Langmuir 1997, 13, 1451-1456
1451
Ion Binding and the Apparent Selectivity Coefficient for Ion Flotation Gregory G. Warr School of Chemistry, University of Sydney, New South Wales 2006, Australia Received June 25, 1996. In Final Form: December 12, 1996X A microscopic site-binding ion-exchange model is developed for the binding of counterions to surfactantcoated interfaces. This model is used to describe several features of effective or thermodynamic selectivity coefficients for ion binding at air/solution interfaces as determined by surface tension or ion flotation, which depend on the Gibbs surface excess. The dependence of selectivity on electrolyte concentration is derived, and theoretical predictions are compared with experiment. The model also permits the determination of specific binding constants for individual ions from experimental data. The model is used to explain differences between selectivity coefficients at micelle surfaces and air/solution interfaces using various techniques.
Introduction We have recently demonstrated a rapid, efficient, and robust method for determining the competitive binding of counterions to surfactant films adsorbed at the air/solution interface.1-4 In this approach, known as ion flotation, gas is bubbled through a surfactant solution in a flotation column, forming a foam at the top. The solution is sampled during a flotation run, and the concentrations of competing ions remaining in solution are determined. Competitive binding of two ions A- and B- is described by an ion-exchange equilibrium of the type
A-(ads) + B-(aq) h A-(aq) + B-(ads) The equilibrium constant for this type of exchange is given by
KAB- ) -
ΓB-[A-] ΓA-[B-]
(1)
where Γ denotes surface excess. In a flotation experiment, equilibration at the bubble surface is rapid for most situations5 and counterions are stoichiometrically removed from the solution by surfactant adsorbed at the air/solution interface. In this approach to solution flotation, the need to assay the foam is avoided by applying a mass balance to the solution phase. When a bubble (or an element of the interface) passes through the flotation column, an element of area dA is exposed to the solution. Once equilibrium is established, the amount of solute 1 removed from the bulk and transported to the interface is Γ1 dA. The amount removed is equal to V dc1, where V is the volume of solution and dc1 the change in concentration.1,6 This leads to a simple relationship between concentrations of two competing ions in a flotation column during a flotation experiment.1
ln[B-] KAB- ln[A-] + C -
(2)
where C is a constant of integration, which depends on the initial ion concentrations. X Abstract published in Advance ACS Abstracts, February 15, 1997.
(1) Morgan, J. D.; Napper, D. H.; Warr, G. G.; Nicol, S. K. Langmuir 1994, 10, 797. (2) Thalody, B.; Warr, G. G. J. Colloid Interface Sci. 1995, 175, 297. (3) Morgan, J. D.; Napper, D. H.; Warr, G. G. J. Phys. Chem. 1995, 99, 9458.
S0743-7463(96)00634-8 CCC: $14.00
This approach involves the same experimental quantity as surface tension measurements, the (Gibbs) surface excess, Γ. Although individual surface excesses are not obtained directly in ion flotation, they can often be calculated without difficulty. The important point is that both of these techniques yield quantities which are not sensitive purely to specific binding. Ion flotation achieves a macroscopic separation between bulk solution and a foam, which contains surfactant (+counterion)-coated interfaces as well as entrained solution. It is thus analogous to the situation encountered in micellar ultrafiltration experiments, where a micellecontaining solution is in contact with a solution containing monomer surfactant plus electrolyte but no micelles.7,8 Similarly in an osmotic stress experiment, equilibrium is established between a lamellar or other phase and an external solution which may also contain electrolyte and is again comparable with the ion flotation experiment.4,9 In contrast, counterion binding is often studied using a local or microscopic probe technique. This may involve a micelle or interfacially-solubilized indicator which senses the local H+ concentration through its hydrolysis equilibrium,10,11 any of a suite of fluorescence or absorption probe techniques,12 or the use of reactive solubilizates.13 With such techniques a local measure of ion binding and selectivity is obtained, but the question remains as to whether different local techniques probe the same neighborhood. It is axiomatic that specific binding of ions to interfaces is a local phenomenon rather than a long-range one. Ions in the diffuse layer near a charged interface are not expected to be selectively taken up, except by differences in their valence. Thus experiments which measure the entire surface excess should be less sensitive to ion (4) Patrick, H. N.; Warr, G. G. J. Phys. Chem. 1996, 100, 16268. (5) Morgan, J. D.; Napper, D. H.; Warr, G. G.; Nicol, S. K. Langmuir 1992, 8, 2124-9. (6) Galvin, K. P.; Nicol, S. K.; Waters, A. G. Colloids Surf. 1992, 64, 21. (7) Lissi, E. A.; Abuin, E. B.; Sepu´lveda, L.; Quina, F. H. J. Phys. Chem. 1984, 88, 81. (8) Warr, G. G.; Grieser, F.; Healy, T. W. J. Phys. Chem. 1983, 87, 1220-3. (9) Parsegian, V. A.; Rand, R. P.; Fuller, N. L.; Rau, D. C. Methods Enzymol. 1986, 127, 400. (10) Hall, R.; Hayes, D.; Grieser, F.; Thistlethwaite, P. J. Colloids Surf. 1991, 56, 339. (11) Perera, J. M.; Stevens, G. W.; Grieser, F. Colloids Surf. 1995, 95, 185. (12) Lissi, E.; Abuin, E.; Valenzuela, E.; Chaimovich, H.; Araujo, P.; Aleixo, R. M. V.; Cuccovia, I. M. J. Colloid Interface Sci. 1985, 103, 139. (13) Loughlin, J. A.; Romsted, L. S. Colloids Surf. 1990, 48, 123
© 1997 American Chemical Society
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Warr
specificity than local ones, but at least for these experiments the definitions are unambiguous. The Gibbs surface excess ought not depend on how you measure it. The purpose of this paper is to investigate the relationship between such experimentally-determined surface excesses and the microscopic binding of counterions to a surface, in this case an adsorbed surfactant layer. A microscopic ion-binding model is developed, and its predictions are tested experimentally. The objectives are to elucidate the relationship between the measured ionexchange selectivity coefficient and the microscopic binding coefficients, to see what experimental factors affect the measured value, and to determine in what circumstances the two can be related unambiguously.
A simple description of counterion binding is the formation of a 1:1 association or complex between the surfactant S+ and the counterion, A- or B-. The binding of ions may be described by an equilibrium of the type
B-(aq) + S+(aq) h SB(surface) The surfactant in this model simply provides a generic “surface site” for adsorption of the counterion. The surface site may be charged or uncharged for the purpose of defining the adsorption equilibria. The 1:1 stoichiometry is the important feature, as is discussed below. In what follows the effect of interactions between adsorbed counterions is neglected, even though electrostatic interactions will be significant. This is justified on the grounds that specific effects due to the identity of the adsorbed ion, A or B, are negligible. Despite one or two claims to the contrary, ion-ion interactions do not play a large role in determining ion selectivity.5 Bloch14 used this type of description of counterion association to examine monovalent and divalent ion association at spread (insoluble) monolayers, but it is equally valid for adsorbed (soluble) films or, indeed, for micelles.15 This is also essentially the same approach as is used in the charge-regulation description of acidic or basic charged surface groups.16 In that case the association involves the formation of a covalent bond in a hydrolysis reaction, but this need not be the case for the binding of other ions. The equilibrium constants for binding according to this scheme, and neglecting activity coefficients, are
ΓS+[A ]0 -
KA )
ΓSA
ΓSB ΓS+[B-]0
(3)
where ΓSX is the surface excess of complex (X ) A or B) and ΓS+ is the surface excess of uncomplexed surfactant. The subscript 0 denotes the concentration adjacent to the charged surface. This can be related to the bulk concentration through the PoissonBoltzmann equation for either ion
[A-]0 ) [A-]∞eeψ0/kT
KB )
eψ0/kT
ΓS+[A ]∞e -
ΓSB ΓS+[B-]∞eeψ0/kT
An alternative formulation of the problem expresses the equilibria directly in terms of bulk concentrations. For either ion we then have
ΓSA
K′A ) KAeeψ0/kT
ΓS+[A-]∞
The competitive binding of B over A at the interface may now be expressed in terms of the specific binding equilibria as
KBA )
A-(aq) + S+(aq) h SA(surface)
ΓSA
KA )
K′A )
Theory
KA )
the ion size model,17 the present model does not seek to be so specific. Here differences between the ions are described by the binding constant, and no attempt is made to identify them with any particular microscopic mechanism. The ion-binding equilibria may be written in terms of bulk concentrations as
KB K′B ΓSB[A-]∞ ) ) KA K′A ΓSA[B-]∞
(4)
We refer to this quantity as the binding selectivity coefficient, as it describes the selectivity among those ions actually bound to the surface groups. The electrostatic part of the binding cancels in the exchange process. In a foam fractionation or ion flotation experiment, or in surface tension studies of counterion binding, the equilibrium between dissolved A and B and the total (Gibbs) surface excess is determined experimentally.18-20 This includes both specificallyadsorbed ions in the form of an SX (or some other stoichiometry) “complex” and electrostatically-bound X-, and is denoted by ΓX(X ) A or B)
KBA(app) )
ΓB-[A-]∞ ΓA-[B-]∞
(5)
We refer to this as the apparent selectivity coefficient. The relationship between the two quantities must be clarified in order that a meaningful interpretation of competitive counterion binding take place. Previously we have considered the general thermodynamic properties of ion exchange at the surfactant interface.3 This paper is directed at showing what is needed to use this quantity to obtain information about specific interactions. Case I: No Added Electrolyte. In the absence of added electrolyte, the Gibbs surface is electrically neutral and satisfies the charge balance.
ΓS+(tot) ) ΓA- + ΓB-
(6)
The total surface excess of an ion, ΓX-, includes both specifically adsorbed ions in the form of SX and electrostatically bound X-. This may be written explicitly using the Poisson-Boltzmann expression for the electrostatic component of the binding as follows.
∫ ([A ] ∞
where ψ0 is the surface potential of the film, e the electron charge, k the Boltzmann constant, and T the absolute temperature. The subscript ∞ denotes bulk concentration, notionally at infinite distance from the interface. Note that all ions are regarded as sensing the same surface potential. Some models have previously been based on differences in ion size or hydration, suggesting that ions may be regarded as point charges residing at different distances from the plane of surface charge and hence sensing a different local potential. Quite apart from some difficulties with
[A-] is the concentration of ion A, and ψ(x) is the electrostatic potential at a distance x from the interface. Note that the integral term is affected only by the valence of the counterion. For
(14) Bloch, J. M.; Yun, W. Phys. Rev. A. 1979, 12, 443. (15) Hartland, G. V.; Grieser, F.; White, L. R. J. Chem. Soc., Faraday Trans. 1 1987, 83, 591. (16) Healy, T. W.; Chan, D. Y. C.; White, L. R. Pure Appl. Chem. 1980, 52, 1207.
(17) Morgan, J. D. P. Ph.D. Thesis, University of Sydney, 1994. (18) Okuda, H.; Ikeda, S. J. Colloid Interface Sci. 1989, 131, 333. (19) Okuda, H.; Ozeki, S.; Ikeda, S. J. Colloid Interface Sci. 1987, 115, 155. (20) Okuda, H.; Ikeda, S. J. Phys. Chem. 1985, 89, 1140.
ΓA- ) ΓSA +
) ΓSA + [A-]∞
-
x
0
∫ (e ∞
0
- [A-]∞) dx
eψ(x)/kT
- 1) dx
(7)
Ion Flotation
Langmuir, Vol. 13, No. 6, 1997 1453
competing monovalent ions then this is a constant, and the total surface excess of ion A may be expressed as
ΓA- ) [A-]∞(ΓS+K′A + C)
(8)
where C ) ∫0∞(eeψ(x)/kT - 1) dx, the Boltzmann factor. We may now rewrite the effective selectivity coefficient in terms of equilibrium constants for binding
KBA(app) )
ΓB-[A-]∞ ΓA-[B-]∞
experimental test,1,12 but may be the cause of some inconsistencies in comparing data from separate studies under different conditions. Equation 11 strictly applies only for a mixed solution of the same surfactant ions but with different counterions, which is hardly a common situation. In addition, the ionic strength effect cannot easily be investigated simply by increasing surfactant concentration, due to interference from micelles and surfactant mesophases. The role of added electrolyte needs to be investigated. Case II: Added Electrolyte. If one or more of the competing ions is present as an added electrolyte, then the charge balance for the interface must include the co-ion of the surfactant.
[A-]∞[B-]∞(ΓS+K′B + C)
ΓS+(tot) + ΓM+ ) ΓA- + ΓB-
(13)
[B ]∞[A ]∞(ΓS+K′A + C)
Assuming no specific adsorption of the co-ion, its surface excess is given by the Poisson-Boltzmann equation
) -
-
C ΓS+ ) C K′A + ΓS+ K′B +
(9)
ΓS+(tot) ) ΓA- + ΓB-
or
ΓS+ ) ([A-]∞ + [B-]∞)C
K′A + I-1
- 1) dx (14)
ΓS+ ) ([A-]∞ + [B-]∞)C - [M+]∞C′ ≈ ([A-]∞ + [B-]∞)C
ΓS+ ) C
(11)
Thus KAB(app) always be between KAB and 1, tending to 1 at infinite dilution and approaching the binding selectivity coefficient KAB only at high ionic strength. At constant or nearconstant ionic strength, KAB(app) should be independent of the ratio of competing ions. This is supported by experiment both at air/solution interfaces and in micellar systems.3,21 Inspection of eq 11 shows that the apparent selectivity coefficient will, like the binding selectivity coefficient, display the usual properties of an equilibrium constant, such as the product rule.3,22
KCA(app) ) KCB(app)KBA(app)
-eψ(x)/kT
As it arises from a negative surface excess, C′ will typically be much smaller than C. Therefore in the charge balance
(10)
where I is the ionic strength of the solution (1:1 electrolyte). This charge balance result is important, as it eliminates the dependence of ion selectivity on surface composition or surface charge density, ΓS+. In principle ΓS+ would change with surfactant concentration or with surface composition (either surfactant mixtures or changing counterion ratios); however, the apparent selectivity coefficient depends only on individual binding constants and the total electrolyte concentration according to
K′B + I-1
∞
0
(15)
To a good approximation then, the effective binding coefficient is unchanged by the use of an indifferent electrolyte instead of mixing surfactants with different counterions. This permits us to test the ionic strength dependence of the apparent selectivity coefficient and to treat cases I and II as effectively identical. This applies equally well to situations where three or more salts are present. The diffuse layer charge must always balance the surface charge remaining after bound ions are considered; i.e., for any number of counterions X- (neglecting co-ions)
ΓS+ + ΓSA + ΓSB ) ΓSA + [A-]∞C + ΓSB + [B-]∞C
KBA(app) )
∫ (e
≡ C′[M+]∞
Note that the effective selectivity coefficient cannot be related directly to the binding selectivity coefficient but only to the individual binding equilibrium constants. The relationship between the two selectivity coefficients depends critically on the value of the ratio C/ΓS+. The charge balance relationship may be written as
C ) ([A-]∞ + [B-]∞)-1 ) I-1 ΓS+
ΓM+ ) [M+]∞
(12)
This is true as long as the selectivity coefficients are measured at the same electrolyte concentration, as is often the case in an (21) Abuin, E. B.; Lissi, E. J. Colloid Interface Sci. 1991, 143, 97. (22) Morales, M. C.; Waissbluth, O. L.; Quina, F. H. Bol. Soc. Chil. Quim. 1990, 35, 19.
∑
[X-]∞ ) CI
(10a)
ions,X
Case III: Interacting Surfaces. Up to this point only isolated interfaces have been considered. However in ion flotation it is not certain that the surfaces of the lamellae are noninteracting or that any such interactions are constant with time. What would be the effect of interactions between two charges surfaces on the selective binding? For this we consider such a system, exemplified by a surfactant lamellar phase in equilibrium with a reservoir of competing ions at their bulk or “infinitedistance” concentrations. Between the surfaces the same ion-binding equilibria exist as previously described, and the same definitions may be made. The difference arises in constructing the charge balance condition between two surfaces separated by a distance D. Here the charge balance of the interface requires that the integral over electrostatically “bound” ions be taken only out to the midplane between the surfaces.
ΓA- ) ΓSA + [A-]∞
∫
D/2
0
(eeψ(x)/kT - 1) dx
(16)
As D is a property of the system (D is no different for ions A and B), the apparent selectivity coefficient may be derived as before but with the constant C now a function of surface separation.
KBA(app) )
(ΓS+K′B + C(D))
ΓB-[A-]∞ ) ΓA-[B-]∞
(ΓS+K′A + C(D))
(17)
where C(D) ) ∫0D/2(eeψ(x)/kT - 1) dx, the Boltzmann factor, is integrated to the midplane separating the surfaces, D/2. In the case of interacting surfaces, the surface potential, surface charge density (ΓS+), and C may all vary with surface separation.
1454 Langmuir, Vol. 13, No. 6, 1997
Warr
Table 1. Selectivity Coefficients of Iodide over Bromide for the Different Surfactants and Conditions initial [Br-]/M
surfactant
1.70 × 10-3 1.70 × 10-3 3.0 × 10-4 1.0 × 10-4 1.0 × 10-4
DTAB TTAB CTAB
2.0 × 10-4 ∼2 × 10-4
CTAB1 CEDAB27 c a
initial [Cl-] or [acetate]/M
initial [I-]/M 4.16 × 10-4 4.1 × 10-4 3.1 × 10-4 1.0 × 10-4 1.0 × 10-4 1.0 × 10-4 ∼3 × 10-4
1.71 × 10-3 a 2.0 × 10-3 b
IKBr -(app)
8.9 ( 0.8 12.0 ( 2.8 7.15 ( 0.30 4.42 ( 0.24 9.2 ( 1.3 5.5 ( 0.2 5.85 ( 0.6
Chloride. b Acetate. c Hexadecylethyldimethylammonium bromide.
The usual boundary condition for dealing with interacting surfaces is constant surface potential or constant surface charge, these being mutually exclusive. As with an isolated surface, charge balance dictates that
ΓS+(D) C(D)
) ([A-]∞ + [B-]∞) ) I
at all separations and all surface charges. Hence constraining surface charge has no particular virtue or convenience, as ΓS+ is always exactly compensated by C. If the surfaces approach each other at constant surface potential, then the selectivity coefficient has the same form and properties as for an isolated interface; i.e.
KBA(app) )
KBe-eψ0/kT + I-1 K Ae
-eψ0/kT
+I
(18)
-1
In this situation KAB(app) is independent of separation, as long as the interacting system is kept in equilibrium with a solution of constant ionic strength. At most surface separations encountered in ion flotation, constant charge and constant potential interactions are effectively identical, and hence the selectivity coefficient should be unaffected by interactions. However, in situations where surface separations may be particularly small (such as very dry foams or within lamellar or other surfactant self-assembly phases4), the constant potential approximation would be inappropriate. In such situations the apparent selectivity coefficient will depend on separation due to changes in the surface potential, even though the nonelectrostatic components of the adsorption equilibria, KA and KB, are unchanged. KAB(app) is thus a robust experimental quantity which should be independent of interfacial composition, of whether co-ions are present, and to a good approximation of interactions between surfaces.
Experimental Section In order to test the ionic strength dependence of the apparent selectivity coefficient, two approaches have been employed. The competitive binding of iodide over bromide to alkyltrimethylammonium surfactants was determined so that the head group type is constant throughout. Three surfactants, dodecyltrimethylammonium bromide (DTAB), tetradecyltrimethylammonium bromide (TTAB), and hexadecyltrimethylammonium bromide (CTAB), were used. These form stable foams at quite different concentrations, allowing the ionic strength to be varied widely (see Table 1). Potassium iodide or chloride was added to each surfactant solution at a concentration of 1-5 × 10-4 M, and flotation was carried out for 1-3 h. Ionic strength effects were independently tested in two separate experiments. In the first, a dilute solution of CTAB and potassium iodide was prepared in excess sodium acetate (2.0 mM). As the acetate ion binds extremely weakly to quaternary ammonium surfactants, it does not compete effectively with either bromide or iodide.23-25 In the second, DTAB (23) Evans, L.; Paul Thalody, B.; Morgan, J. D.; Napper, D. H.; Nicol, S. K.; Warr, G. G. Colloids Surf. A 1995, 102, 81. (24) Thalody, B.; Warr, G. G. Submitted to J. Colloid Interface Sci. (25) Brady, J. E.; Evans, D. F.; Ninham, B. W.; Grieser, F.; Warr, G. G. J. Phys. Chem. 1986, 90, 1853.
Figure 1. Theoretical dependence of apparent selectivity constant on ionic strength for KBA ) 10 and K′A ) 10, 100, 103, and 104. was mixed with dilute potassium iodide and concentrated sodium chloride solutions. Chloride is also a more weakly binding ion than either bromide or iodide. Solution conditions are listed in Table 1. All flotation runs were carried out as described previously, with ion concentrations determined by ion chromatography.1 Unlike the case of our previous studies, however, all concentrations in this work were measured by both absorbance and conductivity detectors, and give good reproducibility in all cases.
Results and Discussion Properties of KB A(app). The key prediction for the apparent selectivity coefficient is that it should depend on ionic strength and on very little else (eq 11). This emerges naturally from the electroneutrality condition of the interface. It is not after all surprising that higher ionic strengths and therefore thinner diffuse layers should lead to greater counterion condensation and hence greater selectivity. For although we choose to express the equilibrium between bulk and bound ions, the binding process occurs at the interface and ions in the Stern layer must also be in equilibrium with those in the diffuse layer adjacent to the surface. The dependence of selectivity coefficient on ionic strength follows from eq 11. It is not possible to simply relate KBA(app) and KBA: the values of the individual binding constants, and particularly their magnitudes compared with I-1, are the important quantities. If plotted as KBA(app) versus I-1, eq 11 has a sigmoidal shape not unlike that of an acid-base equilibrium. This is shown schematically in Figure 1 for a range of binding constants, but all with KBA ) 10. At low ionic strengths KBA(app) tends to 1, and at high ionic strength, it tends toward KBA. Between these two extrema there is a “rollover” region spanning approximately two decades in I. An interesting property of eq 11 is that the median value of KBA(app) occurs at a very particular ionic strength, I*.
Ion Flotation
Langmuir, Vol. 13, No. 6, 1997 1455
Figure 2. Apparent selectivity coefficient versus ionic strength, showing how individual binding constants of both ions may be determined from the median value of KBA(app) (and KAB(app)). Here K′A ) 103 and K′B ) 102.
I Figure 3. Determination of KBr -(app) from ion flotation -4 experiments using eq 2. (a) 1 × 10 M CTAB + 1 × 10-4 M KI; (b) 3 × 10-4 M TTAB + 3 × 10-4 M KI; (c) 1 × 10-4 M DTAB; (d) 1.7 × 10-3 M DTAB + 4 × 10-4 M KI + 1.7 × 10-3 M NaCl. -
The median value of KBA(app) is
1 KBA(app) ) (KBA + 1) 2
(19)
Expanding KBA(app) using eq 11 and using eq 3 to define KBA yields the following result:
K′AI* ) 1
(20)
The different curves in Figure 1 show the net effect of this result. KBA(app) increases from 1 to its maximum value over a transition region involving two decades of I, and for larger K′A, this transition region moves to lower ionic strengths. This offers a potential method for obtaining individual ion-binding equilibrium constants from flotation data. The result obtained in eq 20 is true for all KBA(app), whether greater or less than 1. In addition to inferring K′B from the limiting value of KBA(app), it is therefore possible to separately determine K′A and K′B, by plotting KBA(app) and KBA(app)-1 against I and identifying the median value. This is illustrated in Figure 2. Experimental Test of the Ion-Binding Model. The results of our flotation experiments for the selective binding of iodide and bromide are shown in Figure 3, plotted according to eq 2. The selectivity coefficients are I summarized in Table 1, which clearly shows that KBr differs substantially for the different conditions. This is at odds with intuition, which suggests that the selectivity coefficients should be the same for the same head group types but consistent with the theory developed above. The apparent selectivity coefficient of iodide over bromide is plotted against total electrolyte concentration in Figure 4. This includes CTAB data from the present study and some work published earlier.1 Note particularly that the selectivity coefficients are virtually identical at the same ionic strength, although in one case the surfactant is DTAB and in the other it is CTAB with added acetate. This is consistent with predictions of indifference to added salt (case II). These data yield a binding constant for bromide ion of 1.6 × 103 M-1, although there is insufficient data to be too precise. At high concentration the limiting value is I - ) 13 ( 2, giving a binding constant approximately KBr for iodide of 2.1 × 104 M-1. (This can also be obtained by plotting KIBr against ionic strength.) This value for -
I Figure 4. Variation of KBr -(app) with electrolyte concentration determined from ion flotation experiments (squares). Also shown are the results of Grieves27 (triangle) and Morgan1 (circle). The solid line indicates the fit to the data with K′I- ) 2.1 × 104 I26 and K′Br- ) 1.6 × 103, giving KBr - ) 13. -
I KBr - agrees extremely well with a value of 13 ( 3 obtained at a micelle surface from a fluorescence-quenching method, which should be sensitive only to surface-bound ions.26 There is relatively little previous work on the selectivity of iodide over bromide in ion flotation, although published results are also consistent with our experiments. Grieves et al.27 used ion flotation to determine anion-exchange selectivities in hexadecylethyldimethylammonium broImide solutions, obtaining an average value of KBr - ) 5.7 ( 0.2 at ionic strengths between 0.1 and 0.6 mM. Although it has a slightly different head group, this surfactant would be expected to behave similarly to CTAB. Their data seemed to show a slight increase with increasing ionic strength, but this was inconclusive. In fact those authors used this and similar data to conclude that there was no ionic strength dependence in flotation selectivity coefficients, although the evidence in either direction must now be regarded as scant. Grieves et al.’s result is included for comparison in Figure 4 and is pleasingly consistent with the present work, forming part Iof a slow overall increase in KBr -(app) with electrolyte concentration. Our data on bromide and iodide thus clearly demonstrate the kind of concentration dependence expected from -
(26) Abuin, E. B.; Lissi, E.; Bianchi, N.; Miola, L.; Quina, F. J. Phys. Chem. 1983, 87, 5166. (27) Grieves, R. B.; Bhattacharyya, D.; The, P. J. W. Can. J. Chem. Eng. 1973, 51, 173.
1456 Langmuir, Vol. 13, No. 6, 1997
the site-binding model. However our accumulated data on bromide/chloride competitive binding, including the present experiments and some earlier work using CTAB, are inconclusive. This is due to a combination of factors. First, the low selectivity of bromide over chloride means that the accuracy with which KBA(app) must be measured is much greater than that for bromide/iodide, and secondly, the lower absolute value for K′Cl- puts the high concentration limit of KBA(app) out of feasible experimental Brrange. Hence only small changes in KCl - (app) would be observed, and it would be difficult to distinguish a trend from experimental scatter. The same is true for the bulk of published ion selectivity data.6,17,27-29 By and large the selectivity coefficient is so close to unity that trends are lost in the experimental scatter29 or concentration dependence has not been determined over a sufficiently wide range of electrolyte concentrations.1,27,28 There is one related case in the literature where ultrafiltration and probe studies have been compared for cationic micellar solutions containing thiosulfate and bromide at different electrolyte concentrations.7 Here the behavior is qualitatively consistent (28) Grieves, R. B.; The, P. J. W. J. Inorg. Nucl. Chem. 1974, 36, 1391. (29) Grieves, R. B.; Burton, K. E.; Craigmyle, J. A. Sep. Sci. Technol. 1987, 22, 1597.
Warr
with the present work, although it deals with monovalent/ divalent exchange. At high electrolyte concentrations the two experimental techniques yield coincident results, but at low enough sodium bromide concentration they differ, and this is explained as being due to the greater role for the diffuse part of the double layer surrounding the micelles. Conclusions A site-binding model for monovalent-monovalent ion exchange has been developed, and its predictions have been tested against experimental ion selectivities determined from ion flotation. The key prediction, that the measured selectivity coefficient will depend on electrolyte concentration, is verified by our experiments and successfully explains discrepancies in published data. This model also predicts that addition of electrolyte or interactions between surfactant films will have little effect on measured selectivities under most conditions, also consistent with experimental observations. Acknowledgment. This work was funded by the Australian Research Council. I wish to thank Ms. Leoni Kellaway for her careful experimental work. LA960634C
