A Kinetic Study on Photocatalytic Oxidation of Phenol in Water by Silica-Dispersed Titania Nanoparticles

Journal of Colloid and Interface Science 232, 1–9 (2000) doi:10.1006/jcis.2000.7154, available online at http://www.idealibrary.com on

A Kinetic Study on Photocatalytic Oxidation of Phenol in Water by Silica-Dispersed Titania Nanoparticles Z. Ding, G. Q. Lu,1 and P. F. Greenfield Department of Chemical Engineering, The University of Queensland, Queensland 4072, Australia Received June 18, 1999; accepted August 11, 2000

of the photocatalyst is the ease and efficiency of the recovery of the photocatalyst. However, the photocatalytic activity of supported photocatalysts is normally lower than that of the suspended photocatalyst (12). One way to obtain a better separation of photocatalysts from solution in the suspension system is by producing larger photocatalyst particles. Since the late 1980s, many efforts have been concentrated on the synthesis of photocatalyst in supported form, from silica gel (13–15), pillared clay (15, 16), to zeolite (17). Furthermore, composite photocatalysts have also been tried, such as SiO2 –TiO2 aerogel (18) and SiO2 –TiO2 xerogel (19). In addition to the better recovery of photocatalyst from the solution, those supports or mixtures were widely reported as good adsorbents for the organics. More importantly, among them, silica was believed to be a very good medium, which not only facilitates adsorbing organics but also transfers those adsorbed compounds to active sites on TiO2 (14), and the dispersion of the TiO2 particles was also good (15). In the present work, we aimed to synthesize SiO2 –TiO2 mixtures with nanometer-sized TiO2 (anatase) particles. A simple kinetic model based on the work of Turchi and Ollis (6) will be developed to study the effects of different TiO2 concentrations and anatase crystal sizes on the activities of silica-dispersed photocatalysts.

Photocatalytic oxidation of phenol in water was carried out with nanoparticles of silica–titania mixtures, which were synthesized under different temperatures and silica-to-titania ratios. The crystal size of TiO2 (in anatase phase) was determined to be in the nanometer range and it increased with increasing autoclaving temperature. Furthermore, there was no obvious relationship between the size and the SiO2 /TiO2 ratio at the same preparation temperature. A specific reaction rate constant (ks ) was used for comparison of photocatalytic activity of different samples. It was found that ks decreases with increasing anatase size and TiO2 concentration. A kinetic model was developed to describe the effect of the crystal size and titania concentration on the reactivity of the SiO2 –TiO2 samples. °C 2000 Academic Press Key Words: SiO2 –TiO2 photocatalyst; anatase size; TiO2 concentration; photocatalytic oxidation.

INTRODUCTION

The past two decades have witnessed growing interest in an advanced oxidation technique—heterogeneous photocatalysis, for wastewater treatment and water purification (1, 2). The photocatalysis process can break down a large variety of organic compounds, especially trace organics, to carbon dioxide, water, and mineral ions (3). Complete mineralization during the reaction is the greatest advantage over the conventional techniques. The TiO2 semiconductor has been reported as the most promising photocatalyst for this system because of its low cost and relatively high efficiency (4, 5). The mechanism of the complex photocatalytic reaction involving TiO2 as photocatalyst was discussed in great detail and several kinetic models have been developed (6–10). However, most studies deal with pure TiO2 particles and information on the relationship between the photocatalytic activity and physical properties of the photocatalyst in supported or mixture forms is very limited, although using TiO2 supported or -coated photocatalyst is becoming popular (11). In a heterogeneous photocatalytic system, the solid photocatalyst can either be suspended in the solution or be supported on substrate materials. The advantage of immobilization

EXPERIMENTAL

The SiO2 –TiO2 mixtures were prepared by mixing anatase sol and silica (fumed, 14 nm) in four SiO2 -to-TiO2 ratios (by weight), 9 : 1, 4 : 1, 2 : 1, and 1 : 1. All chemicals were supplied by Aldrich Australia. The anatase sol was synthesized following Ichinose’s route (20). First a 0.1 M TiCl4 solution was hydrolyzed with ammonia solution (1 : 9) and the resulting gel (H4 TiO4 ) was washed thoroughly with distilled water. To this titanic acid gel, 30% of H2 O2 was added with a H2 O2 /Ti molar ratio of 4 and the solution was diluted with distilled water to reach a final titania concentration of 0.2 M. The thick solution was stirred overnight and anatase sol was obtained after the solution was kept in an autoclave for 6 h at four different temperatures, 100◦ C, 160◦ C, 200◦ C, and 250◦ C. The anatase sol was thoroughly mixed with silica and dried and finally calcined at 500◦ C for 3 h. The samples thus prepared were labeled as

1 To whom correspondence should be addressed. E-mail: maxlu@cheque. uq.edu.au.

1

0021-9797/00 $35.00

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DING, LU, AND GREENFIELD

SiO2 –TiO2 T -n, where T represents temperature and n stands for the SiO2 /TiO2 ratio. The crystal structure of TiO2 was examined using a Philips PW 1840 powder diffractometer with cobalt K α radiation and the crystallite size was determined by the Scherrer equation (21). The concentration of TiO2 was obtained by using an atomic absorption spectrometer (Varian, Spectr AA-30). Nitrogen adsorption was conducted on a gas sorption analyzer (Quantachrome, NOVA 1200). The surface area was calculated by the BET equation while the external surface area and pore volume were determined using the t-plot method and BJH method, respectively. The true density (solid density) was measured with a He pycnometer (Micromeritics 1330). The average particle size of SiO2 –TiO2 agglomerates in water was determined by a lightscattering-based particle sizer (Malvern MasterSizer/E). The photocatalytic activity of the samples prepared was tested in a batch reactor. The solution containing photocatalyst and the model organic compound, phenol, was charged in a Pyrex cylinder with a cooling water jacket, surrounded by four UV light tubes (Sylvania, blacklight, 356 nm fluorescent lamps, 8 W). The starting concentration of phenol was 10 mg/l. A catalyst loading of 0.5 g/l was used. The solution was under continuous stirring and oxygen bubbling at flow rate of 400 ml/min. The concentration of phenol was measured on an UV–visible spectrophotometer (Varian, DMS 90) using the standard colorimetric method (22). RESULTS

The XRD patterns of the photocatalyst samples with the same autoclaving temperature but different SiO2 /TiO2 ratios are shown in Fig. 1, taking the 100-n series as representative. Figure 2 shows the XRD patterns of samples, represented by the

FIG. 2. XRD patterns for T -1 samples: effect of autoclaving temperature.

T -1 series, with the same SiO2 /TiO2 ratios and different temperatures. It is seen that all samples contain pure anatase phase without rutile phase being detected. The peaks for anatase become sharper with increasing autoclaving temperature. The calculated crystallite size of anatase together with the concentration of TiO2 , surface area, pore volume, and density are summarized in Table 1. The effect of the synthesis conditions on the anatase size is shown in Fig. 3. Obviously, the anatase crystallite size is dependent on the autoclaving temperature. A higher temperature results in a larger anatase size, which confirms that reported by Ichinose et al. (20). The addition of SiO2 has no remarkable effect on the anatase crystallite size under the same autoclaving temperature. However, by comparing the anatase size between SiO2 –TiO2 and TiO2 , which was prepared under the same conditions without adding SiO2 , it can be seen that SiO2 is helpful in separating and stabilizing the TiO2 particles. Although there is no big difference in crystallite size among SiO2 –TiO2 samples, TABLE 1 Some Physical Properties of SiO2 –TiO2 Samples Anatase Concn. of Total External size, TiO2 , surface surface Pore True Apparent area area volume density, density, Sample R CTi no. (nm) (mol%) (m2 /g) (m2 /g) (ml/g) ρs (g/ml) ρp (g/ml)

FIG. 1. XRD patterns for 100-n samples: effect of SiO2 /TiO2 ratio.

100-1 100-2 100-4 100-9 160-1 160-2 160-4 160-9 200-1 200-2 200-4 200-9 250-1 250-2 250-4 250-9

7.73 8.11 7.09 7.68 9.11 9.35 9.10 9.31 11.37 11.38 11.46 11.48 13.72 13.56 13.92 13.19

35.7 21.5 16.0 6.37 39.5 22.1 16.0 6.59 34.5 21.7 16.2 6.59 38.1 24.7 17.3 7.69

204 189 206 204 166 178 183 193 156 166 167 193 147 167 172 186

191 184 179 168 166 177 173 161 141 134 141 164 125 134 143 153

0.624 0.755 0.772 1.082 0.805 1.022 1.131 0.943 0.626 0.555 0.534 1.155 0.660 0.502 0.782 0.838

2.726 2.549 2.472 2.318 3.245 2.933 2.688 2.578 3.286 3.040 2.922 2.701 3.093 2.924 2.852 2.649

1.009 0.872 0.850 0.661 0.898 0.734 0.665 0.751 1.075 1.131 1.141 0.656 1.017 1.185 0.883 0.823

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PHOTOCATALYTIC OXIDATION OF PHENOL IN WATER

TABLE 2 Photocatalytic Activity of SiO2 –TiO2 Samples

FIG. 3. Effect of synthesis condition on anatase crystallite size.

the anatase size of TiO2 is much bigger than their corresponding SiO2 –TiO2 samples. Furthermore, variations in anatase size are more obvious under lower autoclaving temperatures, which indicates that the smaller anatase crystallites are easier to agglomerate. Adding SiO2 is beneficial in preventing the agglomeration of nanometer crystallites. Figure 4 shows the relationship between the anatase size and external surface area, since external surface area is more important in photocatalysis system (23). It can been seen that for all samples with different ratios of SiO2 /TiO2 , the external surface area decreases while the anatase size increases. In addition, the

Sample no.

k (min−1 )

Correlation coefficient, r 2

ks (min−1 )

100-1 100-2 100-4 100-9 160-1 160-2 160-4 160-9 200-1 200-2 200-4 200-9 250-1 250-2 250-4 250-9

0.00829 0.00806 0.00635 0.00686 0.00914 0.00798 0.00728 0.00627 0.00541 0.00486 0.00460 0.00524 0.00300 0.00393 0.00400 0.00367

0.998 0.995 0.995 0.992 0.997 0.994 0.998 0.987 0.997 0.974 0.988 0.983 0.974 0.993 0.976 0.978

0.0232 0.0375 0.0397 0.1077 0.0231 0.0361 0.0455 0.0951 0.0157 0.0224 0.0284 0.0795 0.0079 0.0159 0.0231 0.0477

decreasing rate in external surface area with increasing in anatase size is the highest for samples with the highest TiO2 concentration. It is clear that the amount of TiO2 and the anatase size play an important role in controlling the external surface area. The photocatalytic activity of SiO2 –TiO2 in the oxidation of phenol in water is illustrated in Fig. 5. It is seen that the reaction follows pseudo-first-order kinetics and the reaction rate constant, k, is shown in Table 2. Since the catalyst samples are in mixture form and only TiO2 is active in the oxidation of phenol, therefore a specific reaction rate constant, ks , was defined as the reaction rate constant normalized by the concentration of TiO2 for comparison of the activities of different samples. It reflects how efficiently the active phase, TiO2 , performs. The relationships between ks and the anatase size and concentration of TiO2 are shown in Figs. 6 and 7, respectively. From these figures, it can be seen that ks is inversely proportional to the anatase size and the concentration of TiO2 . DISCUSSION

The mechanism of the heterogeneous photocatalysis process has been studied by many research groups. Turchi and Ollis’s hydroxyl radical attack mechanism is presently used to develop a kinetic model. It is believed, in this mechanism, that hydroxyl radicals but not photogenerated holes are the main oxidant in the oxidation of organic compounds in water (6). In addition to this useful assumption of hydroxyl radicals, inert species could also uptake and cause loss of the hydroxyl radicals (24). The reaction chain started from the excitation of the photocatalyst is shown below, of which only reactions related to the photogenerated holes and hydroxyl radicals are discussed: (I) Excitation FIG. 4. Relation between external surface area and anatase size.

hν

TiO2 → h + + e−

k1

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DING, LU, AND GREENFIELD

FIG. 5. Photocatalytic activity of SiO2 –TiO2 in oxidation of phenol in water. (a) n = 1; (b) n = 2; (c) n = 4; (d) n = 9.

(II) Recombination h + + e− → heat

k2

(III) Hole trapping · h + + OH− a → OHa

k3

(IV) Hydroxyl radical attack OH·a + R1 ↔ R2

k4 /k5

OH·a + Cinert → inactive species

k6 ,

where “a” stands for the species adsorbed or close to the surface of the photocatalyst. In Turchi and Ollis’s mechanism, all four steps were discussed on the basis of the possibility of adsorption of the reactant on the surface of the particle. In this study, these four cases were simplified into one because the main interest is in the effect of the crystallite size and TiO2 concentration. In addition, because the initial concentration of phenol, 10 ppm, was quite low, the reaction between the intermediates and hydroxyl radicals was neglected; thus, the main organic reactant, R1 , to hydroxyl radicals would be phenol. Therefore, the reaction rate equation for

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PHOTOCATALYTIC OXIDATION OF PHENOL IN WATER

−

d[R1 ] = k4 s[OH·a ][R1 ] − k5 s[R2 ]. dt

[3]

The steady-state assumption is used for the concentration of the photogenerated holes and hydroxyl radicals. Moreover, it is assumed that the concentrations of the photogenerated holes and electrons are the same and recombination is the main consumption for the holes, which means the dependence of the reaction rate on the light intensity was following half-order kinetics. The back reaction of hydroxyl radical attack of R1 is also insignificant, and is therefore neglected in Eqs. [2] and [3]. Then, the expressions for [h + ] and [OHa· ] can be written as s [h + ] = [OH·a ]

FIG. 6. Relationship between ks and anatase size.

a single particle can be derived as d[h + ] = k1 I − k2 [h + ][e− ] − k3 s[h + ][OH− [1] a ] dt d[OH·a ] · = βk3 s[h + ][OH− a ] − k4 s[OHa ][R1 ] + k5 s[R2 ] dt − k6 s[OH·a ][Cinert ] [2]

k1 I k2

[4]

βk3 [OH− a ] = k4 [R1 ] + k6 [Cinert ]

s k1 I. k2

[5]

Substituting Eqs. [4] and [5] into Eq. [3], one can get the reaction rate expression for a single particle: q βk3 k4 [OH− k1 a ] d[R1 ] k6 [Cinert ] k2 √ − s I [R1 ]. = k [R ] 4 1 dt 1 + k6 [Cinert ]

[6]

When the initial concentration of the organic compound is high, there is more organic reactant adsorbed or close to the surface of the particle, thus 1 ¿ k4 [R1 ]/k6 [Cinert ] and Eq. [6] could be rewritten as s d[R1 ] k1 √ − − s I. [7] = βk3 [OHa ] dt k2 At low initial concentration, the surface of the particle is not covered mainly by organic compound and consumption of hydroxyl radicals by inert species becomes important, thus 1 À k4 [R1 ]/k6 [Cinert ] and Eq. [6] can be further written as d[R1 ] βk3 k4 [OH− a ] − = dt k6 [Cinert ]

s

k1 √ s I [R1 ]. k2

[8]

Equation [8] is valid for this study, since the initial concentration of phenol is 10 ppm and the degradation of phenol follows pseudo-first order, which is shown in Fig. 5. Equation [7] represents the situation with high initial concentration where the degradation would follow zero-order kinetics. If the reaction parameters, such as the initial concentration of organic compound, pH, the illumination intensity, the concentration of oxygen, the geometry of the photoreactor, etc., are kept the same, Eq. [8] can be further simplified as

FIG. 7. Relationship between ks and concentration of TiO2 .

−

√ d[R1 ] = K s I [R1 ], dt

[9]

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DING, LU, AND GREENFIELD

where βk3 k4 [OH− a ] K = k6 [Cinert ]

s k1 . k2

[10]

it is possible that there are more particles below that dimension and also the amorphous TiO2 has not been taken into account. However, the deviations are small. For a single TiO2 particle, the absorption of light is given as (25)

Therefore, the specific reaction rate constant can be written as √ Ks I . ks = CTi

Iabs = [11]

Equation [9] gives the simplified reaction rate expression for a single titania particle. The calculation of the reaction rate for the whole suspension of photocatalyst, which is in the mixture form, can be carried out in two steps. Since the single particle sizes for both SiO2 and TiO2 are extremely fine, in the nanometer level, the agglomeration of these ultrafine particles in water cannot be prevented. Therefore, first, the reaction rate for each agglomeration will be developed and second, the reaction rate for the whole suspension will be derived in a similar way. The shape of TiO2 particles is assumed to be cylindrical, of which the diameter and height are equal to the dimension of the particle calculated from XRD data. A similar assumption is also made for SiO2 particles, of which the dimension is 14 nm. Furthermore, the surface of these cylindrical particles is assumed to be the external surface, which can be easily reached by light and organic compounds. Figure 8 shows the relationship between the measured and calculated external surface areas. It can be seen that there is a clearly linear relationship between them, indicating that the above assumption is valid. It is also noted that the slope of the line is not equal to one. Since the dimension of the TiO2 particles is the average anatase size calculated from XRD,

1 π R 2 I0 [1 − exp(−αγ R)], 4

[12]

where α is the averaged absorption coefficient having a value of 1.4 × 105 cm−1 at a wavelength of 350 nm (26), γ is the shape factor, and R is the dimension of the TiO2 particle. The shape of the agglomerate is assumed to be cubic with the dimension of D and the light beams are vertical to one side of the agglomerate. This approximation is widely used by Modestov and Lev (9). However, in their study, the photocatalyst is in pure TiO2 form, while here a mixture of SiO2 and TiO2 is used. Moreover, it is believed that SiO2 is transparent for near-UV light (27). Therefore, the changing of the light intensity along the depth of the agglomerate is modified as I = I0 exp(−nσ z),

[13]

where n is the amount of TiO2 particles in a unit volume of the agglomerate, σ is the effective illuminated area of the particle, and z is the depth of the agglomerate. n=

ρp D 3 CTi ρp CTi = 3 ρTi vTi D ρTi vTi

[14]

σ =

1 π R 2 [1 − exp(−αγ R)]. 4

[15]

Integrating the reaction rate for a single particle, Eq. [9], over the whole agglomerate, one can get the reaction rate, ra , for each agglomerate: ZZZ Z D√ √ 2 K sn I [R1 ] d x d y dz = K sn D [R1 ] I dz. ra = 0

[16] Substituting the effective illumination intensity, I , from Eq. [13], into Eq. [16], one gets ¢¤ £ ¡ 2K s D 2 1 − exp − 12 nσ D p ra = I0 [R1 ]. σ

FIG. 8. Relationship between calculated external surface area (Sc ) and measured external surface area (St ).

[17]

Equation [17] gives the reaction rate expression for one agglomerate, of which the photocatalyst is in the mixture form. The whole suspension can be treated as a mixture of agglomerates and organic solution. It is believed that phenol and water have little absorption under near-UV illumination. Therefore, the reaction rate in the whole suspension, r , can be obtained by integrating Eq. [17] over the photoreactor, which has a cylindrical

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PHOTOCATALYTIC OXIDATION OF PHENOL IN WATER

value of αθ D is far larger than 1. Therefore, the approximation for σ 0 can be written as

shape of 4 cm in radius L and 30 cm in height H : ZL r =

σ 0 ≈ D2.

ra N 2π z H dz

[26]

0

£ ¡ ¢¤ ZL √ 4π N H K s D 2 [R1 ] 1 − exp − 12 nσ D I z dz. [18] = σ 0

The corresponding reaction rate expression becomes r =

The variation in the light intensity can be derived in a similar manner: I = I0 exp(−N σ 0 z) 0

[19]

σ = D [1 − exp(−αθD)]

[20]

Ccatalyst N = ρp D 3

[21]

ρp CTi , ρTi

[22]

θ=

2

where N is the amount of agglomerates in the unit volume of the photoreactor, θ is the fraction of volume taken by TiO2 for each agglomerate, σ 0 is the effective illuminated area of the agglomerate, and z is the distance between the present cylindrical surface and the inner cylindrical surface of the photoreactor. Substituting I into Eq. [18] by Eq. [19], one can obtain the reaction rate for the whole suspension: ¢¤√ · £ ¡ I0 2 8π H K s D 2 1 − exp − 12 nσ D r= 0 σσ Nσ0 µ ¶ µ ¶¸ 1 2 1 0 0 − L exp − N σ L − exp − N σ L [R1 ]. [23] 2 Nσ0 2 If the dimension of the agglomerate is in the submicrometer range, which means that both the values of αγ R and αθ D are far less than 1, an approximation can be made for σ and σ 0 : 1 σ ≈ παγ R 3 4

· ¶ µ Ccatalyst L K 0 2ρp D − L exp − R Ccatalyst 2ρp D µ ¶¸ Ccatalyst L 2ρp D exp − [R1 ], − Ccatalyst 2ρp D

[28]

where 40π H K K = αγ

√

I0

.

[29]

Therefore, ks =

µ

¶ αLCcatalyst CTi − L exp − αCcatalyst CTi 2ρTi µ ¶¸ αLCcatalyst CTi 2ρTi exp − [25] [R1 ]. − αCcatalyst CTi 2ρTi 2ρTi

r =

[24]

Substituting the expression of σ , σ 0 , n, N , and θ into Eq. [23] gives √ · I0

Equations [25] and [27] give the reaction rate under the two different conditions, suspension with small or large agglomerate. For the former condition, since the difference between the single particle and the agglomerate is not big, the reaction rate is more related to the density of the pure TiO2 , which is around 4.0 g/cm3 , but not the apparent density of the photocatalyst. In addition, the concentration of TiO2 in the sample has a similar effect on the reaction rate as the photocatalyst concentration. In this study, we are more interested in the latter condition, since from our experience, the agglomeration always occurs and the size is in the tens of micrometer range for the mixture samples. The Malvern particle size analysis result, which is based on the light scattering mechanism, shows that the dimension of the agglomerates for the SiO2 –TiO2 samples is around 30 µm. Since the parameters, such as H , K , I0 , α, and γ , can be treated as the same for all the activity test experiments, Eq. [27] can be further simplified as

0

σ 0 ≈ αθ D 3 .

20π H K r = αR

√ · ¶ µ Ccatalyst L 40π H K I0 2ρp D − L exp − αγ R Ccatalyst 2ρp D ¶¸ µ Ccatalyst L 2ρp D [R1 ]. exp − [27] − Ccatalyst 2ρp D

If the dimension of the agglomerate is of tens of micrometers, the

=

¶ µ · Ccatalyst L 2ρp D K0 − L exp − RCTi Ccatalyst 2ρp D µ ¶¸ Ccatalyst L 2ρp D exp − − Ccatalyst 2ρp D K 0 f (ρp D) . RCTi

[30]

From Eq. [30], it can be seen that the crystallite size and the

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DING, LU, AND GREENFIELD

actor. The effects of the anatase size and TiO2 concentration on the activity of the samples were well explained by that model. NOMENCLATURE

FIG. 9. Influence of anatase size, TiO2 concentration, and suspensibility on the efficiency of the photocatalyst.

concentration are the two important parameters in determining the activity of the photocatalyst. There is an obvious reciprocal relationship between ks and R and CTi . However, the true relationship is more complicated, because ρp is R and CTi dependent. From Eq. [30], it is also clear that the value of ks decreases with increasing value of ρp D, which can be treated as an indicator of the suspensibility. Since the settling velocity of the agglomerate is a function of ρp D 2 , the higher the value of ρp D 2 , the faster the settling of agglomerate, and thus the worse the suspensibility. Therefore, ks is positively related to the suspensibility of the agglomerate, which was also observed in our previous studies (23). To verify the above deduction, a figure is plotted for ks vs f (ρp D)/(RCTi ), as shown in Fig. 9. It can be seen that there is a very good linear relationship with a correlation coefficient of 0.974. The slope is equal to the value of K 0 , which is 7.21 × 10−9 min−1 . Therefore, Eqs. [28] and [30] well explain the relationship between the photocatalyst efficiency and their physical properties. CONCLUSION

A series of SiO2 –TiO2 samples with different crystallite sizes and TiO2 concentrations were synthesized and applied as photocatalyst in oxidation of phenol in water. The autoclaving temperature has a strong effect on the crystallite size which in turn influences the external surface area of the samples. Adding SiO2 has proved to be an effective means to prevent the growing of the anatase size particularly for samples prepared from low autoclaving temperature. The parameter ks was defined for comparison of the activity of different samples. A kinetic model was developed for the photocatalyst in a mixture form in a slurry re-

k, k1 , k2 , k3 , reaction rate constant k4 , k5 , k6 , K, K0 ks specific reaction rate constant, min−1 I effective illumination intensity, einstein · m−2 · s−1 s surface area of a single particle, m2 I0 illumination intensity reaching the inner cylindrical wall of the photoreactor, einstein · m−2 s−1 R dimension of a single particle, m n amount of TiO2 particles in unit volume of the agglomerate, m−3 CTi concentration of TiO2 , mol% volume of a single particle, m3 vTi x, y, z coordinates ra reaction rate for an agglomerate, mg · l−3 · min−1 D dimension of an agglomerate, m L radius of the photoreactor H height of the photoreactor N amount of agglomerates in the unit volume of the photoreactor, m−3 Ccatalyst concentration of the photocatalyst, g · l−1 β proportionality constant (accounts for other suppliers of OH· ) α averaged adsorption coefficient, cm−1 γ shape factor of the particle σ effective illuminated area of the particle, m2 ρp apparent density of the photocatalyst, g · cm−3 ρTi true density of TiO2 , g · cm−3 0 σ effective illuminated area of the agglomerate, m2 θ fraction of volume taken by TiO2 for each agglomerate REFERENCES 1. “Heterogeneous Photocatalysis” (M. Schiavello, Ed.), Wiley Series in Photoscience and Photoengineering, Vol. 3. Wiley, Chichester, 1997. 2. “Photocatalytic Purification and Treatment of Water and Air” (D. F. Ollis and H. Al-Ekabi, Eds.). Elsevier Science, Lausanne, 1993. 3. Serpone, N., and Khairutdinov, R. F., in “Semiconductor Nanoclusters” (P. V. Kamat and D. Meisel, Eds.), Studies in Surface Science and Catalysis, Vol. 103, p. 417. Elsevier, New York, 1996. 4. Sclafani, A., Palmisano, L., and Eavi, E., J. Photochem. Photobiol. A: Chem. 56, 113 (1991). 5. Legrini, O., Oliveros, E., and Braun, A. M., Chem. Rev. 93(2), 671 (1993). 6. Turchi, C. S., and Ollis, D. F., J. Catal. 122, 178 (1990). 7. Blake, D. M., Webb, J., Turchi, C., and Magrini, K., Solar Energy Mater. 24, 584 (1991).

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