Kinetic Studies on the Catalytic Degradation of Rhodamine B by Hydrogen Peroxide: Effect of Surfactant Coated and Non-Coated Iron (III) Oxide Nanoparticles

Iron (III) oxide (Fe3O4) and sodium dodecyl sulfate (SDS) coated iron (III) oxide (SDS@Fe3O4) nanoparticles (NPs) were synthesized by the co-precipitation method for application in the catalytic degradation of Rhodamine B (RB) dye. The synthesized NPs were characterized using X-ray diffractometer (XRD), vibrating sample magnetometer (VSM), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and Fourier transform infra-red (FT-IR) spectroscopy techniques and tested in the removal of RB. A kinetic study on RB degradation by hydrogen peroxide (H2O2) was carried out and the influence of Fe3O4 and SDS@Fe3O4 magnetic NPs on the degradation rate was assessed. The activity of magnetic NPs, viz. Fe3O4 and SDS@Fe3O4, in the degradation of RB was spectrophotometrically studied and found effective in the removal of RB dye from water. The rate of RB degradation was found linearly dependent upon H2O2 concentration and within 5.0 × 10−2 to 4.0 × 10−1 M H2O2, the observed pseudo-first-order kinetic rates (kobs, s−1) for the degradation of RB (10 mg L−1) at pH 3 and temperature 25 ± 2 °C were between 0.4 and 1.7 × 104 s−1, while in presence of 0.1% w/v Fe3O4 or SDS@Fe3O4 NPs, kobs were between 1.3 and 2.8 × 104 s−1 and between 2.6 and 4.8 × 104 s−1, respectively. Furthermore, in presence of Fe3O4 or SDS@Fe3O4, kobs increased with NPs dosage and showed a peaked pH behavior with a maximum at pH 3. The magnitude of thermodynamic parameters Ea and ΔH for RB degradation in presence of SDS@Fe3O4 were 15.63 kJ mol−1 and 13.01 kJ mol−1, respectively, lowest among the used catalysts, confirming its effectiveness during degradation. Furthermore, SDS in the presence of Fe3O4 NPs and H2O2 remarkably enhanced the rate of RB degradation.


Introduction
Mushrooming industrialization and urbanization are primarily responsible for deteriorating the surface and sub-surface water quality, causing hazardous effects on both aquatic organisms and human health. Among water contaminants, dyes and pigments, which are widely discharged from textile, pharmaceutical, paint, rubber, cosmetic, and confectionary industries effluents [1,2], pellets (NaOH: 97%, Merck, Mumbai, India) were used as supplied. All the other reagents used during the experimental work were of reagent grade. All the solutions were prepared in deionized (DI) water. The stock solutions of NaOH (1.0 M) and SDS (1.0 × 10 −2 M) were prepared in DI water. The stock solution (500 mgL −1 ) of dye was prepared by dissolving 50 mg RB in 100 mL DI water. Likewise, 250 mL stock solution of H 2 O 2 was prepared by dissolving 25 mL of H 2 O 2 in DI water. The stock solution of HCl (0.1 M) was prepared in 100 mL DI water.

Synthesis and Surfactant Coating of Fe 3 O 4 Magnetic NPs
Magnetic nanoparticles were synthesized by adopting the co-precipitation method as described in the literature [34]. Briefly, Fe 3 O 4 NPs were synthesized by mixing 20.0 g of FeCl 3 (0.4 M) and 10.0 g of FeCl 2 .2H 2 O (0.2 M) into a 1.0 L conical flask. These iron salts were dissolved in 300 mL DI water. The mixture was purged with N 2 gas and stirred for about an hour. Then, liquor ammonia (25%) was added drop-wise in the flask. The pH of the solution in flask was further increased to~10 by adding 2.0 M of NaOH solution. The temperature of the solution was then raised to 70 • C with stirring and purging of N 2 gas for 5 h. Black precipitate was formed in the flask. It was filtered, washed with acetone, and thereafter with DI water to a neutral pH value. The precipitate was then dried at 70 • C in a vacuum oven. The synthesis of Fe 3 O 4 NPs can be given by the following reaction: To prepare the SDS-coated Fe 3 O 4 NPs, FeCl 3 .6H 2 O (20 g, 0.40 M), FeCl 2 .4H 2 O (10 g, 0.20 M), and SDS (8.64 g, 0.10 M) were taken into the conical flask of 1.0 L capacity containing 300 mL DI water. The overhead stirrer was used to mix the reactants properly. The solution was stirred vigorously for 45 min under the N 2 gas atmosphere. Then, 200 mL of 25% ammonium hydroxide solution was added drop-wise into the above solution until the pH of the resulting solution reached 9-11. The pH of the reaction medium was further raised to 14 by adding 2.0 M NaOH solution drop-wise. The mixture was then stirred vigorously under N 2 gas purging for 5 h. The black precipitate that formed was filtered and washed with acetone and DI water until the pH came to a neutral value.

Characterization
The crystallinity and phase composition of Fe 3 O 4 and SDS@Fe 3 O 4 NPs were studied by X-ray diffraction (XRD: MiniFlex II, Rigaku, Tokyo, Japan) analysis equipped with a Cu K α radiation source (with λ = 1.5406 nm). The surface functionalities present over Fe 3 O 4 and SDS@Fe 3 O 4 NPs surface were determined by Fourier infra-red spectrometer (FT-IR: Nicolet iS50, Thermo Fisher Scientific, Madison, WI, USA). The surface morphology and particle size were analyzed by scanning electron microscopy (SEM: JSM-5600LV, JEOL, Tokyo, Japan) and transmission electron microscopy (TEM: CM120, Philips, Amsterdam, The Netherlands). The magnetic properties of Fe 3 O 4 and SDS@Fe 3 O 4 NPs were determined using a vibrating sample magnetometer (VSM: 7307, Lakeshore, Westerville, OH, USA).

Degradation Kinetic Experiments
A Genesys 10S UV-visible spectrophotometer (Thermo Fisher Scientific, Madison, WI, USA) was used to monitor the change in the absorbance intensity of RB during its degradation under the varying reaction conditions. The spectrophotometer was provided with multiple cell holders in which a 3.0 mL quartz cuvette with a path length of 10 mm was used to measure absorbance. All the kinetic experiments were performed at a constant temperature of 25.0 ± 0.2 • C by using a thermostatic water-bath. A 0.1% w/v of magnetic Fe 3 O 4 NPs was put together with RB solution with an initial concentration of 10 mg L −1 into a three necked round bottom flask of 100 mL capacity. Solution pH was adjusted by adding hydrochloric acid or sodium hydroxide solution and monitored by using a pH meter. The reaction vessel containing RB solution and magnetic Fe 3 O 4 NPs was kept in the water-bath to equilibrate with the required temperature. The reaction was started with the addition of 5.0 × 10 −2 to 4.0 × 10 −1 M H 2 O 2 and zero time was taken when the half of the amount of H 2 O 2 was added. The concentration of RB was spectrophotometrically analyzed at its maximum absorbance wavelength (λ max : 554 nm) at constant time intervals. All the kinetic experiments were carried out under pseudo-first-order conditions in which H 2 O 2 was kept in excess over RB. The progress of the reaction gradually resulted in the decrease of RB concentration and the values of the pseudo-first-order rate constants were obtained from the slopes of the plots of ln (absorbance) versus time. Each kinetic run was carried out in triplicate to check their repeatability and the rate constant was observed to be within the error limits of~5%.  Figure 1B shows the XRD patterns for SDS@Fe 3 O 4 NPs with reduced peak intensity due to the SDS coating over Fe 3 O 4 surface. This confirms crystalline-to-amorphous transition of Fe 3 O 4 NPs due to SDS coating during SDS@Fe 3 O 4 NPs synthesis [36].

Fourier Transform Infrared Spectroscopy (FTIR)
The FT-IR spectra of Fe 3 O 4 and SDS@Fe 3 O 4 NPs are shown in Figure 2. The two peaks at 585 and 435 cm −1 , as shown in Figure 2A, correspond to the Fe-O bond vibrations of Fe 3 O 4 NPs [37]. From these observations, it is confirmed the spinel structure of Fe 3 O 4 NPs and also inferred the existence of the difference in the bond length in Fe-O. The peak at 3424 cm −1 in Figure 2A was associated to the O-H stretching vibrations arising from the hydroxyl group due to the presence of water molecules associated with Fe 3 O 4 [38]. The H-O-H bending of water molecules in Figure 2A is observed at 1631 cm −1 in Fe 3 O 4 NPs [39]. The FTIR spectrum of SDS@Fe 3 O 4 NPs is shown in Figure 2B, which displayed a new absorption peak at 1252 cm −1 due to the stretching vibration of S=O groups of SDS and the presence of peaks at 2929 cm −1 and 2842 cm −1 , which were assigned to the stretching mode for aliphatic C-H groups of SDS [40]. The peak at 1635 cm −1 in SDS@Fe 3 O 4 ( Figure 2B) was attributed to the H-O-H bending of water molecules and that at 3431 cm −1 was due to stretching vibration of hydroxyl group on the surface of the NPs. The presence of two peaks at 547 cm −1 and at 474 cm −1 in Figure 2B is attributed to Fe-O bonds in SDS-modified Fe 3 O 4 [41]. Thus, the FTIR results confirmed successful synthesis of Fe 3 O 4 NPs and their surface modifications through the adsorption of SDS molecules.

Scanning Electron Microscopy (SEM)
The SEM micrograph of the synthesized magnetite (Fe 3 O 4 ) NPs is shown in Figure 3A. It can be observed that the NPs exhibit spherical surface morphology, having a particle size lower than 100 nm scale with low polydispersity. The SEM image of the SDS@Fe 3 O 4 NPs is shown in Figure 3D

Transmission Electron Microscopy (TEM)
The TEM micrograph of pristine Fe 3 O 4 NPs ( Figure 3B) on the scale of up to 20 µm shows their spherical shape with a narrow range particle size distribution centered at 9 ± 2 nm, as demonstrated by the histogram in Figure 3C. The TEM image of the SDS@Fe 3 O 4 NPs is illustrated in Figure 3E. After coating with SDS, the size of SDS@Fe 3 O 4 NPs appears to be smaller, as shown by the histogram ( Figure 3F). This might be due to the coating of Fe 3 O 4 NPs with SDS, which hinders NPs agglomeration.

Vibrating Sample Magnetometer (VSM)
The magnetic behavior of Fe 3 O 4 and SDS@Fe 3 O 4 NPs was studied by using VSM. As it may be seen in Figure Figure 4. Comparatively lower magnetic saturation of SDS@Fe 3 O 4 NPs might be due to their coating with SDS [42]. In order to avoid aggregation of Fe 3 O 4 NPs, which may severely reduce their catalytic efficiency, coating with SDS was executed in this work. In any case, as for the large magnetic saturation and superparamagnetic property of SDS@Fe 3 O 4 NPs (Figure 4), such a coating did not affect the high efficiency in magnetic separation and recovery.

Degradation of RB by H 2 O 2
The repetitive scans of the reactant mixture containing RB (10 mg L −1 ) and H 2 O 2 (2 × 10 −1 M) were recorded at constant time intervals of ten minutes in the visible region (460-600 nm). The temperature and pH were kept constant at 25 ± 0.2 • C and 3, respectively. These spectra, which are shown in Figure 5A, indicated that the absorbance intensities at λ max (554 nm) progressively decreased with time. A decrease in the absorbance intensities was due to the degradation of RB by H 2 O 2 .
The degradation of RB can be represented by the following representative reaction and rate Equation (1): where k obs is the observed value of the rate constant and was calculated from the slope of the plot of ln where k is the specific rate constant with respect to H 2 O 2 concentration. The values of k and x were respectively obtained from the intercept and slope of the plot of log k obs versus log [H 2 O 2 ].

Degradation of RB in the Presence of Fe 3 O 4 and SDS@Fe 3 O 4 NPs
The addition of 0.1% w/v of Fe 3 O 4 NPs to the solution containing RB and H 2 O 2 increased the rate of degradation of RB, as is evident from the decrease in the rate of absorbance intensities with time, which is presented in Figure 5). The increase in the degradation rate of RB can be attributed to the catalytic role of Fe 3 O 4 NPs. The degradation rate was further increased in the presence of 0.1% w/v SDS@Fe 3 O 4 NPs as displayed in Figure 5C.
In order to assess the effect of pH, the degradation rate of RB was studied in the pH range 1-10 by adjusting it with HCl/NaOH solutions. The observed results are presented in Figure 7. The plot of the rate constant versus pH (Figure 7) demonstrates that the values of the rate constant increase with pH until pH 3. Thereafter, on further increasing the pH beyond 3, the values of the rate constant decreased. Thus, a peaked behavior plot was obtained with the maximum degradation rate at pH 3.  Figure 8A. Furthermore, as it may be seen in Figure 8B, the influence of SDS@Fe 3 O 4 concentration on the RB degradation rate showed the same pattern observed for Fe 3 O 4 , but with higher values of the rate constant. The observed enhancement in the rate of the RB degradation in presence of Fe 3 O 4 can be described through the production of highly reactive hydroxyl radicals due to the interaction between the NPs and H 2 O 2 [43,44], followed by the formation of peroxyl radicals and the subsequent oxidation of RB by these radicals, as described by the following reactions:  (vii). The increase in the amount of the NPs increases the production of HO * radicals (step (i)) and, therefore, an enhancement in the RB degradation rate was observed with the increase in the NPs dosage, which is coincident with previous observations [45]. As shown in Figure 6, the RB degradation rate increased from 0.4 to 1.7 × 10 4 s −1 with increasing H 2 O 2 concentration in the absence of NPs. In Figure 9, under the presence of NPs, larger degradation rates are represented, varying between 1.  (Table S1 in the Supplementary Materials). However, as it may be seen in Figure 9, in the presence of Fe 3  , the side reactions scavenged the HO * radicals and decreased the concentration of free radicals available to oxidize the dye and, therefore, the rate of the reaction decreased [46]. The rate of degradation of RB was highly pH-dependent and, as it is shown in Figure 7, the maximum rate of degradation was observed at pH 3 in the presence and the absence of NPs. At high concentrations of H + ions (pH < 3), peroxide gets solvated to form stable oxonium ions, which enhanced the activity of H 2 O 2 and restricted the generation of hydroxyl radicals [47][48][49]. Moreover, the excess of H + ions acts as hydroxyl radical scavenger and, with the increase in H + ions, the concentration of HO * radicals decreases, thus, decreasing the rate of reaction [48]. Furthermore, the strong electrostatic interaction between the anionic surfactant head groups and cationic dye molecules at lower pH also decreases the rate of RB degradation. The observed lower rate of reaction at higher pH may be related to the formation of the Fe 3+ -complexes, which decreases the dissolved Fe 2+ ions that were available to generate free radicals [49]. The higher degradation rate of RB in the presence of SDS@Fe 3 O 4 NPs in comparison with bare Fe 3 O 4 NPs that is observed in Figure 8, might be due to the larger capture of RB by SDS@Fe 3 O 4 than by Fe 3 O 4 . Thus, the generated free radicals at the NPs surface can readily attack the attached RB and thus leading to the increase in RB degradation rate. Binding of RB to the SDS@Fe 3 O 4 surface can be explained by the electrostatic interaction between the anionic surfactant and protonated cationic dye at pH 3 [50].

Effect of SDS Concentration and Fe 3 O 4 NPs Dosage on RB Degradation
The addition of SDS at varied concentrations (5.0 × 10 -4 to 5.0 × 10 −2 M) to a solution containing RB (10 mgL −1 ), H 2 O 2 (2.0 × 10 −1 M), and Fe 3 O 4 (0.1% w/v) NPs at pH 3 resulted in an increase in the rate of the degradation reaction, as shown in Figure 10. On the other hand, an increase in the amount of Fe 3 O 4 NPs from 0.02% to 0.2% w/v at a fixed concentration of SDS (2.0 × 10 −2 M) also increased the rate of RB degradation, as shown in Figure 11.
The presence of SDS micelles (D n ) partitions RB into micellar (RB mic ) and aqueous pseudo-phases resulting into the retardation of RB oxidation with H 2 O 2 in the presence of SDS, which may be related to the electrostatic repulsion and, therefore, separation between the species involved in the reaction. However, in the presence of Fe 3 O 4 , micellised RB (RB mic ) is incorporated to the NPs surface to form RB mic −Fe 3 O 4 where H 2 O 2 interacts to form reactive HO * radicals readily available to oxidize RB at the same site. Therefore, RB degradation is catalyzed and the rate of the reaction increases with increasing SDS concentration in the presence of Fe 3 O 4 NPs ( Figure 10) and also with increasing the amount of Fe 3 O 4 NPs in the presence of SDS (Figure 11). In Figure 10, a two steps increase of the degradation may be observed, which may be related to the formation of premicellar aggregates below the critical micelle concentration (cmc) of SDS and micelles above cmc [8,10,51,52], then increasing micelles formation with SDS concentration. Regarding Figure 11, at a SDS concentration above cmc, an increasing degradation rate occurred under increasing Fe 3 O 4 concentration, as previously observed in Figure 8 and explained by reactions (i) to (vii). These results are in agreement with previous studies on RB photocatalytic degradation [53,54].

Effect of Temperature on RB Degradation
The effect of temperature on RB degradation (10 mg L −1 ) in aqueous solutions in the presence of H 2 O 2 (2.5 × 10 −1 M) and at pH 3 was studied at varied temperatures ranging from 25 to 60 • C (because above 60 • C, due to thermal disintegration of H 2 O 2 and free radicals, the rate of RB degradation slowed down) in the absence or in the presence of Fe 3 O 4 NPs (0.1% w/v), Fe 3 O 4 NPs (0.1% w/v) together with SDS (2.0 × 10 −2 M) or SDS@Fe 3 O 4 (0.1% w/v).
The energy of activation was calculated using the Arrhenius equation Equation (5), which gave a straight line plot for log k versus 1/T.
where E a is the activation energy (kJ mol −1 ), R (8.314 J mol −1 K −1 ) is the universal gas constant, T is the temperature in Kelvin (K), A o is the frequency factor, and k obs is the measured first-order rate constant. The E a was determined from the slope and values are given in Table 1.
The value of ∆H (enthalpy of activation) and ∆S (entropy of activation) were calculated using the Erying equation Equation (6).
where k B is the Bolzmann's constant and h is the Plank's constant. A plot of ln (k obs /T) versus 1/T produces a straight line and the values of ∆H and ∆S may be obtained from the slope and the intercept, respectively. The so determined ∆H and ∆S values are given in Table 1.
As it may be seen in Table 1

Conflicts of Interest:
The authors declare no conflict of interest. Furthermore, the funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.