Evaluation of kinetic pseudo-order in the photocatalytic degradation of ofloxacin

: Ofloxacin is an extensively used efficient antibiotic. However, since it is a refractory pollutant, it is found in water sources, requiring methods to remove it from the environment. Advanced Oxidation Processes (AOPs) offer efficient alternatives since it yields complete degradation not achieved in adsorption or membrane processes. Kinetics of degradation process require monitoring the "pseudo-order" of it to deliver evaluation of the proposed AOPs. Most studies assume ofloxacin degradation follows pseudo-first or -second order processes, whereas for full removal of refractory pollutants – lower pseudo-orders are required. This study presents a simple procedure to evaluate pseudo-orders of AOPs. Photolysis of 20  M ofloxacin follows pseudo-zero order, with half-life time (t 1/2 ) of ~ 60 min. Very low TiO 2 concentration in heterogeneous catalysis (0.2 mg L -1 ) has no influence but increasing catalyst to 2.0 mg L -1 reduces t 1/2 to 20 min, increasing pseudo-order to 0.8. Similar results are obtained with 2.0 mg L -1 H 2 O 2 homogenous catalysis. Combining H 2 O 2 with TiO 2 reduces t 1/2 , but pseudo-order increases further (1.2). The conclusions are (1) ofloxacin can be effectively degraded by both heterogenous and homogenous photocatalysis, (2) combined photocatalysis yields higher pseudo-order, being less prone to achieve full removal, (3) analysis of specific pseudo-order in AOPs of refractory pollutants helps to further elucidate the efficiency of the process presented.


Introduction
Ofloxacin (OFL) is a third-generation fluoroquinolone antibiotic, that has been extensively used to prevent or treat human and animal bacterial infection due to its broadspectrum antibacterial properties [1]. Accordingly, it was found at significant concentrations in surface water and wastewater treatment plants (up to 1.8 g L -1 ), and even 20 folds larger concentrations in hospital effluents [2]. It is considered refractory to biodegradation [3], thus it requires specific and effectives methods to remove it from the environment. Advanced Oxidation Processes (AOPs) may offer an effective alternative to remove refractory pollutants in water [4]. AOPs in general and photocatalysis in particular are widely studied and reviewed [5] due to advantages as high efficiency, low cost, practicality, and environmental friendliness. An important superiority over other methods as adsorption, membrane separation or flocculation is that those cannot completely decompose pollutants and they only separate them from the water, whereas AOPs-if performed effectively-yields complete decomposition of the organic pollutants [6].
Several studies on AOP processes for the removal of refractory fluoroquinolone antibiotics in general and OFL in particular were reported in the last years. This includes direct photochemistry (photolysis) [7] and the influence of natural colloids on it [1], photocatalytic degradation combining UV/TiO2 and UV/TiO2/H2O2 [2], use of photo-assisted microbial fuel cells with LiNbO3/CF photocatalytic cathodes [8], UV combined with hydrogen peroxide or persulfate [9,10], heterogenous persulfate catalysis with Mn doped CuO particles [11] or MnCeOx composites [4]. Fenton based processes combining MnFe2O4 magnetic particles [3], ozonation and peroxone processes [1] were found also successful.
Such vast amounts of research during the last years is ascribed to the environmental importance of removing low concentration of such refractory antibiotics from water. In the process of describing the degradation achieved by such AOPs, usually "rate laws" are developed. Rate laws describe the relationship between the concentrations of reactants and the rate of a specific reaction. In most cases such laws helps to elucidate the full kinetic process, and in some cases-even the mechanism [12]. A full rate law should include the concentrations of all the reactants in a process. For example, Batakliev et al. [13] present a series of proposed mechanisms for the decomposition of ozone, considering all possible participants including light, free electrons, molecular and atomic oxygen, and even "third particles" (additional chemicals or compounds. Such full mechanism rate laws are usually complicated, and include several experimentally determined rate coefficients, and the concentrations of all participants influencing at different orders, whereas the "kinetic order" of a participant is an experimentally determined parameter, defined as "the power dependence of the rate on the concentration of each reactant" [14].
When the focus is mostly on one of the components of the process, as in the catalyzed degradation of refractory pollutants as ofloxacin, and all other participants in the reaction are in non-limited amounts, and/or kept constant, a simpler rate law might be defined as [15]: where is the reaction rate, kapp is the apparent rate coefficient, A is the concentration of the pollutant in case, and napp is the apparent or "pseudo" reaction order [16,17]. The term "apparent" or "pseudo" is used to acknowledge the fact that all other influencing parameters (catalyst/degradation agent, temperature, light, etc.) were kept constant [18]. In most cases the to allow comparison between parameters in different reaction mechanisms, the dimensionless "relative concentration at time t" is defined as [A](t)= Ct/C0 (the ratio of actual to initial concentration).; thus A0 = 1. This is convenient since it yields apparent kinetic coefficients that always have dimensions of time -1 , regardless of the order of the process [19].
Equation (1) can be easily integrated if napp≠1, and the concentration at time t can be calculated if the kinetic rate coefficient kapp and the pseudo-order napp are known, using And for the specific case of pseudo-first order, were napp=1, the integration yields: Since it is impossible to numerically compare kinetic rate coefficients for different pseudo-order processes, it is helpful to define the time taken for the concentration of a reactant to fall to half its initial value as the "half-life time" (t1/2) [17] . Half-lives times can be evaluated by solving mathematically Eq. And for napp=1: It is interesting to note that for all orders except napp=1, half-life times strongly depends on the initial concentration. Thus, when interested in the degradation of a refractory pollutant, the rate law is crucial for the determination of the efficiency of the process. In this sense, the specific pseudo-order of the pollutant is of course important.
In most studies presenting degradation of OFL, the order is found empirically by fitting the relative concentration (Ct/C0) at several times of measurement to a pseudo first or even pseudo second order process [1,4,6,7,10,11,20]. In all those cases the fit is based on 5-10 experimental data points. However, it should be emphasized that high pseudo-orders yield higher degradation rates ( [ ] ) and lower half-life times at large concentrations, but at very low pollutant concentrations -lower orders yield better performance. For example, consider different suggested degradation processes yielding the same half-life times at an initial pollutant concentration of 1 μM: If the process is pseudo-first order, halflife time will remain constant, independent from the initial concentration (see Eq.3). However, this is will not be the case for a "pseudo second order" or a "pseudo-zero order" (see Eq.2). If the initial concentration increases by ten folds to 10 μM, the half-life time of the pseudo second order will indeed be beneficiated and decrease by 10-fold. But if the initial concentration is very low (for example 0.01 μM) the half-life time will increase 100 times, yielding almost no efficient degradation. On the other hand, for the "pseudo zero order" process, reaction rate will remain unchanged, and half-life times at the low concentration will be reduced 100 fold-thus at lower concentration such low order processes should be preferred [21]. This study focuses on the photocatalytic degradation of OFL by combining UV/TiO2, UV/ H2O2 and UV/TiO2/H2O2, and in this sense it is similar to previous studies [2], although our work was performed at considerably lower catalysts concentration. The studyt also presents a procedure that allows to better evaluate the pseudo-order of degradation processes in general, and by that-might allow relatively objective comparison of the efficiency of refractory pollutants removal using AOP processes.

Optimization procedure
The optimization procedure to find the pseudo-order that exhibits the best fit to each of the treatments was performed as described in Rytwo et al. [21]: From the large amount of data (120-250 data points) in each experiment, a "bootstrap" [22,23] procedure was performed by choosing 5 sets of 20 values for each experiment. Values of kinetic rate coefficient (kapp) and pseudo-order (napp) were found by evaluating [A](t) using Eq. (2) and finding to each treatment the best possible parameters using the "Solver" algorithm in Excel® software, to minimize the root mean square error (RMSE) between all measured and calculated [A](t) values in the treatment. Half-life times were evaluated with Eq.(3). Such procedure yielded the pseudo-order that yields the best fit, and its relevant half-life time. As a comparison a similar procedure was perform fixing pseudo-orders to 0, 0.5, 1 and 2, and finding the optimal kapp (and accordingly, t1/2) for each fixed pseudo-order. As can be understood, RMSE for those evaluations-based only on optimization of kapp and without optimizing napp-were considerably higher than in the cases when optimizations were evaluated based on both kapp and napp. All calculation results are concentrated in Table 1. It should be noted that since the ranges of values for Ct/C0 are 0-1, RMSE values for the best fit are indeed very low (<0.0001), as can be observed also from the fact that measured and best lines in Figs. 1-5 are in complete match.

Photolysis
The photodegradation of OFL at an initial concentration of 20 µM (7.23 mg L -1 ) with no catalysts (photolysis experiment) is shown in Figure 1. Red squares show the experimental measured results, whereas lines are evaluated as described in section 2.1. Note that dashed line describing the best fit is directly above measured results, making it very difficult to distinguish between them. As shown in Table 1, the best fit is at a pseudo-order of ~0.3, thus pseudo-orders of 0 and 0.5 exhibit also a quit close fit, with relatively low RMSE values. Half-life time as evaluated from kinetic coefficient and pseudo-order (Eq. (3)) yields approximately 59.2 min, and the sensitivity of this parameter to the pseudo-order is not very significant for all the range of pseudo-orders 0-1. It can be seen that high pseudo-orders (1,2) deliver underestimate at high relative concentrations and overestimate the remaining concentrations at low relative concentrations.  Table 1).  Table 1).

Heterogenous photocatalysis with low concentration of TiO2
TiO2 is the most popular photocatalyst for the photodegradation of organic refractory pollutants [20]. In most heterogenous photocatalysis based AOP processes, concentration of the catalyst is from tens to thousands mg L -1 [24]. Figure 2 shows photodegradation of a 20 µM OFL solution, under UV irradiation, with the addition of high quality catalytic TiO2 as a heterogeneous catalyst, at very low concentration (0.2 mg L -1 ). It should be mentioned that such low concentration has been found to be relatively effective in the photocatalysis of bisphenol-S [21]. However, in this case such catalysts concentration does not exhibits any improvement when compared with photolysis without catalysts, and half-life times and pseudo-orders are almost the same for both treatments. Figure 3 shows photodegradation of a 20 µM OFL solution, under UV irradiation, with the addition of 2 mg L -1 = 58.8 M H2O2 as homogenous catalyst. It should be emphasized that this is a very low concentration compared with the added in most previous studies [1][2][3]11,25]. However, in another recent study on photodegradation of BPS [21], such H2O2 concentration lowered t1/2 to about half of the photolysis value. In this case, the effect is even more impressive, and t1/2 is lowered from almost 1 h to ~21 min. On the other hand, pseudo-order increases to about 0.7. Lower pseudo-orders (0, 0.5) underestimate the remaining concentration at large irradiation times (and low remaining relative concentrations), whereas a high pseudo-order (2) overestimates it.  Table 1).

Heterogenous photocatalysis with high concentration of TiO2
Considering (as mentioned in 2.2.2) that in most cases the usually used concentration of heterogeneous catalysts is relatively high, we tested degradation of 20 µM OFL solution, under UV irradiation, with the addition of 2 mg L -1 high quality catalytic TiO2, and results are shown in Figure 4. As can be seen from Table 1, t1/2 is similar to the one obtained with 2 mg L -1 H2O2, but the pseudo-order is slightly higher (0.83 instead of 0.70). It is interesting to compare the results with the previous experiment reported in 2.2.2, with one order of magnitude lower amount of TiO2: at the low concentration no effect at all was observed, and results were almost identical to those obtained with no catalyst at all. Not in all cases higher amount of catalysts lead to more effective process: In the degradation of BPS lowering the concentration of TiO2 indeed reduced the efficacy, but in clay based catalysts it improved considerably the efficiency of the process by lowering both t1/2 and napp [21], presumably due to reduced light dispersion by the colloids in suspension [26].
It should be mentioned that such clay-based catalysts where also preliminary tested for the photodegradation of OFL but were found completely ineffective (results not shown). Thus-photodegradation processes, as any other water treatment method, are very specific, and an efficient catalyst for one pollutant might be completely ineffective for other.  Table 1). Figure 5 shows photodegradation of a 20 µM OFL solution, under UV irradiation, with the addition of 2 mg L -1 each-H2O2 and TiO2. It is interesting to notice that combination of both catalysts changes the process and yields a considerably higher value of pseudo-order (~1.2 instead of 0.7-0.8). A decrease in the half-life time is observed (from ~20 to 16 min), but a detailed observation of the results leads to the conclusion that if the purpose in the end is full removal of OFL, the combination of H2O2 and TiO2 is as the matter of fact less effective than when the catalysts are added separately. For example, if we compare Figs. 3, 4 and 5, we can see that at t≈65 min the measured concentration in the combined H2O2 and TiO2 process is approximately 11% of the initial concentration, whereas in Fig.4 when there is only TiO2, remaining OFL is only about 7.5%, and with H2O2 alone- (Fig.3) only 5.4%. This happens even though t1/2 for the combined process is 16.3 min compared to 19.8 or 20.7 min for TiO2 or H2O2 alone, respectively. This simple example emphasizes that the conception at first sight that higher pseudo-orders should be preferred-is erroneous, and for effective complete removal the benefits of lower pseudo-orders are significant.  Table 1).

Methods
The degradation of ofloxacin in all experiments was measured in batch experiments in a 100-mL UV-C-transparent quartz glass (refractive Index n = 1.5048), 5.3-cm diameter beaker placed in a Rayonet RMR-600 mini photochemical chamber reactor (Southern New England Ultraviolet Company, Branford, CT, USA), as described in previous studies [15,21,27]. The photoreactor was equipped with eight RMR 2537A lamps (254 nm wavelength), each lamp emitting an average irradiance flux of 19 W m -2 at 254 nm, equivalent to an overall intensity of 152 W m -2 , as measured in the center of the chamber using a Black Comet SR spectrometer with an F400 UV-VIS-SR-calibrated fiber optic probe equipped with a CR2 cosine light receptor (StellarNet Inc., Tampa, Florida, USA). The same spectrometer was used to measure the spectrum of the solutions during experiments using a 20 mm pathlength DP400 dip probe cuvette placed inside the beaker. The solutions were constantly mixed with an external stirrer (VELP Scientifica, Usmate Velate, Italy) rotating at 100 rpm. Spectra were measured using the SpectraWiz software (Stellar-Net Inc., Tampa, Florida, USA) every 10-20 s for 50-70 min. Data was transformed to comma separated values (CSV) files, and absorption at the maximum absorption band of OFL (288 nm, 288=24240 M -1 cm -1 ) was downloaded after subtracting a baseline value at 450 nm. To allow comparisons between parameters in different reaction mechanisms, the "relative dimensionless concentration at time t" [A](t) was evaluated [28] as Ct/C0 = ODt/OD0 (the ratio of actual to initial concentration, or actual to initial light absorbance); thus A0 = 1. Such procedure led to >120-250 data points for each experiment. Analysis of the data was performed as described in subsection 2.1. The experiments performed were as follows:

•
This study aims to present photocatalyzed degradation of the refractory antibiotic ofloxacin while emphasizing the importance of determining the specific pseudo-order of a process in the advanced oxidation photocatalysis of refractory pollutants. • OFL can be photo catalytically degraded in minutes, depending on the pollutant concentration and the specific process chosen (e.g., type of catalyst and its concentration, type of light and its intensity, etc.). Of course that other compounds in solution may interfere and delay or in some cases even accelerate the degradation [15].

•
The general assumption in most reported studies that AOPs are pseudo-first or pseudo-second order process, should be further examined. In this study, for example, all processes were neither pseudo-first nor -second order. Furthermore, it should be considered that at low concentrations a low pseudo-order can achieve completely removal, whereas a high pseudo-order process will lower pollutants concentration faster at the beginning but leave remains of pollutant in the treated water.

•
Anachronistic linearizations performed in the past to determine the kinetic coefficients, are no longer required, and might be avoided even by using relatively simple and available worksheet software packages, as presented in this study-or using relatively simple computer codes. A simple worksheet for the evaluation of pseudoorders and half-life times when concentrations at different times along the degradation process are known was added to this manuscript and is available as "supplementary material".

Supplementary Materials:
The following are available online at www.mdpi.com/xxx/s1, Worksheet W1: An example of kinetic parameters determination using "Solver" by Excel® Data Availability Statement: All raw data can be available from the authors.