Sorption of lead (II), cobalt (II) and copper (II) ions from aqueous solutions by γ-MnO₂ nanostructure

The phase and purity of the products were firstly examined by XRD. Figure 1 shows a typical XRD pattern of the as-synthesized samples. Curves (a) and (b) are the XRD patterns of the two products obtained for 3 h and 4 h. Curves (c) and (d) are the XRD patterns of the two products obtained for 5 h and 6 h, respectively. All reflection peaks can be readily indexed to hexagonal γ-MnO₂ phase. However, the as–prepared sample achieved clearly crystal structure for 5 h.

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The morphologies and structure information were further obtained from SEM and TEM images. Figures 2(a)–(c) show an SEM image of the as-prepared γ-MnO₂ which was synthesized at the different ratios between H₂O and C₂H₅OH: (a) H₂O:C₂H₅OH = 2:1 (sample M1), (b) H₂O:C₂H₅OH = 1:1 (sample M2), (c) H₂O:C₂H₅OH = 1:2 (sample M3). As a result, γ-MnO₂ nanospheres with nanostructure were formed in the alcohol (KMnO₄:C₂H₅OH = 1:2). It is clear that the flocculation occurred in the water solution (figure 2(a)). Figure 2(c) also shows that the products of γ-MnO₂ consisted of a large amount of uniform nanospheres, with size of about 10 nm. Figure 2(d) shows the TEM image of the as-prepared γ-MnO₂ nanospheres (sample M3) and the TEM image further demonstrates that the obtained product has uniform sphere morphology. The TEM image also provides the size of γ-MnO₂ nanospheres from 10 to 18 nm. The BET surface area of the as-synthesized product (sample M3) was determined to be about 65 m² g⁻¹.

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The pH is one of the imperative factors governing the adsorption of the metal ions. The effect of pH was studied from a range of 2 to 6 under the precise conditions (at optimum contact time of 120 min, 240 rpm shaking speed, with 0.1 g of the adsorbents used, and at a room temperature of 24 °C). From figure 3, with γ-MnO₂ used as adsorbent, it was observed that with increase in the pH (2–6) of the aqueous solution, the adsorption percentage of metal ions (lead, cobalt and copper) all increased up to the pH 4, as shown above. At pH 4, the maximum adsorption was obtained for all the three metal ions, with 98.9% adsorption of Pb(II), 54.1% of Co(II) and 41.3% adsorption of Cu(II).

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The increase in adsorption percentage of the metal ions may be explained by the fact that at higher pH the adsorbent surface is deprotonated and negatively charged, hence attraction between the positively metal cations occurred [10].

The relationship between contact time and the adsorption percentage of heavy metals from aqueous solution with γ-MnO₂ adsorbent is shown in figure 4. The effect of contact time was studied at a room temperature of 24 °C, at intervals of 20 min. From the obtained result it is evident that the adsorption of metal ions increased as contact time increased. The adsorption percentage of metal ions approached equilibrium within 80 min for Pb(II), 120 min for Co(II) and 180 min for Cu(II); with Pb(II) recording 92.47% adsorption, Co(II) 81.51% and Cu(II) 89.24% adsorption. This experiment shows that different metal ions attained equilibrium at different times.

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The Freundlich (1906) equation [11–20] is an empirical equation based on adsorption on a heterogeneous surface. The equation is commonly represented as

$$\begin{eqnarray}&&{\rm log} {{q}_{{\rm e}}}={\rm log} {{K}_{{\rm F}}}+(1/n){\rm log} {{C}_{{\rm e}}},\end{eqnarray} \tag{ 2 }$$

where C_e (mg L⁻¹) is the equilibrium concentration and q_e (mg g⁻¹) is the amount of adsorbed metal ion per unit mass of the adsorbent. The constant n is the Freundlich equation exponent that represents the parameter characterizing quasi-Gaussian energetic heterogeneity of the adsorption surface. K_F is the Freundlich constant which indicates the relative adsorption capacity of the adsorbent. The Freundlich model was chosen to estimate the adsorption intensity of the sorbate on the sorbent surface. The experimental data from the batch sorption study of the three metal ions on γ-MnO₂ nanostructures were plotted logarithmically (figure 5) using the linear Freundlich isotherm equation.

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The linear Freundlich isotherm constants for Pb(II), Co(II) and Cu(II) on γ-MnO₂ nanostructure are presented in table 1. The Freundlich isotherm parameter 1/n measures the adsorption intensity of metal ions on the γ-MnO₂ nanostructure. The low 1/n values of Pb(II) (0.067), Cu(II) (0.064) and Co(II) (0.164) less than 1 show the favorable sorption and confirm the heterogeneity of the adsorbent. Also, they indicate that the bond between heavy metal ions and γ-MnO₂ are strong. The adsorption capacity K_F of the adsorbent was calculated from the isothermal linear regression equation. The K_F value of Pb(II) (137.40 L g⁻¹) is greater than that of Cu(II) (59.98 L g⁻¹) and Co(II) (40.55 L g⁻¹), suggesting and confirming that Pb(II) has greater adsorption tendency towards the γ-MnO₂ nanostructure than the other two metals.

The Langmuir model [11–20] assumes that uptake of metal ions occurs on a homogenous surface by monolayer adsorption without any interaction between adsorbed ions. The linearized form of the Langmuir equation is given by the relation

$$\begin{eqnarray}&&\frac{{{C}_{{\rm e}}}}{{{q}_{{\rm e}}}}=\frac{{{C}_{{\rm e}}}}{{{q}_{{\rm m}}}}+\frac{2}{{{q}_{{\rm m}}}{{K}_{L}}},\end{eqnarray} \tag{ 3 }$$

where q_m is the sorption capacity and K_L is Langmuir constant.

The Langmuir isotherm model was chosen for the estimation of maximum adsorption capacity corresponding to complete monolayer coverage on the γ-MnO₂ surface. The plots of specific sorption (C_e/q_e) against the equilibrium concentration (C_e) for Pb(II), Co(II) and Cu(II) are shown in figure 6 and the linear isotherm parameters, q_m, K_L and the coefficient of determinations are presented in table 2.

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The data in table 2 with high values of correlation coefficient (R² = 0.998–0.999) indicate good agreement between the parameters and confirm the monolayer adsorption of Pb(II), Co(II) and Cu(II) ions on to γ-MnO₂ nanostructure surface. Furthermore, the sorption capacity q_m, which is a measure of the maximum sorption capacity corresponding to complete monolayer coverage, showed that the γ-MnO₂ nanostructure has a mass capacity 200 mg g⁻¹ for Pb²⁺, 90.91 mg g⁻¹ for Co²⁺ and 83.33 mg g⁻¹ for Cu²⁺.

An important characteristic of the Langmuir isotherm is expressed in a dimensionless constant equilibrium parameter, S_F, also known as the separation factor, given by

$$\begin{eqnarray}&&{{S}_{{\rm F}}}=\frac{1}{1+{{K}_{{\rm L}}}{{C}_{0}}}\cdot \end{eqnarray} \tag{ 4 }$$

The data in table 2 shows that the dimensionless parameter S_F remained between 0.008 and 0.059 (0 < S_F < 1) at lowest concentration and between 0.0016 and 0.025 (0 < S_F < 1) at highest concentration, i.e. the separation parameters S_F for the three metals are less than unity indicating that γ-MnO₂ nanostructure is an appropriate adsorbent for the three metal ions. The smaller S_F value indicates a highly favorable adsorption [20, 21]. However, S_F value of Co (II) > Cu (II) > Pb (II) indicates that in a mixed metal ion system, Pb(II) will be adsorbed faster than Co(II) and Cu(II).

Redlich–Peterson isotherm [11–20] is a hybrid isotherm featuring both Langmuir and Freundlich isotherms, which incorporate three parameters into an empirical equation. Then, the Redlich and Peterson equation, designated the 'three parameter equation', may be used to represent adsorption equilibria over a wide concentration range. The linearized form of the Redlich–Peterson equation is given by the relation

$$\begin{eqnarray}&&{\rm ln} \left( {{K}_{{\rm RP}}}\frac{{{C}_{{\rm e}}}}{{{q}_{{\rm e}}}}-1 \right)=\beta {\rm ln} {{C}_{{\rm e}}}+{\rm ln} {{\alpha }_{{\rm RP}}},\end{eqnarray} \tag{ 5 }$$

where K_RP (L g⁻¹), α_RP (L mg⁻¹) and β are the Redlich–Peterson isotherm constants. The value of β is the exponent which lies between 0 and 1. In the limit when the β values tend to zero the Redlich–Peterson isotherm approaches Freundlich isotherm model at high concentration and is in accordance with the low concentration limit of the ideal Langmuir condition when the β values are all close to 1.

The Redlich–Peterson isotherm constants could be predicted from the plot between ${\rm ln} \left( {{K}_{{\rm RP}}}\frac{{{C}_{{\rm e}}}}{{{q}_{{\rm e}}}}-1 \right)$ versus lnC_e. However, this is not possible as the linearized form of Redlich–Peterson isotherm equation contains three unknown parameters α_RP, K_RP and β. Therefore, a minimization procedure is adopted to maximize the coefficient of determination R², between the theoretical data for q_e predicted from the linearized form of Redlich–Peterson isotherm equation and the experimental data. The Redlich–Peterson isotherm plots for the three metal ions (Pb(II), Co(II) and Cu(II)) are presented in figure 7 and the isotherm parameters are given in table 3.

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The data in table 3 indicated that, the higher R² values for Redlich–Peterson show the agreement of experimental equilibrium data with the Redlich–Peterson isotherm equation. This was expected, because degree of heterogeneity (β) is included and this equation can be used successfully at high solute concentrations. Langmuir is a special case of Redlich–Peterson isotherm when constant β is unity.

It has been suggested that linearization plots may not be a significant basis to reject or accept a model. To further analyze the suitability of the three models (Freundlich, Langmuir and Redlich–Peterson), their fitness to the experimental data was assessed. The fitness of the data was established using a single statistical parameter (R²) which is called the coefficient of determination [18, 19]. The coefficient of determination values for the three models as shown in table 4 shows that the three models are applicable in describing the data of Co(II) and Cu(II) (as all R² > 0.90), whereas the adsorption process of Pb(II) is described by the Langmuir and Redlich–Peterson isotherm models.

The pseudo-first-order rate model equation given by Lagergren in 1898 is [20–29]

$$\begin{eqnarray}&&\frac{{\rm d}q}{{\rm d}t}={{k}_{1}}({{q}_{{\rm e}}}-q),\end{eqnarray} \tag{ 6 }$$

where q_e is the amount of solute adsorbed at equilibrium per unit weight of adsorbent (mg g⁻¹), q is the amount of solute adsorbed at any time (mg g⁻¹) and k₁ is the adsorption constant. Integrating equation (6) with conditions q(0) = 0 and q(t) = q_t, the kinetic rate expression becomes

$$\begin{eqnarray}&&{\rm log} ({{q}_{{\rm e}}}-{{q}_{t}})={\rm log} {{q}_{{\rm e}}}-\frac{{{k}_{1}}t}{2.303}\cdot \end{eqnarray} \tag{ 7 }$$

The first-order rate constant k₁ (min⁻¹) can be obtained from the slope of the plot of log(q_e–q_t) against time t, as shown in figure 8(a) and table 5. The adsorption first-order rate constants were found to be 4.606.10⁻³, 0.0115 and 4.606.10⁻³ min⁻¹ for metal ions Pb(II), Co(II) and Cu(II), respectively.

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If the adsorption process can be described by pseudo-first order equation, there should be good linear relationship between log(q_e–q_t) and t. In the present study, the plot of log(q_e–q_t) versus time t was not linear over the entire time range, the correlation coefficients in this model for all metal ions were low. Also, the theoretical q_e values estimated from the first-order kinetic model were not in accordance with the experimental values. This suggests that this adsorption system is not a first-order reaction, indicating that more than one mechanism was involved in adsorption.

Adsorption kinetics was explained by the pseudo-second-order model given by Ho and McKay as follows [20–29]

$$\begin{eqnarray}&&\frac{{\rm d}q}{{\rm d}t}={{k}_{2}}{{({{q}_{{\rm e}}}-q)}^{2}}.\end{eqnarray} \tag{ 8 }$$

With the boundary conditions q(0) = 0, q(t) = q_t the solution of equation (8) is

$$\begin{eqnarray}&&\frac{t}{q}=\frac{1}{{{k}_{2}}q_{{\rm e}}^{{\rm 2}}}+\frac{1}{{{q}_{{\rm e}}}}t.\end{eqnarray} \tag{ 9 }$$

Additionally, the initial adsorption rate h (mg mg⁻¹ min⁻¹) can be determined as

$$\begin{eqnarray}&&h={{k}_{2}}q_{{\rm e}}^{{\rm 2}},\end{eqnarray} \tag{ 10 }$$

where k₂ (g mg⁻¹ min⁻¹) is the second-order rate constant determined from the plot of t/q against t, as shown in figure 8(b) and table 5.

The plots of t/q versus t are linear for different metal ions. The adsorption second-order rate constants were found to be 1.88.10⁻³, 1.25.10⁻³ and 1.45.10⁻³ g mg⁻¹ min⁻¹ for metal ions Pb(II), Co(II) and Cu(II), respectively. The initial sorption rate, h, is the highest for Pb(II) and the lowest for Cu(II), which reflects the affinity of the sorbent for these absorbate species.

The results showed that the theoretical q_e values calculated from pseudo-second order kinetic model were very close to the experimental values of equilibrium sorption with correlation coefficients of determination higher than 0.999. The pseudo-second-order adsorption mechanism was predominant for adsorption of metal ions Pb(II), Co(II) and Cu(II) by γ-MnO₂. The applicability of this model showed that the sorption process is complex and involves more than one mechanism.

Because the pseudo-first-order and pseudo-second-order kinetic models cannot identify the diffusion mechanisms, the most commonly used technique for identifying the diffusion mechanism involved in the adsorption process is to use the intra-particle diffusion model.

The intra-particle diffusion model used here refers to the theory proposed by Weber and Morris, based on the following equation for the rate constant [26–30]

$$\begin{eqnarray}&&{{q}_{t}}={{k}_{{\rm d}}}{{t}^{1/2}}+C,\end{eqnarray} \tag{ 11 }$$

where q_t is the quantity of metal ions adsorbed at time t (mg g⁻¹), k_d the initial rate of intra-particular diffusion (mg L⁻¹ min ^−1/2), and C is the y-intercept which is proportional to the boundary layer thickness.

According to this model, when the metal ion solution is mixed with the adsorbent, transport of the metal ions from the solution through the interface between the solution and the adsorbent occurs into the pores of the particles. If adsorption of a solute is controlled by the intra-particle diffusion process, a plot of q_t versus t^1/2 gives a straight line [26–28]. Figure 9 illustrates the diffusion of Pb(II), Co(II) and Cu(II) ions within γ-MnO₂ as a function of time and shows that intra-particle diffusion occurred in two stages, first linear portion (stage I) and second curved path followed by a plateau (stage II). In stage I, the metal ions were up taken by γ-MnO₂. This is attributed to the utilization of the most readily available adsorbing sites on the adsorbent surfaces. In stage II, very slow diffusion of adsorbate from surface site into the inner-pores is observed. Thus, the initial portion of adsorption of Pb(II), Co(II) and Cu(II) ions by γ-MnO₂ adsorbents may be governed by the initial intra-particle transport of Pb(II), Co(II) and Cu(II) ions controlled by surface diffusion process and the later part is controlled by pore diffusion. The intra-particle diffusion constants for all two stages (k_d1, k_d2) are given in table 6.

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