Kinetic Modeling for Microwave-Enhanced Degradation of Methylene Blue UsingManganese Oxide

is study was originally performed to compare the MnO2-based degradation of aqueous methylene blue (MB) under microwave irradiation(MW-) enhanced and conventional heating(CH-) enhanced conditions. e degradation process and kinetics were investigated to elucidate the microwave effect on the reaction. e results showed that all three tested conditions, sole MnO2, MnO2/CH, and MnO2/MW, followed the third-order (second upon MB and �rst upon MnO2) kinetic model. However, a higher degradation rate of MB was available under the MW-enhanced process, which implies that the “athermal effect” of MWmight be of more bene�t for the generation of electrophilic oxygen ions (O2 , O, and O) to degrade MB. e results showed that the degradation percentage of MB could reach 100%, corresponding to 92% total organic carbon (TOC) removal under microwave irradiation at pH 7.20 for 10min.


Introduction
Approximately 10000 various industrial dye and pigments and over 7 × 10 5 tons of these dyes are annually produced worldwide [1].Consequently, the acute impact on the ecosystem arising from dyes and pigments released into wastewater is inevitable.Methylene blue (MB), a type of thiazine dye, is widely used as a photosensitizer commonly employed in solar cells, a photodynamic antimicrobial agent in biological materials, a test compound in semiconductor photocatalysis, and a surface modi�er of semiconductor colloids [2][3][4].Other than a marked quantity of colorful wastewater generated from various industrial processes, the biodegradable resistance of MB suggests that physicochemical treatments are indispensable for effectively controlling pollution [5,6].
Microwave (MW) irradiation as an activation source for chemical reactions has been studied recently.Because most organic compounds do not absorb electromagnetic energy in the S-band (2.4 GHz) of the MW extent [7], applying materials that absorb considerable MW and then effectively transfer this energy to reactants is inevitable [8].According to the Poynting formulation, the time-averaged dissipated power density  diss.(d) at any position  within lossy material is given by where  is the angular frequency,  0 is the dielectric permittivity of vacuum,  ′′  is the dielectric loss, and  () * is the electric �eld strength; the dissipation of MW energy results in heating of the irradiated medium [9].Heating is a conventional method for activating chemical reagents, and the signi�cance of temperature on chemical reaction rate is well known.Except for the thermal effect on a medium, MW could allow an induced organization in an irradiated medium, called the "athermal effect, " "nonthermal, " or "spe-ci�c effect" of electromagnetic irradiation [10].e level of coupling with the electric �eld of MW radiation relies on the dielectric constant of the material.e dielectric constant determines the ability of the material to be polarized by an electric �eld [10].Rapid heating arises from interaction of International Journal of Photoenergy MW with either dipolar molecules or ionic species [9].Some researchers believe that acceleration of MW-enhanced reaction rates may be attributed to a distinct mode of transferring heat to reactants and mediums; however, others believe that absorption of MW radiation has a speci�c athermal effect on MW-absorbing molecules.e reasons for the so-called athermal effect must be fully understood and explored [11].
Manganese oxide (MnO 2 ) has been reported to have a high dielectric constant of nearly 10 000 [12]; therefore, excellent coupling with MW radiation can be expected.MW irradiation may produce interesting effects in comparison with conventional heating (CH).In natural soil and aquatic environments, MnO 2 plays a crucial role in governing the mobility and toxicity of numerous organic and inorganic compounds because of the various oxidation states of manganese [13,14].With excellent semiconductivity, porosity, and mixed-valent properties, MnO 2 has been used or synthesized recently as a catalyst by the reoxidation of manganese from a lower valence to a higher valence in many technological applications [15,16].
Numerous studies have reported the photocatalytic decomposition of MB on TiO 2 [17,18] and the adsorption of MB onto various materials [19,20].Few studies have focused on the oxidative degradation of MB using manganese oxide during a spontaneous reaction [21,22].However, no previous study has described the MW-enhanced MnO 2 catalytic reaction and explored the athermal effect of MW on MB degradation.Hence, strict comparisons among reactions performed under similar conditions, such as the reaction medium, temperature, time, and open/closed vessel for MW-enhanced MnO 2 (MnO 2 /MW), CH-enhanced MnO 2 (MnO 2 /CH), and sole MnO 2 systems, were studied.All chemicals used in this study were of AnalaR grade, and the solutions were prepared with ultrapure water produced using a Milli-� water puri�cation system (Milli-�-Academic, Millpen RIOS16).e used MnO 2 particles were purchased from TOSOH Co. and con�rmed to be pyrolusite, a 1 × 1 tunneled (or molecular sieve) structure, by using an X-ray diffractometer (XRD, Philips PANalytical X'pert PRO MPD).e surface area, porosity, and charge of MnO 2 were measured using a surface analyzer (Micrometrics ASAP 2010), porosity analyzer (Micrometrics ASAP 2010), and electrophoresis instrument (Malvern Nano-ZS90), respectively.e results are shown in Table 1.In Table 2, the literature values of dielectric constants for each material in reference to a vacuum and the temperature and the frequency at which they were measured are given.temperature under an N 2 atmosphere overnight.e initial concentration of MB was 10 mgL −1 .e MnO 2 concentration was maintained at 2 gL −1 , and the reacting volume of solution was 100 mL.e test solutions were adjusted to the desired pH (pH meter, HACH Sension 156) using dilute NaOH and HNO 3 solution.System pH was not controlled during the reaction process because both organic and inorganic buffer agents might be oxidized, which could signi�cantly in�uence MB degradation [23].e pH during the reaction was not monitored but measured aer each batch reactor was taken at the speci�c reaction time because the pH electrode interferes with MW irradiation.e MW apparatus (CEM, MARS-5) with a frequency of 2450 MHz used in this study had an adjustable power setting and monitored temperature.e Erlenmeyer �ask containing MB and MnO 2 suspension was cap sealed with para�n �lm and placed on the rotary table in the MW oven as a batch treatment; each batch reactor was taken at a speci�c reaction time prior to solution analyses.To clarify the effect of temperature and electromagnetic wave on the reaction, a parallel experiment using a conventional electric heater was also conducted.e Erlenmeyer �ask containing the same suspension and pretreatment was placed into a watercirculating temperature-controlled shaker, maintained at 25 and 50 ∘ C, and gently stirred at 100 rpm (Firstek Model-B603 DL) to stimulate the rotator in the microwave oven.

Experimental
At the desired time, a �ask was taken from the microwave oven or temperature-controlled shaker, cooled, and then the suspension pH was measured.is represented the reaction pH.Immediately, the suspension was �ltrated through a Millipore membrane �lter with a pore size of 0.2 m.e �ltrates were pretreated for various analyses and stored at 4 ∘ C. All experiments were conducted in duplicate, and all data presented were the averages of duplicate analyses.

Analytical Methods.
To determine the change of MB concentration in the solution following the reaction, a UV-vis spectrometer (Varian Cary 50 Bio) is oen used as the major instrument.Generally, two types of information can be extracted from UV-vis analysis results.Identi�cation of the speci�c molecules is based on the characteristic absorbance peaks in the UV-vis spectra in a full scan, and determining the concentration of the speci�c molecule is based on the absorbance intensity of the characteristic peak.e degradation or removal of MB was substantially determined by the intensity of absorbance peaks at 665 nm.However, the possible intermediates or products were rarely identi�ed according to the shi of characteristic absorbance peaks, which can be obtained using the full scan of UV-vis wavelengths [23,26].erefore, two data types of UV-vis spectra were extracted to speculate reactions in this study.First, the absorbance at 665 nm has been a prevalent method used to represent the MB concentration in previous studies and was used in this study.Second, because MB could be transformed or degraded to other forms of organic compounds in reaction with MnO 2 , using the full UV-vis wavelength scan was necessary.e total organic carbon (TOC) of the sample was determined using a TOC analyzer (O-I, Carbon Model 1010).

Effect of MW Power on the Solution Temperature. MW radiation interacts with materials of high dielectric constant
and consequently leads to volumetric heating.Water is an excellent medium for MW-enhanced chemical reactions because of its high dielectric constant.Figure 1 shows the evolution of measured temperatures for MB solution under varying powers of MW radiation.e measured temperature in the MB solution increased with both time and MW power.e heating rate of MW was calculated from the slope of linear regression of temperature from 1 to 10 min in Figure 1, and being 1.6, 2.9, and 5.0 ∘ C/min for 100 W, 200 W, and 300 W, respectively.At 20 min the temperature reached 55 ∘ C, 75 ∘ C, and 90 ∘ C under 100 W, 200 W, and 300 W MW irradiation, respectively.To refrain from overvolatilizing the water during the reaction, the 200 W MW and a maximum of 10 min of reaction time were used to compare with conventional heating at 50 ∘ C in the following experiments.

Spectra of Full UV-Vis Wavelength Scan.
To compare the degradation efficiency, the UV-vis absorption spectra of MB treated under various conditions at pH 4.75 for 10 min are shown in Figure 2. e absorbance of UV-vis 665 nm was used to evaluate the MB quantity in the solution because the maximal absorbance peak occurred at this spectrum.e absorbance of MB treated under MW irradiation without MnO 2 is similar to that of the original MB solution, implying that sole 200 W MW irradiation is unable to degrade MB. e peak absorbance of MB treated with MnO 2 at 25 ∘ C decreases by approximately 60%, and the higher heating temperature results in the more declination of absorbance peak for MB.For conventional heating at 50 ∘ C (CH), the corresponding degradation ratio is approximately 85%.In contrast, the absorption peak at UV-vis 665 nm descends signi�cantly by 99% under the MnO 2 /MW system.e solution temperature  forms a precursor of surface complex.Electrons transfer from the organic compound to the surface bound Mn(IV) on the MnO 2 solid surface, subsequently resulting in the release of organic oxidation products and Mn(II) reductively dissolved from MnO 2 into bulk solution.In such condition, MnO 2 plays the role of the oxidant in reaction.Nevertheless, Mn(II) could be oxidized by dissolved oxygen (DO) in solution to form Mn(IV) (hydro)oxide precipitates again.In this condition, MnO 2 serves as the role of catalyst and DO acts as the oxidant in reaction.e role of MnO 2 depends on the occurrence rate of Mn(II) oxidation [31].Mn(II) is not oxidized by molecule oxygen for several years, unless mineral surfaces or microorganisms catalyze this slow redox reaction [32].erefore, the solution pH beyond the pH  promotes the readsorption of free Mn(II) ions in solution back onto MnO 2 surface, on which it leads to the surface catalytic oxidation [22].e rate constant for the degradation of MB using sole MnO 2 , MnO 2 /CH, and MnO 2 /MW was determined for pH 2.17, 4.75, and 7.20.Figure 3 shows the kinetics of MB degradation as a third-order (second upon MB and �rst upon MnO 2 ) model for various conditions, as shown in ( International Journal of Photoenergy e kinetics were modeled assuming a second-order reaction with respect to MB, which was veri�ed by plotting 1/[MB] as a function of the reaction time with a slope of  ′ obs (Figure 4 and Table 3).A statistical approach is more appropriate than correlation coefficient to determine �goodness of �t� of a model for experimental data [33].e paired t-test was used to examine the difference between the observed and the predicted variable, with a signi�cant level of 0.05.As Table 3 showed, the results of paired t-test suggest that in all systems the observed and predicted variables (1/[MB]−1/[MB]  ) did not reveal signi�cant difference (all P ≥ 0.05), con�rming the third-order kinetic model is of statistically reasonable for this reaction.Assuming a �rst-order reaction with respect to this MnO  because of the constant concentration of MnO  , the rate constants  obs in L  mol − s − were then calculated and are shown in Table 4. Values of log  obs are plotted as a function of pH in Figure 5. e apparent reaction order with respect to H + was determined as the slope of the straight line log  obs = f (pH), and equal to 0.362, 0.161, and 0.157 for sole MnO  , MnO  /CH, and MnO  /MW, respectively.e rate constant  for (2) was calculated to be 1.76 × 10  , 3.50 × 10  , and 8.92 × 10  M −. s − for the system of sole MnO  , MnO  /CH, and MnO  /MW, respectively.e relative effects of MW on MB degradation are twofold.As the rate constant revealed, energy application considerably enhances the rate of MB degradation using MnO  .e rate constant of the system heated at 50 ∘ C (MnO  /CH) increases two times than that of the sole MnO  system, and 200 W MW irradiation drastically elevates 5.1 times the degradation rate of MB using MnO  .Figure 1 shows that the solution temperature reached 50 ∘ C in 10 min under 200 W MW irradiation, meaning that during the reaction period of the MnO  /MW system, the solution temperature is lower than 50 ∘ C most of the time.e second in�uence of MW on MB degradation using MnO  consists in the alleviation of pH dependence.e kinetics of MB degradation using MnO  show a signi�cant pH-dependence with a stoichiometry of 0.362; however, its value declines to 0.157 for the MnO  /MW system (Figure 5).Although the pH elevation increases the amount of the negative-charged site and, consequently, promotes the adsorption of cationic MB molecules, the MW application leads to a more efficient MB degradation in low pH circumstances.

Blue-Shi of Absorbance Peak for Dye Solution with Time.
To compare the progression of MB degraded using MnO  under various conditions, UV-vis spectroscopy was used to identify the organic compounds in the solution.Because the reaction is too quick under pH 7.20 and too slow under pH 2.17, to clearly distinguish the curve differences, the evolution of absorbance peaks with time were discussed with the case conducted at a pH of 4.75.Figure 6    at pH 4.75 compared with possible intermediary-degradation compounds.e UV-vis characteristic peak ( max ) for azure B (AB), azure A (AA), azure C (AC), and ionin (TH) was 650, 640, 618, and 600 nm, respectively, and is shown in Figures 6(b) to 6(e).In the sole MnO 2 system (temperature controlled at 25 ∘ C), the UV-vis absorbance peak for the dye solution shis from 665 nm ( max for MB) to 650 nm ( max for AB) at a reaction time of 5 min and is retained at the same wavelength with intensity descent in the system with a reaction time of 10 min.However, the absorbance peak shis to 600 nm ( max for TH) at a reaction time prolonged to 24 h.In the MnO 2 /CH system, two distinguishable absorbance peaks at 640 nm ( max for AA) and 618 nm ( max for AC) were observed at 5 min.At 10 min of reaction time, only the peak of 618 nm remained with an abating peak intensity.e absorbance peaks in the MnO 2 /MW system show a more marked blue-shi and less intensity compared to that of the sole MnO 2 and MnO 2 /CH systems at the same reaction time.e absorbance peak appears at 618 nm ( max for AC) and 600 nm ( max for TH) for 5 min and 10 min in the MnO 2 /MW system, respectively.Zhang et al. [3] indicated that, in the TiO 2 photocatalyzed system, the peak 665 nm of MB blue shied by as much as 20 to 650 nm; this shows the N-demethylation of MB.Our previous study showed that, in a MnO 2 suspension system, MB was cleaved through N-demethylation, in which reactions azure B (AB), azure A (AA), azure C (AC), and thionin (TH) were stepwise generated under room temperature [22].N-dealkylation of dyes containing auxochromic alkylamine groups is important for catalytic degradation.e color of the MB solution turned less intense during the gradual degradation of all or part of the auxochromic groups (methyl or methylamine) with time evolution.In the sole MnO 2 system, MB was catalytically degraded to TH until 24 h of reaction time.In contrast, MW signi�cantly enhanced this degradation process in MnO 2 suspensions and shortened the duration from 24 h to 10 min.A less intense absorbance peak at 600 nm was coherently observed in MnO 2 /MW.Brie�y, for a chemical reaction to occur, it is necessary to activate the reactants.Heating is a conventional method in chemistry to activate a reactive medium.e elevation of temperature induces an increment of kinetic energy in molecules and, consequently, enhances the collision rate.However, among these collisions, only a few have sufficient energy and the proper orientation to lead to the product.Heating causes an isotropic excitation of molecules, and that is why all collisions are inefficient.According to the Eyring formulation, an excitation tool that would be able to favor efficient collisions by modifying the energy distribution of molecules (i.e., an anisotropic excitation) could enhance the reaction rate.At identical temperatures of a reaction medium (i.e., the same average value of the energy distribution), but for different distributions of the kinetic energies of molecules, different reaction rates could be observed.Athermal effects in chemistry have been partially based on this premise.Under MW irradiation, MnO 2 , a strong microwave absorbent, can signi�cantly absorb and transfer MW energy, indicating that a strong absorbent could engender large amounts of "hot spots, " which could enhance the degradation of molecules [1,7].e electrophilic oxygen ions (O 2 − , O − , and O 2− ) that are derived from lattice oxygen on MnO 2 show high activity in catalytic reactions and could participate in the degradation of MB [22].e vacancies of lattice oxygen are lately replenished by molecular oxygen dissolved in solution, which is known as the Mars van Krevelen mechanism [34].
Because the energy of microwave photons is too low (approximately 10 −5 ev) compared to chemical bonds, no breaking of chemical bonds can be induced by absorption of microwave photons.erefore, MW cannot induce any shiing in chemical equilibrium but can accelerate the rate of MB degraded.As shown in Figure 4, MB was degraded to the TH in 5 min for the MnO 2 /MW system, 10 min for the MnO 2 /CH system, and 24 h for the sole MnO 2 system.is implies that the simultaneous combination of microwave and MnO 2 can effectively degrade MB and its intermediates (i.e., AB, AA, AC, and TH) produced in the process of MB degradation, eventually driving the intermediates to total mineralization.
Although this study focused on the kinetics of MB degradation, the equilibrium of reaction could be discussed by comparing the �nal state conducted under room temperature with that under CH.e chemical equilibrium will shi to counteract an imposed change in temperature, according to Le Chateller's principle.As Figure 3  is lower than that for sole MnO 2 (conducted at room temperature) under all pH conditions employed.is result suggests that the degradation of MB using MnO 2 could be an endothermic reaction, which was also corroborated by the literatures [14,35].

Total Organic Carbon (TOC) Analysis.
To gain insights into overall pollutant removal and mineralization, TOC analysis was conducted to evaluate the decontamination of all residual carbon-containing metabolites more appropriately [36,37].e TOC of the original 10 mg MB L −1 solution was 5.71 mg TOC L −1 , which coincides with the theoretical calculation of total carbon for an MB molecule (6 mg TOC L −1 ). Figure 7 shows the ratio of the remaining TOC (TOC) to original TOC (TOC 0 ) in dye solution with varying pH at 10 min for various testing conditions.e MB solution irradiated under MW for 10 min shows no TOC descent, indicating that sole MW energy is insufficient to break and mineralize an MB molecule.In the MnO 2 suspension systems without any irradiation, the ratio of TOC/TOC 0 decreases when pH increases.is result is in agreement with that of UV-vis, as shown in Figure 3.Because the precursor complex formation or the adsorption reaction of organics onto an MnO 2 surface is crucial for all heterogeneous solid/solution reactions, this result could be ascribed to the increase of positively charged sites on MnO 2 elevating the adsorption of cationic molecules, including original MB and its intermediates AB, AA, AC, and TH, and then consequently promote mineralization.
Although no speci�c UV-vis peak is observed for the MB solution aer reaction with sole MnO 2 at pH 7.20 (�gure not shown), the TOC in the solution still remained as high as approximately 45%.ese results might show that at a pH of 7.20, MB is degraded to compounds that are colorless in UV-vis; however, some small organic compounds that may not have been detected using UV-vis contributed to the remaining TOC in the sole MnO 2 case.By contrast, CH and MW could signi�cantly enhance TOC degradation in MnO 2 suspensions.e TOC removal in the MnO 2 /MW system at pH 7.20 for 10 min is approximately 92%.Although increasing temperatures could reverse the adsorption of MB and its intermediates onto MnO 2 , the advantages of great amounts of electrophilic oxygen ions derived from a MnO 2 lattice under MW irradiation catalyzing MB into mineralization appear to overcome the disadvantage of adsorption inhibitions.

Conclusion
e degradation of MB using MW-enhanced MnO 2 was sig-ni�cantly higher than that using sole MnO

Con�ict of �nterests
e authors declare no competing �nancial interests and no direct �nancial relation with the commercial identity mentioned in this paper.

F 1 :
Effects of MW power on MB-containing solution temperature changes with time.
shows the absorbance measurements obtained in various reaction times International Journal of Photoenergy

F 6 :
(a) UV-vis spectroscopy of MB aer different reaction times under various radiation conditions, compared to (b) AB, (c) AA, (d) AC, and (e) TH standard compounds in aqueous solution.
Procedure.MB removal using MnO 2 was performed in a 125 mL Erlenmeyer �ask.Before the batch experiments, the MnO 2 suspensions were aged at room T 1: e measured physicochemical properties of MnO 2 .
[28]re 3shows the kinetics of MB degradation pro�les using sole MnO 2 , enhanced by CH, or enhanced by MW at various pH values.MB shows a sharp decline in the initial 5 min of reaction time and signi�cant pH-dependent degradation.eexperimentconductedata pH of 2.17 in the system of sole MnO 2 and MnO 2 /CH shows a lower MB degradation, compared with other systems; however, at the same pH, MB degradation is considerably enhanced by MW irradiation (MnO 2 /MW) and approaches approximately 92% removal in the initial 2 min.Our previous research showed that MB displays a lower removal beneath pH zpc of MnO 2 (4.70) because cationic MB was weakly adsorbed onto the positively charged MnO 2 surface[27].When under system pH is beyond the pH zpc , strong affinity between cationic MB and negatively charged MnO 2 exerts MB degradation[28]because heterogeneous degradation initiates with the formation of a precursor complex between target contaminants and surface-bound [29,30] MW is the transfer of electromagnetic energy to thermal energy and is energy form conversion, rather than heat transfer.erefore,MWcanpenetratematerialsanddepositenergy; heat can be generated throughout the volume of the material and is temperature independent.Because the energy delivery doses do not rely on diffusion of heat 2 /CH_2.17MnO 2 /MW_2.17MnO 2 _4.75 MnO 2 /CH_4.75MnO 2 /MW_4.75MnO 2 _7.2 MnO 2 /CH_7.2MnO 2 /MW_7.2F3:Kinetics of MB degradation and the third-order kinetic model (line).from the material surfaces, MW can achieve instantaneous heating of materials.Synergistic effects of MW and MnO 2 on the degradation of MB can be concluded.A marked blue shi of the main absorption peak from UV-vis 665 nm to 600 nm was observed for the MnO 2 /MW system at 10 min.ephenomenonsuggeststhatMBwasdegraded and new intermediates were generated in the solution.3.3.Kinetics of MB Degradation.Mn[29,30].In addition, the oxidative degradation of MB must be coupled with a half reduction reaction.Two possible reduction reactions in this system are dissolved oxygen (DO) reduction and MnO 2 -reduced dissolution.It has been well known that organics are oxidatively degraded by MnO 2 via a surface mechanism.e�rstlyadsorbedorganic compound 5 MnO 2 _2.17 MnO 2 /CH_2.17MnO 2 /MW_2.17MnO 2 _4.75 MnO 2 /CH_4.75MnO 2 /MW_4.75MnO 2 _7.2 MnO 2 /CH_7.2MnO 2 /MW_7.2F4:Plot of 1/[AMO] versus time for AMO degradation, [MnO 2 ] = 2 g/L (0.0023 M), and [MB] = 10 mg/L (31.297M).eslope and correlation coefficient of regression line are displayed in Table3.

5
T 3: e linear equation and correlation coefficient of regression line in Figure4.
showed, both sole MnO 2 and MnO 2 /CH system the MB degradation approximately approached pseudoequilibrium at 20 min; therefore, the reaction results at 30 min were considered as the equilibrium state.e amount of remained MB for MnO 2 /CH system 2 or CH-enhanced MnO 2 .e degradation kinetics of MB, including three tested systems (sole MnO 2 , MnO 2 /CH, and MnO 2 /MW), �ts a third-order (second upon MB and �rst upon MnO 2 ) kinetic model well and is pronouncedly pH dependent.However, the rate constant  of MB degradation is 1.76 × 10 5 , 3.50 × 10 5 , and 8.92 × 10 5 M −1.7 s −1 for the systems of sole MnO 2 , MnO 2 /CH, and MnO 2 /MW, respectively.MB was stepwise degraded to AB, AA, AC, and TH and �nally mineralized to CO 2 and H 2 O. MW irradiation noticeably accelerates MB degradation but does not induce any shiing in chemical equilibrium.e enhancement of MW on MB degradation using MnO 2 could be caused by the stronger MW adsorbent markedly absorbing microwave energy and generating abundant electrophilic oxygen ions (O 2 − , O − , and O 2− ) to degrade MB.