Sorption studies of europium on cerium phosphate using Box-Behnken design

Amorphous cerium phosphate was prepared and characterized. Three-level Box-Behnken design (BBD) was employed to analyze the effect of process variables such as initial pH (2–6), contact time (60–180 min), and sorbent amount (0.05–0.15 g) on the sorption capacity of europium. Analysis of variance (ANOVA) revealed that the main effect of initial pH and sorbent amount has a substantial impact on the sorption of Eu(III). Probability F-value (F = 3 × 10-3) and correlation coefficient (R2 = 0.97) point out that the model is in good accordance with experimental data. The maximum sorption capacity of Eu(III) was found to be 42.14 mg g-1 at initial pH 6, contact time of 180 min, and a sorbent amount of 0.05 g. Sorption isotherm data was well explained by the Langmuir model and monolayer Eu(III) sorption capacity was obtained as 30.40 mg g-1. Kinetic data were well described by the pseudo-second-order model. Thermodynamic data suggested that the process is endothermic and spontaneous.


Introduction
Rare earth elements (REEs) are a group of metals consisting of 15 lanthanide elements including yttrium and scandium. Owing to their superior physical and chemical properties, they are significant for several progressive technologies [1]. Among them, europium (Eu) is an active metal; a trace amount of europium may greatly enhance the properties of metals [2]. Europium is used in light-emitting diodes (LEDs), LCDs, and fluorescent lamps. Because of the growing demand for LEDs and LCDs, it is becoming a more vital element for the electronic industry [3]. Europium is also used in nuclear reactor control rods because of its neutron absorption effectiveness 1 . The demand for europium supply has been increasing every day. However, europium sources are not equally distributed on Earth, and the production of europium in the world is mostly in China [3]. Therefore, recovery of europium and other REEs from alternative sources such as electronic waste and wastewater has become an important issue.
On the other hand, during the operation of nuclear power plants radioactive europium ( 152 + 154 Eu) is produced in low-level radioactive waste solutions together with 137 Cs. Because of its long half-life, separation of europium from radioactive wastes before discharge is very significant [4]. Recovery and removal of europium from a different type of waste solutions are of great importance not only from the point of their limited resource availability but also for the mitigation of their quantity for disposal as radioactive wastes.
Sorption is one of the most promising techniques due to its advantages of high efficiency, low operation temperature, and high selectivity. Various types of materials such as goethite [5], aluminum silicate [6], aluminum oxide [4], functionalized magnetic chitosan [7], montmorillonites [8], manganese oxides [9], biomass [10] and algae [3] were used as sorbents/ion exchangers to remove and separate europium from radioactive waste and aqueous streams.
Insoluble salts of tetravalent metals are composed of tetravalent metal salts and anions like phosphate, molybdate, antimonate, etc. Inorganic ion exchangers/sorbents consisted of tetravalent metal acid salts are highly stable in strong acids, oxidizing solutions, and ionizing radiations. They show selectivity for certain metal ions. In particular, they are attractive for applications where organic resins cannot be used because of their degradability [11]. Cerium(IV) tungstate [12], titanium(IV) phosphates [13,14], poly-acrylamide based cerium(IV) phosphate [15], zirconium(IV) molybdate [16] have been utilized for the sorption of europium ions.
Cerium phosphate compounds have been prepared [17][18][19] and used for the separation of some radionuclides [15,20] from hazardous waste solutions. But so far, there is no study reported in the literature focused on the sorption behavior of neat cerium phosphate towards europium.
In the present study, amorphous cerium phosphate was prepared, characterized, and used as a sorbent for the separation of Eu(III) ions from aqueous solution. Response surface methodology (RSM) was utilized to analyze the effect of initial pH, contact time, and sorbent amount on sorption capacity. For this aim, Box-Behnken Design (BBD) with 3 variables was employed. Equilibrium isotherm, kinetic and thermodynamic studies were conducted to assess the sorption behaviors.

Preparation of cerium phosphate
The precipitation of amorphous cerium phosphate was reported by Hanna et al. [21]. According to this procedure, the stoichiometric amount of Ce(SO 4 ) 2 •4H 2 O and K 2 HPO 4 was dissolved in deionized water and equimolar (0.012 mol L −1 ) solutions of Ce(SO 4 ) 2 •4H 2 O and K 2 HPO 4 were prepared separately. K 2 HPO 4 solution was added to Ce(SO 4 ) 2 •4H 2 O solution dropwise with continuous stirring until the final pH of the solution was 2. The mixture obtained was stirred for 1 h more and kept 24 h at ambient temperature for aging. The yellow-colored precipitate was washed with deionized water to obtain a constant pH value. The formed gel was separated by centrifuge and dried at 60 o C.

Identification and characterization
Cerium phosphate powders were identified and characterized by X-ray Diffraction (XRD), scanning electron microscope (SEM), Fourier transform infrared (FTIR), and thermal analyses (TGA-DSC). XRD pattern was recorded by Philips X'Pert Pro diffractometer (Philips Research Laboratories, Eindhoven, Netherlands) .
FTIR data (400-4000 cm −1 ) were acquired by Perkin Elmer Spectrum Two model FTIR-ATR spectrometer (PerkinElmer, Inc. Waltham, MA USA). SEM images were collected using the Thermo Scientific Apreo S model scanning electron microscope (Thermo Fisher Scientific Inc., Waltham, MA, USA). TGA-DSC data were obtained by TA Instruments SDT Q600 up to 1000 o C with a heating rate of 10 o C min −1 (TA Instruments SDT Q600: TA Instruments, New Castle, DE, USA).

Statistical design of experiments
Response surface methodology (RSM) is a useful tool to evaluate the interactions of process variables [22]. RSM is composed of statistical and mathematical techniques to design experiments, establish numerical models, study the effects of variables, and search for the optimum combinations of factors. In experimental design methodology, variables vary from one experiment to the next simultaneously. As the variables may affect each other, the value of one variable can depend on the value of other variables [23].
Three-level designs have been suggested by Box and Behnken (1960) for fitting the response surfaces. In these designs, 2 k factorials are combined with incomplete block designs. The resulting designs are composed of a reduced number of required runs which make them efficient [24].
To investigate the effect of initial pH (X 1 ) , contact time (X 2 ) , and sorbent amount (X 3 ) on Eu(III) sorption, a three-level BBD has been used. According to BBD, a total of 15 runs with three replicates at center points were carried out. Statistical analyses were performed by Design Expert 12 software (Stat-Ease, Inc., Minneapolis, MN, USA). The effect of variables on Eu(III) sorption was investigated by batch method. The contact between sorbent and Eu(III) ions in solution was provided in a temperature-controlled shaker at 150 rpm by adding 0.05 g sorbent in 30 mL of liquid phase. When the sorption equilibrium was achieved, samples were filtered and Eu(III) concentrations were determined by ICP-OES.
Sorption capacity ( Q) was calculated using Eq. (1): is defined as the ratio of metal concentration in the sorbent phase to solution-phase [25] and it is determined by Eq. (2): In Eqs. (1) and (2), C o and C e are the initial and equilibrium concentrations of Eu(III) ion in solution (mg L −1 ), V is the volume (mL) and m is the mass of the sorbent (g).
The ranges and levels of the variables (low, center, high) are presented in Table 1. Variable − 1 0 + 1 Initial pH X 1 2 4 6 Contact time (min) X 2 60 120 180 Sorbent amount (g) X 3 0.05 0.10 0.15 The general model equation including linear and quadratic terms for the estimation of optimum response is as follows: In Eq. (2), b o denotes the intercept. b i , b ii and b ij signify linear effects, quadratic effects and dual effects, respectively. The second-order polynomial equation related to the model can be written as follows: carried out in a temperature-controlled shaker at 298 ± 1 K for 120 min.

Kinetic studies
Kinetic experiments were conducted between 15 and 360 min of contact time. 30 mL of 100 mg L −1 Eu(III) solutions were separately contacted with 0.05 g sorbent at pH 4. Kinetic models were applied to test the experimental data.

Thermodynamic studies
Experiments were carried out at 303, 313, 323, and 333 K for the determination of thermodynamic parameters For all experiments, initial and equilibrium concentration of Eu(III) ions were measured by ICP-OES.

Characterization studies
XRD pattern of cerium phosphate is depicted in Figure 1a. It is seen that cerium phosphate has an amorphous structure. Figure 1b represents the IR spectrum of the cerium phosphate powders. The broad peak at 3196 cm −1 is assigned to -OH stretching vibrations and the peak at 1633 cm −1 is attributed to -OH bending vibrations of water molecule [26]. The bands around 992 cm −1 and 513 cm −1 correspond to P-O stretching and O-P-O bending mode of vibration, respectively [21].
TGA-DSC thermogram of cerium phosphate is demonstrated in Figure 1c. The thermogram was taken between 10 o C and 1000 o C at a uniform heating rate of 10 o C min −1 . The TGA curve shows a continuous decrease in the mass as a function of temperature. There are two weight loss regions. The weight loss between 25 o C and 310 o C, is mainly from the dehydration of physisorbed water molecules. Condensation of POH groups occurs from 310 o C to 1000 o C. The total weight loss is about 17.31%. In the DSC curve, the endothermic peak around 75 o C is attributed to the dehydration of water. The sharp exothermic peak at 620.33 o C is due to the crystallization of cerium polyphosphate. SEM image of cerium phosphate powders is given in Figure 1d. Particles tend to form aggregates. Smaller particles with an approximate size of 80 to 120 nm were detected.
SEM image and EDX data after Eu(III) sorption are presented in Figure 1e. There is no significant change in the SEM image after sorption. Particle size distribution is not homogeneous and aggregates can be seen. The presence of Eu(III) on the sorbent surface was confirmed by EDX data. The weight percentage of elements on the surface was also provided in Figure 1e.

Statistical analysis
BBD utilized in this study consists of 12 factorial and 3 replicate points. Experimental variables in coded and actual forms along with the response are presented in Table 2. A second-order polynomial equation was used to express the relationship between independent variables and the response. The regression coefficients of parameters were determined and data were fitted to a secondorder polynomial equation as given by Eq. (5): The statistical significance of the model is checked by ANOVA [27]. Table 3 represents the ANOVA results, coefficients, and P values. In Table 3, the model F value of 15.93 suggests that the proposed model is significant. The correlation coefficient (R 2 ) was found to be 0.97. It means that predicted capacity values are in good agreement with the experimental ones.
The smallest level of importance leading to rejection of the null hypothesis is described as the P-value.
When P < 0.05, the main effect and dual effects are regarded as statistically significant [28]. The main effect of initial pH (P = 7.0 × 10 −4 ), the main effect of sorbent amount (P = 6.0 × 10 −4 ) , and dual effect of initial pH and sorbent amount (P = 7.0 × 10 −3 ) were determined to be significant.
The positive value of coefficient belonging to pH (X 1 = 7.65) points out that pH has a positive effect on the sorption of Eu(III). It means that the uptake of Eu(III) increases as pH increases. The sorbent surface is mostly protonated at lower pHs. Eu(III) ions in solution compete with H + ions for the active surface sites. As the pH increases, the number of H + ions in the solution decreases, and the sorption of Eu(III) becomes more favorable [29]. It is seen from Figure 2a that the sorption capacity of Eu(III) increases in the pH range of 2 −6.
Maximum Eu(III) uptake is 21.87 mg g −1 at pH 6. Contact time (X 2 = 1.51) has a positive effect on sorption.
Eu(III) sorption capacity slightly increases from 13.85 to 16.88 mg g −1 (Figure 2b). However, the coefficient of sorbent amount (X 3 = − 7.78) has a negative value. This implies that the sorption capacity of Eu(III) decreases with the increasing sorbent amount. Eu(III) uptake decreased from 27.03 to 11.46 mg g −1 with the increase in sorbent amount from 0.05 to 0.15 g (Figure 2c).

3D Response surface plots
The relation between the dual effects of independent variables and Eu(III) sorption capacity (Q) was given in 3D surface plots (Figure 3). Figure 3a displays the change in Q values depending on initial pH (X 1 ) and contact time (X 2 ) . Maximum Q was found to be 24.39 mg g −1 in 180 min, at initial pH 6 by holding the sorbent amount at 0.10 g.

Isotherm studies
The effect of initial Eu(III) concentration on sorption was determined between 25-400 mg L −1 . Figure 4 demonstrates the relation between Q, K D, and Eu(III) ion concentration at equilibrium. Eu(III) uptake The sorption equilibrium data are expressed by sorption isotherms. Isotherms clarify the relationship between the metal concentration in the solution at equilibrium C e and the mass of the metal sorbed per unit mass of sorbent q e .
Langmuir's theory assumes that sorption occurs at specific homogeneous sites within the sorbent. Langmuir model in its linear form [30] is expressed as: where q m is the maximum amount of the metal ion per unit weight of adsorbent to form a complete monolayer , C e is the equilibrium concentration of metal ion (mg L −1 ) and b is a constant related to the sorption energy (L mg −1 ) . q m and b values are calculated from the slope and intercept of the linear plot between C e /q e and C e . q m , b, and correlation coefficient (R 2 ) values calculated from the isotherm are given in Table 4. q m value was estimated to be 30.40 mg g −1 . An R 2 value of 0.99 indicates that the sorption data can be explained well by the Langmuir model.
The separation factor ( R L ) [31], which is based on the Langmuir model, can be represented as in Eq. : where b is the Langmuir constant (L mg −1 ) and C o is the initial metal ion concentration (mg L −1 ) . If the value of R L is between zero and one (0 < R L < 1), the sorption is favorable. The calculated values of R L were plotted against initial Eu(III) concentration as shown in Figure 5. It can be deduced from Figure 5 that Eu(III) sorption is favorable for all concentrations under investigation. Freundlich adsorption isotherm [32] and its linear form can be described by Eq. (8) and Eq. (9), respectively: where q e is the equilibrium adsorption capacity (mg g −1 ) , C e is the metal concentration at equilibrium, K f and n are constants related to adsorption capacity and intensity, respectively. The values of n and K f are shown in Table 4. Dubinin-Radushkevich isotherm [33] is expressed as: ε is the Polanyi potential given by Eq. (11), where β is a constant related to the mean free energy of adsorption (mol 2 J 2 ) −1 , q e is the amount of solute adsorbed at equilibrium (mg g −1 ) , q m is the theoretical saturation capacity (mg g −1 ) , R is the gas constant (R = 8.314 J mol −1 K −1 ) and T is the temperature (K). The adsorption mean free energy E (kJ mol −1 ) can be calculated as follows: When the value of E is below 8 kJ mol −1 , the sorption process can be considered as physical sorption. However, the sorption process follows a chemical mechanism if the value of E is between 8-16 kJ mol −1 . The D-R isotherm constant and the value of E are summarized in Table 4. The adsorption mean energy value was obtained as 0.50 kJ mol −1 . This value indicates that physical sorption plays a dominant role in the sorption process.
The comparison of Eu(III) sorption capacity of amorphous cerium phosphate with some other sorbents reported in the literature is presented in Table 5. As can be seen in Table 5, the obtained Eu(III) uptake value of cerium phosphate is comparable to the values reported in the literature. On the other hand, the uptake capacity of cerium phosphate can be enhanced by surface modification or doping of other elements.

Thermodynamic studies
The effect of temperature on Eu(III) sorption was examined at 303, 313, 323 and 333 K.  Thermodynamic data provides information about the spontaneity of the sorption process. The values of ∆ H o , ∆ S o and ∆ G o were estimated using Eqs. (13), (14) and (15) [36]: In the equations above, K D is the thermodynamic equilibrium constant (mL g −1 ) , R is the universal gas constant (8.314 J mol −1 K −1 ) , T is the temperature (K), V is the solution volume (mL) and mis the mass Thermodynamic parameters for Eu(III) sorption are given in Table 6. The negative values of ∆ G o obtained at 303, 313, 323, and 333 K point out the spontaneity of the Eu(III) sorption process.  [37]. The values of ∆G o obtained in this study are within the ranges of physisorption mechanism.

Kinetic studies
Kinetic experiments were conducted between 5 and 360 min of contact time. The experimental kinetic data were evaluated using pseudo-first and pseudo-second-order kinetic models. Pseudo-first order model is expressed as: The integrated form of the equation is: where k 1 is the first-order rate constant (min −1 ), q t and q e are the amount of metal ion adsorbed (mg g −1 ) at time t and equilibrium, respectively [38,39]. k 1 and q e can be obtained from the slope and the intercept of the plot.
Pseudo-first order kinetic model is not suitable to describe the sorption of Eu(III), because the R 2 value is relatively low and the calculated q e values are not per the experimental data.
The pseudo-second order model [40] is based on sorption capacity of sorbent and it is given by Eq. (18): where k 2 is the second order rate constant (g mg −1 min −1 ) . Integrated linear form of the equation is expressed as: The kinetic plot of t/qt versus t for Eu(III) sorption is presented in Figure 7. q e and k 2 can be calculated from the slope and the intercept of the plot. The pseudo-second-order model parameters q e , k 2, and R 2 are provided in Table 7. Depending on R 2 values, the pseudo-second-order model suggests a better fit to experimental data. Kinetic model k 1 (min −1 ) q e (mg g −1 ) R 2 Pseudo-first order 0.008 6.15 0.72 k 2 (g mg min −1 ) q e (mg g −1 ) R 2 Pseudo-second order 0.007 31.65 0.99

Conclusion
In this study, amorphous cerium phosphate was synthesized via a one-step method. Characterization studies were performed by XRD, SEM, FTIR, and thermal analyses. The relation between independent variables (initial pH, contact time, sorbent amount) and Eu(III) sorption capacity (Q) was investigated by Box-Behnken design. The effect of initial pH and sorbent amount on Eu(III) sorption was found statistically significant by the evaluation of regression analyses and ANOVA. The correlation coefficient (R 2 = 0.97) points out the good agreement between actual and predicted Q values. The F value of the model was found to be 15.93 and it shows the significance of the model. 3D response surface plots were described to evaluate the dual effects of variables.
The maximum Eu(III) sorption capacity of cerium phosphate was obtained as 42.14 mg g −1 at initial pH 6, contact time of 180 min, and sorbent amount of 0.05 g.
Langmuir model is the best to describe the sorption of Eu(III) and monolayer Eu(III) sorption capacity was found to be 30.40 mg g −1 . The positive value of ∆ H o expresses the endothermic character of sorption. A decrease in ∆G o values with increasing temperature supports the assumption that the sorption process is spontaneous. Based on the value of R 2 , the pseudo-second-order model was best to fit the kinetic data.
Overall results point out that amorphous cerium phosphate is an easily prepared sorbent capable of removing Eu(III) ions from a slightly acidic aqueous solution.