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Polymer Degradation and Stability 110 (2014) 492e497

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Polymer Degradation and Stability

journal homepage: www.elsevier .com/locate/polydegstab

A statistical experimental design approach for photochemicaldegradation of aqueous polyacrylic acid using photo-Fenton-likeprocess

Samira Ghafoori, Mehrab Mehrvar*, Philip K. ChanDepartment of Chemical Engineering, Ryerson University, 350 Victoria St., Toronto M5B 2K3, ON, Canada

a r t i c l e i n f o

Article history:Received 2 September 2014Accepted 16 October 2014Available online 25 October 2014

Keywords:Poly(acrylic acid)Photo-Fenton-likeTOC removalRSMStatistical analysisProcess optimization

* Corresponding author. Tel.: þ1 416 9795000x655E-mail address: mmehrvar@ryerson.ca (M. Mehrv

http://dx.doi.org/10.1016/j.polymdegradstab.2014.10.00141-3910/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

The present study investigates the degradation of poly(acrylic acid) in aqueous solution by a photo-Fenton-like process. Batch experiments are carried out to model and optimize the process. The effectsof the initial concentration of poly(acrylic acid), the initial concentration of Fe3þ, and the H2O2 dosage asindependent variables on the total organic carbon (TOC) removal as the response function are studiedusing response surface methodology (RSM). The significance of the independent variables and theirinteractions are tested by means of analysis of variance (ANOVA) with 95% confidence level. The sta-tistical analysis of the results indicated satisfactory prediction of the system behavior by the developedmodel. The optimum operating conditions to achieve maximum TOC removal are also determined. Themodel prediction for maximum TOC removal is compared to the experimental result at optimal operatingconditions. A good agreement between the model prediction and experimental results confirms thereliability of the developed model.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Polyacrylic acid (PAA), one of the widely used synthetic water-soluble polymers, has broad applications in pharmacy, paint in-dustry, dentistry, and hair-styling products [1]. Due to elevatedvolumes of production and consumption, the synthetic water-soluble polymers are constantly discharged into the aquatic envi-ronment. Therefore, they may have harmful effects on the wildlifeand the human health as they are not amenable to biodegradation[2,3,4]. Also, due to their water solubility that makes them invisible,less attention has been centered on the degradation of this type ofpolymers [5]. In the recent decades, advanced oxidation technolo-gies (AOTs) have been found as a promising alternative to degradecompounds that are not degradable by the conventional means[6,7,8,9]. Applications of AOTs for treating wastewater containingrecalcitrant and inhibitory organics have risen drastically duringthe past few decades [10]. Among AOTs, the photo-Fenton processhas been applied for the degradation of broad range of contami-nants, predominantly refractory organic pollutants [3,11,12]. In thephoto-Fenton-like process, H2O2 in a catalytic cycle reacts with ironions as the catalyst. This process involves the production of reactive

5; fax: þ1 416 9795083.ar).

15

and non-selective hydroxyl radicals and can initiate the degrada-tion reactions by reacting with the organic molecules. In photo-Fenton-like process, a powerful, non-selective source of oxidation(�OH) is generated fromH2O2 in the presence of Fe3þ ions accordingto the following simplified reactions [3,13,14]:

Fe3þ þH2O2/Fe2þ þ HO�

2 þHþ (1)

Fe2þ þH2O2/Fe3þ þ �OHþ OH� (2)

Fe3þ þH2O!hvFe2þ þ �OHþ Hþ (3)

H2O2!hv2�OH (4)

The free radical species mediate fast degradation of targetorganic compounds [15,16]. Photo-Fenton processes have beenrarely studied for degradation of high molecular weight com-pounds. On the other hand, the photo-Fenton-like process likewiseother AOTs is a multifactor system that different factors such as theinitial concentration of target compounds, the initial dosage ofoxidants, pH and other operating conditions have effect on theprocess efficiency [17,18]. The optimization of the factors by clas-sical methods needs extra time, materials, and large number of

S. Ghafoori et al. / Polymer Degradation and Stability 110 (2014) 492e497 493

experiments. Also, classical methods fail to consider the combinedeffects of all the parameters involved. A statistical experimentaldesign could overcome the limitations of conventional methodsand consequently optimize the affecting factors [5,19]. Responsesurface methodology (RSM) as a reliable statistical tool in multi-variate system fits the studied experimental domain in the theo-retical design through a response function. In this study, theexperimental design for the PAA photodegradation by photo-Fenton-like process is investigated in a batch recirculation sys-tem. The effects of the initial concentration of PAA, the initialconcentration of Fe3þ, and the H2O2 dosage on the percent TOCremoval were studied using a three-factor three-level Box-Behnkenexperimental design combined with RSM and quadratic program-ming. The optimal operating conditions to achieve maximum TOCremoval were obtained and validated experimentally.

2. Materials and methods

2.1. Materials

PAA (35% wt) with an average molecular weight of13 � 104 g mol�1, H2O2 (30% wt), and FeCl3.6H2O were purchasedfrom Sigma Aldrich and were used as received. NaOH (99%) andH2SO4 (99%) used to adjust pH were supplied by EMD Chemicalsand used as received.

2.2. Experimental setup and procedure

A laboratory-scale batch recirculation photoreactor providinguniform light distribution was used in this study. The system rep-resents the simplest mathematical model for both mass and radi-ation balances. A small annular photoreactor (model SL-LAB fromSiemens Inc.) with the annular space of 1.33 cmwas used as part ofa recycle system including a centrifugal magnetic pump (Model RK-72012-10 from ColeeParmer), an all glass heat exchanger (forcontrolling the temperature), and a large volume tank with pro-visions for sampling and temperature measurements as presentedin Fig. 1. The system was also equipped with a by-pass valve tocontrol the flow rate and to provide a relief to the pump pressure.The lamp (model LP4130 from Siemens Inc.) sealed with the quartzsleeve was positioned at the centerline of the photoreactor with

1

3

79

8

Fig. 1. Schematic diagram of the experimental setup batch with recirculation system: (1) ReCooling water in, (7) Water out, (8) Bypass, and (9) Collection tank.

stainless steel housing. The pHwas adjusted by adding few drops of1N NaOH or H2SO4 as needed and it was measured by a portable pHmeter (230A plus, Thermo Orion).

The following protocol was pursued in conducting each exper-iment. The PAA solution was diluted to achieve the desired PAAconcentration in a 4-L solution. The lamp was turned on for 30 minbefore the beginning of each experiment to stabilize the light in-tensity. The solutionwas fed to the system and the temperaturewaskept constant at 25�C during each experiment by means of a heatexchanger. The samples were taken from the collection tank atdifferent time intervals during a total reaction time of 120 min. TheTOC concentration of the samples was monitored by a TOC analyzer(Apollo 9000, Teledyne Tekmar, USA).

3. Experimental design

The operating conditions to maximize the TOC removal in thephoto-Fenton-like process was obtained using a three-factor three-level Box-Behnken experimental design combined with responsesurface modeling. The Box-Behnken design, a modified centralcomposite design, is known as an independent, rotatable quadraticdesign having no fractional factorial points [9,20]. In this type ofdesign, the variable combinations are at the center and the mid-points of the edges of the variable space [21]. Also, compared toother types of experimental design such as full factorial design, theBox-Behnken experimental design needs fewer runs [22]. In thisstudy, the effects of three independent variables on the TOCremoval were investigated. The independent variables were theinitial concentration of PAA (A), the initial concentration of Fe3þ

dosage (B), and the initial concentration of H2O2 (C) that werecoded as �1, 0, and þ1 as presented in Table 1. The total number ofexperiments (N) was 15 which could be calculated as follows:

N ¼ k2 þ kþ cp (5)

where k is the number of factors and cp is the number of replicatesin the central point. The critical experimental levels were chosenbased on the preliminary experimental results and the literaturevalues. Therefore, the data from Box-Behnken designwas subjectedto the following quadratic model which is a second order equationthat correlates the dependent and independent variables:

2

4

6

5

servoir tank, (2) Pump, (3) Flow meter, (4) UV-C photoreactor, (5) Heat exchanger, (6)

Table 1Independent variables and their coded levels based on Box-Behnken design.

Independent variables Symbols Coded levels

�1 0 1

[PEO]0 (mg L�1) A 20 40 60[Fe3þ]0 (mg L�1) B 3 5 7[H2O2]0 (mg L�1) C 500 900 1300

S. Ghafoori et al. / Polymer Degradation and Stability 110 (2014) 492e497494

Y ¼ b0 þXk

i¼1

bixi þXk

i¼1

biix2i þ

Xk�1

i¼1

Xk

j¼2

bijxixj þ e (6)

where Y, b0, bi, bii, and bij are the predicted response, the constantcoefficient (intercept term), the linear coefficients, the quadraticcoefficients, and the interaction coefficients, respectively. The pa-rameters xi and xj are independent variables, where k and e are thenumber of factors and the residual term allowing uncertaintiesbetween observed and predicted values, respectively. The codedvalues of the process parameters in Equation (6) could be deter-mined as follows [23]:

Xi ¼xi � x0Dxi

(7)

where Xi is dimensionless coded value of the ith independent var-iable, xi is the un-coded value of the ith independent variable, x0 isthe un-coded value of the independent variable at the center point,and Dxi is the step change. STATISTICA (trial version 10.0) andDesign-Expert (trial version 9.0) were used for the regression andthe graphical analysis of the data. The significance of independentvariables and their interactions were tested using the analysis ofvariance (ANOVA). An alpha (a) level of 0.05 was used to determinethe statistical significance in all analyses. Three-dimensional sur-face plots and two-dimensional contours were developed whileholding a variable constant in the quadratic model. The experi-mental and predicted values were compared to validate the model.The optimal operating conditions to maximize the TOC removalrate were also determined using a numerical technique built in thesoftware.

4. Results and discussions

4.1. RSM model development

Table 2 illustrates the results of the three-factor three-level Box-Behnken experimental design for the percent TOC removal by the

Table 2Three-factor three-level Box-Behnken design for RSM.

Run Independent coded variables TOC removal (%)

A B C Observed Predicted

1 �1 �1 0 78.46 78.132 1 �1 0 61.47 63.423 �1 1 0 88.37 86.424 1 1 0 73.28 73.615 �1 0 �1 72.23 75.556 1 0 �1 63.02 64.067 �1 0 1 89.06 88.028 1 0 1 75.31 71.999 0 �1 �1 74.25 71.2710 0 1 �1 85.64 84.2711 0 �1 1 83.86 85.2312 0 1 1 87.74 90.7213 0 0 0 76.16 76.2514 0 0 0 75.95 76.2515 0 0 0 76.64 76.25

photo-Fenton-like process for the degradation of aqueous poly(-acrylic acid). The observed and predicted results for the percentTOC removal are also depicted in this table. By applying multipleregression analysis on the design matrix and the responses given inTable 2, the following quadratic equation in terms of coded factorswas determined to predict the percent TOC removal:

Y ¼ 76:25� 6:88Aþ 4:62Bþ 5:10Cþ 0:47AB� 1:13AC

� 1:88BC� 4:41A2 þ 3:56B2 þ 3:07C2 (8)

In this equation, Y is the response function (percent TOCremoval), A, B, and C are the coded terms for three independentvariables; the initial concentration of PAA, the initial concentrationof Fe3þ, and the initial concentration of H2O2, respectively.

4.2. Statistical analysis

The significance of the fit of the quadratic equation for theexperimental data was tested by means of the ANOVA as shown inTable 3. An alpha (a) level of 0.05 or 95% confidence level was usedto determine the statistical significance in all analyses. Results wereassessed with various descriptive statistics such as p value, F value,the degree of freedom (df), the determination coefficient (R2), theadjusted determination coefficient (R2adj), the sum of squares (SS),and the mean sum of squares (MSS), as presented in Table 3. Thesignificance of each coefficient in Equation (8) was determined bythe Fisher's F-test and values of probability > F. As shown in Table 3,a small probability value (p < 0.0110) indicates that the model washighly significant and could be used to predict the response func-tion accurately. The goodness of fit of the model was validated bythe determination coefficient (R2). The high values of regression(0.9461) and the adjusted regression coefficients (0.8490) indicatethat the developed quadratic model could adequately describe thesystem behavior within the selected range of operating parameters.The adequate precision, signal to noise ratio, greater than 4 (10.21in this case) shows that the model could be used to navigate thedesign space defined by the Box-Behnken design. The normality ofthe data could be checked through the normal probability plot ofthe residuals. If the points on the plot lie on a straight line, theresiduals are normally distributed as confirmed in Fig. 2. Theassumption of constant variance was tested by plotting internallystudentized residual versus predicted values as illustrated in Fig. 3.The studentized residuals are found by dividing the residuals bytheir standard deviations. As is evident from this figure, the pointsare scattered randomly between the outlier detection limits �3and þ3. Therefore, it can be concluded that the predictions ofexperimental data by the derived quadratic models for the percent

Table 3ANOVA for prediction of TOC removal rate by the quadratic model.

Source Sum ofsquares

df Meansquare

F value p-value*

Prob > FRemark

Model 942.9771 9 104.7752 9.749104 0.0110 SignificantAeA 378.6752 1 378.6752 35.23489 0.0019 SignificantBeB 171.0325 1 171.0325 15.9142 0.0104 SignificantCeC 208.3861 1 208.3861 19.38987 0.0070 SignificantAB 0.9025 1 0.9025 0.083976 0.7836AC 5.1529 1 5.1529 0.479466 0.5195BC 14.10003 1 14.10003 1.311976 0.3039A2 71.84908 1 71.84908 6.685399 0.0491 SignificantB2 46.6963 1 46.6963 4.344988 0.0915C2 34.71467 1 34.71467 3.230123 0.1322Residual 53.73583 5 10.74717Pure error 0.2502 2 0.1251Cor total 996.7129 14

p < 0.05 is considered as significant. Cor total ¼ Corrected total sum of squares.

Fig. 2. Normal probability plot of the residuals.

Fig. 4. Comparison of predicted TOC removal rates versus actual values.

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TOC removal rate are quite satisfactory. Also, a high correlationbetween observed and predicted data shown in Fig. 4 indicatestheir low discrepancies.

4.3. Effect of model parameters and their interaction

The significance of each model parameter was determined bymeans of Fischer's F-value and p-value. The F-value is the test forcomparing the curvature variance with residual variance andprobability > F (p-value) is the probability of seeing the observed F-value if the null hypothesis is true. Small probability values call forrejection of the null hypothesis and the curvature is not significant.Therefore, the larger the value of F and the smaller the value of p,the more significant is the corresponding coefficient [24]. As shownin Table 3, the p-value less than 0.05 indicate the model parametersare significant. Therefore, all three independent variables havesignificant effect on the percent TOC removal based on their p-value. However, the initial concentration of Fe3þ showed less sig-nificant effect compared to the initial concentration of PAA and theinitial H2O2 dosage. Also, as is evident in Table 3, the quadratic ef-fect of the initial concentration of PAA has significant effect on theresponse function.

Fig. 3. Internally studentized residuals versus predicted values.

4.4. 3D response surface and 2D contour plots

The interaction effects between the independent variables areillustrated in three dimensional (3D) response surface and twodimensional (2D) contour plots (Figs. 5 and 6). These figures are thegraphical representations of the regression analysis. In such plots,the response function of two factors are presented while all othersare at the fixed levels. As shown in Fig. 5a and b and the corre-sponding contour plot (Fig. 6a and b), the higher initial concen-tration of PAA results in lower percent of TOC removal which is dueto the UV absorption by the polymer molecules. This results inreducing UV absorption by the oxidizers (Fe3þ and H2O2) andconsequently producing less �OH which is the main cause of poly-mer degradation. However, the effect of the initial concentration ofPAA is less pronouned at lower concentrations. As Figs. 5a, b, and cand the corresponding contour plot (Figs. 6a, b, and c) show, thehigher concentrations of Fe3þ and H2O2 are, the higher the percentTOC removal is, which is expected based on the Reaction (1)e(4).Higher concentrations of oxidizers lead to the higher generation of�OH which is responsible to attack the polymer molecules.

4.5. Optimization of the process parameters

In order to obtain the optimum operating conditions to maxi-mize the TOC removal (response function), Equation (8) is consid-ered as the objective function. The optimization was carried out bymeans of the numerical technique built in the Design Expert Soft-ware 8.0.5 which searches the design space to achieve the goal ofoptimization in the range of independent factors. The optimumvalues to achieve the maximum 92.44% TOC removal rate after120minwere 23mg L�1 PAA, 7mg L�1 Fe3þ, and 1300mg L�1 H2O2.The obtained optimal operating conditions were used in anotherexperimental run to validate the model prediction. The TOCremoval of 90.35%, obtained experimentally, confirms the reliabilityof the model.

5. Conclusions

The application of a three-factor, three-level Box-Behnkenexperimental design combined with RSM and quadratic program-ming was investigated for the photo-Fenton-like degradation ofPAA in aqueous solution. The developed mathematical modelprovided a critical analysis of the simultaneous interactive effects ofthe independent variables. The adequacy of the proposed modelwas tested using various descriptive statistics. The statistical

Fig. 5. 3D response surface exhibiting the interactive effects of the factors on thepercent TOC removal: (a) [PAA]0 and [Fe3þ]0, (b) [PAA]0 and [H2O2]0, (c) [Fe3þ]0 and[H2O2]0.

Fig. 6. 2D Contour plots exhibiting the interactive effects of the factors on the percentTOC removal: (a) [PAA]0 and [Fe3þ]0, (b) [PAA]0 and [H2O2]0, (c) [Fe3þ]0 and [H2O2]0.

S. Ghafoori et al. / Polymer Degradation and Stability 110 (2014) 492e497496

analysis using ANOVA indicated that the developed quadraticmodels were highly accurate and predictive. Good agreement be-tween quadratic model predictions and observed values alsoconfirmed the accuracy of the developed model. The initial con-centration of PAA, the initial concentration of Fe3þ, and the initial

H2O2 dosage had significant effect on the percent TOC removal. Theoptimal operating conditions to achieve the maximum TOCremoval rate (92.44%) in the selected range was determined to be23 mg L�1 PAA, 7 mg L�1 Fe3þ, and 1300 mg L�1 H2O2, respectively.Finally, the model prediction for the maximum TOC removal wasvalidated by an additional experimental run at the obtained opti-mum operating conditions. The validation results clearly confirmedthat a three-factor, three-level Box-Behnken experimental designcombinedwith RSM and quadratic programming is an effective toolfor mathematical modeling of the photo-Fenton-like process.

S. Ghafoori et al. / Polymer Degradation and Stability 110 (2014) 492e497 497

Acknowledgment

The financial support of the Natural Sciences and EngineeringResearch Council of Canada (NSERC) and Ryerson University isgratefully appreciated.

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