Extended Quantum Yield: A Dimensionless Factor Including

Article pubs.acs.org/IECR

Extended Quantum Yield: A Dimensionless Factor Including Characteristics of Light Source, Photocatalyst Surface, and Reaction Kinetics in Photocatalytic Systems R. Shidpour,†,§ M. Vossoughi,*,†,‡ A. R. Simchi,† and M. Micklich§ †

Institute for Nanoscience & Nanotechnology, Sharif University of Technology, Tehran, Iran Chemical & Petroleum Engineering Department, Sharif University of Technology, Tehran, Iran § Department of Chemistry, University of California, Riverside, Riverside, California, 92521 United States ‡

ABSTRACT: Quantum yield relations were extended by adding effective conditional parameters in photodegradation of organic pollutants such as intensity of light, wavelength of light, average distance from light source, concentrations of dye/pollutant and photocatalyst, and volume of reactor. The geometry of light source and thin film and particulate photocatalytic systems were considered in analysis. Extended quantum yield that is a dimensionless factor is applicable in various types of dye and photocatalyst. This extended quantum yield allowed us to classify photodegradation as reported by scientific groups, performed in various operational conditions in order to identify the degree of similarity among these photocatalytic systems.

1. INTRODUCTION Oxide semiconductors such as titanium dioxide (TiO2)1−3 and zinc oxide (ZnO)4,5 are very influential photocatalysts in degradation of organic pollutants dissolved in water and other solvents. Although they have a band gap (about 3.3 eV) close together, the electronic structure of them is quite different. This difference offers ZnO some advantages over TiO2. Lifetime ZnO has shown to be more exciton about 60 mV at room temperature. Longer lifetime for excitons enhances the yield of photocatalyst prior to the recombination of electron−hole. ZnO absorbs a larger fraction of UV spectrum and absorbs more light than TiO2.6,7 Also strong luminescence in ZnO facilitates the study of electron−hole pairs recombination. In the photodegradation of organic compounds under UV-light illumination, ZnO is more efficient than TiO2, as it generates H2O2 more efficiently,8 it has higher mineralization rates,9 and it has more active sites per surface area.5 However, the major disadvantage of ZnO compared with TiO2 is that surface defects in ZnO lead to the rapid electron−hole recombination. It seems that the parameters affecting photocatalytic systems can be divided into three categories. 1) The operational parameters related to photoreactors such as light intensity, light’s wavelength, light distribution, and temperature. 2) The shape, crystalline structure and size, and other physicochemical properties of solid semiconductors such as TiO2 and ZnO. 3) The parameters related to solution effect on kinetics of reaction such as pH, temperature, and adsorption coefficient of pollutants. Some efforts have been done to model photocatalytic systems. Puma et al.10 have presented a dimensionless mathematical model for a novel, thin film, slurry fountain photocatalytic reactor for water or wastewater treatment. This model extends the applicability of the horizontal water fountain model to a parabolic profile and was validated with experimental results from the photocatalytic oxidation of indigo carmine dye in a pilot-scale reactor using titanium dioxide (TiO2) as the photocatalyst. In another work, Cassano et al.11 have begun to analyze © XXXX American Chemical Society

heterogeneous reactions in aqueous media, involving the presence of both fine particles of titanium dioxide and UV radiation. In this model, the photocatalytic oxidation of trichloroethylene was used. Puma et al.12 developed a simple mathematical model presented for slurry, annular, photocatalytic reactors that still retains the essential elements of a rigorous approach while providing simple solutions. This model extended the applicability of the thin-film model of photocatalytic reactors previously presented to include the case of geometrically thick photoreactors. However, the reported works have illustrated different aspects of photocatalytic reactors, but the general model connecting the above three category parameters has not been presented. To address this problem, one way is that defining relation between operational parameters (first category) and characteristics of photocatalyst and solution. To compare the similarity of photocatalytic systems, we extended the quantum yield definition to take into account parameters influential in photodegradation including light intensity, wavelength, surface area in a particular system, surface area in thin film systems, concentration of organic pollutant/dye and photocatalyst, percentage of degradation, time, and volume of photoreactor. Extended quantum yield in the form of a dimensionless factor nominated Shid-factor was applied to compare reported catalytic systems. It was concluded that this dimensionless factor can completely summarize practical photocatalytic systems with regard to operational conditions, photocatalyst characteristics, and light source properties. Received: May 30, 2014 Revised: July 7, 2014 Accepted: July 9, 2014

A

dx.doi.org/10.1021/ie5021987 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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2. THEORETICAL FRAMEWORK: DEFINITION OF DIMENSIONLESS EQUALITY FACTOR TO COMPARE PHOTOCATALYTIC SYSTEMS The researchers have mentioned various parameters affecting degradation of organic pollutants.13−15 These parameters can be divided into three parts: 1) Parameters related to photocatalyst materials such as composition, size of crystallite, shape of particles, calcination/ annealing temperature, defects and impurities, loading of noble/ transition metals, effects of doping, and surface area. 2) Parameters related to the media containing organic pollutants such as pH, oxidant/electron acceptor, chemical composition of organic pollutant, pollutant’s initial concentration, concentration of photocatalyst, interfering substances, dissolved oxygen, and kinetics of oxidation reaction. 3) Parameters related to operational conditions such as temperature, light intensity, wavelength average, and dynamic regime of fluid. Because of various conditions of experiments, it is essential to make a fair comparison among photocatalytic systems working with different experimental conditions including light intensity, light wavelength, light source position, distributed light uniformity, degradation percentage, and degradation time as well as the concentration of photocatalyst and pollutants in solution. One way to compare photocatalytic systems is using the definition of quantum yield and extending quantum yield relation by considering operational parameters and other effective factors in photocatalytic systems. 2.1. Point Source of Light with Particulate Photocatalyst. Our model assumes that the light source (lamp) has a spherical shape and its diameter is negligible compared to lm (mean distance from source), and we nominate it as point light source. In many experiments, light emits from the point source of light and passes through the fluid or gas containing reagents and a transparent wall. Upon the receding of light from the point source, its intensity decreases proportionate to the reverse square of mean distance from source (lm), and intensity at the media surface can be shown by P ∝ (Psource/l2m).16 Part of the originally emitted light can be absorbed by some components such as pollutant/dye or solution before reaching the catalyst, so we can say light intensity after absorption in walls and solution/dye environment equals to P = γ(Psource/lm2 ) where γ is the transmission coefficient. In addition, it is very difficult to achieve uniform irradiance of the entire catalyst surface,16 and also all of the photons that came to the surface of the catalyst cannot generate electron−hole pairs because of various nonradiative relaxation. These two phenomena can be summarized in this equation, Preal = αP. The real power (Preal) is the real intensity of light passing through media and reaching the surface of the catalyst and generating electron− hole pairs. The dimensionless coefficient α (which its value between 0 and 1) is illustrative of the nonideality of irradiation, and it indicates the reduction of lamp intensity (P). So we have Preal = αγ

also has its value between 0 and 1) and is associated with the activity catalytic center and surface morphology. The quantum yield (QY) is defined as number of decomposed molecules number of accident photons

(2)

QY =

N0 − N DN0 = Nphoton Nphoton

(3)

where N0 is the initial number of molecules, N is the number of remained molecules, D is the fraction of photodegradation (between 0 and 1), and Nphoton is the number of accident photons DN0Ephoton

QY =

Prealt

=

ρs NADC0V0hc PrealtλmM 0

(4)

where Ephoton is the energy of one photon with wavelength λm, Preal is the power of accident light in [Watt], t is the physical time in [s], ρs is the density of solution (≈ 1000 kg/m3), C0 is the initial concentration of pollutant molecules in [ppm], V0 is the volume of pollutant molecule in [L], M0 is the molecular mass of pollutant, NA is Avogadro’s number (≈ 6.022 × 1023), h is Planck’s constant, c is the speed of light, and λm is the wavelength for monochrome light or average wavelength for light spectrum in [cm]. We know that the reaction kinetics, specific surface area, distance from light source, and the photocatalyst’s concentration are important. We rewrite QY to this form 3 ⎛ ρ NADV0hc ⎞⎛ Srealtreduced Cphotocatalyst ⎞ ⎟ QY = ⎜ s ⎟⎜⎜ ⎟ λm3lm2 ⎝ tM 0 ⎠⎝ ⎠

⎛ ⎞ C0λm2lm2 ⎟ × ⎜⎜ ⎟ 3 ⎝ PrealSrealtreducedCphotocatalyst ⎠

(5)

where treduced equals t/(ln(1/(1 − D))) in which D is the fraction of degradation (0 < D < 1), and t is the time in minutes. It was defined by the first-order or pseudo-first-order kinetics. The kinetics reaction determines the relation between t and D. Sreal is the real surface area that relates to the apparent specific surface area of the photocatalyst (Sa) [m2/gr]. Cphotocatalyst is the concentration of the photocatalyst in [ppm]. lm is the mean distance of light source from the surface of photocatalytic action in [cm]. Surprisingly, the third phase of eq 5 is a dimensionless factor that is nominated as the “Shid-factor” Shid =

⎞⎛ ⎞ λm2lm2 C0 1 ⎛⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 3 αβγ ⎝ Cphotocatalyst ⎠⎝ PsourceSatreduced ⎠

(6)

where Psource is the intensity of light source in [Watt]. The Shid-factor can be considered as a new factor to evaluate the photocatalytic systems. It includes all of the necessary operational parameters related to light source, solution, and photocatalyst. Obviously, it cannot fully describe the complex nature in photocatalytic systems, but it may be considered as a “counting number of quality of photocatalyst”. The relation between the Shid-factor and the quantum yield is

Psource lm2

QY =

(1)

The effects of crystallite size, shape, morphology, dopant, and composition of the photocatalyst can be reflected in real surface area (Sa real). Therefore, Sa real = βSa in which Sa is the apparent specific surface area of the photocatalyst (that it can be measured by BET). In this picture, β is a dimensionless coefficient (that

Shid = B

⎞ ⎛ λm3lm2 tM 0 ⎟ (QY )⎜⎜ 3 ⎟ ρs NADV0hc ⎝ SatreducedCphotocatalyst ⎠

(7)

dx.doi.org/10.1021/ie5021987 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Table 1. Values of the Shid-Factor, the Equality Factor, in Various Photocatalytic Systems with Point Source Light and Particulate Photocatalysta pollutant

photocatalyst

C0 pollutant (ppm)

Cphotocatalyst (ppm)

λm (nm)

l (cm)

P (W)

Sa (m2/gr)

D (%)

t (min)

Shid × 104 (without unit)

ref

RB MB MB MB SG-GC MB AO7 MB MB MB MB MB MB RB RB MB MO RB IC MB RB ARB MB MB MB MB MB MB MB MB MB MB MB MB

TiO2 TiO2 ZnO ZnO TiO2 TiO2 TiO2 TiO2 ZnO ZnO TiO2 TiO2 ZnO ZnO TiO2 ZnO TiO2 TiO2 TiO2 ZnO TiO2 TiO2 TiO2 TiO2 P-25 TiO2 TiO2 TiO2 TiO2 C-TiO2 ZnO TiO2 TiO2 TiO2 ZnO

100 5000 20 5 20 10 100 20 6 2 3.56 153 30 5 20 15 20 25 20 50 25 250 50 7.5 25 40 10 6 10 25 5 5 19 5 5

500 20000 600 250 2000 500 1000 1000 500 400 100 160 1000 200 1000 800 1000 1670 1000 1000 1670 400 1670 100 500 4000 2222 625 100 500 200 1000 2800 200 1500

365 470 365 365 254 365 420 365 365 365 352 365 254 365 470 420 365 313 410 365 313 254 365 352 365 365 656.28 254 254 365 470 400 365 550 365

10 10 36 30 10 10 10 30 30 10 20 10 30 10 10 20 10 10 10 10 10 10 10 10 10 10 40 15 10 10 10 10 10 8 5

250 250 200 300 250 400 250 400 125 200 20 4 300 250 250 300 250 250 250 16 250 250 250 20 250 125 300 20 8 250 300 500 250 100 500

50 7 10 10 8.5 10 50 130 10 10 74 134 50 10 60 234 152 40 144 10 74 10 22 27 45 93 100 40 98 120 10 58 58 227 100

99 99 85 86 95 99 97 99 59 85 68 80 90 99 96 90 99 99 99 70 99 73 88 66 99 94 92 80 25 80 10 90 75 36 60

15 50 20 16 10 30 30 30 20 14 30 120 30 70 30 20 30 45 40 90 45 80 60 90 150 60 120 120 60 120 20 120 240 240 150

61683.4971 24656.1189 24560.3126 14832.0903 8162.3929 2409.5116 2253.5534 1668.1234 1019.8045 828.7547 653.1872 573.4180 525.0773 379.3400 363.8173 287.5940 253.6328 157.1852 142.5123 99.6686 84.9650 70.7112 32.0031 29.6387 17.1343 11.8151 9.6394 4.2025 0.9071 0.5357 0.2691 0.1949 0.0120 0.0014 0.0005

17* 18 19 [55] 20* 21* 22* 23* 24* 25* 26 27* 28* 29* 30 31 32* 33* 34* 35* 36* 37* 38* 39 39* 40* 41 42 43* 57* 44* 45* 46* 47 48

All of the data were extracted from published reports. The * sign points to published works that they were not clearly reported essential data, and the ■ sign is representative of our previous ZnO-based photocatalytic system. Authors of other references have sent us the exact desired data.

a

Table 2. Values of the Shid-Factor, the Equality Factor, in Various Photocatalytic Systems with Point Source Light and Particulate Photocatalyst That the Flux of Light Has Been Reported Instead of Powera pollutant

photocatalyst

C0 pollutant (ppm)

Cphotocatalyst (ppm)

λm (nm)

l (cm)

P (W/cm2)

Sa (m2/gr)

D (%)

t (min)

Shid × 103 (without unit)

ref

MB MB MB MB MB kyj4 kyj3 MB

Ag/ZnO TiO2 ZnO Au/ZnO Pt/ZnO TiO2 TiO2 TiO2

32 10 300 10 10 10 10 10

1200 500 1000 100 100 200 200 1000

340 254 365 365 365 253.7 253.7 545

5 5 30 6 6 5 5 5

0.68 0.001 0.008 0.000 47 0.000 47 0.014 72 0.014 72 0.014

4.34 50 10 16.1 19.1 47 55 100

98 94 96 72 60 80 72 84

4 10 90 60 60 180 180 360

977129.56 574681.00 22856.10 16813.51 5285.68 3.33 1.41 0.28

49* 50 51* 52* 52* 53* 53* 54*

All of the data were extracted from published reports. The * sign points to published works that were not clearly reported as essential data. Authors of other references have sent us the exact desired data. a

As shown in eq 7, the Shid-factor contains more information than the quantum yield, because now it contains operational parameters related to reactor, light source, and reaction kinetics. We apply eq 6 to calculate the Shid-factor for our experiment and to compare it with other research works; the values of the Shid-factor related to other reported photocatalysts including

TiO2 and ZnO for degradation of MB and RB were calculated. The values of the Shid-factor have been presented in Table 1. In this table, the parameters mentioned in eq 6 extracted from the literature were considered as the input variables. The Shid-factor as the output value enables us to compare the true efficiency of C

dx.doi.org/10.1021/ie5021987 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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photocatalytic systems. As shown, our previous work55 has been placed in the fourth rank with 14832 scores. Sometimes, instead of light intensity, the light flux (Pflux) measured by a photometer is reported. In this case, it is better if eq 8 is used. The values of eq 8 are shown in Table 2 Shid =

⎛ ⎞ λm2 1 ⎛⎜ C0pollutant ⎞⎟⎜ ⎟ ⎟ 3 αβγ ⎜⎝ Cphotocatalyst ⎟⎠⎜⎝ PfluxSatreduced ⎠

hence would be quite useful for both experimental and modeling works. In the next step, further investigation such as effect of being thin film and shape of light source can be considered. In order of separating operational parameters from surface phenomena and evaluating the different photocatalytic systems, the traditional quantum yield was extended and included volume of reactor, concentration of photocatalyst and dye, light wavelength, intensity or flux of light, distance between light source, reaction kinetics, and specific surface area. Using one dimensionless factor (Shid-factor) with its near relation to quantum yield, many recently reported works conducted at different conditions were investigated without needing the details of their surface phenomena complexity. It was concluded that the Shid-factor is a numerical tool to compare a photocatalytic system with various operational parameters.

(8)

where Preal = αPflux in which 0 < α < 1, and Pflux is the intensity of light source in [Watt/cm2].

3. DISCUSSION 3.1. Complexity of Photocatalytic Systems: α,β,γ. The Shid-factor is dimensionless and provides a quantitative value for each photocatalytic system regardless of the details of interface between the solid surface and media, only using operational condition and kinetics of reaction. The initial concentration of pollutant is important, because in high concentration light can be absorbed by organic pollutant/dye. Light absorption in the walls and in solution included solvent (water) and chemical components (dye) were reflected in γ that it is a dimensionless function, and it can be identified from the Beer−Lambert law. The effects of nonuniformity of light source, low energy photon that cannot excite the solid atoms and nonradiative relaxation were reflected in α, and it is a complex function. If we consider α = 1, it means that the light penetrates uniformly into all the media without being absorbed in the media. Something such as composition, size of crystallite, shape of particles, defects, and impurities, loading of noble/transition metals, and effects of doping were reflected in β as a dimensionless complex function. If we consider β = 1, it means that the photocatalyst surface remains fresh, and there is no fouling on the surface. Kinetics of reaction identifies the relation between physical time (t) and degradation percent with treduced. In first-order kinetics, the reduced time (treduced) has a logarithmic relationship with degradation. Also the effect of temperature can be reflected in the kinetics relation. In addition to the above considerations, we suppose that all volumes of the liquid media including photocatalyst and organic pollutant/dye as well as chemical substances are stirred vigorously and the diffusion coefficient is infinite. 3.2. Physical Meaning Shid-Factor. It is essential to mention that in this analysis, the photocatalytic system was considered as a black box, and, instead, we focused on the light and degraded organic pollutant as the input and the output of the system, respectively. Other complex phenomena related to the black box such as the radiation intensity, photon transfer, chemistry of photocatalyst, and organic pollutant were totally summarized in α, β, and γ coefficients. With regard to eq 7, the near relation between the Shid-factor and quantum yield is clear. Actually, the Shid-factor is an extended quantum yield, and it comprises operational conditions and reactor characteristics in its definition. With considering time, volume of photoreactor, light source, photocatalyst concentration, and solid-solution interaction, one dimensionless factor was extracted that can be used in various types of pollutants and photocatalysts because the Shid-factor is not directly dependent on them. Here, our aim was developing an easy tool for making a fast comparison for the performance of photocatalytic systems and not a full description of the whole photocatalytic system complexities. This modeling containing a meaningful factor,

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AUTHOR INFORMATION

Corresponding Author

*Phone: +98 21 66164104. Fax: +98 21 66005417. E-mail: [email protected]. Corresponding author address: Institute of Nanoscience & Technology, Sharif University of Technology, Tehran. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are thankful to those who helped us (mainly the authors writing articles denoted without an * in Tables 1 and 2) through putting at our disposal complementary information on their research works.

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