Journal of Chemical Technology and Biotechnology J Chem Technol Biotechnol 83:1454–1465 (2008)

Response surface methodology appliedfor Orange II photocatalytic degradationin TiO2 aqueous suspensionsCamelia Betianu,1 Florentina A Caliman,1 Maria Gavrilescu,1 Igor Cretescu,1

Corneliu Cojocaru1 and Ioannis Poulios2∗1Faculty of Chemical Engineering and Environmental Protection, Dept. of Environmental Engineering and Management, ‘‘Gh. Asachi’’Technical University, Bd. Mangeron 71A, 700050, Iasi, Romania2Laboratory of Physical Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

Abstract

BACKGROUND: Heterogeneous photocatalysis is influenced by a number of parameters involving synergisticeffects; hence, an experimental strategy design that considers interactions between the main variables is needed.The response surface methodology was applied for the investigation of photodegradation of 20 mg L−1 Orange II inaqueous solutions and for optimization of color removal efficiency. Preliminary studies were performed to identifythe parameters to be selected for optimization.

RESULTS: The input variables considered for experimental design were: solution initial pH, oxidizing agent (H2O2)initial concentration and UV-A irradiation time. The multivariate experimental design allowed the developmentof a quadratic response surface model to be used for the prediction of color removal efficiency over the full rangeof the experimental region. Under the optimum conditions established in the region of experimentation (pH = 6.9,[H2O2]0 = 183 mg L−1 and t = 32 min), a 100% color removal efficiency was obtained in experiments.

CONCLUSIONS: It was found that the variables considered have important effects on color removal efficiency.The results demonstrate that the use of experimental design strategy is indispensable for successful investigationand adequate modeling of the process because the interdependence of the reaction parameters cannot be neglected. 2008 Society of Chemical Industry

Keywords: photocatalysis; response surface methodology; optimization; azo dyes; TiO2

INTRODUCTIONTextile processing is one of the most importantbut also most polluting industries in the world.One of the main problems associated with thetreatment of textile wastewaters is the removal ofdyes. A substantial amount of dyestuff is lost duringthe dyeing process, resulting in significant damageto industry losses and constituting an importantenvironmental threat.1 Owing to relatively low fixationand reduced efficiencies of the biological processesgenerally employed in remediation of effluents fromtextile wastewaters, around 20% of the unfixed dyesare discharged into the environment.2 Apart from thefact that they can lead to eutrophication, some dyes orresulting by-products are toxic and mutagenic for floraand fauna, and their release in natural environmentsprovides the potential danger of bio-accumulation thatmay eventually affect humans through the food chain.Along with the unconsumed dyes, textile wastewatersmay be charged with surfactants and, sometimes, tracemetals.

Among the different types of dyes used in textileindustries, 60–70% are azo compounds. These dyesand their degradation intermediates may exhibithighly carcinogenic properties. The aromatic ringsin the azo dye molecular structure are generally non-biodegradable and lead to an increase in the toxicityof effluents.

The variety and stability of the aromatic struc-tures found in azo dyes make their mineraliza-tion by conventional methods difficult. Physical andchemical treatment processes are usually employed,such as adsorption, ion exchange, reverse osmo-sis or ultrafiltration. These result in transfer ofthe pollutant from liquid to solid phase andinvolve high costs for regeneration and/or post-treatment. Biological treatments are not very effi-cient because these compounds are resistant toaerobic degradation, and anaerobic processes mayreduce the azo bond to potentially carcinogenic aro-matic amines that are more dangerous than the dyeitself.3

∗ Correspondence to: Ioannis Poulios, Laboratory of Physical Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, 54124 Thessaloniki,GreeceE-mail: poulios@chem.auth.gr(Received 7 March 2008; revised version received 9 April 2008; accepted 14 April 2008)Published online 27 May 2008; DOI: 10.1002/jctb.1973

2008 Society of Chemical Industry. J Chem Technol Biotechnol 0268–2575/2008/$30.00

RSM applied to Orange II photocatalytic degradation

Heterogeneous photocatalysis may be consideredamong the most efficient processes for wastewatertreatment.2–9 A general description of heterogeneousphotocatalytic oxidation under artificial or solarirradiation is presented in several excellent reviewarticles,10–13 therefore, the various stages of thephotocatalytic process will not be presented here.

Orange II (Acid Orange 7) is a mono-azo dyeextensively used in textile, food and cosmeticsindustries14 and has, as can be seen in Fig. 1, twotautomeric forms, azo and hydrazone.15

The photodegradation of Orange II has been studiedextensively on different catalysts, such as pure, dopedor supported TiO2, as well as ZnO under both naturaland artificial irradiation.15–24

Heterogeneous photocatalysis is influenced by cata-lyst loading, initial pollutant concentration, pH, radi-ant flux, aeration, presence of other substances orimpurities, and photoreactor geometry.13 The major-ity of studies concerning the effect of these factorsupon the process were performed using the univariateapproach, in which one parameter is varied while theothers are kept constant. However, the great number ofinfluencing parameters involves synergistic effects, as aresult of interactions between the variables. Hence, theapplication of the conventional univariate experimen-tation methodology is frequently inadequate for pro-cess optimization. The univariate methodology usuallyrequires many experimental runs, is time consumingand does not necessarily allow effective optimization ofthe process. Therefore an alternative is used, such asexperimental statistical design, in order to overcomethese drawbacks. The design and statistical analysisof experiments have resulted in the development of aresponse surface model (RS-model) used for processoptimization and prediction of the interaction betweenvariables, reducing the number and, consequently, thecost of experiments.

An optimization approach such as response surfacemethodology (RSM) has proven to be a reliablestatistical tool in the investigation of photocatalyticprocesses.25–32

In this work, multivariate analysis using theRSM was used, changing simultaneously pH,H2O2concentration and irradiation time, in order todetermine the optimal conditions for degradation of

Figure 1. Tautomeric forms of Orange II in solution.

azo dye Orange II. Since the photocatalytic process isaffected by a great number of parameters, it was ratherdifficult to perform an experimental design containingall these parameters. Therefore, preliminary experi-ments were carried out to find the most importantfactors effecting the photocatalytic degradation of thestudied dye that should be selected for optimization.

EXPERIMENTALMaterialsOrange II (MW = 350.32) was purchased from Fluka(Fluka Chemie AG, Switzerland). TiO2 P-25 Degussa(anatase/rutile = 3.6/1, surface area 56 m2 g−1) wasused for all the photocatalytic experiments, exceptwhere otherwise mentioned in the text. TiO2-A (100%Anatase, ∼10 m2g−1) and ZnO (∼10 m2 g−1) werepurchased from Merck (Merck Chemicals Ltd, UK),while TiO2 UV-100 (150 m2 g−1) was obtained fromSchachtleben Chemie (Sachtleben Chemie GmbH,Germany).

Procedures and analysisExperiments were conducted in a closed Pyrex cell of500 mL capacity. Air required to ensure the presenceof oxygen as an electron acceptor in the system wasbubbled though a port at the upper part of the photore-actor. Before irradiation, the reaction mixture was leftfor 30 min in the dark in order to achieve maximumadsorption of the dye onto the catalyst surface.

Irradiation was carried out with a 9 W centrallamp. The spectral response of the irradiation source(Osram Dulux S 9W/78 UV-A), according to themanufacturer, ranges between 350 and 400 nm, witha maximum at 366 nm and two additional weak linesin the visible region. The photon flow per unit volumeof the incident light was determined by chemicalactinometry using potassium ferrioxalate.33 The initiallight flux, under exactly the same conditions as in thephotocatalytic experiments, was evaluated as being1.26 × 10−4 Einstein min−1.

In all experiments, 500 mL of Orange II solutioncontaining the appropriate amount of semiconductingpowder was magnetically stirred before and duringirradiation. Specific quantities of sample were with-drawn at periodic intervals and filtered through a0.45 µm filter (Schleicher and Schuell) in order toremove the catalyst particles. To assess the extent ofcolor removal, changes in the concentration of the dyewere determined from its characteristic absorptionband using a UV-VIS spectrophotometer ShimadzuUV-1700 PharmaSpec. Owing to the fact that a lineardependence exists between the initial concentration ofthe pollutant and the absorption at 485 nm, this wave-length was used for spectrophotometrically monitoringthe photodecomposition in all experiments.

For control of pH in the acid and alkaline area,solutions of H2SO4 (0.1 N) and NaOH (0.1 N),respectively, were used. The pH values of the solution

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C Betianu et al.

were monitored with a Metrohm pH-meter, while thereaction temperature was kept constant at 25 ± 0.1 ◦C.

RESULTS AND DISCUSSIONKinetics of heterogeneous photocatalyticdegradation of Orange IIFigure 2 shows the change in the absorption spectrumof 20 mg L−1 (0.571 × 10−4 mol L−1) Orange II underUV-A irradiation in an aqueous solution containing0.5 g L−1 TiO2 P-25. The UV-Vis spectrum of OrangeII consists of two main characteristic absorption bands:the first is situated in the UV region (230 nm) andarises from the adjacent aromatic rings structures andthe second, in the visible region (485 nm), derivesfrom the chromophore group.19 One may observethat the absorption spectrum gradually decreasesin intensity with increasing irradiation time up to60 min. Disappearance of the 485 nm absorption bandindicates the degradation of the chromophoric groupsresponsible for the characteristic color of the azo dye.Apart from the degradation of the colored group, thereis also a drastic decrease in the absorbance values atwavelengths below 300 nm, due to the attack andbreaking of the aromatic rings of the dye, as one cansee in Fig. 2.

Results of the irradiation of 20 mg L−1 Orange IIsolution containing, respectively 0.5 g L−1 of TiO2 P-25, TiO2-A, TiO2 UV-100 and ZnO are depicted inFig. 3, where the amount of the organic moleculepresent in the supernatant, as determined fromspectrophotometric measurements, is plotted as afunction of irradiation time. It is obvious that under theexperimental conditions used, the removal of dye colorwas around 95% after 60 min of UV-A exposure in thepresence of TiO2 P-25, while in the case of ZnO,it was completed after 30 min irradiation. However,even though ZnO exhibited the best catalytic activityunder the conditions studied, its application is limited

Figure 2. Spectral response of 20 mg L−1 Orange II during thephotocatalytic degradation in the presence of 0.5 g L−1 TiO2 P-25 atpH = 6.5 (00: 20 mg L−1 Orange II solution without catalyst; 0: 20 mgL−1 solution Orange II in the presence of P-25 in the dark).

by corrosion and photocorrosion that may result in anincrease in the toxicity of the solution. It is well knownfrom the literature that below pH = 9, dissolutionof ZnO takes place, which increases by illuminationas a result of the attack of the Zn–O bonds by thephotogenerated holes.34,35 This leads to a release ofZn2+ ions into the suspension and to an increase ofthe toxicity, taking into account that for the bacteriaVibrio fischeri the EC50 for Zn2+ is 1.62 mg L−1.36

On the other hand, experiments carried out by UV-A irradiation in the absence of the photocatalyst, aswell as in the dark in the presence of TiO2 P-25 haveshown that in both cases, no significant degradation ofthe pollutant occurred.

The amount of catalyst added into the system isan important parameter, since it strongly depends onthe geometry of the photoreactor, the nature of theorganic compound, the working conditions, as well asthe incident light intensity.37,38

Aimed at finding the most efficient catalystconcentration, experiments were conducted varyingthe TiO2 P-25 dose in the solution in the range0.5 g L−1 to 4 g L−1. The influence of the catalystconcentration on the initial degradation reaction rate ispresented in Fig. 4, which shows that under the givenexperimental conditions an optimum amount equalto 0.5 g L−1 P-25 exists. Further increase in catalystdosage leads to enhancement of the light reflectanceand consequently to a decrease in the efficiency ofphotodegradation, as one may see in Fig. 4.

The initial degradation rate of the organic pollu-tants can be described by the Langmuir–Hinshelwoodmodel, developed by Turchi and Ollis39 and acceptedby a great number of researchers. The Lang-muir–Hinshelwood rate expression has been usedwith success for determining the relationship betweenthe initial degradation rate and the concentration ofthe organic substrate in the case of the reactionsoccurring at the solid–liquid interface within the het-erogeneous photocatalytic processes and is expressedby the equation:

ro = dCdt

= krKCo

1 + KCo(1)

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

conc

entr

atio

n (m

g L

-1)

illumination time (min)

Figure 3. Photodegradation of 20 mg L−1 OR II as a function ofirradiation time in the presence of (�) 0.5 g L−1 ZnO; (ž) 0.5 gL−1 TiO2 P-25; (�) 0.5 g L−1 TiO2 UV-100; (�) 0.5 g L−1 TiO2 –A;Blank studies: (�) UV-A only; ( ) TiO2 P-25 only.

1456 J Chem Technol Biotechnol 83:1454–1465 (2008)DOI: 10.1002/jctb

RSM applied to Orange II photocatalytic degradation

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0

0.1

0.2

0.3

0.4

0.5

r o (

mg

L-1

min

-1)

TiO2 P-25 concentration (g L-1)

Figure 4. Dependence of the initial degradation reaction rate (ro) onthe concentration of TiO2 P-25 for constant dye concentration (20 mgL−1).

where: ro = initial rate of disappearance of the sub-strate; Co = initial dye concentration; K = equilibriumconstant for adsorption of the organic substrate ontothe photocatalyst; kr = reaction rate constant describ-ing the tendency of the organic compound to bedegraded after adsorption (limiting rate of reactionat the maximum coverage in the studied experimentalconditions).

The rearrangement of the Equation (1) in the linearform is commonly used to demonstrate linearity whenplotted as the inverse reaction rate versus the inverseof the initial pollutant concentration:

1ro

= 1kr

+ 1krK

1Co

(2)

The effect of modifying the initial concentration ofOrange II upon the initial photocatalytic reaction rate(ro) is presented in Fig. 5.

The resulting curve is reminiscent of a Langmuirtype isotherm for which the rate of decompositionfirst increases sharply due to increase in the amountof dye adsorbed on TiO2 P-25 until a saturationvalue is reached. The initial reaction rates ro wereindependently obtained by the linear fit Co − t inthe range of dye concentrations 5–70 mg L−1. Tocalculate the initial reaction rate, the experimentaldata obtained up to 20% dye removal were used,in order to minimize variations as a result ofcompetitive effects of the intermediates, pH alteration,etc. It is well known that the intermediate productsformed during photodegradation undergo furtherphotocatalytic oxidation, while the simultaneousrelease of H+ influences the pH of the solution,resulting in the change of the initial conditions.

The dependence between the ro−1 and Co

−1 valuesis shown in the inset of Fig. 5. The kr and K valuescalculated according to Equation (2) from the slope ofthe straight line (R2 = 0.974) and from the interceptwith the ro

−1 axis were kr = 0.55 mg L−1 min−1

(0.156 × 10−5 mol L−1 min−1) and K = 0.15 mg−1 L(5.025 × 104(mol L−1)−1, respectively.

Effect of the initial pH on the photocatalyticdegradation of Orange IIThe effect of the initial pH of the solution on thephotodegradation process is very important since itinfluences the photocatalyst characteristics, such asthe electric charge of the particles, the sizes of theaggregates formed, the position of the conduction andvalence bands of the semiconducting catalysts, as wellas the extent of adsorption of electron donors ontotheir surface.

In Fig. 6, the initial reaction rate values of thephotodegradation of Orange II are given in the pHrange from 2.65 to 8.6. It is obvious that the rate

0 10 20 30 40 50 60 70 800.0

0.1

0.2

0.3

0.4

0.5

initi

al r

eact

ion

rate

, ro (

mg

L-1

min

-1)

Co (mg L-1)

0.00 0.05 0.10 0.15 0.200

1

2

3

4

5

r o-1 (

mg

L-1

min

-1)

Co-1 (L mg-1)

Figure 5. Plot of ro versus Co for Orange II at different initial concentrations at constant catalyst concentration (0.5 g L−1 TiO2 P-25). The insetshows the linear transform of ro

−1 versus Co−1 according to Equation (2).

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C Betianu et al.

0 100.0

0.1

0.2

0.3

0.4

0.5

0.6in

itial

rea

ctio

n ra

te, r

o (m

g L

-1 m

in-1

)

pH2 4 6 8

Figure 6. Effect of pH on the initial reaction rate of the photocatalyticdegradation of 20 mg L−1 Orange II at constant concentration ofcatalyst (0.5 g L−1 TiO2 P-25).

of photodegradation reaches a maximum at pH = 3,then decreases until a value of pH situated aroundthe zero charge point of TiO2, followed by anotherslight increase in the pH region 5.5–7.35 and a smalldecrease above this.

The effect of pH on the photocatalytic reaction isexplained primarily by the surface charge of TiO2

(point of zero charge pzc ≈ 5.6) and its relationwith the dissociation constant of the sulfonic groupof Orange II, which is a slightly acidic anionic dye.According to previous studies, Orange II adsorptiononto the TiO2 surface takes place through the oxygenof the hydrazone form or the oxygen atoms of thesulfonated group.15

The TiO2 surface consists of amphoteric zonesthat may become positively or negatively chargeddepending on the pH of the solution. The percentageof resultant species on the surface of TiO2 are TiOH ≥80%, at 3 < pH < 10, TiO− ≥ 20% at pH > 10 andTiOH2

+ ≥ 20% at pH < 3.40

Hence, the reaction rate increases up to a pH valueof 3 owing to the strong electrostatic attraction forcesbetween the positively charged catalyst surface and theionized sulfonic group of the dye. This is confirmedalso by the strong dye adsorption onto the catalystsurface observed in the acidic pH range.

Further decrease of reaction rate to a minimumaround 5.5 units may be due to a decrease of TiO2

+

percentage with increasing pH, and to aggregationof the catalyst particles. Previous studies measuringmean particle size have shown that the size of TiO2

P-25 remains constant (300 nm) in acid and basic pH,while this increases (to 2–4 µm) when the dispersionreaches the point of zero charge.41 Indeed, aroundthe point of zero charge, the surface charge resultsin zero electrostatic surface potential, which cannotproduce the interactive rejection necessary to separatethe particles within the liquid. Further modificationof pH leads to reduction of aggregation and, hence,to enhancement of light absorption, resulting in an

increase of photodegradation rate in the pH range5.5–7.3.

Effect of the H2O2 addition on the photocatalyticdegradation of Orange IIThe addition of powerful oxidants, such as hydrogenperoxide (H2O2), in suspensions of TiO2 is a commonpractice due to the fact that, in many cases, it resultsin an increase of the photo-oxidation rate.42 This canbe explained through the dual role of this oxidant,which acts as an acceptor of the photogeneratedelectrons, promoting charge separation according toEquation (3), and its reaction with the superoxideradicals, leading additionally to production of hydroxylradicals according to Equation (4):

H2O2 + e− → OH− + OH• (3)

H2O2 + •O2− → OH • +OH− + O2 (4)

However, an excess of H2O2 may be detrimentalto the process owing to the scavenging action onholes or HO• or to formation of peroxo compoundsthat may have a negative effect on the photocatalyticaction. This explains the necessity for using an optimalconcentration of the oxidant to achieve the maximumeffect in the process.

The influence of H2O2 concentration on the initialreaction rate (ro) of Orange II degradation is presentedin Fig. 7. It is clear that the reaction rate increaseswith increase of oxidant concentration, its highestvalue being reached at 200 mg L−1 H2O2. Under theseconditions, the addition of H2O2 in the suspensioncontaining 20 mg L−1 Orange II and 0.5 g L−1 TiO2

P-25 accelerated the photo-oxidation of the dye by afactor of ∼4.

Response surface modelingThe design of experiments (DoE) and RSM consists ofmethods and mathematical-statistical tools generally

0 40 80 120 160 2000.0

0.5

1.0

1.5

2.0

initi

al r

eact

ion

rate

, ro

(mg

L-1

min

-1)

H2O2 (mg L-1)

Figure 7. Effect of H2O2 on the initial reaction rate of thephotocatalytic degradation of 20 mg L−1 Orange II at constantconcentration of catalyst (0.5 g L−1 TiO2 P-25).

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RSM applied to Orange II photocatalytic degradation

used to optimize the performance of a real systemsubjected to a set of controllable input variables alsoknown as independent variables, design variables orfactors.43,44

The first step in RSM involves the provision of anappropriate functional form to explain the relationshipbetween the response of interest (in this case the colorremoval efficiency, defined as the percentage ratiobetween the difference in dye concentration beforeirradiation and after t min of UV-A exposure (Co − Ct)and the initial dye concentration Co) and controllableinput variables (factors). The most commonly usedfunctional form in RSM is the polynomial regressionmodel, known also as the RS-model. Estimation of theabove RS-model requires selection of an appropriateexperimental design to obtain information concerningthe response variable in an efficient manner. Thecentral compositional design (CCD) is the mostpopular one due to its easy of use in sequentialexperimentation. In the present work the RSM wasapplied to develop a RS-model to predict the removalefficiency as a function of experimental factors overthe whole region of experimentation. The importantfactors that influence the color removal efficiency wereconsidered to be the pH of the solution, the initialconcentration of the oxidizing agent (H2O2) and theUV-A irradiation time (since insufficient irradiationduration leads to decrease of the process efficiencyirrespective of the values of the other two factors).The actual values of these design variables, as well astheir coded levels, are given in Table 1.

The CCD is a DoE method that can be appliedefficiently to develop the second-order RS-model.The CCD consists of three distinct sectors: (1) fullor fractional design in which the factor levels arecoded to the usual low (−1) and high (+1) values;(2) axial points localized on the axis of each variable ata distance α from the designed centre; and (3) centrepoints that can be replicated to provide an estimationof the experimental error variance. Based on CCD,a quadratic approximation of the response may bewritten as:43–46

Y = b0 +n∑

i=1

bixi +n∑

i=1

biix2i +

n∑i<l

bilxixl + ξ (5)

where Y denotes the predicted response (predictedremoval efficiency), xi refers to the coded levels of thefactors, b0, bi, bii, bil are the regression coefficients, nisthe number of factors and ξ is the statistical error. The

CCD used for the response surface modeling of thephotocatalytic process is given in Table 2.

The regression coefficients of the RS-model werecomputed using the multiple linear regression (MLR)method in order to minimize the sum of squares ofthe residuals. Thus, the least square estimations of theregression coefficients can be written as:43,44,46,47

b =(

XT

X)−1

XT

Y (6)

where b is a (u × 1) vector of regression coefficients, Xis a (N × u) matrix of the independent variables levels,Y is a (N × 1) experimental vector of the response,N is the number of experimental runs and u is thenumber of regression coefficients that appear in thefinal RS-model. According to the experimental designpresented in Table 2, a response quadratic model wasestablished, which may be written in terms of codedfactors as follows:

Y = 83.193 + 4.38x2 + 19.68x3 − 8.238x21

− 7.914x23 + 1.625x1x3 (7)

subject to:

xi ∈ �; � = {xi| − α ≤ xi ≤ +α}; ∀i = 1, 3

where x1, x2 and x3 are the coded levels of the factorsand α = 1.215 is the star point in experimental designthat gives the bounds of the valid region � (region ofexperimentation).

It should be mentioned that all the regressioncoefficients retained in Equation (7) are significant,i.e. the significance of individual regression coefficientswas tested by means of a Student’s t-test.43 Theanalysis of variance (ANOVA) was employed to checkthe significance of the second-order RS-model. Thestatistical significance of the second-order regressionmodel was determined by the F-value, which is ameasure of the variance of data about the mean,based on the ratio of the mean square of groupvariance due to error.44 The more the F-value departsfrom unity, the more certain it is that the designvariables adequately explain the variation in the meanof the data. Having the F-value and correspondingdegree of freedoms, the P-value is then calculated.If the P-value is low, one may conclude that theRS-model is statistically validated for prediction of

Table 1. Design variables and their coded and actual values used for experimental design

Actual values of coded levels

Design variable (factors) Symbol −α −1 0 +1 +α∗

Initial pH x1 2.2 3 6.5 10 10.6Initial concentration of hydrogen peroxide, [H2O2]0 (mg L−1) x2 37 50 110 170 183Irradiation time, t (min) x3 7.85 10 20 30 32.15

∗ α = 1.215 (star or axial point for orthogonal CCD in the case of 3 independent variables).

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C Betianu et al.

Table 2. Central composite orthogonal design and experimental response

Factors (controllable input variables)

Initial pH Initial concentration of H2O2 Time of irradiation ResponseRemoval efficiency

Run number (N) and typea pH, Levelb x1 [H2O2]o, mg L−1 Levelb x2 t min Levelb x3 Y (%)

1 O1 10 1 170 1 30 1 91.172 O2 3 −1 170 1 30 1 87.353 O3 10 1 50 −1 30 1 85.564 O4 3 −1 50 −1 30 1 81.765 O5 10 1 170 1 10 −1 47.726 O6 3 −1 170 1 10 −1 50.407 O7 10 1 50 −1 10 −1 44.638 O8 3 −1 50 −1 10 −1 47.319 S1 10.6 α 110 0 20 0 73.7410 S2 2.2 −α 110 0 20 0 68.6111 S3 6.5 0 183 α 20 0 95.8812 S4 6.5 0 37 −α 20 0 70.6913 S5 6.5 0 110 0 32.15 α 96.2414 S6 6.5 0 110 0 7.85 −α 47.0615 C1 6.5 0 110 0 20 0 82.8616 C2 6.5 0 110 0 20 0 82.45

a O = orthogonal design points, C = center points, S = star or axial points.b −1 = low value, 0 = center value, +1 = high value, +/−α = star point value.

Table 3. Analysis of variance (ANOVA) of response surface model

Source DFa SSb MSc F-value P-value R2 Radj2

Model 5 5156.588 1031.317 62.932 <0.0001 0.969 0.954Residual 10 163.878 16.388Total 15 5320.466

a –degree of freedom; b - sum of squares; c - mean square

the observed response. Most investigators accept theRS-model for prediction if the P-value is less than0.05. Table 3 is the ANOVA table for the RS-modeldeveloped. The ANOVA table summarizes the sumof squares of residuals and regressions together withthe corresponding degrees of freedom, F-value, P-value and ANOVA coefficients (i.e. coefficients ofmultiple determination R2 and adjusted Radj

2 statistic).The mathematical expressions used for calculation ofthe ANOVA estimators (i.e. SS, MS, F-value, R2,Radj

2) are widely presented in the literature concerningRSM.42,43

According to the ANOVA table, the F-value isquite high and the P-value is smaller than 0.0001.In addition, the R2 value for removal efficiency is0.969, close to 1, which is desirable, and the predictedR2 is in agreement with the adjusted coefficient ofdetermination R2

adj. All these statistical estimatorsreveal that the RS-model is statistically acceptablefor the prediction of the response over the range ofexperimentation considered (valid region). Likewise,the model adequacy can easily be investigated byexamination of the residuals, which may be definedfor any observation j, as:44

ej = Yj − Yj ∀j = 1, N (8)

where Yj is an estimate of the correspondingobservation Yj . Examination of the residual (ej) shouldbe an automatic part of any analysis of variance(ANOVA). If the model is adequate, the residualsshould not have any structure, meaning that theyshould contain no obvious patterns.44 The plot ofpredicted and experimental responses, as well as theplot of the residuals versus the number of experimentalruns (N) is shown in Fig. 8.

The results reported in Fig. 8 show the goodness-of-fit between the RS-model and the correspondingexperimental set of observed data. It should be notedhere that the RS-model in terms of coded variables,i.e. Equation (7), is more useful for optimizationpurposes since the valid region for any individualcoded variable involves the same interval of variation,i.e. from −α up to +α. For the graphical representationand analysis of the response surface it is worthconverting the RS-model in terms of coded variablesto an RS-model in terms of actual variables. Hence,the RS-model in terms of actual variables may bewritten as:

Y = −18.233 + 7.814pH + 0.073[H2O2]0 + 4.832t

− 0.672pH2 − 0.079t2 + 0.046pH t (9)

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RSM applied to Orange II photocatalytic degradation

(a) (b)

Figure 8. (a) Experimental data, plotted against predicted data for removal efficiency and (b) residual analysis of RS-model.

Figure 9. Response surface and contour-line plots for [H2O2]0 and pH variables, holding the other variable at its center level t = 20 min.

subject to:

2.2 ≤ pH ≤ 10.6; 37 ≤ [H2O2]0 ≤ 183 (mg L−1);

7.85 ≤ t ≤ 32.15(min)

The empirical coefficients that appear in Equa-tion (9) were computed by substitution, being depen-dent on the values of the regression coefficients fromEquation (7) and the operating range of each designvariable. The effects of the design variables uponthe color removal efficiency (response) were inves-tigated by means of graphical response surface analy-sis. Graphical representations of the response surfaceare shown in Figs 9–11 using three-dimensional andcontour-line plots.

Figure 9 indicates the effects of initial concentrationof oxidizing agent (H2O2) and solution pH upon themagnitude of the predicted response, i.e. color removalefficiency. As can be observed, the highest value ofremoval efficiency is achieved for pH = 5.5–7.5. AtpH values below and above this interval the value ofresponse gradually decreases.

Regarding the influence of oxidizing agent concen-tration, it is clear that the removal efficiency increaseslinearly with increasing concentration of H2O2.

Figures 10 and 11 show that the irradiation time thas the most effect upon removal efficiency, comparedwith the other design variables. Increasing theillumination time up to 25 min leads to a strongincrease of predicted response (removal efficiency),but this increasing trend moderates, approaching anasymptotic plateau for t > 25 min.

Response surface optimizationThe optimization problem consists in searching (bysimulation) for the input combination of designvariables that maximizes the investigated response(removal efficiency). The response function in termsof coded variables, i.e. Equation (7), was used foroptimization of the experimental conditions. Thus, theformulation of the objective function for optimizationmay be written in this case as:

maxx

{Y (x1, x2, x3, )

}(10)

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C Betianu et al.

Figure 10. Response surface and contour-line plots for t and pH variables, holding the other variable at its center level [H2O2]o = 110 mg L−1.

Figure 11. Response surface and contour-line plots for t and [H2O2]0 variables, holding the other variable at its center level pH = 6.5.

subject to:xi ∈ �, ∀i = 1, 3

The basic gradient method of steepest ascent wasemployed to find the optimal solution of the objectivefunction (Equation (10)). In this approach, a sequenceof points x(k+1)

i and a sequence of steepest ascentdirections di, are generated iteratively as follows:45,48

x(k+1)

i = x(k)

i + d(k)

i λ(k)

i (11)

where, for maximization of objective function, thedirections of steepest ascent are computed as48

d(k)

i =(∂Y/∂xi

)x((k)√√√√ n∑

i=1

(∂Y/∂xi

)2

x((k)

(12)

The search step λi was adjusted at each iteration kand for each individual variable so as to have a suitablestep-length along the steepest ascent direction withoutviolating any bounds of the valid region � (i.e. regionof experimentation). The stopping criteria applied todetermine if the optimization method had converged

used the change in objective function value in the lasttwo iterations. If the change was equal to or less than1 × 10−6, the optimization routine was stopped. Thusthe stopping criteria may be written as:46,48

ε =∣∣∣∣∣Y (k+1) − Y (k)

Y (k)

∣∣∣∣∣ ≤ 1 × 10−6 (13)

Some of the results of optimum searching by meansof the gradient method of steepest ascent are listed inTable 4 as an example.

As one can see from Table 4, the optimal solutionwas established at iteration k = 113 when convergenceto ε = 10−6 is achieved. By applying a step adjustingroutine, the value of individual step-lengths isdecreased as the current point is located closer tothe bounds of the valid region since violation of thevalid region must be avoided. The optimal values ofactual factors are given in Table 5, together with thecorresponding predicted and experimental responses.

According to the results given in Table 5, theoptimal solution given by the gradient methodleads to the following optimum conditions: pH∗ =6.9; [H2O2]0

∗ = 183 mg L−1 and t∗ = 32 min. Theexperimental color removal efficiency was 100% and

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RSM applied to Orange II photocatalytic degradation

Table 4. Optimization of response surface function Y (x1, x2, x3) by gradient method

pH [H2O2]0 (mg L−1) t (min)

k x1 d1 λ1 x2 d2 λ2 x3 d3 λ3 Y (k) ε

0 0 0 0 0 0.217 0.091 0 0.976 0.408 83.193 –1 0 0.046 0.020 0.019 0.311 0.133 0.398 0.949 0.277 89.865 0.0802 0.001 0.103 0.048 0.061 0.427 0.189 0.661 0.898 0.191 93.015 0.0353 0.006 0.158 0.083 0.142 0.551 0.256 0.833 0.819 0.135 94.723 0.0184 0.019 0.185 0.112 0.283 0.665 0.314 0.944 0.724 0.099 95.984 0.01335 0.040 0.172 0.097 0.492 0.756 0.262 1.016 0.632 0.060 97.226 0.01296 0.056 0.145 0.074 0.690 0.809 0.187 1.054 0.570 0.040 98.238 0.01047 0.067 0.124 0.059 0.841 0.841 0.131 1.077 0.526 0.030 98.974 0.00758 0.074 0.108 0.050 0.952 0.863 0.092 1.093 0.493 0.024 99.505 0.00549 0.080 0.096 0.043 1.031 0.880 0.064 1.105 0.465 0.020 99.884 0.003810 0.084 0.087 0.038 1.087 0.892 0.044 1.114 0.443 0.017 100.15 0.0027. . . . . .

113 0.116 0.0094 0.003 1.215 0.983 0 1.204 0.185 0.001 100.85 1 × 10−6

Table 5. Optimal point in terms of actual operating variables

pH∗[H2O2]0

∗

(mg L−1)t∗

(min)

Predicted

Y∗ (%)Experimental

Y∗ (%)

6.9 183 32 100.85 100

the difference between experimental and predictedoptimum is within the limit of the model error.

CONCLUSIONSDoE and RSM were applied for the investigation andoptimization of photocatalytic degradation of OrangeII by UVA-light exposure. The RS-model developedunder this methodology proved to be adequate forthe prediction of color removal efficiency under thetested experimental conditions. The response surfacefunction was optimized using the steepest ascentgradient method. The optimization method led tothe following optimal values of design variables:pH∗ = 6.9; [H2O2]0

∗ = 183 mg L−1 and t∗ = 32 min,ensuring 100% color removal efficiency.

Thus, the response surface model suggested that analmost neutral pH solution combined with increasedoxidant concentration and relatively high irradiationtime will lead to significant improvement of the colorremoval efficiency of the studied dye in aqueoussolution.

The resulting optimum concentration of oxidizingagent is in good agreement with the preliminary studyconcerning the influence of individual factors uponthe process, which shows that a concentration rangebetween 100 and 200 mg L−1 H2O2 is best from thepoint of view of the reaction rate. However, whenthe oxidant was added in the system, the resultsconcerning the effect of pH were slightly differentto those obtained in the univariate study, showing thatinvestigation of the interdependence of influencingfactors is important. In the multivariate system, theoptimum pH value is almost the same as the naturalpH of the dye solution (6.5).

The results of this study demonstrate that the useof the experimental design strategy rather than aunivariate approach is necessary to ensure adequatemodeling of the photocatalytic process since theinterdependence of the reaction parameters cannotbe ignored.

NOTATIONb regression coefficientsb vector of regression coefficientsCo initial bulk-solute concentration;d direction of steepest ascentDF degree of freedome residual errorF-value ratio of variancesi and j subscripts (integer variables)K adsorption constantk iteration for optimum searchingkr reaction rate constantMS mean squareN number of experimental runsn number of factorsP-value statistical estimatorR2 coefficient of multiple determinationRadj

2 adjusted statistic coefficientr0 initial reaction rateSS sum of squarest irradiation timeu number of regression coefficients in final RS-

modelX matrix of the independent variables levelsY predicted color removal efficiencyY color removal efficiency (experimental value)Y experimental vector of the responsex factors coded level* superscript indicating optimal values of

variables

Greekα star point in experimental design

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C Betianu et al.

ε convergence (stopping) criteriaλ step lengthξ statistical error� region of experimentation

ACKNOWLEDGEMENTSThis work was done partially in the Laboratory ofPhysical Chemistry at the Aristotle University ofThessaloniki, Greece with financial support from theErasmus Program, and partially at the Departmentof Environmental Engineering and Management,Faculty of Chemical Engineering and EnvironmentalProtection within the ‘‘Gh. Asachi’’ TechnicalUniversity of Iasi, Romania, with financial supportprovided by Romanian Ministry of Education andResearch through Program IDEI, Grant ID 595,Contract No. 132/2007, in the frame of theNational Program for Research, Development andInnovation II.

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