75% removal of fluoride was observed taking initial concentration 10 mg·L⁻¹ and adsorbent dose of 1 mg·L⁻¹ within 2 h of contact time. When the concentration of fluoride is increased, the competition for the active adsorption sites also increased and the adsorption process was gradually declined [18] . The findings are displayed in Figure 7.

The surface charge of the materials is usually determined by the Zero Point Charge (ZPC). The adsorption of the specific adsorbate on adsorbent depends on the surface charge of the adsorbent. Figure 8 depicts the pH of the solution after adsorption vs pH before adsorption [19] . The horizontal portion of the graph parallel to the X-axis indicates the ZPC of the material. The ZPC value of mesoporous MCM-41 is found to be 2.8 [20] . From that, it was concluded that the adsorbent surface had a positive charge (cationic) in aqueous medium.

The pH of the aqueous solution plays an important role which controls the adsorption at the water adsorbent interface [21] . Therefore, the adsorption of fluoride on MCM-41 was examined at different pH from 1.5 to 10.5 keeping other

parameters constant as shown in Figure 9. The percentage of fluoride removal was found to be more than 50% at acidic pH, whereas it was less than 40% at basic pH. At 301 K the maximum sorption capacity was found to be 63.05 mg·g⁻¹ for fluoride and at pH 6.3 (Figure 9). The following reactions are considered to understand the fluoride adsorption behaviour under various pH values [22] [23] ,

H F ↔ H + + F − (2)

≡ S O H + H + ↔   ≡ S O H 2 + (3)

≡ S O H + O H − ↔   ≡ S O − + H 2 O (4)

≡ S O H 2 + + F − ↔   ≡ S F + H 2 O (5)

≡ S O H + F − ↔   ≡ S O − + O H − . (6)

The overall reaction can be written as

≡ S O H + H + + F − ↔   ≡ S F + H 2 , (7)

where ≡ S O H , ≡ S O H 2 + and ≡ S O − are the neutral, protonated and deprotonated sites on MCM-41 respectively and ≡ S F , active site fluoride complex. Equation (3) reflects the ionization of HF in solution at low pH. At low pH values, HF is weakly ionized (pKa = 3.2) in solution, in that case, fluoride uptake capacity is reduced when pH is very less than 6.0, since a fraction of fluoride becomes unavailable for adsorption process. When the adsorption system (fluoride solution/MCM-41) was operated at 7 > pH > 6.0, the reaction site becomes protonated according to Equation 4 as there was so much proton available in the acidic medium leading to the enhancement of fluoride adsorption (Equation (3)) compared to fluoride adsorption at neutral pH (Equation (7)). The fluoride adsorption decreased sharply at pH > 7.29 due to the increased repulsive forces between the negatively charged fluoride ions and the SO⁻ (Equation (6)). It may be concluded that the mechanism of fluoride removal on MCM-41 follows both adsorption and ion-exchange mechanism [24] .

The rapid adsorption of fluoride took place within 90 min is depicted in Figure 10. After that adsorption becomes slow and almost reached equilibrium within 120 min. When the contact time is increased up to 8 h, no further appreciable adsorption took place (less than 1%) indicating that complete adsorption [25] occurred within 2 h. Thus, all the adsorption experiments were conducted for 2 h.

Langmuir isotherm

For estimation of maximum fluoride uptake (q_m) at different fluoride concentrations (2 - 25 mg·L⁻¹) the Langmuir sorption model was adopted. The Langmuir isotherm [26] is expressed as

1 q e = 1 q m 1 b 1 C e + 1 q m (8)

where q_e is the equilibrium quantity adsorbed (mg·g⁻¹), C_e is the equilibrium concentration (mg·L⁻¹), q_m is the maximum adsorption capacity (mg·g⁻¹) and b

is the Langmuir constant. The linear plot of 1 C e vs 1 q e (Figure 11(a)) with

higher R² value indicates the monolayer adsorption on mesoporous MCM-41. The values of q_m and b were calculated from the slope and intercept respectively are presented in Table 3.

Freundlich isotherm

The linear form of the Freundlich isotherm [27] equation is expressed as

ln q e = ln k f + 1 n ln C e (9)

where q_e is the adsorbed amount (mg·g⁻¹), C_e is the equilibrium fluoride concentration (mg·L⁻¹), k_f (mg·g⁻¹) is the Freundlich constant related to adsorption capacity and n is the constant related to energy of intensity of adsorption. The value of k_f and n (Table 3) are obtained from the linear plot of lnq_e vs lnC_e (Figure 11(b)). n values lying between 1 and 10 also indicate the favourable conditions for adsorption isotherms as well. From the adsorption studies, it is found that the Langmuir adsorption model is better fitted than Freundlich one. It was also supported by χ² values. Both χ² values and Dimensionless equilibrium parameter (R_L) [28] are reflected in Table 4.

Thermodynamic parameters viz. standard free energy change (ΔG⁰), standard enthalpy change (ΔH⁰), standard entropy change (ΔS⁰), activation energy (E_a), were calculated as follows. Considering the sorption distribution coefficient K₀, equation of free energy of sorption process, is given by

Δ G 0 = − R T ln K 0 (10)

where ΔG⁰ is the standard free energy change (kJ·mol⁻¹), R is the universal gas constant (8.314 J·mol⁻¹·K⁻¹) and T is the temperature in Kelvin. As per the method proposed by Khan and Singh [29] , the sorption distribution coefficient K₀

for sorption reaction was determined from the slope of the plot ln ( q e C e ) against

C_e at various temperatures and extrapolating to zero C_e. The sorption distribution coefficient may be expressed as

ln K 0 = Δ H 0 R T + Δ S 0 R (11)

where ΔH⁰ is standard enthalpy change (kJ·mol⁻¹) and ΔS⁰ is standard entropy change (kJ·mol⁻¹·K⁻¹). The values of ΔH⁰ and ΔS⁰ can be obtained from the slope and intercept of a plot of lnK₀ against 1 T respectively. The values of activation energy (E_a) and sticking probability (S^*) were calculated from the experimental data. These were calculated using a modified Arrhenius type equation related to surface coverage as expressed in Equation (12).

S * = ( 1 − θ ) exp − ( E a R T ) (12)

where, θ is surface coverage,

θ = ( 1 − C e C 0 )

where, C₀ and C_e are the initial and equilibrium fluoride concentrations respectively. The plot of ln ( 1 − θ ) against 1 T will give a linear plot with intercept of lnS^* and slope of E a R . In the sorption process, temperature plays a major role as

influencing factor, the sorption of mesoporous MCM-41 was monitored at three different temperatures 301, 306 and 311 K under optimized conditions. The thermodynamic parameters viz. ΔG⁰, ΔH⁰, ΔS⁰and E_a, were calculated with the help of Equations (9)-(11) and are presented in Table 5. The endothermic behaviour of adsorption is clearly indicated by +ve ΔH⁰ value and –ve ΔG⁰ value indicates the spontaneous nature of the adsorption process. From the low value of ΔS⁰, it may be concluded that there is no marked change in entropy occurred during the adsorption process. However, the increase of randomness at the solid solution interface during adsorption may be predicted from +ve ΔS⁰. ΔH⁰ (2.3016 kJ·mol⁻¹) value indicates that the adsorption process is a physico-chemical adsorption process rather than a pure physical or chemical one, as heats of chemisorption generally fall into the range [30] [31] of 80 - 200 kJ·mol⁻¹. The value of S^* (0.10) indicates that adsorption mechanism does not follow purely chemisorption.

In order to investigate the sorption mechanism of fluoride removal both Pseudo first and second-order kinetic models are used at different experimental conditions. Pseudo-first-order kinetic model is represented as

log ( q e − q t ) = log q e − K a d 2.303 t (13)

where q_t is the amount of fluoride on the surface of the sorbent MCM-41 at time t (mg/g) and K_ad is the equilibrium rate constant (min⁻¹). Figures 12(a)-(c) show the linear plots of pseudo-first-order for sorption of fluoride onto MCM-41 at 301 K, 306 K and 311 K respectively.

The most popular linear form of pseudo-second-order kinetic model is expressed as

t q t = 1 h + t q e (14)

where, q t = q e 2 k t / ( 1 + q t k t ) , the amount of fluoride on the surface of the mesoporous MCM-41 at any time, t amount (mg·g⁻¹), k being pseudo-second-order rate constant (gm·g⁻¹·min⁻¹), is the amount of fluoride sorbed at equilibrium (mg/g) and the initial sorption rate, h = k q e 2 (mg·g⁻¹·min⁻¹). The value of q_e, k and h of the pseudo-second-order equation were obtained experimentally for fluoride sorption at different temperatures viz. 301, 306 and 311 K. The plot of t

vs t q t gives a straight line with higher correlation coefficient R² values. This is

higher than that observed pseudo-first-order model indicating the applicability q_e of the pseudo-second-order model. Figures 13(a)-(c), depict the linear plot of pseudo second order for sorption of fluoride on MCM-41 at 301, 306 and 311 K respectively. Overall results revealed the value of q_e is increasing with the increase of initial Fluoride concentration and temperature. These values are reflected in Table 6.

The actual and predicted removals (%) of fluoride on MCM-41 are found very close to each other. It is calculated by applying BBD techniques. The details of RSM approach for the optimization of fluoride adsorption on MCM-41 is also described. The suitability of regression model for fluoride adsorption on MCM-41 is suggested from the results, observed in Table 7. It is revealed that the predicted values are quite close to the experimental one. It is clear from the Table 8 that p-value of all linear terms; all square term, and pH*Conc. terms are less than 0.05.

In this study, the effects of the predominant variables (pH and Conc.) on the response (% removal) are depicted in Figure 14. Response model plot is depicted in Figure 15, which is very supportive to predict the optimum values for the desired response. The relation between various adsorption parameters and response can be explained by the examination of contour plots as a function of two factors by holding the other factors at central level. The strength of a particular variable is appraised by the magnitude of the coefficient and the nature of the variable is indicated by the subtraction or addition sign in the equation [32] .

Model suggested that 77.88% of fluoride removal from aqueous solution should be achieved at conditions i.e., at Conc. (10 mg/L), pH (6.3) and CT (120 min). The experiments were also conducted at the aforementioned condition and found more than 75% removal efficiency. The experimental and theoretical results closely match with each other. The percentage error difference between the experimental and predicted value is very low, which validity the findings of response model curve. It also indicates that the proposed model is adequate for obtaining most favorable value in the range of the studied parameters.