KINETICS, ISOTHERMS, AND THERMODYNAMIC MODELING OF LIGHT LANTHANIDES(III): La(III) AND Gd(III) USING Mn–Ni NANOPARTICLES

. The sorption of light lanthanides, La(III) and Gd(III) on Mn–Ni nanoparticle was studied at varying ions concentrations, pH, contact time and temperatures. The kinetics of sorption of La(III) and Gd(III) were investigated, the experimental data were analyzed using the pseudo-first-order, pseudo-second-order forms, Elovich, and intra-particle diffusion models. The sorption kinetics of investigated ions was described by pseudo-second-order model. The experimental isotherms data were analyzed using Freundlich, Langmuir, and Temkin models were used to analyze the sorption isotherm data of ion exchange of La(III) and Gd(III) on Mn–Ni nanoparticle. The best fit was obtained by the Langmuir model with high correlation coefficients (R 2 = 0.995) with a maximum monolayer adsorption capacity of 8.81 mg/g.


INTRODUCTION
Rare-earth elements (REE) have technical importance due to their wide application in different areas [1,2] as these elements are named "The Vitamins of Modern Industry" [3].They are used for electronic purposes, metallurgy, medical science, and optical technology.Gadolinium is a rare earth metal that has similar properties as other rare earth metals, making it difficult to separate Gadolinium from the others.Gadolinium has been extracted from Earth's crust in the form of their minerals, such as monazite and gadolinite.Gadolinium is widely used for applications in various fields, including medicine and chemical industries, and thus its concentration in the environment is important to note [4,5].La(III) is one of the most abundant rare earth elements.Rare earth elements are extensively used in metallurgy, lasers, textiles, petroleum agriculture, magnets, and batteries.A Swedish chemist Carl Gustav Mosander discovered La(III) in 1839, but in 1923, it was isolated in the pure form.Rare earths were originally used to designate the lanthanides which includes oxides of scandium, yttrium, lanthanum and 14 elements following lanthanum in the 3rd row of the periodic table, i.e. from cerium to lutetium [6].The demand for REE has grown rapidly over the years, more than its supply rate.Many techniques are used for the recovery of REE to overcome this problem, such as ion exchange [7], co-precipitation [8], membrane [9], solvent extraction [10], electrochemical [11] and adsorption [11].Desorption techniques are widely used due to their fast, easy operation and low cost.The efficiency of the adsorption process depends on the accessibility of the adsorbent.The main objective of the present work is directed to study the sorption of La(III) and Gd(III) from waste solution using strongly cationic exchange Mn-Ni nanoparticle using batch technique.The effects different parameters on the sorption processes will be investigated such as contact time and concentration.Kinetics model and sorption isotherm parameters were calculated, and the data showed that the ion exchange of La(III) and Gd(III) on Mn-Ni nanoparticle was spontaneous and endothermic in nature.

EXPERIMENTAL
All reagents and chemicals were of analytical grade purity and used without further purification.pH measurements were performed using pH meter, model 601A, USA.The concentration of La(III) and Gd(III) in solutions was measured by using Shimadzu UV-1800 spectrophotometer.Mn-Ni nanoparticle ion exchange material was prepared by hydrothermal method produces very small particle 18.19 nm as calculated from XRD results using Scherrer formula as described earlier by EL-Aryan [12,13] as follow, 0.5 M of MnCL2, 0.5 M of NiCL2 and 1.0 M of urea (CO(NH2)2) were dissolved in 100 mL of deionized water under vigorous a magnetic stirrer at room temperature to form a homogeneous solution.Then, the resulting solution was transferred into a Teflon-lined stainless-steel autoclave (100 mL) to carry out hydrothermal reactions at a certain temperature100 o C for 24 h to form Mn-Ni nanoparticle.After the autoclave was allowed to cool to the room temperature naturally, the product collected was washed with distilled water and the obtained material was dried in an oven at 60 o C for 2 days.

Sorption studies
The sorption of La(III) and Gd(III) on Mn-Ni nanoparticle were determined by batch equilibration technique, as a function of different pH values.0.05 g of Mn-Ni nanoparticle was shaken with 5 mL of 50 m g / L of La(III) and Gd(III) solution at v /m ratio of 100 mL/g.The mixture was placed overnight (sufficient to attain the equilibrium) in a shaker thermostat adjusted at 25, 45 or 65 ± 1 o C.After equilibrium, the solutions were separated by centrifugation and the concentration of La(III) and Gd(III) in the solution were determined using Shimadzu UV-1800 spectrophotometer.The pH values of the solutions were measured before and after equilibrium using pH meter.The percentage ions adsorption by the ion exchangers was calculated from equation 1: (%) uptake = (Ci-Ct) /Ci × 100 (1) where Ci is the initial ion concentration and Ct is the ion concentration in mol L −1 at time t.

Kinetics model
The kinetic analysis of the adsorption process for La(III) and Gd(III) on Mn-Ni nanoparticle was carried out by mixing the exchanger with metal ions solution at 50 mg/L with a v/m ratio of 100 mL/g in a shaker thermostat at 25 ± 1 o C. The kinetic of the adsorption systems were studied using the pseudo-first-order, pseudo-second order, Elovich power model.The intraparticle diffusion model investigated the mechanism of adsorption.The pseudo first-order kinetic model of Lagergren [14] given by the equation 2: where qe is the quantity adsorbed at equilibrium (mg/g) and qt is the quantity absorbed at time t (mg/g).k1 is the rate constant for the pseudo-first-order sorption (min -1 ).A linear graph with negative slope is expected from the plot of ln(qe-qt) against t at different concentrations, k1 and qcal can then be obtained from the slope and intercept respectively.The pseudo-second-order kinetic model [15], presented in equation 3: where K2 is the rate constant of the pseudo-second-order kinetic equation in g/mg min -1 , qe is the maximum sorption capacity in mg/g and qt (mg/g) is the amount of sorption at time t.Linear graphs are obtained from a plot of t/qt against t from which qe and k2 can be calculated from the slope and intercepts.The Elovich kinetic model in its linear and nonlinear form is expressed by the equation 4 and 5, respectively [16]: q t = β ln(α β t) (5) where qt is the quantity of adsorbate adsorbed at time t (mg/g), α is a constant related to chemisorption rate and β is a constant which depicts the extent of surface coverage.The two constants (α and β) can be calculated from the intercept and slope of the plot of qt versus ln t, respectively.The intraparticle diffusion model by Weber and Morris [17] expressed by the mathematical relation in equation 6: where qt (mg g -1 ) is the amount adsorbed at time t and K3 (mg g -1 min -1/2 ) is the rate constant for intraparticle diffusion.Insight into the thickness of the boundary layer can be obtained from the value of C, large intercept suggests great boundary layer effect.A plot of qt versus t0.5 can give a linear or multilinear suggesting that intraparticle diffusion is involved in the adsorption process or two or more steps govern the adsorption process.However, if a linear graph is obtained and the plot passes through the origin then intraparticle diffusion is said to be the sole rate-limiting step [16].

Isothermal studies
The equilibrium of an adsorption process, adsorption isotherm is suitable in describing the distribution of adsorbate molecules between the liquid and the solid phase [18].Three adsorption isotherms, viz: the Langmuir, Freundlich and Temkin models were used to analyze the adsorption data.Important in formation such as adsorption mechanism, favorability of adsorption process and adsorbate-adsorbent affinity may be obtained.The Langmuir isotherm [19] which assumes a surface with homogeneous binding sites, equivalent sorption energies, and no interactions between adsorbed species is expressed by the mathematical relation 7: where Ce is the equilibrium concentration of ions (mg/L), qe is the quantity of ions adsorbed onto the adsorbent equilibrium(mg/g), qmax is the maximum monolayer adsorption capacity of adsorbent (mg/g) and KL is the Langmuir adsorption constant(L/mg).The plot of Ce/qe against Ce gives a straight line with a slope and intercept of 1/qmax and 1/qmax KL respectively.KL is an important tool in the calculation of the dimensionless equilibrium parameters (RL) that explains the favorability of adsorption process; RL is calculated by the mathematical relation in equation 8: The Freundlich isotherm [20] that is an empirical model not limited to monolayer coverage alone but also describe multi-layer adsorption.It is expressed mathematically as in equation 9: where qe is the quantity of ions adsorbed at equilibrium (mg/g), Ce is the concentration (mg/L) of ions in solution at equilibrium; Kf and n are Freundlich constants incorporating the factors affecting the adsorption capacity and adsorption intensity respectively.The plots of Ln qe against Ln Ce gives a linear graph with slope 1/n and intercept log Kf from which n and Kf can be calculated, respectively.The Temkin isotherm assumes linear rather than logarithm decrease of heat of adsorption while ignoring extremely low and very high concentration.It also assumes uniform distribution of bounding energy up to some maximum bonding energy.It is expressed by equation 10 [21]: where qe is the amount of adsorbate adsorbed at equilibrium (mg/g); Ce is concentration of adsorbate in solution at equilibrium (mg/L).B is a constant related to the heat of adsorption and it is defined by the expression B¼ RT/b, b is the Temkin constant (J/mol), T is the absolute temperature (K), R is the gas constant (8.314J/mol K), and A is the Temkin isotherm constant (L/g).From the plot of qe vs. lnCe, B and A can be calculated from the slopes (B) and intercepts (BlnA), respectively [22].

RESULTS AND DISCUSSION
The effect of shaking contact time on La(III) and Gd(III) adsorption onto Mn-Ni nanoparticle was studied using a fixing concentration in the range of (5-360 min).At the conditions of 25 mg adsorbent, 5 mL volume, pH 5.1, 25 o C and 100 mg/L of La(III) and Gd(III) as shown in (Figure 1).The uptake increased quickly in the beginning, and then the adsorption equilibrium was obtained after 360 min and 240 min for La(III) and Gd(III), respectively.After that, the adsorption efficiency became constant.Based on these results; the equilibrium time in all adsorption experiments was 360 min and 240 min for La(III) and Gd(III) respectively [23].In addition, it was observed that the adsorption rates of Gd(III) were very rapid in the initial 60 min, during which 80% of Gd(III) was absorbed, while the adsorption rates of La(III) were slowly in the initial 120 min, during which 23% of La(III) was absorbed onto Mn-Ni nanoparticle ion exchange material, under similar conditions.Also (Figure 1) a and b show the adsorption capacities, qe increased gradually of La(III) and Gd(III) onto Mn-Ni nanoparticle ion exchange material, respectively.The rapid adsorption may be attributed to the availability of more active sites on the adsorbent surface at the initial stages, and gradual occupancy of these active sites reduced the efficient interactions between metal ions and the adsorbent and adsorption rate became slower [24].The dissimilarity in adsorption rates between La(III) and Gd(III) can be explained by the adsorption of these ions at different sites on the adsorbent.The adsorption of La(III) is likely due to ion-exchange reactions and electrostatic attraction with negatively charged functional groups on the Mn-Ni nanoparticle ion exchange material, surface that are readily accessible by the adsorbate, resulting in rapid adsorption.The adsorbate requires a longer time to diffuse through cracks or pores in the alginate-based adsorbent before reaching the active sites.Whereas the subsequent slow step may be due to the competition between metal ions for the remaining available surface sites and the diffusion of metal ions into the inner surface of adsorbent beads [25].
The effect of initial concentration on the adsorption capacity of La(III) and Gd(III) onto Mn-Ni nanoparticle ion exchange material at the optimum pH = 5.1 and at room temperature, the results show that the equilibrium sorption capacities of the Mn-Ni nanoparticle ion exchange material increase with increasing the initial La(III) and Gd(III) concentration.This is because of an increase in the chances of contact between the adsorbent and adsorbed material.Also, because the higher the initial La(III) and Gd(III) concentration, the higher the driving force of the concentration gradient at solid-liquid interface which causes an increase of the amount of La(III) and Gd(III) adsorbed on the adsorbent [24].When the initial concentration of La(III) and Gd(III) increases from 50 to 400 mg/L, the amount of La(III) and Gd(III) adsorbed onto Mn-Ni nanoparticle ion exchange material at equilibrium (qe) increases from 4.82 to 9.36 mg/g and from 4.76 to 8.62 mg/g for Mn-Ni nanoparticle, respectively.

Adsorption kinetics
The parameters of the various kinetics model and the validation results have been reported (Table 1).The pseudo-second order assumes that the rate of adsorption of solute is proportional to the available sites on the adsorbent.The reaction rate is dependent on the amount of solute on the surface of the adsorbent.The pseudo-first-order kinetics fit shows a better linear relationship with high correlation coefficient of R 2 > 0.973 for La(III) while the pseudo-second-order kinetics shows a better linear relationship with high correlation coefficient of R 2 > 0.91 for Gd(III) for all experimental conditions as shown in Figure 2 and Table 1.Moreover, calculated values of qe from the pseudo-second-order kinetics was 6.14 mg/g are in close proximity to experimental results 4.76 mg/g, indicating that adsorption of Gd(III) onto Mn-Ni nanoparticle is in accord with pseudo-second-order kinetics, that is assumed the chemisorption may be the rate-limiting step through sharing or exchange of electrons between the adsorbent and adsorbent [26].The adsorption of La(III) onto Mn-Ni nanoparticle could be fit also by the pseudo-first-order kinetic model where qe experimental was 4.818 mg/g is more closed with qe calculated that was 4.42 mg/g as in Table 1.The intra-particle diffusion model has been widely applied to examine the rate limiting step during adsorption.The adsorption of solute in a solution involves mass transfer of adsorbate (film diffusion), surface diffusion, and pore diffusion.In the intra-particle diffusion if the line of plots of qt versus t½ passes through the origin, intra-particle diffusion controls the adsorption process.In our study as shown in (Figure 3), the plots of qt versus t½, involved two linear steps take place with correlation coefficients (R 2 > 0.97).The sharper first stage portion (a) is attributed to the diffusion of adsorbate though the solution to the external surface of adsorbent or the boundary layer diffusion of solute molecules.The second portion (b) describes the gradual adsorption stage until equilibrium is reached.During these two stages, La(III) and Gd(III) are slowly transported via intra-particle diffusion in the particles of Mn-Ni nanoparticle and are finally retained in the pores.The slope of the line of the first stage is called the intra-particle linear portion of the first stage does not pass though the origin, indicating there is a boundary layer resistance between adsorbent and adsorbate and There are different mechanisms that control the adsorption process [27].There are four main mechanisms that describe the transfer of solute from a solution to the adsorbent.The first is called mass transfer (bulk movement) of solute particles as soon as the adsorbent is dropped into the solution.This process is too fast; thus, it is not considered during the design of kinetic systems.The second mechanism is called film diffusion; it involves the slow movement of solutes from the boundary layer to the adsorbent's surface.When the solute reaches the surface of the adsorbent, they move to the pores of the adsorbent third mechanism.The final mechanism involves rapid adsorptive attachment of the solute on the active sites of the pores; being a rapid process [27].In general, it is observed that values of K3 of Gd(III) is more than the values of La(III) of the adsorption on Mn-Ni nanoparticle ion exchange material.
The Elovich kinetic model is useful in describing adsorption on highly heterogeneous adsorbents with a fast rate and helps to predict the mass and surface diffusion, activation, and deactivation energy.The constants α and β can be obtained from the slope and intercept of the plot of qt vs ln t and are show in (Figure 4) and listed in Table 1.In the case of using the Elovich equation, the correlation coefficients (R 2 ) are obtained in the range of 0.99 for La(III) and 0.85 for Gd(III) onto Mn-Ni nanoparticle, respectively.

Adsorption isotherms
The values of qmax and KL were determined by plotting Ce/qe versus Ce (Figure 5) and their values are given in Table 3.It was noted that the vales of correlation coefficient R  The Plots of Ln qe against Ln Ce gives a linear graph with slope 1/n and intercept Ln Kf from which n and Kf can be calculated, respectively.1/n is related to the intensity of the adsorption.Freundlich adsorption isotherm constants KF and n were determined from the intercept and slope of a plot of Ln qe versus Ln Ce (Figure 6).Table 2 reports the various parameters obtained from the Freundlich isotherm plots.Isotherms with 1/n < 1 indicate the high affinity between both adsorbate and adsorbent and imply the presence of chemisorption reaction.The values of 1/n obtained in this study were observed to be less than unity which indicates favorable adsorption.The vales of correlation coefficient R 2 was 0.931 and 0.872for adsorption of La(III) and Gd(III) onto Mn-Ni nanoparticle, respectively.The data were fitted with Langmuir model better than Freundlich model indicating homogeneous adsorption should have occurred on the surface of Mn-Ni nanoparticle [28].
The Temkin isotherm model considers the interactions between adsorbent and metal ions and is based on the assumption that the free energy of adsorption is a function of the surface coverage [29].Temkin model shows in (Figure 7) was used for the further analysis.And different from the Langmuir and Freundlich models, Temkin model assumes that adsorption energy decreases linearly with the surface coverage and is more applicable to chemical adsorption process [23].The actual experimental data complied with the Temkin model in a relatively small coverage range, where chemical adsorption took place.Therefore, the obtained comparatively weak linear correlation coefficients were 0.894 and 0.828 of La(III) and Gd(III) onto Mn-Ni nanoparticle, respectively, was fit with the Temkin model manifested that the chemical adsorption was not the only dominated interaction for La(III) and Gd(III) onto Mn-Ni nanoparticle.

CONCLUSION
The prepared Mn-Ni nanoparticle has highly efficient adsorption of La(III) than Gd(III) from aqueous solution.The maximum adsorption percentage for La(III) and Gd(III) attained at pH 5.1.
The adsorption efficiency of La(III) and Gd(III) was 96.36 and 95.13, respectively.The equilibrium time for adsorption of La(III) and Gd(III) was attained at 240 min and 180 min, respectively.The adsorption capacities for La(III) and Gd(III) was 9.36 and 8.62 mg/g, respectively.The adsorption capacity of Mn-Ni nanoparticle was highly dependent on the initial La(III) and Gd(III) concentrations.The sorption of the studied La(III) and Gd(III) from aqueous suspension using the Mn-Ni nanoparticle was fitted well to Langmuir and pseudo second order equations.Thus, the Mn-Ni nanoparticle could be excellent adsorbent for adsorption of La(III) and Gd(III) from aqueous solutions comparing with other adsorbents.

Figure 1 .
Figure 1.Effect of contact time on the sorption of (a) La(III) and (b) Gd(III) onto Mn-Ni nanoparticle ion exchange material at initial metals concentration of 50 mg/L.

Figure 2 .
Figure 2. Linearization of the kinetic data through: (a) pseudo first order and (b) pseudo second order for La(III) and Gd(III) adsorption by Mn-Ni nanoparticle ion exchange material.

Figure 3 .
Figure 3. Linearization of the intra-particle diffusion portion (a) and portion (b) for La(III) and Gd(III) adsorption by Mn-Ni nanoparticle ion exchange material.

Table 1 .
Kinetic parameters for La(III) and Gd(III) adsorption by Mn-Ni nanoparticle ion exchange material.

Table 2 .
Summarized Langmuir, Freundlich and Temkin isotherm parameters for La(III) and Gd(III) adsorption by Mn-Ni nanoparticle.

Table 3 .
A comparison of the isotherm parameters for La(III) and Gd(III) adsorption onto various adsorbents.