Optimization of a nanoparticle ball milling process ...

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Srdjan Petrovic a,d,*. , Ljiljana Rozica,d, Vesna Jovic c, Stevan Stojadinovic b, Boško Grbica, Nenad Radic a,. Jelena Lamovec c, Rastko Vasilic b a University of ...
Advanced Powder Technology xxx (2018) xxx–xxx

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Advanced Powder Technology journal homepage: www.elsevier.com/locate/apt

Original Research Paper

Optimization of a nanoparticle ball milling process parameters using the response surface method Srdjan Petrovic´ a,d,⇑, Ljiljana Rozˇic´ a,d, Vesna Jovic´ c, Stevan Stojadinovic´ b, Boško Grbic´ a, Nenad Radic´ a, Jelena Lamovec c, Rastko Vasilic´ b a

University of Belgrade, IChTM-Department of Catalysis and Chemical Engineering, Njegoševa 12, Belgrade, Serbia University of Belgrade, Faculty of Physics, Studentski trg 12-16, 11000 Belgrade, Serbia University of Belgrade, IChTM-Centre of Microelectronic Technologies, Njegoševa 12, Belgrade, Serbia d University of Belgrade, IChTM – Centre of Excellence in Environmental Chemistry and Engineering, Njegoševa 12, Belgrade, Serbia b c

a r t i c l e

i n f o

Article history: Received 7 December 2017 Received in revised form 15 May 2018 Accepted 21 May 2018 Available online xxxx Keywords: TiO2-CeO2nanopowder Planetary ball milling Response surface methodology Photocatalytic degradation

a b s t r a c t Nanocrystalline TiO2-CeO2 powders were synthesized from their TiO2 and CeO2 oxides using mechanical ball milling process. The response surface method is applied to identify optimal parameters for the synthesis of TiO2-CeO2 photocatalyst. Analysis of variance and main effect plot are used to determine the significant parameters and set the optimal level for each parameter. Regression analysis showed good agreement of experimental data with the second-order polynomial model with a coefficients of determination: R2 = 0.991, R2Adj. = 0.940 and R2Pred. = 0.983. Under optimal experimental conditions of TiO2:CeO2 weight percentage ratio 71:29, milling speed 200 rpm, and milling time 115 min the highest photodegradation efficiency was achieved. On the basis of the above statistical analysis, it was found that the band gap energy of TiO2-CeO2 nanoparticles decreases with the increase of the milling speed and milling time with constant TiO2:CeO2 weight percentage ratio. Obtained results suggest that mechanical ball milling process is a rapid, efficient and low energy consumption method to synthesize TiO2-CeO2 photocatalyst. Ó 2018 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.

1. Introduction Titanium dioxide (TiO2) based materials have shown great potential as powerful photocatalysts for various significant reactions, because of their chemical stability, non-toxicity and high reactivity [1–4]. Also, titanium dioxide is well known and important n-type semiconducting material for the degradation of a vast number of organic pollutants under UV light irradiation due to its relatively wide band gap (anatase phase: 3.2 eV and rutile phase: 3.0 eV) [5]. These processes are based on the irradiation of the semiconductor with light energy that is greater than its band gap, generating electron/hole pairs that initiate a heterogeneous photocatalytic reaction. However, a high rate of recombination between excited electron / hole pairs limits the photocatalytic activity [6,7]. To overcome these limitations coupling of TiO2 with other metal oxides such as WO3 [8], SnO2 [9], ZrO2 [10] and Fe2O3 [11] was widely investigated. Especially, CeO2 has attracted a lot of attention due to its optical and catalytic properties associated with ⇑ Corresponding author at: University of Belgrade, IChTM-Department of Catalysis and Chemical Engineering, Njegoševa 12, Belgrade, Serbia. E-mail address: [email protected] (S. Petrovic´).

the redox pair Ce3+/Ce4+ [12–14]. In addition, CeO2 increases the specific surface area and diminishes the crystallite size [14] supporting the stability of the anatase phase [15]. Coupled TiO2CeO2 nanocomposites also feature a specific electron transfer process that increases the production of the electron/hole pairs and improves the photocatalytic activity [16]. Many techniques have been applied for preparing of TiO2 and TiO2-CeO2 powders such as: sol–gel synthesis [17], hydrothermal synthesis [18], co-precipitation method [19] and flame spray pyrolysis [20]. These conventional methods predominantly included multi step procedures, demanded the utilization of toxic metal–organic precursors, and expensive equipment. Also, long processing times are required, which is detrimental for industrial fabrication purposes [21]. Therefore, the mechanochemical process has gained importance over conventional synthesis, and it yielded large quantities of desired product at ambient conditions within a very short processing time [22]. Alongside, present day industrial applications demand comprehensive theoretical simulations before actual experimental design. A central composite design (CCD) is the most commonly used response surface designed experiment. CCD are a factorial or fractional factorial design with center points, augmented with a group

https://doi.org/10.1016/j.apt.2018.05.021 0921-8831/Ó 2018 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.

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of axial points (also called star points) that let an estimation of curvature. The design and statistical analysis of experiments have resulted in development of the response surface modeling (RSM) used for process optimization and prediction of the interaction between variables, reducing the number of runs and consequently, the cost of experiments [23]. Main objective of this method is to attain maximum performance by finding the appropriate operating point. A second-order response surface model has been used to develop an equation for predicting selected process response, based on the data collected with statistical design of experiments [24]. The analysis of variation (ANOVA) shows extent of agreement i.e., how the observed data fit into the assumed second-order RSM model. Moreover, the RSM model allows process optimization with limited number of experimental data. Desirability is simply a mathematical method to find the optimum. The goal of optimization is to find a good set of conditions that will meet all the goals, not to get to a desirability value of 1.0. In this study, an environmentally friendly and sustainable approach, dry reactive milling, was employed to synthesize TiO2CeO2 nanopowders using the CCD design of experiments. The effects of selected process variables (TiO2:CeO2 weight percentage ratio, milling speed, and milling time) on TiO2 phase composition, microstrain, and crystallite size have been discussed. The main objectives were to optimize the nanoparticle ball milling process and investigate the parameters that influence the photodegradation efficiency. The optimal conditions of ball milling process were also demonstrated from the model obtained via experimental data.

2. Materials and methods 2.1. Mechanochemical synthesis of TiO2-CeO2 nanopowders Commercially available TiO2 powder (>99% purity, Alfa Aesar GmbH & CoKG) and CeO2 powder (99.9% purity, Johnson Matthey-Alfa Product) were used as starting materials. TiO2-CeO2 nanopowders were synthesized in the absence of solvent via mechanochemical process using a high energy ball mill (Fritsch planetary mill Pulverisette 7 premium line). Milling was done at atmospheric conditions in a silicon nitride (syalon, Si3N4) vial (volume of 80 cm3) using 25 silicon nitride balls with 10 mm of diameter, keeping powder sample to ball mass ratio at about 1:10 throughout the experiment. Quantity of powder used in each run was 4.87 g. Effect of mechanochemical synthesis conditions on the obtained nanopowders was studied by varying milling time (15–141 min), milling speed (150–400 rpm), and TiO2:CeO2 weight percentage ratio (90:10–40:60). All samples were calcined at 500 °C for 2 h, which resulted in the formation of TiO2-CeO2 photocatalysts.

2.2. Materials characterization The phase structure of samples was analyzed by X-ray diffraction method (XRD), using a Rigaku Ultima IV diffractometer in Bragg-Brentano geometry, with Ni-filtered CuKa radiation (40 kV, 40 mA, k = 1.54178 Å). Structural and microstructural parameters of the TiO2-CeO2 samples were estimated by the Williamson-Hall (WH) plots [25]. The microstructures of TiO2-CeO2 nanopowders were examined by Scanning Electron Microscope (SEM) JEOL 840A, Oxford Instruments INCAPentaFET x3 system. The accelerating voltage used was 20 kV. UV–Vis diffuse reflectance spectra (DRS) of catalysts were obtained using UV–Vis spectrophotometer (Specord M40 Carl Zeiss). In order to understand the reason for band gap narrowing

of pure and CeO2 doped TiO2 sample, band gap energies were calculated from the equation:

Eg ¼

1240 k

ð1Þ

where Eg is the band gap (eV) and k (nm) is the wavelength of the absorption edges in the spectrum. The reflectance measurements were converted to absorption spectra using the Kubelka-Munk function, F(R). The absorbance F(R) can be expressed as F(R) = (1R)2/2R, were R represents the reflectance. Band gap energy was estimated by plotting [F(R1)]g as a function of the photon energy (ht). The best linear relation was obtained for g = 1/2 indicating that direct allowed transitions are responsible for the measured optical band gap. 2.3. Photocatalytic tests The photocatalytic degradation of methyl orange (MO) was carried out in an open cylindrical thermostated Pyrex cell of 6.8 cm in diameter, corresponding to the surface area accessible to the light of 36.3 cm2. The experiments were performed with 100 mL of solution containing 8 mg/L MO added to 100 mg of TiO2-CeO2 samples. Irradiation of the solution was performed under the UV lamp (Solimed BH Quarzlampen), with a power consumption of 300 W, housed 25 cm above the top surface of the solution. Illumination intensity on the top of the photocatalytic reactor was 850 lx. Prior to illumination, the suspensions were magnetically stirred in the dark for 30 min to achieve adsorption–desorption equilibrium. Aliquots of suspensions were collected at different time intervals for a total of 150 min. The aliquots were filtered through a 0.20 lm syringe membrane filter into standard quartz cuvettes with an optical path of 1 cm and directed to UV–Vis spectrometer (Thermo Electron Nicolet Evolution 500) to check the degradation of MO via its absorption peak at 464 nm. These absorption data were used in the determination of degradation of MO through comparison with the absorbance at a certain time as a percentage of the initial absorbance. The efficiency of the MO photodegradation (g) was calculated using the following equation [26]:



ðC 0  CÞ  100 C0

ð2Þ

where C0 represents the initial concentration and C represents the concentration after t minutes of photocatalysis. 2.4. Design of experiments RSM is derived from mathematical and statistical techniques. This method can be used for studying the effect of several factors at different level and their influence on each other [23]. The 3-factor, 5-level CCD, which is a widely used form of RSM, was chosen to identify major parameters influencing MO degradation efficiency and the interactions among following parameters: TiO2: CeO2 weight percentage ratio, milling speed, and milling time. These parameters are denoted as X1, X2, and X3 respectively. For statistical calculations, the variables was coded as according to the following equation:

xi ¼

Xi  X0 Dx

ð3Þ

where xi is the dimensionless coded value of each independent variable, X0 is the value of Xi at the center point, and Dx is the step change value. A design of 17 experiments was formulated for three factorial (23) designs and three replicates at the central points, four star

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points, and six axial points were employed to the second-order polynomial model. The general form of the second-order model is:

Y ¼ bo þ

k k k X k X X X bi X i þ bii X 2i þ bij X i X j þ e i¼1

i¼1

ð4Þ

i¼1 j>1

where Y is the predicted response, Xi, Xj,. . .,Xk are the input variables that affect the response Y, X2i , X2j ,. . ., X2k are the square effects, XiXj, XiXk, and XjXk are the interaction effects, b0 is the intercept term, bi are the linear terms, bii are the square terms, bij are the interaction terms, and e is a random error [23]. The data obtained from the CCD experiments were analyzed using Stat-Ease Design Expert (Version 8.0) software. This software was used for regression analysis of the obtained data and estimate of the coefficient of regression equation. ANOVA statistical testing of the model in the form of linear, squared, and interaction terms was utilized to test the significance of each term in the equation and integrity of fit of the regression model obtained [23]. The optimum values of selected variables were obtained by solving the regression equation and by analyzing the response surface plots as well. 3. Results and discussion During the course of the mechanochemical process via ball milling, accumulated potential energy with shear and friction forces is transferred from milling balls to the material. This energy induces severe plastic deformation and creates new interfaces and defects in materials, which potentially leads to a substantial improvement in catalytic properties of the final product [27]. Therefore, the present study investigates the effect of parameters of ball milling process on structural and microstructural properties, and photocatalytic activity of TiO2-CeO2 nanopowders using response surface methodology. RSM identifies the relationship between the independent parameters (TiO2:CeO2 weight percentage ratio, milling speed, and milling time) and response variables (photodegradation efficiency of MO after 45 min). Minimal and maximal values of variables and the full experimental plan with respect to these values in actual and coded forms are listed in Table 1. Each parameter was coded at five levels:  a,  1, 0, + 1, and + a. The design used for optimization and responses observed and predicted for 17 experiments is presented in Table 2. As usual, the experiments were performed in random order to avoid systematic error. In addition, three central replicates were added to the experimental plan to calculate pure experimental error. In Fig. 1 selected diffraction patterns of TiO2-CeO2 nanopowder samples synthesized by a matrix of experimental plan (Table 2) are presented. The results are grouped in order to easy visualize the influence of selected parameters: content of CeO2 (Fig. 1a), milling time (Fig. 1b), and milling speed (Fig. 1c). From the XRD patterns, it is evident that all samples are mainly composed of anatase and rutile phases of TiO2 and cubic CeO2 phase. The XRD patterns of samples in Fig. 1a (Run 5 (X1 = 40:60, X2 = 275 rpm, X3 = 77.50 min), Run 8 (X1 = 65:35, X2 = 275 rpm, X3 = 77.50 min) and Run 12 (X1 = 90:10, X2 = 275 rpm, X3 = 77.50 min) show characteristic

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anatase and rutile titania peaks. However, the intensity of main anatase reflection at 25.45 (1 0 1) and rutile reflection at 27.58 (1 1 0) gradually decreases with the increase of CeO2 content. On the other hand, the intensity of CeO2 (1 1 1) reflection at 28.69 increases as the amount of CeO2 increases from 10% to 60%. XRD patterns of samples in Fig. 1b (Run 10 (X1 = 65:35, X2 = 275 rpm, X3 = 14.43 min), Run 8 (X1 = 65:35, X2 = 275 rpm, X3 = 77.50 min), and Run 11 (X1 = 65:35, X2 = 275 rpm, X3 = 141.57 min)) show that milling time significantly affects the intensity of main anatase and rutile reflections. Weak reflections of CeO2 phase in Run 11 and Run 8, obtained with prolonged milling time, indicate that the mean crystallite size was reduced in comparison to sample Run 10 obtained for milling time of 14.4 min. To evaluate the effect of milling speed, Fig. 1c presents XRD patterns of samples Run 4 (X1 = 65:35, X2 = 149 rpm, X3 = 77.50 min), Run 8 (X1 = 65:35, X2 = 275 rpm, X3 = 77.50 min), and Run 13 (X1 = 65:35, X2 = 401 rpm, X3 = 77.50 min). It can be observed that by increasing the milling speed (149–401 rpm) XRD diffraction peaks became broader and less intense. At higher milling speed, more collisions take place between the milling balls and powders. Consequently, an increase in local temperature and pressure at the collision sites induces anatase-to-rutile phase transformation in the TiO2 nanopowder [28]. The ratio of these two crystalline forms of TiO2 (anatase (1 0 1) peak at 2h = 25.34° and rutile (1 1 0) peak at 2h = 27.49°) in the samples were calculated according to the Spurr equation [29]:

f ¼1

1 1 þ 1:265 IIRA

ð5Þ

where f is the content of rutile in the samples, and IA and IR are the X-ray intensities of anatase and rutile peaks, respectively. Also, a high milling speed may have an impact on the lattice strain and thus Williamson–Hall Eq. (6) was used to obtain the particle size of TiO2-CeO2 nanopowders. Williamson and Hall proposed a method for deconvolution of size and strain broadening based on the peak width as the function of 2h. If a linear fit is obtained from the equation:

bhkl ¼

Kk þ 4e sin h D cos h

ð6Þ

it is possible to derive the crystallite size (D) from the intercept, and the micro-strain (e) from the slope. K is a constant equal to 0.94 for spherical shaped particles, k is the wavelength of the X-ray (1.54178 Å for CuKa radiation) and h is the peak center. Fig. 2 represents the W-H plot for samples Run 10 (X1 = 65:35, X2 = 275 rpm, X3 = 14.43 min), Run 8 (X1 = 65:35, X2 = 275 rpm, X3 = 77.50 min), and Run 11 (X1 = 65:35, X2 = 275 rpm, X3 = 141.57 min). The linear fit of experimental data shows considerably varying slope, suggesting that the micro-strain distribution differs. Considering all reflections of the anatase phase for a qualitative calculation, the micro-strain for sample Run 10 is 0.2% and 0.12% for sample Run 11 (Table 3), thus suggesting that micro-strains decreases when the milling time is increased. It should be stressed that all samples were exposed to the relatively high annealing temperatures (500 °C) before XRD measurements. Probably, these con-

Table 1 Actual and coded values of independent variables used for experimental design. Variable and designate

TiO2 : CeO2 weight percentage ratio (X1, %) Milling speed (X2, rpm) Milling time (X3, min)

Ranges and actual values of coded levels a

1

0

+1

+a

90:10 149 15

80:20 200 40

65:35 275 77.5

50:50 350 115

40:60 400 141

a = 1.682 (axial point for CCD). Please cite this article in press as: S. Petrovic´ et al., Optimization of a nanoparticle ball milling process parameters using the response surface method, Advanced Powder Technology (2018), https://doi.org/10.1016/j.apt.2018.05.021

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Table 2 Applied CCD matrix for ball milling process and photodegradation efficiency of MO with TiO2-CeO2 photocatalysts. Run

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

X1

1 +1 1 0 +a 1 +1 0 0 0 0 a 0 +1 +1 0 1

X2

1 +1 +1 a 0 1 +1 0 0 0 0 0 +a 1 1 0 +1

X3

+1 +1 +1 0 0 1 1 0 0 a +a 0 0 +1 1 0 1

Photodegradation efficiency of MO, (%) Exp.a

Pred.b

78.0 42.0 70.0 85.0 31.0 74.0 44.0 68.0 70.0 67.0 72.0 80.0 47.0 52.0 50.0 69.0 69.0

78.56 42.21 70.31 87.29 32.67 74.48 42.19 68.29 68.29 66.63 69.94 78.33 49.29 52.16 48.44 68.29 70.09

a = 1.682. a b

Experimental values of response. Predicted values of response by RSM proposed model.

Fig. 1. XRD patterns of the studied samples within experimental plan: (a) Run 5 (X1 = 40:60, X2 = 275 rpm, X3 = 77,50 min), Run 8 (X1 = 65:35, X2 = 275 rpm, X3 = 77.50 min), and Run 12 (X1 = 90:10, X2 = 275 rpm, X3 = 77.50 min); (b) Run 10 (X1 = 65:35, X2 = 275 rpm, X3 = 14.43 min), Run 8 (X1 = 65:35, X2 = 275 rpm, X3 = 77.50 min), and Run 11 (X1 = 65:35, X2 = 275 rpm, X3 = 141.57 min); (c) Run 4 (X1 = 65:35, X2 = 149 rpm, X3 = 77.50 min), Run 8 (X1 = 65:35, X2 = 275 rpm, X3 = 77.50 min), and Run 13 (X1 = 65:35, X2 = 401 rpm, X3 = 77.50 min.

ditions enable relaxation of structure resulting in the decrease of microstrain for prolonged time of milling. This is in accordance in literature data [30–32]. Also, the particle size systematically decreases with increasing milling time and it reaches a value of 15 nm for 140 min of milling, which is quite consistent with the reported literature data for other composite powders [33–36]. As Table 3 shows, the crystallite size and micro-strain of anatase TiO2 phase in TiO2-CeO2 nanopowders decreases with an increase of the CeO2 amount. In the case increasing milling speed, the size of the crystallite is reduced significantly. On the other hand, when increasing the milling speed from 149 to 401 rpm the rutile weight fraction increases from 17.6 to 32.4% as a consequence of the transformation of TiO2 anatase to rutile phase. The effect of decreasing TiO2 crystallite size and increasing rutile content with impurity addition was also observed when TiO2 was doped with Cu or Fe [37,38]. The authors proposed that doping

by second element creates a higher number of defects, most likely oxygen vacancies, inside the TiO2 crystal lattice, thus accelerating the anatase-to-rutile transition and retarding the crystallite growth. The external morphology of the prepared TiO2-CeO2 nanopowder was studied using SEM and the images are shown in Fig. 3. The SEM analysis shows that, in all the samples, the nanoparticles are irregular in shape, randomly organized, and tend to form agglomerates. Highly aggregated, more or less, spherical shaped particles were observed for the TiO2 whereas quite big flake-like morphology was observed for the CeO2. In addition, the surface morphology and particle size were significantly changed after ball milling speed was increased from 149 rpm (Fig. 3a) to 401 rpm (Fig. 3b). Influence of CeO2 loading, presented on Fig. 3a, 10% and Fig. 3b, 60%, show that grain size virtually unchanged while high content of CeO2 form more CeO2 agglomerates. After increasing milling time

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Fig. 2. Particle size determination from W-H plot derived from X-ray data: (a) Run 10 (X1 = 65:35, X2 = 275 rpm, X3 = 14.43 min); (b) Run 8 (X1 = 65:35, X2 = 275 rpm, X3 = 77.50 min); (c) Run 11 (X1 = 65:35, X2 = 275 rpm, X3 = 141.57 min).

from 14 min (Fig. 3e) to 140 min (Fig. 3f), particles have a stable shape but size was increased with prolonged time. Also evenly distributed CeO2 is notice for shorter milling time. To investigate optical absorption properties of TiO2-CeO2 samples, the diffuse reflectance absorption spectra (DRS) were examined in the range of 300–600 nm. The measured reflectance spectra were transformed into Kubelka-Munk function (F(R)). Moreover, the absorption edge values of the samples Run 4 (X1 = 65:35, X2 = 149 rpm, X3 = 77.50 min), Run 8 (X1 = 65:35, X2 = 275 rpm, X3 = 77.50 min), and Run 13 (X1 = 65:35, X2 = 401 rpm, X3 = 77.50 min) were determined by plotting F(R) versus the wavelength as shown in Fig. 4. Literature survey shows that the

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incorporation of cations into TiO2 results in the shift of the absorption edge to the visible light region (400–800 nm), while respective threshold of pure titania is at 387 nm, corresponding to band gap value of 3.2 eV) [39]. The extension of TiO2 spectral response into the visible region after addition of metal oxides generally improves the overall photocatalytic activity despite issues (like blocking of the reaction sites) could occur along with promoting charge recombination [40]. Obtained absorption shifts are in accordance with the decrease in the band gap energy below of 3.2 eV, in relation to the increase of milling speed in case of a constant value of the added CeO2, as may be observed in Fig. 4. Narrowing of the band gap achieved in this case is due to the combined effect of lattice strain and lattice defects induced by the ball milling. In addition, in the cases of increasing the amount of CeO2, a decrease in band gap energy was obtained (Table 3). This observation was probably due to electronic coupling between the wide band gap of TiO2 with the narrow band gap of CeO2. Since achieved band gap of 2.62 to 3.19 eV falls into the visible region of spectrum, ball milled TiO2-CeO2 samples are suitable for visible light photocatalysis. The photocatalytic activity of TiO2-CeO2 samples obtained at different ball milling conditions was evaluated in terms of photodegradation of MO under UV irradiation. UV–Vis spectra of the photocatalityc degradation of MO over TiO2-CeO2 nanopowder (Run 4 (X1 = 65:35, X2 = 149 rpm, X3 = 77.50 min)) is presented in Fig. 5. At initial, MO exhibits the maximum absorption wavelength at 464 nm. The absorbance intensity of MO gradually decreases with the increase of exposed time from 0 to 180 min. A reasonably high degradation rate by 85% of MO within 45 min is detected over the surface of this photocatalyst. Using the absorption spectra of all the produced samples, it was possible to calculate the corresponding photodegradation efficiencies by applying Eq. (2). Fig. 6 shows time profiles of the photodegradation of MO over the prepared photocatalysts. From the data in these curves, the apparent rate constant (K) was calculated by the integral method for an irreversible monomolecular first order reaction [41]:

r A ¼ 

dC A ¼ KC A dt

ð7Þ

If the batch reactor works at constant density, then:

 ln

C0 C

 ¼ Kt

ð8Þ

where C is the concentration at time t, and C0 is the initial concentration. Reasonable linearity was obtained by applying the first

Table 3 Physical parameters of the prepared TiO2-CeO2 photocatalysts. Sample

Anatase crystallite size (nm)

Rutile phase fraction

Micro-strain (%)

Band gap energy (eV)

Run Run Run Run Run Run Run Run Run Run Run Run Run Run Run Run Run

30.5 12.4 15.5 30.5 16.5 28.2 19.4 22.1 22.0 23.9 15.1 37.6 12.7 15.5 18.4 22.4 18.9

0.19 0.40 0.39 0.18 0.28 0.18 0.27 0.23 0.22 0.18 0.26 0.25 0.32 0.19 0.20 0.23 0.27

0.33 0.27 0.26 0.20 0.17 0.29 0.17 0.13 0.13 0.20 0.09 0.43 0.14 0.13 0.12 0.13 0.08

3.00 2.62 2.82 3.19 2.85 3.00 2.89 2.89 2.91 3.08 2.83 2.94 2.78 3.15 2.97 2.90 2.92

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

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Fig. 3. SEM micrograph of (a) Run 4 (X1 = 65:35, X2 = 149 rpm, X3 = 77.50 min), (b) Run 13 (X1 = 65:35, X2 = 401 rpm, X3 = 77.50 min), (c) Run 12 (X1 = 90:10, X2 = 275 rpm, X3 = 77.50 min), (d) Run 5 (X1 = 40:60, X2 = 275 rpm, X3 = 77,50 min), (e) Run 10 (X1 = 65:35, X2 = 275 rpm, X3 = 14.43 min) and (f) Run 11 (X1 = 65:35, X2 = 275 rpm, X3 = 141.57 min).

Fig. 4. (a) DRS spectra of samples: Run 4 (X1 = 65:35, X2 = 149 rpm, X3 = 77.50 min), Run 8 (X1 = 65:35, X2 = 275 rpm, X3 = 77.50 min), and Run 13 (X1 = 65:35, X2 = 401 rpm, X3 = 77.50 min); (b) Plot of transformed Kulbeka-Munk function versus ht.

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Fig. 5. UV–Vis spectra of the photocatalityc degradation of MO.

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order kinetic equation (Fig. 6). The relationship between ln (C0/C) and t was fitted with a linear regression line (R2 > 0.97). The calculated values for apparent rate constant are reported in Table 4, showing that the highest value corresponds to the sample Run 4 (X1 = 65:35, X2 = 149 rpm, X3 = 77.50 min). However, increase of milling speed to 401 rpm, keeping the other parameters constant, leads to the drop of apparent rate constant by 75%. Such behavior could be ascribed to the transformation of anatase-to-rutile phase due to increased milling speed. The K value for TiO2-CeO2 sample with 10 wt% is approximately 7 times higher than for sample with 60 wt% CeO2 identical experimental conditions. However, when the amount of CeO2 increased over 35 wt% photocatalytic activity decreased either as a result of blocking the photosensitive sites or increased number of electron-hole recombination centers. The most likely various interfaces formed between TiO2-CeO2, created by ball milling process, the both promote photoinduced charge separation and suppress recombination of electrons and holes that is basic contribution for increased photocatalytic activity. To investigate the combined effect of mentioned process variables on the MO photodegradation efficiency, experiments were performed according to the experimental design matrix (Table 2). The application of the RSM based on the estimates of the parameters indicate an empirical relationship between the response of MO photodegradation efficiency and input independent variables expressed by the following quadratic model:

Y ¼ 68:29  13:58X 1  11:30X 2 þ 0:98X 3  0:38X 1 X 2  0:88X 2 X 3  4:52X 21 þ 7:67X 21 X 2  3:89X 21 X 22

ð9Þ

A positive sign of the terms in Eq. (9) indicates a synergistic effect, while a negative sign indicates an antagonistic effect of the response. Coefficients in empirical Eq. (9) were obtained by means of Stat-Ease Design Expert (Version 8.0) software, with confidence level of 95%. The quality of the model developed was evaluated based on the correlation coefficient (R2) value. R2 value of 0.9915 and considerably high predicted R2 value of 0.9830 are advocating for high correlation between the experimental and model predicted values (Table 2, Fig. 7). This indicates that applied regression model provides an explanation of relationship between the independent variables and response.

Fig. 6. Photodegradation of MO under UV irradiation using TiO2-CeO2 photocatalysts. Inset shows the plot of ln(C0/C) versus time.

Table 4 Apparent first-order kinetics equations and relative parameters for photodegradation of MO with TiO2-CeO2 photocatalysts. Sample

Kinetics equation

K (h1)

R2

Run Run Run Run Run Run Run Run Run Run Run Run Run Run Run Run Run

ln(C0/C) = 0.04180 t  0.048 ln(C0/C) = 0.00954 t  0.011 ln(C0/C) = 0.03372 t  0.029 ln(C0/C) = 0.04319 t  0.025 ln(C0/C) = 0.00531 t  0.048 ln(C0/C) = 0.03640 t  0.034 ln(C0/C) = 0.00819 t  0.008 ln(C0/C) = 0.03006 t  0.021 ln(C0/C) = 0.03122 t  0.032 ln(C0/C) = 0.02957 t  0.024 ln(C0/C) = 0.03198 t  0.014 ln(C0/C) = 0.04088 t  0.027 ln(C0/C) = 0.01138 t  0.007 ln(C0/C) = 0.01342 t  0.016 ln(C0/C) = 0.01190 t  0.012 ln(C0/C) = 0.03028 t  0.029 ln(C0/C) = 0.03120 t  0.024

2.5074 0.5724 2.0232 2.5914 0.3186 2.1864 0.4914 1.8036 1.8732 1.7742 1.9188 2.4528 0.6828 0.8052 0.7134 1.8168 1.8726

0.9926 0.9846 0.9954 0.9915 0.9767 0.9948 0.9739 0.9935 0.9929 0.9934 0.9889 0.9908 0.9926 0.9894 0.9909 0.9927 0.9948

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Fig. 7. Comparison plot between the experimental and model predicted efficiency photodegradation of MO using TiO2-CeO2 photocatalysts.

Please cite this article in press as: S. Petrovic´ et al., Optimization of a nanoparticle ball milling process parameters using the response surface method, Advanced Powder Technology (2018), https://doi.org/10.1016/j.apt.2018.05.021

S. Petrovic´ et al. / Advanced Powder Technology xxx (2018) xxx–xxx

8

Table 5 Analysis of variance values for fitted polynomial model of the MO photodegradation using TiO2-CeO2 photocatalysts. Source of variance

Sum of squares

Degrees of freedom

Mean of squares

F-Test

Probability > F

X1 X2 X3 X1 X2 X2 X3 X21 X21X2 X21 X22 Model Residual Lack of Fit Pure error Total

2517.13 722.00 13.17 1.13 6.13 254.29 195.07 61.22 3750.34 32.13 30.13 2.00 3782.47

1 1 1 1 1 1 1 1 8 8 6 2 16

2517.13 12.30 13.17 1.13 6.13 254.29 195.07 61.22 468.79 4.02 5.02 1.00

626.67 179.75 3.28 0.28 1.52 63.31 48.56 15.24 116.71