Photocatalytic Degradation of Phenol and Phenol Derivatives Using a Nano-tio 2 Catalyst: Integrating Quantitative and Qualitative Factors Using Response Surface Methodology

Due to the toxicity effects and endocrine disrupting properties of phenolic compounds, their removal from water and wastewater has gained widespread global attention. In this study, the photocatalytic degradation of phenolic compounds in the presence of titanium dioxide (TiO 2) nano-particles and UV light was investigated. A full factorial design consisting of three factors at three levels was used to examine the effect of particle size, temperature and reactant type on the apparent degradation rate constant. The individual effect of TiO 2 particle size (5, 10 and 32 nm), temperature (23, 30 and 37 °C) and reactant type (phenol, o-cresol and m-cresol) on the apparent degradation rate constant was determined. A regression model was developed to relate the apparent degradation constant to the various factors. The largest photocatalytic activity was observed at an optimum TiO 2 particle size of 10 nm for all reactants. The apparent degradation rate constant trend was as follows: o-cresol > m-cresol > phenol. The ANOVA data indicated no significant interaction between the experimental factors. The lowest activation energy was observed for o-cresol degradation using 5-nm TiO 2 particles. A maximum degradation rate constant of 0.0138 min −1 was recorded for o-cresol at 37 °C and a TiO 2 particle size of 13 nm at a D-optimality value of approximately 0.98. The response model adequately related the apparent degradation rate constant to the factors within the range of factors under consideration.


Introduction
Phenols, also termed total phenols or phenolics, are important due to their widespread use in many manufacturing processes.However, these chemicals pose a serious threat to many ecosystems, water supplies and human health because of their inertness, toxicity, endocrine disrupting abilities and carcinogenic behavior [1,2].The United States, Canada and the European Union have included some phenols in their list of priority pollutants [3][4][5].Phenol is commonly employed in the manufacturing of phenolic resins, bisphenol A, caprolactam and chlorophenols such as pentachlorophenol [1].Cresols are isomeric mono-substituted phenols.Commercially, cresol is produced as a by-product from the fractional distillation of crude oil and coal tars and the gasification of coal.Phenol and its derivatives have been identified in effluents from petroleum refining [6] pulp and paper manufacturing [7], coal processing [8] and chemical production facilities [9].Oil-shale processing is another industry that produces effluents containing phenol and cresols [10].
Removing phenolic compounds from wastewaters and drinking water supplies has received widespread attention recently because of their toxic and endocrine disrupting properties [11].Phenols can be removed by physical processes such as flocculation, precipitation, granular activated carbon (GAC) or reverse osmosis (RO) [12].Enzymes and microorganisms have also been employed to remove phenols.Studies by Cooper and Nicell [13] have shown over 97% phenol removal using an enzymatic process.However, using enzymes is impractical because of high catalyst cost and short-lived catalytic activity [13].Biological processes have also been used to remove phenolic compounds.However, in many cases, phenols are inhibitory to microorganisms at threshold levels [14,15].
Inadequate removal of phenolic compounds by conventional biological treatment methods has forced researchers to develop alternative treatment approaches.Advanced oxidative processes (AOP) are successful in removing complex organic contaminants because they can achieve complete oxidation [16].AOP offer a distinct advantage over many conventional treatment methods, such as biological processes, because faster degradation rates are accomplished and contaminants are degraded rather than transferred from one phase to another.In addition, there is no requirement for by-product disposal [17].AOP processes can be configured using a combination of chemical and physical agents such as a combination of oxidizing agents, an oxidizing agent plus ultraviolet, catalyst or ultrasound and a catalyst plus ultraviolet [18].In all AOP processes, the degradation of organics is mediated by the generation of •OH radicals [19].Recent overwhelming research interest in using TiO 2 as a photocatalyst is attributed to its excellent abilities in completely degrading a wide array of organic compounds to CO 2 plus H 2 O [15,20,21].Hence, in the present work, TiO 2 was selected to examine the degradation of several phenolic compounds.Titanium dioxide exists primarily as anatase, rutile and brookite.In comparison to rutile and brookite, the anatase phase is catalytically more active [22,23].Factors such as the type of photocatalyst and the composition, light intensity, initial substrate concentration, amount of catalyst, particle size, pH of the reaction medium, ionic components in water, solvent types, oxidizing agents/electron acceptors, mode of catalyst application and calcinations temperature can affect the photocatalytic degradation of organic compounds [24].The impact of various factors on photocatalytic reactions has been reported in many studies; however, few studies have examined the interaction effects of different variables on process performance.Studies assessing the impact of interaction factors on TiO 2 photocatalysis are limited [25,26] and in an effort to address this knowledge gap, this work will examine the effects of TiO 2 particle size, temperature and the chemical structure of similar structures (phenol and mono-substituted isomers (cresol isomers)) on the photocatalytic degradation rate.
Response surface methodology (RSM) is a collection of statistical techniques used to develop, improve and optimize processes.RSM tools are useful in predicting the effect of individual experimental factors, as well as locating interactions between the factors.RSM has been used extensively to assess the impact of quantitative variables on a response variable [27][28][29]; however, the use of this technique is limited, especially in cases involving quantitative, as well as qualitative variables [30,31].The effect of single, squared and interaction terms on the response variable can be demonstrated using second order models.Examining the effects of quantitative, as well as qualitative variables on a response variable is routinely employed for analyzing data in disciplines such as science, social science and business [32,33].Developing response models using qualitative and quantitative factors have been reported in several studies [34][35][36]; however, the technique has not been applied extensively in science and engineering applications.
One objective of this study was to develop a statistical model that relates the apparent degradation constant to TiO 2 catalyst particle size, temperature and reactant structure and subsequently, to assess the effects of the different factors on the apparent degradation rate constant.Another objective was to determine the optimum TiO 2 particle size for the maximum degradation of phenol and mono-substituted phenol isomers (o-cresol and m-cresol) with respect to the activation energy of the photocatalyst.

Phenols and Cresols
Phenol (99% purity) and m-cresol (99% purity) were procured from Sigma-Aldrich (Oakville, ON, Canada).o-Cresol (99% purity) was purchased from Anachemia Chemicals Ltd. (Toronto, ON, Canada).The chemicals were stored at 21 °C, and stock preparations were prepared on an as needed basis.The stock solutions were covered with Aluminum foil and refrigerated.

Titanium Dioxide
TiO 2 nanoparticles were procured from Alfa Aesar (Ward Hill, MA, USA).The characteristics for the three different TiO 2 anatase nanoparticles are shown in Table 1.Stock water suspensions of the TiO 2 nanoparticles (10,000 mg L −1 ) were prepared and stored at 21 °C.The TiO 2 suspensions were pulse-sonicated at 20 kHz for 15 min using a VWR model 75HT sonicator (VWR, Mississauga, ON, Canada) to ensure homogeneous mixing prior to the reaction with the different reactants.

Experimental Design and Statistical Analysis
A three-factor, three-level full factorial design was conducted for a complete analysis of the different reaction conditions (Table 2).The change in structure between the different chemicals (phenol, o-cresol and m-cresol) was selected as the qualitative factor (z).The quantitative factors were temperature and particle size.The levels for temperature, a quantitative factor (x 1 ), were 23 °C, 30 °C and 37 °C, and the TiO 2 particle size levels (denoted as factor x 2 ) were 5 nm, 10 nm and 32 nm.The full experimental design is shown in Table 3. Statistical analysis of the data was conducted using Minitab 15 (Minitab Inc., State College, PA, USA) and Polymath 6.2 (Willimantic, CT, USA).Notes: 1 Experiments conducted at a wavelength = 300 nm; 2 The average and standard deviation for triplicate samples.Expt # = Experiment number.

Degradation Experiments
Photocatalytic reactions were performed using a modified Rayonet RPR-100 UV photocatalytic chamber (The Southern New England Ultraviolet Company, Branford, CT, USA) (Figure 1).In order to regulate and monitor the temperature, the photocatalytic chamber was placed in an environmental chamber set at 37 °C (MaxQ 5000, Barnstead, IA, USA).The photochemical reactor was constructed with 16 monochromatic phosphor-coated UV lamps on an outer perimeter (The Southern New England Ultraviolet Company, Branford, CT, USA).The lamps are capable of radiating 300-nm UV light.The irradiance (9 mW cm −2 ) was measured using a UVX Radiometer (UV Process Supply, Chicago, IL, USA).Prior to initiating the experiments, the lamps were turned-on for at least 1 hour to ensure that full intensity was achieved.
The reaction vessels (25 mm ID × 250 mm) were constructed from Pyrex ® and fused quartz tubing (UV transmittant clear fused quartz (GE 214, Technical Glass Products Inc., Painesville Twp., OH, USA)).The Pyrex ® upper portion of the vessel was connected to the fused quartz bottom using a graded seal (Technical Glass Products, Inc., Painesville Twp., OH, USA).The reaction tubes were wrapped in Aluminum foil before placing them in the reaction chamber, so as to prevent the initiation of the reaction from extraneous light sources.The tubes were placed on a 5-rpm carrousel in the reaction chamber.The 50-mL reaction mixture consisted of TiO 2 slurry (1 mg mL −1 TiO 2 ) and reactant (100 mg L −1 ).All the solutions were prepared with Milli-Q ® grade water.The TiO 2 concentration selected was based on work by Gogate and Pandit [16].The reactant level (100 mg L −1 ) was based on work from previous studies (Ray et al. [37]).Studies by Ray et al. [37] have concluded that the phenol degradation rate was optimum at concentrations ranging from 50 to 100 mg L −1 with a catalyst concentration of 1 mg mL −1 .The mixture was purged for 2 minutes with oxygen (BOC, Windsor, ON, Canada).After purging, the tubes were sealed immediately with Teflon ® septa and an Aluminum crimp cap (Cobert Associates, St. Louis, MO, USA).Next, the tubes were conditioned to the desired experimental temperature (30 °C or 37 °C) in an incubator (Blue M Electric Company, White Deer, PA, USA) for 10 minutes.
Immediately after initiating the reaction, a 1-mL sample was removed by inverting the reaction vessel.The sample was placed in an Aluminum foil wrapped vial and stored at 4 °C.In order to maintain a constant reaction volume and catalyst concentration, 1 mL of the 1 mg mL −1 TiO 2 slurry was injected into the reaction vessel.The reaction was initiated by removing the Aluminum foil wrap and placing the tubes onto a rotating carrousel in the vessel, which housed the reaction tubes.The contents of the tubes were mixed using magnetic stirrers.Samples were removed at 5-minute intervals.The sample tubes were centrifuged (IEC Centra-8, International Equipment Company, Nashville, TN, USA) at 4000 rpm for 8 minutes to separate the TiO 2 particles from the aqueous solution.After centrifugation, the clear centrate was removed and injected into 2-mL amber vials and stored at 4 °C.All experiments were conducted in triplicate.Controls were prepared under the following conditions: TiO 2 /no UV (dark), no TiO 2 /UV (photolysis control) and no TiO 2 /no UV (normalized control).Controls were prepared to assess the changes in the reactant concentration due to the addition of the TiO 2 slurry (1 mg mL −1 TiO 2 ) and UV.

Surface Area Measurements
The TiO 2 nanoparticle surface area (m 2 g −1 ) was determined using a Brunauer-Emmett-Teller (BET) gas adsorption technique in a Quantachrome NOVA 1200e surface area analyzer (Quantachrome Instruments, Boynton Beach, FL, USA).The instrument temperature was set at 77 K, and nitrogen (BOC, Windsor, ON, Canada) was the adsorbate.The relative pressure (P/P o ) range was 0.0 to 0.3.

Analytical Methods
Samples were analyzed using a Dionex UltiMate 3000 high-performance liquid chromatograph (HPLC) configured with an UltiMate photodiode array detector (PDA) (Dionex, Sunnyville, CA, USA) and a Dionex Acclaim™ 120 C18 3 μm 120Ǻ 2.1 × 100 mm analytical column (Dionex, Sunnyville, CA, USA).The oven temperature was set at 45 °C.The phenol analysis was isocratic and was conducted using an eluent consisting of acetonitrile (20%) (HPLC grade, Burdick & Jackson, Muskegon, MI, USA) plus Milli-Q ® water (80%).The flow rate was set at 0.4 mL min −1 with a sample injection volume of 25 μL.The analysis was conducted at 191, 210, 226 and 274 nm.The detection limit for phenol was 5 μg L −1 .The analysis of o-cresol and m-cresol was conducted under isocratic conditions using an acetonitrile (40%) plus Milli-Q ® water (60%) mixture.The flow rate was set at 0.4 mL min -1 with a sample injection volume of 25 μL.The analysis was conducted at 210, 226 and 273 nm.The detection limits for m-and o-cresol were 8 μg L −1 and 5 μg L −1 , respectively.All degradation experiments were conducted at an initial pH of 7 [38].The pH of the reactor solution was adjusted to pH 7 before the reaction using 1 M HCl and 1 M NaOH.The pH was not adjusted during the reaction.The pH was determined using a pH meter (Symphony, VWR, Mississauga, ON, Canada).

Optimization Study
A response surface optimization study was conducted using the data from Table 3.In this study, the response variable is the apparent degradation rate constant (k).A modified second-order model (Equation ( 1)) proposed by Draper and John [34] was used to correlate the experimental variables (reactant type (z), temperature (x 1 ) and TiO 2 particle size (x 2 )) with the response, k′.
Y is the predicted response; β o is a constant; β I is the linear coefficient; β ii is the squared coefficient; β ij is the cross-product coefficient; and i and j are the index numbers for pattern, x 1 , x 2 ,…, x k .The quantitative factors are designated by x. is a constant due to the qualitative factor, , and is the coefficient for the term.ɛ is the random error.
For 2 quantitative and 1 qualitative factor, Equation (1) becomes: Polymath 6.2 (Willimantic, CT, USA) was used to analyze the data and to develop the model.An analysis of variance (ANOVA) was performed to evaluate the model.The D-optimality index was used to establish optimum conditions for maximizing the degradation rate constant [26].Validating of the model was conducted by correlating the predicted and experimental degradation rate constants and using the Anderson-Darling (AD) statistic [39].

Photolytic and Photocatalytic Degradation
A comparison of the different light and dark conditions (TiO 2 /no UV (dark control), no TiO 2 /UV (photolysis) and TiO 2 /UV (photocatalysis)) was used to demonstrate the importance of irradiating the aqueous system containing the TiO 2 catalyst and reactant with UV light.Phenol degradation was examined under all of the conditions ((TiO 2 /no UV (dark control), no TiO 2 /UV (photolysis) and TiO 2 /UV (photocatalysis)) (Tables 3 and 4, Figure 2).The residual concentration profile indicated very little catalytic activity in controls with TiO 2 and no exposure to UV.In the presence of UV plus the TiO 2 catalyst, the increase in phenol degradation was greater when compared to the system containing only the TiO 2 catalyst.The trend observed for phenol under the different reaction conditions shown in Figure 2 was similar to the data for m-cresol and o-cresol [40].The dependence of the photolytic reaction as a function of temperature for the different reactants is shown in Table 4. Dark controls were used to assess the significance of UV light and TiO 2 on the degradation of a reactant.In the absence of light, the photocatalyst should remain inactive, since there were no photo-generated electrons to mediate the degradation of the reactant.Therefore, any observed degradation would be attributed to the adsorption onto the catalyst.Dark controls were prepared for all experimental conditions and in all of the conditions examined, the reactant profiles were similar.
The reactant concentration for the dark controls was reduced by approximately 3% over a one-hour sampling period.Hence, phenol removal due to adsorption with subsequent degradation was minimal and did not contribute significantly to the photocatalytic process.A careful examination of the data in Tables 3 and 4 strongly suggests that photocatalysis, as well as photolysis mediated the degradation of the reactants when TiO 2 was activated by UV.
The rate constant, k 1 (min −1 ), hereafter referred to as the apparent degradation rate constant, is considered as the response.The integrated first-order kinetic expression (Equation ( 4)) ((-) ln (C/C o ) versus time (mins) is plotted for the following conditions: (1) the absence of TiO 2 and the presence of UV (photolysis); and (2) the presence of TiO 2 plus UV (photocatalysis) for the three reactants (Figure 3).The experimental apparent degradation rate constant was determined from the slope of Equation (3).Least-squares regression values (r 2 ) of the degradation rate constant data for phenol, m-cresol and o-cresol photolysis (r 2 > 0.9747) and photocatalysis (r 2 > 0.9372) suggest a reasonably good fit between ln (C/C o ) and time.Though the residual reactants concentrations were used to evaluate the degradation process, it should be noted that total organic carbon (TOC) removal measurements are also suitable.

Figure 3.
First-order kinetic plots for photolytic and photocatalytic studies using 300 nm.The experimental conditions were as follows: (a) phenol, 5-nm TiO 2 and 37 °C; (b) m-cresol, 5-nm TiO 2 and 37 °C; and (c) o-cresol, 5-nm TiO 2 and 30 °C (see Table 3).Values are the average and SD for triplicate.An example plot for phenol degradation using different catalyst particle sizes is shown in Figure 3.The 27 conditions examined and the response variable are shown in Table 3.In the presence of the 5 nm-and 10 nm-sized TiO 2 catalyst, a substantial increase in the apparent degradation rate constant clearly indicate the addition of a catalyst coupled with UV increased the degradation of phenol, m-cresol and o-cresol.The apparent degradation rate constants for reactions conducted with 32-nm TiO 2 particles showed a relatively small increase in the photocatalytic activity when compared to photolysis.

Effect of the Variables on the apparent degradation constant
The impact of various reaction variables on the UV/TiO 2 photocatalytic degradation of substrates, such as di-(2-ethylhexyl) phthalate (DEHP) and dibutyl phthalate (DPB), has been extensively reported in several studies using a one-factor-at-a-time approach [41][42][43].Employing a one-factor-at-a-time approach is problematic because the interaction between different factors could also affect the response variable.In the present work, the effect of three experimental factors on the apparent degradation rate constant was examined.A rise in the apparent degradation rate constant with increasing temperature was observed for phenol, m-cresol and o-cresol at each particle size (5, 10 and 32 nm) (Figure 4).The increase in the degradation rate constant was most likely due to the enhanced collision frequency with increasing reaction temperature [41].Note for the three particle sizes under consideration, the average value for the change in the rate constant (min −1 ) per °C rise for phenol, m-cresol and o-cresol was 0.00005-0.0001,0.0008-0.0002and 0.0005-0.0003,respectively.The largest change in the rate constant (min −1 ) per °C was associated with o-cresol.Increasing the temperature by 14 °C caused the phenol degradation rate constant to increase by approximately 60% for the 5-nm particles; however, no significant increase was observed for the substituted phenols.An optimum apparent degradation rate constant was observed for 10-nm particles with phenol, m-cresol and o-cresol (Figure 4).This trend is in agreement with studies which have examined the relationship between particle size and photocatalytic reactivity.Increasing the ) photocatalytic activity with decreasing particle size for TiO 2 nanoparticles containing anatase and rutile in various proportions was demonstrated in studies by Almquist and Biswas [44].This trend could be attributed to the off-setting contributions of a high surface area, as well as changes in the structural and electronic properties of the TiO 2 as the particle size decreases in the nanometer scale [43].Similar work with anatase concluded that 11-nm TiO 2 particles yielded the highest photonic efficiency [45].According to Zhang et al. [46], TiO 2 nanoparticles less than 10 -nm have a tendency to form stable agglomerates in aqueous solution.These agglomerates are classified as primary and secondary particles and denoted as non-aggregated and aggregated particles, respectively.Studies by Zhang et al. [46] and Lin et al. [47] have shown that the degradation rates for primary particles are greater than those for secondary particles.Lower surface areas are associated with aggregates when compared to the individual particles and hence, lower reaction rates are expected with increasing the size of the agglomerates.In this study, similar or lower reaction rates for the 5-nm TiO 2 nanoparticles in comparison to the 10-nm nanoparticles was likely associated with the formation of aggregates [46].The data clearly indicate that an increase in the apparent degradation rate constant resulted in greater photocatalytic efficiency.The optimum apparent degradation rate constant observed with 10-nm particles is similar to work reported by Ray et al. [27] for phenol degradation by 9-nm nanoparticles.
The selectivity of the TiO 2 catalyst for the different substrates is reflected by the change in the apparent degradation rate constant with the substrate chemical structure.Increasing the apparent degradation rate constant for the different substrates was as follows: o-cresol > m-cresol > phenol, for each particle size (Figure 4).The differences in the apparent degradation rate constant between phenol and the cresol isomers could be explained by examining the intermediates formed during the degradation pathway.The degradation mechanism is dependent on the position of the substituted methyl group relative to the OH group on the benzene ring.The addition of •OH radicals in the photocatalytic oxidation process proceed by an electrophilic addition reaction [48].According to Bhatkhande et al. [20], different intermediates are produced depending on the position of the substituted group with respect to the OH position on the benzene ring.During the hydroxylation of cresols, the ortho site between the OH and methyl functional groups in m-cresol are susceptible to attack by •OH radicals.Hence, only three sites are available to react with the •OH radical [17].A reduction in the number of available sites for •OH attack in the m-cresol structure when compared to o-cresol could be a possible cause for the lower apparent degradation rate constant.

Combined Effects of the Experimental Variables
The apparent degradation rate constants for all of the photocatalytic experiments (Table 3) were statistically analyzed to assess the effects of the experimental variables on the apparent degradation rate constant.The ANOVA analysis (Table 5) indicates that the factors under consideration on the apparent degradation rate constant are significant at a 95% level of confidence.The p-values for particle size, temperature and reactant suggest that they were significant.An interaction was observed only for a paired combination of particle sizes.No mixed interaction terms were significant within the factor space evaluated because the p-values for the terms were >0.05 at a 95% level of confidence.Contour plots were generated to determine the relationship between the factors.The optimum conditions that resulted in the maximum photoactivity conditions for effective degradation are shown in the contour plots.The contour plots were developed using Equation (6).The contour lines represent values of the apparent degradation rate constant in terms of a combination of factors including temperature versus reactant (Figure 5a), particle size versus reactant (Figure 5b) and particle size versus temperature (Figure 5c).An increase in response is observed with increasing coded values for temperature and reactant (Figure 5a).A maximum apparent degradation rate constant value is indicated on each contour plot at the optimum condition for each factor (temperature, particle size and reactant).The particle size versus temperature contour plot (Figure 5c) indicates the highest rate at 37 °C and a particle of approximately 10 nm for the three reactants (phenol, m-cresol and o-cresol).The contour plot for particle size versus reactant (Figure 5b) demonstrates the impact of the structural properties of the reactant on the degradation rate constant.Under the different temperature conditions (23, 30 and 37 °C), the degradation rate trend for the different reactants was as follows: o-cresol > m-cresol > phenol.The effectiveness of the different factors on influencing the degradation rate constant was the particle size followed by the reactant structure and then temperature (Figure 4).The two-factor interaction plot (Figure 6) suggests no significant interaction between the different factors.Note that the intersecting profiles indicate factor interaction, while parallel profiles are an indicator that the factors are independent.

Model Development
A quadratic polynomial was developed to relate the coded factors and the response using Polymath.Minitab was used to model the data based on selected second-order (quadratic) model.The regression analysis was conducted using coded units (Table 2).The ANOVA data is shown in Table 5.The regression model (Equation ( 5)) explained 97.33% of the variation in the degradation rate constant values.The predicted R 2 of 0.9362 is in reasonable agreement with the adjusted R 2 of 0.9615.The model is predictive, since the calculated F-value (82.1) is greater than the critical F-value (3.4).This shows that the model equation is reliable within the range of factors under consideration.This model (Equation ( 5)) contains insignificant and significant terms in the quadratic equation.The modified model equation (Equation ( 6)) was developed by neglecting the insignificant terms in the quadratic equation (Equation ( 5)) (Table 3).The predicted values based on the modified model are depicted in Table 5.The predicted values obtained from the two equations (Equations ( 5) and ( 6)) are shown in Figure 7.The comparison indicated no significant difference between the predicted response values for the two models (Figure 7).k = 0.10985 + 0.00833 x 1 -0.00266 x 2 + 0.00189 x 1 2 -0.003994 x 2 2 -0.000158 x 1 x 2 + 0.001672 z -0.000200 z x 1 + 0.000392 z x 2 (5) k′ = 0.01111 + 0.00833 x 1 -0.00266 x 2 -0.00399 x 2 2 + 0.01672 z (6) In this study, the D-optimal criterion was employed to determine the maximum degradation rate.The D-optimal criterion selects design points from a list of candidate points, such that the variances of the model regression coefficients are minimized.MINITAB (Minitab inc., State College, PA, USA), a statistical software program, was used to generate the optimal value.The D-optimality index varies between zero (worst case) and one (ideal case) for all of the factors.The software searches for all possible factor settings and computes a value for the largest D-optimality value.A D-optimality of 0.98 with a maximum response value of 0.0141 min −1 was recorded for o-cresol at 37 °C and a TiO 2 particle size of 11 nm (Figure 8).In comparison, for the experiment conducted with o-cresol at 37 °C and a 10-nm particle size catalyst, the response was 0.0128 min −1 with a standard deviation of 0.005 min −1 .The experimental response was approximately 9.2% less than the predicted maximum response of 0.0141 min −1 .

Assessment of the Model
A plot of the experimental rate constant values versus the model predicted values provided an indication of the goodness of fit (Figure 7).An R 2 value of 0.9626 for the modified model (Equation ( 6)) indicates a reasonable fit.The Anderson-Darling (AD) test was also used to determine the adequacy of the model.The AD statistic for Equation (6) (Figure 9) confirmed a normal-fit for the probability distribution of the residuals.The calculated AD statistic (0.139) was less than the critical value of 0.799 for a sample size of 27 and the associated p-value (0.971) of the AD statistic was significant at a 5% level (greater than 0.05) [49].A lower value of the computed AD statistic compared to the critical value confirmed a normal-fit for the probability distribution of residuals.From this analysis, it appears that the response surface regression model is able to predict the photocatalytic degradation of phenol, m-cresol and o-cresol within the temperature range for TiO 2 catalysts diameter ranging from 5 to 32 nm.

Activation Energy
A catalyst functions by increasing the reaction rate and lowering the activation energy.Studies by Pande et al. [50] have shown that 15-nm Cu 2 O nanoparticles are able to reduce the activation energy by approximately 71 kJ mol −1 and hence, increase the reaction rate by 2.4 × 10 7 -fold.The reaction rate constant, k app , can be derived from the Arrhenius equation (Equation ( 7)).

RT
where k app is the rate constant; A is a constant; E a is the activation energy; R is the universal constant and T is temperature (K).The activation energy (E a ) was obtained from a plot of ln k app versus 1/T.The activation energy data tabulated in Table 6 show activation energies as a function of particle size and substrate.No significant correlation between the activation energies and catalyst particle sizes was observed for the three reactants.Evidence by Musselwhite et al. [51] has shown that the activation energies for cyclohexenone hydrogenation by 2.9-7.1 nm colloidal platinum nanocatalysts were similar irrespective of the catalyst particle size.However, studies by other researchers have reported conflicting data.Shah et al. [52] claim that decreasing catalyst particle sizes correlated with decreasing activating energies, while studies by Patil et al. [53] show a proportional increase in activation energy with increasing particle size for the degradation of Congo red dye.Photocatalytic activation energies typically range from 5 to 15 kJ mol −1 in aqueous solutions [54].The activation energies reported for the catalytic degradation of selected chemicals with the Degussa P25 catalyst range from 13.6 to 24.8 kJ mol −1 (Table 7).In this study, the activation energies for o-cresol, m-cresol and phenol (7.0 to 17.1 kJ mol −1 ) are comparable to those from previous studies.For m-cresol, a statistical analysis using Tukey's method revealed a significant difference between the activation energy for the 5-nm particle in comparison to those for the 10-nm and 32-nm particles (activation energies labeled with superscripts a and b) (Table 6).When comparing the activation energies for different particle sizes, no significant statistical difference was observed for phenol and o-cresol.A significant statistical difference between the activation energies for o-cresol versus m-cresol and phenol was observed for 5-nm and 10-nm particle size catalysts.For the 32-nm particle size catalyst, the activation energies (superscript c) were statistically the same for phenol, m-cresol and p-cresol.Notes: All values are averages for triplicate samples; data set pairs labeled using dissimilar letters (a, b) within the same columns are statistically different at a 95% confidence interval using Tukey's procedure [49]; data set pairs labeled using dissimilar numbers (c, d) within the same rows are statistically different at a 95% confidence interval using Tukey's procedure [49].
Table 7. Activation energies for selected reactants using Degussa P25 catalyst.

Conclusions
The novel modeling technique used and described in this study can be used in similar studies involving the use of both quantitative and qualitative factors.The study indicated that effluents containing phenol, o-cresol and m-cresol mixtures within the levels under consideration were treatable using TiO 2 photocatalysis.The optimum values of experimental factors were determined for the maximum degradation of the three compounds.The optimum values of the factors indicated can be adopted for further laboratory experiments and pilot-scale organic pollutants removal processes.
The conclusions from this study are as follows: 1.Ten nanometer diameter TiO 2 particles combined with an operating temperature of 37 °C were the optimum conditions to effectively degrade the reactants.2. The apparent degradation rate constant trend for the reactants was as follows: o-cresol > m-cresol > phenol.
3. No interaction effects were observed between the experimental factors (particle size, temperature and reactant).The interaction was observed only for a paired combination of particle sizes.4. The modified response surface regression model was adequate for relating the apparent degradation rate constant to the experimental factors within the range of conditions under consideration.5.The apparent degradation rate constant followed an Arrhenius temperature dependence with an increasing linear trend for the three reactants.6.The activation energy was lowest for the degradation of o-cresol using 10-nm TiO 2 particles.
Similar studies with immobilized TiO 2 nanoparticles are recommended for future work and pilot-scale studies are required before commercial application.

Figure 2 .
Figure 2. A comparison of the residual concentration profiles for phenol under the following conditions: (a) 5-nm TiO 2 particles; (b) 10-nm TiO 2 particles; and (c) 32-nm TiO 2 particles.Temperature = 30 °C, and wavelength = 300 nm.Values are the average and SD for triplicate samples. PhotolysisPhotocatalysis

Figure 4 .
Figure 4. Main effect plots for the experimental factors.

Figure 5 .Figure 6 .
Figure 5. Contour plots of the apparent degradation rate constant for (a) temperature versus reactant; (b) particle size versus reactant; and (c) particle size versus temperature.

Table 1 .
The TiO 2 catalyst surface area.

Table 3 .
Photocatalytic reaction apparent degradation rate constants for different experimental conditions.
1Average and standard deviation for triplicate samples; 2 SD = standard deviation.

Table 5 .
ANOVA results for the experimental response at different factor levels.

Table 6 .
Activation energies for o-cresol, m-cresol and phenol for different TiO 2 particle sizes.