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Synergistic Effects in Extraction and Separation of Praseodymium(III) and Neodymium(III) with 8-Hydroxyquinoline in the Presence of 2-Ethylhexyl Phosphonic Acid Mono-2-Ethylhexyl Ester Dongbei Wu* Department of Chemistry, Tongji UniVersity, 1239 Siping Street, Shanghai 200092, People’s Republic of China
Qian Zhang and Borong Bao Department of Chemistry, Shanghai UniVersity, Shangda Street, Shanghai 200444, People’s Republic of China
In this paper, the extraction behaviors of praseodymium(III) from an aqueous chloride-acetate medium, using 8-hydroxyquinoline (HQ), 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (P507, HL) and their mixture, were studied, using ultraviolet-visible light (UV-vis) absorption spectroscopy. The binary equilibrium constants (log K1, log K2) for the complex formation PrL3‚3HL and PrQ3 in the organic phase were determined to be -1.98 for 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester and -11.54 for HQ, respectively. The overall equilibrium constant (log K12) for the ternary species PrQ2L10H9 was estimated to be 6.01. The largest synergistic enhancement factor was calculated to be 5.39, corresponding to a HQ:P507 concentration ratio of 3:7 at pH 3.6. When P507 was added into HQ, the entire stripping could be achieved at an aqueous sulfuric acid concentration of ∼0.02 M. In addition, for praseodymium(III) and neodymium(III), the mixture of HQ and P507 showed higher separation selectivity than HQ or P507 alone, which is important for potential industrial applications. 1. Introduction Rare earths (scandium, yttrium, and lanthanides) are important elements, from an industrial point of view. They are extensively used in the astronavigation, luminescence, nuclear energy, and metallurgical industries.1-4 Praseodymium, which is one of the most abundant rare earths, is of current interest, because it is used in the production of atomic batteries,5 whereas neodymium is the basis of the most common solid-state lasers used in material processing, medicine, etc.6 With the ever-increasing demand for high-purity rare earths and their compounds, the separation and purification of these elements recently have gained considerable importance. Solvent extraction is used to separate and purify rare-earth elements on an industrial scale. Acidic organophosphorous extractants, such as di-2-ethylhexyl phosphoric acid (P204) and 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (P507), are widely used for this purpose.7,8 However, even with the above extractants, separation and purification are still known to be difficult, because of their similar chemical and physical properties, especially for the neighboring rare-earth elements. Therefore, there is a growing interest in the development of new extractants and extraction systems for separating them as a group or from each other. 8-Hydroxyquinoline (HQ) is a type of strong ligand for metal ions and is widely used for extraction.9,10 However, to our knowledge, data on the extraction of rare earths using this extractant seem to be quite scare, regardless of whether the extractant involves HQ alone or mixtures of HQ and another extractant. In fact, HQ is a good candidate for the extraction of rare-earth ions, and, under favorable experimental conditions, a high degree extraction can be achieved.11 Synergistic extraction * To whom correspondence should be addressed. Tel.: +86-02165982287. Fax: +86-021-65982287. E-mail Address: wudongbei@ mail.tongji.edu.cn.
is a phenomenon that sometimes occurs when favorable extraction conditions are produced, especially for a mixture of extractants with different characteristics (e.g. anionic and cationic or solvating agents). Synergistic extraction has been widely used for the separation and purification of rare-earth elements, because of its higher extraction efficiency and morepronounced separation selectivity. There are a few reports on the synergistic extraction of lanthanide ions by HQ and bis(1phenyl-3-methyl-2-pyrazolonc-4-yl) phthaldionc or 1-phenyl3-methyl-4-benzoyl-5-phrazolone.11,12 However, until now, no information on the synergistic extraction and separation of praseodymium(III) and neodymium(III) with HQ and acidic extractants has been available. While researching the extraction and separation of praseodymium(III) and neodymium(III) with HQ, we found a synergistic effect in the mixtures of HQ and P507, which are used for the extraction and separation of praseodymium(III) and neodymium(III). In this work, the extraction behaviors of praseodymium(III) from an aqueous chloride-acetate medium, using HQ, 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (P507, HL), and their mixture, are investigated. Because the separation of praseodymium(III) and neodymium(III) has been a challenging task, the mutual separation of praseodymium(III) and neodymium(III) with HQ alone and with the mixtures of HQ and P507 should be discussed. The objective of this work is to study, in detail, the effect of various experimental parameters, such as aqueous phase pH, extractant concentrations, buffer ion concentration, and ion strength, on the extraction and synergistic effects. To predict the separation possibility of praseodymium(III) and neodymium(III), the effects of pH on the extraction of neodymium(III) with HQ alone and with mixtures of HQ and P507 were studied. In addition, the stripping of praseodymium(III) with sulfuric acid (H2SO4), hydrochloric acid (HCl), or nitric acid (HNO3) was investigated, relative to its possible use in the industry.
10.1021/ie070098r CCC: $37.00 © 2007 American Chemical Society Published on Web 08/17/2007
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2. Experimental Section
Table 1. Values of the Equilibrium Constant and Distribution Coefficient of Pr3+ with P507 as an Extractant
2.1. Materials. 8-Hydroxyquinoline (HQ) and 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (P507, 99%) were used as received. Solutions of HQ and P507 were prepared by dissolving appropriate amounts into a heptane medium. Stock solutions of rare earths were prepared from their oxides via dissolution in concentrated HCl and standardized by ethylenediamine tetraacetic acid (EDTA) titration with xylenol orange as the indicator. All the other reagents were analytical grade. 2.2. Apparatus. A spectrophotometer model (Shimadzu, Model UV-365) was used to measure the absorbance. A pH meter (Model pHs-3C, calibrated daily with pH 4.01 and pH 6.86 standard buffer solutions) was used to measure the pH value in the aqueous phase. 2.3. Extraction and Analytical Procedure. Liquid-liquid extraction was performed by shaking an equal volume (5.0 mL) of aqueous and organic phases in centrifuge tubes using a mechanical shaker with a stirring speed is 60 rpm at a temperature of 303 ( 1 K. After phase separation, the concentration of trivalent rare-earth ions in the aqueous phase was determined spectrophotometrically at 655 nm, using Arsenazo(III) as an indicator at pH 2.8 in a chloroacetic acidsodium hydroxide buffer solution. The concentration of trivalent rare-earth ions in the organic phase was obtained by mass balance. The distribution coefficient (D) was taken as a ratio of the concentration of trivalent rare-earth ions in the organic phase to that in the aqueous phase. The initial trivalent rareearth ion concentration had been constant at 0.7 mM. Unless stated otherwise, the ionic strength of the aqueous phase was kept at 0.1 M via the addition of sodium chloride. The pH value was maintained using an acetate buffer solution and adjusted via the addition of HCl or NaOH. 3. Results and Discussion 3.1. Equilibrium Time. The apparent distribution coefficient (D) for the extraction of praseodymium(III) from a 0.7 mM solution at pH 5.4 by 0.04 M HQ in heptane is measured at different phase contact times. D is observed to increase with phase contact time, up to 40 min, and then stabilizes. It is concluded that the equilibration time for this system is ∼40 min. In subsequent experiments, a contact time of 60 min is adopted to ensure complete equilibration. 3.2. Extraction of Pr3+ by P507 Alone. As a rule, the solvent extraction of the trivalent rare-earth ion with P507 can be expressed by the following equation:8 K1
+ Ln3+ (a) + 3H2L2(o) 798 LnL3‚3HL(o) + 3H(a)
(1)
where “a” denotes the aqueous phase and “o” denotes the aqueous organic phase. H2L2 represents the dimeric form of P507, and Ln3+ denotes the trivalent rare-earth ion. The relationship between the distribution ratio D1 and the extraction equilibrium constant K1 can be described as follows:
log D1 ) log K1 + 3 log [H2L2](o) + 3pH
(2)
The analytical data for the extraction of the Pr3+ ion by P507 from a 0.1 M NaCl solution are given in Table 1; the value of log K1 is calculated to be -1.98. 3.3. Extraction of Praseodymium(III) by HQ Alone. Although HQ is a strong ligand for metal-ion extraction and is widely used in liquid-liquid extraction, data on the extraction or synergistic extraction of rare-earth elements are very scarce.
[P507] (M)
pHeq P507 Concentration 2.95 2.93 2.92 2.9 2.89 2.88 2.87 2.86
0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
D1
log K1
0.27 0.41 0.66 1.09 1.73 1.97 2.72 3.75
-1.84 -1.98 -2.03 -1.99 -1.96 -2.05 -2.03 -2.00 -1.98 0.003
average standard deviation pH Value 2.27 2.39 2.48 2.59 2.74 2.84 2.91
0.02 0.02 0.02 0.02 0.02 0.02 0.02
0.07 0.14 0.32 0.78 1.37 3.50 5.41
-1.94 -2.02 -1.92 -1.87 -2.08 -1.97 -1.99
Therefore, the extraction of praseodymium(III) with HQ must be investigated in detail. The Pr3+ ion in the aqueous phase can form a variety of complexes in the presence of an acetate ion. However, under the experimental conditions, it is sufficient to consider only the first complex, as defined by β
Pr3+ + Ac- T Pr(Ac-)2+
(3)
The total amount of praseodymium(III) in the aqueous phase (Prt) then is given by
Prt ) Pr3+ + Pr(Ac-)2+ ) Pr3+(1 + β[Ac-])
(4)
The value of the stability constant (β) for praseodymium(III) is taken from the literature.13 The extraction equilibrium of praseodymium(III) from a chloride-acetate solution with HQ can be expressed as Kex
+ Pr3+ aq + 3HQ(O) 798 PrQ3(O) + 3Haq
(5)
where Kex is the equilibrium constant. It is assumed that the extractant exists predominantly as a monomeric species,
Kex )
[PrQ3](O)[H+]aq3 [Pr3+]aq[HQ](O)3
(6)
The distribution coefficient (D) of the praseodymium(III) then can be written from eqs 4 and 5 as
D)
[PrQ3](O) [Pr3+]t
)
Kex[HQ]3 [H+]3(1 + β1[Ac-])
(7)
To confirm the aforementioned mechanism, the extractions of praseodymium(III) from 0.1 M NaCl with HQ alone in heptane, as a function of extractant concentration (0.02-0.10 M) and pH (at a constant HQ concentration of 0.04 M) are studied. The relevant log-log plots (Figures 1 and 2, respectively) are linear, with approximate slopes of 3.0, indicating the extraction of complexes to be PrQ3. Figure 3 gives the effect of the Ac- concentration ([Ac-]) on the extraction. The slope of the plot of log D - 3pH versus log [Ac-] (approximately -1.0) suggests that the first complex of Pr3+ with Ac- is the predominant species under the
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Figure 1. Effect of pH on the extraction of praseodymium(III) with 8-hydroxyquinoline (HQ) at concentrations of (2) 0.02 M (B) and (9) 0.04 M (aqueous phase with 0.1 M NaCl, T ) 30 °C) (C).
Figure 3. Effect of acetate ion concentration on the extraction of praseodymium(III) (9) with HQ alone (D) and (b) with the mixtures of HQ and P507 (3:7 mol/mol) (E). (Conditions: [NaCl] ) 0.1 M, T ) 30 °C, pH 5.40 ( 0.02, extractant concentration ) 0.04 M.)
Figure 2. Effect of HQ concentration on the extraction of praseodymium(III) (Conditions: [NaCl] ) 0.1 M, T ) 30 °C, [Ac-] ) 0.08 M, pH 5.40 ( 0.02.)
experimental conditions that have been used, which is in accordance with the previous assumption. Similarly, the effect of the chloride ion on the extraction is investigated, and the result demonstrates that the chloride ion has no influence on the extraction (not illustrated). According to the aforementioned results, the extraction mechanism of Pr3+ with HQ alone can be expressed as follows:
PrAc
2+
K2
Figure 4. Synergistic extraction of praseodymium(III) with different mixtures of HQ and P507. (Total concentration ) 0.02 M in heptane, [NaCl] ) 0.1 M, T ) 30 °C, pH 3.6 ( 0.1, [Ac-] ) 0.08 M.)
If the synergistic extraction of praseodymium(III) by mixtures of P507 and HQ from a chloride-acetate medium is expressed as K12
-
+ 3HQ 798 PrQ3 + Ac + 3H
+
(8)
The values of the extraction equilibrium constant calculated for praseodymium(III) under different conditions are in the range of log k2 ) -11.52 ( 0.14. Equilibrium constants are widely independent of the HQ concentration (0.03-0.1 M), pH value (5.04-6.17), and Ac- ion concentration (0.02-0.16 M). 3.4. Extraction of Praseodymium(III) by Mixtures of P507 and HQ. Figure 4 gives the extraction of praseodymium(III) by mixtures of P507 and HQ in heptane, showing not only an evident synergistic effect but also an optimum when the concentration ratio of P507 to HQ ([P507]:[HQ]) is equal to 7:3. According to Xu et al.,14 the largest synergistic enhancement factor, which is expressed as Dmax/(DP507 + DHQ), is calculated to be 5.49 at pH 3.6.
Pr3+ (a) + nH2L2(o) + mHQ(o) 798 PrL2nQmH(2n+m-3)(o) + 3H+ (a) (9) the distribution ratio D12 and the equilibrium constant K12 of the synergistic extraction reaction should be
D12 ) DT - D1 - D2 )
[PrL2nQmH(2n+m-3)](o)
) [Pr3+](t) [Pr L2nQmH(2n+m-3)](o) [Pr]3+ (a) (1 + β[Ac ])
and
(10)
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K12 )
[PrL2nQmH(2n+m-3)](o)[H+](a)3 [Pr3+](a)[H2L2](o)n[HQ](o)m
)
D12(1 + β[Ac-])[H+](a)3 [H2L2](o)n[HQ](o)m
(11)
where DT denotes the total distribution ratio of the mixture system, and the terms D1 and D2 denote the distribution ratios of P507 and HQ, respectively. Taking the logarithms of both sides of eq 12 and transforming gives
log[D12(1 + β[Ac-])] ) log K12 + 3pH + n log [H2L2](o) + m log [HQ](o) (12) To determine the extracted complex in the (P507 + HQ) system, a series of experiments are performed. As shown in Figure 5, the plots of log D12 versus pHeq at fixed concentrations of P507 and HQ give straight lines with slopes of 3.0, meaning that three H+ ions are librated in the process of cation exchange. Similarly, at fixed aqueous phase pH and concentration of another extractant, the plots are linear, with approximate slopes of 5.0 for P507 and 2.0 for HQ, respectively, indicating n ) 5 for P507 and m ) 2 for HQ in the extracted complex with praseodymium(III) (Figure 6). The effect of acetate ion on the synergistic extraction is illustrated in Figure 3, which suggests that the first complex of Pr3+ with Ac- is the predominant species under this experimental condition. Ultimately, the prediction that the chloride ion exerts no effect on the synergistic extraction is confirmed by plotting the chloride ion concentration versus the distribution coefficient D (not illustrated). According to eq 12 and the values of m and n, the values of log K12 can be calculated to be 6.01 (Table 2). Comparing the values of K1, K2, and K12, it is easy to understand that the complex of praseodymium(III) with the mixtures of P507 and HQ is more stable than that with P507 or HQ alone. Actually, the following hypothetical complex formation may occur simultaneously in synergistic extraction: β1
PrL3‚3HL + 2H2L2 + 2HQ 798 PrQ2L10H9
Figure 5. Effect of equilibrium pH on the extraction of praseodymium(III) with mixtures of HQ and P507: (9) [HQ]:[P507] ) 3:7 (F) and (b) [HQ]:[P507] ) 1:1 (G). (Conditions: [NaCl] ) 0.1 M, T ) 30 °C, [HQ] + [P507] ) 0.04 M.)
Figure 6. Effect of extractant concentration on the extraction of praseodymium(III) with mixtures of HQ and P507: (9) for HQ-Pr: pH 3.55, [P507] ) 0.02 M and (b) for P507-Pr: pH 3.55, [HQ] ) 0.02 M. (Conditions: [NaCl] ) 0.1 M, T ) 30 °C, [Ac-] ) 0.04 M.)
(13) (14)
dielectric constants of diluents, the extraction percentages increase in the following order:
where β1 and β1 are formation constants that can be expressed as
dichloromethane < chloroform < toluene < xylene < carbon tetrachloride < cyclohexane < heptane
β2
PrQ3 + 5H2L2 798 PrQ2L10H9 + HQ
log β1 ) log K12 - log K1 + log β log β2 ) log K12 - log K2 The values of β1 and β1 are calculated to be 9.70 and 17.52, respectively, which indicates that equilibrium (eq 17) contributes more to the synergistic extraction. A possible explanation is that the extracted complex of praseodymium(III) with HQ is less stable than that with P507; therefore, the subsequent reaction of praseodymium(III) with HQ is easier than the reaction of praseodymium(III) with P507.15 3.5. Effect of Dilution on the Extraction. The effects of dilution on the extraction are investigated at pH 5.40 with 0.04 M HQ alone and with the mixtures of 0.012 M HQ + 0.028 M P507 (Table 3). The results indicate that, with decreasing
Therefore, heptane is considered to be the best diluent for praseodymium(III) extraction with the given extractant mixture. 3.6. Stripping. An amount of 0.04 M (HQ + P507) organic phase loaded with praseodymium(III) (C ) 0.7 mM) is back-extracted with HCl, HNO3, and H2SO4. The concentration of praseodymium(III) in the aqueous phase is determined, and the stripping efficiency versus the concentration of HCl, HNO3, and H2SO4 is shown in Figure 7. It is found that the stripping efficiency of H2SO4 is the strongest, HNO3 is the weakest, and HCl is the moderate. The complete stripping of praseodymium(III) can be achieved in one stage at H2SO4 concentrations as high as 0.02 M. Therefore, the sulfuric acid is a strip agent of choice from the mixed (HQ + P507) system and will have potential industrial application.
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Ind. Eng. Chem. Res., Vol. 46, No. 19, 2007 Table 2. Values of Extraction Equilibrium Constants of Pr3+ with the Mixtures of HQ and P507a [HQ] (mol/L) 0.02 0.02 0.02 0.02 0.02 0.02 0.001 0.002 0.003 0.004 0.006 0.008
[P507] (mol/L)
pHeq
D12
log D12 (1 + ss[Ac])
log K12
0.004 0.006 0.008 0.01 0.012 0.014 0.02 0.02 0.02 0.02 0.02 0.02
3.87 3.85 3.82 3.83 3.83 3.84 3.21 3.31 3.4 3.46 3.57 3.64
2.41 9.69 42.6 117.2 391.9 640.1 4.38 20.9 44.2 74.1 148.7 311.3
0.86 1.46 2.10 2.54 3.07 3.28 1.11 1.79 2.12 2.34 2.64 2.97
6.14 5.92 6.03 5.95 6.08 5.93 5.98 6.06 6.03 6.00 5.95 6.02
average standard deviation a
Figure 7. Stripping of praseodymium(III) with HCl, HNO3, and H2SO4 from the loaded organic phase (0.028 M [P507] + 0.012 M [HQ] ) 0.04 M).
6.01 0.066
β ) 50, [Ac-] ) 0.04 M.
Table 3. Effect of Dilution on the Extraction Degree of Pr3+ with HQ Alone and with the Mixtures of HQ and P507a Extraction Efficiency (%) dilution
dielectric constant
for 0.04 M HQ alone
for 0.04 M extractant mixtureb
dichloromethane chloroform toluene xylene carbon tetrachloride cyclohexane heptane
9.08 4.90 2.36 2.28 2.24 2.05 1.92
1.7 4.8 5.2 10.9 14.2 39.6 54.5
14.0 14.7 16.7 17.9 18.7 46.0 67.6
a pH ) 5.40, [Ac-] ) 0.08 M. b Composition of mixture (3:7 mol/mol): 0.012 M [HQ] + 0.028 M [P507] ) 0.04 M.
Table 4. Values of pH1/2(Pr) and pH1/2(Nd) with HQ Alone (0.04 M) and Its Mixtures with P507a Value
Figure 8. Effect of equilibrium pH on the extraction degree of praseodymium(III) and neodymium(III) with HQ alone and its mixtures with P507 (3:7 mol/mol): (0) for Nd3+, [HQ] ) 0.02 M (S); (O) for Nd3+, [HQ] + [P507] ) 0.04 M (R); (9) for Pr3+, [HQ] ) 0.02 M (T); and (b) for Pr3+, [HQ] + [P507] ) 0.04 M (W). (Conditions: [NaCl] ) 0.1 M, T ) 30 °C.)
3.7. Separation of Praseodymium(III) and Neodymium(III). As is well-known, it is quite difficult to separate praseodymium(III) and neodymium(III) using a single extractant, because of their almost equal ion radii (r(Pr3+) ) 101.3 pm, r(Nd3+) ) 99.5 pm).13 Therefore, it has been a challenging task in the field of separation engineering. To explore the separation possibility of praseodymium(III) and neodymium(III), the effects of pH on the extraction of neodymium(III) with HQ alone and with the mixtures of HQ and P507 are studied under the same experimental conditions as those used for praseodymium(III) (see Figure 8). If the values of pH1/2 are used to compare the extraction ability and selectivity, it is clearly shown that the extractability for neodymium(III) is almost equal to that of praseodymium(III) with HQ as an extractant and is more efficient than that of praseodymium(III) with the mixtures of HQ and P507 (see Table 4). Moreover, from Table 5, it can be observed that, with decreasing pH values, the separation factors, which are defined as S ) DPr/DNd, increase greatly. For example, at pH 2.0, the separation coefficient SPr/Nd becomes a value of 7.26, which is large enough to provide easy separation of both ions.
a
parameter
P507
HQ
HQ + P507a
pH1/2(Pr) pH1/2(Nd) ∆pH1/2(Pr-Nd)
2.66 2.58 0.08
5.31 5.27 0.04
2.44 2.22 0.22
Composition of mixture: 0.012 M [HQ] + 0.028 M [P507] ) 0.04 M.
Table 5. Effect of pH on the Distribution Ratios and Separation Coefficient of Pr/Nd with the Mixtures of HQ and P507a Value parameter
pH 2.0
pH 2.1
pH 2.3
pH 2.5
pH 2.7
DNd DPr SPr/Nd
0.35 0.048 7.26
0.55 0.096 5.79
1.39 0.38 3.69
3.50 1.49 2.35
8.80 5.89 1.50
a Composition of mixture: 0.012 M [HQ] + 0.028 M [P507] ) 0.4 M; [Pr3+] ) [Nd3+] ) 0.7 mM.
4. Conclusions The extraction and separation of praseodymium(III) and neodymium(III) from an aqueous hydrochloric acid (HCl) medium, using 8-hydroxyquinoline (HQ), 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (P507, HL), and their mixture, have been studied. The following conclusions can be drawn: (1) The extractability for praseodymium(III) with P507 is much greater than that with HQ alone, and the values of the extraction equilibrium constant are -1.98 for P507 and -11.54 for HQ, respectively. In the HQ extraction system, it can be
Ind. Eng. Chem. Res., Vol. 46, No. 19, 2007 6325
concluded that the acetate ion (Ac-) is complexed with Pr3+ and extracted into the organic phase together with Pr3+. (2) The mixed HQ and P507 system shows a distinct synergistic effect on the praseodymium(III) extraction equilibrium constant (6.01), and the corresponding extraction equation can be deduced to be K12
PrAc2+ (a) + 5H2L2(o) + 2HQ(o) 798 PrQ2L10H9(o) + + Ac(a) + 3H(a)
(3) The effect of diluents on the extraction demonstrates that, with decreasing dielectric constants of diluents, the extraction degree increases in the following order:
dichloromethane < chloroform < toluene < xylene < carbon tetrachloride < cyclohexane < heptane Heptane can be considered to be a suitable diluent for the praseodymium(III) extraction system. (4) Lower stripping acidity is required for the mixed HQ and P507 system, which would be of practical value in the separation and purification of praseodymium(III) from rare earths. (5) The effects of pH on the extraction of neodymium(III) with HQ alone, and with the mixtures of HQ and P507, are studied under the same experimental conditions as those of praseodymium(III). The results indicate that the mixed (HQ + P507) system has better separation ability for Pr/Nd than HQ alone. Overall, the mixed HQ + P507 system shows higher extraction efficiency, as well as larger separation coefficients for Pr/Nd, and it seems to have a potential industrial application. Acknowledgment The present work has been supported by Program for Young Excellent Talents in Tongji University (No. 2006KJ059).
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ReceiVed for reView January 16, 2007 ReVised manuscript receiVed June 1, 2007 Accepted July 10, 2007 IE070098R
