957
J. Phys. Chem. 1985,89,957-963
Kinetics and Mechanism of Platlnum Depositlon by Photoelectrolysis in Illuminated Suspensions of Semiconducting Titanium Dioxide J. S. Curran,* J. Domenech? N. Jaffrezic-Renault, and R. Philippe Laboratoire de Physico-Chimie des Interfaces, UA 404 C.N.R.S.Ecole Centrale de Lyon, BP 163, 69130 Ecully, France (Received: July 30, 1984)
The rate of photoelectrochemical platinum metal deposition onto titanium dioxide particles in suspension in aqueous platinum hexachloride solutions illuminated by ultraviolet light has been studied quantitatively at different light intensitites, salt concentrations, etc. It is proposed that the semiconductor particles are subject to strong internal electric fields which lead to efficient hole-electron-pairseparation but that the titanium dioxide contains a large number of traps which cause recombination especially at high light intensities. The recombination is enhanced by the form adopted by the electrical field when several metal spots exist on the oxide grains, as has been observed.
Introduction Considerable interest has been shown in the photoelectrochemistry of suspensions in recent years, especially with respect to their ability to photoelectrolyze water. We have developed a model for this process and shown that the conventional explanation in terms of a photodiode can only be used if a highly reducing couple is present in the solution.’ This means that such systems may in general be of only limited interest as solar generators of fuels. In this work we have chosen instead to investigate another aspect of their behavior-as three-dimensional high surface area “electrodes” for the recovery of noble metals from very dilute solution. The semiconducting particles are not “electrodes” in the sense that they are not connected to an external circuit but are supplied with the necessary energy by photons which create electron-hole pairs and thus an electronic current in each particle which can be regarded as a miniature photodiode. As discussed below, the rather positive potentials of the noble metal deposition reactions lead to effective charge carrier separation since the semiconductor particles are polarized by the growing metal deposit. Hence the quantum yield of deposition is quite high. There are no reports that we are aware of in the literature dealing with the kinetics of the formation of such deposits. It has simply been shown that the process takes place on titanium dioxide in particular when particles are illuminated in the UV region for a number of metals such as platinum, palladium, silver, and copper.’ In preliminary experiments we investigated copper because its concentration is easy to follow by using a specific electrode, but we were unable to obtain reproducible results, which may be due to a problem of stability of the deposits. Thus we chose instead platinum, whose recovery from dilute solution is of economic interest and which is a favorable case from the chemical and electrochemical point of view. Experimental Procedures Photodeposition was carried out in a simple Pyrex thermostat4 reactor at 30 ‘C. The light source was a Phillips HPK 125 125-W medium-pressure mercury vapor lamp. Any laterally scattered or transmitted light was reflected back into the cell by aluminum foil surrounding the reactor. Unless otherwise stated 40 mL of a suspension containing 100 mg of T i 0 2 (Degussa) in a 2 X M solution of sodium hexachloroplatinate (Johnson Matthey) was used. During each run the suspension was vigorously stirred while being bubbled with pure argon in order to eliminate any oxygen present. Great care was taken to prevent the formation of a film of light-absorbing metalized T i 0 2 on the window which formed the bottom of the cell by limiting the runs to 30 min before which time no deposit takes place. The water used was double distilled in quartz, and chemicals were of Analar grade. The rate of the *Present address: Technology Transfer, Eastern Electricity, Wherstead, Ipswich, England. Present address: Chemistry Department, University of Barcelona, Barcelona, Spain.
photoelectrochemical deposition reaction was followed by measuring the concentration of hexachloroplatinate ion left in solution a t different times after illumination. Samples of 4 mL were withdrawn and centrifuged, and the clear solution was analyzed by atomic absorption spectroscopy using a Perkin-Elmer 360 instrument. Oxygen was detected with an Orion 9708 Clark type electrode. The agglomeration state of the suspension was investigated by using sedimentation rate techniques with a Horiba CAPA 500 particle analyzer. Transmission electron micrographs were obtained with a Philips Nanoscope EM420 instrument using samples prepared by dispersion of the powder.
Results (1) Blank Runs. Experiments were conducted in the reactor using a T i 0 2 suspension without platinum in solution and in a platinum solution without T i 0 2 in suspension. With T i 0 2 alone in suspension no change whatsoever is observed during 30 min of illumination. With hexachloroplatinate alone a rather rapid drop in the pH is observed; at full lamp power the pH decreases to 2 in less than a minute. We have not investigated this purely photochemical process for which there is little information available in the literature, since no platinum loss occurs from the solution. Hence the only effect of the photochemical reaction is that all the observations made must be considered to have been at pH 2. Nevertheless it seems likely that this pH change is due to catalysis of the ligand exchange reactions by UV light PtC162- + H 2 0
-
PtCl,0H2-
+ HCl
for which there is some evidence.2 In any case no change in the absorption spectrum of the solution occurs, and hence the platinum remains in the 4+ oxidation state in solution. ( 2 ) Agglomeration Measurements. It is well-known that particle suspensions show a tendency to agglomerate unless suitable precautions are taken. This fact has been up to now ignored by workers in the field of the photoelectrochemistry of suspensions. In order to show its importance we have measured the average particle diameter at low ionic strength for various pH values. The results are shown in Figure 1. The increase in average diameter with increasing pH is as might be expected since the point of zero charge for T i 0 2 is known to be in the region of pH 6-7.3 It is more important, however, that the measured diameter under the reaction conditions of pH 2 is about 1 bm whereas the average diameter of the TiOz grains used in these experiments was observed to be in the region of 0.02 pm. Hence the number of these grains in each agglomerate approaches 1Os. Some measurements were also made of the average particle diameter during the photodeposition process. These observations confirm that the agglom(1) Curran, J. S.;Lamouche, D. J . P h p . Chem. 1983, 87, 5409. (2) Cushing, J. R.;Hubbard, A. T. J. Electroanal. Chem. Interfacial Electrochem. 1969, 23, 183. (3) Foissy, A.;M’pandou, A.; Lamarche, J.; Jaffrezic-Renault,N. Colloids Surf. 1982, 5, 363.
OQ22-3654/85/2089-0957$01.5Q/Q0 1985 American Chemical Society
958 The Journal of Physical Chemistry, Vol. 89, No. 6, 1985
Curran et al.
10
3
1
5
1
9
11
+
pH
Figure 1. Variation of the average diameter of Ti02 agglomerates in suspension with pH: 5 mg of TiOz in 400 mL of a mol L-I solution of sodium nitrate.
5.ia
n( mg per g TiO,)
/
60
50
Figure 3. Square of the initial deposition rate (IDR) plotted as a function of the light flux as a fraction of full power by using data in Figure 2.
40
3:
2(
11
10
20
30
t (mn)
Figure 2. Amount of platinum deposited as a function of time for a number of different light fluxes. On they axis is plotted the difference between the initial concentration of Pt'" in solution and that measured at time t , that is, the mass of Pt deposited in milligrams per gram of Ti02(m),the initial concentration being 2 X lo-' mol L-'. The light flux is expressed as a percentage of full light power: (X) loo%, (0)42%,(A) 17%, (0) 6.7%, ( 0 )2.6%, (V) 1%.
eration number does not change during the deposition. ( 3 ) Influence of Light Intenrity on the Deposition Rate. The light flux absorbed by the suspension was varied from full lamp power down to 1% power by using neutral density filters, and the M solution of hexachloroplatinate deposition rate from a 2 X was measured as described above. The results are displayed in Figure 2 where the amount of Pt deposited as a function of time is plotted. The curves show a general feature of this particular photodeposition; the process occurs in two stages, a rapid initial one followed by a slow second one whose rate is less sensitive to the reaction conditions. The most easily treated parameter is the initial deposition rate (IDR) given by the slope of the curves in Figure 2 for t = 0. The initial rates are plotted in Figure 3 for different light intensities. At this early stage in the reaction, light absorbed by the metal deposit which becomes considerable at later stages is negligible. Very small metal particles absorb strongly in the UV and visible range, the absorption changing from mainly UV to uniformly absorbing as the particle size increases." The (4) Schmidt-Ott, A.; Schurtenberger, F.; Siegmenn, H. C. Phys. Rev. Lett 1980, 45, 1248.
Pt solution also absorbs the light used in these experiments, that is, the Hg lines at 404.7,365.0, 334.0, and 313.0 nm. Thus there is a compensation effect since Pt metal absorption increases as PtCl,Z- absorption decreases. The end result as we have checked by diffuse transmission measurements is that at the beginning of the reaction at least, the amount of light absorbed in the T i 0 2 particles does not vary to a significant extent. This fact established, the striking result of this series of measurements is that, as clearly shown in Figure 3, the initial deposition rate (IDR) is not proportional to the light intensity but appears rather to be proportional to its square root. This result is discussed below. A more useful way of looking at the same results is to calculate the quantum yield of the photoelectrochemical reaction (7)defined by no. of electrons consumed in Pt deposition It(') = no. of photons absorbed in the T i 0 2
4~ d[Pt4+](initial) V(initia1) = I dt where N is Avogadro's number and I , the absorbed light flux, is expressed in photons per second. This flux was calculated by using the manufacturer's data corrected for transmission via the Pyrex cell window, etc. Results are illustrated in Figure 4. Although it has to be admitted that errors may be considerable, it seems safe to conclude that quantum yields are quite high at low light intensities and that at higher light intensities 7 N kZ-'/'
k being a constant. ( 4 ) Effect of Initial PtC1,2- Concentration. The initial concentration of the platinum salt was varied by a factor of 10 and the IDR measured at quite low illumination intensity (to obtain a good quantum yield). The results of these experiments are shown in Figure 5 in terms of quantum yield. It is reasonable to suppose that the ionic strength remains constant since it is dominated by the pH in the concentration range of PtCl,*- used. However corrections must be made for the amount of light absorbed in the ( 5 ) Delcourt, M. 0.; Kagouche, N.; Belloni, N o w . J . Chim. 1983, 7, 131. (6) Bohren, C. F. Am. J . Phys. 1983, 51, 323. (7) Kraeutler, B.; Bard, A. J. J. Am. Chem. SOC.1978, 100, 4317.
The Journal of Physical Chemistry, Vol. 89, No. 6, 1985 959
Platinum Deposition by Photoelectrolysis
1; (io)
60
I T
50
2.10-1
I
40
i+\+
30
20
2
4
6
8
PH
10
Figure 6. Initial deposition rate as a function of the pH of the solution. Initial PtC1,2- concentration 2 x IO-’ mol L-l; illumination 7%.
10
0
50
y
100
(%)
n (m9.g-1:
’0
Figure 4. Quantum yield of photodeposition q as a function of light flux absorbed by the TiO, corresponding to the fundamental band: bandband transition, calculated from the data in Figure 2 and the lamp
7;
A
(XI
T
30-
2
0
[ ~ t l ]( 1~0 3 r 4 . 1 ~ ~ )
4
Figure 5. Variation of the initial quantum yield of deposition with initial concentration of PtC16,- ion, using 7% of lamp power.
T i 0 2 rather than in the PtC162- solution. This was done according to I(Ti02) a’(Ti02) 1
-
I (incident)
-
a’(Ti0,)
+ apt4+)
1+-
a(Pt4+) a’(Ti02)
where CY is the molar extinction coefficient for PtC16’- and a’ the diffuse absorption coefficient for the TiO, suspension. The latter quantity was measured by using large-area photocells and filters, but errors are difficult to eliminate. However it may be safely concluded that 7) hardly varies with the initial value of the hexachloroplatinate concentration. The practical consequence is that metals in very dilute solution can be deposited just as rapidly as those in more concentrated solution-the interpretation of this result with respect to the mechanism is left to the Discussion section. ( 5 ) Effect of p H on Initial Deposition Rate. The IDR was measured for p H 2 (no buffer), 7 (phosphate buffer), 9 (borate buffer), and 10 (KOH). The results are displayed in Figure 6 where the quantum yield can be seen to decrease with increasing pH. The ionic strength is not constant for this series of measurements, but as shown below the IDR is not significantly affected by the ionic strength in this range of values at least. With respect to the stability of the platinum complex is it known that PtC16’-
0
10
20
io
t(mn)
Figure 7. Effect of temperature on the rate of deposition of Pt. Initial concentration 2 X la-’ mol L-’, lamp power 6.7%. The inset shows a plot of the logarithm of the initial deposition rate vs. reciprocal of temperature, from which an activation energy of 19 kJ mol-’ can be calculated. (0) 20 OC, ( 0 )40 OC, (A) 50 “c.
is not thermodynamically stable at high pH but is kinetically so. On the time scale of the experiments it was verified that even at pH 10 the absorption spectrum of the solution stayed unchanged. (6) Effect of Temperature on Initial Deposition Rate. Both initial and slow-stage deposition rates are accelerated at higher temperatures, as shown in Figure 7. Admittedly the temperature range investigated was rather small, but if it is assumed that Arrhenius behavior is obeyed an activation energy of 19.3 kJ mol-’ can be calculated from the data in Figure 7 for the initial phase of reaction. Such a low value might be expected for a photoelectrochemical process exhibiting rapid Faradaic kinetics. Since as proposed below the second slow phase of the reaction is diffusion controlled, the activation energy corresponding to this stage has no direct significance. (7) Effect of Ionic Strength on Rate of Deposition. The ionic strength was adjusted to higher values with sodium nitrate, which has no optical absorption at the wavelengths concerned and which
960
The Journal of Physical Chemistry, Vol. 89, No. 6, 1985
Curran et al.
m (n?3.!3-')
40
I 0
20
10
30
t ( mnJ
Figure 9. Effect of oxygen on the photodeposition rate with full lamp mol L-I. Argon bubbling power and initial PtCbz-concentration2 X (0)oxygen bubbling.
0
20
10
30
t(mn)
Figure 8. Effect of ionic strength on the deposition of Pt with 10096 lamp power and an initial concentration of PtCb2-of 2 X lo-' M L-I. Sodium nitrate was used to adjust the ionic strength (X) 0.0 M, ( 0 )5 X 1V2M, ( 0 ) 0.1 M, ( 0 )0.5 M, (A) 1.0 M.
is not specifically adsorbed by the Ti02 The results are illustrated in Figure 8 where the photodeposition is shown at five different ionic strengths. It is clear that the only important influence of ionic strength is on the second or slow phase of the deposition. This is not due to changes in the agglomeration number since this varies to only a small extent with ionic strength. ( 8 ) Effect of Oxygen and the Photoanodic Reaction. At a pH of 2 the reduction of oxygen is thermodynamically more favorable than the electrocrystallization of platinum, and hence depending on the respective electrode kinetics and concentrations of the competing reactants either of the two processes Can dominate. This is the reason it was considered necessary to bubble the solutions with argon during experiments in order to eliminate any traces of oxygen, especially since oxygen is likely to be the main product of the photoanodic reaction:
I
I
1
2
i ( g . 1-11
Figure 10. Quantum yield of photodeposition as a function of the mass of TiO, added to 40 mL of a 2 X lo-' mol L-I solution of Pt'" ion.
The effect of saturating the solution with pure oxygen is shown in Figure 9, where it is obvious that oxygen reduction does indeed compete with the desired reaction but only a t the beginning of the deposition, during the fast stage. The slow-stage deposition rate is unaffected by oxygen, which may mean that low residual metal concentrations may be reached even in the presence of oxygen, though this remains to be confirmed. As regards the photoanodic reaction, oxygen was detected in solution by an oxygen electrode during photodeposition in a closed reactor without argon bubbling, but in very small amounts compared to the amount of platinum deposited. This nonstoichiometry of reaction products has been previously observed and attributed to adsorption of the oxygen on the surface of the Ti02.* Separate experiments using gas-phase chromatography failed to reveal the presence of any chlorine over the suspension9during illumination, but some chlorine evolution cannot be rigorously excluded bearing in mind the possible adsorption of small quantities on the large T i 0 2 surface present.
(9) Effect of Quantity of T i 0 2 in Suspension. The mass of powder in suspension determines the fraction of the available light absorbed by the powder rather than being absorbed elsewhere, especially in the solution. This is illustrated by the data in Figure 10, where it can be seen that suspensions of more than 1.Og L-' ensure that practically all the light is absorbed by the TiO, and not the hexachloroplatinate complex. All the measurements reported above were made under such conditions, Le., with 2.5 g L-'of TiOz in suspension. (10) Nature of the Metal Deposit. Figure 11 shows an electron micrograph of a particle after 30 min of illumination. After only 5-min illumination the particles have the same appearance but there is a much larger proportion of particles without any visible deposit. Here is direct evidence of the crucial fact that the platinum deposition does not occur in only one spot on the particle but in many positions. This somewhat surprising result enables us to explain the dominant features of the kinetics of the deposition, for example, the onset of the slow phase. From the point of view of metal recovery, it is interesting that under suitable conditions up to 40% by weight of platinum can be deposited on the oxide particles, the deposit being of the same form, in other words a large number of microcrystallites about 10-20 A in diameter.
(8) Mills, A.; Porter, G. J. Chem. Soc., Faraday Tram. 1 1982,78,3659. (9) Herrmann, J.-M.; Pichat, P. J . Chem. Soc., Faraday Tram. 1 1980, 76, 1138.
Discussion The main features of this and perhaps other photodeposition and photoelectrolysis reactions can be understood in terms of
2H20
+ 4h+
-
0,+ 4H+
Platinum Deposit ion by P hotoelect rol ys is
The Journal of Physical Chemistry, Vol. 89, No. 6. 1985 961
Figure 11. Electron micrograph of the platinum deposited on T i 0 2 grains after 30 min of illumination under the same conditions as in Figure 6. Magnification 656000 X.
conventional photoelectrochemistry if the special three-dimensional nature of the system is kept in mind. The basic approach is to consider the TiO,/Pt particle as a sort of microphotodiode in suspension. It is not our intention to discuss the nucleation process per se as it is in any case not accessible using our data, but it can at least be said that this stage of the process does not appear to present any special difficulties as we observe no inhibition period at the beginning of the reaction. There is, however, a crucial question which raises itself already at this point in the process-is nucleation a rare or a frequent event? It would seem that it is a frequent one if one simply examines the electron micrographs, but this is not necessarily the case as will be argued below, as it could be more likely that the process begins with the formation of a single metal deposit which increases the likelihood of a second nucleation event in its immediate vicinity. In any case the point of departure is to consider the electronic structure of a T i 0 2 particle with a single metal microelectrode upon it, regardless of whether such entities exist at any time during the reaction. The two-dimensional energy diagram, of the type habitually constructed for planar devices or for photoelectrodes, is depicted in Figure 12a. The three parameters required to construct this diagram are the flatband potential of Ti02(a well-studied subject for the rutile form of T i 0 2 but not for the anatase form),I0 the potential of an electron in the metal deposit, and the height of the potential barrier between the metal and the semiconductor. The flatband potential of the Ti02, Vb is given, taking an average of the literature results, by J‘b(NHE) = -0.2 - 0.059pH for the anatase form.1° This potential, fixed by the nature of the material and the proton-exchange equilibrium at the interface, determines the energy of an electron at the Ti02/electrolyte interface. The potential of an electron in the metal microelectrode is fixed by the Fermi level of the electrolyte, in our case defined by the redox equilibrium Pto/PtC162- as follows:
E = Eo
+
Figure 12. (a) Energy diagram on the normal hydrogen electrode scale in one spatial dimension for a Ti02 grain with a single metal spot of Pt in suspension in PtC162-solution at pH 2. (b) Same energy diagram in two spatial dimensions using equipotential contours. The variation of the potential on the surface in the surface coordinate X is indicatcd.
The third and more contentious value is the height of the potential barrier between the metal and the semiconductor, v b . This is normally estimated as the difference in electron affinities between the metal and the Ti02, the latter in the absence of any surface charge. This in turn can be related to the flatband potential at the point of zero charge theoretically if the electron affinity of the metal is known precisely. We prefer to adopt a value experimentally measured on a single crystal, since there is a large spread in the available electron-affinity values. Thus we use v b = 0.5 v.” This picture should be essentially correct if the respective equilibria are able to establish themselves and if there are no special effects due to the small size of the object. It is known that metal particles begin to behave like macroscopic metal electrodes if they are bigger than a few atoms in size, and as regards the semiconductor, since it consists in our case of around 1 O5 atoms, a band structure should be established. The T i 0 2 used in these experiments is microcrystalline as X-ray powder photos demonstrate but may have considerable band tails as, for examle, reflection spectra indicate. Since the metalsemiconductor assemblies do not undergo any heat treatment, it is unnecessary to consider interdiffusion and possible effects of high doping,I2 and since no hydrogen is present the structure of the contact metal-semiconductor is not modified by hydrogen incorporation in the metal.” Nevertheless the representation of the suspended particle in Figure 12a is not adaequate since it does not take account of the three-dimensional geometry of these special systems which is essential to their understanding. Due to the assumed cylindrical symmetry of the object, a representation in two dimensions can
In [Pt4’] = 0.55 ( 1 1 ) Yamamoto. N.; Tonomura. S.; Tsubomura, H. J . Elecrrochem. Soc. 19112, 128. 444.
(10) Ward, M. D.; White, J. R.; Bard, A. J. J . Am. Chem. Sm. 19113.105. 27.
G. A.; Bard, A. J. J . Phvs. Chem. 1W3,87, 1979. (13) Aspnes, D. E.; Heller. A. J . Phys. Chem. 1983, 87, 4919. ( 1 2) Hope,
962
The Journal of Physical Chemistry, Vol. 89, No. 6, 1985
\
rNHE: t---.”e I
I
p
ti,
,
:-I
I
1-2
Figure 13. Energy diagram under the same conditions as in Figure 12 but for the case of a Ti02grain with multiple metal spots present on its
surface. be used as shown in Figure 12b. Here is included the variation in the potential along the surface which is fmed electrochemically and which in turn determines the potential distribution inside the particle. Due to its small size the semiconducting sphere can be assumed devoid of charged donors; it thus behaves as a dielectric.’ The field at each point in the sphere can in principle be found by solving the relevant Laplacian v2v= 0 using as boundary conditions the potential a t the surface which is indicated schematically in Figure 12, but here we restrict the discussion to less rigorous procedures since in any case the boundary conditions are not really well understood. The principal problem is that the object itself is of around the same dimensions as the typical lengths over which the potential drops concerned can be achieved in the solution (two Debye lengths N 60 A) and in the semiconductor (0.5 X l/dielectric strength = 50 A). Thus the field has to be “smoothed out” in a more or less arbitrary way such as we have shown in Figure 12. One interesting feature of this diagram is that although electrons can be thought of as being directed toward the metal deposit and holes to the TiOz-electrolyte interface, in fact the electron drift is not oriented directly toward the metal and in addition is nearly parallel to the surface in the immediate vicinity of the metal. If this is accepted, then it must also be admitted that electrons have a good chance of reaching the TiOz surface in the region of the metal by lateral diffusion, thereby nucleating a new metal spot. This argument may not be necessary to explain the appearance of many metal spots on each grain of T i 0 2 as one could simply assume multiple nucleation at the very beginning of the deposition, but it does seem a more persuasive approach. The electric field within a particle having a number of spots on it is necessarily much less effective in separating electron-hole pairs as can be seen simply by inspection of Figure 13 where such a situation is depicted. The overlapping of the polarized zones leads to their mutual cancellation, and in much of the volume of the grain recombination will be greatly increased. This is even more true if one takes the argument a little further to consider the situation under illumination. The dome-shaped (in two dimensions) form of the electric potential has necessarily the effect of forcing holes to accumulate at the center of the structure, thus flattening out the electric field even more. The consequence is that hole-electron pairs being unseparated in the volume recombine and pairs unseparated at the interface lead to the Occurrence of back reactions. We are now in a position to try to explain in general terms the main features of the kinetics of the deposition reaction armed with the essential fact that the appearance of multiple spots on the
Curran et al. grains leads to their partial or almost total deactivation. It is also important to bear in mind that the size of the agglomerates is such that the grains at the outside receive much more light than those at the center. A rough calculation based on the absorption coefficients of the Hg lines concerned gives a factor of 20. Thus qualitatively speaking at the beginning of the reaction the deposition rate on the grains at the outside is about 5 times faster than on those near the center-these grains are the first to become deactivated by the accumulation of a large number of spots and subsequently serve mainly to shield the still active inner grains from illumination. The deposition can continue at a lower rate, but in the second phase of the reaction one is probably observing a diffusion-limited rate since evidently reactants and products must diffuse from the outside to the active inside of the agglomerate and vice versa. P r d i n g in the order of data presentation we explain at least qualitatively the other major features of the deposition p r w - t h e loss of quantum yield at high light intensity, the lack of influence of the platinum ion concentration, and the influence of pH and of ionic strength. The presence of zones where there is little, if any, polarization allows recombination to become important; this recombination can be expected to be of the Shockley-Read-Hall type proceeding via recombination centers whose density is probably quite high since the microcrystals show signs of a certain amount of disorder (band tails). In addition it can be stated with confidence that the concentrations of electrons and holes can be of the same order of magnitude in at least some parts of the same recombination zones. Hence in the expression for the bulk recombination rate per unit volume RE
where c, is the electron concentration, ch is the hole concentration, ci is the intrinsic carrier concentration, and T , , ~are their lifetimes. RE becomes dependent on both c, and c,, with the result that the quantum yield decreases at higher light intensities. It should not be forgotten also that the hole accumulation effect alluded to above, which may even further decrease the yield, may be more pronounced at higher light intensities and contribute to the dramatic drop in yield. The slow phase of the deposition is not influenced by the light intensity since it is a diffusion-controlled process where the rate of mass transport of PtC16’- through to the inner part of the agglomerates controls the rate of deposition. The electron-hole pairs not consumed in the deposition either simply recombine or are consumed in back and/or side reactions. The PtC16’- ion concentration has a small (but not directly proportional) positive influence in the initial phase and a more marked influence on the slow phase. During the initial period there is no diffusion problem and the PtC16’- ion concentration at the microelectrode is the same as it is in the bulk of solution. Hence its influence (if any) is through the polarization of the grain since the potential of the microelectrode could be expected to follow the usual Nernst behavior. The concentration changes correspond to changing the polarization over a range of 50 mV. This is not large compared to the 150-mV overall polarization of the grain. In addition it should be stated that the average field is of the order of lo6 V cm-’ which is a value in the range where the carrier velocity saturates and recombination is not influenced any further by increasing polarization. In the slow phase in the limiting case the PtC1,Z- ion concentration is zero at the microelectrode and its potential is fixed, if at all, by another equilibrium such as Oz/OH-. However mass transport control should mean that the rate of the reaction is directly proportional to PtC162- concentration. Such data as we have obtained to date, though in need of confirmation, show this behavior. With respect to the pH, we do not have a satisfactory explanation for the inhibition (if the data are sufficient to warrant this assertion) of the reaction at higher pH values. It would be more logical to expect on the basis of the arguments illustrated in Figure
The Journal of Physical Chemistry, Vol. 89, No. 6. 1985 963
Platinum Deposition by Photoelectrolysis
12 that the effect of the pH would be the reverse since it would lead to rather a large increase of up to 360 mV in the potential drop experienced by the particle. One possibility is that the metal microelectrode is no longer held at its redox potential, the maximum potential drop that the solution can allow over the short distance concerned (10 A) being surpassed. If in addition one assumes that the high negative surface charge on the oxide affects the concentration of negatively charged PtClS2-in the vicinity of the metal spots, then the pH effect can be rationalized. This approach is consistent with the observation that the ionic strength when increased has the effect of accelerating the reaction somewhat. The ionic strength determines the Debye length in solution through the relation xDL (A) II 3.09([NaN03] [H+])’/, = 3 30 8,
+
+
The shorter the Debye length the more the potential drop that can be developed over the same distance. Hence for the grains already in possession of several metal spots the modulation of the potential on the surface is accentuated at higher ionic strength with the concomitant beneficial effect of hole-electron-pair separation in the semiconductor. This trend as the data show is more marked at a later stage in the process when the grains are well covered with spots. As regards the other parameters such as oxygen level, temperature, etc., the explanations are much more obvious and no further comments are required on the remarks in the Results section except perhaps in the case of temperature variation. Such variation as we have imposed affects transport and recombination in the semiconductor to a negligible degree. The redox potential, the flatband potential, and the Debye length hardly vary, and thus we are left only with diffusion in solution and kinetics at the interfaces to explain the data. Platinum deposition is known to be a slow electrochemical reaction as indeed is oxygen evolution in the vast majority of cases, and thus the activation energy is of the order of, say, 50 kJ mol-’. This value is not entirely reflected in our data since the competition between recombination, back reactions, and deposition is a much more complex affair, but the order of magnitude is correct. The above arguments now allow a kinetic expression to be derived on the basis of the hypothesis of a “dead layer” which develops progressively on the outside of the agglomerate which receives the most light and becomes rapidly passivated due to field cancellation by multiple spot development. Let this zone have a thickness a and the agglomerate a radius r. The deposition rate R per agglomerate is given to a first approximation by the fraction of incident light absorbed in the active rather than the dead zone, multiplied by a quantum yield 7 R = ?IF exp(-nu) In this expression the factor F accounts for any effects due to reflection, etc., and is an absorption coefficient for the wavelengths concerned averaged over an angle of incidence of 2ir and enhanced to take into account internal reflection. The assumptions are that &a a and that planar diffusion is a good approximation the deposition rate per grain, RD is given by the formula
D
R, = 4ar2-[Pt4+] U
where an effective diffusion coefficient D is used to describe diffusion in the biphasic dead zone. The condition corresponding to the distinct break in the reaction kinetics into two stages, a light intensity controlled stage and a diffusion controlled stage, is that R is essentially unchanged from its initial value when diffusion control takes over. This means in other words that a&
