Photocatalytic Transformation of Organic Compounds in the

reaction with phenol and alcohols, and the trend observed with naked TiO2 is retained. ...... Visible Light Driven Photocatalytic Reactor Based on...
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Langmuir 2000, 16, 8964-8972

Photocatalytic Transformation of Organic Compounds in the Presence of Inorganic Ions. 2. Competitive Reactions of Phenol and Alcohols on a Titanium Dioxide-Fluoride System† C. Minero,* G. Mariella, V. Maurino, D. Vione, and E. Pelizzetti* Dipartimento di Chimica Analitica, Universita` di Torino, Via Pietro Giuria 5, 10125 Torino, Italy Received April 19, 2000. In Final Form: July 11, 2000

The photocatalytic transformation of phenol has been investigated on naked TiO2 and on TiO2/F (0.01 M F-) at pH 3.6 in the presence of different alcohols (tert-butyl alcohol, 2-propanol, and furfuryl alcohol). On the basis of a detailed kinetic analysis and the time evolution of the intermediates, it is suggested that on naked TiO2 the oxidation of phenol proceeds for 90% through the reaction with surficial bound hydroxyl radical, the remaining 10% via a direct interaction with the holes. On TiO2/F the reaction proceeds almost entirely via homogeneous hydroxyl radicals because of the unavailability of surface-bound hydroxyl in the presence of fluoride ions. The use of alcohols as a diagnostic tool for the analysis of the photocatalytic mechanism is discussed.

Introduction The nature and role of active species leading to degradation of organics on irradiated titania have been deeply investigated, but are still under active debate.1-5 After the photoexcitation of the semiconductor the primary oxidant species, h+, reaches the surface and reacts with surface hydroxyl groups or molecular water. The trapped hole is usually described as an adsorbed hydroxyl radical whose nature is probably represented by the spin resonance between hydroxyl and lattice -O-. However, controversial was the role of direct electron transfer to the hole versus •OH radical oxidation of the organics.6-9 Although most evidence favors the •OH radical mechanism, hole oxidation has been suggested for compounds lacking abstractable hydrogen and for some aromatic compounds, as evidenced by diffuse reflectance flash photolysis.10 The fluoride displacement of the surficial hydroxyl group of titanium dioxide in aqueous solution has been shown to introduce relevant modifications in the kinetics and mechanism of the photocatalytic degradation of phenol.11 A variety of anionic species in aqueous solution undergoes † Part of the Special Issue “Colloid Science Matured, Four Colloid Scientists Turn 60 at the Millennium”.

(1) Bahnemann, D. W.; Cunningham, J.; Fox, M. A.; Pelizzetti, E.; Pichat, P.; Serpone, N. In Aquatic and Surface Photochemistry; Helz, G. R., Zepp, R. G., Crosby, D. G., Eds.; Lewis Publ.: Boca Raton, FL, 1994; pp 261-316. (2) Hoffmann, M. R.; Martin, S. T.; Choi, W.; Bahnemann, D. W. Chem. Rev. 1995, 95, 69-96. (3) Pelizzetti, E.; Minero, C. Electrochim. Acta 1993, 38, 47-55. (4) Kesselman, J. M.; Weres, O.; Lewis, N. S.; Hoffmann, M. R. J. Phys. Chem. B 1997, 101, 2637-2643. (5) Bahnemann, D. W.; Hilgendorff, M.; Memming, R. J. Phys. Chem. B 1997, 101, 4265-4275. (6) Krautler, B.; Bard, A. J. J. Am. Chem. Soc. 1978, 100, 59855989. (7) Carraway, E. R.; Hoffman, A. J.; Hoffmann, M. R. Environ. Sci. Technol. 1994, 28, 786-793. (8) Mao, Y.; Schoneich, C.; Asmus, K. D. J. Phys. Chem. 1991, 95, 10080-10089. (9) Kormann, C.; Bahnemann, D. W.; Hoffmann, M. R. Environ. Sci. Technol. 1988, 22, 798-804. (10) Draper, R. B.; Fox, M. A. Langmuir 1990, 6, 1396-1401.

inner-sphere ligand substitution reaction with the surface hydroxyl as follows:

tTiOH + X- f tTiX + OH-

(1)

Fluoride ion, as extensively discussed in the previous paper,11 replaces the basic hydroxyls (as confirmed by infrared and X-ray photoelectron spectroscopy),12,13 according to the above reaction (where X- ) F-), for which an equilibrium constant K1 ) 8 × 10-7 has been reported.14 The comparison with the equilibrium constants in homogeneous solution for ions similar to Ti4+ (e.g., Zr4+, Hf4+, VO2+) shows that the log (K1) for OH- and F- complexation is 4.5-5.0,15 then comparable with the reported pK1. At pH ) 3.6 the surface coverage by fluoride ions was maximum.11 The reaction rate was strongly dependent on the surface coverage by tTi-F species (concentration of fluoride ions and pH). It was argued that, for a surface covered by fluorine, the redox process of degradation would follow different routes from those in the presence of tTi-OH species. When the surface is hydroxylated the reaction would proceed with surface-trapped holes and direct electron transfer. When the surface is covered by fluorine, it was concluded that the kinetic pathways for reaction with subsurface holes and with free •OH in solution are predominant. It was also deduced that the direct electron transfer is at maximum 10% in respect to the overall reaction rate on fluorinated titania. As a consequence, most of the reaction would proceed on fluorinated titania through the free •OH radical pathway. However, the experiments were silent about the relative role of water(11) Minero, C.; Mariella, G.; Maurino, V.; Pelizzetti, E. Langmuir 2000, 16, 2632-2641 (12) Van Veen, J. A. R. Z. Phys. Chem. 1989, 162, 215-229. (13) Sanchez, J.; Augustynski, J. J. Electroanal. Chem. 1979, 103, 423-426. (14) Herrmann, M.; Kaluza, U.; Bohem, H. P. Z. Anorg. Chem. 1970, 372, 308-313. (15) Sillen, L. G.; Martell, A. E. Stability Constants of Metal-Ion Complexes; Special Publ. Nos. 17 and 25. The Chemical Society: London, 1964, 1971.

10.1021/la0005863 CCC: $19.00 © 2000 American Chemical Society Published on Web 09/19/2000

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Langmuir, Vol. 16, No. 23, 2000 8965

mediated oxidation (through free •OH radical) and direct electron transfer.11 The kinetic analysis of the experimental results as a function of the fluoride concentration and pH left some questions still open. On naked TiO2 it was not possible to quantify the relative role of reaction with surface-trapped hole versus direct electron transfer, the role of interactions of organics with the surface, and the role of the back reaction on recombination centers. Through experiments reported on TiO2/F the relative role of free •OH reaction versus direct electron transfer was only estimated.11 The effect of alcohols on the photocatalytic rate of transformation has often been interpreted in terms of discriminating between direct hole oxidation and reaction with •OH radicals (either adsorbed or free).16,17 In a previous study on the photocatalytic degradation of 2,4dichlorophenoxyacetic acid at pH 3 the initial step was established to be the direct hole oxidation, whereas below and especially above pH 3 it shifts progressively to an • OH radical-mediated mechanism.18 The hole-mediated path gives CO2, as expected from one-electron oxidation of the carboxy group. In addition, the degradation rate is little affected by alcohols. Similarly, methanol does not affect salicylic acid degradation at pH 4.19 However, for 2,4-dichlorophenoxyacetic acid the •OH-mediated path results in low yields of CO2, indicating that the mechanism shifts to the attack of •OH radical to the aromatic ring, which is strongly inhibited by the alcohols. Interestingly, 2,4-dichlorophenol degrades predominantly through an • OH-mediated process at pH 3, as witnessed by the strong alcohol inhibition.18 However, the direct electron abstraction from the alcohol could also occur according to

h+ + R2CHOH f R2CHOH•+ f R2CHO• + H+

(2)

It has been suggested that this reaction could be relevant with respect to hydrogen abstraction at high alcohol concentration.20 We report here on the effect of different alcohols at different concentrations on the kinetics of degradation of phenol both on naked TiO2 and TiO2/F. The surface coverage by fluoride ions impedes the surface trapping of photogenerated holes (as tTiO•), with the possibility to discriminate, by comparison with naked TiO2, the surfacemediated pathway from that taking place via free •OH radicals. Experimental Section All degradation experiments have been carried out using TiO2 Degussa P25 as photocatalyst, after prior irradiation and washing to avoid possible interference from ions adsorbed and residual carbon. Phenol, catechol, quinol, and NaF (Aldrich) were used as received. HClO4, HNO3, and NaOH (reagent grade) were used to adjust the pH. Aqueous solutions of phenol and previously prepared suspensions of catalyst were mixed in the cells used for the irradiation experiments (final volume 5 mL). The cells containing the reaction slurry were kept in the dark in a water bath at a temperature (16) Richard, C.; Boule, P. New J. Chem. 1994, 18, 547-552. (17) Richard, C.; Bosquet, F.; Pilichowski J.-F. J. Photochem. Photobiol., A 1997, 108, 45-49. (18) Sun, Y.; Pignatello, J. J. Environ. Sci. Technol. 1995, 29, 20652072. (19) Tunesi, S.; Anderson, M. A. J. Phys. Chem. 1991, 95, 33993405. (20) Rabani, J.; Jamashita, K.; Ushida, K.; Stark, J.; Kira, A. J. Phys. Chem. B 1998, 102, 1689-1695.

Figure 1. Photocatalytic degradation of phenol (2 × 10-4 M) without fluoride (top) and with fluoride 0.01 M (bottom) in the presence of different amounts of tert-butyl alcohol. TiO2 0.1 g L-1, pH 3.6. close to that of the lamp housing used for illumination until they reached the working temperature (about 50 °C). Irradiation was carried out in cylindrical Pyrex glass cells (4.0 cm diameter, 2.3 cm height) on 5 mL of the aqueous suspensions using a 1500-W Xenon lamp (Solarbox, Co. Fo. Megra, Milan, Italy) equipped with a 340-nm cutoff filter. The samples were stirred magnetically during irradiation. Total photon flux (340-400 nm) in the cell and temperature during irradiation were (1.6 ( 0.2) × 10-5 mol of photons min-1 and 50 ( 5 °C, respectively, for all illuminating devices. The ratio of the measured rate of disappearance and the photon flux gives the photon efficiency. After the established irradiation time and filtration through 0.45-µm cellulose acetate membranes (Millipore), the whole sample was analyzed by HPLC for phenol and other dihydroxybenzenes. They were detected by HPLC using a Rheodyne 7125 injector, an RP C18 column (Lichrochart, Merck, 12.5 cm × 0.4 cm, 5 µm packing), high-pressure two-pump gradient (Merck Hitachi L-6200), and a UV-Vis detector (Merck Hitachi L-4200).

Results Different alcohols, namely 2-propanol, 2-methyl-2propanol (tert-butyl alcohol), and furfuryl alcohol, were examined for their effect on phenol degradation on naked TiO2 and TiO2/F. Figure 1 shows some examples of their effect on the degradation of phenol. The pseudo-first-order rate constants are reported in Table 1. Experiments such as that reported in Figure 1 have been averaged over three different runs, either performed at different times,

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Table 1. Observed Pseudo-first-Order Rate Constants (min-1) for Degradation of Phenol (2 × 10-4 M) on TiO2 0.10 g L-1 at pH 3.6 (HNO3)a observed rate constants, min-1

TiO2 naked

TiO2/F

a

[alcohol], M

tert-butyl alcohol

2-propanol

furfuryl alcohol

0 0.001 0.0013 0.002 0.005 0.01 0.013 0.02 0.05 0.10

(5.6 ( 0.6) × 10-2 2.6 × 10-2 2.1 × 10-2 1.45 × 10-2 1.0 × 10-2 7.8 × 10-3

(5.6 ( 0.6) × 10-2 1.9 × 10-2 1.6 × 10-2 1.1 × 10-2 6.3 × 10-3 4.5 × 10-3

(5.6 ( 0.6) × 10-2 1.5 × 10-2 1.2 × 10-2 7.8 × 10-3 2.6 × 10-3 1.2 × 10-3 -

0 0.001 0.002 0.01 0.02 0.10

0.15 ( 0.03 5.7 × 10-2 2.8 × 10-2 6.7 × 10-3

0.15 ( 0.03 3.2 × 10-2 1.8 × 10-2 3.8 × 10-3

0.15 ( 0.03 3.6 × 10-2 2.0 × 10-2 4.9 × 10-3 1.1 × 10-3

TiO2/F indicates addition of [F-] ) 0.01 M.

or with different illuminating devices. The reproducibility is within (15%. At the highest alcohol concentrations the phenol degradation rate becomes very low, and affected by even higher uncertainty. In addition, at very long times secondary reactions could take place. The time evolution of substrate concentration corresponded to first-order exponential rate law (until 1/e). The initial rate was calculated by r ) k C0, where k is the exponential decay constant and C0 is the initial substrate concentration. A work that examined the influence of other organics on the degradation rate of phenol indicated that the photodegradation rate was mainly determined by the total amount of aromatics present in the aqueous medium, independently from their nature (but only substituted phenols were considered). The rate was scarcely affected (at 10 times concentration) by the presence of aliphatic compounds (alcohols and carboxylic acids).21 On TiO2/F the effect of alcohol inhibition is pronounced. In the absence of any scavenger with phenol 2 × 10-4 M, the rate constant is 0.15 min-1, which decreases to 0.057 (with 0.01 M tert-butyl alcohol) and to 6.7 × 10-3 min-1 (with 0.1 M tert-butyl alcohol). For comparison the rate constant for 0.01 M phenol is 2.5 × 10-3 min-1 under the same experimental conditions. The presence of 2-propanol 0.01 M decreases the rate constant to 0.032 min-1. Furfuryl alcohol is more effective, decreasing to 0.036 (at 0.001 M) and to 0.0049 min-1 (at 0.01 M). Furfuryl alcohol seems to behave with similar reactivity of phenol on the basis of the overall organic loading. On naked TiO2 in the presence of 0.01 M tert-butyl alcohol the pseudo-first-order rate constant for the degradation of phenol (2 × 10-4 M) decreases from 0.056 to 0.026 min-1. For comparison at 0.01 M of phenol (i.e., the same organic loading) the rate constant is 2.3 × 10-4 min-1. Then the presence of 50-fold excess of tert-butyl alcohol decreases only 2 times the phenol degradation rate. The degradation rate constant of phenol decreases further to 7.8 × 10-3 min-1 in the presence of 0.1 M tert-butyl alcohol. 2-Propanol 0.01 M is slightly more effective, decreasing the phenol degradation rate constant to 0.019 min-1. Experiments with phenol 1 × 10-3 M, not reported in Table 1, showed a decrease from 8.8 × 10-3 min-1 to 1.7 × 10-3 M in the presence of 0.1 M 2-propanol. Furfuryl alcohol decreases the phenol (2 × 10-4 M) degradation rate constant from 0.056 min-1 to 1.5 × 10-2 M (at 0.001 M furfuryl alcohol); it is ca. 10 times more reactive than 2-propanol. (21) Marcı`, G.; Sclafani, A.; Augugliaro, V.; Palmisano, L.; Schiavello, M. J. Photochem. Photobiol., A 1995, 89, 69-74.

The relative experimental rates (r in the presence of alcohol/rate in its absence) are plotted in Figure 2 as a function of the inverse alcohol concentration (for the rationale of this plot see below) according to

[P] r )b+m r0 [A]

(3)

Figure 2 (bottom) shows that in the presence of fluorinated titania the relative rate r/r0 versus [P]/[A] (where [A] is the molar alcohol concentration) is linear with a very small intercept. In the presence of naked titania, at the same pH of the bottom figure, Figure 2 (top) shows that the intercept b is small only with furfuryl alcohol, whereas a nonnegligible intercept is shown by tert-butyl alcohol and 2-propanol. Some degradation experiments have been performed also at different phenol concentrations (1.0 × 10-4 and 3.0 × 10-4 M) at the ratio [P]/[A] ) 0.01 for the three alcohols investigated. Although the absolute rates are different, the ratios r/r0 were found to agree within the experimental errors with those shown in Figure 2 for phenol 2 × 10-4 M. Discussion The data of Table 1 and Figure 2 can be rationalized by a kinetic analysis on the basis of reactions depicted in Scheme 1. This scheme considers that bulk holes, formed upon photon absorption, migrate to the surface where they can interact with surficial water or hydroxyl groups (t TiOH) to form •OH or tTiO•, respectively, or be trapped as subsurface holes. As trapped, the hole may interact with organics through direct electron transfer both through surficial -O- or -Ti- species. Through •OH or tTiO• it reacts via a mediated pathway. The distinction is important because, as will be clear below, the intermediates formed in the two paths may be different. An issue often raised is whether the initial oxidation of the organic substrate occurs on the surface of the photocatalyst or in solution. On naked TiO2, increasing evidence on the basis of different experimental techniques is given for a surface mechanism.7,22-24 Thus concentra(22) Lawless, D.; Meisel, D.; Serpone, N. J. Phys. Chem. 1991, 95, 5166-5170. (23) Minero, C.; Catozzo, F.; Pelizzetti, E. Langmuir 1992, 8, 481486.

Photocatalytic Transformation of Organic Compounds

Langmuir, Vol. 16, No. 23, 2000 8967 Scheme 1. Simplified Kinetic Pathways for Phenol (P) and Alcohol (A) Reactions under Photocatalytic Conditionsa

a Pathways through adsorbed water or surface hydroxyl groups are depicted together because they are reciprocally alternative in the presence or absence of fluoride ions (see text).

relation of the rate with the substrate, electron scavenger concentration, and the absorbed light. The published analysis gives the correct dependence of the rate on the substrate concentration (Langmuirian or peaked shape versus [substrate]). For the purpose of this paper a simplified analysis will be carried out, in consequence to the fixed concentration of the substrate on which the rate is calculated. In particular, the network of interrelated pathways of electron/hole formation and recombination, and electron scavenging by oxygen can be combined, assuming a net rate of hole formation proportional to the absorbed light (k0) under stationary conditions. Following Scheme 1, and applying the stationary state hypothesis to {h+}, {h+tr}, and [•OH] (or {tTiO•})

d{h+}/dt ) 0 ) k0 - k′1{h+}{H2O} - k2{h+} Figure 2. Rates for degradation of phenol (2 × 10-4M) in the presence of various amounts of different alcohols relative to that measured in the absence of alcohol: (top) TiO2 P25 Degussa 0.10 g L-1 at pH 3.6 (HNO3); (bottom) TiO2/F system (as above with addition of [F-] ) 0.01 M). Full lines: linear interpolation according to eq 3; dotted lines: model calculation according to eq 6 (for parameters see Table 3).

tions should be expressed as surface concentrations, and only for •OH radical reactions, the concentrations are expressed over the solution volume. Owing to the low hydrophobicity of both phenol and alcohols used, and the (relatively) low concentration used, the surface concentration can be assumed proportional to the bulk concentration. The surface concentration {I} is proportional to the solution concentration of I by {I}) KI [Ifree]/(CcatS), where S is the specific surface area (m2 g-1), and Ccat is the concentration of powdered catalyst (g L-1) over the entire volume of the solution. The partition coefficient KI may be constant as the total analyte concentration CIf0, or KI itself is low, or even a complex function of CI depending on the adsorption isotherm.25 A detailed kinetic analysis of the primary events for photocatalysis, recently published,26 led to a complex (24) Warman, J. M.; de Haas, M. P.; Serpone, N.; Pichat, P. J. Phys. Chem. 1991, 95, 8858-8863. (25) Minero, C. Light and Chemically Driven Reactions and Equilibria in the Presence of Organic and Inorganic Colloids. In Marine Chemistry. An Environmental Analytical Chemistry Approach; Gianguzza, A., Pelizzetti, E., Sammartano, S., Eds.; Kluver Academic Publishers: Dordrecht, 1997, p 39. (26) Minero, C. Catal. Today 1999, 54, 205-216.

(4a)

d{h+tr}/dt ) 0 ) k2{h+} - k5{h+tr}{P} - k6{h+tr}{A} (4b) d[•OH]/dt ) 0 ) k′1{h+}{H2O} - k3 [•OH] [P] k4 [•OH] [A] (5a) d{tTiO•}/dt ) 0 ) k′1{h+}{tTiOH} k3 {tTiO•}{P} - k4 {tTiO•}{A} (5b) the concentrations {h+}, {h+tr}, and [•OH] or {tTiO•} are given as a function of phenol ({P}, [P]), and alcohol ({A}, [A]) concentrations. Assuming from the above discussion at fixed catalyst concentration that {P} ) KP [P] and {A} ) KA [A], and equating k′1{H2O} ) k1, or alternatively k′1{tTiOH} ) k1, the rate r of phenol disappearance in the presence of alcohol is given by eq 6 (actually for fluorinated titania).

where r0 is the rate (measured) in the absence of alcohol. For the case of naked titania, the rate expression is very close to eq 6, except for the term 4, which has a residual dependence on the partition constants KA and KP. Actually,

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Table 2. Rate Constants of Selected Substrates with •OH30 and SO -• Radical31 4 •OH

phenol anisole tert-butyl alcohol 2-propanol furfuryl alcohol H2O

1.4 × 6.0 × 108 1.9 × 109 1.5 × 1010 -

1010a

k3/k4b

SO4•-

1 23.3 7.4 0.9 -

not available 5 × 109 4 × 105 3.2 × 107 not available k3[P] can hold for the investigated ranges of [A]/[P]. The worst case is that of butanol, for which at the lowest concentration the ratio k3[P]/k4[A] can be as high as 0.4. Under these conditions, the term 4 reduces to k3Kp[P]/ k4KA[A] for naked titania, and, under the hypothesis k5KP[P] . k6KA[A], eq 7 follows.

k3 KP[P] r/r0 ) R + (1 - R) k4 KA[A]

(7)

where R ) b ) k2/(k1+k2), and the slope m of eq 3 is [k1/ (k1+k2)](k3KP/k4KA). This equation is the rationale for eq 3. It can be applied to the case of tert-butyl alcohol and 2-propanol on naked titania. As shown in Figure 2, the experimental data are quite well correlated with a straight line, as predicted by eq 7. This equation was also tested in experiments with benzoic acid in the presence of naked and fluorinated titania,27 showing a good fit to the data. It shows that in great excess of alcohol, the rate of phenol disappearance is due only to the (weighted) direct electron transfer, as expected from the kinetic Scheme 1. The intercept b is given by the ratio of the rate for hole trapping with respect to rate of hole trapping plus that of hole transfer to water (or tTiOH). The slope m of eq 3 depends on the ratio k3/k4 (free •OH- or tTiO•-mediated oxidation) weighted by (1 - R), which is the ratio of the rate of hole transfer to water (or tTiOH) with respect to hole transfer water (or tTiOH) plus subsurface trapping. Data of direct electron transfer to the sulfate radical of tert-butyl alcohol and 2-propanol can be used as reference. (27) Minero, C.; Mariella, G.; Maurino, V.; Pelizzetti, E. In preparation.

The sulfate radical has been suggested to react by outersphere electron transfer.28,29 Table 2 reports the more relevant literature data for the presently investigated compounds. For tert-butyl alcohol, direct electron transfer is about 4 orders of magnitude less than with phenol (actually anisole). If the same holds for the electron transfer to the hole, the above hypothesis on the rates k5{h+tr}{P} . k6{h+tr}{A} is supported. Thus, for butanol it may be suggested that k5KP[P] . k6KA[A] even for large values of [A]. It follows that R ) k2/(k1 + k2) ) 0.10, signifying that about 10% of the reaction of phenol on naked TiO2 proceeds through direct electron transfer through trapped holes, whereas 90% of the overall degradation rate proceeds through the tTiO•-mediated pathways. Actually, the rate ratio via direct or mediated oxidation of phenol β ) rdirect/(rdirect + rmediated) is related to the alcohol concentration by

1/β ) 1 +

k1k6k3 k2k5k4

1+ 1+

k5[P] k6[A] k3[P]

(8)

k4[A]

This relation for [A] f0 reduces to βo ) k2/(k2 + k1), indicating that the intercept R of eq 7 gives the rate ratio via direct or mediated oxidation of phenol in the absence of alcohol. Data obtained on naked TiO2 reflect the reactivity of both phenol and alcohols with surface-trapped holes, which are unable to form free •OH radicals. Radiation experiments undoubtedly showed that free •OH radicals react at diffusion-controlled rate with TiO2 colloids. Then, no free •OH radicals are allowed to leave the catalyst surface.22 The values of k3KP/k4KA are 1.4, 14.6, and 17.7 on naked TiO2 versus 0.93, 7.4, and 23.3 from data of Table 2 for furfuryl alcohol, 2-propanol, and tert-butyl alcohol, respectively. Because the slope of the plots of Figure 2, according to eq 7, is very near the independently measured k3/k4 ratio (see Table 2), it follows that (1 - R)KP/KA is close to one. This in agreement with the low value of R (see the intercept). However, the surface adsorption of phenol also has to be comparable to that of tert-butyl alcohol, as may be expected. A preferential specific interaction of phenol with the surface with respect to the alcohol could hardly be envisaged. As a consequence of the above discussion, the fraction of direct electron transfer k2/(k1 + k2) must be the same also in the presence of other alcohols on naked titania. For 2-propanol and furfuryl alcohol the intercept given by term 2 in eq 6 is increasingly smaller. Qualitatively, the smaller intercepts may be due to the increase in the denominator of term 2 of the relative weight of k6KA[A]. Again, if the parallelism with the reactivity of the sulfate radical can be assumed, k6 must increase passing from tert-butyl alcohol to 2-propanol and furfuryl alcohol (although no data are available for the last), leading to an increasingly lower intercept. As for tert-butyl alcohol, KP/KA will be near unity. Under these circumstances, and especially when k6KA[A] > k5KP[P], eq 6 transforms in a straight line function, with b ) 0 and m ) (k5k4k2 + k1k3k6)/[k4k6(k1 + k2)]: (28) Steenken, S. In Free Radicals in Synthesis and Biology; Minisci, F., Ed.; Kluwer Acad. Publ.: Dordrecht, 1989; pp 213-231. (29) Neta, P.; Madhavan, V.; Zemel, H.; Fessenden, R. W. J. Am. Chem. Soc. 1977, 99, 163-164.

Photocatalytic Transformation of Organic Compounds

[

]

k5 k3 [P] r/r0 ) R + (1 - R) k6 k4 [A]

Langmuir, Vol. 16, No. 23, 2000 8969

(9)

The actual slope m is greater than k3/k4 in the range KA[A]/KP[P] > k5/k6 > k3/k4. Rearranging eq 6 taking k3/k4 as known from that experimentally determined by eq 7, a linear form results where a known term is proportional to [A]/[P], with a slope k6/k5. Besides the scatter of data, an estimate of k5/k6 of the order of 120 can be derived. This result is in good agreement with the above hypotheses and the ratio of reactivity of anisole and 2-propanol with sulfate radical (see Table 2). As it is clear from the above discussion, when k6KA[A] becomes of the order of k5KP[P], not only the intercept is decreased, but also the slope of the straight line fitting the data is increased. Quantitatively, the effect can be explained by the following analysis. Let eq 6 be fit by a straight line mx + b, like eq 3. This can be accomplished by the least-squares method, which is the minimization with respect to parameters m and b of the integral of the square of errors between the original function and the interpolating straight line mx + b, where x ) [P]/[A]. This procedure makes it possible to obtain the parameters m and b as a function of the parameters of eq 6. For purpose of simplicity, let’s here assume that k3[P]/k4[A] . 1 (without this assumption the equations are only a little bit more involved). The actual straight-line parameters are:

b(x) ) R[1 + 6/xw - 2(3 - 2xw) ln(xw + 1)/x2w2] (10a) m(x) ) z(1 - R) + 6R[(2 + xw) ln(1 + xw) 2xw]/x3w2 (10b) In this way eq 6 is fit by a new function

r/r0 ) xm(x) + b(x)

(10c)

where x ) [P]/[A], w ) k5KP/k6KA, R ) β0 ) k2/(k2 + k1), and z ) k3/k4 (or k3KP/k4KA on naked titania). Note that both the straight-line parameters depend on the value of the product xw ) k5KP[P]/k6KA[A], which is the ratio of the direct electron transfer rate of P and A. The errors of interpolation using this new function are of the order of few percent, mainly when b(x) * 0. The slope m(x) both for wxf0 and wxf∝ is m(x) ) z(1 - R). Thus for intermediate values of wx, the actual slope is higher than z(1 - R), showing a maximum for a certain value of wx (unfortunately the analytical solution is not possible). The intercept is b(0) ) 0 and b(∝) ) R. The case of wxf∝ was treated above for tert-butyl alcohol. In this case the straight line is given by r/r0 ) R + z(1 - R) x, as obtained in eq 7. When the fit of the rate data by a straight line is accomplished in a restricted range of experimentally j and b h accessible values of x ) xmin...xmax, the average m (m and b of eq 3) are obtained by the minimization with respect to m and b of the definite integral in the chosen interval of the square of errors between the original function using eq 6 and the interpolating straight line. The resulting dependence is analytical, but cumbersome. The values of m j and b h deduced in this way are plotted in Figure 3 as a function of w ) k5KP/k6KA, assuming the values of z ) k3/k4 for each used alcohol as obtained by the fit with eq 6. The value of R ) βo ) k2/(k2 + k1) ) 0.10, calculated from experiments with tert-butyl alcohol, was the same for the three alcohols. Figure 3 shows that m j and b h increase and decrease through a maximum, as suggested above. Note that m j is very near the limit z (1

Figure 3. Average slopes and intercepts of eq 3 using R ) 0.10, and for each alcohol the values of k3/k4 from best fit with eq 6 (see Table 3). Dotted lines and arrows indicate the best fitting value of w according to the experimentally found m and b.

- R), and b h ) 0 or b h ) R for wf0 or wf∝, respectively, as discussed above. For the case of tert-butyl alcohol, assuming z ) k3/k4 ) 20 from Table 3, the slope and intercept consistent with that reported in Table 3 are obtained with a value of w j and b h are ) 2 × 104 (see Figure 3A). As w is high, both m invariant with respect to w, and thus either the value of R or z(1 - R) can be obtained with confidence, according to eq 7. Note that this ratio of reactivity of phenol and tert-butyl alcohol with subsurface holes is of the order of that reported for anisole/tert-butyl alcohol with sulfate radical. For the case of 2-propanol, assuming z ) k3/k4 ) 13.5, both the obtained m j ) 14.6 and b h ) 0.05 are in good

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Minero et al.

Table 3. Best Fit Results of Experimental Data According to Eq 3, and Best Fit Values of z and w with Eq 6 eq 6 with R ) 0.11 (naked); R ) 0.01 (TiO2/F)

eq 3 conditions TiO2/F + tert-butyl alcohol TiO2/F + 2-propanol TiO2/F + furfuryl alcohol TiO2 + tert-butyl alcohol TiO2 + 2-propanol TiO2 + furfuryl alcohol a

slope

intercept

corr. coeff.

18.6 ( 0.4 10.4 ( 0.7 1.1 ( 0.1 17.6 ( 0.8 14.6 ( 0.4 1.4 ( 0.1

0.005 0.008 0.01 0.10 ( 0.01 0.05 ( 0.01 ≈0

0.9997 0.997 0.998 0.997 0.998 0.998

z)k3/k4 18.6 ( 0.3 10.4 ( 0.4 1.2 ( 0.1 19.3 ( 0.6 13.5 ( 0.5 1.4 ( 0.1

w)k5/k6 (8 ( 4) × 102 (1 ( 0.5) × 103 5a (1.5 ( 0.6) × 104 (4 ( 1) × 102 5a

corr. coeff. 0.9996 0.998 0.998 0.996 0.997 0.998

Fixed value.

agreement with that obtained through the fitting (see Table 3), when wopt ) k5KP/k6KA ) 300 ( 100 (see in Figure 3B). This value is the same order of magnitude of that estimated using sulfate radical data (see Table 2). Figure 3C shows the calculation results for the case of furfuryl alcohol. In this case the value of the intercept (