Dogmas and Misconceptions in Heterogeneous Photocatalysis. Some

Sep 13, 2005 - Thus, the major conclusion that can be drawn from the above reflections is that the simple LH kinetic model cannot universally describe...
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J. Phys. Chem. B 2005, 109, 18515-18521

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Dogmas and Misconceptions in Heterogeneous Photocatalysis. Some Enlightened Reflections A. V. Emeline,† V. K. Ryabchuk,‡ and N. Serpone*,⊥,§ Kanagawa Academy of Science and Technology, Kawasaki-shi, Kanagawa, Japan, Department of Photonics, Institute of Physics, St.-Petersburg State UniVersity, St.-Petersburg, Russia, and Dipartimento di Chimica Organica, UniVersita di PaVia, Via Taramelli 10, PaVia 27100, Italia. ReceiVed: May 5, 2005

In a recent article, Ollis1 analyzed heretofore reported photocatalyst kinetics of surface photochemical reactions that take place in heterogeneous systems and that rely heavily on the Langmuir-Hinshelwood (LH) kinetic model to interpret the experimental observations. This model assumes a fast adsorption/desorption equilibrium step and a subsequent slow surface step. His interesting analysis of the experimental results reported in 2000 by Emeline and co-workers,2 Xu and Langford,3 and Martyanov and Savinov4 prompted our reexamination of the LH kinetic model along with several other dogmas that continue to propagate in the heterogeneous photocatalytic landscape. This short article discusses some of these issues and reexamines certain misinterpretations. Specifically, we reexamine (1) the a priori assumed validity of the LH kinetic model in heterogeneous photocatalysis, (2) the recombination of photogenerated free charge carriers on the solid (metal oxide) photocatalyst by the band-to-band recombination pathway, and (3) the mistaken assertion1 that the kinetics of a heterogeneous photoreaction are either only first-order dependent or half-order dependent on photon flow (i.e., light irradiance).

1. Langmuir-Hinshelwood Kinetic Model The first dogma concerns the nearly universal robotic application of the Langmuir-Hinshelwood (LH) kinetic model to interpret the kinetic data of heterogeneous photoreactions.5 In the 1980s, we were among those6 that used the LH kinetic model to infer that photoreaction occurred on the catalyst surface. However, soon thereafter we recognized that the kinetics were simply a manifestation of saturation-type kinetics, in general, and were not attached to any single kinetic model. Whoever first reported the concentration dependence of the rate of a photochemical reaction taking place on a heterogeneous catalyst approximated the kinetic data to the hyperbolic function of eq 1 and subsequently gave it an interpretation in terms of the LH kinetic model for which the usual kinetic expression is described by eq 2:

Y) Rate )

ax b+x kLHKL[M]

1 + KL[M]

(1)

(2)

in which b-1 ) KL () kads/kdes) is the Langmuir adsorption constant, and a ) kLH is the apparent LH rate constant for the reaction. Initially, this interpretation of the data to infer an LHbased mechanism for the heterogeneous photoprocess was a brilliant “chef-d’oeuvre” in the early days of investigating photochemical reactions on surfaces. The extension of the LH kinetic model to photoinduced processes on surfaces originated from heterogeneous catalysis (e.g., see ref 7), in which the LH model finds its “raison d’eˆtre” through the Langmuir adsorption isotherm.8 * Corresponding author. E-mail: [email protected] or serpone@ vax2.concordia.ca. † Kanagawa Academy of Science and Technology. ‡ St.-Petersburg State University. ⊥ Universita di Pavia. § Professor Emeritus, Concordia University, Montreal, Canada.

The above notwithstanding, in the 1960s the photochemical group of Rapoport and co-workers9 proposed a different interpretation of the kinetic data, which they interpreted as the simple photochemical process summarized in reactions 3-5:

S + hV f S*

kabs

(3)

S* f S

kd

(4)

S* + M f f Products

kr

(5)

They did so without any a priori bias toward a particular model. In this description, the absorption of light by the surface of the photocatalyst yields excited states of surface sites S*, which is determined by the absorption cross-section kabs of potential surface-active centers S. The nonradiative decay of these active centers (reaction 4) back to ground-state S is a spontaneous reaction that occurs through first-order kinetics, kd. The reaction of reactant molecules, M, with S* at the surface occurs via second-order kinetics kr (e.g., M might be H2 and CH4 in a gas-solid system or phenol in a solution-solid system). Application of the steady-state approach for the exited state of the surface site (d[S*]/dt ) 0) in this rather simplistic mechanism yields an expression (eq 6) for the initial rate that is identical to the functions given by eqs 1 and 2, namely,

Rate )

kabskr F[S][M] kd + kr [M]

(6)

in which F is the photon flow (or light irradiance), [S] is the initial concentration of the light absorbing surface centers, and [M] is the initial concentration (or pressure) of the reactant. Equation 6 can be reduced to eq 2 by substituting kabsF[S] for kLH and kr/kd for KL. We hasten to note that the physical sense of the constant KL ) kr/kd is entirely different from the sense given in the LH kinetic treatment.2 The parameter 1/kd ) τd in eq 6 reflects the lifetime of the surface-active center S*, whereas

10.1021/jp0523367 CCC: $30.25 © 2005 American Chemical Society Published on Web 09/13/2005

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the LH reverse constant 1/kdes ) τdes (see above) denotes the lifetime of molecules at the surface in an adsorbed state Mads. When kr is taken as the rate constant for the reaction between the surface-active center S* and the molecule M, the lower limit of τd can be estimated from approximations of the experimental rate dependencies embodied in eq 6. The estimated τd values for various systems (TiO2/H2/CH4,10 MgO/O2 and CaO/O2,11 MgAl2O4/H2/O2,12 KBr/O2,13 and AgBr/O214) scale in a wide time range from seconds to microseconds. A similar mechanism was proposed for the photooxidation of gaseous H2 by O2 prephotoadsorbed on KBr15 and on MgF2, CaF2, SrF2, and BaF2.16 Decay times (τd) ranging from 10-2 to 10-4 s have also been determined for the spontaneous decay: O2*(ads) f O2(ads) of excited (presumably singlet 1∆g O2-like) adsorbed species. It is worth noting that the mechanism suggested by eq 6 is in fact of the Eley-Rideal type (ER).10-16 The remarkable resemblance of the experimental kinetics predicted by the LH and ER reaction mechanisms has been discussed previously.17-20 Regardless of the type of mechanism, however, the dependence of the rate of a photocatalytic reaction on photon flow F is referenced only by the kLH dependence on photon flow. The term kLH ) kabsF[S] in eq 6 is such an example. Thus, even at the simplest level of mechanistic understanding of a photoprocess, two different mechanisms (includes the LH mechanism) yield the same kinetic functionality for the photoinduced surface reaction in liquid-solid and gas-solid systems. It is also relevant to point out that even a reaction occurring in a strictly homogeneous phase of the type given by reaction 7 will yield an expression similar to eq 2, and, as Ollis1 has pointed out, there are several examples in enzyme kinetics5 in which this is observed (recall the Michaelis-Menten kinetics). This is not uncommon; in fact it is rather typical of kinetic studies. That is, an appropriate mechanism must always describe the corresponding kinetic behavior of the experimental system, and although a proposed mechanism might appropriately describe the experimental kinetics, it is not a sufficient condition to conclude that such a mechanism is the actual pathway for the reaction. This is the so-called “golden rule” of any kinetic study: the kinetic data alone do not unequivocally establish the actual mechanism. A proposed mechanism must always be supported by other evidence outside the field of kinetics. Unfortunately, too many ignore this rule in heterogeneous photocatalysis.

A + B a C f f products

(7)

Approximately 15 years ago, in their classic article, Turchi and Ollis19 showed that a photoinduced process in heterogeneous systems may be far more complex than first imagined and that the meaning of the Langmuir adsorption coefficient (KL) may vary from one mechanism to another. In this regard, Serpone and co-workers21 showed that the formation of intermediates also gives a different meaning to the “Langmuir” constant. Nonetheless, a significant number of studies continue to report Langmuir adsorption/desorption constants for a variety of systems while ignoring the obvious discordance between the data from different sources. In an earlier study,2 we reported that the so-called Langmuir constant is a function of light irradiance (photon flow), which we have reproduced in Figure 1. The figure also depicts the simultaneous interdependence of the kinetics of the photodegradation of phenol over UV-irradiated TiO2 on light irradiance and on the concentration of the reactant. Figure 2 illustrates the corresponding analogous dependencies of the initial rates rF(p) of the photoadsorption (i.e., photoreduction) of oxygen on UV-irradiated ZrO2 particles on pressure p at different light

Figure 1. (a) Dependencies of the rate of photodegradation of phenol over UV-irradiated TiO2 on the concentration of phenol at different photon flows of actinic light at 365 nm: ∆ ) (1) 0.06∆0, (2) 0.12∆0, (3) 0.29∆0, (4) 0.5∆0, (5) 0.65∆0, (6) 0.86∆0, and (7) ∆0; Fo ) 1.1 ( 0.3 × 1017 photons cm-2 s-1. (b) Dependencies of the LH rate constant kLH (left axis; curve 1) and the LH adsorption coefficient KL (right axis; curve 2) on the photon flow of 365 nm light. Reproduced with permission from ref 2; Copyright (2000) Elsevier.

irradiances.22 These experimental observations alone call into question the validity of the simple LH kinetic model in interpreting the results of a heterogeneous photoprocess occurring on a photocatalyst surface. The misconceptions about the relevance of the LH kinetic model in heterogeneous photocatalysis are based on certain beliefs about the Langmuir adsorption isotherm. Accordingly, we need to remind ourselves of some of the fundamental tenets that define this adsorption model that may or may not apply to a particular system. Thus, a typical fractional surface coverage θ for an ideal uniform solid surface by reactant molecules M is given by eq 8:

θ)

KL[M] 1 + KL[M]

(8)

in which KL () kads/kdes) is the Langmuir constant (i.e., adsorption coefficient). This expression is based on three other fundamental postulates:8 (1) the reactant M molecules form only a monolayer and are chemisorbed reversibly on the surface, (2) adsorption involves only one adsorbed species per surface site, and (3) the energy of the adsorbed species is the same at any site and is not affected by the adsorption of species on adjacent

Misconceptions in Heterogeneous Photocatalysis

J. Phys. Chem. B, Vol. 109, No. 39, 2005 18517 photoinduced deactivation of the excited state of surface site S*.

S*+ hV f S

(9)

In classical photochemistry, this is not a common process of decay for excited states. However, its analogue can easily be found in laser physics. This is the so-called stimulated emission of radiation process. In recent studies,2,22 we have decoded reaction 9 as the trapping of free charge carriers by the surface defects S (reaction 10), followed by a recombination through surface-active centers (reaction 11). This leads to a complete description of the whole set of experimental dependencies of reaction rates on the concentration of reagents (pressure for gaseous systems) and on light irradiance for both gas-solid and liquid-solid heterogeneous systems.

Figure 2. (top) Dependencies of initial rates for the photoadsorption of oxygen on ZrO2 particles rF(p) on pressure p at different photon flows (Fo ) 1 × 1015 photons cm-2 s-1): (1) F ) Fo; (2) F ) 0.78Fo; (3) F ) 0.5Fo; (4) F ) 0.3Fo; (5) F ) 0.1Fo. (bottom) Dependencies of the LH parameters kLH (curve 1) and KL (curve 2) on photon flow as F/Fo for Fo ) 1 × 1015 photons cm-2 s-1. Reproduced with permission from ref 22. Copyright (1998) American Chemical Society.

sites (i.e., the enthalpy of adsorption ∆Hads is independent of surface coverage). Moreover, the KL constant has an exponential dependence on ∆Hads. Postulate 3 is seldom verified experimentally, thus the less friendly Freundlich and Tempkin isotherms were introduced for the adsorption process.8 In heterogeneous photocatalysis, these postulates are seldom if ever followed experimentally, especially 1 and 3; yet they are neglected, thereby giving rise to the mistaken assumption that the LH kinetic model is applicable to the kinetic data without any forethought. In heterogeneous catalysis, the LH kinetic model accounts, in some cases, for experimental observations7 because, unlike heterogeneous photocatalysis in which adsorption/desorption equilibria may not be established during the photoreaction,1 in thermal catalysis the (dark) equilibria may be achieved. The fact that the Langmuir model works at all in the latter case, even though “real” catalyst surfaces are not ideal uniform surfaces, has been taken to mean that there are domains on the solid’s surface that act as ideal uniform surfaces where reversible adsorption occurs and the tenets of the Langmuir isotherm may indeed be valid.8 On the basis of the golden rule of kinetics, the dependence of the Langmuir constant on light irradiance can easily be obtained from reactions 3-5 by a slight modification, namely, the addition of another step (reaction 9) that describes the

S + e- (h+) f S- (S+)

(10)

S- (S+) + h+ (e-) f S

(11)

Ollis1 recommends the steady-state approach for the surface coverage of reactant molecules to describe the experimental data obtained by other groups in terms of a modified LH mechanism when adsorption/desorption equilibrium cannot be achieved. Such coverage depends on light irradiance through the consumption of the molecules in the photoreaction. His interpretation was successfully applied with some minor but essential assumptions for the dependence of the Langmuir constant on light irradiance that was reported in our earlier studies.2 However, the golden rule states explicitly that without additional evidence (other than kinetic), no single mechanism can describe the actual events in a photoinduced heterogeneous process. In fact, the steady-state approach applied to the simple mechanism of reactions 3-5 remains silent as to the type of surface reaction, whether it is an ER reaction or an LH-type reaction. After the mechanism embodied in reactions 3-5 is slightly modified by the addition of reaction 9, the reaction may either be of the ER type if M denotes molecules in the gas or liquid phase or be of the LH type if M is an adsorbed molecule Mads. At the same time, for the LH process, the application of the steady-state approach on reactions 3-5 to the light-irradiance-dependent surface concentration of adsorbed molecules, Mads (reaction 12; Mrem represents reactant molecules that are removed from the surface through some pathway), allows one to easily obtain a kinetic expression with the same functionality as the one reported by Ollis.1

Mads + hV f Mrem

(12)

As an example, it is instructive to analyze the kinetic behavior of the following mechanism:

S + hV f S*

(3)

S* f S

(4)

S* + Mads f Product

(5)

Msoln + Z f Mads

(13)

Mads f Msoln + Z

(14)

Mads + hV f Msoln + Z

(15)

Here, the first three steps are the same as those found in the mechanism of reactions 3-5. However, the type of reaction is rather evident: it is a LH-type process because the reaction

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involves adsorbed molecules (as also considered by Ollis1). Reaction 13 in the above mechanism is the adsorption of M molecules in the dark on surface adsorption sites Z. Reaction 14 is the dark desorption of adsorbed molecules Mads. Thus, reactions 13 and 14 are responsible for the dark adsorption/ desorption equilibrium that follows the Langmuir isotherm. Finally, reaction 15 is the photodesorption of adsorbed molecules Mads that decrease the dark equilibrium surface coverage. Therefore, in reaction 15, surface coverage changes without the formation of a reaction product. Recall that reaction 4 in the above mechanism is a spontaneous deactivation of the active state of a surface center (not photoinduced). This latter step is a necessary and critical step; otherwise, where the surface coverage is low, the steady-state approach could not be applied to the mechanism of reactions 3-5 and 13-15. That is, in such a case, the surface concentration of S* would constantly increase, which is a point that was not considered by Ollis for the •OH radical concentration in his proposed mechanism.1 In our mechanism of reactions 3-5 and 13-15, the rate of product formation is given by eq 16:

d[P] ) k5[S*][Mads] dt

(16)

in which [S*] and [Mads] can be determined through the steadystate approach. Thus,

d[S*] ) k3F[S]n - k4[S*] - k5[S*][Mads] ) 0 dt

(17)

and

d[Mads] ) k13[Msoln][Z] - k14[Mads] - k15F[Mads] dt k5[S*][Mads] ) 0 (18) To distinguish the role of photodesorption from that of photoreaction, we can assume that the rate of photodesorption is much greater than the rate of photoreaction. That is, the photodesorption step (not the photoreaction step) is the process responsible for establishing the steady-state for adsorbed molecules under irradiation (i.e., k15F[Mads] . k5[Mads][S*]). However, this system can also be solved without such an assumption, and the final equation will have the same dependencies on light irradiance and concentration, making it difficult to distinguish the roles played by photodesorption and photoreaction because their respective rate constants are coupled in a final expression of the kinetics, unlike expression 18 in which the two rate constants are decoupled. Accordingly, eq 18 is simplified so that the steady-state concentrations for S* and Mads are then given by

[S*] )

[S*] )

k3F[S] k4 + k5[Mads]

k3F[S](k14 + k15F) k4k14 + k4k15F + k5k13[Msoln][Z]

(19a)

(19b)

and

k3k5k13F[S][Msoln][Z] d[P] ) dt k4k14 + k4k15F + k5k13[Msoln][Z]

(21)

If we now consider photodesorption as the major path for the drop in surface coverage (i.e., photodesorption is more effective than dark desorption (k14 , k15); otherwise the mechanism transforms into the simple LH kinetic model), then

k3k5k13F[S][Msoln][Z] d[P] ) dt k4k15F + k5k13[Msoln][Z]

(22)

which is completely consistent with the experimental dependencies observed in our earlier studies,2,22 as given by eq 23:

dC aFC ) dt (bF + dC)

(23)

in which R, β, and γ are empirical constants that are independent of both light irradiance and concentration, and C is concentration. Accordingly, there is another mechanism that corresponds to the experimental results. The essential part here is that the steady-state approach has been applied to the surface coverage and the major pathway to establish this steady-state is photodesorption and not a photoreaction. In our earlier study,2 we further demonstrated that even if the Langmuir (dark) adsorption equilibrium was established during the photoreaction, the steady-state approach on the concentration of active centers S* would yield the same reaction rate dependencies on light irradiance and the concentration of the reagent that the LH kinetic model would. Consequently, there is no difference in the kinetic dependence, irrespective of which species, S or M, the steady-state approach is applied to. Moreover, because the steps in the mechanism of reactions 3-5 and its modifications are rather simple, one can easily add as many intermediate steps as desired or needed to describe various possible pathways with the same kinetic results. Thus, the major conclusion that can be drawn from the above reflections is that the simple LH kinetic model cannot universally describe photoprocesses in heterogeneous systems. Accordingly, reported values of Langmuir constants are tenuous at best, and reporting them should be avoided without strong corroborating evidence that confirms the proposed mechanism. Such LH constants have very little, if any, physical meaning, and consequently, the simple LH kinetic model that theoretically describes very nicely the kinetic data (reaction rates) of surface processes in a heterogeneous system can be a deceptive, delusory model. 2. Band-to-Band Recombination Pathway Another no less significant misconception in heterogeneous photocatalysis is the a priori assumption that free charge carriers recombine through a bimolecular pathway (reaction 24). The trapping of charge carriers by defects and the carrier recombination that occurs through such defects, that is, recombination centers R, (reactions 25 and 26) are completely ignored in the photocatalytic landscape:

e- + h+ f hV (and/or heat)

(24)

e- (h+) + R f R- (R+)

(25)

R- (R+) + h+ (e-) f R

(26)

versus

[Mads] )

k13[Msoln][Z] k14 + k15F

(20)

Substitution of the steady-state concentrations into the equation for the reaction rate (eq 16) yields

The latter process is more effective in real, wide band-gap

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solids.23-26 For instance, at the moderate light irradiance typically used in photocatalytic experiments (∼1016 photons cm-2 s-1), with a maximal value of the absorption coefficient of the solid at ∼105 cm-1 and with lifetimes of charge carriers around ∼10-9 s, the free charge carrier concentration is ∼1012 cm-3. In contrast, the typical concentration of defects (intrinsic defects and impurities) in so-called “pure” solids is ∼10141015 cm-3. A single recombination event occurring through the defects is more efficient than the band-to-band recombination of the free charge carriers (reaction 24). The issue here is that band-to-band recombination requires the fulfillment of no less than two important conditions: (1) the conservation of energy, and (2) the conservation of momentum, both of which significantly decrease the efficiency of the band-to-band recombination process. For radiative recombination, the energy conservation law can easily be accounted for by the emission of photons with the corresponding energy. The momentum conservation ph are the momenta of the law given by eq 27 (in which b pe and b recombining photoelectron and photohole, respectively) demands that the algebraic sum of two rather large values (eq 28, in which a is a constant of the crystalline solid) must be very small to be equal to the momentum of the photon (eq 29; λ is the photon wavelength). Because the momentum of the photons pph is nearly 0, compared to the momentum of free charge b carriers, the possibility for recombination through the band-toband pathway is restricted only to those electrons and holes that possess the same momentum. In other words, in the context of classical physics, it would require that two fast moving particles endure strong straight collisions and possess very similar velocities (provided their effective masses are similar). Clearly, the number of charge carriers having the same momentum will be very small. In addition, for the particular case of TiO2, the levels at the bottom of the conduction band and at the top of the valence band are displaced relative to each other in momentum space. Therefore, charge carriers that occupy those states in the conduction and valence bands cannot recombine through the radiative pathway without phonon assistance. Such a phonon-assisted recombination process involves a three-body interaction; therefore the process will occur with very low probability. In contrast, for nonradiative charge carrier recombination, there are no strong restrictions for momentum conservation because the emitted phonons can always account for the difference in momentum between the electrons and the holes. However, the energy conservation restriction becomes very significant in this case. For instance, for TiO2, 3 eV of energy must be dissipated through the emission of phonons in a one-step recombination process, which is a very costly and unlikely occurrence.

b pe + b ph ) b p ph

(27)

h 2πa

(28)

b pe ≈ b ph ≈ pb ph ≈

h 2πλ

(29)

For the recombination of charge carriers through defects (recombination centers), there are no restrictions from momentum conservation and energy conservation laws; therefore, energy conservation and momentum conservation are easily fulfilled by the emission of photons.27 Even if radiative recombination through defects was for some reason forbidden, it would be easier to expend the excess energy in a two-step (or multistep) process rather than in a one-step band-to-band

recombination event. Accordingly, because of both concentration and probability, the recombination of charge carriers through defects in wide band-gap solids (e.g., TiO2, ZnO, ZrO2, and others) is a more effective process. Consequently, the belief that free charge carriers recombine through a bimolecular recombination pathway is yet another misconception in heterogeneous photocatalysis. 3. Dependence of the Kinetics on Photon Flow Because the concentration of defects in solids is typically greater than the concentration of free photogenerated charge carriers, carrier concentration should scale almost linearly with photon flow (almost, because there is always a small but nonzero finite probability for band-to-band recombination and other factors that may also play a role). Moreover, because of the greater concentration of recombination centers and the higher probability of charge carrier trapping by such centers (defects), electrons and holes simply cannot “feel” the concentration of the charge carriers of the opposite sign at moderate light irradiance. (Note that, in the photoexcitation of the solid by a laser pulse, the concentration of photogenerated charge carriers could be greater than the concentration of defects; therefore, band-to-band recombination could then play a significant role under such conditions). Accordingly, the square-root dependence of the reaction rate on photon flow arising from bimolecular recombination is another misconception often considered in heterogeneous photocatalysis. Studies that follow this belief continue to claim that the bimolecular recombination of charge carriers occurs, even if the experimental dependence of the reaction rate on photon flow had a fractional reaction order anywhere from 0 to 1 (e.g., see Figure 3). In recent studies,2,22 we demonstrated that the sublinear dependencies of reaction rates on photon flow originate from a competition between the chemical pathway of decay of the active state of surface centers (S* in reactions 3-5) through interactions with reactant molecules and the physical pathway of decay of the active state through recombination, in which the surface-active centers also play the role of surface charge carrier recombination centers. Our data showed explicitly that, depending on the concentration of the reactant molecules, the dependence of the reaction rate on photon flow (light irradiance) does in fact vary from zero-order kinetics at low concentrations of reactant M to first-order kinetics at sufficiently high concentrations of M in the same range of light irradiance (not stronger and not weaker). Accordingly, at intermediate concentrations, the order of the reaction on photon flow is between 0 and 1 (Figure 3), and the square-root dependence is simply a particular case lying within this range. The problem often seen in this regard is that studies typically measure the dependence on photon flow only at one (often random) concentration that does not reflect the complete mechanism. In fact, the interdependence of reaction rates on photon flow and on concentration was a significant finding in our studies. This is not just a particular behavior of a singular heterogeneous system. Rather, it is a common phenomenon in heterogeneous photochemistry and photocatalysis. 4. Fitting and Treatment of the Kinetic Data From the above discussion, another issue that we often encounter in studies of heterogeneous photocatalysis concerns the limitation(s) of certain equations used often to quantitatively describe the photocatalytic events. For instance, a set of experimental kinetic data could easily be fit to the hyperbolic

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Figure 4. Plots showing the similarities in fitting hypothetical experimental data (solid circles) using the two equations indicated (see text).

in heterogeneous photochemistry in which the kinetics of the photostimulated adsorption of gas molecules on a uniformly irradiated surface were described by eq 31.28-30

Q ) Q∞

Figure 3. (top) Dependencies of the rates of the photodegradation of phenol over UV-irradiated TiO2 on the relative photon flow F/Fo of the actinic light at 365 nm and at different initial concentrations of phenol: (1) 0.027 mM, (2) 0.053 mM, (3) 0.106 mM, (4) 0.213 mM, (5) 0.427 mM, (6) 0.638 mM, (7) 0.851 mM. Reproduced with permission from ref 2. Copyright 2000, Elsevier. (bottom) Dependencies of the initial rates of the photoadsorption of oxygen on ZrO2 particles rF(p) on photon flow as F/Fo for Fo ) 1 × 1015 photons cm-2 s-1 at different initial oxygen pressures: (1) 2.8 Pa; (2) 0.28 Pa; (3) 0.11 Pa; (4) 0.055 Pa; (5) 0.028 Pa. Reproduced with permission from ref 22. Copyright (2000) American Chemical Society.

function of eq 1, but it could also be approximated using the exponential function of eq 30.

Y ) a(1 + e-bx)

(30)

Figure 4 illustrates the plots of a hypothetical set of kinetic data fitted with eq 1 and with eq 30. The near congruence of the two curves clearly indicates that, within the typical experimental errors in kinetics, the difference between the two plots is negligible. Yet, to propose a suitable mechanism that would describe the experimental curve of the dependence of the reaction rate on the concentration of the reactant using eq 30 would be a challenge in itself. In other words, the choice of a model to describe the experimental data must be done with some prior reflection, even if the model seems theoretically simple and attractive (e.g., the Langmuir model). Some functions have very similar behavior, especially in the limited range of variables (e.g., concentrations, time) that are typically available in experiments. As a particular case, we consider a classic problem

(t +t τ)

(31)

in which Q is the photoadsorption capacity, Q∞ denotes the ultimate photoadsorption capacity of the photocatalyst,31 t is time, and τ is a constant. For many years, no reasonable mechanism(s) could be proposed from such a description. However, the experimental data could also be approximated by the simple function of eq 30, which did provide a very simple mechanistic interpretation of reactions 3-5 if the efficiency of the second step (reaction 4), which involves the deactivation of surface-active centers, was negligible. At the end of the 1950s and early 1960s Solonitsyn examined the kinetics of the photostimulated adsorption of oxygen on a zinc oxide specimen28 and correctly deduced that the observed kinetics did not correspond to the actual kinetics because of the nonuniform irradiation of the ZnO sample. Subsequently, he assumed that the nonuniform irradiation of ZnO is analogous to the nonuniform distribution of adsorption centers under dark conditions. He further suggested that, in such cases, the kinetics could be described by the logarithmic function in eq 32,

∆P(t) ) A ln(1 + BFt)

(32)

in which P is the pressure of oxygen, and A and B are constants. That was a first and a very crucial assumption that defined other studies of photoadsorption for which the experimental kinetic data could be interpreted by eq 32. However, the data could also be fit to other functions, for example, to root dependence functions and multiexponential decay functions, albeit often for no valid reasons. Note that the mechanistic details of photoadsorption were unknown at the time. Regardless, this example is a good illustration to show that different functions can describe the same experimental data. Unfettered, Solonitsyn continued to investigate the real kinetics on a uniformly irradiated surface to establish a reasonable mechanism for the photoadsorption of gases on solids. He followed a different approach by considering what the kinetics of photoadsorption on a uniformly irradiated surface would be if the kinetics on a nonuniformly irradiated surface were described by a logarithmic function. His efforts ultimately led to eq 31. Note again that the starting point of this rather inverse approach was the assumption that a logarithmic function could describe the kinetics on a nonuniformly irradiated surface. Henceforth, the kinetics of photoadsorption were described by eq 31, which became known as the Solonitsyn kinetic model. Equation 31 was later verified experimentally using a vacuum setup in which the powdered

Misconceptions in Heterogeneous Photocatalysis metal-oxide sample could be stirred inside the cell to achieve (on average) a uniformly irradiated surface.29 In summary, the above discussion emphasizes that the a priori blind application of different approximations and models to interpret experimental kinetic data in heterogeneous photocatalysis, without strong valid reasons, should be avoided. 5. Concluding Remarks Regarding our experimental results and their approximations, there is no other direct evidence to corroborate the mechanism of the photodegradation of phenol2 except that the mechanism is self-consistent and that it can also describe the kinetics of heterogeneous photoprocesses in both gas-solid and liquidsolid heterogeneous systems. For gas-solid systems, there is direct evidence of the validity of the mechanism.22 Because the decay of the active state of surface-active centers occurs through recombination with charge carriers of the opposite sign, we expect that in the spectral region, where no such charge carriers are generated, the Langmuir constant KL will be independent of light irradiance. In contrast, in the spectral region of photoexcitation, which leads to the generation of charge carriers of both types, the KL constant indeed depends on light irradiance. In other words, there is a spectral variation of the Langmuir constant behavior that is predicted and experimentally verified for the O2/ZrO2 heterogeneous system by the photoexcitation of the metal-oxide specimen in the V-type and F-type color centers. The title of our earlier article2 was certainly not understated, as suggested by Ollis.1 In an earlier submission of that study, a reviewer commented that the article brought nothing new to the field of heterogeneous photocatalysis. Yet, our findings, along with the proposed treatment of the kinetic observations and data, and the suggested mechanism were rather remarkable. Despite these experimental findings and the recommendations of Ollis1 that are reemphasized here, the deceptive LH kinetic model will no doubt continue to be used by many because of its simplicity in fitting the experimental results in heterogeneous photocatalysis. Acknowledgment. We are grateful to the Japanese Society for the Promotion of Science for a fellowship to A.V.E. and to the Ministero dell′Istruzione, Universita e Ricerca (MIUR, Roma) for support of our work in Pavia. References and Notes (1) Ollis, D. F. J. Phys. Chem. B 2005, 109, 2439. (2) Emeline, A. V.; Ryabchuk, V. K.; Serpone, N. J. Photochem. Photobiol., A 2000, 133, 89. (3) Xu, Y.; Langford, C. H. J. Photochem. Photobiol., A 2000, 133, 67. (4) Martyanov, I.; Savinov, E. J. Photochem. Photobiol., A 2000, 134, 219. (5) (a) Wu, J.-F.; Hung, C.-H.; Yuan, C.-S. J. Photochem. Photobiol., A 2005, 170, 299. (b) Xu, T.; Cai, Y.; O′Shea, K. E. Ext. Abstr. ACS Natl. Meet., DiV. EnViron. Chem. 2005, 45, 335. (c) Raillard, C.; Hequet, V.; Le Cloirec, P.; Legrand, J. Water Sci. Technol. 2004, 49, 111. (d) McMurray, T. A.; Byrne, J. A.; Dunlop, P. S. M.; Winkelman, J. G. M.; Eggins, B. R.; McAdams, E. T. Appl. Catal., A 2004, 262, 105; (e) Al-Rasheed, R.; Cardin, D. J. Chemosphere 2003, 51, 925. (f) Li, X. Z.; Liu, H.; Cheng, L.; Tong, H. J. EnViron. Sci. Technol. 2003, 37, 3989. (g) Arsla, I.; Balcioglu, I. A.; Bahnemann, D. W. Dyes Pigm. 2000, 47, 207. (h) Arsla, I.; Balcioglu, I. A.; Bahnemann, D. W. Appl. Catal., B 2000, 26, 193. (i) Martinez, M. A.; Nunez, A.; Lopez, R.; Morales, F.; Nunez, O. Acta Cient. Venez. 1999, 50, 81. (j) Augugliaro, V.; Galvez, J. B.; Vasquez, J. C.; Lopez, E. G.; Loddo, V.; Munoz, M. J. L.; Rodriguez, S. M.; Marci, G.; Palmisano, L.; Schiavello, M.; Ruiz, J. S. Catal. Today 1999, 54, 245. (k) Ilisz, I.; Laszlo, Z.; Dombi, A. Appl. Catal., A1999, 180, 25. (l) Noguchi, T.; Fujishima, A.; Sawunyama,

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