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On the Mechanism of the Interfacial Reaction in Extraction of Rare Earth Metals by D2EHPA.

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Dev. Chem. Eng. Mineral Process., 11(5/6), pp. 539-555,2003.
On the Mechanism of the Interfacial
Reaction in Extraction of Rare Earth
Metals by D2EHPA
Akihiro Tomita, Tatsuo Kanki*, Noriaki Sano,
Tsuyoshi Asano and Shingo Imai
Department of Chemical Engineering, Himeji Institute of
Technology, Shosha 21 67, Himeji 671-2201, Japan
The mechanism of interfacial reaction was discussed based on the constituent
of the crystal film which forms at the interface and the practical behavior of
interfacial tension with the aid of intermolecular potential determined by ab
initio molecular orbital calculation. It was shown that there are three different
reaction zones depending on hydrogen ion and extractant concentrations. A
couple of extractant monomer(s) and/or its anion(s) first react with a
lanthanide ion to form I :2 intermediate complex. At the concentration zone
where the crystal formation occurs, the 1:2 intermediate complex reacts with
adjacent extractant monomer or its anion to form crystallized I :3 complex. At
lower extractant concentrations, the I :2 intermediate complex reacts with
extractant monomer or its anion and further with extractant dimer to form the
stable 1:6 complex which should dissolve into the organic phase. At higher
extractant concentrations, the 1:2 intermediate complex reacts with extractant
dimer to form the stable 1:6 complex dissolving into the organic phase.
*Authorfor correspondence (kanki@mech.eng. himeji-tech. ac.jp).
539
A. Tomita et al.
Introduction
Di-2(ethylhexyl) phosphoric acid (DZEHPA) is used in industry for separation
and purification of rare earth metals due to its high selectivity. The
equilibrium properties and rate processes for extraction of rare earth metals
have been extensively researched by many authors [l-51. However, the
existing kinetic models are diverse and a definitive kinetic model has not yet
been proposed because of lack of exact information about elementary reactions
at the liquid-liquid interface.
There are two key points that reflect upon the situation of the reaction at
the interface. One is the formation of crud at the interface, and the other is the
behavior of interfacial tension. Hughes et al. [6] investigated the effect of
flocculants and solid silica for preventing the crud formation in the
organic/aqueous solutions used for extraction of uranium and copper. Hughes
et al. [7] investigated the role of silica on phase separation for extraction of
copper aiming at specifying the physicochemical conditions where the crudfree extraction process could proceed. However no research is available on the
treatment of the crud formation in connection with the reaction mechanism.
Vandegrift et al. [81 investigated the concentration dependency of interfacial
tension to estimate the equilibrium interfacial concentration of extractant.
Many researchers followed their idea to estimate the interfacial concentration,
but concentrating only on the extractant.
In this paper, we dealt with the extraction of europium and of samarium by
D2EHPA and discuss the mechanism of interfacial reaction considering the
crud which should carry the information about the species of intermediate
complexes, and the interfacial tension which can be related to the interfacial
concentrations. We found that a crystal film forms at the interface of D2EHPA
in n-heptane/aqueous solutions when the rare earth metal is extracted at
specific hydrogen ion and extractant concentrations, and that the film
consisted of 1:3 (1 metal to 3 ligands) intermediate complexes. We also
measured the interfacial tension in the process of extraction at the hydrogen
ion and extractant concentrations where crystal formation does not occur, and
showed that the surface-active species are the extractant monomer, its anion,
and 1:2 intermediate metal complex. The stability of the 1:2 complex was
evaluated by ab initio molecular orbital calculation. The mechanism of
interfacial reaction was discussed on the basis of the experimental insights
above, and a new kinetic model for extraction of rare earth metal by DZEHPA
was proposed.
540
Extraction of Rare Earth Metals by D2EHPA
Experimental Details
(i) Reagents and solutions
Organic solutions were prepared by dissolving the desired amount of DZEHPA
(Daihachi Chemical Industry Co., Ltd., Japan) in n-heptane without further
purification. The concentrations of D2EHPA monomer (HR; R = C16H34P04)
were adjusted in the range of
to 0.5 kmol/m3. Aqueous solutions were
prepared by dissolving europium chloride and samarium chloride into distilled
water. Each lanthanide concentration was adjusted at 10” to 2 x los2kmol/m3.
Ionic strength of the aqueous solution was adjusted at 1.O km01/m3 with NaCl.
Concentration of hydrogen ion was adjusted in the range of
to 3.2 x lo-*
kmol/m3 with HCl. Each chemical except D2EHPA was of guaranteed grade.
(ii) Observation of crystal f i l m formation
15ml aqueous solution was contacted calmly with the same amount of organic
solution in a beaker. The solid film starts to form at the interface if the
extractant concentration and pH are adequately adjusted. The film is white in
colour and can be easily distinguished by eye. The formation process of the
crystal film was observed every ten minutes, and the presence of the film was
confirmed an hour later after contacting two phases. The concentration zones
where the crystal film forms were determined by changing hydrogen ion and
extractant concentrations. The temperature was kept at 2OOC.
The crystal films were collected by filtrating the organic solution, after
removing the aqueous solution by a syringe, after 24 hours. The films
collected on the filter were cleaned with distilled water, and then by nheptane. Thereafter, the films were dried at room temperature for 24 hours.
The films were observed by field emission scanning electron microscope (FESEM). The atomic constituents of the solid films were quantitatively analysed.
In analysis, the lanthanide, phosphorous, and carbon atoms were selected for
target elements. The contents of europium, samarium and phosphorus were
measured by inductively coupled plasma emission spectroscopy (ICP), and
that of carbon was measured by infrared absorption after combustion. The
film was also analysed by electron probe micro analysis (EPMA).
(iii) Measurements of the interfacial tension
The interfacial tension was measured by the Wilhelmy plate method using a
platinum plate (Kyowa Interface Science) of 24 mm width, lOmm height with
thickness 0.15 mm. Up and down motion of the plate was controlled digitally
54 I
A . Tomita et al.
by a microcomputer, with 17 mm being scanned by one step in 3 seconds. The
weight was detected every step by a microbalance (AELZOO; Shimadzu) and
the maximum value was recorded by the computer for the interfacial tension.
(iv) Measurements of extraction rate
The rate of extraction of europium was measured using the funnel type
cylindrical extraction cell with an inner diameter of 30 mm having a capillary
tube attached at the bottom. The volume of organic phase and that of aqueous
phase were set at the same volume of 20ml. The organic phase was contacted
very calmly with the aqueous phase. The organic phase was sampled at
appropriate time intervals; the water phase was removed very carefully by
observing the water phase falling through the capillary. The metal in the
sampled organic phase was inversely extracted into the 1N HN03 aqueous
water. The concentration was measured by UV-visible spectrophotometer
(Shimadzu UV-16OOPC).
Results and Discussion
(i) Concentration zones where the crystalfilm forms
Figure 1 shows the concentration zones in the [(HR)2]-[H’] plane where the
solid film was observed to form in the europium extraction solution systems at
[Eu”] = 2 x 10” kmol/m’ and at 2 x lov2kmol/m3. Figure 2 shows the
concentration zones where the film forms in samarium extraction solution
systems at [Sm3’] = 2 x lo-’ kmoYm’ and at 2 x
km01/m3. In the case of
km0Vm3, for
the europium extraction solution system at [Eu3’] = 2 x
instance, the film forms when the extractant concentration [(HR)2] is in the
range of 5 x 10” to 5 x lo‘* kmol/m3 and the hydrogen ion concentration [H’]
is below
kmoVm3. Solidification does not occur at concentrations outside
this zone. However, it is found that micro emulsions are formed near the
interface in the organic phase at higher concentrations outside that zone. The
concentration zones are seen to be almost the same, independent of the species
of lanthanide element.
(ii) Constituent of the crystalfilm
According to the FE-SEMphotograph of the crystal film, the solid film is seen
to be composed of needle-like crystals [9]. The atomic constituents of the
solid films determined by ICP and EPMA are shown in Table 1. The table
clearly shows that the respective solid films are composed of 3 phosphorus
542
Extraction of Rare Earth Metals by D2EHPA
-----
o
00
00 l e e
em!
00
oo,‘ee
e$ 00 o
00
+10” lo4 10.’ 10”
lo-’ 1 0 ‘ ~
lo-’ 10’
[(FR)2][kmol/m3]
b) [Eu’+]=2~10-~
kmol/m’
a) [Eu3+]=2xlO-’kmol/m’
Figure 1. Concentration zone where crystal film forms in europium
extraction solution system.
00
00
op/cp
00
0
+I
10’’
10‘~
10” lo4 I O - ~10.’
lo-’ 10’
[kmol/m3]
a) [Sm”] =2x10-’kmol/m’
10.’
10.~
10.’
10” 10’’ 10.’ 10’
[(Tiii)2~[ ~ m o l / m ~ l
b) [Sm3+]=2xl0” kmol/m’
Figure 2. Concentration zone where crystal film forms in samarium
extraction solution system.
atoms and 48 carbon atoms, and a lanthanide element in the unit of monomer.
Since DZEHPA molecule is composed of one phosphorus, 16 carbon, and 4
oxygen atoms, the solid film can be identified to be the polymer of 1:3
intermediate complexes, namely of one lanthanide element to three DZEHPA
ligands.
(iii) Behavior of the interfacial tension
Figures 3 and 4 show, respectively, the interfacial tensions of europium and of
samarium extraction solution systems measured at lower DZEHPA
concentrations where crystal film formation does not occur. These figures
indicate that the interfacial tension is greater when the concentration of
metallic ion is higher and when the concentration of hydrogen ion is higher. It
543
A. Tomita et al.
is noted that the interfacial tension is almost independent of species of the rare
earth element. The lines in Figures 3 and 4 indicate the interfacial tensions
predicted from the Gibbs-Langmuir equation derived by assuming that the 1:2
intermediate complex, in addition to the D2EHPA monomer and its anion,
should be adsorbed at the interface [see Appendix; and the physicochemical
constants are listed in Table 21. If this is the case, the interfacial tension must
be included in the term of the ratio of lanthanide ion concentration to square
of hydrogen ion concentration [Ln]/[H]’ [ 101. For instance, the interfacial
tensions when [Ln] = 5 x loq3kmol/m3 and [HI = 10-2 kmol/m3 ([Ln]/[H]’ =
50) and those when [Ln] = 5 x
kmol/m3
km01/m3 and [HI = 3.16 x
([Ln]/[HI2 = 50) should lie almost on a single line. The corresponding data are
concentrated on a single line and are well correlated with the Gibbs-Langmuir
equation. This supports the idea that the 1:2 intermediate complexes should be
surface active and be adsorbed at the interface.
Table 1. Atomic constituents of crystal films, atomic ratios determined by ICP.
Crystal film
Eu-containedfilm
Sm-contained film
Ln
P
C
1
3.26
48.28**
1*
2.88*
-
1
3.3
48.89**
** By infrared absorption.
Table 2. Physicochemical constants.
&m
[m3/kmol]
rHR* [kmol/m’]
2.1 3x10-’
K, [kmoVm3]
KPd [m3/kmol]
rR-* [kmol/m’]
rEuRZ*
[kmol/m2]
2 . 1 3 1~0-’
rSmRZ*
[kmol/rn’]
1 . 91~Om’
1.9x10-’
K1 [m-‘I
Eu extraction system
Sm extraction system
7.0~
10’
7.1~10’
Alternatively, if we assume that the 1:l intermediate complex should be
adsorbed at the interface, we can find from the Gibbs-Langmuir equation that
the interfacial tension must be included in the term of the concentration ratio
544
Extraction of Rare Earth Metals by D2EHPA
50
40
30
2
-E
2.
20
10
0
1
~~
Figure 3. Relation between interfacial tension and dimer extractant
concentration, europium extraction solution system.
40
30
20
5x10"
--
lo4
5 ~ 1 3.16110-~
0 ~
10
10"
lo-*
--
-
Figure 4. Relation between interfacial tension and dimer extractant
concentration, samarium extraction solution system.
[Ln]/[H]. But the interfacial tensions when [Ln] = 5 x
kmol/m3 and [HI =
lo-*kmol/m3([Ln]/[H] = 0.5) and those when [Ln] = 5 x
kmol/m3 and [HI
=
km01/m3 ([Ln]/[H] = 0.5) lie on distinctly separate lines. Therefore, the
1:l intermediate complex can be excluded as a candidate of equilibrium
surface-active species.
545
A . Tomita et al.
(iv) 1:2 intermediate complex as equilibrium surface-active species
In order to evaluate the stability of the 1:2 intermediate complex, we
calculated the intermolecular potentials between D2EHPA ligand and rare
earth element and between 1:l complex and the ligand using Gaussian 98 for
ab initio molecular orbital calculation. We selected the Hartree-Fock
approximation method and STO-3G and LANLZDZ for the basis sets. In
calculation, yttrium was selected for the rare earth element because the basis
sets for europium and samarium are not available. We first executed the
geometry optimization and calculated the structure energies of D2EHPA
monomer, its anion, n-heptane, and of water molecules and then calculated the
intermolecular potentials between two respective molecules at arbitrary
separation distances. The structures of the 1:1 and 1:2 intermediate complexes
were determined so that the intermolecular potentials might take the lowest
values. To simplify the calculation, each molecule is assumed to be in a nonpolarized ideal solution.
Figure 5 illustrates the intermolecular potential curve between two
D2EHPA molecules, that between DZEHPA and water molecules, that
between D2EHPA and n-heptane molecules, and that between two water
molecules. The bonding energies of these pairs of molecules and the
respective bonding distances are given in Table 3. From these calculations, we
find that a pair of D2EHPA molecules can exist stably as a dimer in nonpolarized solvent. Also, a DZEHPA molecule can bond with a water molecule
more strongly than water molecule does with water molecule. According to the
equilibrium experiment for partition, the reagent DZEHPA is known to exist as
a dimer in the organic phase [11, 121. From measurements of interfacial
tension, DZEHPA is known to exist as a monomer or its anion at the interface
[lo, 121. Our molecular orbital calculations are consistent with these
experimental results.
Table 3. Bonding energies and intermolecular distances between relative
soecies. basis set: STO-3G.
Distance
Bonding energy
Species
[angstrom]
[kJ/mol]
D2EHPA dimer
1.45
-154
(HR-HR)
HzO - H20
1.75
-24.7
DZEHPA - HzO
546
1.7
-73.9
Extraction of Rare Earth Metals by D2EHPA
s 0.20
5
5 0.10
\
c,
rb
.
CI
a
0
C
g#
0.0
2
I
3
0
s0!-0.10
E
0
*
-0.20
0
2
4
6
Distance [A]
8
101
Figure 5. Intermolecular potentials, basis set: STO-3G.
Figure 6. Intermolecular potential depending on the distance between rare
earth metal (yttrium) ion.
The intermolecular potential between ion of rare earth element and
D2EHPA anion is shown in Figure 6. This figure shows that the potential has a
minimum value at the distance 1.86 angstroms. The minimum potentials, the
bonding energies of 1:l intermediate complex, and of 1:2 intermediate
complex are given in Table 4 where the bonding energy of 1:2 intermediate
complex is lower than that of 1:l intermediate complex. Therefore, the 1:2
intermediate complex is much more stable than 1:1 intermediate complex. This
is consistent with the discussion above for the stability of intermediate
547
A. Tomita et al,
complexes based on the behaviour of interfacial tension. For reference, the
optimised structures of D2EHPA dimer and 1:2 intermediate complex are
shown in Figure 7.
Table 4. Bonding energies of intermediate complexes, basis set: LanLZDZ.
Species
Bonding couple
Bonding energy [kJ/mol]
~
1:1 complex (MR~')
M3+ - R
-1290
1:2 complex ( M R ~ + )
M R ~ +- R
-1390
(v) Changes in concentration of extracted metal with time
Figure 8 shows changes in concentration of europium extracted into the
organic bulk phase (except film or micro emulsion) with time. The curves are
correlated with the equation: c = c w [l-exp)-k(A/V)t]: k is the m a s s transfer
rate; c W the asymptotic concentration at ; A the interfacial area; and V is the
volume of organic phase. At low extractant concentrations, extraction occurs
only slightly (k = 3.2 x lo-' ds).
At the extractant concentration zone where
the solid film forms, extraction occurs (k = 1.3 x lom5ds).
At high extractant
concentrations, extraction occurs but the rate is smaller when compared with
the rate where the solid film forms (k = 7.3 x
ds).
Most of the europium
elements are taken into the solid film In this zone, micro emulsions are formed
and some lanthanide leaving from the aqueous phase are taken with them. We
consider that the formation of the micro emulsion prevents formation of the
1:6 stable complexes taken into organic phase.
(vi) Scheme of interfacial reactions
Based on the experimental insights above, assisted with ab initio molecular
orbital calculations, we here propose a new mechanism for interfacial
reactions including formation of crystal films, with the physical scheme as
shown in Figure 9. A pair of monomer extractant(s) and/or its anion(s) firstly
react with lanthanide ion to form surface-active 1:2 intermediate complex.
There are three pathways to be considered for the reaction scheme depending
on the concentration zone. Case (a) where crystal formation occurs, the 1:2
intermediate complex then reacts with neighbouring extractant monomer or its
anion to form 1:3 intermediate complex. The 1:3 intermediate complexes exist
at relatively high density and are rapidly agglomerated together to form
clusters, and grow into crystal films. For Case (b) in the concentration zone
548
Extraction of Rare Earth Metals by D2EHPA
1 a) D2EffPAdimer.
b) 1:2 complex
Figure 7. Optimized structures of D2EHPA dimer and 1:2 complex.
0.60
‘ ~ o .~. ,. . . . . . . . . . . . . . . . . . . . .
1
[(HR)J =1.7x1Oskmol/m3
1
OSo
0.40
1
[(HR):] =2.5xIO5 kmol/m3
A
[(HR)J =2.5x10’ km0Vm3
0.30
0.20
0.10
0.0
0
20
40
60
80
100
120
140
Time [min]
Figure 8. Changes in time passage of concentration of extracted europium
in organic phase at various extractant concentrations, [Eu]= 5 . 0 ~ 0-3
1
kmol/m3, pH=4.
where, crystal formation does not occur, when the extractant concentration is
lower, the 1:3 intermediate complex reacts before solidification with surface
active extractant or its anion and with dimer extractant in the organic phase to
form 1:6 stable complex. The stable complexes dissolve rapidly into the
organic phase. In Case (c) when extractant concentration is higher, some of
the 1:2 intermediate complex is attacked by dimer extractants in the organic
phase to form the stable complex that should dissolve into the organic phase.
549
A. Tomita et al.
k !hterface
A H
\
K R
+
--+RI Rn t+RHo r R
H
+
KK
t
Ln3+
/
'+'
+.
H+or mne
(SOZfid)
2Ht sHtor none
Ln3+
a) At the concentration zone where the crystal formation occurs.
Ln3+
\
-
w' +2H+aHt
RRtRorK
+
2H+*Ht (x ncme
Htor none
b) At lower extractant concentrations.
I
+ kHz0
c) At higher extractant concentrations.
Figure 9. Assumed physical scheme of interfacial reactions, R=C16H3Q04.
However, most of the complex is taken with surface-active extractant dimers
to form micro emulsions.
Conclusions
We have discussed the mechanism of interfacial reaction in rare earth metal
extraction solution systems on the basis of the constituent of the crystal film
that forms at the interface, and also the experimental effect of the interfacial
tension. The results are summarized below. In the process of extraction of rare
earth metal, the surface active 1:2 intermediate complex should be formed
550
Extraction of Rare Earth Metals by D2EHPA
when europium or samarium is extracted from aqueous to organic phases, and
be adsorbed at the liquidliquid interface, as well as DZEHPA monomer and its
anion.
At specific hydrogen ion and extractant concentrations, the crystal film
forms at the interface. The crystal film is composed of 1:3 intermediate metal
complexes. At higher extractant concentrations, micro emulsions are formed
near the interface in the organic phase.
There are three reaction schemes depending on the extractant concentration
and pH. Case (a) where the crystal formation occurs, the 1:2 intermediate
complex reacts with DZEHPA monomer or with its anion to form 1:3
intermediate metal complex. Case (b) when the extractant concentration is
lower, the 1:2 intermediate complex reacts with D2EHPA monomer or its
anion and with DZEHPA dimer to form stable 1:6 metal complex. Case (c)
when the extractant concentration is higher, some 1:2 intermediate complexes
are attacked by DZEHPA dimers in the organic phase to form stable 1:6 metal
complex, but most of them are taken into micro emulsions.
Acknowledgments
The authors are grateful to M. Higashira, T. Uematsu and Y.Kishida, students
at Himeji Institute of Technology, for their assistance in the extraction
experiments. One of the authors (A.T.) also gratefully acknowledges the
financial support of a Grant-in-Aid of The Japan Science Society.
Nomenclature
DZEHPA, monomer extractant
Proton dissociation constant
Adsorption constant
Dimerization constant
Equilibrium constant
Lanthanide element
M Metal element
rig Saturated interfacial excess of species I
Concentration of metal in organic phase
C
Ca Asymptotic concentration
Mass transfer rate
k
V Volume of organic phase
A Interfacial area
HR
Ka
Kad
Kdm
KI
Ln
551
A . Tomita et al.
Subscripts
species (HR,R‘,EuR2, SmR2)
i
ad adsorbing species
References
(11 Geist. A., Nitsch, W. and Kim, J-11. 1999. On the kinetics of rare-earth extraction into
DZEHPA. Chem. Eng. Sci., 54,1903-1907.
[2] Hirai. T.,Onoe, N. and Komasawa, 1. 1993. Separation of europium from samarium and
gadolinium by combination of photochemical reduction and solvent extraction. J. Chem.
Eng. Japan, 26,64-67.
[3] Kondo, K., Momota, K. and Nakashio, F. 1990. Equilibrium and kinetics of solvent
extraction of europium with didodecylmonothio-phosphoricacid. J. Chem. Eng. Jupun, 23,
30-35.
[4] Mori, Y., Ohya, H.;
0110,
H. and Eguchi, W. 1988. Extraction Equilibrium of Ce(III),
Pr(lI1) and Nd(II1) with Acidic Organophosphorus Extractants. J. Chem. Eng. Jupan, 21,
86-91.
[5] Danesi, P.R. and Vandegrift, G.F. 1981. Kinetics and Mechanism of the Interfacial Mass
Transfer of Eu” and Am” in the System Bis(2-ethylhexyl) Phosphate-n-Dodecane-NaCIHC1-Water. J. Phys. Chem., 85,3646-3651
[6] Hughes, K.C. and Forsyth, M.T. 1996. Phase Disengagement Problems in Solvent
Extraction. Proc. ISEC ‘96, pp.751-756, The University of Melbourne, Melbourne,
Australia
[7] Hughes, C.A., Evans, H.A. and Warren, L.J. 1996. Investigation of the Role of Silica in the
Formation of Cruds in a Hydroxyoxime/Sufuric Acid Solvent Extraction System. Proc,
ISEC ‘96, pp1277-1282, The University of Melbourne, Melbourne, Australia
[8] Vandegrift, G. F. and Horwitz, E.P. 1980. Interfacial Activity of Liquid-liquid Extraction
Reagents-1. J. Inorg. Chem, 42, 119-125
(91 Tomita, A., Kanki, T.; Asano, T. and Sano, N. 2000. Formation of Crystal Film at Interface
in Process of Extraction of Rare Earth Metals by D2EHPA. J Chern. Eng. Jupun, 33, 661664
[lo] Kim, H.,Kanki, T. and Asano, T. 1996. Behaviors of Interfacial Tension and Reaction
Mechanism of Surface Active Species in Metal Extraction System by D2EHPA. Kugaku
Koguku Ronbunshu, 22,837-845
[ I l l Komazawa, I., Otaka, T. and Higaki, Y. 1981. Equilibrium Studies of the Extraction of
Divalent Metals from Nitrate Media with Di-(Zethylhexyl) Phosphoric Acid. J.Inot-g.
NucLChem., 43, 3351-3356
552
Extraction of Rare Earth Metals by D2EHPA
[12] Miyake, Y., Matsuyama. H., Nishida, M.; Nakai, M.; Nagase, N. and Tcramoto, M. 1990.
Kinetics and Mechanism of Metal Extraction with Acidic Organophosphorus Extractants
(1): Extraction Rate Limited by Diffusion Process. Hydrometullurgy,24, 19-35
Appendix
The adsorption process including dimerization and dissociation processes can
be expressed in the following equilibrium equations:
-
(HR), A 2%
HRod
(A-1)
H’ + R i
04-31
where Kd,,,is the dimerization constant; Kd is the adsorption equilibrium
constant; and K, is proton dissociation constant. The “over bar” represents the
species in the organic phase. Assuming that lanthanide ions react with
adsorbing extractant(s) and/or its anion(s) to form 1:2 surface-active complex,
the equilibrium equations can be expressed as follows:
Ln3++ 2HRd
Ln3++ 2 R i
Ln$.& + 2H’
(A-4)
(A-6)
where Ki, (i = 1 to 3) are the equilibrium constants, which can be related as
K, = KrKp = K&;. According to the Gibbs-Duhem equation, the interfacial
tension can be related to the interfacial excess of relative species as:
When changes in [Ln]and [HI are very small, then from Equations (A-1)-(A6):
553
A. Tomita et al.
(A-9)
(A- 10)
Equation (A-7) can be then written as:
The interfacial excess concentrations of relative chemical species are
expressed as:
where c’ , Oi (I = HR, R and LnR2 ) and 0, indicate the saturated interfacial
excess concentration of species i, the adsorption site of species I, and the
vacant site, respectively. The relation between 0, and 4 is expressed as:
e,=1-eHR-eR--e,,
(A-15)
From Equations (A- 12)-(A- 15), we can get 6, as:
e,
=
- (1 +a)+ & i q T s
(A- 16)
2ax2
where x , a and c are defined by:
(A-17)
Substituting Equations (A- 12)-(A-17) into (A-1 l),and integrating the resultant
equation, we get the following equation for the interfacial tension:
554
Extraction of Rare Earth Metals by D2EHPA
(A-18)
where yo is the interfacial tension for the n-heptanelwater system. X,A and B
are defined as:
555
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