3.2.1. Effect of pH
In order to explain the sorption behavior and mechanism of the aqueous species of U (VI), the distribution species of U (VI) as a function of pH was calculated. The effect of pH was investigated in the range 2.5-7 on Fe3O4 and in the range 2.5-6 in case of Fe3O4/HA. As pH increases with the pH of the solution, Fig. 4. The relative distribution of aqueous U (VI) species in solution at a concentration of 2×10−4 mol/L is presented in Fig. 5, using Visual MINTEQ ver. 3.0.33l (Gustafsson 2012). It is clear that the soluble uranyl hydroxo complex (UO2)3(OH)5+ and (UO2)4(OH)7+ are the predominant species at pH range 5.0-7.0 that favors the interaction betwee the functional groups that exist at magnetite surface (=FeOOH) in addition to the presence of carboxylic and phenolic group on humic acid (Li and Kaplan 2012).
3.2.2. Sorption kinetics
Kinetic investigations were performed to elucidate the mechanism of adsorption of metal ions, explain how fast the rate of chemical reaction occurs and also to know the factors affecting the reaction rate. Among them three kinetic models (the Lagergren’s pseudo-first order kinetic model, pseudo-second order model and intraparticle diffusion models) were used for examination of our experimental data.
The pseudo first order equation was suggested by Lagergren, for the adsorption of solid-liquid systems. It is generally expressed as follows:
$$\log ({q_e} - {q_t})=\log {q_e} - (\frac{{{k_1}}}{{2.303}})t{(2)}$$
The sorption data were also investigated by pseudo second order mechanism. In this model, the rate-limiting step is the surface adsorption that involves chemisorption (Ahmed et al 2017).The pseudo-second-order adsorption kinetic rate equation is expressed as:
(3)
Where qe and qt (mg/g) refer to the amount of metal ions adsorbed on both adsorbents at equilibrium and at time (t), respectively. k1 is the rate constant of pseudo first order (min−1) while k2 (gmg−1 min−1) is the rate constant of the second-order adsorption.
The rate constants were calculated and tabulated in Table (1). As the calculated equilibrium sorption shows, capacity (qe) from second-order kinetic model is consistent with the experimental data, Table (1). Therefore, the sorption can be described by pseudo second order kinetic model, Fig. 6a, b, c.
The intraparticle diffusion model is expressed as the following equation:
qt = kit1/2 + C (4)
Where k3 (mg g−1 min−0.5) is the intra-particle diffusion rate constant and C is the intercept which is proportional to the boundary layer thickness, Fig. 6c. The linear relationships that do not pass through the origin point that infers the intraparticle diffusion is not the dominant mechanism in processes occurring during the sorption of U(VI) ions on Fe3O4 and Fe3O4/ HA and other mechanisms such as film diffusion or particle diffusion may control the sorption process (Jaeshik et al. 2012) and the parameters are listed in Table (1).
3.2.3. Isotherm models
In this study, three isotherm models were tested to find the best fitting equations such as: Langmuir and Freundlich models. In Langmuir isotherm model, the linear form is represented by the following equation:
(5)
Where, qe is the amount adsorbed (mg/g), Ce is the equilibrium concentration of the metal ion (mg/L), and Qo and b are Langmuir constants related to the adsorption capacity and binding energy between the adsorbent and the adsorbate, respectively. These constants can be calculated by plotting of Ce/qe against Ce. The results are illustrated in Fig. (7a,b) and Table (2).
The linear equation of Freundlich model is commonly represented as:
log qe = log K f + (1/n)log Ce (6)
Where Kf and n are the Freundlich constants characteristics of the system, indicating the adsorption capacity and the adsorption intensity, respectively that were estimated from the plot of log qe versus log Ce, Fig. (8a,b) and tabulated in Table (2 ). The R2 values for the Langmuir equation in case of the two investigated adsorbents are higher than those obtained from the Freundlich equation.
A comparison of the adsorption performance of Fe3O4 and Fe3O4/HA with other adsorbents was reported in Table 3. The results implied that the investigated adsorbents can used efficiently for the uptake of U(VI) from aqueous medium.