J. Phys. Chem. 1988, 92, 1893-1897 and then to the protonated carbazole (Le., the spectrum labeled as 900 “ C in Figure 1). B. Evidence of Solutes Embedded in the Porous Supports. The word “embed” has been used without proof here and elsewhereS5An important question regarding the interaction of adsorbates and porous supports is whether the solutes are adsorbed on the specimen surface or are actually “embedded” in the pore walls of porous supports. To deduce the answer for this question, we have carefully observed the emission intensity of adsorbates at various sintering temperatures of Vycor glass. As discussed in the previous section, the dehydration of porous supports upon sintering should enlarge the size of the pore as a result of desorption of free water and loss of hydroxyl groups on the pore walls. If the adsorbates are really embedded in the pores of porous supports, the amount of adsorbates (Le., the concentration of emissive species) should increase with increasing the sintering temperatures. It is known4 that the condensation of silanols from one wall with those from opposite wall of the porous glass can occur at a sintering temperature higher than 600 OC. This results in rapid pore closure and a shrinkage of porous glass. Under this condition, the number of pores available (Le., the available surface area for adsorption) will decrease. This should lead to a decrease in the concentration of emissive species inside the pores at higher sintering temperature. The observed emission intensity will then be reduced if the adsorbates are indeed embedded in the pores of porous supports. Our experimental observations show a gradual increase in the emission intensity of embedded 9,lO-dp in the sintered Vycor glass up to -500 “C followed by a rapid decrease in the intensity for higher sintering temperatures. Moreover, we also observed that the emission of embedded species is from the entire sample rather than from the surface alone. One might argue that the observed change in the emission intensity is due to the difference in the adsorbate emission yield of hydrogen-bonded 9, lO-dp, protonated 9,10-dp, protonated dihdydro-9,10-dp, and protonated carbazole
1893
as generated chemically at various sintered temperatures of Vycor supports. We believe that this is not the case because the relative emission yields of those emissive species are quite similar in fluid solutions. Furthermore, we are currently investigating22the embedded species in Vycor supports where the adsorbates do not undergo the surface-induced transformation to further confirm our supposition.
V. Conclusion The low-temperature (77 K) emission technique has been used to examine the photophysical properties of embedded 9,lO-dp in the sintered Vycor supports. For the sintering temperatures between 25 and 300 “C, the polar groups of Vycor glass lead to the formation of hydrogen-bonded 9,lO-dp. At the sintering temperatures of 400,600, and 900 “C, the Bransted acid sites of Vycor glass provide a surface-induced transformation of embedded 9,lO-dp into protonated 9,1O-dp, protonated dihydro-9,10-dp, and protonated carbazole, respectively. The enhancement in the Bransted acidity of Vycor glass is a result of an increase in the number of the siloxane bridges upon sintering. For the first time, we provide an indirect line of evidence that the adsorbed 9,lO-dp is really embedded in the pores of Vycor supports. When the sintering temperature of Vycor supports rises from 25 to 400 “C, and then to 900 “C, the emission intensity of adsorbates gradually increases and then rapidly decreases. This is consistent with the gradual increase in the size of pores followed by the rapid pore closures of Vycor glass upon sintering. Acknowledgment. Financial support from the Research Corp., the Northern Illinois University Graduate School, and the Northern Illinois University College of Liberal Arts and Sciences is acknowledged. We thank the reviewers for a critical comment on the manuscript. (22) Lin, C. T.; Hsu, W. L., work in progress.
Kinetics for Electron Transfer from Laser-Pulse- Irradiated Colloidal Semiconductors to Adsorbed Methylviologen. Dependence of the Quantum Yield on Incident Pulse Width Yoshio Nosaka? and Marye Anne Fox*t Department of Chemistry, Technological University of Nagaoka. Nagaoka, 940-21 Japan, and Department of Chemistry, University of Texas at Austin, Austin, Texas 78712 (Received: June 1 , 1987; I n Final Form: November 9, 1987)
The dependence of the quantum yield for reduction of adsorbed methylviologen 9 on the pulse width At and intensity of the incident laser pulse was measured on colloidal CdS stabilized with poly(acry1ic acid) and on colloidal TiOz stabilized with poly(viny1 alcohol). The relationship among 9, At, the laser intensity, and the rate constants for electron transfer (k,), hole decay (kh), and electron-hole recombination ( k , ) was deduced from a quantitative reaction kinetics model. On colloidal TiOz, differences in @ were observed for 30-ps and IO-ns incident pulses, requiring that k, > lolo SKI,kh > 1O’O SKI,and k, > cm3 s-’. On colloidal CdS, however, no dependence of @ on At was observed, indicating that k, > 3 X 10” S C ’ , k, < 3 X lo-’ cm3 s-I, and k h / k ,
> 1. Abk, 5.1
log (slpholon] k,lk.) Figure 5. Same as Figure 4 except for the assumption that Atk,
> 1 and Ptk, 10" s-', kh > 10" s-I, and k, > 10" cm3 s-I are obtained on colloidal TiO,. Graetzel et al.14reported the kinetics for trapped electrons and trapped holes measured by picosecond absorption. Although they found a hole-trapping rate of 4 X lo6 s-I, we estimate a value for kh in our sample as greater than 1O'O s-l. This discrepancy is probably caused by a 3-unit p H difference between the two experiments, because the basic hydroxide groups at the surface of TiO, are considered to be deep traps for valence-band holesS3The presence of stabilizing polymer, which acts as a hole scavenger, may also increase the apparent value of kh. Acknowledgment. We are thankful to the Japan Society for the Promotion of Science for partial fellowship support for Y.N. in the U S . Support of this work from U.S. Department of Energy, Basic Energy Sciences, Fundamental Interactions Branch, is also gratefully acknowledged. The use of the equipment at the Center for Fast Kinetics Research, a facility supported by the National Institutes of Health and by the University of Texas at Austin, is greatly appreciated.
accumulated density ( ~ m - of ~ )electron-hole pairs induced by one laser shot. Therefore, the value of No is expressed as
No) = k J
d[h+]/dt = -k,[h+]
+ g(t)
- k,[e-] [h+] + g(t)
('41) (A2)
where [e-] and [h+] are densities ( ~ m - of ~ )the conduction-band electron and valence-band hole in the colloidal particle, respectively. The function g(t), expressed in units of cm-3 s-', is presumed to be proportional to the time profile of the laser pulse, which can be approximated by eq A3 by taking t = 0 at the peak of the laser pulse g(t) = ( ( U / T ) ' / *exp(-rut2) N~
('43)
('45)
In experiments, Nocan be calculated by using the molar absorption coefficient e (M-' cm-I) and the laser intensity: No = Pe[photon]
(Ab)
/3 = 10"pNA/(0.2M,)
('47)
where and where [photon], a value proportional to the incident laser intensity, is the concentration (micromolar) of photons absorbed in a solution having the absorbance of 0.2 cm-' (see Experimental Section). In this equation, NAis Avogadro's number (mol-I), and p and M , are the density (g/cm3) and molecular weight (g/mol) of Ti02. Empirically, the numerical values of @ are 1.004 X lOI7 and 1.447 X 1017cm-2 for polycrystalline CdS and anatase TiO,, respectively. In the reaction scheme of eq 1-4, all of the photoinduced conduction-band electrons are assumed to react with either valence-band holes or surface-adsorbed MV2+. With this assumption, the observed 9 can be calculated by eq A8. In order to solve
9 = Jk,[e-]
dt/N,
(A!)
eq A1-A8 numerically, a standard program for personal computers was used.2s The style of the associated differential equations (A1 and A2) shows that the product k,[photon] can be treated as one parameter. After the computation for various kinetic values, the relationship between 9 and [photon] can be obtained. In the cases where Ark, >> 1 and Atk, > l/At, the differential equations can be solved by adopting a steady-state approximation for [e-] and [h']. The light intensity is assumed to be a constant, Le., g ( t ) = g'. Thus, the following equations are obtained: kh[h+] = k,[e-]
Appendix In accordance with the reaction scheme of eq 1-4, the reaction rate for e- and h+ may be expressed as follows: d[e-] /dt = -k,[e-] - k,[e-] [h+]
dt
k,[e-]
+ k,[e-] [h+] - g' = 0 9 = k,[e-]At'/N,
(A91 ('410) ('41 1)
where At'= No/g' = (4 In ( 2 ) / ~ ) ' / ~ ( g ( O ) / g ' ) A t (A12) Equations A9-Al2 give the following relationship: (1
- a)/@' = Nok,/(k,khAt?
(A13)
or, with eq A6 (1 - @)/a2 0: ~[phOtOn]k,/(k,khAt)
('414)
When Atkh > 1, this relationship fairly well describes the curves of Figure 4. Equation A14 is the same as that used in our previous papers. 13,22 Registry No. MVZt, 4685-14-7; CdS, 1306-23-6; Ti02, 13463-67-7; PAA, 9003-01-4; PVA, 9002-89-5; MV", 25239-55-8.
where a = 4 In (2)/(At),
('44)
At is the laser-pulse width at half-height (fwhm), and No is the
(25) Merrill, J. R. Using Computers in Physics; Houghton Mifflin: New
York, 1976.
