Background

Advanced oxidation processes (AOPs) are physicochemical procedures, which are designed to remove environmental organic and inorganic pollutions. Photo catalysis, the current interest of AOPs, is applied for decontamination of environmental organic pollutions [1–4]. The photo catalysis, under suitable light illumination, produces hydroxyl radical (●OH) and hole (h+) which are powerful and non-selective oxidants to degrade a variety of organic compounds [5–7]. Zinc oxide (ZnO) with great advantage in absorption a larger fractions of the solar spectrum, is one of the photo catalyst that removed several environmental contaminants under visible-light irradiation [8–11]. To enhance the visible-photo activity of ZnO, doping the transition metals such as manganese (Mn) has been prepared [12]. In the most cases, the evaluation of the photo degradation was carried out by a traditional method (one variable at a time), which is not only costly and time consuming but also often leads to misinterpretation of Experimental results [13–19]. Since the photo degradation is dependent on several effective parameters such as irradiation time, pH value, photo catalyst loading and substrate concentration [11, 20], it needs to preform too many experiments for finding the optimum condition. While the managing of these experiments is difficult, the real world of photo degradation’s experiments is very expensive because of chemicals, instruments, time of the researchers and etc. Therefore, prediction of the optimal condition seems necessary. Recently the response surface methodology (RSM) was used as an efficient technique for these purposes (simulation the condition) [21–26]. In the methodology, central composite design (CCD) was used for experimental-design and fitting the performed (actual) results with a polynomial equation in vicinity region of the optimum condition to make a model [27]. The model relates the responses (sometimes yield) and the variables of the photo degradation process [28]. However, no study has been conducted on application of the RSM that have been reported on the photo degradation of ortho-cresol (o-cresol) by manganese-doped zinc oxide (Mn-doped ZnO) nanoparticles as photo catalyst. In this work, the optimum condition was simulated by the RSM and then visualized by 3D plots in vicinity region of reported optimum condition [29]. The predicted optimum of the responses and the variables were confirmed by the actual responses of the laboratories experiments.

Experiment

Empirical methodology

O-cresol (99%, Fluka), NaOH (99% Merck), H2SO4 (95%-97%) are of reagent grade, obtained from Merck which used without further purification. Mn-doped ZnO nanoparticles (photo catalyst) were synthesized according to procedures that is previously described [12]. Photocatalic degradation of o-cresol was performed in a designed batch photo reactor with Philips lamp (23 watt) as visible light source [30]. Throughout the study, a desired concentration of o-cresol solution was mixed with an appropriate amount of photo catalyst in the photo reactor. At specific time intervals, aliquot samples were withdrawn from the bulk solution and filtered through 0.2 μm polytetrafluoro ethylene (PTFE) filters. The concentration of o-cresol was measured using UV-visible spectrophotometer (shimadzu, uv-1650pc).

Statistical methods

To find the optimum conditions of the photo degradation, the experiments were designed by RSM and CCD (Table 1 the design is in code). The design with four effective variables (Table 2) was run by the design-expert version 8.0.7.1. The plan was included 16 factor points (2n), 8 axial points (2n), and 6 center points (replications) the total numbers of performed runs were 30 experiments. The designed actual responses were fitted to the linear, 2FI, quadratic and cubic models by CCD. The fitting was based on a second order polynomial model (Eq. 1) by a multiple regression analysis [27],

Y = β 0 + ∑ i = 1 4 β i χ i + ∑ i = 1 4 β i i χ i 2 ∑ i = 1 3 ∑ j = i + 1 4 β i j χ i χ j + ε
(1)
Table 1 Experimental-Design of o -cresol photo degradation
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Table 2 Independent variables and their levels employed in the central composite design
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where Y (photo degradation %) represents the response variable, β 0 is the constant term, β i represents the coefficients of the linear parameters, xi represents the variables, β ii represents the coefficients of the quadratic parameter, β ij represents the coefficients of the interaction parameters and ε is the residual associated to the experiments. The significance and adequacy of the model was determined by a few numbers of statistical evidences that appear in analysis of variance (ANOVA) as output of the CCD method. These evidences include Fisher variation ratio (F-value), probability value (P-value), Lack of Fit, coefficient of determination R-squared (Rd2), adjusted R-squared (RAdj2), predicted R-squared (RPred2) and adequate precision of Predicted Residual Error of Sum of Squares (PRESS). Most of these parameters are clearly defined in the experimental design texts. PRESS is a signal-to-noise ratio, which compares the range of the predicted values at the design points to the average prediction error. The ratios greater than 4 indicate adequate model discrimination [30]. RAdj2 and the RPred2 are the measurement of the amount of variation around the mean and the new explained data, respectively. The very significant is the Fisher test where P-value is compared with F-value. F-value is a statistically valid measure of how well the factors described the variation in the data about its meaning while P-value represents the degree of significance of each variable. Mathematically, F-value is given by the ratio of mean square due to model variation by that due to error variance (Eq. 2). The high value of F-value indicates significance and adequacy of the model,

F − value = S r 2 / S e 2
(2)

where Sr2 and Se2are mean of the model and residuals square respectively, obtained by dividing the sum of squares of each of the two sources of variation, the model, and the error variance, by the respective degrees of freedom (DF) [27]. For a variable having a P-value smaller than 0.05, response would be influenced at a confidence level of 0.95.

Analysis of the results

Satisfactory adjustment of the model

Table 3 shows the ANOVA of the quadratic model for the photo degradation. A high F-value (Fmodel = 143.12) was obtained while there is only 0.01% chance of occurrence of noise, indicating substantial significance of the model. The Prob > F (<0.0001) of model is much smaller than 0.05 which indicates the most terms of the model including (X1, X2, X3, X4, X2X3, X2X4, X22, X32, X42) are significant (reckoning that the values greater than 0.1 are indication of the model terms are not significant). Pure errors such as experimental errors are minimal as the Lack of Fit is not significant ((=1.72).

Table 3 Analysis of the variance for photo catalytic degradation of o -cresol parameters
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Rd2 provide a measure of how much variability in the observed response values can be explained by the experimental factors and their interactions. In this study, as obtained Rd2 (0.9926) indicates that the model is capable of accounting for more than 99.26% of the variability in the responses. In addition, the RAdj2 (0.9856) is in reasonable agreement with (<0.20) with the RPred2 (0.9644) which confirms the aptness of the model. Moreover, the adequate precision (47.067) shows remarkable signal (> > 4). These observations can be corroborated by regression plots. Further, Figure 1a shows the actual values versus predicted values of the photo degradation %, which indicated an excellent agreement between actual and predicted responses. A residual plot allowed visual assessment of the distance of each observation from the fitted line (Figure 1b). The residuals randomly scattered in a constant width band about the zero line. Figure 1 (c) shows the histogram of the residuals in allowed visual assessment of the assumption. As observed, the measurement errors in the response variable were normally distributed. This ensured model (quadratic) was suitable to navigate the design space and a satisfactory adjustment of the polynomial model to the experimental data.

Figure 1
figure 1

(a) Scatter plot of predicted photo degradation % value versus actual photo degradation % value (b) residual plot of model and (c) histogram of residuals with normal overlay.

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The quadratic expression model for the photo degradation

The quadratic model displayed in Eq. (3) expresses the relationship between responses of actual variables and the variables themselves.

Y = − 616.18340 + 0.31631 X 1 + 132.45247 X 2 − 174.38646 X 3 − 1.70016 X 4 – 0.019661 X 1 X 2 − 0.026875 X 1 X 3 + 3.02083 E − 004 X 1 X 4 – 10.29688 X 2 X 3 − 20703 X 2 X 4 – 0 , 013750 X 3 X 4 + 1.67535 E − 004 X 1 2 – 6.61621 X 2 2 − 24.63750 X 3 2 + 0.025781 X 4 2
(3)

Where X 1, X 2, X3 and X4 are demonstrated in Table 2. The positive sign in front of the terms indicates synergistic effect while negative sign indicates antagonistic effect. From the equation, the photo degradation % has been linear and quadratic effects by the four process variables (X 1, X 2, X3 and X4). The linear effects are irradiation time (X1), pH (X2), photo catalyst amount (X3), concentration of o-cresol (X4) and the second order effects are square of the variable (X12, X22, X32 and X42). In addition, the interactions effects of (X1X2, X1X3, X1X4, X2X3, X2X4) were observed in the model. The local optimums in terms of the actual variables can be determined by differentiating Eq. 3 for irradiation time (Eq. 4), pH (Eq. 5), amount of photo catalyst (Eq. 6), and o-cresol concentration (Eq. 7).

∂ Y / ∂ X 1 X 2 , X 3 , X 4 = 0
(4)
∂ Y / ∂ X 2 X 1 , X 3 , X 4 = 0
(5)
∂ Y / ∂ X 3 X 1 , X 2 , X 4 = 0
(6)
∂ Y / ∂ X 4 X 1 , X 2 , X 3 = 0
(7)

Response surface 3D plots

Simulation is used when the real system cannot be engaged, because it may be inaccessible, dangerous, unacceptable, and expensive to perform. In photo degradation of o-cresol, the main limitations are expensive chemicals and instruments, time of experiments and numerous errors in the multiple experiments. Based on the validated model, the 3D plots presented the numerous predicted (simulated) responses with the four variables and one response (Table 2) of the photo degradation (Figure 2). As a preliminary study, the effect of pH, photo catalyst amount and o-cresol concentration on photo degradation was investigated during the irradiation time while two variables in each case held constant (e.g. Figure 2a). As observed, the photo degradation illustrated a peak at particular amount of pH, photo catalyst and o-cresol during the irradiation time. Therefore, a large numbers of experiments were simulated by end of 240 minutes of irradiation time while it was only one variable kept constant in each case (Figure b, c, d). Figure 2(b) shows the interaction between photo catalyst amount (1.0 – 2.0 g/L) and o-cresol concentration (25 – 45 mg/L) simultaneously with constant pH 8.2. As shown, the photo degradation % was decreased with increasing the o-cresol concentration for all the range of photo catalyst concentration. The reduction may be due to this reasons that o-cresol can be degraded directly by the generated holes (h+) over photo catalyst surface. In a high o-cresol concentrate solution, o-cresol molecules can compete with H2O to attract the h+ which is a limited agent [31]. On the other hand, the photo degradation % was increased with increasing photo catalyst amount up 1.6 g/L for all the concentration of o-cresol. This can be attributed to the fact that the increase in the effective surface area of the photo catalyst, which in turn leads to enhanced production of ●OH radicals. However, when the amount of photo catalyst was increased in excess of the optimum (1.6 g/L), the photo degradation % decreased. The decreased efficiency observed above the optimum photo catalyst loading may be attributed to the interception of light by the excess of photo catalyst particles in solution as known screen effect [8].

Figure 2
figure 2

Response surface 3D plots indicating the effect of interaction between process variables on photo degradation of o -cresol (a) Interaction between irradiation time and pH while holding the photo catalyst amount at 1.5 g/L and o -cresol concentration at 35 mg/L (b) Interaction between photo catalyst amount and o -cresol concentration while holding pH at 8.2 at end of 240 minutes of reaction time (c) Interaction between photo catalyst amount and pH while holding o -cresol concentration at 35 mg/L at end of 240 minutes of reaction time (d) Interaction between o -cresol concentration and pH while holding photo catalyst at1.5 g/L at end of 240 minutes of reaction time.

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Figure 2(c) shows the interaction between pH (6-10) and photo catalyst amount (1.0 – 2.0 g/L) with constant o-cresol concentration 35 mg/L. As it is shown, the photo degradation % increased slightly with increasing pH from pH 7 to 9 in the range of photo catalyst amount. The increase in the photo degradation % may be due to increasing adsorption of o-cresol on the photo catalyst surface [32]. Moreover, It has been reported that, in slightly alkaline solution (pH=8), ●OH radicals are more easily generated by oxidizing the available OH− on the photo catalyst surface [33]. Thus, generally, the photo degradation % is expected for becoming enhanced with increasing pH owing to the availability of ●OH radicals for the reaction. However, a decrease in photo degradation % was observed above the optimum. This can be attributed to the reduction for o-cresol adsorbed on the photo catalyst surface in the region of pH [31]. It should be noted as well that the radicals are rapidly scavenged in the presence of excess concentrations of OH- and therefore would not have the opportunity to react with the substrates [33].

Figure 2(d) shows the interaction between pH (6-10) and o-cresol concentration (25 – 45 mg/L) with constant photo catalyst amount 1.5 g/L. As observed, the acceptable photo degradation % was obtained at 35 mg/L of o-cresol concentration. Any increase in the concentration resulted in diminishing photo degradation %. The decrease in photo degradation % may be due to the reason that the o-cresol concentration increased while the active sites of photo catalyst remained constant [34]. As a result, the optimum photo degradation was 60% (average) in the condition (pH 8.2, photo catalyst amount 1.6 g/L and o-cresol concentration 35 mg/L at 240 minutes of irradiation time). The optimum was validated by performing the similar experimental methodology [20]. As observed, the experimental values were reasonably close to the simulated values that indicated the high validity and adequacy of the model.

Conclusion

The optimization and modeling of o-cresol photo degradation was studied by RSM. The experiments were designed with four effective factors including irradiation time, pH, photo catalyst’s amount and o-cresol concentration by the CCD. The CCD considered 30 runs to obtain actual responses. To suggest a model for the photo degradation process, the responses were fitted with a quadratic model. The ANOVA confirmed the high validity of the model by using excellent evidences such as high F-value (143.12), very low P-value (<0.0001), non-significant lack of fit, the R2 (0.99), and the adequate precision (47.067). The results of simulated 3D plots for the photo degradation (60%) were agreed with experimental results (63%). This study indicates the success of RSM to simulate the optimum condition of o-cresol photo degradation % under visible-light by Mn-doped ZnO nanoparticles as photo catalyst.