Adsorption isotherms are prerequisites to understand the nature of the interaction between adsorbate and the adsorbent used for the removal of organic pollutants. An adsorption isotherm describes the relationship between the amount of adsorbate up taken by the adsorbent and the adsorbate concentration remaining in solution (
26). There are many equations for analyzing experimental adsorption equilibrium data. The equation parameters of these equilibrium models often provide some insight into the adsorption mechanism, the surface properties and affinity of the adsorbent for adsorbate (
26-
28). The parameters obtained from different models provide important information on the surface properties of the adsorbent and its affinity for the adsorbate. In present study, Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich (D-R) isotherms were utilized in order to analyze the MB adsorption by the MPS. The equations and the linear forms of these models are presented in
Table 2 (
7,
12,
14), and the results are shown in
Table 3.
In the equations presented in
Table 2, q
max (mg/g) is the maximum adsorption capacity of the adsorbent, K
L (L/mg) is the Langmuir constant, n and K
F (L/mg) are the Ferundlich constants and the intensity of adsorption, respectively, Q (mg/g) is the amount of MB dye adsorbed per unit mass of the adsorbent, Q
m (mg/g) is the capacity of the intended adsorbent, R (8.314 J/mol.K) is the universal gas constant, T (K) is the absolute temperature, K is the Dubinin–Radushkevich model constant (mol
2/kJ
2). E, is the mean adsorption energy and A ((RT/bt) 1na
t) and B (RT/bt) are the constants of Temkin isotherm (
4,
6,
20,
21).
The Langmuir equation is valid for monolayer adsorption onto a completely homogenous surface with a finite number of identical sites with negligible interaction between adsorbed molecules (
26).
Figure 5 shows the Langmuir (C
e/q
e vs. C
e) plots for adsorption of MB. R
L, and the correlation coefficients for the Langmuir isotherm are presented in
Table 3. The essential features of the Langmuir isotherm may be expressed in terms of equilibrium parameter R
L, which is a dimensionless constant referred to as a separation factor or equilibrium parameter:
where C
0 is the initial concentration and K
L is the constant related to the energy of adsorption (Langmuir constant). The values of R
L indicate the type of isotherm to be irreversible (R
L = 0), favorable (0 < R
L< 1), linear (R
L = 1) or unfavorable (R
L > 1). Value of separation for adsorbent is found to be less than unity, confirming thereby the favorable adsorption process. The isotherms of MB on MPS were found to be linear for the entire concentration range studies and the correlation coefficients were extremely high (R
2 > 0.99) as shown in
Table 3. As
Table 3 shows, the maximum adsorption capacity of the MPS in the Langmuir model was obtained as 15.87 mg/g which is considered as a favorable rate compared to other similar studies (
Table 4) (
29-
32). The Freundlich isotherm (
33) is derived by assuming a heterogeneous surface with a non-uniform distribution of sorption heat over the surface.
Figure 5 shows the Freundlich (log q
e vs. log C
e) plots for adsorption of MB.
Table 3 shows the Freundlich adsorption isotherm constant and its respective correlation coefficients. Heat of adsorption and the adsorbent–adsorbate interaction on adsorption isotherms were studied by the Temkin isotherm (
34).
Figure 5 shows the Temkin (q
e vs. ln C
e) plots for adsorption of MB. The constants obtained for the Temkin isotherm are shown in
Table 3. Langmuir and Ferundlich isotherms do not provide any information about the surface adsorption mechanism. Therefore, other isotherm models, such as Dubinin-Raduchkevich, are used for estimating the mechanism of surface adsorption. Raduchkevich in 1949 and Dubinin in 1965 proposed that the adsorption curve depends on the structure of the adsorbent pores (
35). The plot of ln q
e vs. ε
2 at for MB is presented in
Figure 5. The constant obtained for D–R isotherms are shown in
Table 3. The mean adsorption energy (
E) gives information about the chemical and physical nature of adsorption (
36).
As
Table 3 depicts, MB dye adsorption on the MPS has a high compliance with the Freundlich model (R
2 = 0.999). This shows that the surface of the adsorbent is heterogeneous and the adsorption of MB dye on the adsorbent is multilayer. This finding is in line with the results that reported previously by El-Qada at al. (
21) and Altenor et al. (
37). Also, in this study, the value of n coefficient in the Freundlich model was found to be 2.182 which indicate a high tendency toward adsorbing the MB dye onto the MPS and this fact had been demonstrated by R
L in advance. The coefficient 1/n in the Freundlich model is a value between 0 - 1 which represents the adsorption intensity of adsorbate to adsorbent. In the present study, 1/n was revealed as 0.458 which indicates the favorable adsorption of the adsorbate (
37).