6,1991 1093 Table I. Results of Fits According to Equation Data Sets Shown in Figures 1 and 2 data set c h , mol/g Ti02 Figure 1A 2.86 x 1o-B Figure 1B 9.24 X lo-' Figure 2A 2.0 x 10-5 Figure 2B 2.5 X lo4 Figure 2C 8.9 X 10-I
O.O6/ 0.04
R
1
L
I ( mJ I p u l s e )
Figure 2. Dependence of transient absorbance at pulse end, on laser pulse energy for the system Ti02 (1.6g/L)/X-at pH 1: (A) 0.1 M KI, measured at 385 nm; (B) 0.1 M KBr, measured at 390 nm; (C)0.1 M KC1, measured at 370 nm. I
h', e-
qZc+
TIOZIA-, ' 0
TiOzIA, 0
Figure 3. Three-state excitation/reaction scheme for charge transfer in Ti02 colloids. come back to this model later on, but would now like to introduce an alternative model based on laser-induced depletion of surface-adsorbed reactants (MV2+or X-). Depletion of photon-absorbing states by high photon fluences of pulsed lasers is a common phenomenon and can be exploited to determine properties of photochemical systems, such as process quantum yields or extinction coefficientsof metastable speciesV2lProvided the depleted state cannot be repopulated within the duration of excitation, comparison of the concentration of absorbing states and that of the photons absorbed provides a qualitative criterion for the pulse energy range in which depletion must be taken into account. In the case of excitation of Ti02 by 355 nm photons, depletion of the photon-absorbing state would require pulse energies in excess of 100 mJ, or 2 orders of magnitude higher than those used in this work. If, on the other hand, we assume that reactions 3 and 4 require adsorption of reactants on the particle surface,we have also to consider the possibility of depletion of adsorbed species. Taking colloidal Ti02 particles (1.6 g/L, pH 1)with 20 nm radius as an example, and assuming total coverage of the particles with ions of radius 0.215 nm (corresponding to the ionic radius of I-, certainly a serious underestimation for description of adsorption of hydrated I-), 3.0 X 1015ions will be present in adsorbed form in the reaction volume used in this work (7.07 X cm3). This figure must be compared to the number of photons absorbed by the semiconductor in the same volume, which is 5.0 X 1014photons for 1mJ of 355nm radiation. This simple order-of-magnitude estimation shows that depletion of surface-adsorbed reactants cannot be neglected a priori. A quantitative description of this effect is possible by noting its analogy with a one-photon process in a three-state system (Figure 3). Here A and D denote suitable acceptors or donors present at the particle surface;the state reached by photon absorption is that of separated e-cb and h++ while the final state is reached after charge transfer to the adsorbed
5 for
the
0.148 0.073 0.204 0.058 0.028
reactant. This last step may also include previous carrier trapping. Since transit times of e-cband h+.,b to the surface of the particles can be assumed to be shorter than 10 ps,% and recombination-limited lifetime of trapped electrons and holes is shorter than 1 ns if the number of carrier pairs per particle exceeds 100,n*zr'the steady-state condition for the intermediate state is fulfilled in the case of 10-ns excitation and the time dependence of the individual steps can be neglected.28*90The concentration on photoproduced transients A- or D+, CT,is given by CT = cah{I- exp(-t@I))
(5) where Cad8 is the concentration of adsorbed species, t the extinction coefficient of Ti02 at 355 nm, 0 the quantum yield, and I the photon fluence, which is proportional to pulse energy. Referring to Figure 3, we can identify e-cb-h+vb recombination (reaction 2) and e,b or h+,b reactions competing with reactions 3 or 4as possible factors that can reduce the observed quantum yields below unity. The solid lines in Figures 1 and 2 are the results of fits of eq 5 to the data. All sets of data could be well simulated in this way. The method used is equivalent to that termed "partial saturation method" for the determination of triplet-triplet extinction coefficientsS2l The fits were stable for I < 4 mJ/pulse in the Ti02/X- system and for I < 0.5 mJ/pulse in the Ti02/MV2+ system. At higher pulse energies, the experimental data tended to be somewhat higher than the plateau values predicted from fits in the low pulse energy region. For each data set, values of t#~ and C a b were obtained from the fits. The results for the measurements of Figures 1 and 2 are shown in Table I. Dependence of cad, and ip on System Parameters. Families of curves analogous to those of Figures 1and 2 were measured at different reactant concentrations, Ti02 concentrations, and pH values. Figure 4 shows the influence of MV2+concentration on the results obtained at three different Ti02 concentrations. The relationshipsbetween the inverses of adsorbed ( C a b ) and bulk ( c ) concentrations are linear, as predicted by a Langmuir adsorption isotherm, the simplest form of which can be written as
Values of k A and c: for different systems are collected in Table 11. Since eq 6 presupposes the absence of coadsorbants, k A is just an apparent adsorption coefficient which does not reflect a unique adsorption-desorption equilibrium. It can be seen from Figure 4 and Table I1 that k A depends on the concentration of TiO2, and on pH. On the other hand, the value of c z , the concentration of adsorbed (26)Gritzel, M., Frank,A. J. Phys. Chem. 1982,86, 2964. (27)Rothenberger, G.; Moeer, J.; Gritzel, M.; Serpone,N.; Sharma, D. K.J. Am. Chem. SOC.1985,107,8054. (28)Arbour, C.; Sharma, D. K.; Langford, C. H. J.Phys. Cheh. 1990, 94,331. (29)Carmichael, I.; Hug, G. L. J. Phys. Chem. 1988, 31, 4036. (30)Hug, G. L.;Carmichael, I. J. Photochem. 1986,31, 179.
1094 Langmuir, Vol. 7, No. 6,1991
Grabner and Quint
0 0
~ ~ 1 0 4
4 x 1 0 4 l/[MVZ'I
Table 11. Results of Analysis of Data by Equation 6 for Different Systems and Conditions amt of
reactant MV2+ MV2+ MV2+ MV2+ I-
pH
TiO2, g/L
10 10 10 11 1
0.27 0.4 0.8 0.8 1.6
c z , mol/g
of Ti02 5.78 X 10-6 5.68 X lo4 5.56 X lo4 5.88 X 10" 2.6 X lod
kA, M-' 2.42 X 10' 2.02 X 10' 1.23 X 10' 1.79 X 10' 30.9
species corresponding to maximum possible coverage, is independent of these parameters. While k A is much higher for MV2+than for I-, the reverse holds for cZ. Another relation of interest is that between quantum yield, @, and adsorbed concentration, c h , as obtained from fits according to eq 5. Figure 5 shows the dependence of l/@ on 1 / C a b for the system Ti02/MV2+,the data having been taken at various bulk MV2+ concentrations, Ti02 concentrations, and pH values. It is apparent that a linear relationship is obtained that reveals little, if any, influence of these parameters. Formally, this relation is described by @=
k3cnh
+
4 r lo5
(IIMoll
Figure 4. Inverse of adsorbed concentration, obtained from fit according to eq 5, vs inverse of bulk concentration in the system Ti02/MV*: at pH 10 (A) 0.8 g/L TiO2; (B) 0.4 g/L TiO2; (C) 0.27 g/L T102.
(7) k3cab k' k3 being the rate constant for MV'+ formation (reaction 3) and k' a rate constant for a first- or pseudo-first-order reaction of e-cb. An entirely analogous result is obtained for the system TiOZ/I-; again, linearity between l/@ and l/c,h prevails for all systems irrespective of bulk I- concentration, Ti02 Concentration, and pH. The regression line obtained from the data in Figure 5 from eq 7 allows estimation of the value of the quantum yield corresponding to the maximum adsorbed concen= 0.32 cortration as determined from eq 6. This is amax respondingtocrr= 5.7 X 10~mol/gofTiO~forthesystem Ti02/MV2+, and = 0.33 corresponding to c z = 2.6 X mol/g of Ti02 for the system Ti02/1-. The influence of pH on @ and C a b for the system Ti02 (1.6 g/L)/I- (0.1 M) is shown in Table 111. Both parameters are seen to decrease with increasing PH. Applicationof the Nosaka and Fox Model? We now turn to the alternative treatment of pulse-energy-dependent data, based on competition between charge transfer at the interface and second-order electron-hole recombination. Assuming a steady-state of e,b and h+,b during irradiation, these authors have derived a relation between
lo51/[MV2'l,d,(g
TiOzlMol)
Figure 5. Inverse of quantum yield w inverse of adsorbed concentration, as obtained from fib according to eq 5, for the system TiOz/MV2+: ( 0 )0.27 g/L TiOz, pH 10; (A)0.4 g/L TiOa pH 10;(0)0.8 g/L TiO2, pH 10; (A)0.8 g/L TiO2, pH 9,9.5,10.5, 11, 11.5. Table 111. Dependence of Results of Fits According to Equation 5 on pH for the System 0.1 M I- in 1.6 g/L Ti02 DH c d . mol/a of Ti09 @ 1 2.0x 106 0.204
1.78 X lo6 1.44x 106 1.43 x 10-5 0.9 x 106
1.5 2 2.5 3
0.174 0.176 0.133 0.132
quantum yield and laser pulse energy
where j3=-
k3k4 At k2
At is the pulse duration, P the pulse energy, and f a factor relating pulse energy and concentration of photons absorbed in the reaction volume. If we take the system TiO2/ MV2+as an example, 123 will be the rate constant for e-cb transfer to MV2+and kr for h+,b transfer to any donor at the surface; k2 is the rate constant for electron-hole recombination. Relation 8 is equivalent to
= (82 + 2/3fP)"2 - j3 (10) which describes dependence of transient concentration on pulse energy in the framework of this model. It turns out that fits of individual data sets such as those shown in Figures 1and 2 are equally well possible by eqs 5 and 10. This happens because distinction between exponential and square-root functions is not possible with confidence within the error limits imposed by the data. In Figure 6, we have collected results of the treatment of the data in the system Ti02/MV2+ according to eqs 8-10. The linear dependence of the quantity (1 - @)/@onthe concentration of absorbed photons shows success of the fit by eq 10. The slope of the regression line being just the kinetic parameter j3 defined in eq 9, it turns out that j3 depends on Ti02 concentration. The insert in Figure 6 shows that a linear relation is obtained between /3 and bulk MV2+concentration. Since k2 must be independent of the concentrations of Ti02 and MV2+,dependence of the charge-transfer rate constants k3 or k4 on these parameters has to be assumed. Proportionality between j3 and bulk MV2+concentration could then signify that k3 is a pseudo-first-order rate constant for reaction between CT
Charge Transfer Reactions in Ti02 Colloids I
10-5
2 1 ~ 5
3x1F5
.
[Photon) IM)
Figure 6. Treatment of data in the system TiOz/MV2+ at pH 10 according to eqs 8-10: large figure, application of eq 8 for ( 0 ) 2 X lo-' M MV2++ 0.8 g/L TiO2, ( 0 )2 X 1 W M MV2++ 0.4 g/L TiO2; insert, dependence of parameter fi (defined in eq 9) on bulk MV2+concentration for 0.8 g/L TiO2.
e-cb and bulk MV2+, without need of assuming MV2+ adsorption, or, if this assumption is not to be dropped (as we shall discuss shortly), that the data reflect the linear region of an adsorption isotherm. This, however, would mean that coverageof particles with MV2+must necessarily be low, which leads us back to the hypothesis of depletion of adsorbed species which is the basis of the model introduced in this work.
Discussion The Case for Reactant Adsorption. Two alternative models have been used to interprete the nonlinear dependence of pulsed-laser-induced transient formation on photon fluence. Treatment of experimental data obtained at various concentrations of reactant and semiconductor show that an internally consistent model can be built by assuming that nonlinearity is due to laserinduced depletion of surface-adsorbed reactants. In contrast, the alternative model proposed by Nosaka and Fox? although equally well able to interprete individual data sets, appears less consistent when adsorption of reactants is assumed, since it then also leads to the conclusion that their depletion should be taken into account. Is there any additional evidencefor reactant adsorption? Prompt formation of transient within the time course of exciting pulses is frequently taken as an indication in this direction. This argument is not, however, necessarily conclusive since estimation of diffusion-controlled rate constants for reaction of molecules or ions with colloidal particles using the Stokes-Einstein relation yields quite high values (>loll M-l s-l), owing to the large hydrodynamic radii of the particles.5 Diffusion effects would then possibly show up at very low reactant concentrations only if attainable time resolution is of the order of about 100 ns. To check this point, we have looked at a possible absorption increase in a M MV2+solution with 0.8 g/L Ti02 at pH 10. No such effect could be seen although a build-up with a half-time of 0.7 ps would be expected if a rate constant of 1011 M-1 s-l is assumed. It therefore seems unlikely that diffusion of MV2+from the bulk plays a role in the unprotected colloids used in this work. The signal increases observed in other studies of TiOz/MV2+ s y s t e m ~ may ~ ~ ~beJrelated ~ to the fact that protected sols with concomitant alteration of conditions for carrier trapping and adsorption were used. Considering prompt formation of MV'+ and indirect it seems that the evidence from other st~dies,*J~J"'~
Langmuir, Vol. 7, No. 6, 1991 1095 assumption of reactant adsorption cannot be abandoned. The present study then shows that depletion of adsorbed reactants is an important factor influencing yields at high photon fluences. It is not possible, at present, to assert that the model based on depletion can give a complete picture of the photon fluence dependence; it could be that second-order electron-hole recombination contributes to some degree to the observed behavior. In view of the consistency of the depletion model, we feel that it nevertheless merits some further discussion. Two groups of results emerge from the analysis of data by the depletion model: adsorption properties of reactants on the one hand, and factors influencing quantum yields on the other. Adsorption Properties of Reactants. The concentrations of adsorbed species obtained from the simulations all conform to a Langmuir-type behavior (Figure 4). It should be noted here that a similar treatment of quantum yields as a function of bulk concentrations can be misleading unless they have been determined in the low pulse energy region where transient absorption is still linear. This was shown to hold, e.g., for formation of (SCN)z'- in Ti02 colloids in acetonitrile* but is doubtful in aqueous systems.4J2 The regression lines obtained from the Langmuir analysis for the Ti02/MV2+ data at various Ti02 concentrations and pH values (Figure 4 and Table 11) all converge to the same y-axis intercept, indicating that a value of maximum possible coverage with MV2+,independent of these parameters, can be determined. The resulting value of 5.7 X lo+ mol of MV2+/g of Ti02 is much smaller than values previously obtained3' by a centrifugation method, which may be due to the fact that in the latter case ions in outer adsorption layers are also detected, which do not take part in the charge-transfer process. It is difficult to estimate the space required for a MV2+ion adsorbed on the particle surface; taking 0.4 nm as rough value for the radius and assuming again a particle radius of 20 nm, the coverage is estimated to be only about 5%. A comparable result (about 6%) is obtained for I- with an ion radius of 0.215 nm, but as stated above, the actual value should certainly be higher. Nevertheless, the resulting values of maiimum coverage are certainly well below 100% and indicate that adsorption is possible only at certain sites, the greater part of the surface being either occupied by other adsorbates or physically unsuited for adsorption. The apparent adsorption coefficients for MV2+, IZA, obtained from the Langmuir treatment depend on Ti02 concentration as well as on pH. We have already noted that this result is not unexpected since coadsorbanta will influence the adsorption behavior. Interestingly, k~ actually increases with decreasing Ti02 concentration. A possible rationalization of this behavior is to assume competition of MV2+ with another reactant, present in concentration c' in the bulk and with adsorption coefficientk~',for the available adsorption sites. Equation 6 then has to be modified to
The observed behavior indicates that the concentration of this coadsorbant increases with increasing Ti02 concentration. This possibility,along with the small coverage values obtained, may reflect the fact that the semicon(31)Chandraaekaran, K.;Thomas, J.K. J. Chem.Soc.,FaradayTrans. 1 1984,80, 1163.
1096 Langmuir, Vol. 7, No. 6,1991
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ductor colloids, if chemically prepared as is generally the nection, that the maximally obtainable quantum yields in case, carry chemisorbed species that reduce accessibility the present study were considerably below unity. of the surface for reactants added to the solutions. With regard to the third possibility, it has been shown by Rothenberger et al.27that if the average number of Changing the pH influences the surfacic charge of the ecb-h+,b pairs per particle is low, their recombination will particles; this is reflected in the pH dependence of adbe governed by a kinetic law that is formally of first order sorbed concentrations and adsorption coefficients (Tables and independent of intensity. In our conditions, a pulse I1and 111),in agreement with earlier studies on adsorption of 1mJ at 355 nm will produce about lo3carrier pairs per of organic acidss2and inorganic anions33on hydrous oxide particle of 20-nm radius within 10 ns. It can be inferred surfaces. The increase of the 12'- quantum yield with that transit times to reactants do not exceed 10 ps;s decreasing pH (Table 111)closely follows the concomitant therefore, on average only one pair will be present at any increase of cab, in agreement with eq 7. time, largely fulfilling the condition for intensityA further interesting point is that of the fate of the independent recombination. Second-order recombination radicals after reaction. Kamat8 has argued that the then requires a considerably higher photon flux, as reaction (SCN)' + (SCN)- occurs on the Ti02 particle available in picosecond e ~ p e r i m e n t s . ~ ~ ~ ~ ~ surface in acetonitrile because of lack of the predicted We thus reach the conclusion that if carrier recombisignal growth after the pulse. In the present work, the nation is to playa role in the conditions of 10-nsexcitation, expected increase in 12'- absorbance should have a halfit must be a very fast process competing with transfer to time of less than 20 ns at the lowest I- concentrations that reaction centers. This is consistent with the fact that we can be used, an effect which is not detectable in our case. failed to detect the absorption of any trapped species in On the other hand, transient Raman spectra of MV'+ and Ti02 colloidswithout added reactants at pulse energies of (SCN)2*-in aqueous Ti02 sols suggest that these radical about 1 mJ. This observation supports the conclusion ions are fully solvated by H2O 5 ns after the end of the that the particle surface carries in any case enough species pump pulse.6 to remove all photogenerated carriers which escape pairFurther reaction of the radicals is markedly influenced wise recombination. It should also be noted in this context by the vicinity of the colloidalparticle. The formal secondthat the absorption of the OH radical adduct to MV2+ order rate constants found in the present work for initial (A= 470 nm, €470 = 22 000 M-' cm-l, pK = 9.724)in a decay of X2'- exceed tabulated diffusion-controlled rate M solution of Ti02 (0.8 g/L, pH 9) containing 5 X constants for bimolecular reactionM by up to 1 order of MV2+was not measurable at 1.8 mJ/pulse. This is believed magnitude. This result may be caused by an ionic strength to be due to the presence of OH scavengers, such as adeffect on the reaction. Furthermore, at least part of the sorbed 2-propanol, on the particle surface. On the other radical anions can react upon encounter with suitable hand, formation of MV2+ oxidation products has been reducing sites of the particle, e.g., e-cb trapped at Ti4+ observed in continuously irradiated Ti02 sols and attribsites or radicals produced by e-cb transfer, affording a uted to OH attack.37 The reasons for this apparent disrecombination pathway on a time scale longer than the crepancy are not clear at present; a possibly important laser pulse. Such slower recombination steps provide a factor could be that continuous irradiation affords time possible explanation for the fact that I-oxidation quantum yields obtained in steady-state i r r a d i a t i o n ~ ' ~ . ~are ~ 3 6 ~ ~ for phototransformation and subsequent desorption of adsorbed scavengers. Further work is needed to resolve this considerably lower than 12'- yields measured in experiproblem. ments with pulsed lasers. Factors Influencing Quantum Yields. The depenConclusions dence of 3 on cade shown in Figure 5 indicates that, for a We have shown that the results of laser-photon-fluencegiven system of colloid and reactant, the quantum yield dependent measurements of transient formation in nonis governed by a competition between the reaction under protected aqueous Ti02 colloids containing MV2+or Xstudy and another first-order, or pseudo-first-order, recan be consistently interpreted in the framework of a model action of the same charge carrier. For this competing based on adsorption of reactants on the surface of the reaction, three possibilities can be envisaged: carrier colloidal particles and depletion of adsorbed species a t trapping at sites from which fast transfer to reactants is high photon fluences. While the ability of this model to no longer possible; reaction with suitable coadsorbants; provide a complete picture must be assessed by future pairwise recombination of eb, and h+,bat low pair densities experiments, most of its results point to the importance per particle. of adsorption processes for understanding photoinduced The first two of these possibilities are largely equivalent, processes in these systems. the main difference being that it may be possible to influence quantum yields by changing the distribution of Acknowledgment. This work was supported by the adsorbed species. It is interesting to note, in this conJubilaumsfonds der dsterreichischen Nationalbank and by the Fonds zur Forderung der wissenschaftlichen For(32)Kummert, R.; Stu", W. J. Colloid Interface Sci. 1980, 75,373. schung. (33) sigg, L.; Stu", W. Colloids Surf.1981, 2, 101. Registry No. MV2+, 1910-42-5; KI, 7681-11-0;KBr, 7758(34) Neta, P.;Huie,R.E.; Roes, A. B.J.Phys. Chem. Ref. Data 1988, 17. 1027.
- . I
(35)Reichman, B.; Byvik, C. E.J. Phys. Chem. 1981,85, 2255. (36)Harvey, P. R.; Rudham, R. J.Chem. Soc., Faraday Trans. 1988,
84, 4181.
02-3;KCl, 7441-40-7; TiO2, 13463-67-7.
(37)Bahnemann, D. W.; Fischet, C.-H.; Janata,E.;Henglein, A. J. Chem. SOC.,Faraday Trans. 1 1987,83, 2559.
