Hydrothermal synthesis of LaFeO3 nanoparticles adsorbent: Characterization and application of error functions for adsorption of fluoride

Graphical abstract


Description of protocol
Fluoride is one of the soluble ions in water resources that originate from natural and artificial sources including wastewater discharge of different industries and fluoride glass production industry [1]. It is also a natural element among minerals, geochemical sediments, and natural water systems, which enters the food chain through drinking water or feeding on plants. When its content in water is low, it should be added to water artificially. The presence of fluoride in water is essential to prevent dental decay [2]. On the other hand, if its content exceeds the desired level, it causes dental fluorosis and skeletal fluorosis [3]. This condition causes weakening of tooth and bone structure. It also declines growth and even in severe cases, it causes paralysis and death [4,5].
Today, various methods are used to remove organic and inorganic pollutants including absorption, biosorption, and adsorption by active alumina and manganese oxide coated with alumino along with various coagulators such as alum, ferric sulfate, ferro sulfate, ferric chloride, anionic, cationic, and nonionic organic polymers [6][7][8][9]. Physical adsorption is an efficient and economical method. Extensive research has been conducted on the adsorption of fluoride using different adsorbents including activated carbon [8]. It has also been proven that the adsorption process is a reliable treatment solution owing to minimum investment, convenient design and operation, and insensitivity to toxic compounds [9].
Recently various rare earth materials such as lanthanum, lanthanum modified activated alumina, lanthanum oxide, lanthanum impregnated green sand, cerium, and yttrium have been used as sorbents for the removal of fluoride from water [10][11][12]. Though lanthanum has got a good affinity for fluoride, there are some difficulties related to its use as an adsorbent. Recently, the magnetic properties of lanthanum ferrite nanoparticles (LaFeO 3 NPs) have been extensively studied but the magnetic study of LaFeO 3 NPs is rare [10]. Ant ferromagnetic nanoparticles always show unusual magnetic properties due to their finite-size effects, surface anisotropy effects, interface effects and shape anisotropy effect [10][11][12]. The nano-size of LaFeO 3 NPs system has been majorly investigated as an alternative. Various types of LaFeO 3 NPs can be synthesized by many methods such as sol-gel, co-precipitation, bull milling, sonochemical, and hydrothermal [10]. The hydrothermal method is one of the most powerful and widely used methods for the production of nanostructures; this has attracted a great deal of attention due to its simplicity and cost [13].
The main purpose of this study is to synthesize LaFeO 3 NPs and investigate its effectiveness on the removal of fluoride from its aqueous solution. The impact of various operating factors such as contact time, LaFeO 3 NPs dosage, pH, temperature and initial fluoride concentration on the fluoride adsorption process was studied to ascertain their optimum conditions. The adsorption kinetics, isotherm, and thermodynamics of the fluoride adsorption process on LaFeO 3 NPs will also be studied. Error functions were also employed to compare the fit of adsorption isotherm and kinetic models in order to limit error between the predicted and experimental values.

Preparation of LaFeO 3 NPs
Lithium nanostructure was used with poly vinyl pyrrolidone (PVP) coating agent, and was then dissolved in distilled water using hydrothermal method with equal ratios of iron salt (Fe(NO 3 ).9H 2 O) and lanthanum salt (La(NO 3 ) 3 .6H 2 O) (that is, 0.2 g each was dissolved in 20 mL of distilled water and added to each other).
In another container, 0.5 g of PVP which had been dissolved in 40 mL of distilled water (at a temperature of 25 C) was added to the reaction container. After vigorous stirring for 30 rpm, NaOH alkaline agent was added to the reaction container in order to raise the pH to 11. Next, the intended solution was transferred to an autoclave and placed inside an oven for 24 h at 200 ⁰C. Thereafter, the obtained solution was washed several times with distilled water and ethanol and then dried in an oven for 30 min at 343 K.
Characterization of nanometer-sized LaFeO 3 NPs X-ray diffraction (XRD) patterns on the LaFeO 3 NPs were taken by means of a Philips diffract meter model PW1800 (The Netherlands). The X-ray source was Cukα with 1.541 nm wavelength. Scanning electron microscopy (Mira 3-XMU instrument capable of 700,000 x magnifications) was used to study the morphology of the LaFeO 3 NPs. Fourier-transform infrared spectroscopy (FT-IR) analysis of LaFeO 3 NPs was done using a JASCO 640 plus machine (4000À400 cm À1 ) at room temperature to determine the functional groups presently involved in the fluoride adsorption process.

Batch adsorption experiments
The effects of different parameters such as pH (3, 5, 7, 9 and 11), contact time (15,30,60,90, and 120 min), temperature (303, 308, and 318 K), initial fluoride concentration (15,20,25,30 and 40 mg/L) and LaFeO 3 NPs dosage (0.1, 0.5, 0.7, 0.9 and 1 g/L) on the fluoride adsorption process were studied. A specified amount of adsorbent (LaFeO 3 NPs) was added to Erlenmeyer flasks containing 100 mL of the solutions to be treated having different concentrations of fluoride. The pH of the solution was adjusted by adding 0.1 N HCl or 0.1 N NaOH. The flask with its contents was stirred for a specified time at 150 rpm. The resulting solution was centrifuged and the supernatant was analyzed for the residual fluoride concentration. The initial and final (or residual) fluoride concentrations in the solutions were determined using a UV-vis spectrophotometer (Shimadzu Model: CE-1021-UK, Japan) at a wavelength of maximum absorbance (l max ) of 570 nm [14]. The pH was measured using a MIT65 pH meter. The removal efficiency (%R) was calculated based on the following formula [15,16]: The amount of fluoride adsorbed on LaFeO 3 NPs, q e (mg/g) was calculated based on the following formula [17]: Where C 0 and C e are the initial fluoride concentration (mg/L) and equilibrium liquid phase concentration of fluoride (mg/L) respectively; C f is the final fluoride concentration (mg/L), V is the volume of the treated fluoride solution (L) and M is the amount of LaFeO 3 NPs used (g).

SEM, XRD and FTIR analysis on the synthesized LaFeO 3 NPs
The scanning electron microscopy (SEM) image of LaFeO 3 NPs is shown in Fig. 1. The LaFeO 3 NPs appears lamellar in arrangement. The surface area of an adsorbent determines its adsorption capability [18]. High porosity was observed on the LaFeO 3 NPs which indicates that there will be a high level of contact with the fluoride ions [20].The X-ray diffraction (XRD) patterns of LaFeO 3 NPs is shown in Fig. 2.
The FTIR analysis on theLaFeO 3 NPs (Fig. 2) indicates the existence of ¼CÀ ÀH bend of alkenes (793.85 cm À1 ), and CÀ ÀH bend of alkanes (1461.97 cm -1 ). The peak 1633.57 cm -1 shows the presence of CÀ ÀC stretch (in-ring) of aromatics. The presence of OÀ ÀH stretch, H-bonded of alcohols, phenols (3406.12 cm -1 ), which are also strong and broad bands can be observed. The OÀ ÀH bands are very important sites for adsorption [21]. The hydroxyl group effect is more felt due to the hydrogen bonding with other hydroxyl bonds since they do not exist in isolation establishing a stable structure [21,22]. The XRD result shows that the LaFeO 3 NPs owns a crystalline structure which improves the process of adsorption by means of physical adsorption [19,20]. Maximum peak of around 2u = 32.5 (with very high intensity) was also observed on the XRD image (Fig. 3). The average crystallite size (D) of LaFeO 3 NPs nanoparticles was calculated by the Scherer formula (D h,k,l = 0.9l/β h,k,l cosu, where l is the wavelength (1.542 Å), β is the full width at half maximum (FWHM) of the line, and u is the diffraction angle) [23,24]. The average diameter of the LaFeO 3 NPs adsorbent (D) was calculated to be 35 nm.

The effect of pH and temperature
The parameter, pH directly influences the electrostatic interaction between compounds in adsorption processes [25]. To obtain optimal pH value, experiments were carried out by varying the   Fig. 4. Fluoride reduction was maximum at the temperature of 308 K, which is accepted as the optimum temperature. The temperature increase from 308 to 318 K also allowed the fluorine to desorb to the solution due to damage to the active sites in the adsorbent [26]. Also, it is clear from Fig. 4 that the removal percentage of fluoride increased from 93.75%-98.525 % as the pH was increased from 3 to 5 at the temperature of 308 K but decreased as the pH was increased to 11. Many researchers have reported that the adsorption process is affected by the cationic and anionic forms of the solution due to competition for adsorption among the H + and OH-ions with the adsorbate [27]. In this study, the decrease in the removal efficiency of fluoride as the pH increased may be attributed to electrostatic repulsion [28] between the positively charged LaFeO 3 NPs and the cationic fluoride. The adsorption of fluoride was more favorable in the acidic environment due to the presence of H + on the adsorbent [29]. The increased amount of H + and reduction of OH-as well as the increase of positive ion can be the reason for the reduction in fluoride removal efficiency on the adsorbent surface [30]. This is also due to the competition of the fluoride ions with excess OH-ions for the adsorption sites at higher adsorption pH [29,30].

The effect of adsorbent dosage
As seen in Fig. 5, the removal of the fluoride increased with increasing the amount of adsorbent (LaFeO 3 NPs) from 0.1 to 0.9 g/L at different temperatures (303, 308 and 318 K). Maximum fluoride uptake of 98.5 % was observed at an adsorbent dosage of 0.9 g/L and temperature of 308 K. This implies that increasing LaFeO 3 NPs dose increased the number of active sites available for the adsorption of fluoride. Therefore, the studied adsorbent has a high adsorptive potential, which at very low adsorbent values has a very high uptake of fluoride. With increasing the adsorbent dosages above the optimum (0.9 g/L), the fluoride removal was decreased, which is due to the accumulation of adsorbent particles and the development of electric repulsive force between the adsorbent particles. It can be pointed out that all active sites of the adsorbent were not available to the adsorbate, with this phenomenon being observed more in the batch adsorption process [31].

The effect of fluoride concentration and contact time
It is important to note that the adsorbate concentration plays a significant role in the removal of pollutants from aqueous solutions and the interaction between the adsorbent and adsorbate species. The effect of concentration on the fluoride adsorption by the LaFeO 3 NPs was investigated at different initial fluoride concentrations (15,20,25,30, and 40 mg/L) at pH of 5, contact time of 15 min and LaFeO 3 NPs dosage of 0.9 g/L at different temperatures (Fig. 6). The amount of fluoride adsorbed on LaFeO 3 NPs (q e ) was increased with increasing fluoride concentration. Also, the percentage of fluoride adsorbed was increased as the initial concentration of fluoride was increased from 15 to 20 mg/L but decreased when the fluoride concentration was increased further at different times of contact. This decrease in efficiency of fluoride removal may be as a result of the over-saturation of the active sites of the adsorbent by the adsorbate [32].
The effect of contact time (15,30,60, 90 and 120 min) on the removal of fluoride was studied at pH of 5, LaFeO 3 NPs dosage of 0.9 g/L, and fluoride concentration of 25 mg/L at different fluoride concentrations (Fig. 6). From Fig. 6 it can be seen that the removal of fluoride increased as contact time increases from 10 to 60 min. Maximum removal of fluoride was achieved in the first 60 min (94.75 %) at the concentration of 20 mg/l. The adsorption of fluoride in the initial minutes was high, including the adsorption rate (Fig. 6) because of reduced fluoride concentration and reduction of the active sites present on the adsorbent surface [33]. The removal efficiency decreased after 60 min because the adsorption sites were occupied [34].

Sorption kinetics fitting
It is important to emphasize that the optimal contact time is determined based on the adsorption kinetics tests. Kinetic studies are done to observe the mechanism controlling an adsorption process [26]. Kinetic models of adsorption including pseudo-first-order, pseudo-second-order, intraparticle diffusion, fractional and zero-order models were used to test the kinetic data. The equations of kinetic models with the description of the kinetic parameters are stated in Table 1. The kinetic parameters were obtained from the plots of the kinetic models at the optimum conditions of pH 5 and nanoparticles dose of 0.9 g/L. The agreement between the predicted kinetic model values and the experimental data was confirmed by the regression coefficients (r 2 ).
The nonlinear forms of pseudo-first-order, pseudo-second-order, intraparticle diffusion, fractional and zero-order models were used to test the kinetic data. In order to evaluate the validity of the adsorption mathematical kinetic models with the experimental results, a number of error functions are available in the literature. The use of only the regression coefficient (r 2 ) for isotherm and kinetic data analysis is not enough, because the experimental results may have high r 2 values. Therefore, it is necessary to diagnose the result of regression for residue analysis. The applicability of the kinetic model to describe the adsorption process, apart from the regression coefficient (r 2 ), was further validated by the normalized standard deviation (NSD), average relative error (ARE) and standard deviation which are defined as Eqs. (3)-(5), respectively:  Table 1 Kinetic models employed to describe the fluoride adsorption by LaFeO 3 NPs with their respective equations and parameters description [28,29].

Kinetic model Equation Parameters description
Pseudosecondorder q t ¼ k2p q 2 e t 1þq e k2p t k 2p = rate constants of the pseudo-second order (g/mg min); q e = adsorbate amounts at equilibrium (mg/g); q t = amount of adsorbate removed at time t (mg/g).
Pseudo-firstorder q t ¼ q e 1 À exp Àk 1p t À Á Â Ã k 1p = rate constants of the pseudo-first-order (min À1 ); q e = adsorbate amount at equilibrium (mg/g); q t = amount of adsorbate removed at time t (mg/g) Intra-particle diffusion q t ¼ kpt 0:5 þ C q t = amount of adsorbate adsorbed at equilibrium (mg/g); k p = intraparticle diffusion rate constant (mg/L min À0.5 ); C = the intercept which give information about the thickness of the boundary layer Fractional power Zero-order q t ¼ q e À k 0 t q e = adsorbate amounts at equilibrium (mg/g); k 0 =constant Where N is the number of performed experiments, P is the number of parameters of the fitted model, and r 2 is the coefficient of determination; q t exp and q t cal are the experimental and calculated amounts of fluoride adsorbed on LaFeO 3 NPs at time t (mg/g). The model with the highest values of r 2 and the lowest values of SD best represents the process. The smaller NSD and ARE values indicate a more accurate estimation of q t values [20,25]. The nonlinear adsorption kinetics results obtained are presented in Table 2. It is observed that the pseudo-second-order kinetic model best described the kinetic experimental data with the value of r 2 closer to unity (0.8577). The pseudo-second-order possesses lower values of NSD (0.8873), ARE (0.7120), and SD (0.0106) when compared with the other kinetic models. This means that the fluoride adsorption onto LaFeO 3 NPs is a chemical type of adsorption [35]. This also indicates that the calculated values of q t (q t cal ) obtained from the pseudo-second-order model extremely correspond with the experimental values of q t (q t exp ).

Equilibrium isotherms and fit error evaluation
In different adsorption investigations, the study of the adsorption of pollutants on the surface of adsorbents, determining the adsorption capacity (q m ) and adsorption isotherm models that best fit the experimental data are of great importance to many researchers. The way a pollutant is adsorbed on an adsorbent can be interpreted through the study of adsorption isotherms. Isotherms can represent the relationship between the pollutant concentration present in the solution and the amount of pollutant adsorbed by the solid phase when both phases are at equilibrium. The equations of isotherm models with the description of their parameters are stated in Table 3. The correlation coefficient (r 2 ) is used to judge whether experimental data follow isotherm models [36]. In addition to r 2 , the parameters of average relative error (ARE), Marquardt's percent standard deviation (MPSD) and Hybrid error Table 2 Nonlinear kinetic parameters for adsorption of fluoride onto LaFeO 3 NPs at optimal condition (pH: 5, nanoparticles dose: 0.9 g/L, temperature =308 K). function (HYBRID), root mean squared error (RMSE), and normalized standard deviation (Dq(%)) were also evaluated, which can be described as Eqs. (4), (6)-(9), respectively:

Model r 2 NSD ARE(%) SD
Dq % ð Þ ¼ 100 Where q ei exp is the observation from the batch experiment i, q ei cal is the estimate from the isotherm for the corresponding q ei exp , Nis the number of observations in the experimental isotherm and p is the number of parameters in the regression model; q c is the value that is calculated from model fit and q e is calculated from test elements. The smaller MPSD and HYBRID values indicate a more accurate estimation of q e value [20]. MPSD and HYBRID functions were used in addition to r 2 because the number of parameters in the regression model (that is, p parameter) is effective in them.
The isotherm plots for fluoride adsorption by LaFeO 3 NPs at the optimum conditions of pH 5, LaFeO 3 NPs dose of 0.9 g/L, and temperature of 308 K is shown in Fig. 7. Considering the r 2 values obtained for the theoretical models evaluated (Table 4), it can be observed that the six isotherm models (Langmuir, Freundlich, Temkin, Koble-Corrigan, Redlich-Peterson and Dubinin-Radushkevich) present firm adherence to the experimental data. This shows the good agreement between the calculated q e and the experimental q e values for all isotherms. By evaluating the values of Table 3 Isotherm models employed to describe the fluoride adsorption by LaFeO 3 NPs with their respective equations and parameters description [37][38][39]. all the error functions applied to the adjusted models, the Freundlich and Koble-Corrigan models were the most suitable to describe the observed phenomenon. Its fit into the Freundlich model suggests a heterogeneous and multilayer adsorption of the fluoride on the LaFeO 3 NPs surface. Since the Freundlich model describes a chemical adsorption process, it supports the kinetic approach which denoted a chemical behavior of the adsorption of fluoride on LaFeO 3 NPs. The monolayer adsorption capacity of LaFeO 3 NPs (q m ) was obtained as 2.575 mg/g. An adsorption intensity (n) value of 2.488, which is within 1-10 (1 <n< 10) obtained for the fluoride adsorption proposes that the adsorption process on LaFeO 3 NPs is favorable [20].

Thermodynamic studies
Temperature has a great impact on the adsorption process, so the thermodynamic study. The thermodynamic parameters including the standard Gibbs free energy (DG ), enthalpy change (DH ), Where, R is the universal gas constant (8.314 J/mol/K) and T is the absolute temperature in K. The thermodynamic parameter, Gibb's free energy change (DG ) is calculated using K a obtained from the Langmuir isotherm. The values of DH and DS were evaluated from the intercept and slope of the regression plot of DG versus T (Fig. 8).
All the values of DG were negative; this shows that the fluoride adsorption process by LaFeO 3 NPs was spontaneous (DG < 0) and feasible [40]. The decreased amount of DG with the increase in temperature indicates that the increase in temperature resulted in an increase in spontaneity. The negative DH value of adsorption reaction on LaFeO 3 NPs (À0.5057 kJ/mol) indicated that the process was exothermic (DH < 0) [41]. According to Le Chatelier's principle, increasing the temperature reduced the reaction rate. Entropy change (DS = -0.0115 kJ/mol.K) of fluoride adsorption by LaFeO 3 NPs is negative, suggesting that the degree of freedom at solid-solution level declines during the adsorption [30]. The negative value of DS may be caused by the decrease in the efficiency of the reaction with higher temperatures [42,43].

Comparison of LaFeO 3 NPs with other adsorbent materials on fluoride removal
The removal of fluoride on LaFeO 3 NPs was compared with other adsorbent materials employed by several authors in terms of percentage removal efficiency ( Table 6). The fluoride removal efficiency of 94.75 % obtained using LaFeO 3 NPs indicates that it can be applied for fluoride removal from its  aqueous solution. Generally, the results obtained by the authors shown in Table 6 show that the different adsorbents can be harnessed for the removal of fluoride via the adsorption process.

Conclusion
The removal of fluoride on lanthanum ferrite nanoparticles (LaFeO 3 NPs) was found to be dependent on the initial pH, temperature, dosage of LaFeO 3 NPs, contact time, and initial fluoride concentration. Under optimal conditions of fluoride concentration of 20 mg/L, pH of 5, LaFeO 3 NPs dosage of 0.9 g/L, temperature of 308 K, and contact time of 60 min, maximum percentage removal of 94.75 % was obtained. Adsorption kinetics, isotherm, and thermodynamics were studied for fluoride ions removal on LaFeO 3 NPs. The monolayer adsorption capacity of LaFeO 3 NPs was 2.575 mg/g. The adsorption process fitted well into the Freundlich, Koble-Corrigan and pseudo-second-order kinetic models considering the values of the regression coefficients (r 2 ) and error functions used. The fluoride adsorption on LaFeO 3 NPs was found to be favorable, exothermic and spontaneous in nature. Its spontaneity was increased with temperature. From the study, it can be concluded that the LaFeO 3 NPs prepared by the hydrothermal method can be used for the effective reduction of fluoride