6004
J . Phys. Chem. 1988, 92, 6004-6009
Magnetic Study of Catalytic Particles: Application to NiKeO, A. Mauger, Groupe de Physique des Solides, E N S , UniversitP Paris VII, 2 Place Jussieu, 75007 Paris CPdex 05, France
M. Escorne, V. Paul-Boncour, A. Percheron-Guegan,*J. C. Achard, Laboratoire de Chimie MPtallurgique des Terres Rares, C N R S , 1 Place A . Briand, 921 90 Meudon, France
and J. Barrault Laboratoire de Catalyse Organique. UniversitP de Poitiers, 40 Avenue du Recteur Pineau, 86022 Poitiers CPdex, France (Received: August 28, 1987)
In this work, we present a new method to determine the particle size distribution of nickel-supported catalysts, based on the analysis of magnetic properties beyond the superparamagnetic approximation. Field-cooled magnetization curves of Ni supported on CeO, reduced under hydrogen at two different temperatures (250 and 400 "C) have been measured for T < 620 K. Below 500 K, a progressive spin freezing of nickel particles is evidenced by the observation of a remanent magnetization and a deviation of the magnetic susceptibility from the Curie-Weiss law. We show that the blocking of the nickel particles ~ ) that the two samples differ by the particle size distribution, although is due to a strong strain anisotropy (3 X lo6 erg ~ m - and the mean size d is about the same (7.8 nm). We conclude that the difference in the catalytic activity between the two samples cannot be explained by a difference of surface area.
1. Introduction
Catalysts of transition metal deposited on rare-earth oxide have been recently investigated in order to provide new catalytic systems for isomerization,' water gas shift reaction,2 hydrogenation rea ~ t i o n ,and ~ , ~automotive exhaust cataly~is.~Our studies on cobalt and rare-earth oxide system in C O hydrogenation3 showed the influence of the nature of the rare earth on the catalytic properties. We have also tested nickel supported on cerium oxide in this reaction and observed a significant effect of the reduction temperature during the preparation of the catalyst on the catalytic properties. When reduced at 250 *C under hydrogen, Ni/Ce02 behaves like a classical Ni/SiOz or Ni/Al2O3 catalyst. However, when the reduction temperature is raised up to 400 "C, the catalysts become inactive and it is necessary to perform the reaction at 400 "C instead of 250 "C to obtain some catalytic properties6 To explain such a decrease of activity, we can invoke either a strong decrease of surface area or a strong interaction between the nickei and the support. The question is then, what is the surface area? H2 and C O chemisorption experiments failed to answer this question, since when the reduction temperature increases, the H 2 chemisorption vanishes and the C O chemisorption increases by a factor of 2. Such a result only shows that an interaction of the reactant with CeO, should be taken into account and it becomes impossible to deduce a number of active sites. We therefore tried to determine the particles size distribution by physical method as X-ray diffraction (XRD), transmission electron microscopy (TEM), and magnetization measurements. In fact magnetization measurements prove to be the only way of investigation of the particles size distribution since XRD spectra revealed that Ni particles are too large to be sizeable and the contrast between nickel and cerium was too weak in TEM images. Since the nickel particles are large in both N i / C e 0 2 compounds, the sample is not in the superparamagnetic phase, even at room temperature, so that previous (1) Le Normand, F.; Girard, P.; Hilaire, L.; Ravet, M. F.; Krill, G.; Maire, G. J . Catal. 1984, 89, 1. (2) Mendelovici, L.; Steinberg, M. J. Catal. 1985, 96,285. (3) Barrault, J.; Guilleminot, A.; Achard, J. C.; Paul-Boncour, V.: Percheron-Guegan, A.; Hilaire, L.; Coulon, M. Appl. Catal. 1986, 22, 273. (4) Sudhakar, C.; Vannice, M. A. J . Catal. 1985, 95, 227. (5) Yao, H. C.; Yu Yao, Y . F. J. Catal. 1984, 86,254. (6) Barrault, J.; Guilleminot, A.; Paul-Boncour, V.; Percheron-Guegan, A,; Achard, J. C.; Hilaire, L., to be published.
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models of superparamagnetism used by other authors to determine the particle sizes' cannot be used in our case. Therefore we determine the particle-size distribution (f( V)) from the analysis of magnetic properties, following the pioneering work by Weil in Cu/Co This paper is organized as follows: in the section 2 we present the theoretical model which describes the spin freezing of the magnetic particles. In section 3, the experimental magnetic properties of our samples are reported. In section 4, the magnetic anisotropy and granulometry of the samples are derived from the fit of the experimental data by the theoretical model. 2. Theory
2.1. Theoretical Background. We first assume that the Ni particles are single magnetic domains; Le., all the Ni atoms that belong to the same particle are spin-polarized along the same axis. For a spherical particle, it is straightforward to show that the single domain is stable provided the diameter d is smaller than a critical value9 d
< 9y/2irMs2
where M , is the saturation magnetization per unit volume and y the superficial energy density of a Block wall. Second, we assume the magnetic interaction between Ni particles is negligible. This hypothesis is necessary for the following reason. Magnetic measurements are only sensitive to magnetic clusters. If the magnetic interaction between the Ni particles is negligible, the magnetic clusters are identical with the Ni particles; Le., the magnetic moments of Ni atoms belonging to the same particle are aligned ferromagnetically along a common local quantization axis; however, there is no correlation between the quantization axes of two particles. To the contrary, if the magnetic interaction between Ni particles is significant, the system undergoes a transition to a ferromagnetic ordered phase at a finite Curie temperature T,, which depends on the concentration x of Ni atoms in the matrix. The ferromagnetic phase below T,(x) corresponds to a spontaneous alignment of the magnetic moments (7) Bonneviot, L.; Che, M.; Olivier, D.; Martin, G. A,; Freund, E. J.Phys. Chem. 1986, 90, 2112. (8) Weil, L. Colloque National de MagnCrisme: Centre National de la Recherche Scientifique: Paris, 1957; p 147. (9) See, for example: Herpin, A. ThCorie du MngnCtisme; Presses Universitaires de France: Paris, 1968; p 753.
0 1988 American Chemical Society
The Journal of Physical Chemistry, VO~.92, NO. 21. 1988 6005
Magnetic Study of Catalytic Particles between the grains. In terms of percolation, T,(x) is then the temperature at which a magnetic cluster of infinite size is being formed. Since, in principle, the range of the magnetic interaction is larger than the nearest-neighbor distance, the infinite magnetic cluster may be formed even if the Ni particles are small. This argument corrects a previous statementlo that the existence of large particles could be inferred from the observation of ferromagnetism. It also points out that the geometric distributionAV) is not related to the magnetic granulometry when the interparticle interaction cannot be neglected. As x decreases, the mean distance between particles increases and the magnetic interactions between the particles decrease. Therefore T J x ) decreases, and vanishes for some Ni concentration, x,, referred to as the magnetic percolation threshold.” Therefore, we can define the criterion x
0 Hc = x,(T)/[2Mo(T)I H, = x l ( T ) / [ 6 M o ( T ) ] where
x1 is
if x I
98%) on cerium dioxide (EGA CHEMIE, 99.9%, BET 20 m2 g-l). It is dried on a sandbath and then in an oven at 120 OC. The sample is reduced 10 h under purified hydrogen at 250 and 400 OC (samples 1 and 2, respectively) with a heating rate of 4 "C min-'. Reducibility measurements6 show that the nickel is completely reduced at both temperatures. The samples are handled in a glovebox under purified argon. Samples for magnetic measurements (0.1 g) are put either in a quartz tube sealed under vacuum or in an Araldite tube" sealed under purified argon. 3.2. Magnetization Data. Magnetic measurements have been performed with a Foner magnetometer on samples 1 and 2 in the temperature range 4.2 < T Q 620 K, using an equipment which has been described elsewhere.I6J7 The field-cooled process is performed at a rate 0.01 K S-I between the two temperatures investigated, separated by an interval of about 15 K. After the selected temperature has been reached, the sample is still left under the magnetic field H, = 15 kG for 1000 s so that it can be checked that thermal equilibrium is reached. Then H i s decreased from 15 kG to 0 G at the rate of 5 G s-'. The observation time to = 1000 s is spent after H has been set to zero, before the remanent magnetization is measured. Note that the time spent during the decrease of H is not included in the definition of to because the time dependence of M ( H ) is negligible at the time scale of the experiments unless H i s close to zero. The results are illustrated in Figure 1. The accuracy on the experimental values of M ( H ) is f 0 . 2 emu 8-I. The initial slope of the M ( H ) curves at H
-
(16) Escorne, M.; Leroux-Hugon, P. Rev. Phys. Appl. 1973, 8, 289. (17) Escorne, M. Rev. Sci. Instrum. 1987, 58, 127.
T(K)
Figure 2. Field-cooled magnetic susceptibility xFC and remanent magnetization MR (observation time lo3 s) as a function of temperature, for sample reduced at 400 "C.
6-
I 4-
2.
lo
Ol 0
200
400
T(K)
Field-cooled magnetic susceptibility xFCand remanent magnetization M R (observation time lo's) as a function of temperature, for sample reduced at 250 " C . Figure 3.
0 is the field-cooled magnetic susceptibility xFC, reported for both samples in Figures 2 and 3. The quantities reported in they axis of these figures are experimental data divided by the weight of the nickel constituent in the samples. At high temperature, xFC first increases as T decreases, as predicted by the Curie law, but
The Journal of Physical Chemistry, Vol. 92, No. 21, 1988 6007
Magnetic Study of Catalytic Particles TABLE I: Saturation Magnetization ( M ) and Percentage of Nickel Deduced from M . and Chemical Analysis for Both Ni/Ce02 Samples
% Ni
from M,(300 K), from chem compound emu M, anal Ni(7.5%)/Ce02reduced at 250 OC 0.787 8.4 7.5 0.916 7.3 7.5 Ni(7.5%)/Ce02reduced at 400 OC 400
1
- 800 T(K)
-
Figure 5. Critical dimension for blocking Ni particles at the observation time to lo's. Dots are theoretical results deduced from the fit of the
600
~
magnetization data (see with text), for both samples. The full curves are theoretical curves d,(T) for strain anisotropy (y = 3), shape anisotropy (y = 5 ) , and cubic anisotropy (y = 10).
1400 N
z 100
1
-
\\ O0 \ \
600
"C). The small difference with respect to the value T, = 631 K in bulk nickel is presumably due to an interaction with the support. 3.3. Granulometry. In this section, we use the magnetization experiments as a function of temperature to derive the magnetic granulometr y. At T 77 K, the magnetization saturates for H k 10 kG, which proves that, at such temperatures, most of the Ni particles are blocked along the magnetic field and that the coercive field of the particles is smaller than the magnetic field H,,, available in our experiments. Equation 3 is fulfilled for our samples, and eq 1 is an ansatz which we will check later on this paper. From eq 8, we can deduce
~
650
T(K) Figure 4. Square of the magnetization as a function of temperature for both samples (1, reduced at 250 OC; 2, reduced at 400 "C).
then xFCgoes through a very broad maximum at temperature Tf = 320 K for the sample reduced at 250 "C, while a bump is observed at T N 460 K for the sample reduced at 400 "C, the maximum of xFCoccurring at a much lower temperature (- 140 K). This drastic deviation from the Curie law is the evidence of the blocking of Ni particles. The absence of a pronounced cusp at Tf is due to the fact that we have measured xFCinstead of the zero field cooled susceptibility, in contrast with previous experiments on Ni/Si02 for example.I2 The blocking of Ni particles coincides with the onset of a remanent magnetization, which is reported in Figures 2 and 3 for an observation time to lo3 s. Note this onset of the remanent magnetization occurs at a temperature Tb > Tf. This corresponds to the fact that the susceptibility cusp has no physical meaning, in contrast with Tbwhich corresponds to the temperature where the susceptibility first deviates from the Curie law. Any computation of the magnetic granulometry first requires the determination of the parameters M , and T, entering eq 10. M , = Mo(0) is by definition the saturation magnetization at T = 0; it can be well approximated by the magnetization (per unit volume of nickel) measured at 10 kG at 77 K. We have checked that the experimental value of M , is equal, within experimental uncertainty (lo%), to the value obtained for pure bulk nickel (Table I). The Curie temperature T, of the particles can be deduced from magnetic measurements as follows. Close to T, (which implies T > Tb so that eq 4 applies), there is a range of magnetic field
-
f ( V ) is computed by resolving self-consistently eq 9 and 20 using the following procedure. First, we notice the low-field limit of eq 9 can be written
Due to the square power of the volume in the integrant, the magnetic susceptibility is dominated by the contribution of unfrozen Ni particles with the largest volume, V,(T). For the first step of the iteration process, we take advantage of this feature by choosing the distribution f ( V) under the form
f(V) = 6 ( V - VC(T))
(22)
Then the fit of the M ( H ) curves by eq 7 and 8 gives a first estimation of V,(T). ThenAV,(T)] is derived from eq 20. This procedure is repeated at all temperatures. As T varies, V,(T) varies so that the knowledge offlV,(T)] at all temperatures gives the distribution f ( V). We have then to restart the iteration by replacing f ( V) by this new result in eq 7 and 8, instead of eq 20, and so on, until self-consistency is reached. The convergence is actually very fast. The fit of the magnetization curves is already better than 5% at the second iteration step at all magnetic fields. The results are reported in Figures 5 and 6. Instead of V,(T) and f ( V ) , we have reported d,(T) and f ( d ) defined by
where series development of eq 4 and 10 lead to lowest order M(T)
-
Mo(T) a ( T c - T)1'2
(19)
We have reported in Figure 4 the variations of @ as a function of T in the range 550 < T, < 650 K for a magnetic field H = 10 kG which satisfies eq 18. T,, deduced from the extrapolation of the linear variations of @(T) to @ = 0, is T , = 641 K for sample 1 ( T R= 250 "C) and T, = 633 K for sample 2 ( T R= 400
f ( d ) is the distribution function of the effective dimension d of the particles (their diameter if they are spherical). Measurements in the range 4.2 < T < 77 K only show that the remanent magnetization saturates below 7 0 K and that the magnetization curves M ( H ) become temperature independent within 1%. Therefore, the total number of particles with dimensions in the
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Mauger et al.
The Journal of Physical Chemistry, Vol. 92, No. 21, 1988
with the interatomic distance a' = 2.5 b;, the magnetic energy ~ , the anisotropy coefficient density E = 1.74 X lo9 erg ~ m - and x given by eq 24. Such values reported in eq 1 give a critical diameter of the order of 130 nm so that the ansatz d < d, is satisfied in our materials.
,?
' \
/ \* \
\
\
d(nm)
Figure 6. Distribution of the dimensions of the Ni particles in sample reduced at 250 "C (full line) and reduced at 400 OC (dotted line).
range d,(4.2 K) < d < d,(70 K), Le., 1 < d, < 7 nm, represents less than 1% of the total number of particles. The temperature independence of the magnetization curve at T < 77 K also implies that the concentration of Ce3+ ions is negligible; such isolated magnetic ions would behave like a magnetic impurity, Le., would give rise to a Curie-type contribution to the magnetic susceptibility not observed in the experiments. On the same plot in Figure 5, we have also reported the theoretical temperature dependence of d,(T), as given by eq 17a-17d for the three cases y = 3, y = 5, and y = 10. A good fit is obtained for y = 3, showing unambiguously that the strain anisotropy is dominant. The value of x deduced from the fit is x
= 3 x IO6 erg cm-3
Na = -d3 6 where p is the volume occupied per unit weight of bulk nickel (0.1 12 cm3 g-I). S can then be expressed in the form
S = 24Pd2/d3
(24)
which anisotropy is larger than the value 4.2 X lo5 reported for Ni/SiO2l2 and corresponds to a strain of 2.8 X Since N t - N , is limited to 2 s , the shape anisotropy is necessarily smaller than the strain anisotropy in our samples. Therefore the good fit of the experimental data by eq 17a and 17b is not a proof that the particles are spherical, since the shape anisotropy will be masked by the strain anisotropy even if they are rod-shaped. This fit is also consistent with the fact that the cubic anisotropy in Ni is small (~~(0) N -7.5 X lo5 erg C ~ - ~ ) leading I* to a value of x 2 orders of magnitude smaller than the value given in eq 21 so that the cubic anisotropy is negligible. The fit of the d,(T) curve by eq 17a with a coefficient x independent of T in eq 17b shows that the variations of the magnetostriction coefficient A I 9 as a function of T a r e small compared . same holds true for the strain u. If to those of [ M 0 ( T ) ] 3 The the strain is intrinsic, it comes from the surface tension at the nickel-support interface which does not depend on T. For a thermal strain, issuing from a misfit of the lattice parameters between the nickel and the support where am and asare the elastic modulus of the metal and the support, E is the Young modulus, and To is the temperature at which the support and the metal lattices fit together. uth is thus a linear function of T , and dependence on T is small compared to [ M 0 ( T ) I 3 . From our own experiments only, it is then not possible to know whether the strain is intrinsic or thermal in nature. It is usually believed, however, that the intrinsic strain is cancelled by the chemisorption of H,.' Let us now return to the ansatz in eq 1. For a strong axial anisotropy, the superficial energy of a 180" Bloch wall is yp = ~ u ' ( ~ / ~ x E ) ~ / ~
4. Discussion Comparisons between the weight of nickel deduced from chemical analysis and saturation magnetization are in good agreement in both compounds within a 10% experimental error (Table I). This shows that at both 250 and 400 OC the nickel is completely reduced. The particle size distribution, represented in Figure 6 , shows slight differences between the two compounds. For sample 1, reduced at 250 "C, no particle larger than 13 nm has been detected, and a slight maximum is observed around I O nm. For sample 2, reduced at 400 OC, we observe a maximum around 8 nm and also particles larger than 13 nm. Nevertheless, the data in Figure 6 show that the increase of the reduction temperature leads to a particles size redistribution rather than a sintering effect. The presence of smaller particles in the sample reduced at 400 "C compared to the one reduced at 250 "C is not yet explained, but the difference between 8 and 10 nm is not very important. As the significant parameter in catalysis is the surface of the nickel particles, the total nickel surface has been deduced from the size distribution: S = 4 d N . The number (A') of particles per gram of nickel can be deduced from the expression of the volume of the nickel particles
(26)
(18) Bozorth, R. M . In Ferromagnetism; Van Nostrand: Princeton, NJ, 1951; p 569. (19) Lee, E. W.; Asghan, M. A. Proc. R. Sac. London 1971, 326A, 7 3 .
(27)
with 3 = Jtfld')d'n dd'the nth moment of the size distribution of the Ni particles. Both samples 1 and 2 have essentially the same specific area S N 2.8 X lo6 cm2 per gram of nickel, within a few percent. The reason is that the peak inf(d) at d = 8 nm in sample is compensated by the existence of a finite value offld), which although small, contributes significantly to decrease S because S depends on high moments of the distributionf(4. The calculated surface is an upper limit for the nickel active surface, since part of the geometric surface will be in contact with the support and will be not accessible to the reactants. To conclude we can say that although a particle size redistribution fur Ni/CeO, reduced at 400 OC is observed, there are no main differences between the two catalysts. Although significant, the difference of Curie temperature with respect to bulk Ni remains small, so that an alloying effect is negligible. Various magnetic methods have been used previously in the literature to determine the size distribution of Ni particles dispersed in a dielectric medium. In most cases, however, magnetic studies have been performed, assuming s~perparamagnetism.',~~ With these prior works, we notice that, in this limit, eq 19 reduces to
in contrast with the expressions of M ( T ) in ref 7, 12, and 20 where p/Phas been arbitrarily replaced by r. This substitution is valid only if the distribution of volumes reduces to a Dirac distribution f(v) =
a(v- q.
In the other cases, the results must be corrected accordingly (in Appendix A of ref 12, or in ref 20 where DI and D2 must be substituted by M 6 1 / 6and M3'i3using the notation of Primet et a].). The errors in P (or d ) are in general only quantitative and may explain a slight discrepancy in the size of particles measured by TEM, ferromagnetic resonance (FMR), and magnetic susceptibility of superparamagnetism observed in ref 7. The (20) Primet, M.; Dalmon, J. A.; Martin, G. A. J . Card. 1977, 46, 25.
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.
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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
