592
J. Phys. Chem. 1981, 85, 592-594
that both models FE and FG give quite good fits to the cyclobutene data in the higher-temperature region that overlaps the lower-temperature portion of the cyclobutane study. The values of (a') resulting from the calculations vary from 2150 cm-l for both models, at 778 K, to 5150 and 3600 cm-l for models FE and FG, respectively, at 585 K (Table 11). For comparison, the value for cyclobutane2at 778 K was -2290 cm-l (model FE). At comparable temperatures, therefore, the difference between cyclobutane and cyclobutene is not great, even though the critical energy for the former reaction (20 700 cm-') is approximately twice that of the latter (11 300 cm-l). It could be tempting, therefore, to conclude that the correct model for energy transfer probably is one in which the average amount of energy transferred did not vary greatly with the energy content of either of these highly energized species. However, in the present study (Table 11),it can be seen that all of the models of energy transfer used give an adequate fit to the cyclobutene data, while models LG, EG, and GB are such that (AE')does vary with molecular energy content. We have applied models LG, EB, and GB to the cyclobutane data: and they are found to give worse fits than models FE and FG. It is evident that, for a clearer distinction to be made between the various models for energy transfer, it would be desirable, but difficult, to obtain data at much higher
temperatures than those which have been investigated. For the case of efficient collisions, data obtained at low temperatures do not provide adequate distinctions, although they do suffice here to illustrate the failure of a simple exponential model (FE),a conclusion that now has long standingg from steady-state work. Finally, it is evident from the present and earlier VEM work that the assumption frequently used in very low pressure pyrolysis (VLPP) that strong collider behavior adequately described gas-wall encounters at temperatures as high as 1200 K in many casedo is incorrect. The comparative insensitivity of conclusions with respect to the model in VEM work appears to arise from the circumstance that it integrates collisional efficiencies over a wide range of nominal energies from the low to high region; compensating features tend to prevail. We agree in this with a recent conclusion by Gilbert and King." Acknowledgment. We thank Dr. D. F. Kelley for useful discussions. This work was supported by the Office of Naval Research. (9) G. Kohlmaier and B. 5. Rabinovitch, J. Chern. Phys., 38, 1692, 1709 (19 6 . 1 ~ \ - - - - I .
(10)D. M. Golden, G. N. Spokes, and S. W. Benson, Angew. Chem., Int. Ed. Engl., 12, 534 (1973). (11) J. R. Gilbert and K. D. King, Chern. Phys., 49 367 (1980).
Photoassisted Hydrogen Production from Titania and Water S. Sate+ and J. M. White' Depattment of Chemistry, University of Texas at Austin, Austin, Texas 78712 (Received: September 12, 1980)
When Ti02,reduced by H2 or CO, is placed in an ambient of gas-phase water and illuminated with band gap light, H2 is evolved. Adding a small amount of O2completely retards this reaction. A dark reaction of reduced Ti02with water to form H2 also occurs at temperatures above 200 OC. These results show that H2 evolution is not the result of catalytic water photolysis but a photoassisted reaction of water with oxygen vacancies produced by the reduction.
Introduction The photodecomposition of water over heterogeneous catalysts containing compound semiconductors has recently received considerable attention. Some works involve the use of semiconductors alone for achieving this and the results and their interpretation are the subject of some disagreement. Schrauzer and Gath' concluded that water adsorbed on Ti02 or Fe20s-doped Ti02 was catalytically photolyzed in their system, whereas Van Damme and Hall: on the basis of finding only a trace of Hz, concluded that H2 formation arose from the noncatalytic photodecomposition of hydroxyl groups originallypresent on TiOD Kawai and Sakata? on the other hand, found that D2was formed in the dark when gaseous D20was contacted w t h Ti02reduced by CO under UV irradiation. The evolution of D2 was accelerated by illumination and continued even after evacuating D20, but no O2 was observed. The acceleration was ascribed to the photodecomposition of DzO over Ti02on the assumption that oxygen formed was held at the Ti02surface. This assumption is based on the fact that O2as well as H2was formed by the addition of RuOz, 'Research Institute for Catalysis, Hokkaido University, Sapporo 060, Japan.
a good electrode material for O2 evolution, to TiOD Rao et a1.4 have recently reported that Hz and HzOzare produced when reduced Ti02 (in flowing H2 for -6 h at 700-800 "C)is suspended in liquid water and illuminated in bubbling N2. Unreduced Ti02produces neither H2nor H202.
We have already reported that platinized Ti02 is a suitable catalyst for the photolysis of water to H2 and 02 but Ti02alone is not? Moreover, we found that reduced Ti02 produces H2 when illuminated in the presence of gaseous or liquid water as observed by Kawai and Sakatd and Rao et a1.tbut we concluded, in agreement with Van Damme and Hall: that this H2 production is noncatalytic. However, our results require somewhat different interpretation. This brief paper presents the experimental results and our interpretation of them, the latter relying (1) G. N. Schrauzer and T. D. Gath, J. Am. Chern. Soc., 99, 7189 (1977). (2) H.Van Damme and W. K. Hall,J. Am. Chern. SOC.,101, 4373 (1979). (3) T. Kawai and T. Sakata,Chern. Phys. Lett. 72,87 (1980).
(4) M. V. Rao, K. Rajeshwar, V. R. Pal Verneker, and J. DuBow, J. Phys. Chem., 84, 1987 (1980). (5) S. Sat0 and J. M. White,Chern. Phys. Lett., 72,83 (1980).
0022-365418112085-0592$01.25/0 0 1981 American Chemlcal Society
The Journal of Physical Chemistry, Voi. 85, No. 5, 198 1 593
Hydrogen Production from Titania and Water
3
80 120 ILLUMINATION TIME/(min)
40
160
Figwe 1. Evolution of H2 from illuminated, reduced TIO, immersed in liquid water: (a) Ti02 reduced by H2at 750 "C for 4 h; (b) at 700 "C for 6 h; (c) at 600 "C for 3 h (0.1 torr = 1 pmol).
heavily on a model for the energy band diagram of illuminated TiOp
Experiments and Results The experimental apparatus and procedures have been described elsewhere! Ti02 (MCB, anatase) was reduced in flowing H2 (or CO) under various conditions, cooled in H2 or CO, and stored in air. Reduced TiOz (0.25 g) was spread on the flat bottom of a quartz reaction cell and outgassed at 200 "C for -3 h. After introducing water vapor at room temperature, the sample was illuminated by a 200-W high-pressure Hg lamp and the products were analyzed by a mass spectrometer. In every case studied, only H2 was observed in the gas phase and its formation rate dropped to almost zero after a few hours of illumination. The maximum amount of H2 formed increased with the reduction temperature and time and it was larger for H2-reducedTi02than for CO-reduced samples prepared under the same conditions. The results described below were obtained for H2-reduced Ti02. For substrates reduced at temperatures above 700 "C, Hzwas formed even in the dark in agreement with Kawai and Sakata3 but its formation stopped within 30 min. When DzO instead of H 2 0 was used, the products were dominated by Dp Since the amount of HD formed did not exceed the value expected from the isotopic purity of DzO, the hydrogen evolved is believed to come fro-mwater added and not from preexisting surface hydroxyl groups. Support for this also comes from the facta that no increase in HD was observed when D2 (0.12 torr) was added to the H20 reduced Ti02 system under illumination and that no products were formed when Ti02 samples were illuminated in vacuo. Light of energy less than the band gap of Ti02produced no H2, suggesting that photogenerated electrons and/or holes play an important role. The addition of O2 (3.2 X torr) completely inhibited Hz formation and its pressure dropped by a factor of 2 after 1h of illumination. The addition of 13C0 (0.25 torr), on the other hand, had no effect and no 13C02was observed. This is significant since CO is oxidized over Ti02in the presence of band gap light and oxygen. When reduced Ti02 was immersed in liquid water and illuminated, the amount of Hz formed was larger than observed in the gas-phase process. The liquid water-Ti02 system was prepared by cooling the bottom of the reaction cell to 0 "C in order to cryogenically pump water from the reservoir to the cell. After the sample was covered with 0.2-0.3 mL of water, the cell was warmed to -23 "C and then illuminated. The results are shown in Figure 1 for variously reduced TiOz samples. Just as in the gas-phase process, the Hz evolution rate dropped to zero after a few
-1.8
t
O
40
80
120
i
160
TIME/(min)
-
Figure 2. First-order plots of H2 pressures (pmH* pHe)during the reaction of reduced TiO, with gaseous water (-24 torr) at 260 and 300 "C In the dark. TiO, was reduced by H2 at 700 "C for 6 h. p - h = 0.108 torr.
hours and no O2 was detected. The TiOz sample reduced torr (0.13 pmol) at 750 "C for 4 h produced -1.3 X of Hz in the dark (the pressure at time zero of curve a in Figure 1is due to this) and H2 formation was accelerated by illumination. Although the formation of H202was not checked in our experiments, its concentration is limited by photodecomposition to O2 and H20 over TiOP Rao et ala4observed that the addition of H202 (-5 pmol) to their reaction mixture (700 mL) followed by 1 h of illumination brought about a twofold decrease in the Hz02concentration. This implies that the maximum achievable concentration of H202over illuminated Ti02is very low, less than 4 pmol/L. Applying this to our system, 1 X lo5 pmol, at most, of H202could exist in the water. This is much less than the amount of H2 formed (>0.1 pmol). In addition to the above results, we find that Hz is also formed when reduced Ti02samples are heated in gaseous water at temperatures higher than 200 "C. The Hz formation rate in this thermal reaction is proportional to (pmH2 - pH2),where pmH2 is the maximum H2 pressure and pH2 the Hz pressure at time t . The time dependence can, therefore, be described by the first-order equation log (p_Hz - p q = -kt where k is the rate constant. Figure 2 shows plots of this relation for two sets of thermal reaction data. These data are consistent with a mechanism in which water reacts with oxygen vacancies of Ti02 at a rate proportional to their concentration. The activation energy of the thermal reaction is about 24 kcal/mol. It is noteworthy that the Hz formation rate in the liquid water-illuminatedTi02 system also depends on temperature and the activation energy is about 15 kcal/mol between 0 and 23 "C. The photoprocesses, however, do not obey a first-order equation.
Discussion and Conclusions All of our photoresulta are consistent with a mechanism in which a reaction between HzO and oxygen vacancies of reduced TiOz is photoassisted by the production of electron-hole pairs in the solid. This reaction is thermodynamically downhill and not catalytic. The reduction (doping) of Ti02,however, is important in the preparation of active Pt/TiOz ~ a t a l y s t sand ~ * ~the Ti02 electrodes of photoelectrochemical (PEC) cells,' even (6)5.Sat0 and J. M. White, J. Am. Chem. Soc., in press.
594
J. Phys. Chem. 1981, 85, 594-599
though the oxygen vacancies are photooxidized by water. We assume that the bulk oxygen vacancies are retained during the photolysis of water and the active materials therefore have a relatively high conductivity. Ease of photogenerated electron transport from Ti02 to Pt (or other cathode materials) and photochemical activity increase with conductivity. The position of the Fermi level and the thickness of the space charge layer of Ti02 will also be affected by doping. The fact that Ti02 alone is inactive for water photolysis can be described in terms of the energy band diagram of illuminated TiOP8 According to a recent studys in this area, the flat-band potential (electron Fermi level) of Ti02 (rutile) is about 100 mV more negative than the H+/H2 redox potential. This implies that the water photolysis in PEC cells with a TiOz photoanode is energetically possible under open circuit conditions. However, there are some potential drops, for example, across the Helmholtz layer, so that the overvoltage available for H2evolution becomes lower. Even if anatase has a somewhat more negative flat band potential than rutile,1° the overvoltage would be too low for efficient evolution of H2 at the Ti02 surface.l0
Similar overvoltage requirements for the reduction of protons are found with SrTi03.11 Consequently, these semiconductor catalysts show increased photocatalytic activity for water decomposition when a material, such as Pt, is added which readily evolves Hz at a lower overvoltage. In passing, we note that the maximum amount of Hz(1 pmol) produced thermally exceeds that observed in the photoreaction (-0.2 pmol). This difference is readily accounted for since in the photoprocess not all of the surface is illuminated. To summarize, in the process proposed here, water reacts slowly with surface oxygen vacancies to evolve H2and remove the vacancies by filling them with oxygen or hydroxyl species. This is a noncatalytic process but is significantly accelerated by band gap irradiation. Bulk oxygen vacancies are retained during the photoprocess. Experimental support for this proposal come8 from isotope tracing, the effects of reduction temperature and time, and the effects of added O2 and CO. In the photoprocess, photogenerated holes probably oxidize water to produce some oxygen-containing species which react with the oxygen vacancies at the surface.
(7)M. S.Wrighton, D. S. Ginley, P. T. Wolczanski, A. B. Ellis, D. L. Morse, and A. Linze, Proc. Natl. Acad. Sci. U.S.A. 72, 1518 (1975). (8)K.Rajeshwar, P.Sinch, and J. DuBow, Electrochem. Acta, 23, 1117 (1978);H.P. Maruska and A. K. Ghosh, Solar Energy, 20, 443 (1978). (9)M.Tomkiewicz, J. Electrochem. SOC.,126, 1505 (1979). (10)B. Kraeutler and A. J. Bard, J.Am. Chem. SOC,100,5985(1978).
Acknowledgment. This work was supported in part by the Office of Naval Research. (11)M. S.Wrighton, P. T. Wolczanski, and A. B. Ellis, J. Solid State Chem., 22, 17 (1977).
Influence of Concentration Fluctuations on Kinetics of Bimolecular Reactions Richard M. Noyes"' and William C. Gardlner, Jr.** Max-Plenck-Institut fur biophysikeilsche Chemle, 0 3 4 0 0 ettingen, Federal Republic of Germany (Received: March 1, 1980)
In formulatingthe conventional mass-action laws of elementary reaction rates, one normally assumes that reaction proceeds in a homogeneous system with uniform concentration(s)throughout. In fact there are always local fluctuations in concentration, increasing in relative size as the volume considered contains fewer and fewer reactant molecules. We show that experimentally interesting conditions exist where the dissipation rate of local concentrationfluctuationsis less than the local chemical reaction rate. It is then shown that the conventional rate laws for the elementary reactions A products, A + B products, and A + A products are still valid when averaged over the whole reacting system. For the latter case it is even required to consider local fluctuations explicitly in order to derive the conventional rate law at all.
-
Introduction One is accustomed to think of the mass-action rate laws for elementary chemical reactions as being so fundamental and so obviously true that there is no useful purpose in contemplating their validity. Thus for the (irreversible) elementary reaction types A products (1) A + B products (11) A + A products (111) we immediately write -d[A]/dt = kI[A] (1)
--
(1) Department of Chemistry, University of Oregon, Eugene, OR 97403. (2)Department of Chemistry, University of Texas, Austin, TX 78712. 0022-365418112085-0594$01.25/0
-
-
-d[Al/dt = kII[Al[Bl -d[A] /dt = 2kIII[AI2 and their corresponding integrated forms [AI = [AI0 exp(-kIt) [AI-' = [Ala'
+ kIIt
[A]-l = [Alo-l
+ 2kIIIt
(2) (3) (4)
(5) where it has been assumed that the starting concentrations of A and B are equal, and
(6) Various theoretical arguments are used to make these rate laws plausible. They all involve deciding how the time evolution of some hypothetical system is related to the probability of any molecule in it undergoing reaction in the next time interval dt, and how this in turn is related 0 1981 American Chemical Society
