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J . Phys. Chem. 1990, 94, 3152-3155
oxyethanol and ethanol, it might be inferred that Figure IO has little practical significance for dispersions formed by "better" emulsifying agents. However, there are substantial reasons for doubting that either of these ideas will prove to be true. Salager and co-workers prepared emulsions using sodium dodecyl sulfate, petroleum sulfonate/alcohol mixtures, commercial nonionic surfactants, and other common commercial emulsifier formulation^.'^ The interpretation of their experiments is complicated by the fact that, even if the polyoligomeric materials of their formulations are treated as single pseudocomponents, the experimental paths passed through four dimensions and often through a region of three phases.I3 However, the "formulation/WOR map" of Salager is essentially a projection from higher dimensional space onto two dimensions of the behavior shown in Figure 10. Figure 10 shows this behavior more rigorously, by limiting the phase diagram to three thermodynamic dimensions and by plotting the phase and dispersion diagrams in
the number of dimensions (three) required by the dimensionality of the experiments. Thus, in the absence of further experimental evidence to the contrary, we must assume that f o r dispersions of liquids and supercritical fluids prepared from conjugate phases, the dispersion morphology diagram of Figure 10 is generally valid for diverse combinations of amphiphiles, nonpolar compounds, water, and electrolytes, including a wide variety of materials used in common commercial practice. Note Added in ProoJ We have since shown that Figures 9 and 10 also are valid for the inversions of A/B and B/A emulsions, when the temperature is changed at constant system composition. Acknowledgment. This research was supported in part by an appointment of K.-H. Lim to the U S . Department of Energy, Fossil Energy, Post-Graduate Research Program, administered by Oak Ridge Associated Universities.
Photochemical Kinetics of Ultrasmall Semiconductor Particles in Solution: Effect of Size on the Quantum Yield of Electron Transfer Yoshio Nosaka,* Nobuhiro Ohta, and Hajime Miyama Nagaoka University of Technology, Kamitomioka, Nagaoka 940-21, Japan (Received: August 2, 1989;
In Final Form: November 7 , 1989) The quantum yield (9) of photoinduced electron transfer from ultrasmall CdS and In2S3semiconductor particles to surface-adsorbed viologen molecules was measured as a function of the density of adsorbed photons in the particles. At a lower photon density, 9 tends to become constant, and, in the case of In2S3,the smaller particles show a lower 9. In order to explain these observations, a kinetic model of a two-dimensional ladder was proposed. The ratio of the rate constant for electron-hole pair recombination (k,) to that for photoinduced electron transfer (k,) was estimated together with the radius of the particles by adopting the model. The ratio kJk, for CdS was found to decrease by less than a tenth with the change in the particle radii from 2 to 4 nm.
Introduction
Ultrasmall semiconductor particles are useful as photosensitizers to study the solid-surface chemical kinetics by means of the technique of laser flash photolysis, because the solution of them shows no light ~cattering.l-~On the other hand, viologen compounds have been proven to be excellent probes to study the charge transfer at the semiconductor-electrolyte interfa~e.~We studied the electron transfer from a laser-excited CdS colloidal particle to surface adsorbed viologens, paying special attention to its quantum yield.s*6 The quantum yield of the electron transfer at the surface was analyzed as a competitive reaction between recombination of photoinduced electron-hole pairs and the electron transfers6 Recently, we found that the size of colloidal CdS particles can be controlled by adding thiols such as mercaptoethanol.' Relatively narrow-dispersed ultrasmall semiconductor particles can be made easily in aqueous solution. Meisel and co-workers* have recently reported the similar effect of mercap(1) Kalyanasundaram, K.; Graetzel, M.; Pelizzetti, E. Coord. Cfiem.Reo. 1986, 69, 57-125. (2) Homogenous and Heterogeneous Photocatalysis; Pelizzetti, E., Serpone, N., Eds.; NATO AS1 Series C, Vol. 174; Reidel: Dordrecht, The Netherlands, 1986. (3) (a) Henglein, A. Top. Curr. Chem. 1988,143, 113-180. (b) Henglein,
A.; Weller, H. Photochemical Energy Conversion; Norris, J. R., Jr, Meisel, D., Eds.; Elsevier: New York, 1989; pp 161-172. (4) Duanghong, D.; Ramsden, J.; Graetzel, M. J . Am. Cfiem. SOC.1982, 104, 2977-2985. ( 5 ) Nosaka, Y.; Fox, M. A. J . Pfiys. Cfiem. 1986, 90, 6521-6522. (6) Nosaka, Y.; Fox, M. A . J . Pfiys. Chem. 1988, 92, 1893-1987.
(7) Nosaka, Y.; Yamaguchi, K.; Miyama, H.; Hayashi, H. Chem. Left. (Tokyo) 1988,605-608. (8) Hayes, D.; Micic, 0. 1.; Nenadovic, M. T.; Swayambunathan, V.; Meisel, D. J. Phys. Chem. 1989, 93, 4603-4608.
0022-3654 I90 12094-3152SO2.50 I O
toethanol. Using this procedure, we prepared ultrasmall CdS and In2S3semiconductor particles having various average diameters and measured the electron-transfer quantum yield @. When the size of semiconductor is extremely small, several characteristics may differ from bulk semiconductor. One of them is "size quantization effect", which shows the shift of electronic energy level^.^.^ A decrease of the space for photoinduced electron-hole separation may be another size effect.I0 In our previous kinetics analysis: the decrease of the space for photoinduced electron-hole recombination had not been taken into consideration. In the present study, a novel model will be applied to the analysis for the electron transfer at cluster-sized particles. Observed electron-transfer quantum yield can be successfully simulated by the model. The increase in quantum yield with decreasing size has been reported already for a CdS-methylviologen system." However, this phenomenon was not true in the case of In2S3viologen. By the present kinetic model, the decrease of 9 with the decreasing diameter of the particle is explained. Experimental Section
Ultrasmall CdS particles were prepared typically by adding 0.4 mL of 10 mM NazS (obtained from Nacalai Tesque Co.) aqueous solution (M = mol/L) into 19.6 mL of aqueous solution containing 4 Mmol of CdCI, (Nacalai Tesque), stabilizing polymer (0.13 g/L polyacrylic acid, Junsei Chemicals Co.), and 0-60 mM 2-mercaptoethanol (RSH, Tokyo Kasei Co.) at room temperature under red light. The amount of RSH was varied to obtain the (9) Brus, L. E. J . Pfiys. Cfiem. 1986,90,2555-2560 and references therein. (10) Rothenberger, G.; Moser, J.; Graetzel, M.; Serpone, N.; Sharma, D. K. J . Am. Cfiem. Soc. 1985, 107, 8054-8059. ( 1 1) Watzke. H. J.; Fendler, J. H. J. Phys. Cfiem. 1987, 91, 854-861.
0 1990 American Chemical Societv
Photochemical Kinetics of Semiconductor Particles
-'-I
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absorption edge I nm
i
'
'
5'
photon density /
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Id9 (
50 I cm3 C d S ) '
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3753
!
'
Figure 1. Quantum yield of MV*+ as a function of laser-induced photon density (No)in CdS ultrasmall particles of various average sizes. Difference in the size is indicated with absorption edge of the spectrum. Conditions: 0.4 mM CdS, 0.05 g/L polyacrylic acid, 0.62 mM MV2+, pH = 3.9. Curves are calculated with the parameters listed in Table I.
Results and Discussion Effect of Particle Size and Photon Density on the Quantum Yield for CdS. The absorption change at 606 nm, which is characterized as the laser-pulse-induced reduction of methylviologen (MV2+), was measured for an ultrasmall CdS particle solution. The reduction was too fast15to detect with nanosecond laser equipment. Since the incident laser intensity was relatively small in the present experiments, the change in the absorbance after the pulse6 was not observed. The absorbance in the microsecond region after the laser pulse were used to calculate the quantum yield of electron transfer (9)with good precision. The molar absorption coefficient16 of 13 700 M-' cm-I was adopted in the calculation. The plot of 9 as a function of initial concentration of MVZ+can be analyzed basically with a Langmuir adsorption equation as reported previo~sly,'~ indicating that the photoinduced conduction band electrons are transferred to surface-adsorbed MV2+. In the following experiments, MVZ+was (12) Nosaka. Y.; Kuwabara, A.; Miyama, H. J . Phys. Chem. 1986, 90, 1465-1 470. (13) Nosaka, Y.; Igarashi, R.; Miyama, H. Anal. Chem. 1985,57,92-94. (14) Amand, B.;Bensasson, R. Chem. Phys. Lett. 1975, 34, 44-48. (15) Nosaka, Y.; Miyama, H.; Terauchi, M.; Kobayashi, T. J . Phys. Chem. 1988, 92, 255-256. (16) Watanabe, T.; Honda, K. J . Phys. Chem. 1982, 86, 2617-2620. (17) Nosaka, Y.; Fox, M . A. Langmuir 1987, 3, 1147-1 150.
._
3c:
350 wavelengin
L30
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Figure 2. Absorption spectra of ultrasmall In2S3particle solution prepared with various amounts of mercaptcethanol (RSH). Conditions: 0.1 mM In2&, 1 g/L poly(vinylpyrro1idone). n
desired average size of ultrasmall CdS particle^.^ Ultrasmall In2S3 particle solutions were prepared similarly to the case of CdS, except that poly(N-vinylpyrrolidone) or dextran sulfate (Tokyo Kasei) was used as a stabilizing polymer. Methylviologen (MV2+, Aldrich Chemicals) and sulfopropylviologen (1,l'-bis(sulfopropyl)-4,4'-bipyridine, SPV) were used as electron acceptors. SPV was synthesized12and used after repeated recrystallizations. Laser flash photolysis was performed with a homemade N2 laser (337 nm, pulse width (fwhm) of 9 ns). Samples were placed in a IO mm X 10 mm Pyrex glass cell and bubbled with N 2 gas for more than 15 min before the measurement. In order to stir the sample solution, the bubbling was continued during the measurement. The analyzing light from a xenon arc lamp was passed through an appropriate cutoff filter and was collected into a 1.5-mm aperture located at a side of the sample cell. Details of the analyzing system have been described already.I2 The signal was recorded with a digital memory (Riken Denshi TCH-1000 or TCGF-DG-8). Data from each sample were averaged for 10 laser shots by using a personal computer system.13 Incident laser intensity that was attenuated with several sets of glass filters was measured with triplet-triplet absorption of anthracene in a cyclohexane solution by adopting t = 64700 M-' cm-' at 422.5 nm with = 0.71.14 Absorption spectra of an aqueous solution of ultrafine semiconductor particles, which showed no light scattering, were measured with a Hitachi Model 2340 spectrophotometer. Numerical computation for the kinetic model was performed with an EPSON Model PC-286V personal computer and an MV/20000 minicomputer (Nippon Data General).
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absorption edge I nm
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Figure 3. Quantum yield of SPV'- as a function of laser-induced photon density ( N o ) in ultrasmall In2S3particles. The difference of size is indicated with absorption edge of the spectrum. Conditions: 0.2 mM In2S3, 0.5 g/L dextran sulfate, 1 mM SPV, pH = 7. Curves are calculated with the parameters listed in Table I.
used to maintain conditions such that electron transfer occurred with adsorbed MV2+ and not in the solution MV2+. Mercaptoethanol (RSH), which is added to control the size of CdS ultrasmall particles,' may affect the kinetics of photoinduced electron transfer. In order to check the effect, RSH was added after the particle formation. In this case, the optical spectrum of CdS solution was not changed with the addition of RSH, indicating that the coalescence of the particles does not occur with the later addition of RSH. The value of 9 was measured as a function of RSH added in the solution. The added RSH, which is presumably adsorbed on the surface, does not influence 9.This observation coincides with the recent reportla that describes the effect of diethyldithiocarbamate (DTC) adsorbed on CdS particles. The report showed that tightly bound DTC is not involved in the interfacial charge-transfer process to generate DTC radicals. Measurements of 9 at various incident laser intensities were performed for solutions of CdS ultrasmall particles. In Figure 1, typical experimental data are plotted as a function of photon density ( N o ) . No is calculated from the incident laser intensity and absorbance of the CdS solution together with the molecular weight and density of CdS crystals.6 The difference in the size is expressed by the absorption edge of the spectrum for each solution. The curves in Figure 1 were plotted according to the kinetic model described later. Effect of Particle Size and Photon Density on the Quantum Yield for In2S3. The size of ultrasmall In2S3 particles can be changed when RSH is present in the formation procedure as described in the case of CdS. Figure 2 shows the change in the absorption spectra with the amount of RSH added. The shift of the absorption edge is attributable to the quantization effect for ultrasmall semiconductor particle^.^,^ Photoinduced electron transfer was measured for SPV in an aqueous solution containing In2S3ultrasmall particles stabilized with dextran sulfate. The quantum yield was calculated from the absorption change at 602 nm with t = 12800 M-I cm-I,l9 by changing the SPV concentration in solution. The apparent as(18) Kamat, P. V . ; Dimitrijevic, N. M . J . Phys. Chem. 1989, 93, 4259-4262. (19) Willner, I.; Yang, J.-M.; Laane, C.; Otvas, J. W.; Calvin, M. J . Phys. Chem. 1981, 85, 3277-3282.
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The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
'I. 3
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0.6
1.:
0.2
0.3
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3
Figure 4. Kinetic model for the photoinduced reaction at ultrasmall semiconductor. x*l, represents the fraction of particle having n electrons and rn holes, which are both induced by photon absorption. Transitions are represented by eq 2.
sociation constant (Ksp ), obtained from the plot of l / @ vs 1 / [SPV], was 2.6 X lo4 &I. Kamat et aLzohave recently reported the reduction of SPV with laser pulse excitation of In2S3colloid in water-acetonitrile mixed solvent. They reported that the formation of SPV'- was prompt and that the dependence of the quantum yield on SPV concentration was expressed by a Langmuir-type adsorption equilibrium with Kapp= 3 X lo5 M-I. By comparing with their value, the value of Kappin the present observation decreases by 1 order of magnitude. This is explained as the effect of the stabilizing polymer and/or the difference of the solvent. The quantum yield was measured at various incident laser intensities and plotted in Figure 3 for two kinds of In2S3particle solution, which is assigned by wavelength of the absorption edge. Although CP increases with a decrease of photon density, the degree of the increase is small for the smaller particle. Thus, the crossing occurs at about No = IOzo ~ m - and ~ , the larger particle showed a higher electron-transfer efficiency at a lower photon density. This observation is apparently opposed to that in the CdS-viologen system, which is described above and reported by Fendler and co-workers.l' A following reaction model will explain the experimental results. Two-Dimensional Ladder Kinetic Model. In the previous study,6 it was shown that the quantum yield CP of the electron transfer from a laser-excited semiconductor particle to the surface-adsorbed molecule can be expressed by eq 1 when k, >> ( 1 - @)/az= constant-(k,/k,)No
f
No'kr /
ke
1
Figure 5. Relationship between quantum yield for electron transfer @ and N,k,/k, for ultrasmall particles of various volumes, calculated numerically with eqs 2 and 3. 0 indicates the crossing points where N,V = 1 . The broken curve is calculated by eq 1 .6
of the total number is represented by P,.As shown in Figure 4, transitions concerning Pminvolve the following processes: photogeneration of an electron-hole pair with increasing both n and m, charge recombination with decreasing both n and m, and electron and hole transfers from the particle with decreasing n and m, respectively. These processes are indicated with arrows in Figure 4. Since the kinetic scheme in which the reaction is expressed by going up and down between some two levels of the products is referred to as a ladder model, the present model may be named as the two-dimentional-ladder model. In order to simplify the model, the rate constants k, and kh are assumed to be independent of the number of charges, n and m . The recombination rate can be expressed by nmk,/V, here V represents the volume of the particle. Under these assumptions, the time differential of the fraction Pmis expressed by eq 2. Here,
g( r ) is the generation rate6 of photoinduced electron-hole pairs or the rate of photon absorption in units of cm-3 s-'. Provided that all electron-decay processes are involved with the electron transfer, the number of reduced viologen molecules can be calculated by summing up all electron-transfer processes and integrating with respect to time. Thus, the calculated transfer quantum yield is given by eq 3. Here, photon density No is
(1)
obtained experimentally and given by . f g ( t )dt in the numerical
( l / A t ) >> kh holds. Here, k , and kh represent the rate constants for decay of photogenerated electrons and holes, respectively; k, represents the rate constant for electron-hole recombination; and At represents the time width (duration) of the laser excitation pulse. Equation 1 described well the observed data for CdS-MV2+ solution, where the average diameter was estimated to be about 5 nm.6 This relationship between @ and the rate constants was the result of the usual rate equation formulated for electrons and holes in a particle. However, in the case where the particle size is extremely small or the photon density is very low, only a few pairs of the electron-hole are photogenerated and recombine in the particle. This means that "photon density" is not a continuous number, which is suitably used in the usual rate equations. In order to take into account the small particle effect, a new model was proposed. In this model, particles are assigned by two integers n and m, which represent the numbers of photoinduced electron and hole in the particle, respectively. The portion of the number of the particles assigned with two integers n and m against that
At the same condition imposed on eq 1 , that is, when k, >> l / A t and kh
