Adsorption of Congo Red on Pb doped FexOy: experimental study and theoretical modeling via double-layer statistical physics models

Size-controlled Pb0.06Fe0.7O3 nanoparticles (Pb-FeONPs) were fabricated by the thermal coprecipitation method and characterized by FE-SEM, EDX, XRD, and IR techniques. The SEM and XRD images showed the average size distribution and average crystallite size of 19.21 nm and 4.9 nm, respectively. The kinetic model of Congo Red (CR) adsorption onto Pb-FeONPs was verified and found to be a pseudo-second-order reaction. The Langmuir plot was better fitted (R1⁄4 0.990) than other isotherm models with a Qmax (mg/g) of 500 for Congo Red (CR) dye in 40 min. The double-layer statistical physics model based on two energies was used to calculate the significant parameters. The n (stoichiometric coefficient) values obtained from the statistical physics double-layer model were found to be 0.599, 0.593, and 0.565, which are less than 1, indicating the multi-docking process. The regeneration of Pb-FeONPs was used for up to 5 cycles effectively, making the material highly economical. The Pb-FeONPs were fruitfully applied for the removal of CR dye from wastewater on a laboratory and industrial scale.


INTRODUCTION
In recent years, the world has been moving toward huge industrialization. The impact of industrial growth is seen in the form of industrial effluent and solid waste, which contains numerous toxic contaminants (Dehghanian et al. ). Several industries including textiles, pulp, paper, and plastic produce a massive quantity of dye effluents (Zhou et al. ). The treatment of industrial effluents for protecting and making a clean and healthy environment is the prime target of the scientific and intellectual communities (Singh et al. ; Shu et al. ). The adsorption process is a simple and widely used technique for the treatment of wastewater and has a high potential for the reuse of adsorbent (Arshadi et al. ). Azo dye (CR) is being utilized in textile, leather, and foodstuffs. However, it is toxic to the aquatic ecosystem and reported as a potential carcinogen for humans and animals (El-Gamal et al. ). Albadarin et al. reported activated lignin-chitosan pellets for the adsorption of methylene blue (MB) dye (Albadarin et al. ; Khan et al. ). Naushad et al. successfully developed modified activated carbon 2-amino-5-guanidinopentanoic acid for the efficient adsorptive removal of MB from wastewater (Naushad et al. a). Ahmed et al. reported magnesium/iron (Mg/Fe)-layered double hydroxides (LDHs) nanoparticles for the removal of CR dye (Naushad et al. b; Ahmed et al. ). Nanosized materials have a wide surface area, offer efficient, fast adsorption, and are readily spread in an aqueous solution. Nanoparticles with a high number of active vacant sites can be used for the adsorption of toxic materials (Sohrabi et al. ; Jethave et al. a). In this study, Pb-FeONPs were synthesized by a thermal co-precipitation process and their application was explored towards the removal of CR dye, and its determination by UV-Visible spectrometer at 498 nm. The kinetic order, ΔG , ΔH , and ΔS were determined for CR adsorption on the surface of Pb-FeONPs. The isotherm model revealed a possible adsorption mechanism. The double-layer model is ideally tailored to analyze the desorption process. The Pb-FeONPs was regenerated up to 5 cycles and successfully used for the laboratory and industrial scale removal of CR dye from wastewater. The findings from this study are very encouraging due to the effective adsorption and reusability of the adsorbent.

Reagents, instrumentation, and experimental setup
Both chemicals and reagents used in the synthesis and experiments were purchased from Merck, Darmstadt, Germany, and are of analytical reagent grade. Metrohm 713 pH-meter, Bruker S-4800, PM, EDX, X-ray diffractometer Bruker D8-advance, FT-IR Bruker, and Shimadzu UV-1800 spectrophotometer instruments were used for the characterization and execution of experiments. The pH studies were performed in the range pH 3-12.0 and with a mechanical shaker time of 0 to 90 min. The effect of adsorbent dosages was investigated by varying the dose from 50 to 200 mg. The detailed experimental for adsorption of CR dye on Pb-FeONPs is presented in supplementary data.

Preparation of Pb-FeONPs
The Pb-FeONPs were prepared using a co-precipitation method. Firstly, 7.2 g of ferric chloride and 0.61 g of (CH 3-COO) 2 Pb were added into 200 ml of deionized distilled water containing 1 g of sodium lauryl sulfate (SLS) and heated up to 60 C. A 5M NaOH solution was used to maintain the pH of 11 ± 0.2. The solution was continuously heated at 60 C for 2 h. The synthesis of Pb-FeONPs is schematically depicted in Figure 1. The brown stable precipitate was filtered and washed vigorously with distilled water until the filtrate pH was reduced to 7.5. The precipitates were dried in an air oven at 90 C for 12 h. The material was converted to a fine powder and then calcined at 400 C for 3 h.

Statistical physics model for dye adsorption mechanism
To evaluate the experimental effects, three mathematical physics models were used. They believed that the 2-NP adsorbate has generated a fixed and non-fixed number of layers on the surfaces tested (in fact, one, two or more layers) (Nayak & Pal ). According to mathematical mechanics theory and basic theories, these models were formulated.
The adsorption model was derived by considering the assumption of this statistical physics system.
where, n ¼ stoichiometric coefficient (may be an integer or not, lower or greater than 1). The fraction of molecule adsorbed per site of adsorbent when n < 1; that is, multi-docking adsorption is involved and if n > 1, multi-molecular adsorption is assumed, which means a single site is occupied by the number of the molecule. The isotherm can be interpreted within this principle by a single layer method or by simulating the formation of two or more layers. To estimate experimental dye adsorption, the use of a two-energy double-layer model was necessary.

Monolayer adsorption model
The monolayer adsorption model believes that CR dye molecules form a single layer with adsorption energy (ε 1 ). So, the adsorbed quantity (Q) of dye is given by: In this model, there are three variables: C 1/2 is the concentration at half-saturation; N M ¼ receptor sites density on the nanoadsorbent; n ¼ number of dye molecules per site of nanoadsorbent.
The obtained theoretical model values can be fitted with the experimental data. From this, Q sat ; that is, the adsorbed quantity of molecules at saturation, was calculated using the relation: Q sat ¼ n*N M * (1 þ N 2 ). Here (1 þ N 2 ) is the formed layer number. For monolayer N 2 ¼ 0.

Double-layer model
This means that for an additional layer of dye molecules, the first layer must provide acceptor sites, thus requiring two adsorption energies, ε 1 and ε 2 , as mentioned above. This model was equated as given below: Four important variables can be described from Model 2 including n, N M , (significance of n and N M is the same as the previous model). The C 1 and C 2 are the firstand secondlayer concentrations at half-saturation, respectively.

Characterization of Pb-FeONPs
The SEM image of the Pb-FeO nanoparticles showed an average particle size of 19.21 nm (Figure 2(a). The nanoparticles were uniform and well-dispersed in size. The Pb-FeONPs were spherical. However, a few larger particles are also seen due to the aggregation of smaller particles. EDX outcome reveals that nanoparticles composed of Pb, Fe, and O with 11.74, 40.85, and 47.41 wt%, respectively ( Figure 2(b)). The crystalline nature from XRD ¼ revealed the peaks at 31. 82 , 35.74 , 44.58 , 52.81 , 61.83 , and 64.93 with reflection at 111, 200, 100, 220, 311, and 200 miller planes of Pb-FeONP (Figure 2(c)). The average crystallite size obtained from XRD was found to be 4.9 nm. FT-IR spectra of Pb-FeONPs are presented in Figure 2 1,157 cm À1 of C-O bond, and 1,421 cm À1 of C-H bending vibration were observed.

Effect of pH, time and adsorbent dose
The adsorption capability of CR was greater at pH 6.5, and lesser when pH increased from 6.5 to 10.0 and reduced from 6.5 to 3.0 (Figure 3(a)). The maximum percentage of adsorption of about 94.42% was obtained at pH 6.5 and therefore, further experiments were performed at pH 6.5. Above and below pH 6.5, the adsorption was significantly decreased. The Pb-FeONPs with negative charges were lying face down to adsorb positive charge protonated-NH 2 . Due to the above mechanism (opposite charges attracted to each other), CR was adsorbed onto the Pb-FeONPs and its adsorption process became a self-occurring spontaneous reaction. The effect of time for the adsorption of dye on Pb-FeONPs was achieved by varying the time from 0 to 90 min at 298 K. The CR was adsorbed on to the surface of the Pb-FeONPs and settled down on the bottom of the conical flask, the upper supernatant aqueous solution was centrifuged and further used to determine the concentration with UV-visible spectrophotometer at 498 nm. The rate of adsorption was increased up to 40 min after a further increase in time, the adsorption process started to slow down (91.74%) and reached equilibrium (Figure 3(b)). All experiments were conducted in triplicates to validate the adsorption phenomenon. It was clear that the removal of maximum CR dye required a large amount of Pb-FeONPs and this problem was overcome by optimization studies on the amount of adsorbent dosage. The adsorbent dosage significantly influences the adsorption process. As the number of adsorbent (Pb-FeONPs) active sites increases proportionally the adsorption of dye (CR) increases. The findings of Figure 3(c) showed that the adsorption percentage increases with the rise in the dose of Pb-FeONPs from 50 to 200 mg. It was recognized from the data that due to the presence of a large number of adsorption sites, the adsorption efficiency of dyes increased from 69.74 to 94.42 percent.

Kinetic models, adsorption isotherms
The kinetics of CR adsorption on Pb-FeONPs was studied by using Ho and McKay models. Kinetic experiments have been commonly used in the adsorption of dye to the surface of solid nanoparticles (Crini ). The adsorption kinetic rate has a significant contribution to the selection of adsorbents. At the same time, kinetic modeling reflects adsorption rates and allows the determination of adequate rate terms and effective clarification of the reaction process. The equation of pseudo-first and second-order are given below: The pseudo-second-order kinetic analysis between CR and Pb-FeONPs was verified in the present adsorption study, as shown in Figure 4 Table 2. The Langmuir isotherm assumes that the active area of the surface is equal and identical, and the adsorbent surface is homogeneous. On the surface of the adsorbents, the adsorption process of dye takes place via monolayer covering. Each of the active pockets of the adsorbent with maximum adsorption can occupy a single dye molecule. Besides, it was also assumed that around the plane surface of the adsorbent, the binding energies of the dye molecules were uniform. It was used to describe the interaction with adsorbed molecules of monolayer adsorption. The Langmuir isotherm equation is: The linear form of the equation: The plot of Ce/qe vs. Ce is shown in Figure 4(b), which was linear (R 2 ¼ 0.990). Table 2 reveals that the maximal adsorption potential of Pb-FeONPs for CR (qmax ¼ 500 mgg À1 ) was much greater. The multilayer adsorption with the interaction between adsorbed molecules is described by the Freundlich isotherm. The Freundlich isotherm model is described by: The linear form of the equation is: The K f and 1/n values derived from the ln q e vs. ln C e intercept and plot slope are given in Table 2 and plotted in Figure 4(c). The heat of the adsorption and the interaction between adsorbent and adsorbate were clarified and evaluated using the Temkin isotherm model. The isotherm and linear form of Temkin is as follows. The Temkin model is plotted between q e and ln C e (Figure 4(d)).
The isothermal model of Dubinnin-Radushkevich (D-R) is used to understand the adsorption process. D-R model is represented: Average free adsorption energy E, is estimated from B, using the following equation: The D-R isothermal model is used to predict whether the adsorption was physisorption or chemisorption. In Figure 5(a), the plot-estimated constant was observed. The qD, B and R2 values are given in Table 2. The high qD value, and low R 2 , imply that the activation energy measured based on the D-R plot could not be the real one. The equation between Hurkins-Jura (H-J) is expressed as: The measured values of constants A and B from the 1/q e 2 versus log Ce plot ( Figure 5(b)) are tabulated in Table 2. The correlation coefficient of all isotherm models was analyzed. The Langmuir model has the highest R 2 value, with welldefined adsorption of CR onto the Pb-FeONPs. The isotherm models of D-R and H-J demonstrated an unacceptable fit with the experimental results compared to the other isotherms.

Separation factor, thermodynamic parameters and possible mechanism
An essential characteristic of the Langmuir isotherm is the separation factor (RL).
RL values indicate the desirable adsorption process within the 0< RL <1 range. In this study, the RL value of Pb-FeONPs was obtained to be 0.583 (Weber & Chakravorti ) for the initial RHB concentration of 20 mg/L ( Figure 5(c)) and indicates favorable CR adsorption. Multi-layer adsorption is considered, accompanied by the interactions between the adsorbed molecules and the heterogeneous energy distribution of the active sites. Thermodynamic parameters (Figure 5(d)) for the adsorption of CR on to the Pb-FeONPs at various  temperatures of 298, 308, and 318 K were studied. The thermodynamic parameters for the CR-Pb-FeONPs system, including ΔH , ΔS , and ΔG were calculated as a function of temperature (Selim et al. ).
where R (8.314 Jmol À1 K À1 ) and T are in Kelvin. The value of ΔG was calculated from the equation: Table 3 displays thermodynamic parameters obtained from the adsorption of CR on the surface of Pb-FeONPs at different temperatures. The temperature analysis anticipates the exothermic or endothermic existence of the mechanism of adsorption. The variance of the model of CR dye adsorbed on the Pb-FeONPs due to solution temperature is shown in Figure 5(d) (Weber & Chakravorti ). Adsorption is assigned to physisorption when the G is between À20 and 0 kJ mol À1 and chemisorption when the G is between À400 and À80 kJ mol À1 . For CR adsorption on the Pb-FeONPs, the shift in free energy at 298 K was À2,918 kJ mol À1 (Table 3). The increase in the adsorption potential at higher temperatures was due to the increased mobility of the active adsorbent surface sites of dye molecules. The ΔH and ΔS were estimated as À0.008 kJ mol À1 and À0.033 kJ mol À1 , respectively. The negative ΔG showed that the adsorption of CR on Pb-FeONPs is a spontaneous process. The negative ΔH and ΔS reflect the exothermic nature of the solid/solution adsorption and decreased randomness, respectively. The outer parts of nanomaterial (Pb-FeONPs) are normally enclosed with negatively charged -OH groups and positively charged NH 2 groups. The opposite nature of both materials attracts each other, due to which adsorption takes place in solution very effectively. Hence, the adsorption ability of the Pb-FeONPs was efficient as shown in the proposed mechanism ( Figure 6).

INTERPRETATION OF STATISTICAL PARAMETERS
It is important to understand the adsorption isotherms of the CR by the statistical physics model. The results of the twoenergy double layer of the statistical physics model and its relationship in the adsorption of CR onto the Pb-FeONPs are shown in Figure 7 and Figure 8. These figures depict a simple example of adsorption of CR onto the Pb-FeONPs surface. The data from Table 4 reveal the fitting parameters of the two-energy double-layer model; that is, n, N M , Q 0, and adsorption energies ε1 and ε2.

Parameters n, N M and Qe sat
To provide the basic information of the absorption process between Pb-FeONPs and CR, the determination of the n parameter is very important and useful. The multi-docking (n < 1) and (case 2) multi-molecular (n > 1) values are two main instances of the adsorption mechanism (case 1), as opposed to unity. The first case applies to several active sites of Pb-FeONPs that adsorb one ion, while the latter represents the potential to absorb several ions from one active site (Sellaoui et al. ).
All the n values measured were less than 1 as a function of temperature, which showed the horizontal geometry of the adsorbed Pb-FeONPs. Following Figure 9(a), due to thermal collisions, the number of molecules per site increases as the temperature increases. It is fact that the n value never exceeds 1 (at low temperatures), which suggests that there is no dimerization and trimerization until adsorption. As regards the NM parameter, it was observed that the number of active Pb-FeONPs sites contributing to CR capture decreases as the solution temperature increases (Table 4) (Figure 9(b)). It was also found that N M density decreases as a function of temperature. Additional receptor sites were uncovered at high temperatures that are obscured at low temperatures. This depends primarily on the quantity of bonded CR dye per receptor site, the density of the receptor site, and the average number of adsorbed layers (i.e. for the single-layer model, Qesat ¼ n*Nm and the double-layer  model, Qsat ¼ 2n*Nm). The effect of temperature on the capacity of adsorption at saturation is shown in Figure 9(c). The value of Qsat at 298, 308, and 318 K were 438.46, 66.08, and 34.63 mg/g, respectively. The lower interaction between CR molecules and Pb-FeONPs was confirmed by the decrease in the Qsat values with the change in the temperature. This parameter illustrates the exothermic phase in the adsorption mechanism of CR on to the Pb-FeONPs. It was further confirmed by the absorption energetic interpretation (Selim et al. ).

Energetic interpretation
Equations can be used to determine the interactions between the CR and the Pb-FeONPs (Li et al. ): in which C s is the solubility of the PCE molecule.
In Figure 9(d), the evolution of the ε 1 and ε 2 adsorption energies is shown as a function of temperature. The values of adsorption energies are less than 40 kJ mol À1 . This means that physisorption is the adsorption of CR on to Pb-FeONPs. It can also be seen from Figure 9(d) that in the first adsorbed layer, the maximum adsorption energy was observed, as the affinity of the receptor sites on that layer is more important. Compared to adsorbate and adsorbent, this results in less contact between the adsorbate and the adsorbate. Moreover, the energy of adsorption increases as a function of temperature. Therefore, more energy was required to transfer the CR molecules from the liquid phase to the adsorbent surface at elevated temperatures (Dil et

REGENERATION AND INDUSTRIAL APPLICATION
The reusability of the Pb-FeONPs was performed in replicate (n ¼ 5). A 0.1 M HCl was used for desorption of CR from the surface of Pb-FeONPs. It was verified that Pb-FeONPs adsorption potential remains greater than 93% after the fifth cycle of the adsorption-desorption process as shown in Figure 10

CONCLUSION
A cost-effective Pb-FeONPs was prepared. Complete CR adsorption was achieved at pH 6.5 with an adsorption time of 40 min using an adsorption dose of 200 mg. The adsorption process showed that Langmuir with Qmax at 500 mg/g was the second-order of the kinetic and bestfitted isothermal model. The adverse value of G confirms the spontaneity of the adsorption process. It was checked that the adsorption potential of Pb-FeONPs was still greater than 93 percent after the fifth adsorption-desorption period. The n values obtained from the double-layer model of  statistical physics were 0.599, 0.593, and 0.565, which were less than 1, demonstrating the multi-docking process. Pb-FeONPs are regenerated up to 5 cycles and have been successfully used for laboratory and industrial-scale removal of CR dye from wastewater.

DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.