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International Journal of Photoenergy
Volume 2012 (2012), Article ID 607283, 9 pages
Statistical Optimization of Operational Parameters for Enhanced Naphthalene Degradation by Photocatalyst
1School of Municipal and Environmental Engineering, Harbin Institute of Technology (HIT), 202 Haihe Road, Harbin 150090, China
2Institute of Architecture Design and Research, Harbin Institute of Technology, Harbin 150090, China
3State Key Laboratory of Urban Water Resource and Environment, Harbin Institute of Technology (SKLUWRE, HIT), Harbin 150090, China
4Collage of Materials Science and Chemical Engineering, Harbin Engineering University, Harbin 150001, China
Received 11 December 2011; Revised 13 February 2012; Accepted 15 February 2012
Academic Editor: Stéphane Jobic
Copyright © 2012 Aijuan Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The optimization of operational parameters for enhanced naphthalene degradation by TiO2/Fe3O4-SiO2 (TFS) photocatalyst was conducted using statistical experimental design and analysis. Central composite design method of response surface methodology (RSM) was adopted to investigate the optimum value of the selected factors for achieving maximum naphthalene degradation. Experimental results showed that irradiation time, pH, and TFS photocatalyst loading had significant influence on naphthalene degradation and the maximum degradation rate of 97.39% was predicted when the operational parameters were irradiation time 97.1 min, pH 2.1, and catalyst loading 0.962 g/L, respectively. The results were further verified by repeated experiments under optimal conditions. The excellent correlation between predicted and measured values further confirmed the validity and practicability of this statistical optimum strategy.
Naphthalene, as the first member of polycyclic aromatic hydrocarbon (PAH) and one of the 16 PAHs classified as priority pollutants by the Environmental Protection Agency (EPA) of the United States, is a class of persistent organic pollutants of special concern. Naphthalene can be frequently found in many anthropogenic fluxes, such as combustion fumes, used oil, and bilge water, which is exceedingly recalcitrant to degradation due to its inhibitory nature [1–3]. Since it is the most water-soluble PAH, naphthalene is the dominant one in water which has been considered as possibly a carcinogen to humans (EPA 1998, The International Agency for Research on Cancer (IARC) 2002) and has both acute and chronic effects on human and animal health.
A solution to this naphthalene pollution problem has now become urgent. Removing naphthalene from water is possible via many techniques, including biofiltration , microbial degradation [5, 6], anaerobic degradation [7–9], electron beam irradiation , electrolytic aeration , and photocatalysis [12–14]. Among these techniques, biodegradation is expected to be an economical and energy-efficient approach which attracts more and more attentions to investigate the application to treat PAHs. Nevertheless, because of its toxicity and low water solubility, the efficacy of bioremediation still remains a critical point .
Photocatalysis has been proposed as an alternative to degrade refractory organic compounds unquestionably due to the specificity of hydroxyl radicals which represents high reaction rate and low selectivity [16–19]. Although this technique presents critical advantages over other techniques, there are some problems to be resolved urgently. Among these, the commonly mentioned problems are the designs of adequate reactors for efficient utilization of photons and the required higher degradability to persistent organic pollutants. Moreover, this technology has not been successfully commercialized, in part because of the difficulty in separating TiO2 nanoparticles from the suspension . To resolve this problem, TiO2 dispersed on magnetic oxide support (Fe3O4-SiO2) is used in this study as the catalyst for photooxidative degradation of naphthalene which could be reclaimed using ferromagnetic separation processes.
In order to enhance the naphthalene degradation performance, an optimization approach should be employed. Response surface methodology (RSM) is an efficient standard and well-established mathematical optimization procedure which can achieve such an optimization by analyzing and modeling the effects of multiple variables and their responses and finally optimizing the process . This method has been successfully employed for optimization in some photocatalytic oxidation processes [22–26]. However, to the best of our knowledge, the optimization of photocatalytic degradation of naphthalene solution by TiO2/Fe3O4-SiO2 (TFS) catalyst has not been reported. Therefore, the objective of this study was to investigate the effect of TiO2/Fe3O4-SiO2 (TFS) photocatalyst on the treatment of a simulated high-concentration wastewater polluted by naphthalene. The central composite circumscribed (CCC) design method of RSM was employed to determine the optimal process condition for maximizing naphthalene degradation rate.
2. Materials and Methods
2.1. Reagents and Photocatalyst Preparation
FeCl2, FeCl3, NaOH, HNO3, Fe3O4, absolute alcohol, and isopropanol (Tianjin Kermel Chemical Reagent Co. Ltd.) were of analytical grade; naphthalene (Aldrich), Ti(OC4H9)4, 3-aminopropyltriethoxysilane, and tetraethoxysilane (J&K Chemical Ltd Co.) were of reagent grad; all the reagents mentioned above were used as received without further purification. Millipore deionized water was used for dilution.
For now, the TFS photocatalyst has been prepared successfully, and the specific preparation and characterization have been published in other paper . The synthesis route of TFS photocatalyst is shown in Figure 1.
A schematic representation of the photoreactor is shown in Figure 2. The reactor mainly consisted of mechanical stirrer, mercury lamp, quartz cold trap, and beaker. The irradiation experiments were carried out in four parallel 250 mL quartz beakers. The light source was a high-pressure mercury lamp (HPK 125W, Philips) setting in a quartzose cold trap, emitting the near-UV (mainly around 365 nm). The warp of photoreactor was made of polymethyl methacrylate (PMMA), inner surface of which clings silver paper in order to return UV light.
2.3. Multivariate Experimental Design
A 3-factor CCC with six replicates at the center point leading to 20 experiments was employed to optimize the operational parameters for improving naphthalene degradation. For statistical calculation, the relation between the coded values and actual values of independent variable is described as follows. where is the coded value of the independent variable, is the actual value of independent variable, is the actual value of the at the center point, and is the step change of independent variable.
In the study, catalyst loading, pH, and irradiation time were taken as the independent variable and naphthalene degradation rate was the dependent variable or response of the design experiments. By means of multilinear regression method [28, 29], a second-order polynomial function was fitted to correlate relationship between independent variable and response. Quadratic equation for the independent variable was expressed as follows. where represents the predicted response; is the interception coefficient; , , and are the linear coefficients; , , and are the quadratic coefficients; , , and are the interactive coefficients; , , and represent the independent variable studied.
The Design Expert (Version 220.127.116.11, Stat-Ease Inc., Minneapolis, MN, USA) software was used for regression and graphical analyzes of the data obtained. All experimental designs were randomized, and mean values were applied.
As the solubility of naphthalene is 25–30 mg/L at ambient temperature, this study chose to work with the highest concentration in order to show the unique removal efficiency of TFS photocatalyst . In all the photocatalytic experiments, the reaction temperature was kept constant at C. Unless required, pH was not initially modified or controlled in the reactor. When required, initial pH values were adjusted using 4 mol/L NaOH or H2SO4.
All experiments were carried out in 250 mL quartzose beakers comprised of 100 mL aqueous naphthalene solution and the appropriate amount of the TFS photocatalyst powder, stirring at 1000 rpm (higher rotated speed may result in naphthalene volatilization without degradation). Before irradiation, the reaction mixture was premixed in the dark for 20 min to reach adsorption equilibrium.
2.5. Analytical Methods
The residual naphthalene was determined by a high-performance liquid chromatography (LC-10A, Shimadzu Corporation, Kyoto, Japan) equipped with a diode array detector and an Uptisphere C18 HDO column (stationary phase 3 μm, dimensions 150 mm × 3 mm) using a mixture of methanol and deionized water (ratio 80 : 20) as the mobile phase at a flow rate of 1.0 mL/min.
3. Results and Discussion
3.1. Effect of Catalyst Loading on Degradation of Naphthalene
The catalyst loading in slurry photocatalytic processes was an important factor. Figure 3 presents the variation of the first order rate constant and the value of Ct/Co as a function of the catalyst loading, where Ct is the naphthalene concentration at time and Co is the initial concentration of naphthalene. The optimum concentration of the TFS photocatalyst was examined by varying the catalyst amount from 0.25 to 1.50 g/L. The reaction rates () were estimated by fitting the time-course curves using the first-order kinetics [14, 30], which was presented in the inset of Figure 3. It can be seen from Figure 2 that, as the TFS photocatalyst loading increased, the photocatalytic efficiency of the degradation increased firstly and then decreased. At 1.00 g/L catalyst loading, the first-order rate constant reached maximum and the rate of degradation reached a saturation value. By further increasing the catalyst loading, it would lead to the aggregation of the catalyst particles, which, in turn, resulted in the decrease of active sites and the naphthalene photodegradation. Consequently, the operating range of catalyst loading for multivariate experimental design was 0.8–1.0 g/L, taking costs into account simultaneously.
3.2. Effect of pH on Degradation of Naphthalene
It is known that the influence of pH to the photodegradation is substantially complex, which can directly affect the surface charged properties of photocatalyst particles and, by extension, influence the adsorption behavior of substrate molecules on the photocatalyst surface. In the present study, therefore, it was chosen as a predominant operational factor for the photooxidative degradation of naphthalene. Metal oxide particles suspended in water behaved similar to diprotic acids. When TiO2 surface was hydrated, the principal surface functionality was the amphoteric “Titanol” moiety, −TiOH, which took part in the following acid-base equilibrium : where and represented the negative log of the acidity constants of the first and second acid dissociation, respectively. The pH of zero point of charge, , was given as the following equation: In the TFS photocatalyst, TiO2 spreads as a layer over Fe3O4-SiO2 core (Figure 1). Thus as far as surface properties be concerned, TFS was similar to pure TiO2. For TiO2 Degussa P-25, the corresponding surface acidity constants are found to be = 4.5 and = 8.0, and pHzpc has been determined by titration: pHzpc = 6.3 .
Figure 4 presents the variation of the first-order rate constant and the value of Ct/Co as a function of pH. The catalyst loading was 1.0 g/L. It can be noticed that a higher photodegradation effect existed in acid environment, which was assumed to be linked with the surface characteristic of TFS photocatalyst particles. At low pH, hydroxyl radicals were formed on the surface of TFS particles by the reaction of hole () with adsorbed H2O molecule: , which made electron (e-) assemble to the surface of TFS particles and then reacted with adsorbed O2 to , leading to longer lifetime of the electron/hole pair . Moreover, the increased hydrogen ions was beneficial to the production of H2O2 and radicals. The specific reactions were given as follows.
At high pH, the TFS particles’ surface was negatively charged which increased the work function for electron abjection and also trapped of valence-band holes. It made against the photocatalytic reaction. But the reaction rates in pH 8 and 10 were a little increased than those in neutral in this case, because the solutions at different pH had different ionic strength: HNO3 was present at acid solution and NaOH was present at alkaline solution, whereas no ionic species were added at neutral pH 7, and additionally the quantities of ionic also affected the ionic strength.
As seen in the inset of Figure 4, the first-order rate constant of the degradation () at pH 2 was higher than those at other pH values. As a consequence, the operating range of pH for multivariate experimental design was 1.5–2.5.
3.3. Effect of Irradiated Time on Degradation of Naphthalene
Table 1 shows the variation of the degradation rate in the condition of optimal catalyst loading (1.00 g/L) and pH (2) as a function of irradiation time.
As displayed in Table 1, the increase of degradation rate went flatter after 80 min. The degradation rate enhanced 2.5% in the time range of 80~100 min, while the degradation rate enhanced only 1.51% in the time range of 100~120 min which was much lower than the previous three ranges. The irradiation time counted little to the degradation rate of naphthalene after 80 min. Consequently, the operating range of irradiation time for multivariate experimental design was 80–100 min, taking costs into account simultaneously.
3.4. Optimization of Operational Parameters for Enhancing the Naphthalene Degradation
Experimental design and results are shown in Table 2. By applying multiple regression analysis on the experimental data, a second-order polynomial equation was obtained to describe the correlation between the independent variable and the naphthalene degradation rate: where is the predicted naphthalene degradation rate (%); , , and are irradiation time (min), pH value, and catalyst loading (g/L), respectively.
The analysis of variance (ANOVA) was conducted to test the significance of the fit of the second-order polynomial equation for the degradation rate as shown in Table 3.
The value, represented the likelihood of two different groups being statistically different, was 551.40 which implied that the model was significant because values of “Prob > ” less than 0.05 were considered to be significant. There was only less 0.01% chance that a model value this large could occur; the regression mathematical model was a good fit to experimental data. In addition, the model did not show lack of fit. The Pred -squared was 0.9827 which was in reasonable agreement with the Adj -squared (0.9964). The disparity of -squared (0.9982) and Adj -squared was probably originated in the insignificance of term. The Adeq Precision was 64.080 which indicated an adequate signal, measuring the signal to noise ratio. Myers pointed that model adequacies should be checked by 2, Adj-2, Pre-2, Adeq. Precision, and CV (lack of fit > 0.1; 2 > 0.95; (Adj-2–Pre-2) < 0.2; CV < 10; Pre-2 > 0.7; Adeq. Precision > 4) . After calculated, 2, Adj-2, Pre-2, Adeq. Precision and coefficient of variation (CV, 1.00) all satisfied the request of model adequacy; therefore, (7) properly described the degradation rate of naphthalene in this study. From (7), the optimal values of , , and in the actual units were found to be 97.1 min irradiation time, 2.1 pH, and 0.962 g/L catalyst loading, respectively. The maximum predicted value of degradation rate obtained was 97.39%.
Figures 5–7 show the response surface plots and corresponding contour plots based on (7) with one variable being kept constant at its optimum level and the other two variables varied within the experimental range. As can be seen from Figures 4–6, the response surface of degradation rate showed a clear peak, indicating that the optimum conditions were inside the design boundary well. Degradation rate increased with irradiation time, pH, and catalyst loading to optimum conditions, respectively, and then decreased with a further increase. This result indicates that irradiation time, pH, and catalyst loading all had individual significant influences on degradation rate. In addition, the angle of inclination of the principal axis was evidently towards either irradiation time or catalyst loading in Table 1 and Figure 3, respectively, and this indicated that the positive effect of increased irradiation time or catalyst loading levels on degradation rate was more pronounced than pH increased.
3.5. Validation of the Model
In order to confirm the validity of the statistical experimental strategy, the repeated experiments under optimal conditions were carried out (Table 4). As a consequence, the maximum standard error between the observed value and the predicted value was less than 4% which indicated that the quadratic model can predict experimental results well. Furthermore, the standard error was only 2.26% in code 3 when the irradiation time (120 min) was beyond the operating range for multivariate experimental design, from which we can see that the model had extrapolation ability. As been shown, the degradation rate of naphthalene was 95.88%, 96.34%, and 97.03% in the optimal experimental condition, respectively. The observed values enhanced about 4% than nonoptimal experimental values at the same temperature.
The present study focused on the optimization of operational parameters for enhancing naphthalene degradation by TiO2/Fe3O4-SiO2 photocatalyst using the statistical methodology. Based on the central composite design, the maximum predicted value of degradation rate was obtained when the operational parameters were 97.1 min irradiation time, 2.1 pH, and 0.962 g/L catalyst loading, respectively. The high correlation between the predicted and observed values indicated the validity of the model. This result suggested that statistical design methodology offers an efficient and feasible approach for optimization the operational parameters of naphthalene degradation by TiO2/Fe3O4-SiO2 photocatalyst.
The authors gratefully acknowledge the financial support by the National Natural Science Foundation of China (no. 51078100), by the National Creative Research Groups Project (Grant no. 51121062), by the Heilongjiang Science Foundation for Distinguished Young Scholars (Grant no. JC201003), and by the State Key Laboratory of Urban Water Resource and Environment (Grant no. 2010DX11).
- S. C. Wilson and K. C. Jones, “Bioremediation of soil contaminated with polynuclear aromatic hydrocarbons (PAHs): a review,” Environmental Pollution, vol. 81, no. 3, pp. 229–249, 1993.
- B. Guieysse, M. D. Cirne, and B. Mattiasson, “Microbial degradation of phenanthrene and pyrene in a two liquid phase-partioning bioreactor,” Applied Microbiology and Biotechnology, vol. 56, pp. 796–802, 2001.
- A. Lair, C. Ferronato, J. M. Chovelon, and J. M. Herrmann, “Naphthalene degradation in water by heterogeneous photocatalysis: an investigation of the influence of inorganic anions,” Journal of Photochemistry and Photobiology A, vol. 193, no. 2-3, pp. 193–203, 2008.
- K. Maillacheruvu and S. Safaai, “Naphthalene removal from aqueous systems by Sagittarius sp,” Journal of Environmental Science and Health Part A, vol. 37, no. 5, pp. 845–861, 2002.
- H. Pathak, D. Kantharia, A. Malpani, and D. Madamwar, “Naphthalene degradation by Pseudomonas sp. HOB1: in vitro studies and assessment of naphthalene degradation efficiency in simulated microcosms,” Journal of Hazardous Materials, vol. 166, no. 2-3, pp. 1466–1473, 2009.
- Y. Jia, H. Yin, J. S. Ye et al., “Characteristics and pathway of naphthalene degradation by pseudomonas sp. N7,” Journal of Environmental Science, vol. 29, no. 3, pp. 756–762, 2008.
- F. Musat, A. Galushko, J. Jacob et al., “Anaerobic degradation of naphthalene and 2-methylnaphthalene by strains of marine sulfate-reducing bacteria,” Environmental Microbiology, vol. 11, no. 1, pp. 209–219, 2009.
- J. Dou, X. Liu, and A. Ding, “Anaerobic degradation of naphthalene by the mixed bacteria under nitrate reducing conditions,” Journal of Hazardous Materials, vol. 165, no. 1–3, pp. 325–331, 2009.
- M. Safinowski and R. U. Meckenstock, “Methylation is the initial reaction in anaerobic naphthalene degradation by a sulfate-reducing enrichment culture,” Environmental Microbiology, vol. 8, no. 2, pp. 347–352, 2006.
- W. J. Cooper, M. G. Nickelsen, R. V. Green, and S. P. Mezyk, “The removal of naphthalene from aqueous solutions using high-energy electron beam irradiation,” Radiation Physics and Chemistry, vol. 65, no. 4-5, pp. 571–577, 2002.
- R. K. Goel, J. R. V. Flora, and J. Ferry, “Mechanisms for naphthalene removal during electrolytic aeration,” Water Research, vol. 37, no. 4, pp. 891–901, 2003.
- E. Pramauro, A. B. Prevot, M. Vincenti, and R. Gamberini, “Photocatalytic degradation of naphthalene in aqueous TiO2 dispersions: effect of non ionic surfactants,” Chemosphere, vol. 36, no. 7, pp. 1523–1542, 1998.
- S. Dass, M. Muneer, and K. R. Gopidas, “Photocatalytic degradation of wastewater pollutants. Titanium-dioxide-mediated oxidation of polynuclear aromatic hydrocarbons,” Journal of Photochemistry and Photobiology A, vol. 77, no. 1, pp. 83–88, 1994.
- L. Hykrdová, J. Jirkovský, G. Mailhot, and M. Bolte, “Fe(III) photoinduced and Q-TiO2 photocatalysed degradation of naphthalene: comparison of kinetics and proposal of mechanism,” Journal of Photochemistry and Photobiology A, vol. 151, no. 1–3, pp. 181–193, 2002.
- S. V. Mohan, T. Kisa, T. Ohkuma, R. A. Kanaly, and Y. Shimizu, “Bioremediation technologies for treatment of PAH-contaminated soil and strategies to enhance process efficiency,” Reviews in Environmental Science and Biotechnology, vol. 5, no. 4, pp. 347–374, 2006.
- M. Lindner, J. Theurich, and D. W. Bahnemann, “Photocatalytic degradation of organic compounds: accelerating the process efficiency,” Water Science and Technology, vol. 35, no. 4, pp. 79–86, 1997.
- T. Ohno, K. Tokieda, S. Higashida, and M. Matsumura, “Synergism between rutile and anatase TiO2 particles in photocatalytic oxidation of naphthalene,” Applied Catalysis A, vol. 244, no. 2, pp. 383–391, 2003.
- B. Pal and M. Sharon, “Photodegradation of polyaromatic hydrocarbons over thin film of TiO2 nanoparticles; a study of intermediate photoproducts,” Journal of Molecular Catalysis A, vol. 160, no. 2, pp. 453–460, 2000.
- N. Barrios, P. Sivov, D. D'Andrea, and O. Núñez, “Conditions for selective photocatalytic degradation of naphthalene in triton X-100 water solutions,” International Journal of Chemical Kinetics, vol. 37, no. 7, pp. 414–419, 2005.
- M. J. García-Martínez, L. Canoira, G. Blázquez, I. Da Riva, R. Alcántara, and J. F. Llamas, “Continuous photodegradation of naphthalene in water catalyzed by TiO2 supported on glass Raschig rings,” Chemical Engineering Journal, vol. 110, no. 1–3, pp. 123–128, 2005.
- J.-P. Wang, Y.-Z. Chen, Y. Wang, S.-J. Yuan, and H.-Q. Yu, “Optimization of the coagulation-flocculation process for pulp mill wastewater treatment using a combination of uniform design and response surface methodology,” Water Research, vol. 45, no. 17, pp. 5633–5640, 2011.
- I. H. Cho and K. D. Zoh, “Photocatalytic degradation of azo dye (Reactive Red 120) in TiO2/UV system: optimization and modeling using a response surface methodology (RSM) based on the central composite design,” Dyes and Pigments, vol. 75, no. 3, pp. 533–543, 2007.
- A. F. Caliman, C. Cojocaru, A. Antoniadis, and I. Poulios, “Optimized photocatalytic degradation of Alcian Blue 8 GX in the presence of TiO2 suspensions,” Journal of Hazardous Materials, vol. 144, no. 1-2, pp. 265–273, 2007.
- J. F. Fu, Y. Q. Zhao, X. D. Xue, W. C. Li, and A. O. Babatunde, “Multivariate-parameter optimization of acid blue-7 wastewater treatment by Ti/TiO2 photoelectrocatalysis via the Box-Behnken design,” Desalination, vol. 243, no. 1–3, pp. 42–51, 2009.
- A. R. Khataee, M. Zarei, and S. K. Asl, “Photocatalytic treatment of a dye solution using immobilized TiO 2 nanoparticles combined with photoelectro-Fenton process: optimization of operational parameters,” Journal of Electroanalytical Chemistry, vol. 648, no. 2, pp. 143–150, 2010.
- M. Fathinia, A. R. Khataee, M. Zarei, and S. Aber, “Comparative photocatalytic degradation of two dyes on immobilized TiO 2 nanoparticles: effect of dye molecular structure and response surface approach,” Journal of Molecular Catalysis A, vol. 333, no. 1-2, pp. 73–84, 2010.
- L. Y. Wang, H. X. Wang, A. J. Wang, and M. Liu, “Surface modification of a magnetic SiO2 support and immobilization of a nano-TiO2 photocatalyst on it,” Chinese Journal of Catalysis, vol. 30, no. 9, pp. 939–944, 2009.
- S. L. Akhnazarova and V. V. Kafarov, Experiment Optimization in Chemistry and Chemical Engineering, Mir Publishers, Moscow, Russia, 1982.
- H. G. Neddermeijer, G. J. van Oortmarssen, N. Piersma, and R. Dekker, “Framework for Response Surface Methodology for simulation optimization,” in Proceedings of the 32nd Winter Simulation Conference Proceedings, pp. 129–136, Orlando, Fla, USA, December 2000.
- E. Pramauro, A. B. Prevot, M. Vincenti, and R. Gamberini, “Photocatalytic degradation of naphthalene in aqueous TiO2 dispersions: effect of non ionic surfactants,” Chemosphere, vol. 36, no. 7, pp. 1523–1542, 1998.
- M. R. Hoffmann, S. T. Martin, W. Choi, and D. W. Bahnemann, “Environmental applications of semiconductor photocatalysis,” Chemical Reviews, vol. 95, no. 1, pp. 69–96, 1995.
- N. Jaffrezic-Renault, P. Pichat, A. Foissy, and R. Mercier, “Study of the effect of deposited platinum particles on the surface charge of titania aqueous suspensions by potentiometry, electrophoresis, and labeled-ion adsorption,” Journal of Physical Chemistry, vol. 90, pp. 2733–2738, 1986.
- D. Duonghong, J. Ramsden, and M. Grätzel, “Dynamics of interfacial electron-transfer processes in colloidal semiconductor systems,” Journal of the American Chemical Society, vol. 104, no. 11, pp. 2977–2985, 1982.
- R. H. Myers, D. C. Montgomery, and C. M. Anderson-Cook, Response Surface Methodology: Process and Product Optimization Using Designed E xperiments, John Wiley & Sons, Hoboken, NJ, USA, 2002.