J . Phys. Chem. 1989, 93, 3851-3854
3851
Application of the Competitive Preferential Solvation Theory to Facilitated Ion Transport through Binary Liquid Membranes Mariola Szpakowska ZakCad Chemii Fizycznej, Instytut Chemii i Technologii Nieorganicznej, Politechnika Gdanska, U1.Majakowskiego 1111 2, 80-952 Gdansk. Poland
and Otto B.Nagy* Laboratoire de Chimie Organique Physique (CHOP), Universitd Catholique de Louvain, Bdtiment Lavoisier, PI. Pasteur 1 , 1348-Louuain-la-Neuve, Belgium (Received: October 28, 1988)
The transport of K+ and Na+ ions through a binary liquid membrane of variable composition (dichloromethane-chlorobenzene mixtures) has been studied in the presence of dibenzo-18-crown-6 used as carrier. It was shown that transport kinetics obeys the competitive preferential solvation (COPS)theory in the whole concentration range. Detailed comparison of COPS theory and irreversible thermodynamics brought up new evidence favoring the exclusive existence of mixed solvation shells in binary solvent mixtures.
Since the first proposal of their applicability in chemical engineeringl liquid membranes have been studied very actively both from fundamental and technological point of view.2” Their importance is unquestionable in separation science, especially in cases where solute concentrations are relatively low and other techniques cannot be applied efficiently. Therefore, liquid membranes may be applied very efficiently for metal recovery in hydrometallurgy (concentration of metal ion containing solutions before electrolytic extraction),’ heavy metal elimination from polluted waters,8 metal winning from natural waters (uranium extraction from ~ e a w a t e r and ) ~ in many other fields of chemical technology. Therefore, detailed investigation of physicochemical properties and technological behavior of liquid membranes is very important in view of their selective, efficient, and low-cost application in science and technology. Liquid membrane selectivity is highly increased by using carrier molecules having very specific and selective interacting power. Accordingly, much effort has been spent in designing and synthesizing new and more selective carriers.1° Various types of liquid membranes have also been investigated in order to optimize transport efficiency. Only a relatively few studies are devoted to mixed liquid membranes, Le., membranes composed of several solvent components.” However, a detailed knowledge of physicochemical properties and behavior of mixed membranes is very important not only from the fundamental but also the technological point of view. As a matter of fact, the various properties of liquid membranes may be monitored in a continuous way when mixed liquid membranes of variable composition are applied in transport studies. This would allow easy optimization of experimental conditions and use efficient but expensive solvents in a more (1) Li, N . N . U S . Patent 3,410,794, November 12, 1968. (2) Danesi, P.R. Sep. Sci. Technol. 1984, 19, 857. (3) Bartsch, R. A.; Charewicz, W. A,; Kang, S. I. J . Membr. Sci. 1984, 17, 97. (4) Boyadzhiev, L.; Lazarova, 2 . Chem. Eng. Sci. 1987, 42, 1 1 3 1. (5) Cussler, E. L.;Evans, D. F. J . Membr. Sci. 1980, 6, 113. (6) Meindersma, G.W.Procestechniek 1986,41,48. Izatt, R.M.; Clark, G . A,; Bradshaw, J. S.; Lamb, J. D.; Christensen, J. J. Sep. Pur$ Methods 1986, IS, 21. (7) Tavlarides, L. L.; Bae, J. H.; Lee, C. K. Sep. Sci. Technol. 1987, 22,
economical way. Simultaneous use of solvents belonging to different solvent classesI2 is particularly promising since it allows optimization of the relative contributions of specific and general solvent effects. In the present paper facilitated ion transport through a binary mixed membrane will be studied. It is well established in the literatureI3-lSthat physicochemical properties of binary solutions can be successfully analyzed and interpreted in the light of the competitive preferential solvation (COPS) theory. This theory seems to be completely general and widely applicable to many physicochemical techniques such as UV and NMR spectroscopies, kinetics, fluorescence, and nuclear magnetic r e l a x a t i ~ n . l ~It- ~ ~ allows one to explain various physicochemical anomalies such as for instance negative equilibrium constantsI3 and it yields transferable solute-solvent affinity constants. According to COPS theory13 the components S and Z of a binary solvent mixture compete for solvating the solute A to the ) , extent of their electronic-geometric affinity K A ( s ) and K ~ ( ~ respectively. S and Z relax continuously between complexing and solvating states in the solvation shell. The composition of the latter depends not only on these affinity constants but also on the number of potentially available solvent molecules present in the mixture, i.e., on their actual concentrations Cs and Cz (in M units). As a consequence, the solute (concentration CA)is virtually partitioned between the solvent components CA =
XA(S)
+ XA(Z)
(1)
according to a generalized partitioning
where j = S or Z, k = S and Z, and PAti)is the generalized partitioning factor. When solvent-solvent interactions may be neglected, the solvent effects on a given physicochemical property (w)can be considered as additive:
= PA(S)WA(S) + pA(Z)WA(Z)
(3)
(12) B.Nagy, 0.; B.Nagy, J.; Bruylants, A. J . Chem. SOC.,Perkin Trans.
581. . ..
(8) Kitagawa, T.; Nishikawa, Y . ;Frankenfeld, J. W.; Li, N. N.Enuiron. Sci. Technol. 1977, 1 1 , 602. (9) Saito, K.; Uezu, K.; Hori, T.; Furusaki, Sh.; Sugo, T.; Okamoto, J. AIChE J . 1988, 34, 41 1 . (10) Ovchinnikov. Yu.A,; Ivanov, V. T.; Shkrob, A. M. Membrane-actiue Complexones; Elsevier: Amsterdam, 1974. ( 1 1) Hoffenberg, H. B.; Ward, M. Z.; Rierson, R. D.; Koros, W. J. J . Membr. Sci. 1981, 8, 91.
0022-365418912093-3851$01.50/0
2 -. 1972. -7
968. --
(13) B.Nagy, 0.; waMuanda, M.; B.Nagy, J. J . Chem. SOC.,Faraday Trans. I 1978, 74, 2210. (14) B.Nagy, 0.; Szpakowska, M. In Physical Organic Chemistry 1986; Kobayashi, M., Ed.; Studies in Organic Chemistry; Elsevier: Amsterdam, 1987;Vol. 3 1 , p 593. (15) B.Nagy, 0.; wahluanda, M.; B.Nagy, J. J . Phys. Chem. 1979.83, 1961.
0 1989 American Chemical Society
3852
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989
Szpakowska and B.Nagy TABLE I: Initial Rates of K+ and Na+ Transport through Binary Liquid Membranes"
Na+
K+ no. 1
I:,
i
2 3 4 5
6 7 8 9
M
Yzb
C ,,
0
0
0.05 0.1
0.490 0.980 1.961 2.941 3.922 4.902 5.882 7.843 8.824 9.804
0.2 0.3 0.4 0.5 0.6 0.8
10
0.9
11
1
J
X
lo6, M h-I
J
X
43.4 17.9 8.45 8.25 2.63 3.84
lo5, M
h-l
400 177.9
49.2 41.1
0.96 0.56
72.2 31.9
0.25
27.0
27.4
" S = CH2C12 (us = 0.064 M-I); Z = chlorobenzene (uz = 0.102 M-'); carrier, dibenzo-18-crown-6; T = 20 f 0.1 OC. *Volume fraction of component Z. Figure 1. Initial kinetic curves of Na+ transport through CH2CI2( S ) chlorobenzene (Z) binary membranes. The numbering of the curves corresponds to that given in Table I.
TABLE II: Transport Kinetics Parameters Obtained from Theory (JA(S)
uz, M-l
WACs) and WA(z)are the actual properties measured in pure S and pure Z solvents, respectively. When the appropriate equation of this type is developed for a given physicochemical technique its linearization allows one to characterize quantitatively the solute-solvent interactions at hand. In light of its general applicability it appears important to establish whether COPS theory is also applicable to transport kinetics which would allow a deeper understanding of the mechanism of transport phenomena in a general sense. For this purpose a simple system was chosen and analyzed in light of the COPS theory. The transport of monovalent ions (K+, Na+) has been studied in presence of a simple carrier (dibenzo18-crown-6). For practical reasons the membrane was composed of solvents heavier than water and belonging to different solvent classes: a-donor chlorobenzene and halogenated solvent CH2CI2. In this way the relative importance of specific (a-donor ability) and general (polarity, polarizability) solvent effects could be monitored easily in a continuous manner by using mixed membranes of different compositions. Starting from pure CH2C12(S) membrane, an increasing amount of chlorobenzene (Z) was added stepwise until the pure Z membrane (stripping experiment')) was reached. Transport kinetics was then measured in each case by using ion-specific electrodes (see below).
metal ion
Results and Discussion
Figure 2. Effect of membrane composition on
Since the transport was rather slow, only initial rates have been measured. Figure 1 shows that the initial increase with time of solute concentration in the acceptor aqueous phase is linear for each membrane composition. It can also be seen that the linear segments of the kinetic curves are preceded by an induction zone reached after a certain induction time the length of which increases with increasing chlorobenzene concentration (K' shows similar kinetic behavior). This may be due to molecular events at the water-membrane interfaces leading to the mutual penetration of the two phases into each other and also to the establishment of steady-state kinetic conditions. The initial rates determined from the various slopes are collected in Table I. Figure 2 shows explicitly that the transport rate is very efficiently decreased by the *-donor component (chlorobenzene). A similar curve has been obtained also for Na+ (Table I). According to COPS theory the total ion flux ( J ) through a binary liquid membrane is equal to (eq 1, 2, and 3)
with obvious notations. Neglecting the volume change on mixingI3 we can write for dilute solutions Cs = ( 1 - uzCz)/us, where uz and us are the molar volumes of solvent components Z and S,
KA(CB)/KA(CH~CI~)
K+
43.6
Na+
20.0
0.106 (0.102)' 0.1 11 (0.102)'
COPS
- JA(Z))
M h-l 43.22 (43.15)b 3759 (3730)
lo6,
'Official values. bDirectlymeasured values in pure S and Z.
c\
K+ transport through
CH2C12 (S)-chlorobenzene (Z) binary membranes (stripping profile). The theoretical curve has been obtained from data of Table I1 using eq 5.
respectively. By substituting Cs in eq 4 we obtain after some algebra
J=
This expression can easily be linearized into a Scatchard-type equation:
It should be noted that the slope of this linear relationship may be negative, positive, or zero depending on the relative magnitudes of its components. Application of eq 6 to the experimental data (Table I) will yield the corresponding affinity constant ratio
Ion Transport through Binary Liquid Membranes
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3853 SCHEME I
S
S
s S
S
“AtS)‘S -30
I
0 -20
-1 0
Figure 3. Linearization by COPS theory (eq 6) of stripping profile obtained for K+ transport through CHzCll (S)-chlorobenzene (Z) binary membranes: (JAs - J)/C, = 120.6(k13)X 10” - 2.68 (*0.33)(JA(s) - J). Correlation coefficient r = 0.9556; standard deviation u = 5.38 X
10“. K A ( ~ ) / K A ( ~ )Figure . 3 shows that, in agreement with COPS theory, eq 6 is obeyed in the whole concentration range. The results obtained by using eq 6 are collected in Table 11. It can be seen that the calculated transport rate differences (JA(s) - JA$z))are in excellent agreement with their directly measured experimental values. Furthermore, eq 6 allows also the determination of the molar volume of component Z. Noting that uz = (intercept)/(JA(s) - JA(Z))exp - (slope), we obtain uz values in full agreement with their experimental values (Table 11). These results establish clearly that COPS theory may be applied perfectly to the study of transport kinetics in binary liquid membranes. Table I1 shows also that the solute is submitted to a highly preferential solvation as reflected by the affinity constant ratios. The carrier complexed metal ion solute interacts more strongly with the *-donor membrane component. In the case of K+ the solute-chlorobenzene interaction is about 44 times greater than the solute-dichloromethane interaction. In the case of Na+ this interaction ratio amounts to 20. The difference between K+ and Na+ is certainly due to the different experimental conditions but the ion size must play also a definitive role in this connection. As a matter of fact, a differential degree of host-guest interaction between ion and carrier leads to different structures of the ion-carrier complex which in its turn may be differently solvated by the solvent components. The cavity radius of dibenzo-18-crown-6 is 1.34-1.43 A.16This suggests that the potassium ion (radius 1.38 A) fits better into this cavity than the sodium ion (radius 1.02 A).’6 Tighter solute structure allows better solvation. Therefore, it is not surprising that we have [KA(CB)/KA(CHzClz)]K+> [KA(CB)/ KA(CH2CI2)]Na+, where CB designates chlorobenzene. The greater solute-solvent interaction shown by chlorobenzene might be due to its *-electron system which can establish among others an efficient stacking interaction with the benzene rings of the carrier molecule. This stronger solute-solvent interaction may also be responsible at least partially for the slower transport rate observed in pure chlorobenzene. In the stripping experiments realized in the present work the solute A is surrounded initially by solvent molecules S. These latters are stripped off stepwise and replaced by the molecules of solvent Z when the concentration of the newly added component (C,) increases. In pure Z the solute is again surrounded only by one type of solvent molecules (Z). The situation may be described by Scheme I. This scheme is only illustrative and the number of solvating molecules has no meaning here (for discussion of solvation numbers see ref 17). COPS theory tells that if solvent-solvent interactions may be neglected in comparison to solute-solvent interactions, the two solvent components S and Z influence independently the behavior of solute A and this latter
(16) Izatt, R. M.; Bradshaw, J. S.; Nielsen, S . A,; Lamb, J. D.; Christensen, J. J. Chem. Rev. 1985, 85, 27 1 (17) Parbhoo, B.; B.Nagy, 0. J. Chem. SOC.,Faraday Trans. I 1986,82, 1789.
-
z
z
z
z
“AtZ)‘Z I
1
may be considered as partitioned between S and Z . This means also that the intermediate cases where A is surrounded by a mixed solvation shell may be considered as a weighted mixture of solutes having homogeneous solvation shells, Le., surrounded by either S or Z exclusively. But if this virtual microscopic partitioning corresponds to a true physical reality, transport kinetics must imply two parallel and simultaneous fluxes corresponding to the two partitioned solutes: A with pure solvation shell S (flux Js) and A with pure solvation shell Z (flux J z ) . Therefore, according to irreversible thermodynamics, these parallel fluxes must obey the following coupled differential equations (field free case):i8
(7) Dss and Dzz represent the diffusion coefficients of A in pure S and pure Z, respectively. Dsz and DB are cross-term diffusion coefficients obeying the Onsager reciprocity relationship: Dsz = DB. d C A ( i ) / dis~ the concentration gradient of solute across the membrane (one-dimensional (x) diffusion). The very presence of cross terms in eq 7 means that the two fluxes at hand are coupled and cannot be treated independently. In other words, the effect of S on solute diffusion is influenced by the presence of Z and vice versa. This solventsolvent interaction is in complete contradiction with COPS theory which is nevertheless valid in the full concentration range (see above). Since both irreversible thermodynamics and COPS theory are valid but lead to contradictory conclusions, it can be concluded that the transport model used (presence of two fluxes) does not correspond to any physical reality (see Appendix for further more mathematical arguments). Therefore, the microscopic partitioning proved by COPS theory in the absence of significant solvent-solvent interaction is only virtual and only mixed solvation shells exist around the solute in a binary solvent mixture.
Experimental Section Products Used. Dibenzo- 18-crown-6 (EGA Chemical Co., >99%) was used without further purification. NaCI, KC1, LiOH, and picric acid (Merck Chemical Co.) were purified by recrystallization. Demineralized water and freshly distilled chlorobenzene and dichloromethane (Janssen Chimica) were used in each experiment. Kinetic Procedure. Liquid membrane transport experiments were conducted using a thermostated (20 f 0.1 “C) vessel as illustrated in Figure 4. A layer of organic phase (111, 100 mL) made up from dichloromethane-chlorobenzene (CB) mixtures in the whole concentration range and containing dibenzo-18-crown-6 (DBl8C6) as carrier was stirred at 320 rpm by a 10-mm Teflon-coated magnetic stirrer driven by an IKA synchronous motor. The donor (I, 25 mL) and acceptor (11, 70 mL) water phases were stirred at 220 rpm by a home-made IKA motor assembly. (Since all phases are stirred, concentration polarization and convection effects can be safely neglected.) The interfaces I/III and II/III had an area of 9.51 and 25.47 cm2, respectively, and remained quiescent throughout the experiments. The initial compositions of the three phases were as follows: (a) for K+ transport ex-
~
(1 8) Katchalsky, A.; Curran, P. F. Nonequilibrium Thermodynamics in Biophysics; Harvard University Press: Cambridge, M A , 1975.
3854
Szpakowska and B.Nagy
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 A ~ A ( s=) P exp(Xlt) +
Synchronous Motor
Ion Selective Electrode
Q exp (M)
(A41
where P and Q are two constants and X1 and X2 are the two roots of the characteristic equation. Here we have X1,2
= -t/2(Dss
+ Dzz) f 1/2[(Ds- Dzzl2 + ~ D s z D z s I ' / ~ ('45)
This means that the time evolution of ACA(s) (flux Js) is biexponential: JS =
dACA(S) 7 = PAl exp(Xlt) + QX2 exp(X2t)
Since we have from eq A1
the substitution of eq A4 and A6 into eq A7 gives
Therefore, the time evolution of ACA(z)(flux J z ) is also biexponential:
r Motor
Figure 4. Vessel used in liquid membrane transport experiments.
periments; phase I, CKa = 0.5 M in water; phase 11, pure water; phase 111, cD,],O = 5 X M in CH2C12-CB mixed solvents; C 0.5 ~ M, (b) for Na+ transport experiments; phase I, C N ~ = M in water; phase M, C L i o=~ 1.5 X CP,criCacid = 1X = 1.5 X M in water; phase 111, CD,~,,~= 1 X lo4 11, CLIOH M in CH2CI2-CB mixtures. The concentration variations of alkali-metal cations were determined by means of ion-selective electrodes (EDT Co.) placed in the receiving aqueous phases during the kinetic runs. The appropriate calibration curves were established just before the experiments.
Acknowledgment. This work was realized within the Belgian-Polish Cultural and Scientific Exchange Program and was supported by a grant of the Committee of Chemical Sciences of the Polish Academy of Sciences. Appendix By writting dACA(i)/dtfor Ji and ACA(,)for aCAg)/dxin eq 7 (i = S or Z ) , we obtain the following coupled differential equations:
the solution of which can be obtained in the following way. By differentiating eq A1 with respect to time and replacing ACA(Z) by its value taken from eq A l , one obtains the following second-order differential equation which is uncoupled from the variable ACA(z):
This biexponential character of fluxes J s and Jz is in contradiction with all experimental observations and suggests strongly the existence of only one flux of solute in a binary mixed membrane. Furthermore, since only the total ion flux (J)can be measured by ion-selective electrodes, eq A1 and A2 must be added and considered as a single equation J=Js+J
Z
--
dACA T
=
-(Dss + D z s ) A c ~ ( s-) (Dzz
D s z ) A c ~ ( z(A101 )
where CA = CA(s)+ CA(z). By taking into account eq 2 (COPS theory) we obtain dACA ~ S + Dsz)KA(z)CZ - - - - (Dss + D Z S ~ A ( S ) (Dzz ACA dt KA(S)CS+ K A ( Z ) C Z (A1 1) It should be noted that this equation combines actually the principles of both irreversible thermodynamics and COPS theory. If the concentration gradient is not too high the diffusion coefficients remain constant throughout the transport e ~ p e r i m e n t . ' ~ This means that, for a given S-Z mixture, the time evolution of ACA-flux is monoexponential, in full agreement with experiment. On the other hand, eq A1 1 shows that the diffusion rate of A(S) DZS (Dzz + Dsz for A(Z)) in S-Z mixtures while is Dss experimentally it is only Dss in pure S (Dzz in pure Z ) . The discrepancy is due to the cross terms DZSand Dsz. These latter can be zero only when a single ion flux is present, Le., no actual partitioning of the solute takes place.
+
Registry No. K, 7440-09-7; Na, 7440-23-5; CH2C12,75-09-2; dibenzo-18-crown-6, 14187-32-7; chlorobenzene, 108-90-7.
The following solution can be obtained by standard methods:
(19) Bockris, J. OM.; Reddy, A. K.N . Modern Elecfrochemistry;Plenum: New York, 1973; Vol. 1 , p 298.
