Ind. Eng. Chem. Res. 1994,33, 3031-3042
3031
Novel Reactor for Photocatalytic Kinetic Studied Maria I. Cabrera? Orlando M. Alfano? and Albert0 E. Cassano*i* ZNTEC," UNL,I and CONICET,# Giiemes 3450, (3000) Santa Fe, Argentina
I n the past decade a n increasing interest in photocatalytic kinetic studies has been observed, particularly related to promising remediation processes for air and water pollution. Normally, the reacting system includes a suspended solid semiconductor and one or two fluid phases. One of the major problems lies in the difficulties associated with the proper evaluation of the absorbed radiant energy due to the unavoidable system heterogeneities that produce light scattering. A novel form of reactor, combined with a radiation distribution model, has been used to evaluate the volumetric rate of energy absorption during the photocatalytic oxidation of trichloroethylene in water using a suspension of titanium dioxide. All the required information to solve the radiative transfer equation in a one-dimensional photocatalytic reactor is obtained either from radiation theory or from specially designed experiments. The proposed approach permits a correct description of the radiation field inside the heterogeneous reactor and, consequently, a precise accounting of the absorbed photons. The quantum yield concept is revisited to propose a n appropriate and equivalent property for solid photocatalyzed systems. Afterward, the reactor and the model were used to evaluate heterogeneous-system quantum efficiencies.
Introduction In recent years, research on new methods for air and water purification has concentrated its efforts in developing processes to attain the chemical destruction of contaminants; the idea of total recycling (or zero discharge) has been the predominant driving force. One of the concepts that has received an increasing degree of attention is the use of titanium dioxide as a catalyst for the light-induced photolysis of pollutants [Childs and Ollis (19801, Pichat et al. (19821, Schiavello (19851, Pelizzetti and Serpone, (19861, Schiavello (19881, Serpone and Pelizzetti (19891, Pichat and Herrman (19891, Pelizzetti and Schiavello (19911, Ollis and Al-Ekabi (199311. Research in this area, with particular emphasis in proving the feasibility of the idea, has produced significant progress to the point that photocatalytic technologies are presently emerging in the marketplace. Both air and water systems have been studied, but the latter has received considerably more attention. Catalysis by illuminated titanium dioxide is the result of the interaction of the electrons and holes generated in the photoactivated semiconductor with the surrounding medium; thus, as a consequence of light absorption electron-hole pairs are formed in the solid particle that can recombine or participate in reduction and oxidation reactions with the contaminants. In some cases, under certain conditions, reaction with the solid is also possible; this is an undesirable result and, at the same time, when it is irreversible, one feature that excludes the kinetic scheme from being considered a truly catalytic process. Halogenated hydrocarbons, aromatic hydrocarbons, nitrogen-containing heterocyclic compounds, hydrogen sulfide, surfactants, herbicides, metal complexes, and t Paper presented at the Symposium on Catalytic Reaction Engineering for Environmentally Benign Processes, San Diego, March 13-18, 1994. * To whom correspondence should be addressed. Research Assistant from UNL. Professors (UNL) and CONICET Research Staff Members. II Instituto de Desarrollo Tecnoldgico para la Industria Quimica. Universidad Nacional del Litoral. # Consejo Nacional de Investigaciones Cientificas y Tecnicas.
* *
many other compounds have been examined, particularly in water solution. Results indicated that almost any organic and many of the inorganic pollutants produced by the electrical, electronic, agricultural, textile, petrochemical, metallurgical, and many other industries can be completely destroyed or separated. As has frequently occurred in other fields, technological applications have been developed notwithstanding that research has yet to succeed in developing a comprehensive and sound understanding and description of the involved phenomena. The development of a reliable knowledge base is still in its initial stages in which problems related to catalyst preparation and photoactivation, catalyst chemical and mechanical stability, chemistry and kinetic networks of pollutant degradation, intrinsic reaction kinetics including effects of irradiance level and substrate competition, photocatalytic reactor design, and process integration with other water treatment technologies represent some of the main weaknesses [National Research Council (199111. One of the unsolved problems is the correct quantification of the absorbed radiation inside a photocatalytic reactor and, consequently, its proper application in different types of reaction kinetics studies [Schiavello et a1.(1991), Augugliaro et al. (19911, Palmisano et al. (19931, Serpone et al. (199313. This paper addresses some of the aspects related t o the evaluation of kinetic properties that involve the knowledge of the local volumetric rate of energy absorption (LVREA). To this purpose a rather simple experimental device can be used which, combined with reactor analysis and radiative transfer concepts, is suitable t o provide the required information.
Problem Statement In every photochemical process there is a distinct phenomenon originated in the way by which the reaction is promoted. In the absence of mass transport limitations the reaction rate always bears some type of dependence with the rate of radiation energy absorbed by the material volume of reaction. This rate of absorbed energy (a local value per unit reaction volume) has been named local volumetric rate of energy absorption (LVREA) [Irazoqui et al. (197613.
0888-5885/94/2633-3031$04.50/0 0 1994 American Chemical Society
3032 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 A typical phenomenological kinetic parameter where the LVREA is always required is the overall quantum yield. Let us consider a general photochemical reaction, where A is the radiation-absorbing species (a reactant or a catalyst), B another reactant (different from the radiation-absorbing species, for example), and P a product (from either a primary or a secondary reaction). Then, an overall quantum yield can be defined according to Noyes and Leighton (1941) and Calvert and Pitts (1966) in the following way: QOverall
= [no. of molecules (mol) finally decomposed
(e.g., A or B)or produced (e.g., P)/(cm3 s)Y [no. of quanta (einstein) absorbed by reactant or catalyst (e.g., A)/(cm3s)] (1) Similar definitions have been proposed by Pichat (1985) and Braun et al. (1986). The concept has been used for heterogeneous photocatalyticreactions by many authors; among them one can mention Pruden and Ollis (1983), Pichat (19851, and Bahnemann et al. (1991). The definition of eq (1) may be applied to any form of reaction: molecular or chain, stoichiometricor catalytic, etc. It is obvious that it includes, as a particular case, a process that is the result of the primary reaction exclusively. The numerator is always a rate of reaction and the denominator the LVREA. This quantity is said to be well-defined for homogeneous systems, and no particular difficulties are encountered in its experimental determination [Calvert and Pitts (19661,Braun et al. (198611. It is also accepted that the quantum yield is one of the most useful and fundamental quantities in the study of photochemical reaction mechanisms and its determination is strongly recommended for every basic photochemical study. From the direct relationship of its definition with an energy yield, the overall quantum yield also has a very important practical (economical) implication. As far as the radiation participation in the process is concerned, in a photochemical reacting system one may have just radiation absorption (when the medium is homogeneous) or radiation absorption and scattering (when the medium is heterogeneous, like in a solid photocatalyzed process); it may be convenient to recall that a t low temperatures (e.g., below 200 “C) and in the absence of fluorescence, radiation emission within the reacting system is always neglected. In a heterogeneous photocatalytic reaction the definition given by eq (1) has been extended, changed, or applied in different forms [Childs and Ollis, (1980), Schiavello et al. (19911, Augugliaro et al. (1991), Palmisano et al. (1993)l. To some extent, every new proposal is the result of some sort of disagreement with the previous definition but, what is more important, none of them have received a wide acceptation [Serpone et al. (199311. As correctly stated by Serpone et al., since in most photocatalytic systems light scattering is significant and cannot be directly measured, the number of photons actually absorbed is as yet unknown and some proposals [Schiavello et al. (19911, Augugliaro et al. (199111 lack precision in the data. We may add that some of the reported results in these two papers (indifference of the system performance with the particle diameter, for example) seem to be in contradiction with radiation theory. On its turn, Serpone et al.’s paper makes its own proposal of a different entity called “relative photonic efficiency”. Considering that the proposed objective
seems to be mainly aimed at the standardization of a method for comparing different photocatalysts, the described technique may be useful. Essentially it circumvents most of the difficulties associated with the precise evaluation of the absorbed energy or with the production of a result independent of the reactor configuration, by referring all the results t o an equivalent experiment performed with a “standard reaction”. In this way, all the results are reported relative to this reaction. Obviously, all the difficulties are overcome at the price of producing no absolute values of the photonic efficiency. Nevertheless, the question of calculating the quantum yield or some equivalent absolute quantity remains unsolved. One should add that if the LVREA cannot be measured or calculated, the quantum yield cannot be obtained and, what is a t least equal and perhaps more important, the kinetic dependence with respect to the absorbed radiation energy will remain also inaccessible. More on quantum yields will be discussed further below. If, as it is generally stated, one of the main difficulties resides in getting the value of the LVREA, we think that, with a careful reactor design and the use of a rigorous radiation model associated with reactor analysis concepts, the problem can be solved with a minimum of experiments. This type of solution has been very often used to tackle problems otherwise almost impossible or very complicated to attack with direct experimental measurements, a typical example being the use of scattering theory and models to obtain, from simple light scattering experiments, particle size and particle size distributions [Provder (1987), (199111; a powerful software is always part of the experimental procedure. The local rate of absorbed radiation energy per unit volume (LVREA)is a point value (function of position), and it may be easily calculated if one knows the radiation field distribution (the field of spectral radiation intensities). Starting from the radiative transfer equation (RTE) in the absence of emission [Ozisik, (1973), Cassano et al. (199411
and using the appropriate boundary conditions one obtains, upon integration, the spectral radiation intensity. From the value of In,,, the monochromatic (spectral) value of the incident radiation and the spectral LVREA can be immediately derived as indicated by eqs (3) and (4): (3)
Values of the intensity, the incident radiation, and the LVREA can be obtained also for polychromatic radiation performing an integration over the frequency (wavelength) interval. For example, the polychromatic LVREA, at a spatial position x, and describing the integration over the solid angle C2 in a spherical coordinate system, is given by
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 3033 T
(5) Solution of eq (5) can be obtained with conventional computational techniques; the integro-differential nature of eq (2) turns it a much more difficult problem. Actually, not only numerical difficulties are encountered but, what is more important, the volumetric absorption coefficient ( K ) , the volumetric scattering coefficient (u), and the scattering distribution function or angularly dependent phase function @) are difficult to know. The radiative transfer equation for participating and reacting media has been recently revisited [Cassano et al. (199411, but the most valuable contributions can be found in a series of theoretical papers published by Santarelli and co-workers [Spadoni et al. (1978, 1980), Stramigioli et al. (1978, 19821, Santarelli et al. (19821, Santarelli (1983), etc.1; unfortunately these works were not validated with experiments, nor have they provided an answer to the lack of information about the required values of the system parameters ( K ~ o, ,,,and p ) . Clearly, if we can design a simple reactor for which eq (2) may not be too difficult to solve and provide, in an independent way, values of the optical parameters and the phase function ( K ~ u,,, , and p ) , we can obtain the distribution of radiation intensities inside the reactor. Using eq (5) we can get the distribution of the LVREA and, from it, with a simple averaging procedure the value of a reactor volume-averaged rate of energy absorption:
I W G V
lK L
ri f7-' L
A
Figure 1. Flow sheet of the experimental device: A, optical bench; B, reactor; C, W lamp; D, parabolic reflector; E, metallic box; F, to gas exhauster; G , heat exchanger; H, storage tank; I, gas sampling; J, liquid sampling; K, thermometer; L, pump.
NYLON
a
One should notice that eqs (5) and (6) can be used also with monochromatic light; this is an important observation as far as the quantum yield determination is concerned.
Experimental Reactor Figure 1 shows a schematic representation of the experimental device. Radiant energy is supplied by a medium-pressure, mercury arc lamp having a rated power of 360 W [UA-3 UVIARC, General Electric (1959)l. The tubular lamp is placed a t the focal axis of a cylindrical reflector of parabolic cross section. The reflector was made with an aluminum sheet specularly finished and having Alzac treatment [Koller (196611. The principal dimensions are indicated in Table 1. The lamp and the reflector are housed in a metallic box that provided accurate positioning of both the lamp and the reflector. Proper operation of the lamp is controlled by means of a V-A-W meter (Clarke-Hess, Model 255). Figure 2 provides the construction details of the reactor. Its dimensions are given in Table 1. As indicated in Figure 1,the reactor operates as a perfectly stirred, continuous flow tank, inside the loop of a batch recirculating system. It was made of Pyrex glass. The front side is closed by a circular plate made of Pyrex glass. The interior side of the plate was made of ground glass. A Viton O-ring provides the hydraulic sealing. Both the reactor and the radiation emission system are mounted on a triangular optical bench (Ealing) which permits an accurate positioning of the former with respect to the irradiating device. The whole setup
D
U
.PYREX GLASS
REACTION SPACE PYREX WINDOW
'
0
INLET
Figure 2. Details of the experimental reactor. Table 1. Lamp, Reactor, and Reflector Characteristics lamp 360UA-3 reactor
reflector
parameter nominal power diameter arc length inside diameter length plate thickness plate radius volume (VR) total volume (V) parabola characteristic constant distance from vertex of parabolic reflector t o reactor plate length
value 360 W 1.9 cm 15.2 cm 5.2 cm 10.0 cm 0.38 cm 2.7 cm 212.4 cm3 2100 cm3 2.5 cm 14.8 cm 22.0 cm
(reactor-lamp-reflector) is covered by a metallic box that was painted black and is connected to an exhausting system. A shutter allows isolation of the reactor from the lamp; it is in place during the time required by the lamp and the reactor to reach stable operating
3034 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994
conditions (temperature, flow rate, etc.); when it is removed the reaction starts. The experimental device is completed with a storage tank of 2500 cm3 made of Pyrex glass that may have a variable-speed stirrer (Fisher Stedi Speed) or, alternatively, a gas inlet for oxygen saturation; it also has a glass jacketed thermocouple that is connected to a digital temperature meter (Fluke 2190A) and two sampling systems: one for the liquid phase and another for the gas phase (head space). High recirculating flow rate to and from the reactor is provided by means of an all glass and Teflon centrifugal pump (Quickfit) which is operated by means of a variable-speed motor. The liquid flow rate must be high in order to ensure good mixing conditions in the whole reacting system. Between the reactor outlet and the storage tank a heat exchanger made of glass and connected to a thermostatic bath (Lauda W R ) permits ensuring the reaction operating conditions a t 20 “C. Prior to every run, the reactor may be bypassed in order to perform the reacting mixture conditioning procedures in the manner that is described further below. The reacting system must assure the following requisites: (i) very good reproducibility in the irradiating conditions and procedures, (ii) very good mixing in the whole recycle, (iii) differential conversion per pass in the photoreactor, and (iv) absence of gas leaks everywhere.
Reactor Radiation Field Model The reacting system above described was modeled and experimentally validated by Alfano et al. (1994). They have considered a plane-parallel participating and reacting medium [i.e., that can be represented in a onedimensional, rectangular coordinate system]; inside it only radiation absorption and scattering (and obviously reaction) occur. As far as the radiation field is concerned, the system is at steady state and the absorption and scattering coefficients are constant. A one-dimensional model with azimuthal symmetry was assumed. Scattering was considered anisotropic but independent; this last condition can be achieved if the concentration of the scattering centers is not too high [Siegel and Howell, (1992)l. Fortunately, photocatalytic systems quite often fulfill this condition (for example, particle concentrations below 10 x g cm-3 and particle cm). Polychromatic radiation diameters above 3 x enters at one of the reactor faces (x = 0) in a diffuse manner (independent of direction). The other reactor face is transparent to radiation. For this case, the RTE takes on the following form:
with the following boundary conditions:
and where ,u = cos 8. As described previously, the experimental reactor used in this work was designed in such a way that ensured fulfillment of the proposed boundary conditions. In the first case (eq 7.a), the diffise emission a t the plate
of radiation entrance may be accomplished by having a uniform irradiation from outside and the interior side of the plate made of ground glass. In the second case (eq (7.b) a transparent glass window at the opposite end (as the one used) would not have been sufficient. Absorption and out-scattering within the reaction space must be sufficiently important in order to have almost no radiation arrival at the second face; when this is the case, reflection in this face will be unimportant and the boundary condition will be satisfied. Noteworthy, the same condition must be satisfied if one wishes to approach closely the one-dimensionalmodel assumption (in order to have the radiation mean free path as short as possible). Fortunately, titanium oxide suspensions have significant absorption and scattering. Solution of eq (7) with boundary conditions 7.a and 7.b can be obtained by the discrete ordinate method [Duderstadt and Martin (1979)1,and some of the details can be found in Alfano et a1.k (1994) paper. The complete mathematical model includes: (1) a rigorous model of emission for the tubular lampparabolic reflector system derived from previous works published by Alfano et al. (1985, 1986a,b), (2) a model of the radiation field characteristics that exist at the interior face (side with ground glass) of the surface of radiation entrance to the reactor, (3) a very simple model for the recycling reactor system, (4) an independent experimental determination of the radiation absorption coefficient (for the homogeneous phase) and the scattering coefficient (for the suspension of micron size, transparent, spherical particles in water), and ( 5 ) a model derived from the geometric optics [Siegel and Howell (199211 for the scattered radiation distribution (the phase function) that was assumed to respond to a specular, partial reflection process. The mathematical description of the model was solved numerically, and the results were compared with experimental data obtained in the perfectly mixed, isothermal, batch reactor with recycling, almost identical to the one described in Figure 1. Inside the reactor the well-known oxalic acid-uranyl sulfate complex, homogeneous photodecomposition reaction was conducted. Scattering was artificially produced by addition of different amounts of small particles of silica that are chemically inert and transparent to radiation in the investigated wavelength range. In this way, predictions of the scattering effects produced by chemically inactive particles on the homogeneous system could be precisely tested. Figure 3 has been derived from the original work and shows that the results from the model and experimental data had good agreement. Taking as a reference the homogeneous system (without particles), theoretical predictions of the scattering effects never differ by more than 7% from the experimental data. They demonstrate that scattering in a well-stirred system always produces a decrease in the volume-averaged reaction rate (and consequently the volume-averaged absorbed energy) when compared with a purely absorbing system. The interested reader can resort to the original work [Alfano et al. (199411. The scattering model experimentally tested can be extended to solid photocatalytic systems, Le., with active particles. These results are very encouraging but, as indicated before, the crucial point is the provision of the system parameters. This problem will be treated in what follows.
Ind. Eng. Chem. Res., Vol. 33, No. 12,1994 3035
n I
e
k
A
I
? A
0.50 0.0
1
I
2.5 (a)
5.0
1.00
Table 2. Absorption and Scattering Coefficient of Aldrich Titanium Oxide 1 (nm)
K*J,
295 305 315 325 335 345 355 365 375 390 405
(cm2g-l) 4206 4224 4543 4570 4524 4283 3432 1469 182 -0 ZO
U*A
(cm2g-l)
33 795 34 152 33 952 34 377 35 386 36 414 38 409 41 895 43 380 44 782 45 784
and, consequently, separated values of the solid suspension absorption and scattering coefficients will be necessary. Spectrophotometric measurements in the heterogeneous sample produce a value that can be at the best, when scattering in is minimized, the addition of both coefficients (By = K,, cr,,). In a recent, as yet unfinished work, Cabrera et al. (1994) have used a combination of conventional spectrophotometric measurements and special experiments that placed an integrating sphere at the outlet of the spectrophotometer sample cell. This last type of detection collected all the nonabsorbed photons that are scattered in the forward direction. As said before, the almost conventional measurement gave the extinction coefficient (provisions were taken to minimize the scattering in and maximize the scattering out). On the other hand, with a good degree of approximation, the results of the measurements with the integrating sphere provided a value that can be associated with that energy corresponding to forward scattering. The most simple radiative transfer model was applied to the spectrophotometer cell; thus, for each wavelength, the energy measured by the integrating sphere detector could be predicted using just a single adjustable parameter: the absorption coefficient (because the extinction coefficient was known from an independent determination). Using a nonlinear least squares fitting, handled by an optimization program, this adjustment was made employing the model output and the experimental results . There is just one limitation to this technique that is inherent to this type of procedures: once more, even for the simple model, the radiative transfer equation asks for the photon scattering distribution function. The phase function is readily accessible for titanium oxide particle sizes or agglomerates larger than approximately 500 nm (for particle suspensions in water, and wavelengths between 300 and 400 nm); in this case since the size parameter (x = n n & , / A )is greater than 5, the geometric optics applies. Some of the measurements made by Cabrera et al. (1994) included titanium oxide particles that had a nominal size of 200-300 nm, but in water solution they aggregate to form clusters having a mean diameter of the order of 900 nm [Martin et al. (199311. This particular catalyst has been used in this work. Considering the characteristics of the titanium oxide water suspensions, a diffuse reflectance phase function model, taken from the geometric optics [Siegel and Howell (199211, was assumed:
+
. .
i:
B 0.75 2 a \
V
0.50 0.0
2.5
5.0
cur x lo6 (mole crn-’) (b) Figure 3. Photodegradation of uranyl oxalate solutions. Ratio of heterogeneous reaction rate to homogeneous reaction rate as a function of the uranyl ion concentration: (a) C, = 3 x 10-3 g cm-3 and (b) C, = 6 x g ~ m - Keys: ~ . (-) model predictions and (A, 0): experimental data.
System Parameters Three are the required parameters: the volumetric absorption coefficient ( K ” ) , the volumetric scattering coefficient (u,,), and the phase function @). In the described work [Alfano et al. (1994)l the difficulties to get them were somewhat reduced because (i)absorption was produced exclusively by the homogeneous solution, hence absorbance measurements produced directly the absorption coefficient; (ii) scattering was produced by transparent particles (with no absorption in the wavelength range of interest), hence from extinctance measurements of the aqueous suspension the scattering coefficient was obtained; and (iii)the phase function for micron-size particles was surely amenable of theoretical modeling using the concepts derived from the geometric optics. Let us explain what we mean by extinctance measurements. In radiation transport theory, the sum of the absorption coefficient and the scattering coefficient is called the exctinction coefficient [Ozisik (1973), Siegel and Howell (199211. In a homogeneous medium (where there is at the most radiation absorption) a spectrophotometric measurement of the absorbance can be used to obtain the absorption coefficient. With the same reasoning, in a heterogeneous sample (where absorption and scattering coexist) we can get the extinction coefficient through extinctance measurements [Martin et al. (1993)l. Thus, extinctance is -log(l/lo) in a spectrophotometric measurement carried out in a heterogeneous sample. In a more general case (for example working with titania) the scattering centers will also absorb radiation
This assumption is known to be a limiting situation, but it should be a good approximation for clusters of titania of rather irregular shape, made by coalescence of many small particles. Table 2 provides the specific values (i.e.,
3036 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994
per unit particle mass concentration) of the absorption and scattering coefficients for the titanium oxide suspension, as a function of wavelength, taken from Cabrera et a1.k results. For the reactor, a phase function model is also required. The same function provided by eq (8) can be used. It does not seem convenient to use other models (for example, specular, partial reflection) or the Mie theory. It is difficult to conceive some sort of specular reflection in the titanium oxide particles and, on the other hand, Mie theory strictly applies only t o smooth, spherical particles. Besides, both approaches can be applied only if the complex refraction index as a function of wavelength is available; these values, to the best of our knowledge, are known only for the rutile variety of the semiconductor. Conversely, in order t o apply the diffuse reflection phase function model, the only significant assumption has been to consider that the surface is an ideal diffuser (reflection is 100% diffuse). In any event, the choice of a phase function always implies an important assumption because it affects the magnitude and the distribution of the radiation field.
Quantum Yield, Quantum Efficiency, Photocatalytic Yield, and Photocatalytic Efficiency The overall quantum yield (eq (1)is a quantity that originally has been defined for monochromatic radiation and homogeneous systems. In general terms, its definition may be rewritten as follows: [reaction ratel, @'overall,v - [radiation absorption ratel,
(9)
Perhaps one of the most important observations that can be made with regard to the overall quantum yield is that according to eq (91, since the numerator is a rate of reaction, in the general case it will be dependent upon the reactant concentration. The significant conclusion is that, in all but a zero order reaction, the overall quantum yield is not unique and depends, among other variables, on reactant (and sometimes product) concentrations. Braun et al. (1986) have made this point very clear when they remark that even for monomolecular reactions the quantum yield determination must be measured in systems where conversions are very low and changes in reactant concentration are negligible. We may add that, in ,spite of this, in the general case, even if the overall quantum yield is obtained for very low conversions, its value depends on the initial concentration. This is one feature of the quantum yield that is often overlooked, and results are reported for poorly defined conditions. Notwithstanding, there are cases where, within a restricted range of variations and leaving aside the rate dependence with the LVREA, the quantum yield may show negligible dependence with concentrations; hence, for those conditions, the quantum yield has an almost constant value. A typical example is the uranyl sulfate photosensitized decomposition of oxalic acid; under controlled conditions, concentration of the reacting mixture may be changed by 1 order of magnitude and the quantum yield remains constant [Leighton and Forbes (19301, Forbes and Heidt (193411. Photochemists are very much aware of these facts and limitations. The above considerations are valid even for homogeneous systems. The described difficulty can be solved
by reporting for example, in the numerator of e,q (91, initial reaction rates and indicating the initial concentration. Comparisons of different reactions can be made by reporting values at equal initial concentrations. The overall quantum yield has been reported very oRen for polychromatic radiation. This is an incorrect extension of the definition given by eq (9). Braun et al. (1986) have proposed the name of quantum efficacy (or quantum efficiency)for this quantity. It is very simple to show that both values are, in general, different. For example, let us rewrite eq (9) as follows:
and
(11) Using polychromatic radiation:
R
hRvdv*
@pol.
(12)
Notwithstanding that each wavelength contribution to the LVREA can be discriminated experimentally [see for example Claria et al. (198811, with polychromatic radiation we get a single experimental result for the numerator (the value of R ) . Substituting eq (10) into eq (121,
(13) It is clear, as indicated by Braun et al. (1986) that only for Qvindependent of frequency (wavelength), i.e., @pol. = a,, both yields are equal (Qpol.= 17). Hence, polychromatic yields can be determined experimentally, but they should receive a different name. The quantum efficiency proposed by Braun et al. (1986) seems very appropriate. One must add that quantum efficiencies must be reported together with precise data about the spectral characteristics of the absorbed (employed) radiation, information very often neglected. In photocatalyzed systems one of the frequently reported difficulties, namely the correct determination of the rate of absorbed radiant energy (the LVREA),can be solved according to this proposal. In fact, we will use a property derived from the quantum efficiency concept to illustrate the procedure. However, this part of the proposal does not solve the whole problem. Once more, the quantum yield results, even if reported for initial rates at fured concentrations, will not render a unique datum. More information about the operating conditions must be included in reporting experimental data, two typical examples being the oxygen or air concentration and the pH for water environments. Again, as in homogeneous systems, for comparative purposes, these conditions should be standardized and reported accordingly. However, an additional important question must be answered. The catalytic nature of the involved heterogeneous kinetic processes before and after the photonic activation may produce different results if, all conditions kept constant, the surface characteristics of two titanium dioxide semiconductors are different. Hence we
Ind. Eng. Chem. Res., Vol. 33, No. 12,1994 3037 should report results considering also these characteristics of the catalytic solid. This problem was originally envisaged by Chills and Ollis (1980) with their proposal of the photocatalytic turnover number and has been more recently treated in detail by Palmisano et al. (1993). The question is can we separate in the classical overall quantum yield concept those effects associated with (i) a photochemical process, and hence related to a photonic yield, and (ii) a catalytic process, and hence attributable to the characteristics of the solid surface performance? To provide a possible answer, the quantum yield definition should be changed and/or complemented.The numerator should reflect the rate of a heterogeneous (superficial) reaction. On the other hand the result produced by eqs 2-6 corresponds t o a material volume because the RTE represented by eq (2) has the implicit assumption that the medium is pseudo-homogeneous; thus the denominator must be kept as it is indicated by eq (1) with the only difference that now the absorbing species will be the solid photocatalyst (intentionally, we have left aside the case of simultaneous homogeneous reaction). It will be seen that in this way the heterogeneous nature of the reacting system will be shown in the final expression. We agree with part of Childs and Ollis' (1980) proposal in the sense that the rate of a heterogeneous catalytic reaction should be expressed in terms of the number of molecules reacted per unit time and per number of active sites. It so happens that, in general, these active sites are very difficult, if ever, to measure. Lacking this possibility, other forms may be used to obtain an intensive heterogeneous reaction rate. Two of them are frequently encountered: (i) the surface area and (ii) the catalyst mass [Boudart and DjBga-Mariadassou (198411. The first one has a more scientific appeal and the second a more practical attraction. Without a doubt none of them represent what happens in reality, but there does not exist a better, easily measured, available property. what we are saying is that since the number of specific active sites cannot be generally known, true quantum yields for heterogeneous reactions are not amenable to measurement. We are also saying that the employed substitute does not have the same aptitude t o discriminate catalyst reactivities but still can provide additional and useful information. If one adopts the surface area, which seems reasonable, the only remaining question is for photocatalytic reactions involving porous particles, should we use the total surface area or just the external one? The radiation absorption coefficient of thin films and single crystals made of pure titanium oxide has been measured [Mollers et al. (19741, Ghosk and Maruska (197711 and the obtained values range from a few (at 1 = 420 nm) t o lo6 cm-' (at A = 300 nm). Consequently, when a photocatalytic reaction is carried out in solid suspensions with particle sizes having a maximum diameter in the order of several nanometers (d .C 100 nm), the total surface area may be surely available for photonic activation even in a porous material, because the depth of radiation penetration in the solid is of the same order of magnitude; this is a conservative figure because titanium dioxide powders have a looser physical structure than single crystals, for example. When radiation penetrates inside porous particles and there is no chemistry inside the pores, the photons may be wasted (very likely in an electron-hole recombination).
When some of the absorbed photons are wasted, the quantum yield decreases, precisely because it is a measure of the energy yield. Hence the definition still applies. In any event, it is possible that if particles have a larger size (d >> 100 nm), a fraction of the measured surface area may not be available for irradiation. This is a difficult problem that should be analyzed using ideas very similar to those developed in the effectiveness factor concept for catalyst pellets [Thiele (193911. Adopting the total surface area for defining the heterogeneous reaction rate we have ERhet.j]v = [no. of moles o f j species decomposed or produced], time x surface area of catalyst (14)
Equation 14 is very similar to the intrinsic reaction rate of Palmisano et al. (1993) taken from the classical work of Boudart and DjBga-Mariadassou (1984); the only difference is that we have written an equation for monochromatic radiation. For polychromatic radiation, Rhet. j
= L[Rhet.j]v dv
(15)
Then, the two entities for which we suggest the names of heterogeneous-systemquantum yield and heterogeneoussystem quantum eficiency respectively, may be expressed as [Rhet.jIv [molecules mol)^, x [cm3~susp. [@het.j]v= -[=I e; [quanta (einstein)~,x [cm2lCat. (16)
- S,[~,,t.jl, dv [=I molecules (mol) x [cm3~susp,
qhet.j -
quanta (einstein) x [cm2lCat, (17)
The numerators of these expressions are experimental values usually obtained in kinetics studies. The denominators may be calculated with the method proposed in this paper. Once more, one must be aware that neither of the two entities provide unique values since they depend upon several operating conditions such as temperature, reactant and product concentration, pH (in aquatic environments), oxygen or air concentration when they are used in the reaction, etc. All these experimental variations should be standardized t o get data amenable of comparison; clearly, there are no difficulties in adopting one temperature (293 K, for example) and using oxygen-saturated water suspensions, and reporting the initial pH and initial reaction rates obtained a t standardized initial concentrations. One could even conceive the using of standardized irradiating systems for both mono- and polychromatic determinations, but we must mention that with our method it is not necessary; lamps, reflectors, distances, sizes, etc. can be changed with no difficulties because they act as a parameters for the radiation model. In any event, for polychromatic determinations, the spectral distribution of the lamp output power should be kept as constant as possible. We must add that we have departed from the ideas of Palmisano et al. (1993) when they employ a super-
3038 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 Table 8. Experimental Operating Conditions lamp radiation flux at reactor entrance (295-405 nm), q catalyst
temperature oxidant reactant solution (in water)
ficial definition for the photonic absorption because, by its own nature, radiation absorption is a voluminal phenomenon. Equation 2, derived from rigorous radiation theory, uses unequivocally volumetric absorption and scattering coefficients; microscopically, the concept is even clearer. Equations analogous to eqs (16) and (17) can be obtained if instead of the catalyst surface area, the catalyst mass concentrations would have been used. One can also consider the fluid-solid photocatalytic system as pseudo-homogeneous. Then, the more conventional pseudo-homogeneous-system quantum efficiency (or quantum yield for monochromatic radiation), if properly calculated, also provides useful information. Its value can be obtained from the ratio of the pseudohomogeneous initial reaction rate and the volumeaveraged LVREA, producing a result that has units of moles einstein-1.
Experimental Measurements and Results Experiments were carried out to obtain values of the heterogeneous-system quantum efficiency of the photocatalytic decomposition of electronic grade (Carlos Erba, RSE) trichloroethylene (HClC=CClZ; TCE) in water solution using a titanium dioxide catalyst (Aldrich). The decomposition of trichloroethylene in water solution has been studied by Pruden and Ollis (1983), Kenneke et al. (1993), Glaze et al. (19931, etc. The mechanism of TCE degradation is known to some extent. After photonic activation of the catalyst two pathways have been envisaged: (i) an oxidative route resulting in the production of chloride ion and trichlorinated intermediates and (ii) a reductive route resulting in the production of dichlorinated compounds. The first one seems to be produced by hydroxyl radical addition (formed from adsorbed water), followed by oxygen addition and hydrolysis. For the second one, a one-electron reduction has been proposed; the resulting radical may protonate, add oxygen, and hydrolyze. The major end products are chloride ion and carbon dioxide. Regardless of the actual mechanism, an overall quantum yield for the TCE decomposition may be defined. Following Pruden and Ollis (19831, it will be expressed as the ratio of the rate of TCE disappearance and the volumetric rate of energy absorption. The experimental operating conditions are indicated in Table 3. The reactant mixtures (very low concentrations of TCE in ultrapure water) are prepared from a stock solution of water saturated with TCE a t 293 K (6 h of equilibration time). Approximately 2000 mL of ultrapure water (electrical conductivity = 18 MQ)are saturated with pure oxygen by intense bubbling during 30 min at 293 K. The required amount of titanium oxide is added, and oxygen bubbling is maintained
G.E. UA-3 UVIARC 360 W Ha medium pressure P(220-760 nm) = 2 x 10-ceinstein i - l P(295-405 nm) = 6 x einstein s-l 1.14 x lo-' einstein cm-2 s-l Aldrich titanium dioxide (>99%anatase) sp surf. area: 9.6 m2 g-l nominal diam.: 200-300 nm mean diam. of agglomerates: 900 nm concn.: (0.1 and 0.2) x g cm-3 293 K oxygen, saturated at 293 K trichloroethylene (MW= 131.36 g mol-') concn.: (0.22-0.60) x mol cm-3 initial pH: 6
during an additional 30 min. The whole reacting system is flushed with oxygen during several minutes, and immediately after, the storage tank is filled with the water suspension. The circulating pump and the thermostatic bath are turned on, and the desired amount of TCE taken from the stock solution is added to the tank to complete a total volume of 2100 mL. The reacting suspension is recirculated a t 293 K during 1 h. Fifteen hours later, the pump, the thermostatic bath, and the lamp are turned on. After 1 h the system reaches steady state in temperature (293 K). Samples from the storage tank head space are taken at constant time intervals and analyzed in a gas chromatograph (GO; when the head space TCE concentration reaches a constant value, a sample is taken from the liquid for analysis of the initial concentration. At this moment the lamp housing shutter is removed and the reactor radiation entrance window is illuminated, indicating the start of the reaction. Liquid samples are taken at equal time intervals for analysis. Analyses are made in the following way: (i) TCE by GC with flame ionization detectors and (ii) chloride ion and carbon dioxide by means of ion chromatography with conductivity detectors. A typical run lasted for about 10 h. Between different runs the complete reacting system was carefully washed to eliminate small amounts of catalyst that usually stick at the reactor walls, the centrifugal pump, the glass heat exchanger, and the connecting tubes. Results will be analyzed in terms of changes in reactant concentration. During the runs, as a consequence of the HC1 formation, the pH changes from its initial value (pH = 6) to rather acidic conditions (pH E 4). Under these circumstances, the carbon dioxide determination by ion chromatography does not represent the equivalent to the total amount produced by the photocatalytic reaction, but just that part remaining in the aqueous solution; another part of it may have been transferred to the gas phase. Figure 4 presents a set of runs. The TCE concentration is represented as a function of time. The first two curves are results for initial substrate concentrations of 0.22 and 0.60 x low6mol cm-3, respectively, both with g ~ m - ~The . a catalyst concentration of 0.1 x second two curves represent results for initial concentrations of 0.25 and 0.45 x lop6mol cm-3 and with a catalyst concentration of 0.2 x g~ m - ~ From . these experimental data four initial reaction rates can be obtained as will be shown below. The existence of two different catalyst concentrations could have given rise to two different values of the volume-averaged LVREA; correspondingly,two different values of the available surface area exist as well. However, one must note that when the optical density of the system is increased, by increasing either the
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 3039 Table 4. Photocatalytic Quantum Efficiency ~
catalyst concn (g ~ m - ~ ) illuminated catal surf. area (cm2) (&e;(x))L (einstein ~m-~) suljsirate concn (mol cm-3) 5-l) [(R)L]' (mol r] (mol einstein-l) [(&et )do(mol Cast 8-l) vhet (mol cmausp3 einstein-I cmat
0.1 10-3 2039 8.20 x 0.22 x 10-6 7.670 x 0.093 7.990 x 0.0097
-'
0.2 x 10-3 4078 8.20 x 0.60 x 8.569 x 10-l' 0.104 8.926 x 0.0109
0.25 x 8.050 x lo-" 0.098 4.193 x 0.0051
0.45 x 9.320 x 0.114 4.854 x 0.0059
lo-"
With a mass balance in the whole reactor system we get
In eq (201,j is the key component; in our case, TCE. For the one-dimensional model:
0.0
0.6
'
0
I
I
I
5
10
t(h)
Equation 20 can be easily obtained if one considers that the surface area per unit illuminated reactor volume is given by a, = AJVR. If a, is assumed uniform (inde-
I
since the rate of reaction is only a function of x. The heterogeneous reaction rate is
For the initial rates
Figure 4. Experimental results for the photocatalyzed degradation of trichloroethylene. Trichloroethylene concentration vs time g and (b) Cm,= 0.2 x g~m-~. for (a) C,, = 0.1 x Keys: (- - -1: interpolation of the experimental data; ( 0 )CTCE'= 0.22 x mol ~ m - (A) ~ ,CTCE'= 0.60 x mol ~ m - (0) ~ ,CTCE' = 0.25 x mol ~ m - (v) ~ , CTCE'= 0.45 x mol ~ m - ~ .
The heterogeneous-system quantum efficiency results [(Rhet.(x))LIO
optical path length or the catalyst concentration, the volume-averaged value of the LVREA may reach a maximum value and remain constant thereafter. In our case, this constant value was reached for the two used catalyst concentrations (see Table 41, the reason being the large value of the reactor length (L= 10 cm).
Interpretation of the Experimental Data For the one-dimensional model, eq (6) takes the following form:
"i
\-
'
-
1'
In the right-hand side of eq (241, all the data with the exception of the volume-averaged value of the LVREA can be measured. The volume-averaged value of the LVREA can be known from the model as it has been described in this paper. These results can be compared with those obtained with a pseudo-homogeneous-system(conventional)overall quantum efficiency:
(18)
The model provides the value of e;'(x) for each wavelength of interest; hence, eq (18) can be immediately calculated.
n=
[(R(x))L1° -
VT
lim
'I
(25)
3040 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994
Obviously, eq (25) does not furnish, in an explicit way, information about the effect of the specific surface area of the catalyst or the catalyst load, but it provides a direct measure of the efficiency of a given system to use the available, absorbed photons. Table 4 shows all the final results. As was said before, illuminated catalyst surface areas were duplicated in going from the first set of runs to the second. In spite of this, the volume-averaged volumetric rate of energy absorption is the same for all the experiments. Above a catalyst load of 0.1 x g ~ m - the ~ , reactor has reached its maximum photon absorption efficiency; this means that in order to have a different value of the averaged LVREA (a smaller value), the catalyst load in our reactor (with L = 10 cm) must be lower than 0.1 x loW3 g~ m - ~ . These runs provided four different initial reaction rates for the reactant decomposition. These values were calculated using a exponential function interpolation [a exp(-bt)l of the experimental data (Cj vs t). From the value of the product (a x b ) one can obtain the initial value of the pseudo-homogeneous reaction rate (at t = 0). Using eqs (23) and (24) the heterogeneous reaction rate and the heterogeneous-system quantum efficiency were computed. Results were also obtained for the pseudo-homogeneous-systemquantum efficiency (eq 25). As expected, within the range of the employed low substrate concentrations, at constant catalyst concentration, any form of quantum efficiency increases with increasing the TCE initial load. When one uses the definition of the quantum efficiency provided by eq (25), it is observed that increasing the catalyst load, within the range of used catalyst concentrations, always increases the pseudo-homogeneous-system quantum efficiency. However, this may be a misleading conclusion because this improvement is obtained at the price of using twice as much catalyst. Per unit surface area (or what is equivalent, per unit catalyst mass) the heterogeneous-system quantum efficiencies obtained in these experiments are larger for the lower catalyst concentration. From the economical point of view this situation portrays a case where the best technical solution will be the result of a compromise between the cost of the photons and the cost of the catalyst. These particular results indicate that both properties, the conventional quantum efficiency and the heterogeneous quantum efficiency, provide useful information. The pseudo-homogeneous-system quantum efficiency values reported here (from 9.3 to 11.4%)may appear to be rather high. For a similar range of initial TCE concentrations and pH variations, equivalent type of illumination (320-440 nm), but using a different titanium dioxide (Fisher; S, = 7 m2 g-l), a lower oxygen concentration, and a much higher catalyst load (Cmp= 1x g ~ m - ~Pruden ), and Ollis (1983) found values of the quantum efficiency ranging from 0.3 to 1.7%.Very precisely, they have indicated that they have used, as a measure of the absorbed energy, the absorbed photons by a homogeneous actinometer solution placed in the same reaction space. We know that these types of calculations can produce, at best, an approximate indication (and always an overestimation)of the LVREA. From the results of Alfano et al. (1994) we can obtain for our reactor the equivalent information. Under conditions of complete absorption by the uranyl sulfateoxalic acid actinometer, between 295 and 405 nm radiation wavelength, the homogeneous-system,volumeaveraged LVREA is 5.55 x einstein cm-3 s-l. If
one uses this value (that does not consider scattering) instead of the previous volume-averaged LVREA value (that does account for scattering), a pseudo-homogeneoussystem quantum efficiency 6.77 times smaller is obtained; thus, using the homogeneous actinometer value, the conventional quantum efficiencies are significantly decreased: from an original range of 9.3-11.4%, the quantum efficiencies, in terms of TCE disappearance, take on values from 1.4 to 1.7%. Even though this comparison was done for different experimental conditions, one can observe that both results are almost equivalent. Noteworthy, the model can also be used as a substitute for the homogeneous actinometry since results in the work of Alfano et al. (1994) were also reported in this way; i.e., both experimental and theoretical data were obtained and they had good agreement. From these results it can be immediately derived that, due to scattering, only 14.77%of the radiation measured by homogeneous actinometry inside the reactor is effectively absorbed L(0.82 x lop9einstein cm-3 s-lI45.55 x einstein s-l)]. This observation confirms previous assertions that homogeneous actinometry can provide only a lower bound t o quantum yields because scattering is not taken into account [Al-Sayyed et al. (1991)l. In same cases, quantum yield results are reported relative to the radiation flux arriving at the reactor window (a hypothetical value of radiation absorption). Let us look at our data. In our case, from Table 3, q = 1.14 x einstein cm-2 s-l. Using this value, the hypothetical absorbed radiation power inside the reactor einstein cm-2 s-l x JT x (2.612cm2 would be 1.14 x = 2.42 x einstein s-l. The actual absorbed radiation power in the presence of the solid catalyst, when scattering is considered, is 0.82 x einstein cm-3 s-l x 212.4 cm3 = 1.74 x lop7 einstein s-l, or 7.19%of the hypothetical value. The conclusion is very important: radiation flux measurements at the reactor entrance or homogeneous actinometry inside the reactor volume is very misleading because scattering effects are important. Nothing different could have been concluded if one just considers that, in this system, the volumetric scattering coefficient is several times larger than the volumetric absorption coefficient.
Conclusions The main conclusions may be summarized as follows: 1. A one-dimensional, planar photoreactor combined with radiation models derived from the rigorous radiative transfer theory has been used to compute the volume-averaged, volumetric rate of polychromatic radiative energy absorption inside a photocatalytic reactor [Jv0l. dV Jye: dv/Jvol.dVl. The method had been previously validated with experiments in order t o confer reliability to its application for providing a precise way to account for absorption and scattering inside a heterogeneous photochemical reactor. 2. Considering the particular characteristics of the involved photoassisted heterogeneous catalytic reactions, a heterogeneous-system quantum efficiency (heterogeneous-system quantum yield for monochromatic radiation) has been defined. 3. The experimental results indicate the convenience of using both types of yields, the pseudo-homogeneoussystem quantum efficiency (quantum yield for monochromatic radiation) and the heterogeneous-system
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 3041 quantum efficiency, because both results are useful. The first one provides a measure of the semiconductor catalyst aptitude to use the absorbed photons without any specific consideration to its superficial characteristics. The second one helps to discriminate catalytic performances among different solids of equivalent photonic abilities. 4. The proposed methodology and the experimental results indicate that the use of radiation flux measurements at the reactor entrance or homogeneous actinometry inside the reactor volume, for evaluating the absorbed radiation energy in a heterogeneous (solidfluid) photoreactor, may lead to reporting very low quantum efficiencies (quantum yields). The reason is that important scattering effects are not accounted for. 5 . Under normal conditions, scattering effects produced by titanium dioxide-water suspensions in photocatalytic reactors are very significant.
Acknowledgment The authors are grateful to Consejo Nacional de Investigaciones Cientificas y TBcnicas (CONICET) and to Universidad Nacional del Litoral (UNL) for their support to produce this work. They also thank Mr. Antonio C. Negro for his valuable help during the experimental work.
Nomenclature A = area, m2 a, = catalyst surface area per unit suspension volume, m2 m-3 C = molar concentration, mol m4 C, = mass concentration, g m-3 d = diameter, m e a = local volumetric rate of radiant energy absorption, einstein m+ s-l G = incident radiation, einstein m-2 s-l I = radiation intensity, einstein m-2 sr-l s-l L = length, m MW = molecular weight, g m o t 1 n = refractive index, dimensionless p = phase function, dimensionless P = radiant power, einstein s-l q = radiative flux, einstein m-2 s-l r = radial coordinate, m R = reaction rate, mol m-3 s-l Rhet. = heterogeneous reaction rate, mol mi:, s-l s = linear coordinate along the direction Q, m S, = specific surface area, m2g-l t = time, s V = volume, m3 x = spatial position vector, m x = axial coordinate, m; also size parameter, dimensionless Greek Letters p = volumetric extinction coefficient, m-l q = quantum efficiency defined in eq (12), mol einstein-l rh&. = heterogeneous quantum efficiency defined in eq (171, mol m:usp,einstein-1 m,:i 6 = spherical coordinate, rad K = volumetric absorption coefficient, m-l K* = 'mass absorption coefficient, m2 g-l il = wavelength, nm ,u = quantity cos 6, dimensionless v = frequency, s-l vj = j component stoichiometric coefficient u = volumetric scattering coefficient, m-l a* = mass scattering coefficient, m2 g-l 4 = spherical coordinate, rad
Q = quantum yield, mol einstein-l ah&.= heterogeneous quantum yield defined in eq (161,
mol m:usp,einstein-1 mcat.-2
Qoverau = overall quantum yield defined in eq (l), mol einstein-' R = unit vector in the direction of propagation, dimensionless Subscripts cat. = indicates a catalyst property irr. = relative to irradiated volume j = relative to speciesj L = denotes reactor length ox. = relative to oxalic acid p = indicates a particle property pol. = indicates polychromatic radiation R = indicates a reactor property susp. = indicates a suspension property T = indicates a tank property TCE = trichloroethylene ur. = relative to the uranyl ion vol. = relative to a volume property il = indicates a dependence on wavelength v = indicates a dependence on frequency 2 ! = indicates a dependence on direction of propagation 0 = relative to the surface of radiation entrance 1 = denotes a lower limit of integration 2 = denotes an upper limit of integration Superscripts = indicates initial conditions O
Special Sym bok ( ) = indicates average value [=I = indicates "has unit of"
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Abstract published in Advance A C S Abstracts, November 1, 1994. @
