Statistical Physics Model of EBT Adsorption on Pb(II) doped Zinc Oxide Nanoparticles: Kinetics, Isotherm and Reuse Study

ABSTRACT Pb(II) doped zinc oxide nanoparticles (Pb-ZnONPs) was synthesised using the co-precipitation method. The average size distribution of the Pb-ZnONPs is 42.8 nm and further used as an adsorbent to remove Erichrome Black T (EBT) from wastewater. The adsorption of EBT onto the Pb-ZnONPs was best fitted for pseudo-second-order kinetics model, indicating that the adsorption phenomena depend on EBT and Pb-ZnONPs, showing chemisorption phenomenon. The maximum adsorption potential of Pb-ZnONPs (qmax = 200 mgg−1) for EBT is far better than that of the already available adsorbents. The high regression coefficient of freundlich shows that the adsorption can be shown by multi-layer process. The value of ΔG° is negative and temperature increases with an increase in the absolute value increases, suggesting the adsorption of dye onto the Pb-ZnONPs is spontaneous. The decrease in the concentration of adsorbed monolayer (Q0 = nNM) from 411 to 43.55 mg/g with the change in temperature revealed that the adsorption process is exothermic in nature. The Pb-ZnONPs have exhibited a variation of about 7–8% of adsorption compared to the fresh sample after 5th regeneration.


Introduction
Textile wastewater falls under the primary source of water contamination due to the toxic nature of dyes present in the contaminated water and further undergo chemical and biological changes resulting in the unbalanced ecosystem [1][2][3]. To solve the water problems of the society, it is necessary to eliminate dyes (such as EBT) from the wastewater. Dyes manufacturing industries produced wastewater that was treated either by physical or chemical processes before discharging into the environment. These methods, however, are expensive and inefficient to handle a wide variety of dyes related wastewaters. Adsorption process has an ability to remove dyes from diluted solutions effectively, compared to that of other systems due to its added advantages including easy operating and costing effectiveness [4][5][6].
The nanoparticles are small in size with higher surface area, results in the increased adsorption process. In addition to the properties described above, the core shells nanoparticles allow researchers to extract huge amount of dyes in a short period of time. Nanoparticle has many advantages over other bio-adsorbent such as high surface area, availability of active sites and magnetic properties, etc [7][8][9]. Adsorption of dyes on to the nanoparticle was explained in the term of electrostatic attraction mechanism [10,11]. On exposure the EBT dye induces an allergic reaction and causes severe eye irritation. The dyes contaminated water systems undergo lesser photosynthetic processes in marine life due to the adsorption of sunlight by the dyes on the upper surface of water. This process has long-lasting adverse effect on the marine life [12][13][14].

Synthesis of Pb-ZnONPs
The Pb-ZnONPs were synthesised by a thermal co-precipitation method. Firstly, salt ratio of 1:20 (zinc chloride/lead acetate) was added to 200 ml of deionised distilled water. Then, 35 ml of 5 M NaOH was added slowly and with stirring for 2 h at 60°C, resulting in the formation of homogenised particles (Figure 1(a)). A rapidly developed white precipitate was subjected to several washing with deionised distilled water till the suspension of pH was less than 7.5. Then, after the precipitate was filtered and dried at 100°C followed by the calcination process for 3 h at 400°C. The final product was stored for further use.

Statistical physics model for dye adsorption mechanism
By considering the assumption of this statistical physics method [17], an adsorption model was derived. It is considered that the numerous molecules are linked onto receptor sites (N M ) situated on an adsorbent (unit mass). The general reaction is expressed in terms of adsorbate molecules (D) adsorbed on to adsorbent receptor site (R) [15].
where n = stoichiometric coefficient (may be an integer or not, lower or greater than 1).
Fraction of molecule adsorbed per site of adsorbent when n < 1, i.e. multi-anchorage adsorption involved and if n > 1, multimolecular adsorption is assumed as single site occupied by the number of molecules.
Within this theory, the isotherm may be represented by a single layer process or by simulating the creation of two or more layers. The use of a two energy double-layer model was sufficient to experimentally estimate the adsorption of dye. The proposed model using statistical method was explained in the below sections.

Monolayer adsorption model
The monolayer adsorption model believes that EBT dye molecule form single layer with adsorption energy (ε 1 ). Therefore, the adsorbed quantity (Q) of dye is expressed as: In this model, there are three variables: C 1/2 is the concentration at half saturation N M = Receptor sites density on the nanoadsorbent surface and n = Number of associated dye molecules per site of nanoadsorbent The values were by fitting this model with experimental data. The adsorbed quantity (Qe sat ) of molecule at saturation is calculated using the relation: Qe sat = n*N M *(1+ N 2 ). Here (1+ N 2 ) is nothing but the number of layers that are formed, whereas for monolayer N 2 = 0.

Double layer model
If double layer adsorption is represented by the equation: This signifies that the first layer provide acceptor sites for an additional layer of dye molecules, hence involved two adsorption energies ε 1 and ε 2 as described earlier. This model with two different energies can be expressed as: Four important variables are described from this model including n, N M , (significance of n and N M is as same as previous model) and C 1 and C 2 are nothing but the first and second layer concentration at half saturation, respectively.

Multilayer model
Complete adsorbed layers are described in the case of Nc = 1 + N 2 (Layer).

Characterisation of Pb-ZnONPs
The Pb-ZnONPs were prepared using the co-precipitation method. Figure 1(a) represents the typical SEM image of Pb-ZnONPs and reveals the dimension of the sample and its average size as 42.8 nm. It is demonstrated that some particles are large in size due to clubbing of small particles in to big particles. The EDX findings indicated that the material composed of Zn, Pb, and O at concentrations of approximately 42.66, 7.11, and 50.23 weight%, respectively (Figure 1(b)). The better recorded diffraction peak are listed in terms of dhkl and relative strength as 2 theta and absolute intensities. The maximum location as 2 theta depends on instrumental features such as wavelength. The Bragg Law is used to convert dhkl from the observed 2 theta (Figure 1(c)). The actual amplitude of the X-rays, i.e. the amount seen in the peak, may differ by instrumental and experimental parameters. The relative intensities of the peaks of diffraction are independent. The patterns observed in XRD analysis is related to the polycrystalline nature of NPs. The XRD analysis peaks at 33.16° and 63.24° matches with the JCPDS of ZnO which confirmed the formation of Pb-ZnONPs. In FTIR analysis ( Figure 1 The wide surface area and sufficient pore size would generally be helpful in enhancing the ability of adsorption in the process of dye removal. To be precise, the high surface area will provide the dye molecules with ample adsorption sites that have an enormous effect on the adsorption process. The EBT molecule is smaller in size (15.50 Å) [33] than the pore size of the product. In addition, this will allow the porous Pb-ZnONPs to transfer the EBT molecules freely into the interior sections.

Effect of time, pH and adsorbent dose
The contact time is an important factor from industrial and economical point of view. The findings reveal that the initial adsorption rate is very high, owing to the high surface adsorption site concentration and the strong contact between the adsorbate and the adsorbent. Due to the adsorption of EBT molecules onto the sorbent, the concentration gradient decreases over time and contributes to lower adsorption. The graph shows that 75% of the dye was adsorbed within 10 min and further the adsorption reaches to 89% at 60 min and remains unchanged (Figure 2(a)). Fast equilibrium time has an economic benefit for large-scale applications since it requires shorter contact time and hence less energy consumption which results in the decrease of operating costs [34]. The solution pH can influence the adsorbent's aqueous chemistry as well as the surface binding sites shown in Figure 2(b). At pH 6.0 the maximum (97%) adsorption was obtained. Based on the results obtained, further experiments were carried out at pH 6.0. In general, hydroxyl groups that depend on the pH cover the surfaces of metal oxides. The surface charge is positive at pH values lower than pHzpc (i.e. point of zero charge of Pb-ZnONPs, here pHzpc of Pb-ZnONPs = 7.0), neutral at pHzpc, and negative at pH values greater than pHzpc values. At high pHs, the surface of Pb-ZnONPs is negatively charged, by which electrostatic repulsion forces decreases the negatively charged EBT (adsorbate) layer. Therefore, at pH values greater than pHzpc = 7.0, the efficiency of adsorption decreases [13]. The results showed that by increasing the adsorbent dose, the adsorption efficiency was improved. It was found that the removal efficiency (percent) of the dye was improved from 88.51 to 97.75% by increasing the Pb-ZnONPs dosage from 50 to 200 mg ( Figure 2 (c)). The greater number of adsorption sites were available at higher dosages of Pb-ZnONPs which results in the increment of the adsorption percentage.

Kinetic, adsorption isotherms, separation factor
The kinetics of EBT adsorption on to the Pb-ZnONPs was analysed using the Ho and McKay model (Figure 3(a)). This model is widely used to describe the kinetics of dye adsorption on to the solid adsorbents [35]. The results (Table 1) showed that the Ho and McKay equations for the entire adsorption were followed by the adsorption method. The EBT adsorption on to the Pb-ZnONPs best fitted for the Pseudo-Second-Order kinetics model. This indicates that the adsorption phenomena depends on the EBT and Pb-ZnONPs interaction as chemisorption, involving valence forces via electron sharing or exchange may be the rate-limiting step [36] ( Figure S1 and Table S1 given in supplement file). The equilibrium adsorption isothermal model was used to explain the interactive behaviour of adsorbate and adsorbent as illustrated in Figure 3(b). To predict the adsorption potential of the adsorbent, isothermal data is used to design the adsorption process. Equilibrium isothermal experiments were performed at 25°C and pH 6.0 with various initial concentrations (50-200 mgL −1 ) of EBT. To analyse the results obtained from equilibrium adsorption, three models were used such as Langmuir, Freundlich and Temkin [37,38].
The Langmuir, Freundlich and Temkin equation parameters were determined and tabulated in Table 2. It is noted that the maximum adsorption potential of Pb-ZnONPs (q max = 200 mgg −1 ) for EBT is far better than that of already available adsorbents. The Freundlich  equilibrium isothermal equation was used to define the adsorption process experimentally as depicted in Figure 3(c). The K f and 1/n values calculated from the 'ln qe' vs. 'ln Ce' plot intercept and slope are defined in Table 2. This data (  (Figure 3(d)).
The Temkin and Langmuir isotherms shows slightly similar correlation coefficients compared to that of Freundlich. The Freundlich isotherm, thus, gives the best fit to the experimental results. The separation factor (R L ) can be expressed as the fundamental function of the Langmuir isotherm ( Figure S2 given in supplement file). In the 0 < R L < 1 range, R L values indicate the favourable adsorption [40,41]. In this study, for the initial EBT concentration of 50 mg/L, the obtained R L value was 0.0167785, suggesting the favourable adsorption of EBT on to the Pb-ZnONPs.

Adsorption thermodynamic parameters
An in-depth information can be obtained by thermodynamic parameters on the intrinsic energetic changes in the adsorption method. If the value of ΔG° is negative (Table 3), then the absolute value increases with increase in the temperature, suggesting that the adsorption of dye on to the Pb-ZnONPs is spontaneous. The negative value of ΔH° and ΔS° (Table 3) signifies the adsorption process is exothermic in nature and decreased randomness during the adsorption process at the solid/solution interface, respectively [41].

Interpretation of the parameters of statistical physics models
Adsorption capacities of the systems were investigated and deduced that the approximate adsorption capacities have the same order of magnitude. This clarified that the interaction of EBT on to the surface of adsorbent (Pb-ZnONPs) showed identical affinities [42,43]. The best-fitted model is decided based on R 2 values, taking physical consideration into account. Figure 4 illustrates the basic representation of the adsorption of EBT dye molecules on the side of the Pb-ZnONPs receptor with two distinct adsorption interaction energies. Figure 5 indicates the best suited EBT adsorption on to the Pb-ZnONPs isotherm with the two energy double-layer model. Then, Nm, Q, and ε parameters are calculated from the best-fitted model as shown in Table 4. The root mean square error (RMSE) value are given in Table S2 in supplement file.

Analysis of n
The behaviour of EBT dye molecules in the aqueous solution (i.e. before adsorption) and on the adsorbent surface (i.e. after adsorption) can be described using a parameter n. The  n parameter plays two significant roles in terms of interpretation: geometrical position of EBT dye adsorption is defined by its values as calculated by numerical simulations on the adsorbent surface. Indeed, if this value is less than 1, a clear description of this parameter can be attributed to a portion of the adsorbed molecule per site, describing the horizontal adsorption on to surface of the adsorbent. On the other hand, if the value of the n parameter is greater than 1, it describes the number of molecules that interacts with one receptor site [44][45][46]. These results indicated that the adsorption of the EBT dye was a process of multi-molecular separation. Since all the values of n were superior to unity for Pb-ZnONPs, it can be inferred that one or more EBT dye molecules were attracted by each binding site, resulting in the orientation of the adsorbate at different angles in more than one adsorbent surface. It should be remembered that the values of n for EBT adsorption on to the Pb-ZnONPs were observed, while the same situation often existed for other systems. This could be due to the characterisation of identical affinity by the electron active sites for the binding of dye molecules. The effect of temperature on the statistical physics parameter is shown in Figure 6(a), in which distinct patterns were observed. Parameter n, estimated for the EBT-Pb-ZnONPs adsorption systems, decreases (0.527 to 0.466) as a function of the temperature, which was due to the effect of thermal motion. It is also noted that the binding between the EBT-Pb-ZnONPs aggregates in the solution were broken at 318 K, resulting in the reduction of layers formed on the surface of the adsorbent [46,47]. The n value obtained from statistical physics models (0.527 to 0.466) are very close to the value obtained from the Freundlich isotherm (0.697). The close value of n from statistical physics models and Freundlich isotherm confirmed that the adsorption follows the double layer model.

Density of occupied receptor sites, N M
In the case of EBT adsorption on to the Pb-ZnONPs receptor sites, the density of occupied receptor sites, N M , plays a vital role [30]. The increase in temperature prompted the additional receptor sites, resulting in the increase of number of anchorages. These results are in good agreement with the previously adsorbed layer in terms of temperature effect. The decrease in the concentrations (411 to 43.55 mg/g) of monolayer adsorbed (Q 0 = nN M ) ( Figure 6(b)) with the increase in the temperature confirmed that the adsorption process is exothermic in nature [48][49][50].

Analysis of the adsorbed quantity at saturation
Using the parameters n and N M , the monolayer and double layer statistical physics models were investigated by considering the adsorbed quantity at high concentrations (i.e. at saturation) of the EBT dye. These calculations can be performed with Qesat = n*N M (for the monolayer model) and Qesat = 2 n*N M (for the double layer model). Table 4 shows that the value of Qesat decreases from 433.73 to 40.63 mg/g as the temperature of the experimental state increases. These results confirmed that the maximum EBT dye quantity was absorbed by the Pb-ZnONPs. The adsorption of dyes is dependent on various factors, including temperature, pH and concentration of adsorbate. The effect of temperature on the adsorbed potential of the EBT dye was represented in Figure 6(c) in particular [51][52][53].

Adsorption energy
To measure the adsorption energies obtained from the interaction studies of EBT and adsorbent surface, the appropriate model was used and estimated as: For simplicity, the solubility (Cs) of EBT in the water was considered as constant at all temperatures of adsorption and both adsorption energies were tabulated in Table 4. Normally, half-saturation concentrations (C 1 and C 2 ) can be calculated directly by fitting the adsorption data, however, some values have been found to be relatively high, leading to an unreasonable understanding. In this case, both concentrations at half saturation were specifically derived from experimental adsorption results. In the endothermic phase, physical interactions were involved in the adsorption system which was confirmed by measuring the adsorption energies for the removal of EBT using Pb-ZnONPs. At various adsorption temperatures, it was noted that E 1 > E 2 . The effect of temperature on both adsorption energies is shown in Figure 6(d), suggesting that the increase in temperature decreases the energy values [54,55].

Regeneration of Pb-ZnONPs by heating
The cost-effectiveness of the adsorbent is illustrated by the regeneration potential of the adsorbent and this overall mechanism plays a pivotal in the commercial applications. The calcination of Pb-ZnONPs at 400°C for 4 h was performed during the regeneration process. Adsorption experiments were carried out under pre-optimised conditions over the regenerated Pb-ZnONPs. The regeneration and recycling of the adsorbent process was carried out five times to confirm the efficiency of removal of EBT by the Pb-ZnONPs. Figure 7 depicts the adsorption potential following the successive regeneration and reuse of Pb-ZnONPs in the removal of EBT. The results demonstrated that the Pb-ZnONPs has exhibited the variation of about 7-8% lower of adsorption compared to that of the fresh sample after five cycles. This indicates that Pb-ZnONPs can be regenerated with appropriate adsorption ability via the calcination process. Table 5 shows the the comparison of previous reported adsorbent used for the EBT removal with Pb-ZnONPs.

Conclusion
Pb-ZnONPs were synthesised at a constant temperature of 60°C using a co-precipitation method which resulted in particle size of 42.8 nm. These nanoparticles are highly effective in the removal of EBT from the wastewater. The experimental data obtained for the adsorption of EBT on to the Pb-ZnONPs are best fitted to the pseudo-second-order kinetics model. Further, the results from isothermal models indicate that the adsorption phenomena depend on EBT and Pb-ZnONPs as chemisorption. The maximum adsorption potential of Pb-ZnONPs (qm = 200 mgg −1 ) for EBT is far better than that of other adsorbents. The high regression coefficient of Freundlich isotherm shows that the adsorption is a multi-layer process. To better understand the EBT adsorption mechanism, various statistical physics models were used. Based on the double-layer model with two energy sites, the modelling study showed that the uptake of EBT was a double-layer and multidocking adsorption process. The calculation of the adsorption energies derived from the relevant model indicated that the EBT adsorption on to the Pb-ZnONPs is a physical mechanism via calcination process. Finally, the Pb-ZnONPs can be regenerated several times, making the nanomaterial cost-effective.

Disclosure statement
No potential conflict of interest was reported by the author(s).