Photodegradation, kinetics and non-linear error functions of methylene blue dye using SrZrO₃ perovskite photocatalyst

Abstract

The degradation of methylene blue dye-contaminated wastewater via photocatalysis is an efficient approach towards environmental remediation. The SrZrO₃ perovskite photocatalyst was synthesized using the modified Pechini sol-gel method, and characterized using XRD, FESEM, FTIR, and UV–visible spectrophotometer. Crystallite size obtained by the Scherrer and Williamson-Hall methods were 45.56 and 44.50 nm, respectively. The sample exhibited an orthorhombic crystal structure. The optical bandgap was estimated to be 5.31 eV. Kinetic study for the degradation of methylene blue dye using SrZrO₃ in the presence of H₂O₂ showed complete decontamination of the methylene blue dye in the time interval of 90–120 min under visible light irradiation. The degradation efficiency was above 80.1 % under illumination and less than 40.1 % in dark. Kinetic studies were performed by varying the dose of photocatalyst and initial concentration of methylene blue. It was observed that higher dose of the photocatalyst and lower concentration of the contaminant produced higher rate of degradation. The solution pH 3 and catalysts dosage of 200 mg yielded the highest rate of degradation. The experimental data fitted best into the Psuedosecond order kinetic model with the highest R² value, indicating a strong linear relationship. The experimental data was subjected into nonlinear error functions, where the Psuedo-second order kinetic model demonstrated lower values of error functions. The results suggest that the prepared SrZrO₃ photocatalyst coupled H₂O₂ is a promising photocatalyst for the decontamination of methylene blue dye under visible light irradiation.

1. Introduction

The sixth millennium development goal stipulates that everyone has the right to sufficient, safe, accessible and affordable clean water for livelihood. However, water quality has been jeopardized due to anthropogenic activities. Water quality becomes unsafe when contaminated [1]. More than 200 different kinds of pharmaceutical and textile effluents have been reported worldwide in freshwater systems [2,3]. Mehdizadeh et al. [4] reported global threat to water on account of organic waste disposal. According to Bryne et al. [5], freshwater contaminants include organic, inorganic and microbial wastes. Water pollution can cause negative effects, such as diseases, water scarcity and death. Methylene blue dye (MB) effluent is an organic industrial waste from the textile and printing industries that can contaminant freshwater sources, making it unfit for domestic use [6]. The treatment of MB-contaminated wastewater via an efficient process is necessary due to its carcinogenicity and toxicity.

In recent times, perovskite catalysts have received great attention for environmental remediation [7]. They have found applications in chemical sensors, fuel cells, catalyst for energy generation and photocatalyst for wastewater decontamination [8,9]. To be a good photocatalyst, a material must have an acceptable band gap, low charge recombination and photo-corrosion resistance [10]. Photocatalysis is one of the classes of advanced oxidation processes used for decontamination of organic pollutants [[11], [12], [13]]. In this process, photoinduced radical oxygenated species, particularly hydroxyl radicals can oxidize organic pollutants into CO₂ and H₂O [14]. Heterogeneous photocatalysis is one of the advanced oxidation processes used for energy generation and environmental remediation applications [15,16]. Heterogeneous photocatalysts are reported for degradation and removal of dyes, organohalides, petroleum hydrocarbons, heavy metals and pharmaceuticals in soils and liquid effluents [17].

Janaki et al. [18] reported 95 % degradation of MB dye using LaFeO₃ supported bentonite via visible light within 60 min irradiation. In a similar study, Yan et al. [19] reported 96.5 % degradation of 5 mg rhodamine under 30 min using CaTiO₃-g-C₃N₄ photocatalyst under irradiation with a 200 W Xenon lamp (250 nm ≤ λ ≤ 2500 nm). Zhou et al. [20] reported the fabrication of LaNiO₃ nanoparticles modified g-C₃N₄ nanosheets for enhanced visible light driven photocatalysis towards tetracycline degradation. Aravinthkumar et al. [10] synthesized SrTiO₃ nanoparticles for enhanced photocatalytic activity and photovoltaic applications. The photodegradation of MB dye under UV illumination yielded an efficiency of 36 %. In a related work, Aravinthkumar et al. [21] incorporated Fe³⁺ ions in SrTiO₃ nanosphere for high performances of dye-sensitized solar cell and photocatalytic MB dye degradation, and achieved photodegradation efficiency of 82.57 % under visible light irradiation. Ramakrishnan et al. [22] fabricated TiO₂/CeO₂ core/shell nanostructures for photocatalytic degradation of MB and clitoria ternatea dyes. The workers achieved photodegradation efficiencies of 36 and 71 % for clitoria ternatea and MB dyes under UV light illumination for the period of 40 min. Aravinthkumar et al. [9] reported the photocatalytic degradation efficiency of 88 % for MB dye using Cr doped SrTiO₃ interconnected spheres catalyst under visible light illumination. Alvarez-Corena et al. [23] described photocatalysis as a promising wastewater treatment technology for degradation of pharmaceutical contaminants.

SrZrO₃ is a wide band gap perovskite material with an orthorhombic structure. It has excellent dielectric, luminescent, catalytic, protonic properties and has been reported for photoelectrochemical water splitting towards H₂ fuel production under UV light [24]. Literature reports are available for the deployment of SrZrO₃ for luminescence application [25]. It has been reported that SrZrO₃ is promising for photodegradation of MB, since it has been applied for water splitting under UV light [26]. However, SrZrO₃ photocatalyst cannot perform optimally under visible light due to its ultra-wide band gap of $\ge$ 5.0 eV that can only absorb light in the UV region of the spectrum. Nevertheless, coupling SrZrO₃ with H₂O₂ can mitigate recombination reactions, enable photon absorption in the visible region and enhance photocatalytic activity. Therefore, the present work seeks to extend the literature by employing SrZrO₃ coupled with H₂O₂ for degradation of MB under visible light irradiation. The SrZrO₃ nanoparticles coupled H₂O₂ was prepared by the modified Pechini method and investigated for the photodegradation of MB at different variables, including dye concentration, solution pH, catalyst dosage and reaction time. Photocatalytic degradation efficiency under visible light was found to be >80 %, indicating that the catalyst has potential for visible light application.

2. Materials and method

2.1. Reagents

All the chemicals used were of analytical grade zirconium-n-propoxide (Zr(OC₃H₇)₄), 98 % purity; Sr(NO₃)₂ 99 %, methylene blue, CH₃COOH 99 %, ethylene diamine tertra acetic acid (EDTA) 99.5 %, ethane 1,2-diol (HOCH₂CH₂OH), 99 %, and citric acid (H₃C₆H₅O₇) 99%were purchased from Sigma Aldrich.C₂H₅OH (99.5 %; S.G = 0.7951 g/mL), H₂SO₄ (98 %, S.G = 1.84 g/mL), H₂O₂ (30 %), and acetone (99 %; S.G = 0.789–0.792 g/mL were purchased from Guangdong Guang Sci. Tech-Co. Ltd, China(BDH).

2.2. Synthesis of SrZrO₃nanoparticles

The Sol-gel Pechini method was used to prepare SrZrO₃ [27]. Firstly, 5 mL zirconium iso-propoxide (Zr-n-p) was reacted with 0.5 M (40 mL) citric acid under constant stirring for 2 h at 37 $°C$. Thereafter, the temperature was increased to 80 $°C$ to aid dissolution. Secondly, in another beaker, 20 mL (0.1 M) of Sr(NO₃)₂ was reacted with 22 mL of 0.5 M EDTA dissolved in 25 % NH₃ solution. The Sr-EDTA solution was stirred for 2h at 60 $°C$ then, added to Zr⁺⁴ citrate solution with continuous stirring and heated to 100 $°C$ for 2 h. Next, was the addition of 23 mL ethane 1, 2-diol to EDTA - citric acid to the complex. The temperature was raised to 120 $°C$ to promote gel formation. The gel was dried at 400 °C for 4 hand further annealed at 800 °C for 2 h. The synthesized flake was milled into a fine powder using mortar and pestle. The obtained white colored powder was stored in a desiccator for characterization.

2.3. Characterization

The crystal structure was investigated by high-resolution X-ray diffractometer (HR-XRD, PAnalytical X'Pert Pro) operating at 40 kV and 40 mA with Cu K $\alpha$ radiation (1.54060 $\mathrm{\AA }$) from 10 to 90 $°$ (2 $\theta$ angle) using a step size of 0.05 $°$ and a counting time of 0.5 s per step at 25 $°C$ [28]. Surface morphology was determined using field-emission scanning electron microscope (FE-SEM, FEI Nova NanoSEM 450) at a voltage of 20 kV. Elemental composition was obtained using energy dispersive X-ray spectrometer (EDX) attached to the FE-SEM. The FT-IR spectrum was probed between 4000 and 400 cm⁻¹ using Agilent Technologies (Carry 630 FTIR) with the processing soft Omic 7.3 to access bond formation. UV–visible spectroscopy was performed using Jenway 7415 in the wavelength range of 200–800 nm to obtain the absorption spectrum of the synthesized perovskite. Bulk density was determined by tapping [29].

2.4. Photocatalytic test

Photocatalytic test was performed in the dark and under artificial light illumination [30]. Artificial irradiation was provided by a 500 W Halogen arc lamp. Dark photocatalytic test was investigated as follows; 200 mg of SrZrO₃ was added into 50 mL of 5 mg/L MB. The suspension was cycled under darkness for 1 hat 250 rpm, and 2 mL H₂O₂ was added. Then 5 mL of the suspension was withdrawn for every 30 min and centrifuged at 16000 rpm for 10 min to determine residual MB (mg/L). In a similar way, 200 mg of SrZrO₃ was added to 50 mL of 5 mg/L MB in a 250 mL photoreactor mounted on a cyclic vibrator. The suspension was cycled under dark for 1 h, then 2 mL of 2 mM H₂O₂ was added and irradiated with 500 W Halogen arc lamp (Beijing Au Light Technology Co.) with a cutoff filter (λ > 420 nm) with constant cycling from 0 to 150 min. During the irradiation time, 5 mL of the suspension was withdrawn for every 30 min interval and centrifuged at 16000 rpm for 10 min to monitor the rate of photodegradation. Measurements were performed in triplicates in all cases to reduce result dispersion and improve reliability of data. The residual concentration of MB dye in the suspension was monitored using UV–Visible spectrophotometer [31].The equilibrium concentration (C_e) was evaluated from the slope of the calibration curve. The adsorption capacity (q_t) was calculated using Eq. (1).

$$q_t=\frac{\left(C_0-C_e\right)V}{1000m}$$ (1)

where q_t (mg/g) is the amount adsorbed at time t, V (cm⁻¹) is the volume of the solution, and m (g) is the mass of photocatalyst. The percentage photo-degradation efficiency was calculated using Eq. (2).

$$\mathrm{D}(\%)=\frac{C_o-C_t}{C_0}\mathrm{x}100$$ (2)

where D (%) represents the percentage degradation efficiency, Co and C_t are the initial and concentration, respectively at a given time (mg/L).The concentration of MB dye was evaluated using a five-point calibration curve ranging from 0 to 25 mg/L.

2.5. Reusability studies

Reusability study was carried out as described in Refs. [21,32]. Four adsorption/degradation cycles were carried out in order to examine the reusability tests. In this test, 200 mg SrZrO₃ was used repeatedly to degrade 5 mg/L of 50 mL MB for 120 min irradiation under visible light at standard conditions. The progress of the reaction was monitored by measuring the absorbance of aliquot after centrifugation at 664 nm and the percentage degradation calculated. At each cycle, the catalyst was desorbed, washed, dried at 80 $°$ C and annealed at 800 $°$ C before reuse.

2.6. Kinetic studies

The experimental data were fitted into Zero-order [33], Psuedo-first order (PFO) [34], Psuedo-second order (PSO) [35], Elovich, Intra particle diffusion [36] and liquid film diffusion kinetic models [37] to investigate the mechanism of adsorption, photodegradation and rate limiting step.

3. Results and discussion

3.1. Phase analysis

Fig. 1 depicts the XRD pattern of the SrZrO₃ nanoparticles treated at 800 $°C$ for 2 h. The peaks marked with the prefix SZ could be attributed to the orthorhombic phase of SrZrO₃, according to JCPDS card no.01-070-0695 with Bmmb 63 space group [38,39].The peaks were sharp, indicating high crystallinity. The peak marked with the prefix ‘S’ could be traced to the cubic phase of undecomposed strontium from the Sr(NO₃)₂ precursor, according to JCPDS card No. 089–4910. The peak marked ‘*’ located at 2θ = 27.92° traced to the SrCO₃ phase, as also reported by Quinones-Gurrola et al. [40] and Lucena et al. [41].

Fig. 1.

(a) XRD pattern, (b) Williamson-Hall plot of the SrZrO₃nanoparticles.

Peak profile analysis was carried out using Debye Scherrer's (Eq. (3)) and the Williamson-Hall (W–H) method (Fig. 1b and Eqs. (4), (5))). Alfonso-Herrera et al. [42] reported lower average crystallite size for SrZrO₃ annealed in air at 800 $°C$ for 8 h. The crystallite size was determined as reported [28,[43], [44], [45], [46]]. The estimated structural parameters are presented in Table 1.

$$\mathrm{D}=\frac{\mathrm{k}\lambda }{\mathrm{\beta }\cos \mathrm{\theta }}$$ (3)

where D is the Scherer's size or average crystallite size, $\lambda$ = 0.1541 nm is wavelength of the X-ray source for Cu $k_{\alpha }$, $\beta$ = FWHM (in radians), $\theta$ is the Bragg's angle, k is a shape factor numerically equal to 0.9.

$${\mathrm{\beta }}_{\text{hkl}}\cos \mathrm{\theta }=\left(\frac{\mathrm{k}\lambda }{{\mathrm{D}}_{\mathrm{W}-\mathrm{H}}}\right)+4{\epsilon }_{W-H}\sin \mathrm{\theta }$$ (4)

$${\mathrm{D}}_{\mathrm{W}-\mathrm{H}}=\frac{k\lambda }{{\mathrm{Y}}_{\text{intercept}}}$$ (5)

where ${\mathrm{D}}_{\mathrm{W}-\mathrm{H}}$ is the W–H size or crystallite size, and ${\epsilon }_{W-H}$ is the Williamson-Hall microstrain determined from W–H plot. The dislocation density, lattice strain and microstrain were determined according to Eqs (6), (7), (8).

$$\delta =\frac{1}{{\mathrm{D}}^2}$$ (6)

$$\epsilon =\frac{\beta \cos \theta }{4}$$ (7)

$$\mathrm{s}=\frac{d}{D\sqrt{12}}$$ (8)

Table 1.

Structural parameters of SrZrO₃.

Parameter	Magnitude
2θ	32.52940
FWHM	0.1796
d-spacing	0.2634
Crystallite size (Scherer's method) (nm)	45.56
Crystallite size (W–H method) (nm)	44.50
Microstrain (ԑ)	1.66 $\times$ 10−3
Lattice strain (ή)	7.49 $\times$ 10−4
Dislocation density (nm−2)	4.78 $\times$ 10−4
Bulk density (g/mL)	0.35560
Lattice constants	a = 8.2532 b = 8.2662 c = 8.2709
Cell vol. A3 ($\times$ 106 p.m.3)	564.26
Calculated density (g/cm3)	5.3400
hkl plane	212

3.2. Surface morphology

The surface morphology of the sample was recorded at a magnification of $\times$ 50,000 (scale of 1 $\mu$ m) and is shown in Fig. 2a. The surface looks smooth with irregular shape, in agreement with the result of the bulk density (Table 1). Lower particle size and bulk density enhances high electron-phonon coupling in photocatalyst to prevent charge recombination reactions to enhance photodegradation [47,48].

Fig. 2.

(a) FESEM image, (b) EDX spectrograph of the SrZrO₃ nanoparticles.

3.3. Elemental composition

The chemical composition of the synthesized perovskite was investigated using EDX is shown in Fig. 2b. The spectrograph confirmed the presence of Sr, Zr and O elements in the synthesized SrZrO₃ compound, and their equivalent elemental atomic weight percent is shown in the inset of Fig. 2b. The insignificant amount of Ni impurity could be introduced by handling effect.

3.4. Fourier transform infrared spectroscope

The FTIR spectrum of SrZrO₃ nanoparticles in the range of 4000-400 cm⁻¹ is presented in Fig. 3a. While Fig. 3b showed the zoom FTIR of SrZrO₃ nanoparticles. From the Full FTIR spectrum, eleven bands were observed: 3792.34, 3741.75, 3464.84, 3230.92, 3209.58, 2954.31, 2545.55, 2334.61, 1648.43, 1196.99 and 645.57 cm⁻¹. Aravinthkumar et al. [9] and Ouni et al. [49] reported the spectra band positions and absorption peak shift to be influenced by the material composition, lattice constants, microstrain, shape of the material as well as annealing temperature. The bands located at 2545.53 and 2334.61 cm⁻¹ could be assigned to carbonate vibrations and indicative of the carbonate group represent the stretching vibration of the asymmetrical C–O bond in the CO₃²⁻ group [9,35]. The bands above 3000 cm⁻¹ could be associated with water angular deformation associated with O–H stretching. This interpretation agrees with the reported by Katyayan and Agrawal [37] who described spectra band range of 3633–3905 cm⁻¹ to minute traces of moisture (O–H). Triyono et al. [50] also reported the bands above 2000 cm⁻¹ (O–H bond) to stretching vibrations of absorbing ambient moisture. In addition, Perumal et al. [51] and Pan et al. [52] described the broad band around 3426 cm⁻¹ and above to be associated to O–H stretching vibration and bending mode of water molecules due to the O–H/H₂O functional group present in the prepared catalysts due to atmospheric water vapour on the surface of the catalyst. The absorption bands peak at 1648.43–1196.99 cm⁻¹ may be associated with the carbonyl group (C O) from the chelating precursors.

Fig. 3.

(a) FTIR Spectrum of SrZrO₃ nanoparticles, (b) Zoomed-in image of the FTIR result.

The mode of metal-oxygen (Sr–O) bond vibration of the synthesized compound was centered at approximately 648.35 cm⁻¹ (Fig. 3b), indicating the formation of the perovskite structure [35]. This result is consistent with the finger print region for metal-oxygen bond in the wavenumber range of 400–600 cm⁻¹ reported in the literatures [37,51].

3.5. Optical properties

Fig. 4a depicts optical absorption spectrum of the SrZrO₃. A high optical absorbance could be observed near the absorption edge in the UV region, suggesting that the sample is sensitive to UV light. Fig. 4b displays the graph of ($\alpha$ hv)² against photon energy (hv) for the estimation of optical band gap energy. The band gap energy determined in accordance with Tauc formula (Eqn. (9)) was 5.31 eV [53,54]. The optical band gap energy obtained agrees with the report of Cabello et al. [55]. Aside other physical and chemical properties of nanomaterials, the change in the optical band gap energy could be due to various effects such as doping, synthesis technology, strain, particle morphology, annealing temperature, concentration of precursors, solution pH and reactions conditions [23,51,56,57].

$$\alpha hv=C{\left(h\nu -E_g\right)}^m$$ (9)

where $E_g$ is the optical bandgap energy, $h\nu$ is the photon energy, C is a constant, and m is a factor that depends on the type of allowed electronic transition and is numerically equal to $\frac{1}{2}$ for a direct allowed electronic transition.

Fig. 4.

(a) Optical absorption spectrum, (b) Tauc plot of the SrZrO₃.

3.6. Methylene blue linear fit

A five-point linear fit for MB was obtained to study the photodegradation (Fig. 5a). The fit was obtained using 5–25 mg/L concentration of MB. To establish the fit, the absorbance of these concentrations was obtained at 664 nm (the absorption maximum of MB) and plotted against the concentrations to obtain a linear regression equation used to estimate the equilibrium concentration of degraded MB.

Fig. 5.

(a) Linear fit of MB dye, (b) Time-dependent absorption spectrum.

3.7. Degradation studies

3.7.1. Time-dependent absorption spectrum

The result of time-dependent absorption spectrum for the effect of light is shown in Fig. 5b. It was observed that absorbance decrease with increase in time of irradiation at 200 mg of catalyst dosage in 50 mL of 5 mg/L MB dye from 30 to 150 min. The increase in irradiation time changes the color of the suspension to lighter-blue, which is responsible for the bond cleavage of the chromophoric group present in the dye solution [21]. The progress of the reaction was followed by monitoring the decrease in the absorbance of methylene blue at λ_max = 664 nm.

3.7.2. Absorbance and degradation studies in the dark and light illumination

Fig. 6a illustrates the absorbance plot obtained in the dark and light illumination reactions for MB dye degradation using SrZrO₃ assisted H₂O₂. The initial absorbance (0.189) for MB in the dark did not decrease. However, in the presence of light irradiation the absorbance was observed to decrease from 0.189 to 0.080 between the time intervals of 0–150 min. This is an indication that photodegradation occurred. Fig. 6b shows the photodegradation efficiency of MB. The degradation efficiency in the dark and in the presence of light irradiation was 35 % and 80 %, respectively, in the time interval of 30–150 min. This observation showed that photocatalytic degradation of MB was enhanced by increasing the reaction time. Alammar et al. [58] reported degradation efficiencies of 45, 30 and 45 % for MB for 80 min reaction time using prestine SrTiO₃, CaTiO₃ and BaTiO₃ perovskites irradiated with high pressure Hg lamp using10 mg/L of MB and 100 mg catalyst. Bellam et al. [59] reported 60 % degradation efficiency of MB within 150 min reaction time using N₂ doped NiTiO₃ irradiated with visible light using 3.2 mg/L of MB.

Fig. 6.

Effect of photodegradation parameters on MB (a) absorbance, (b) Degradation efficiency, (c) Contact time, (d) Initial MB concentration, (e) Solution pH and, (f) Catalyst dosage.

3.7.3. Adsorption kinetics

The efficiency of SrZrO₃ catalyst for the degradation of MB from aqueous solution was investigated using a batch equilibrium technique by using different amounts of catalyst in a reaction vessel containing 50 mL of MB. The adsorption kinetic studies were studied for different pH values, contact time, catalyst dosage and MB dye concentration.

3.7.4. Effect of contact time

The effect of contact time on degradation efficiency was examined using 50 mL of 5 mg/L MB and 200 mg catalyst from 0 to 150 min. Fig. 6c showed that an increase in the contact time led to a decrease in residual MB concentration. The highest removal efficiency was observed at 120 min. There is no previous work on the use of SrZrO₃ and SrZrO₃ coupled H₂O₂ for which we can compare the present report. Nevertheless, the effect of contact time on degradation efficiency of MB using various catalysts could be found in the literatures. Soltanabadi et al. [60] reported the removal of rhodamine B (30 mg/L; V = 100 mL) within 90 min using visible light irradiation with assisted H₂O₂ for LaFeO₃ supported CuO. The performance of H₂O₂ for LaFeO₃was higher compared to the pure LaFeO₃, thus, supporting the good performance observed for our SrZrO₃ supported H₂O₂. In a related study, Chang and Hu [61] reported over 70 % degradation efficiency for MB, methyl orange, Rhodamine, bisphenol A and phenol using SrTiO₃ supported 20 wt% Ga₂O₃ within 3 h irradiation.

3.7.5. Effect of initial MB concentration

The initial dye concentration is another important variable that can affect adsorption process. The effect of initial MB concentration on degradation efficiency was investigated by varying the initial MB concentration from 5 to 25 mg/L, using catalyst dosage of 200 mg and contact time of 0–150 min. Results showed decreased degradation efficiency of MB with increasing initial MB concentration (Fig. 6d). This behavior could be attributed to the oversaturation of the available photocatalyst active sites [62]. Higher adsorption of pollutant with a high initial concentration of pollutant facilitates more pollutant molecules to get excited on light irradiation, which enhances the photodegradation efficiency. However, at higher concentration reduction in photodegradation is observed due to reduction in the number of photons reaching onto the surface and consequent reduction in the number of OH* radicals and positive hole generation [63].

3.7.6. Effect of pH

The effect of initial solution pH on degradation and removal efficiency was evaluated at pH 3–10, while the initial MB concentration and catalyst dosage were fixed at 5 mg/L and 200 mg, respectively. The degradation efficiency was found to be 80 % in acidic pH 3 and decreased with increase in pH (Fig. 6e). This could be due to surface electrostatic charge, oxidative potential and sorption capacity between the dye molecule and SrZrO₃ nanoparticles surface [64,65]. Yazdanbakhsket al. [66] reported pH 2 as the optimum pH for the removal of Reactive blue 5 dye from aqueous solution containing Ca doped lanthanum nickel trioxide catalyst.

3.7.7. Effect of catalyst dosage

Fig. 6f showed the effect of catalyst dosage. The degradation efficiency was highest at 200 mg. At higher dosage, the degradation was found to decrease. One of the possible reasons might be the turbidity of the solution, which increased with the amount of catalyst and blocked the photons reaching the medium. This phenomenon may result to a smaller number of active photoactive species and consequently reduction in percentage of degradation. Several studies report the photocatalytic rate to first rise along with catalyst loading and then deflate at high dosage due to unavailable active surface sites for exposure and light scattering effects [67].

3.7.8. Reusability studies

The photocatalytic reusability of the synthesized photocatalyst was investigated via stability test. The photocatalytic reusability test of the photocatalyst was studied for MB degradation up to four cycles (Fig. 7). The degradation efficiency of MB was slightly decreased during the four consecutive cycles. The decrease in degradation efficiency could be attributed to the catalyst loss with each cycle due to the procedural approach [18]. The decrease in quantity of the catalyst during processing for reusability could be traced to the reduction in the numbers of active cites (adsorbent) in the MB dye.

Fig. 7.

Degradation efficiency of MB at four consecutive cycles.

3.8. Kinetic models

The models used for describing the experimental data were the Zero-order, PFO, PSO, Elovich, Weber-Morris and Liquid Film Diffusion kinetic rate models [37]. These models were applied to determine the one that best described the uptake and degradation of MB dye in solution. Fig. 8a shows the experimental and fitted plots of Zero-order kinetic model for the effects of catalyst dosage, initial MB concentration and solution pH 3. Mesbah et al. [68] described R² as a viable tool for judging the fitness of a kinetic model. The R² values derived from the Zero-order kinetic model is presented in Table 2. The R² value for the effect of dosage was the highest, indicating lower values of error functions. In addition, values of calculated adsorption equilibrium capacity (q_e(cal)) were noticed to be lower than the experimental adsorption equilibrium capacity q_e(exp). The result of the half-life (t_1/2) and equilibrium constant for zero-order (k₀) were negative for all the experimental variables, signifying that the experimental data did not fit into this model. Therefore, there is need to test other models that may fit best.

Fig. 8.

Experimental and linear fits for the effects of dosage, initial MB concentration and pH 3 for, (a) Zero-order, (b) PFO, (c)PSO, (d) Elovich, (e) Weber-Morris, (f) Liquid film diffusion model for the degradation of MB at 30 $°C$.

Table 2.

Kinetic parameters of Zero-order model.

Parameter	R2	qe(cal)	qe(exp)	K0	t1/2 (min)
Dosage	0.8857	0.1589	0.9916	−0.0055	−451.26
MB (mg/L)	0.6949	0.3460	1.0966	−0.0061	−413.22
Solution pH	0.4759	0.4431	0.9916	−0.4431	−5.68

The experimental and fitted plots for the PFO kinetic model were shown in Fig. 8b. The regression values are presented in Table 3. The R² value was maximum at the initial MB concentration (5 mg/L), while the lowest was found for the effect of solution pH 3. Further to this, the q_e(cal) values for dosage and solution pH 3 were higher than the q_{e (exp)} values. Comparing the results in Table 2, Table 3, it could be observed that the PFO model exhibited higher R² and q_e(cal) values compared to the Zero-order model, suggesting that the PFO model performed better than its counterpart. However, the PFO model like the Zero-order model did not fit well into the absorption process, hence the need to exploit the PSO kinetic model.

Table 3.

Kinetic parameters of PFO model.

Parameter	R2	qe(cal (mg/g)	qe (exp) (mg/g)	k1 (min−1)	t1/2 (min)	$\frac{q_t}{q_{e\left(cal\right)}}$
Dosage (mg)	0.9402	1.0034	0.9916	0.0158	43.99	0.6509
MB (mg/L)	0.9735	0.8206	1.0966	0.0230	30.22	0.9014
Solution pH 3	0.7549	1.9822	0.9916	0.0768	9.02	0.9006

The PFO rate constant (k₁) for the effects of solution pH 3 was highest compared to the effect of dosage and initial MB concentration. This means that at this pH most of the MB change to zwitter ionic form and resulted in the increased adsorption capacity (Table 3) of MB onto the surface of SrZrO₃ and consequently, increase rate of degradation. In addition, the fractional power defined as the ratio of q_t/q_e per unit time was highest for the effect of initial MB concentration. This suggested that at this concentration more MB was adsorbed on the photocatalyst.

The results of the linear plots and the kinetic parameters for the PSO model were shown in Fig. 8c and Table 4, respectively. The coefficient of determination for the variables was nearly unity suggesting that the reaction followed a second order rate constant with higher efficiency. The equilibrium constant (K₂) was highest at solution pH 3 signifying that more MB was adsorbed with subsequent degradation. The t_1/2 for the degradation efficiency was observed to be 2 min, suggesting that the data corresponds to the initial sorption rate. The q_e(cal) values were higher than the q_e(exp), suggesting that all the investigated parameters fit well into the PSO model. The fractional power (q_t/q_e) for the variables was estimated to be 0.660, 0.916 and 0.922 for the effect of dosage, MB concentration and solution pH, respectively, suggesting that the MB adsorption rate on the SrZrO₃ catalyst was proportional to the available sites.

Table 4.

Kinetic parameters of PSO model.

Parameter	R2	qe(cal (mg/g)	qe (exp) (mg/g)	k2 (min−1)	t1/2 (min)	ISR (min−1)
Dosage	0.9103	0.9662	0.9916	0.0431	4.64	0.0402
MB (mg/L)	0.9889	1.1185	1.0966	0.1034	1.93	0.1293
Solution pH	0.9998	0.9954	0.9916	1.0093	0.20	1.0000

Note: ISR is initial sorption rate.

The linear fit for the Elovic kinetic model was depicted in Fig. 8d. The result indicated a near unity of R² for the initial MB concentration (Table 5). The initial sorption rate (α) was highest for catalyst dosage, implying that the adsorption of MB dye on the surface of SrZrO₃ was $>$ 50 %. The fractional surface coverage (θ) for the effect of MB obtained was the highest (Table 5), this is similar to the report of Kajitvichyanukul and Ananpattarachai [37], hence suggesting a good adsorption and degradation process.

Table 5.

Kinetic parameters for the Elovic model.

Parameter	R2	1/β	β	α (g/mg.min2)	θ
Dosage	0.9263	0.3758	2.6606	0.5211	0.3693
MB (mg/L)	0.9987	0.2181	4.5859	0.2262	0.8772
Solution pH	0.9337	0.2052	4.8731	0.2795	0.7589

Fig. 8e illustrated the linear fits for the Weber-Morris Kinetic model. Catalyst dosage has the highest coefficient of determination, R², suggesting less error values (Table 6). The rate of diffusion coefficient (k_id) was highest for the effect of concentration. The initial adsorption (β) was highest for solution pH 3, indicating that the process was pH dependent.

Table 6.

Kinetic parameters of Weber-Morris model.

Parameter	R2	kid (mg.g−1min−1)	β (mg/g)
Dosage	0.9800	0.0736	0.0112
MB (mg/L)	0.9184	0.0879	0.1273
Solution pH	0.7549	0.0776	0.2151

Fig. 8f illustrated the linear fits of Liquid film diffusion kinetic model. The kinetic parameters for the model are shown in Table 7. The equilibrium constant (k_fd) for the sorption was negative indicating a non-film diffusion of the adsorbate through the photocatalyst [33].

Table 7.

Kinetic parameters for Liquid film diffusion model.

Parameter	R2	kfd (mg g−1 min−1)	Intercept
Dosage	0.9399	−0.0157	−0.0074
MB (mg/L)	0.9673	−0.0236	0.2347
Solution pH	0.7546	−0.0768	−0.6883

3.9. Nonlinear error functions analysis

Studies have shown that the error structure of experimental data is usually changed during the transformation of adsorption kinetics into their linear forms [5]. It is for this reason that nonlinearized regression analysis become inevitable, since it provides a mathematical rigorous method for determining kinetic adsorption parameters using original form of kinetic equations. Unlike linear regression, the nonlinear regression usually involves the minimization of error distribution between the experimental data and the predicted kinetic model based on convergence criteria. The following nonlinear error functions were calculated: sum square of errors (ERRSQ), hybrid fractional error function (HYBRID), average relative error (ARE), marquardt's percent standard deviation(MPSD), sum of absolute errors (EABS), standard error (SE), nonlinear chi-square test (χ²), sum of absolute error (SAE), sum of relative error (S_RE), percentage standard deviation (Δq %) and coefficient of non-determination (1-R²) [69].

Table 8 depicts the result of the nonlinear error analysis for zero-order kinetic. The nonlinear error calculated using HYBRID method was highest for solution pH 3, MB concentration and dosage. It was also observed that errors due to HYBRID calculations were higher for the highest dosage. Hence, it was better at lower catalyst concentration.

Table 8.

Nonlinear error values for the zero-order kinetic model.

Parameter	ERRSQ	HYBRID	ARE	MPSD	SAE	SE	Δq (%)	SRE	χ2	1-R2
Dosage	0.6933	69.918	−16.79	0.8397	0.833	0.372	41.99	8.814	4.362	0.0617
MB (mg/L)	0.5634	51.374	−13.68	0.6845	0.751	0.335	34.22	7.220	1.628	0.0321
Soln. pH	0.3008	30.339	−11.06	0.5532	0.548	0.245	27.66	5.806	0.679	0.0576

Table 9 shows the results of the nonlinear error functions for the PFO kinetic model. The error functions are very high indicating that the sorption did not follow the PFO model.

Table 9.

Nonlinear error functions for the PFO kinetic.

Parameter	ERRSQ	Hybrid	ARE	MPSD	SAE	SE	Δq (%)	SRE	χ2	1-R2
Dosage	0.0001	0.0142	0.239	0.012	0.012	0.005	0.598	0.126	0.000	0.0998
MB (mg/L)	0.0762	6.9474	−5.034	0.252	0.276	0.123	12.59	2.655	0.069	0.0176
Soln. pH	0.0001	0.0142	0.239	0.012	0.012	0.005	0.598	0.126	0.000	0.0998

Table 10 shows the result of nonlinear errors for the PSO kinetic model. The error values for ERRSQ, HYBRID, MPSD, SE, S_RE and χ² decreased down the table for the effect of dosage, MB concentration and solution pH 3.

Table 10.

Nonlinear error functions for the PFO kinetic model.

Parameter	ERRSQ $\times {10}^{-4}$	Hybrid	ARE	MPSD	SAE $\times {10}^{-2}$	SE	Δq (%)	SRE	χ2 $\times {10}^{-4}$	1-R2 ${\times 10}^{-2}$
Dosage	6.00	0.0649	−0.5119	0.026	2.00	0.011	1.280	0.269	6.00	8.9
MB (mg/L)	5.00	0.0438	0.3999	0.020	−2.00	0.010	0.100	0.211	4.00	0.005
Soln. pH 3	0.15	0.0015	0.0777	0.004	0.40	0.002	0.194	0.041	0.15	0.3

It should be noted that error function analysis was not conducted on the results of Elovich, Weber-Morris and Liquid film diffusion models. Nonetheless, the nonlinear adsorption kinetics result for the zero-order, PFO and PSO revealed that the PSO kinetic model best described the kinetic experimental data with lower error values. This finding is similar to a literature report on the nonlinear error functions for adsorption of fluoride on LaFeO₃ photocatalyst [68].

3.9.1. Proposed reaction scheme for the photodegradation of MB using SrZrO₃ nanoparticles coupled H₂O₂

The photodegradation of MB dye in presence of SrZrO₃ couple H₂O₂ could be attributed to the combined effects of dissociation of H₂O₂ in the presence of light and the complex transport of highly reactive hydroxyl radical (*OH) in the reactant mixture. Chiou et al. [70] and Saha et al. [71] proposed the following reaction schemes:

$${\mathrm{H}}_2{\mathrm{O}}_2+\mathrm{h}v\to 2^{*}\text{OH}$$ (10)

$$\mathrm{h}{v}^{+}+{\text{OH}}^{-}\to {}^{*}\mathrm{O}\mathrm{H}$$ (11)

$${\mathrm{e}}^{-}+{\mathrm{H}}_2{\mathrm{O}}_2\to {}^{*}\mathrm{O}\mathrm{H}+{\text{OH}}^{-}$$ (12)

$${\mathrm{h}}^{+}+{\text{OH}}^{-}\to {}^{*}\text{OH}$$ (13)

$${\mathrm{e}}^{-}+{\mathrm{O}}_2\to {{}^{*}\mathrm{O}}_2^{-}$$ (14)

$$\text{RH}+{}^{*}\mathrm{O}\mathrm{H}\to {\mathrm{H}}_2\mathrm{O}+{\text{CO}}_2$$ (15)

The first step involves the direct photolysis of H₂O₂ to produce hydroxy radical (Eq. (10)) as a crucial step in improving the rate of photocatalytic reaction. Saha et al. [72] suggest that H₂O₂ is a better electron acceptor than oxygen. This phenomenon decreases the chances of electron-hole (e⁻-h⁺) recombination. In Eqs. (11)–(13) the hydroxyl ion reacts with the holes generated during excitation to produce hydroxyl radical while the electron at the conduction band react with the more H₂O₂ ion to produce more hydroxyl radical and ion simultaneously, which in turn reduced the probability of e⁻-h⁺ recombination. The superoxide radical (^•O₂⁻) as indicated in Eq. (14), is less dominant in affecting the rate of photocatalytic reaction as compared with hydroxyl radicals [70]. In Eq. (15), the organic dye (methylene blue) RH, react with the hydroxyl radical to produce carbon dioxide, water and intermediates. In addition, the surface reaction of H₂O₂ on the surface of SrZrO₃ catalyst may be represented in Eqs. (16)–(20) [73,72].

$${\mathrm{C}}^{+}+{\mathrm{H}}_2{\mathrm{O}}_2\to {\mathrm{C}}^{+}+{\mathrm{H}}^{+}+{\text{HO}}_2^{-}\left({\mathrm{C}}^{+}=\text{Oxidized}\text{catalyzed}\text{surface}\right)$$ (16)

$$\mathrm{C}+{\mathrm{H}}_2{\mathrm{O}}_2\to \mathrm{C}+{}^{*}\mathrm{O}\mathrm{H}+{\text{OH}}^{-}\left(\mathrm{C}=\text{Reduced}\text{catalyzed}\text{surface}\right)$$ (17)

$${\mathrm{C}}^{+}+{\mathrm{O}}_2^{-}\to \mathrm{C}+{\mathrm{O}}_2$$ (18)

$$\mathrm{C}+{}^{*}\mathrm{O}{\mathrm{H}}_2\to \mathrm{C}+{\text{HO}}_2^{-}$$ (19)

$$\mathrm{C}+{}^{*}\mathrm{O}\mathrm{H}\to {\mathrm{C}}^{+}+{\text{OH}}^{-}$$ (20)

It is obvious that in these model equations, H₂O₂ may react with both oxidized and reduced catalyst surface (Eqs. (7), (8))) and both the catalyst and H₂O₂ undergo simultaneous redox reaction. This resulted to generation of more hydroxyl radicals and ions that may, in turn, act as e⁻-h⁺ scavengers to react with the organic molecules. The hydroxyl radicals, to a large extent, play important role in the photocatalytic oxidation process, and in photodegradation of Methylene blue dye. Therefore, the effect of the addition of hydrogen peroxide will yield more hydroxyl radicals in the process hence a better photocatalytic reaction [74,75]. As shown in Eqs. (18)–(20), superoxide, hydroxyl and perhydroxyl radicals reacted on the catalyst surface to further enhance the photocatalytic activity.

4. Conclusion

SrZrO₃ perovskite was synthesized by the sol-gel Pechini method and annealed at 800 $°C$ for 2 h. The sample was characterized using XRD, FE-SEM, FTIR, EDX and UV–visible spectrophotometer. The prepared SrZrO₃ perovskite exhibited orthorhombic phase. Debye Scherrer and Williamson-Hall crystallite size were found to be 45.56 and 44.50 nm, respectively. The FESEM images showed microstructures with a smooth surface. The EDX result confirmed the presence of the constituent elements. The optical band gap was estimated to be 5.31 eV. Photodegradation of the MB using SrZrO₃ coupled H₂O₂ was enhanced in visible light irradiation compared to dark reactions. Photocatalytic activity was investigated for the effects of time, catalyst dosage, adsorbate concentration and solution pH. The optimized time for the degradation studies was 150 min. The degradation efficiency was greater than 80 % under visible light and lower than 40 % in the dark. The experimental data were fitted into Zero-order, Pseudo-first order, pseudo-second order, Elovic, intraparticle diffusion and Liquid-film diffusion kinetic models. The experimental data fitted best into PSO kinetic model due to the higher values of coefficient of determination. Nonlinear error functions were calculated for the various kinetic models to determine lower values of error functions, where the Psuedo-second order kinetic model demonstrated lower values of error functions.

Data availability

The data used for this paper will be made available on request.

CRediT authorship contribution statement

J.N. Tsaviv: Writing – original draft, Visualization, Software, Resources, Methodology, Investigation, Data curation, Conceptualization. I.S. Eneji: Writing – review & editing, Visualization, Validation, Supervision, Methodology, Conceptualization. R. Sha'Ato: Writing – review & editing, Visualization, Validation, Supervision, Methodology, Conceptualization. I. Ahemen: Writing – review & editing, Visualization, Validation, Supervision, Methodology, Conceptualization. P.R. Jubu: Writing – review & editing, Software, Formal analysis. Y. Yusof: Software, Formal analysis.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.