Simple synthesis of novel Lanthanum doped Copper oxide nanoparticles for wastewater treatment: A comparison between Experiment and COMSOL simulation

Photocatalysis is a promsing technique for remediation and decontamination of waste water. This research work focuses on the synthesis of pure and lanthanum (La)- (1, 2 and 3 wt%) doped copper oxide nanoparticles (CuO-NPs) via a simple, cost effective and ecient sol-gel process. Differnet characterization techniques such as UV-vis, PL, SEM, XRD, EDS and FTIR are used to investigate optical, compositonal, structural and morphological properties of the synthesized material. Quite interestingly, doping of rare earth element La has reduced the particle size (52.02 ± 0.04 nm to 42.39 ± 0.02 nm) of CuO-NPs. Additionaly, with doping, the band gap and electron hole recombiantion rate is also reduced. Band gap has shifted towards visible region (3.13 ev to 2.85 ev) which makes it an excellent mateiral for photocataysis. Methylene blue (MB) dye is used as model contamination. Photocatalytic degradation ecieny of 79% is obtained in 150 min by La 0.02 Cu 0.98 O against MB under natural light irrradiation. Band gap is increased upon futher doping which attributes to the reduced catalytic eciency to 73% for La 0.03 Cu 0.97 O. Theoratical photocatalytic activity of CuO-NPs against MB dye with particle size of 50nm is carried out using COMSOL Multiphysics 5.3a Licenced version in order to corelate the experimental and theoratical results.


Introduction
Organic dyes are the most widely used compounds in industries due to their ability to resist fading when exposed to light, perspiration, water, oxidising agents, and microorganisms (Arunadevi et al., 2018; Saratale, Saratale, Chang, & Govindwar, 2011). Due to their widespread use and large-scale manufacturing, dyes are now found in considerable quantities in wastewater (Kazeminezhad & Sadollahkhani, 2014). Roughly 1-15 percent of synthetic textile dyes are estimated to be dumped into e uents during the manufacturing process (Shahabuddin et al., 2018). These dyes are released directly into water bodies, which caused substantial water contamination owing to their carcinogenic nature (Kumar & Pandey, 2017). Due to their enormous moelcular size and complicated structures, the majority of these dyes are hazardous and non-biodegradable and thus can result in major risks and threats to aquatic and human life (Tanwar, Kumar, Mandal, & Chemistry, 2017). Researchers are wokring hard to overcome this problem using different scienti c methods. These dyes are removed via a range of physical, chemical and biological processes such as adsorption, precipitation, ozonisation (Saeed & Khan, 2017). Many of these techniques are non-destructive, insu cient and produce secondary contamination. Furthermore, well-established chemical techniques are non economical. Moreover, aerobic decontamination is ine cient for stable dyes, while anaerobic oxidation process of dyes results in the formation of carcinogenic aromatic amines Copper is one of the most inexpensive metal and has a diverse range of applications, including gas sensors (Mikami,  Copper-based semiconductors do seem to have a small band gap that can be precisely tuned by using different methods to harvest wide range of natural/synthetic radiation (Salavati-Niasari & Davar, 2009).
They were thus extensively employed as a strong heterogeneous photocatalyst. Since the electrons in the conduction band are unstable in phase pure CuO, the majority of the photogenerated electrons migrate to the valance band and recombine with the hole without engaging in the oxidation process (Sonia et al., 2015). This implies that by postponing the recombination of charge carriers in photocatalysis, the overall e ciency of the reaction can be enhanced. In the present study, pure and La doped CuO nanoparticles have been synthesised using a facile sol-gel method. Analyses of the structural and optical characteristics of the nanoparticles as they were produced were carried out using FTIR, XRD, SEM, PL and UV-vis spectroscopy. Additionally, the impact of the La content on the NPs' photocatalytic activity was examined experimentally. The ndings indicate that incorporation of La lowers the band gap of the CuO NPs, thus improving their photocatalytic activity. COMSOL 5.3a Licensced version is used to construct a 2D model of this research work to simulate photocatalytic degradation of MB dye by CuO-NPs in order to study corelation between experiment and simulation.

Method
Sol-gel process is adopted for the synthesis of pure and La (1, 2, 3 wt%) doped CuO-NPs. Aqueous solution of 0.5M copper nitrate and 0.5M citric acid are prepared separately, then stirred at room temperature for 30 minutes to get a homogenous solution. Once dissolved, the stock solution is made by combining the two solutions in a glass beaker while stirring at 50ºc. The pH of the solution was adjusted to 9 by adding an adequate quantity of NH3 solution drop wise. The temperature is gradually increased to 90℃. After 2 hours of continuous stirring, a thick brownish black gel is produced at the bottom of the beaker which is washed and dried in the oven. After nely grounding, it is calcinated at 550℃ for two hours to obtain NPs of pure CuO. Lanthanum nitrate solution of different concentrations (1, 2 & 3 %) was combined with citric acid and copper nitrate solution to synthesizeLa:CuO NPs. Hence, a formulation procedure identical to that used to produce CuO nanoparticles was followed. The ow chart of the procedure is shown in gure 1.

Characterizations
Following the nanoparticle synthesis, their physical characteristics and photocatalytic activity were evaluated. The lattice parameters, bond angles, bond lengths and crystalline size of the NPs were determined using the X-ray diffraction (XRD) method. XRD was performed using an X-ray diffractometer (KAPPA Apex II) and CuKα radiation with a wavelength of 1.5406 Å. Surface morphology of synthesized samples is studied using a Field emission scanning electron microscope (FE-SEM) (TESCAN MIRA 3). Fourier transform infrared spectroscopy (FTIR) using a (FT/IR-4100-A Jasco) spectrophotometer with a spectral range of 500-4000 was used for the chemical analysis. Photoluminescence (FP-8200, JASCO) and UV-vis (UV/1700, Shimadzu) spectroscopy is used to study the optical properties of synthesized pure and La doped CuO-NPs.

Photocatalytic activity
Photocatalytic activity of synthesized pure and La doped CuO-NPs against MB dye, under natural light irradiation was analyzed. In this experiment, 200ml of 1 ppm solution of MB and 20mg of ne powder photocatalyst (pure CuO and La 1, 2 & 3% doped CuO-NPs respectively) were taken. Measurement period of catalytic activity was set to be 150 min. In order to achieve absorption-desorption equilibrium between catalyst and dye, the suspension was stirred in the dark for one hour. Subsequently, this suspension was exposed to natural light irradiation and the reading was taken after every 30 min until 150 min. The color of suspension was shifted from blue to colorless. UV-visible spectrometer was used to analyze the residual solution. Intensity of UV peak at 570 nm was directly related to the MB (%) left in the suspension.
Here, initial absorption is represented by C 0 and C t indicates absorption after various time intervals.
Degradation percentage for all samples is evaluated over 150 min.

COMSOL 5.3(a)
Analytic or numeric approach used in mathematical modeling is very bene cial for solving real-life based physical problems. Out of these two, numeric approach is preferred since a computer can e ciently handle any type and size of data as compared to humans. Finite elemental analysis (FEA) has been used in structural mechanics and it is reported in 1940's (Courant & mathematics, 1994). As a way to have a superior concept of the collaboration of electromagnetic (EM) waves by the Nano based, a commercial FEA software program bundle, COMSOL 5.3a Licensed version, with RF module, is mostly elaborated to construct the 2D model essential for this study work. FEA involves the easy and quick understanding of interaction between EM waves and sub-wavelength device (CuO in this case). This technique enables us to split the whole computation space into nite size elements on which further approximation could be solved.
The geometry of the model is generated by sketching multiple sub-domains in COMSOL using various tools and settings to represent different materials and areas. Schematic diagram of the model is illustrated in gure 8(a). Three types of boundary conditions are utilized in this model namely: continuity boundary conditions (CBCs), scattering boundary conditions (SCBs) and periodic boundary conditions (PBCs). The CBCs are applied to internal sides of structure to ensure continuity of tangential components of the electromagnetic eld whereas the PBCs are applied on the external boundaries to approximate a large structure by considering the unit cell. The SCBs are used to reduce the re ection (Ghosh & Palik, 1997). Perfectly matched layers (PMLs) are another kind of condition that may be used to limit the interior of the computation region. These PMLs are used when the scattering boundaries are not adequately absorbing the incident elds owing to the wave vector's dispersion. These conditions are applied to the rear of the internal continuity boundaries, thus extending the computation domain to half the incident wavelength. When a certain domain is designated as PML, the two subsequent domains act in the same way i.e., the interface of two domains does not present any obstructions to the incoming wave. The wave emerges in the next domain exactly as it is, with no energy loss or modi cation (Iqbal, 2013).
The sub-domain at the bottom is referred to as the excitation port or in-port. This indicates that the model's input power is supplied vertically upward at this port. The value of the input power supplied at this port may be adjusted to any optimal value from the global expression, such as 12700 watts in present case. Additionally, the harmonic propagation mode is an essential clause in the current model.
Meshing is a very important step of solving the model. The physical domains are divided into smaller sub-domains of irregular geometry de ned as element. The element serves as the fundamental unit of the discretization process in order to get the solution. In a model, the elements of each subdomain are connected to one another via points, known as nodes.
Model parameters are xed to conduct a sweep for variables. The model's most often used parameter is wavelength, which spans from 400nm to 1000nm and is con gured to vary in 1nm increments. TMpolarized light may get the necessary information through transmission, re ection, or absorption at different angles. The last step is to set the parametric solver to sweep the model's variables. The wavelength range (400-900nm) is crucial in this simulation. The model is irradiated by s and p-polarized light at a constant angle (0°). Where β represents full width half maxima (FWHM), θ is the Bragg's diffraction angle and λ is X-ray wavelength (1.5406 Å). In Fig. 3b, the size of CuO and La:CuO nanoparticles is shown to be decreased with the increasing concentration of La dopant. The crystallite size evaluated by equation (2)

Morphological and Compositional analysis
Surface morphology and compositional analysis of CuO and La:CuO-NPs is carried out by scanning electron microscope (SEM) and energy dispersive spectroscopy (EDS). Figure 3 (a,b)

Optical studies
The (αhF(R)) 2 = (A⁄s)(hv-E g ) (5) Extrapolating the straight-line parts of the curves in the plot of (αhF(R)) 2 against hv gives the band gap of NPs. The E g values for CuO and La:CuO-NPs were extracted from the plot as represented in gure 4(a).
The band gap of pure CuO was determined to be 3.14 eV, which is consistent with the reported value. Figure 4(b) illustrates the band gap uctuation of the NPs as a function of La concentration. The La doping was observed to reduce the band gap of NPs. This decrease in band gap may be attributed to the presence of impurity states between the CuO's conduction and valance bands due to La doping. As the number of dopant atoms increases, these impurity states coalesce near the conduction band's lowermost edges, reducing the gap between the conduction and valance bands (Rajendran et al., 2016). For 1 and 2% doping of La, band gap has reduced to 3.07 and 2.85 eV respectively but when dopant concentration is increased to 3%, the band gap increases to 3.01 eV. Burstein-Moss (BM) effect is thought to be responsible for this rise in band gap (Tiss et al., 2019). A highly doped semiconductor allows the Fermi level to migrate closer to the conduction band, resulting in an increase in the band gap. As a result, the valance band electron must expend more energy to get to an unoccupied state of the conduction band, causing the band gap to expand (Litter, Navio, & Chemistry, 1996).
The PL spectra illustrated in gure 4(c) are obtained on exciting wavelength of 335nm. Generally, the PL spectra consist of two main regions: UV region (band gap con rmation) and broad band spectrum (characteristic peaks and defects) (Marami, Farahmandjou, & Khoshnevisan, 2018). The spectrum has two characteristic peaks located at 413 nm and 425 nm. The blue emission peak of 413 nm attributes to singly ionized copper (Cu + ) vacancies. The shoulder peak at 425 nm is associated with the surface defects of CuO-NPs due to oxygen vacancies. In pure sample, the cluster of electronic excitations is occurred which is not controlled by material itself which leads to the high rate of electron hole recombination (Sharma et al., 2017). Dopant element (La) is used to control the electron hole recombination. Drop in PL intensity con rms the reduction in the recombination rate, desirable for photocatalytic applications.

FTIR
Chemical composition and bonds of pure and La doped CuO-NPs were examined by Fourier Transformation Infrared (FTIR) Spectroscopy. Figure 4 (Gnanavel, Palanichamy, Roopan, & Biology, 2017). Quit interestingly as the dopant concentration is increased, peak intensity is also enhanced. Besides the absorption bands discussed above, no impurity peak has been identi ed which con rms that the synthesized samples are highly pure. It has been discussed in the SEM and XRD results that the particle size is reduced by the addition of dopant. The PL results revealed that electron recombination rate is controlled e ciently by increasing the dopant concentration. On the other hand, band gap calculated from the UV-vis spectrum shows anomaly. Band gap of pure CuO-NPs is 3.14 eV which is reduced upon doping. For 1 and 2% doping of La, band gap has reduced to 3.07 and 2.85 eV respectively but when dopant concentration is increased to 3%, Burstein Moss effect comes into play and increase the band gap to 3.01 eV. Although for 3% doped sample, electron hole recombination rate and particle size have optimal values to be a good photocatalyst but the increased energy band dominates all the other factors and photocatalytic e ciency is reduced as compared to 2% doped sample. This anomaly suggests that only a limited amount (2%) of La doping is suitable for CuO-NPs to enhance its photocatalytic activity.

Mechanism
The photocatalytic activities are often affected by variations in oxygen vacancy. The electron-hole pairs are separated based on the amount of oxygen vacancies present in the solution. According to Malleshappa et al. (Malleshappa et al., 2015), the photocatalytic activity varies depending on the concentration of defects at the surface level. The charge carrier recombination rate is decreased as the surface defects increases and the particle size reduces, resulting in enhanced photocatalytic activity.
Based on the observations, a plausible pathway for the photodegradation of MB dye over fabricated nanoparticles exposed to sunlight is hypothesized based on the aforementioned reaction steps: According to the mechanism, when CuO-NPs are exposed to sunlight, the valence band (VB) electrons are excited to the conduction band (CB), while an equivalent number of holes are produced in the valence band (VB). These photogenerated free electron hole pairs react with water to produce highly reactive oxidizing agents (O . − 2 , HO * 2 orOH − ). These radicals react with MB dye for the degradation or mineralization process. The proposed mechanism for photocatalysis by CuO and La:CuO-NPs is shown in gure 6.

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Photocatalytic degradation of MB dye follows a pseudo rst order kinetics.
Where t represents the reaction time in minutes and k indicates the apparent reaction rate constant. Initial and nal concentration of aqueous MB after time t is denoted by C 0 and C t respectively. The rate constant This may be the reason for the difference in the end result. Overall, we can say that the trend given by COMSOL is followed by the experiment.

Conclusion
A simple and cost-effective method, sol-gel is used to synthesize pure and La (1, 2 and 3%) doped CuO-NPs. The fabricated material is characterized by XRD, SEM, EDS, PL, UV-vis and FTIR to investigate the structural, compositional and optical properties. The XRD analysis revealed the monoclinic crystal structure of CuO. Moreover, with the increase in dopant concentration, the intensity of XRD peaks is decreased along with a small shift in peak position which con rms the successful doping of La     PL spectra (a) exhibiting reduction in highly intense peaks of 413.7nm and 425.3nm attributing to the reduced electron-hole recombination rate for doped CuO-NPs. FTIR spectra (b) of synthesized material representing a slight shift in intensity and location of peaks as shown in the inset of graph.  Mechanism of reduction in band gap and electron hole recombination rate with doping along with the free radical reaction with pollutant. Photocatalytic e ciency (a) of 51%, 67%, 79%, 73% observed for pure and La (1, 2 & 3%) doped CuO-NPs along with their rate constants (b) showing variation due to the presence of dopant.