J. Phys. Chem. 1988, 92, 6009-6016 Dirac distribution is only one out of various choices arbitrarily made in spin cluster models. We can also cite the log normal distribution2’ and the Poisson distribution.22 None of them, however, gives a reasonable description of the particle size heterogeneity illustrated in Figure 6. In this work, we have shown that the granulometry can be successfully derived from the full study of the magnetic properties, beyond the superparamagnetism approximation. Moreover, the field-cooled method developed here has a great advantage with respect to the usual zero field cooled methods used in prior works; since each particle has its own magnetic easy axes which randomly distribute in space, the remanent magnetization is M R = ‘ l 2 M Oat T = 0, and the factor will change with T i n a complex manner in zero field cooled experiments. This factor should be taken into consideration in the calculation. To the contrary, in field-cooled experiments, this factor is equal to 1 , since the particle moments are blocked along the magnetic field (see eq 8). We thus conclude that our model is an improvement with respect to the previous magnetic methods which already led to results in semiquantitative agreement with those of the TEM granulometry in systems like Ni/Si02 where both magnetic and TEM measurements could be performed.23 Note, however, that the size distribution deduced from TEM experiments is semiquantitative in essence, because the results are deduced from a sampling of a finite number (typically 2000) (21) Xiao, Gang; Chien, C. L. J . Appl. Phys. 1987,61,3308. (22) Khater, A,; Ferre, J.; Meyer, P. J . Phys. C. Solid State Phys. 1987, 20, 1857. (23) Renouprez, A. J. In Catulyse pur les mCtaux; Imelik, B., Martin, G. A., Renouprez, A. J., Eds.; Editions du Centre National de la Recherche Scientifique: Paris, 1984; p 163.
6009
particles, which limits the statistical accuracy.23 The analysis of magnetic properties at a given observation time to also allowed us to determine the strong magnetic anisotropy of the Ni particles. A strong anisotropy has also been evidenced for Ni/Si02 from the analysis of the ac zero field cooled susceptibility x’”(7‘)at frequency v, as a function of to = u-’.I2 Two approximations, however, have been made in ref 12, which we have not made in our analysis. First, Gittleman et al. considered the blocking of the Ni particles takes place at Tfinstead of Tb (in ac experiments Tb corresponds to the onset of a finite imaginary part of the susceptibility x”,( T)). For our samples, we have shown that the difference between Tfand Tb is already large at the long observation time to IO3 s used in the experiments. Moreover, this difference is expected to be an increasing function of v.24 Second, the temperature dependence of the anisotropy factor has been omitted in ref 12. FMR experiments have also been used to determine the magnetic a n i ~ o t r o p ybut , ~ only in superparamagnetic materials, where the thermal average of the anisotropy field ( H a )is small. In presence of blocked Ni particles, however, the thermal fluctuations are too small to average the internal anisotropy. In this case, the F M R is smeared out by a broad distribution of anisotropy fields ( H a ) . The very large anisotropy in these compounds gives evidence of a strong interaction with the support. Magnetic susceptibility and remanent magnetization prove to be the most powerful tool to determine anisotropy in this case.
-
Registry No. Ni, 7440-02-0; C e 0 2 , 1306-38-3. ~~~~
~~
(24) Ayadi, M.; Ferre, J.; Mauger, A,; Triboulet, R. Phys. Reu. Lett. 1986, 57, 1165.
Mechanistic Aspects of the Photooxidation of Water at the n-TiO,/Aqueous Interface: Optically Induced Transients as a Kinetic Probe Alexandra P. Norton, Steven L. Bernasek,* and Andrew B. Bocarsly* Department of Chemistry, Frick Laboratory, Princeton University, Princeton, New Jersey 08544 (Received: October 6, 1987; In Final Form: January 29, 1988)
The method of optically induced photocurrent transients is a powerful tool for probing the mechanisms of photoinduced charge transfer at the semiconductor/electrolyte interface. Using this technique on the Ti02/aqueous interface, we conclude that water oxidation occurs via an outer-sphere process for electrolyte pH 16 This analytical technique involves an essentially instantaneous perturbation of the semiconductor/electrolyte interface by a pulse of photons having energy equal to or greater than the semiconductor bandgap energy and the corresponding observable relaxation of that interface back to the dark condition. The first substantial efforts in this field were conducted by Perone and Richardson using Ti02and CdS electrode^.^^ In these *Authors to whom correspondence should be addressed.
0022-3654/88/2092-6009$01.50/0
studies, the technique was termed a “coulostatic flash” technique” and the resulting transient, a “photopotential” transient. Although ( I ) Fujishima, A,; Honda, K. Nature (London) 1972,238, 37. (2) Ohnishi, T.; Nakato, Y.; Tsubomura, H. Eer. Bunsen-Ges. Phys. Chem. b75, 79,523. (3) Nozik, A. J. Nuture (London) 1975,257, 383. (4) Desplat, J. L. J. Appl. Phys. 1976,47, 5102. (5) Richardson, J. H.; Deutscher, S. B.; Maddix, A. S.; Harrer, J. E.; Schelizinger, D. C.; Perone, S. P. J . Electroanal. Chem. 1980,109,95. (6) Perone, S. P.;Richardson, J. H.; Deutsche, S. B.; Rosenthal, J.; Ziemer, J. N.J . Electrochem. SOC.1980,127,2580. (7) Perone, S. P.; Richardson, J. H.; Deutscher, S. B. J . Phys. Chem. 1981, 85,341. ( 8 ) (a) Gottesfeld, S.; Feldberg, S. W. J . Electroanal. Chem. 1983,146, 47. (b) Feldberg, S. W. J. Phys. Chem. 1970,74,87. (9) Harizon, Z.;Croitoru, N . ; Gottesfeld, S. J . Electrochem. SOC.1981, 128. 551. (IO) Wilson, R. H.; Sakata, T.; Kawai, T.; Hashimoto, K. J. Electrochem. SOC.1985,132,1082. ( 1 1 ) Kawai, T.; Tributsch, H.; Sakata, T. Chem. Phys. Lett. 1980,69,336. ~~~
0 1988 American Chemical Society
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The Journal of Physical Chemistry, Vol. 92, No. 21, 1988
the technology developed provides a powerful mechanistic tool, it has previously been shown by Feldberg* that on theoretical grounds photopotential transients cannot provide information on net electron transfer to solution. Conversely, transient investigations on a series of selenide based semiconductor^^-'^ and on Ti02,i3,14 SnO2,ISand p-InPI6 indicate the utility of the photocurrent response as a kinetic probe. Consequently, we have chosen to configure our experiments to detect the transient photocurrent response of the system of interest. Prior to the studies of Perone and Richardson, capacitance and continuous illumination current-voltage investigations indicated that the redox potential associated with the OH-/02 redox couple lies substantially above the Ti02valence band. This relationship is expected to lead to poor overlap between the donor states of the OH- species and the TiOz valence band edge, producing slow interfacial charge-transfer rates. However, under continuous illumination the current has been found to be high and the interfacial charge-transfer efficiency approximately To explain this behavior, the existence of sub-bandgap surface states has been p r o p o ~ e d . ’ ~These - ~ ~ surface states, isoenergetic with the OH-/02 redox couple, would enhance the interfacial transfer efficiency for holes by mediating charge. Nakato has presented photoluminescence data in support of such statesz5 NishidaI9 and Salvador20have proposed a model where all holes reaching the semiconductor surface are captured by intra-bandgap surface states. These holes then react with solution hydroxide to form oxygen according to the equation 20H-
+ 2hf
-
y20z+ H 2 0
(1)
A large body of indirect evidence also exists which suggests water oxidation occurs via a peroxide intermediate. Bard, using a spin-trapping technique, has seen OH’ radicals photoanodically produced during illumination of Ti02 particles in aqueous solution.26 Salvador, in a number of studies, goes even further by saying that these OH’ radicals play a double role.20 He suggests that the radicals act firstly as an interfacial species active in hole transfer and secondly as the species active in the generation of H202,a possible intermediate in O2 evolution. Further support for this type of model comes from a gas chromatographic study by T ~ k u m a r of u ~irradiated ~ TiQ2 powder in an aqueous benzene solution. In this study, they conclude that water is oxidized to OH’ radicals from holes with the concurrent removal of conduction band electrons by adsorbed oxygen. However, no direct.evidence has been obtained to directly link OH’ formation with O2 production.
(12) Prybyla, S.; Struve, W. S.; Parkinson, B. A. J . Electrochem. SOC. 1984, 131, 1587. (1 3) Hartig, K. J.; Grabner, G.; Getoff, N.; Popikirov, G.; Kanev, S. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 831. (14) Kamat, P. V.; Fox, M. A. J . Phys. Chem. 1983, 87, 59. (15) Frip piat, A,; Kirsh De Mesmacker, A,; Nasielski, J. J . Electrochem. SOC.1983, 130, 239. (16) (a) Cook, R. L.; Dempsey, P. F.; Sammells, A. F. J . Electrochem. SOC.1986, 133, 1821. (b) Cook, R. L.; Dempsey, P. F.; Sammells, A. F. Ibid. 1986, 133, 2287. (17) Van Leeuwen, H. P. Electrochim. Acta 1978, 23, 207. (18) Mavroides, J. G.; Kolesen, D. F. J . Vue. Sci. Technol. 1978, 15, 538. (19) Nishida, M. Nature (London) 1979, 277, 102. (20) (a) Gutierrez, C.; Salvader, P. J . Electrochem. SOC.1986, 133, 924. (b) Salvader, P. J . Phys. Chem. 1985, 89.. 3863. (c) Salvader, P. J . Electrochem. Soc. 1981, 128, 1895. (d) Salvader, P.; Gutierrez, C. J. Phys. Chem. 1984, 88, 3696. (21) Ginley, D. S.; Knotek, M. L. J . Electrochem. SOC.1979, 126, 2163. (22) Siripala, W.; Tomkiewicz, M. Phys. Reu. Lett. 1983, 50, 443. (23) Frank, S. N.; Bard, A. J. J . Am. Chem. SOC.1975, 97, 7421. (24) Noufi, R.; Kohl, S.; Frank, S. N.; Bard, A. J. J . Electrochem. SOC. 1978, 125, 246. (25) Nakata, Y.; Tsumura, A,; Tsubomura, H. J . Phys. Chem. 1983,87, 2402. (26) Jaeger, C. D.; Bard, A. J. J . Phys. Chem. 1979, 83, 3146. (27) Shimamura, Y.; Misante, H.; Oguchi, T.; Kanno, T.; Sakuragi, H.; Tokumaru, K. Chem. Lett. 1983, 1691.
Norton et al. e+
10,
P”Ol0lnode
Co~nl~~.le:lrobr
Figure 1. Schematic representation of the illuminated, transient photoelectrochemical cell, showing the processes occurring a t the working (n-Ti02) and counter electrodes. 0, 0’, R, and R’ represent solution oxidizable and reducible species, respectively. The inset shows the actual cell design.
The approach employed herein is to analyze laser-induced transients as a function of electrolyte composition. In doing so, one can probe the rate-limiting processes associated with the oxidation of H 2 0 , along with certain primary photoinduced reactions occurring at the illuminated n-Ti02/aqueous interface.
Experimental Section Materials. Single crystals of (001) T i 0 2 were reduced in a Lindberg furnace at 800 O C under 1 atm of hydrogen for 2 h to yield an n-type material which had a doping level of 1 X cm-3 as determined by Mott-Schottky plots at 1 kHz. Prior to utilization as an electrode, the T i 0 2 crystal was polished with alumina (Fisher, 0.5 pm). Ohmic contact was made by rubbing the back side of the crystal with an In/Ga eutectic and connecting a wire with conducting Ag epoxy (Epo-tek H31). Insulating epoxy was then used to mount the crystal onto a glass tubing support with care being taken to expose only the flat crystal surface. The exposed area of a typical T i 0 2 electrode was -0.2 cm2. The integrity of the electrode was periodically monitored by taking light and dark current-voltage curves. All electrolyte solutions were buffered and had an ionic strength of 1.28 The ionic strength was kept high to assure that the solution resistance, Rroin,was relatively low. D 2 0 (MSD Isotope, 99.8% D), D2S04(Aldrich, 99.5% D), methanol (Baker, “photorex”), and acetonitrile (Baker, “photorex”) were used without further purification. All solutions used in the isotope experiments were kept under a purge of dry N2 or Ar. To avoid the presence of concentration gradients in the electrochemical cell, each solution was stirred for at least 1 min before the run. There was no measurable difference in the lifetime of the photocurrent transient whether the solution was stirred or not. However, each photocurrent transient was taken under quiescent conditions as the signal-to-noise was better under those conditions. Instrumentation. The electrochemical cell used has a threeelectrode configuration: a SCE capacitatively coupled to a Pt mesh reference electrode (0.47 pF) and a TiOz working electrode. This cell is as described by Perone and R i c h a r d s ~ n ~with ~ ’ ~the ~ ~exception that the single-crystal working electrode is coaxially surrounded by a Pt mesh electrode, which contains a hole to allow
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(28) Handbook of Chemistry and Physics, 88th ed.; Weast, R. C. Ed.; CRC Press: Boca Raton, FL, 1978. (29) Perone, S. P.; Richardson, J. H.; Deutcher, S. B.; RosenthaI, J.; Zeimer. J. N. Faraday Discuss. Chem. SOC.1980, 70, 3 5 .
Photooxidation of H 2 0 at the n-Ti02/Aqueous Interface
The Journal of Physical Chemistry, Vol. 92, No. 21, 1988 6011 on the band bending required. A laser repetition rate of 20 Hz was employed to allow the working electrode to reach a steady state before the next laser pulse.
Analytical Considerations One must consider a convolution of the intrinsic response time of the semiconductor/electrolyte interface (the quantity of interest) and the R C time constant of the combined cell and external components. This analysis can, in part, be carried out by a consideration of equivalent electrical circuits. To this end, three configurations of the reference electrode have been considered as shown in Figure 3: Case A represents the actual experimental design employed, while cases B and C represent alternatives useful in identifying the responses of the reference electrode on the overall cell output. If one uses typical values30 for Rsoln(10 a),c d , (20 pF/cm*), CSCE(0.5 pF/cm2), and Cworhg electrode (5 pF/cm2), one obtains a R C time constant of 1200 ps for case B and a time constant of -300 ps for cases A and C. Qualitatively, this is what is observed; the lifetimes with the external capacitor in the circuit are shorter than the lifetime observed without the 0.47-pF capacitor. It is also observed that the addition of the SCE increases the current. This is due to the presence of the Hg/Hg?+ half-cell in the SCE which provides a faradaic path having a small RCT value at the counter electrode. As the concentration of Hgo and Hg+ are both large, it is not possible for the SCE to be a current limiter in the cell or for the transient to significantly alter the SCE redox potential. Even in the case where the capacitively coupled electrode is employed, the calculated R C time constant is comparable to the expected response time of the semiconductor/electrolyte interface. Thus, useful chemical data cannot be obtained without employing a deconvolution process. These findings are consistent with the results obtained by Wilson for the transient response of a cadmium chalconide based systern.'O Deconvolution of an unknown transient requires a data analysis method which does not require any assumption of the form of the experimental data since the transient may utilize a t-'/* dependence due to diffusion of the oxidized species from the interface, an exponential dependence due to neutralization of charge on the electrode, and/or a t2/3 dependence due to redistribution of ions in the double layer, in combination with an exponential decay due to interfacial charge transfer. Thus, to obtain a more detailed understanding of the charge-transfer kinetics occurring at the Ti02/H,0 interface, a nonlinear least-squares analysis was used to deconvolute the photocurrent transient^.^^ A typical optically induced transient in a pH 14 electrolyte is shown in Figure 4 where one sees the rise time of the signal, 5 ns, limited to the rise time of the laser pulse. Similar results have been reported by Perone.lza The decay, on the other hand, lasts over 100 ps and is not limited to the decay of the laser pulse. A least-squares curve analysis shows the decay not to fit any single functional (exponential, linear, power series, logarithmic) form. Instead, the best fit of the curve is one which consists of two exponentials. A fit of three exponentials or a combination of any of the above mathematical functions did not provide a better fit. Thus, deconvolution is carried out in terms of a two-exponential function. The first exponential, ranging from 1 to 10 ps, is found to depend on the electrolyte composition and to be independent of the external R and C values employed. The second depends on the load resistor and capacitor used as shown in Figure 5 and is chemistry-independent. Having associated the lifetime of the first expotential, T , with an electrochemically interesting process, it can now be considered to be the product of two terms: an interfacial charge-transfer resistance, RCT, and the combined serial capacity of the double layer and the space charge layer, CT (l/CT = l/Csc 1/cdl). As described in the following section, one of our key findings is
-
CELL SET-UP A N D PULSE SEOUENCE
p 0'IE NT 145T AT
n
LASER
Figure 2. General experimental apparatus and pulse sequence for potential-controlled (four-electrode)experiments.
light to directly strike the Ti02. This cell design, which is similar to that employed by Parkinson,12was found to minimize circuit noise. The electrodes were mounted on a Telfon cell mount and terminated with 5 0 4 load. This configuration was then put in a Pyrex cell containing a quartz window which was aligned with the working electrode. A schematic representation of the electrochemical cell can be seen in Figure 1. The instrumentation used in the photocurrent studies is shown schematically in Figure 2. As the bandgap of T i 0 2 is 3 eV, corresponding to a wavelength of 412 nm, the excitation source used was a 337.1-nm laser pulse from a pulsed Molectron UV400 or from a PRA LN103 N2laser. Power readings were taken with a Molectron 53 joulemeter. Photocurrents were measured by employing a 250-MHz 7704A Tektronix scope with a 7126 dual trace amplifier to obtain the voltage drop across the 5 0 4 termination of the cell. Traces were recorded either photographically or by using a scanning boxcar integrator. A Data General Nova 3 computer controlled the boxcar integrator. It also externally triggered the laser, controlled the timing of the delay generator, and signal-averaged the transients. For further data manipulation, the data were transferred to VAX 11/780 computer. A Princeton Applied Research Corp. (PAR) Model 174A potentiostat was used for dark current-voltage scans. It was also used in conjunction with a PAR 5208 lock-in analyzer for Mott-Schottky plots. Certain experiments were conducted under potentiostatic control. The same configuration as above was used with a Pt counter electrode and a SCE reference electrode added. To avoid the effect of the electronics of the potentiostat on the photocurrent decay, a fast switching device (Intersil 5143 analog switch) was employed to disconnect the potentiostat during the experiments. (See Figure 2 for pulse sequence and experimental setup.) To allow for all switchi'ng transient decays, the laser was not triggered until the potentiostat had been switched off for 10 ps. During this time lag, control experiments indicated that the initial potential had only decayed 20-30 mV. Due to the high conductivity of the solutions used, restablishment of the initial potential after the potentiostat was switched on required 100-300 ps, depending
-
+
(30) The following terms are defined: R,,, solution resistance, C, double-layer capacitance, Cwsrhng = working electrode capacitance, and CScE3 capacitance of the SCE reference half-cell. (31) Ware, W. R.; Doemeny, L. J.; Nemzek, T. L. J . Phys. Chem. 1973, 77, 2038.
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The Journal of Physical Chemistry, Vol. 92, No. 21, 1988
Norton et al.
c.w A: ( W . 4 7 @=E)
A SCOPE
Figure 3. Circuit analogs representing the transient photoelectrochemical cell and associated external components. Case A: The actual cell employed, containing a capacitively coupled Pt/SCE counter electrode as shown in Figure 1. Case B: Cell with a single platinum counter electrode. Case C: Capacitive coupling between a single platinum counter electrode and the external measuring components. laser pulse w i d t h
c. C
E L
a 0
0 0
c
r
n
LA
16 80 0
10i20 30
time (ns)
R E S I S T A N C E (ohms)
B
E
0
40
time
-
200,----
80 120
(PSI
Figure 4. Typical photoelectrochemical cell current response to a 10-ns N2 laser pulse. Part A indicates the short time response of the cell
superimposed on the optical output of the laser. The ringing in this curve is due to an impedance mismatch in the cable connecting the cell and oscilloscope. Part B indicates the long time response, showing the photocurrent decay. that T depends strongly on the solution pH. To explore the possibility that variations in pH simply affect C,, capacity data under dark conditions were obtained as a function of pH by using standard phase sensitive ac techniques. System capacity was examined at 1 V of band bending since this degree of band bending was felt to best approximate the maximum band bending under transient conditions. Mott-Schottky analysis of the differential capacitance as a function of potential was employed to determine the degree of band bending. For the pH range tested, 2-14, CT was found to be invariant, ruling out CTas the principal source of variations in 7. Further support for this conclusion comes from Tomkiewicz, who conducted a relaxation spectrum analysis of the TiO,/aqueous interface as a function of Results and Discussion Initial Characterization. Initial studies were aimed at characterizing the effect of changes in transient response with variations in the standard, controllable, interface parameters (Le., electrolyte (32) Tomkiewicz, M. J . Electrochem. Soc. 1979,126, 2220
CAPACITANCE (microfarad)
Figure 5. Response of cell lifetimes
(7,) as obtained by a nonlinear least-squares regression, to variations in the value of external resistive ( R ) and capacitive (C) components. associated with the short time exponetial is found to be independent of the external measuring circuit, while r2, the long time exponential, is a circuit artifact.
pH, semiconductor band bending, incident light intensity, incident wavelength). Previously, Richardson and Perone reported that As the n-Ti02/aqueous transient response was ~H-independent.~~ shown in Figure 6a for small values of the band bending we also see little variation in the magnitude of the peak current (as well as T) with pH. However, if the band bending is increased above -200 mV, a pH dependence is observed. At a band bending potential of 1 V, where the photocurrent transient is similar to that observed under nonpotentiostated conditions, the pH dispersion is a major effect. Similarly, the electrolyte pH (under nonpotentiostated conditions) has a major effect on the maximum photocurrent vs light intensity response (Figure 6b). One sees that the photocurrent magnitude saturates earlier at lower pHs. At pH 14, no saturation was observed even at fluxes sufficient to melt the surface. (The TiO, melting point is 1850 OC. Obvious melting of the surface can be seen by eye and by using a 40X optical microscope.) Figure 7 shows plots of lifetime vs laser power at pH 13. All values plotted in Figure 7 are below the melt threshold. One observes that the lifetime decreases with increasing power. Since power is proportional to the initial valence band hole population, this
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Photooxidation of HzO at the n-Ti02/Aqueous Interface
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The Journal of Physical Chemistry, Vol. 92, No. 21, 1988 6013
d
!
.'2
.1
.4
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.5
POWER (MW/cm2)
e
200
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v
150
-
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