Counterion Binding to Ionic Reverse Micellar Aggregates and Its Effect

Zakharova , Victor V. Syakaev , Mikhail A. Voronin , Farida V. Valeeva , Alsu R. Ibragimova , Yuliana R. Ablakova , Ella Kh. Kazakova , Shamil K. Laty...
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J. Phys. Chem. B 1997, 101, 10295-10302

10295

Counterion Binding to Ionic Reverse Micellar Aggregates and Its Effect on Water Uptake Hamid R. Rabie and Juan H. Vera* Department of Chemical Engineering, McGill UniVersity, Montreal, Quebec, Canada H3A 2A7 ReceiVed: October 9, 1996; In Final Form: September 15, 1997X

A model is developed to predict the binding of counterions, or dissociation fraction of surfactant, at the reverse micellar interface. The model is based on the chemical equilibria between the counterions bound to head groups at the reverse micellar interface and the free counterions in the water pool. No adjustable parameter is used for the calculation of the dissociation fraction. The model is further extended to predict the water uptake. The extended model accurately represents the water content in the organic phase for both single and multiple salt systems.

1. Introduction An ionic surfactant has one or more hydrocarbon tails, which may contain branched chains, and an anionic or cationic head, which may partly dissociate in water. Two tailed ionic surfactants can usually form reverse micelles, also called swollen micelles. Reverse micelles are aggregates of surfactant molecules containing microscopic polar cores of solubilized water, called water pool, in an apolar solvent. The presence of the aqueous environments in an organic medium makes it possible to solubilize proteins, and other hydrophilic molecules, in a bulk organic phase. Reverse micelles formed with anionic surfactants, like Aerosol OT, generally solubilize large quantities of water in the organic phase without the addition of other organic materials.1-4 On the other hand, cationic surfactants usually require a cosurfactant, such as an alcohol, to form reverse micelles.5-17 In both cases, to form reverse micelles by the contact method, it is usually required to add salt to the aqueous phase in contact with the organic phase. The water uptake obtained by titrating an aqueous solution into an organic phase containing a surfactant is different from that obtained by contacting the organic phase with an excess aqueous phase.17 In the titration method, the composition of the water pools is fixed by the composition of the titrant, while in the contact method, the composition of the water pool depends on the exchange of ions between the reverse micelles and the excess aqueous phase. Consequently, the composition of the water pool determines the water uptake.17 The effect of temperature, and of salt type and concentration on the maximum water uptake by the surfactant AOT reverse micellar phase before any excess aqueous phase is formed, was studied by many investigators.18-27 Tosch et al.,28 Fletcher,29 and Aveyard et al.30 have measured the distribution of sodium salts between an aqueous electrolyte solution and a water-inoil (W/O) microemulsion in equilibrium. They also measured the water uptake by the reverse micelles and reported the AOT distribution between the two phases, the size of the reverse micelles, and the values of the interfacial tension. Models have been proposed for solubilization of ions in the reverse micelles when the contact method is employed.31-35 In a recent work,35 we developed a model for extraction of ions into the reverse micelles, discussed the mechanism of ion distribution, and identified the main driving forces for extraction. We found that ion exchange reactions between the surfactant * To whom all correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, November 1, 1997.

S1089-5647(96)03103-3 CCC: $14.00

counterion and the other counterions present in the system, through the addition of salts, are the most important aspect to the explanation of the solubilization of ions. This ion exchange reaction results in the change of the nature of the surfactant counterion. The proposed model gives better predictions than other phenomenological models published in the literature.35 The accuracy of the results obtained with the dimensionless form of the model suggests that the model is physically meaningful. It has also been found that changing the nature of the surfactant counterion has a dramatic effect on water uptake.17,31,36,37 Surfactant molecules are able to dissociate at the reverse micellar interface and, as a result, produce a surface charge density at the inner core of the reverse micelles. The experimental results of Wong et al.38 for the system of AOTheptane-water-NaCl have shown that an upper limit of 28% of the sodium was dissociated from the AOT head groups in the largest water pool of their study, which corresponds to 6 wt % of water in the organic phase. The calculated values for the fraction of surfactant dissociated vary between 20% and 35%.31,39-41 However, the dissociation fraction is greatly influenced by the counterion of the surfactant.31 We present here a mathematical model to predict the dissociation fraction of surfactant in the reverse micelles for various conditions of surfactant concentration, and salt type and concentration, in mixed salt systems. Furthermore, the effect of the degree of dissociation on the water uptake is evaluated and the mathematical model is extended to predict the water uptake. In this work, we investigate the water uptake when contacting a reverse micellar phase with an excess aqueous phase. Some experimental results presented in our previous work37 are recalled for comparison with the predictions of the present model for water uptake. However, there are some new experimental results presented in this work. A detailed description of our experimental procedure and materials has been presented elsewhere.35 The experimental results discussed here have been obtained with two surfactants: the commercial sodium form of AOT, sodium bis(2-ethylhexyl) sulfosuccinate, and the potassium form of AOT. The potassium form of AOT surfactant was made as described by Eastoe et al. from the sodium form of AOT using a liquid-liquid ion exchange process.42,43 2. Modeling There are essentially four distinct regions in reverse micellar systems where a solute can be solubilized. They are (i) the organic continuum, (ii) the interface of the surfactant hydro© 1997 American Chemical Society

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Rabie and Vera V h 0 containing the organic solvent and the surfactant with concentration C h 0s . In the final state (at equilibrium) in a Winsor II system, the aqueous phase has a volume V and it contains the surfactant, chloride anion, and cations at concentrations Cs, CCl, and Ci, respectively. The organic phase of volume V h contains the organic solvent, surfactant (C h s), water, free cations h Cl,f), and in water pool (C h i,f), free chloride in the water pool (C bound cations at the reverse micellar interface (C h i,b). The part of the surfactant in the organic phase that is dissociated has a concentration of C h ds. In this notation, the subscript “b” refers to the counterions bound to the surfactant head groups while the subscript “f” refers to the free counterions in the water pool. In an anionic surfactant system, the anions cannot interact with the reverse micellar interface because of the strong repulsive forces, and they are mainly in the water pools of the reverse micelles in equilibrium with the excess aqueous phase (Winsor II system). Therefore, the assumption that Λ is unity for any solute yields

Figure 1. Solubilization sites according to the active interface model (the Na group is the sodium salt of the AOT surfactant).

philic groups and the water pool in the reverse micelles, (iii) the water pool inside the reverse micelles, and (iv) the excess aqueous phase. These regions are shown in Figure 1. In the following equations, a notation with a bar is used for the organic phase even though the solute may be localized in any of the first three regions while a notation without bar is for excess aqueous phase. The superscript “0” indicates the value of the properties at the initial conditions. All symbols without this superscript denote the values of the properties at equilibrium. Salts and many other solutes such as amino acids are essentially insoluble in organic solvents. Thus, in this study, we only consider the last three regions. Here, we assume that all the surfactant molecules are aggregated. The conditions under which this assumption is valid are discussed elsewhere.44 The partitioning of any species is assumed to occur from the excess aqueous phase to the water pool and from the water pool to the reverse micellar interface. For the water pool of the reverse micelles, the partitioning of any solute from an excess aqueous phase to the water pool of the reverse micelles is characterized by a partition coefficient Λ:

Λ)C h f /C

(1)

where C is the molar concentration of a solute, such as a salt, in the aqueous phase and C h f is the molar concentration of that solute in the water pool. Equation 1, which results from phase equilibrium considerations,44 tacitly assumes that the ratio of the activity coefficients of species i is insensitive to changes in the equilibrium conditions, and it can be included in the partition coefficient. It has been shown that the value of the partition coefficient can be assumed to be unity, even for very low water uptake.35,45 To test the model for the binding of counterions proposed in this work, we have chosen the sodium (or potassium) bis(2ethylhexyl) sulfosuccinate (AOT)-water-in-oil microemulsion system in contact with an excess aqueous phase containing (n - 1) chloride salts, MClz, in addition to NaCl. Since the coion of a surfactant has no significant effect on the ion distribution35 and on the water uptake,17,35,41 for simplicity, we use here the chloride salts of all surfactant counterions. The initial and the final conditions of the system are described as follows. In the initial state, an aqueous phase of volume V0 containing the chloride anion and n different cations with concentration C h 0i , including sodium, is contacted with an organic phase of volume

C h Cl,f ) CCl

(2)

The other implication of such an assumption is that the extraction of solutes into a freshly formed water pool does not change the final concentrations of solutes in the excess aqueous phase, and consequently, it does not affect the overall ion distribution. The concentrations of free ions in the organic phase are defined as moles of ion per unit volume of water pool, while the concentrations of the surfactant and the bound ions in the organic phase are defined as moles of surfactant or bound ion per unit volume of water-free organic phase. This latter volume is the same as the initial organic phase volume, since the solubility of organic solvent in water is very small. It has been found that the fraction of AOT in the bulk water, at equilibrium, is always less than 1%,30,35 so the concentration of surfactant in the organic phase at equilibrium can be assumed to be the same as its initial value, C hs ) C h 0s . The relation between the initial and final volumes of each phase is

h -V h 0 ) wV h V0 - V ) V

(3)

where w is the volume fraction of water in the organic phase at equilibrium and is only a function of ion concentrations at equilibrium.17 2.1. Dissociation Fraction in a Single-Counterion System. First, we study a simple system that contains only one counterion: AOT-heptane-water-NaCl. The counterion of this system is sodium. The dissociation reaction of surfactant can be summarized as

SNa a S- + Na+

(4)

with the following equilibrium constant in terms of concentrations:

KNa d )

h Na,f C h dsC C h Na,b

(5)

It should be noted that KNa d is not a thermodynamic equilibrium constant, since it is defined in terms of concentrations instead of activities. The activity coefficients of the species involved are included in KNa d . The same cosideration holds for other equilibrium constants used in this work. The mass balance of sodium takes the form

VCNa + V h 0C h Na,b + wV hC h Na,f ) V0C0Na + V h 0C h 0s

(6)

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and for the surfactant

C h Na,b + C h ds ) C h 0s

(7)

Combining eqs 2, 3, and 5-7 and the equations of electroneutrality in the water pool and excess aqueous phase results in

TABLE 1: Values of Equilibrium Constants for Ion Exchange and Dissociation Reactions, of the Size and Ionic Parameters, of Minimum Salt Concentration Needed for Formation of Reverse Micelles (Ci,m), and of the Water Uptake Constant (w0•,i)

Na+

KNa d )

f(C0Na + 55.5f/w0) (1 - f)

(8)

where “f” is the fraction of surfactant dissociated and is defined by

f)

C h ds/C h 0s

(9)

In eq 8 w0 is the moles of water per mole of surfactant in the organic phase at equilibrium and is related to w through the following equation:

w0 )

55.5w - w)

C h 0s (1

(10)

Equation 8 can be used to determine the value of the equilibrium constant of dissociation. Wong et al.38 reported a 0.28 fraction of surfactant dissociated and 49.3 mol water per mole of surfactant in heptane for an initial concentration of 67 mM NaCl in the aqueous solution used as titrant for formation of reverse micelles with the titration method. As shown by Rabie et al.,46 at equal electrolyte and surfactant concentrations, the water uptake obtained by the titration method is lower than that obtained by the contact method. This is due to a lower effective ionic strength inside the water pools of reverse micelles formed by the contact method when compared with those formed by the titration method.46 Therefore, for the contact method used in this work, the NaCl concentration to be used in eq 8 should be slightly higher than 67 mM. Since the exact effective concentration inside the water pool is not known, as an assumption, we use here the equilibrium constant corresponding to 67 mM NaCl. This is not a rough assumption considering that a 10% change in NaCl concentration, at 67 mM level, results in less than 1.7% change in the value of the equilibrium constant. Besides, as stated already by Wong et al.,38 the 28% dissociation itself is an approximation. Therefore, using these results and eq 8, the value of KNa d is found to be 0.1486 M. We use this value for KNa d throughout this work to obtain the fraction of surfactant dissociated for different surfactant and salt concentrations (or ionic strength) in the mixed salt systems. We will also use this value for different solvents. Although a solvent has definite effect on the water uptake and size of the reverse micelles, once the reverse micelles are formed, it does not have any significant effect on the reactions happening inside the reverse micelles between different solutes and the surfactant head groups, except for very penetrating solvents.35,44 Therefore, the value of the equilibrium constant found for one solvent can be used for other Winsor II systems with different solvents. Another important relation, which can be obtained combining eqs 2, 3, 6, 7, and the equations of electroneutrality in the water pool and excess aqueous phase, is

CNa ) C0Na

(11)

This equality indicates that the dissociation of the surfactant has no effect on equilibrium concentrations of ions in the aqueous phase. The extra ions released to the water pool, from

K+ Rb+ Cs+ Sr2+ Ba2+

Kis

Kid

τi

Ai (kcal/mol)

Ci,m

w0•,i

1.00 1.96 2.08 2.13 32.6 62.3

0.1486 0.0758 0.0714 0.0698 0.0007 0.0004

4.0 3.2 3.1 3.1 6.0 5.8

99.6 81.6 76.5 68.7 344.1 318.1

0.080 0.060 0.060 0.055 0.035 0.035

6.5 4.7 5.1 6.8 4.8 2.3

the dissociation of surfactant molecules at the reverse micellar interface, are not able to enter the excess aqueous phase because of the need for maintaining the electroneutrality in the reverse micelles. Thus, the overall ion distribution can be obtained independently from the dissociation fraction, assuming that all surfactant molecules are bound to either sodium or other cations. In this case, the model reduces to the previous treatment for the ion distribution.35 2.2. Dissociation Fraction in Multicounterion System. In a multicounterion system, the free counterions in the water pool undergo an ion exchange reaction with the original surfactant counterion bound to the surfactant head group at the reverse micellar interface. For AOT, since the surfactant S is anionic, any Mi,fzi+ cation is exchangeable with the original surfactant counterion, Na+, in the water pool. This ion exchange is represented by a reversible reaction of the form35

ziSNa + Mi,fzi+ h SziMi + ziNaf+

(12)

The equilibrium constant Kis of this reaction in terms of concentrations is

Kis

( )( ) C h i,b C h Na,f

)

zi

C h i,f C h Na,b

(13)

The values of the equilibrium constants for different cations have been reported elsewhere.35 These equilibrium constants were measured by means of ion distribution experiments. The same values are used throughout this work. Therefore, there is no adjustable parameter to fit in this study for counterion binding calculations. This new form of surfactant, SziMi, can also dissociate in the water pool. However, its reaction is not independent from reactions 4 and 12. The dissociation reaction of SziMi in the water pool is then formulated as

SziMi h ziS- + Mi,fzi+

(14)

with the following equilibrium constant

Kid

KNa d

h i,f C h dsC )

) C h i,b

(Kis)zi

(15)

The equilibrium constants of the ion exchange reactions and of the dissociation reactions, for some monovalent and divalent cations, are listed in Table 1 together with the minimum amount of salt needed for the formation of reverse micelles and the water uptake constant. This table also contains the values of the size parameter of ion i, τi, which is a dimensionless ionic radii, and of the ionic parameter Ai, which is obtained from the free energy of hydration. The values of the ion exchange equilibrium constant, the size parameter of the ion, and the ionic parameter

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Rabie and Vera

are taken from the literature.35 The significance of the size parameter of ion, the ionic parameter, the minimum amount of salt for the formation of reverse micelles, and the water uptake constant are discussed in sections 3.1 and 3.2. For a multicounterion system, the mass balance of sodium remains the same as in eq 6. The mass balance of surfactant is then n-1

C h Na,b +

∑1 (ziCh i,b) + Ch ds ) Ch 0s

(16)

where the summation runs over all the counterions except sodium. For each of the other cations present in the initial aqueous phase we write

VCi + V h 0C h i,b + wV hC h i,f ) V0C0i

(17)

Combining the equations of electroneutrality in the organic phase and in the aqueous phase with eqs 2, 6, 16, and 17 results in n

w0 ) w0• exp(Rf)

(20)

n

(ziCi) ) ∑(ziC0i ) ∑ i)1 i)1

(18)

where the summations run over all the counterions. Equation 18 is a useful relation between the initial and equilibrium (Winsor II system) concentrations of ions in the aqueous phase. It indicates that the total equivalent of counterions in the aqueous phase remains at its initial value. If no surfactant molecule is dissociated at the reverse micellar interface, the concentration of the dissociated form of surfactant goes to zero and all surfactant sites will be filled with either sodium or another counterion. Therefore, there is no additional cation released in the water pool from the dissociation of surfactant. In this case, assuming that the value of Λ is unity for each solute, the concentration of any free counterion in the water pool is the same as that in the excess aqueous phase. Therefore, eq 13 can be written based on the concentrations of ions in the excess aqueous phase instead of those in the water pool:

Kis

in section 2.3, the model will be extended to provide an equation that relates the water uptake to the dissociation fraction. It is important to note that even when the above equations are written for the sodium salt of an anionic surfactant, such as AOT, they are general for any other anionic or cationic surfactant. For cationic surfactants, the sodium should be replaced by the original surfactant counterion, and the other cations added to the aqueous phase should be replaced by the other anions added to the aqueous phase. 2.3. Water Uptake Model. The dissociation of surfactant produces a surface charge density at the reverse micellar interface, causing a repulsive force between the surfactant head groups. As the dissociation fraction increases, the repulsive force between the surfactant head groups increases, and consequently, the size of the reverse micelles, and thus the water uptake, increases. For a single-counterion system, the water uptake is assumed to be a function of the dissociation fraction only. As suggested by the experimental data, the following form is proposed:

)

( )( ) C h i,b

CNa

Ci

C h Na,b

zi

(19)

The calculations are performed in two steps for a system containing n different counterions including sodium. Step 1. As explained before, since the dissociation of surfactant has no effect on the concentrations of ions in the excess aqueous phase, these concentrations are obtained assuming that all surfactant sites are filled. Therefore, there are n equations of the type of eq 1, n - 1 equations of the type of eq 17, n - 1 equations of the type of eq 19, and eqs 3, 6, and 18 while setting the value of Λ for any solute equal to 1. It is important to note that the water uptake, w, does not appear in the solution of these equations. Step 2. The concentrations of different species in different regions of the organic phase are calculated using the results of step 1, for the concentrations of ions in the excess aqueous phase, and the following equations: n - 1 equations of the type of eq 17, n - 1 equations of the type of eq 13, and eqs 3, 5, 6, and 16. Then the dissociation fraction is calculated from eq 9. In this step, the water uptake is required for the final solution of the equations. Normally, at this stage, the water uptake is inserted into the model as a known value. However,

where w0• is the water uptake when the dissociation fraction is zero and it corresponds to the water uptake when the aqueous phase is a highly concentrated salt solution. In eq 20, R is a dimensionless water uptake constant and is assumed to be the same for all counterions. In the case of mixed counterions, the following mixing rule is proposed to obtain the value of w0• for the mixture from the single-counterion values: n

w0 ) •

Yiw0•,i ∑ i)1

(21)

where the ionic strength fraction Yi is defined as

zi2Ci Yi )

(22)

n

∑(zk Ck) 2

k)1

The other possible mixing rule is the one similar to eq 21 using the charge fraction instead of the ionic strength fraction. The equivalent fraction is defined similarly to eq 22 with the term z instead of z2. Our calculations for divalent cations showed that the agreement between the predictions of the present model and experimental results decreases significantly when an equivalent fraction is used in eq 21. The present model gives information on the dissociation fraction at the reverse micellar interface, the ion distribution between aqueous and organic phases, and the water uptake. 2.4. Geometrical Considerations. Knowing the water uptake, the size of the reverse micelles and aggregation number can be calculated from different geometrical models from the simplest47 to the more sophisticated one.31 Any of these models, for calculation of size of the reverse micelles, uses the experimental water uptake data. Little differences are observed between the results obtained from different models. Therefore, the key problem is the knowledge of the water uptake. The following geometrical relations have been proposed31,47 for the radius of the water pool, Rwp, and the aggregation number of the surfactant, ns:

Rwp )

3Vww0 As

(23)

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J. Phys. Chem. B, Vol. 101, No. 49, 1997 10299

ns )

36πVw2w02 As3

(24)

where the volume of a water molecule, Vw, is 30 Å3, and As is the area occupied by the head group of a surfactant molecule at the reverse micellar interface. For AOT reverse micelles, Karpe and Ruckenstein47 assumed As to be fixed at 55 Å2, and Leodidis and Hatton31 proposed expressing As as a function of w0 from the experimentally determined dependence of As on w0 measured by Eicke and Rehak:48

As ) 57 - 11 exp(-0.09163(w0 - 10))

(25)

Equation 25 shows that As is a week function of water uptake. Eastoe et al.43 studied the effect of surfactant counterion on the structure and properties of reverse micelles formed by metal bis(2-ethylhexyl) sulfosuccinate. They observed that even for very low water uptakes (w0 < 5), spherical surfactant aggregates are present for the following counterions: Na+, K+, Rb+, Cs+, and Ca2+. Increasing the w0 favors the spherical shape over the cylindrical shape aggregates obtained for transitional metals at low values of w0. They also used the SANS data to calculate the area occupied by the head group of a surfactant molecule (As). They showed that this area was independent of the nature of the counterion for the series of Na+, K+, Rb+, Cs+, and Ca2+ equal to 64 ( 6 Å2. Considering that the results of Eastoe et al.43 were obtained in a different solvent and at very low water uptake (w0 < 5), this area is very close to the 55 Å2 used by Karpe and Ruckenstein.47 Therefore, as a simplifying assumption, we consider that As remains constant at 55 Å2 for all counterions used in this work. This assumption, however, is not crucial for the model presented here. 3. Results and Discussion An interesting observation is the distribution of chloride, the coion in this study, in single- and multiple-counterion systems for different initial concentrations of surfactant and salts for a wide range of water uptakes. Our experimental results in this study showed that the final concentration of chloride in the excess aqueous phase was almost the same as its initial value. A slight decrease was observed, but it was not significant. Similar results have been obtained for cationic surfactant systems.49 This justifies the assumption that the value of Λ is unity for any solute. If the concentration of chloride in the water pool was different from that in the aqueous phase at equilibrium, a difference would be detected between its initial and final concentrations in the aqueous phase at moderate water uptakes. As discussed earlier, the predictions of the model for ion distribution can be obtained in step 1 of our calculations, independently from the dissociation fraction and water uptake. These results for ion distribution are further used to calculate the dissociation fraction and the water uptake, as explained in step 2 of the calculation procedure described in section 2.2. However, the values of the dissociation fraction, f, can be obtained either by using the experimental water uptake data or by using eqs 20 and 21. In the first case, there is no adjustable parameter, while in the latter case, the value of R must be known. The method for evaluating R, which in this case is an adjustable parameter, is explained in section 3.2. 3.1. Dissociation Fraction and Ion Distribution. The numerical results of the dissociation fraction of AOT at the reverse micellar interface in the presence of chloride salts of different monovalent cations (Na+, K+, Cs+) are shown in Figure 2. These results were obtained using experimental water uptake data.37 In the case of sodium in Figure 2, the system

Figure 2. Dissociation fraction as a function of equilibrium equivalents of cations in the aqueous phase for different monovalent cations: initial organic phase, 0.1 M AOT; initial aqueous phase, chloride salt. The lines are the predictions of the present model.

Figure 3. Dissociation fraction as a function of equilibrium equivalents of cations in the aqueous phase for different divalent cations: initial organic phase, 0.1 M AOT; initial aqueous phase, chloride salt. The lines are the predictions of the present model.

contains only one counterion, while in the other cases, there are two counterions present in the system. As shown in Figure 2 for any cation, the dissociation fraction decreased with the initial salt concentration and approached a constant value at higher salt concentrations. More surfactant molecules were dissociated in the presence of sodium than other monovalent cations for the same salt concentration, whereas the dissociation fraction followed almost the same curve for potassium and cesium with a slightly higher dissociation for the latter. Similar results for divalent cations (Ca2+, Sr2+, Ba2+) in chloride salts are shown in Figure 3. Similar to monovalent cations, the dissociation fraction decreased with addition of salt and remained almost constant at higher salt concentrations. Significantly lower dissociation fractions were obtained for divalent cations than for monovalent cations. This is due to the stronger electrostatic interactions of divalent cations with the surfactant head groups. The most interesting aspect of the present model is that there is no adjustable parameter and that no geometrical consideration is needed to account for binding. The only piece of information required is the value of water content in the organic phase at equilibrium. For the sake of completeness, the experimental data and calculated results for ion distribution of different cations (K+, Ca2+, Sr2+, Ba2+) in chloride salts are shown in Figure 4. The experimental conditions were similar to those used in Figures 2 and 3. In this figure, the equilibrium concentration of sodium in the excess aqueous phase is plotted as a function of the initial salt concentration. It is important to note that no sodium was

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Figure 4. Equilibrium concentration of sodium in the excess aqueous phase as a function of initial salt concentration for different cations: initial organic phase, 0.1 M AOT; initial aqueous phase, chloride salt. The lines are the predictions of the present model. The experimental data are from present work.

added initially to the aqueous phase. The presence of sodium in the aqueous phase at equilibrium is due to the exchange of the surfactant counterion with the added cation. Barium released more sodium into the aqueous phase than other cations. The data for cesium, not shown in Figure 4, were close to those of potassium but slightly higher. The solid lines are the predictions of the model. As explained before, the numerical results were obtained independently of the water uptake and of the dissociation fraction. Additional results on ion distribution equilibria and also on dimensionless representation of the ion distribution have been reported elsewhere.35 As shown in Table 1 and in Figures 2-4, cations with larger ion exchange equilibrium constants are preferentially drawn toward the reverse micellar interface; however, they dissociate less. Divalent cations have larger values of ion exchange equilibrium constants and lower dissociation when compared to monovalent cations because of stronger electrostatic interactions. Monovalent cations with the same hydrated size (K+, Rb+, Cs+) have almost the same ion exchange and dissociation equilibrium constants, while divalent cations with the same hydrated size (Ca2+, Sr2+, Ba2+) have significantly different ion exchange and dissociation equilibrium constants. This is due to the difference in the hydration free energy.35 As shown in Table 1, within the cations with the same charge number, decreasing the τi or Ai favors the increase of the ion exchange equilibrium constant and the decrease of dissociation equilibrium constant. As shown previously,30 in the contact method, a minimum amount of salt is necessary to pass from a Winsor type III to a Winsor type II, or reverse micellar system. This minimum amount of salt varies with the nature of the counterion introduced into the system through the addition of salt. In Table 1, the minimum amount of salt needed to form reverse micelles is listed for different cations. As shown in this table, this minimum amount of salt is greater for cations with greater dissociation constant or smaller ion exchange equilibrium constant. Our experimental results showed that reverse micelles were not formed with chlorides of Li+, Be2+, and Mg2+. Similar observations were made by Leodidis and Hatton.41 According to the conclusions drawn from the results of Table 1, one can expect to obtain significantly greater dissociation with these cations in comparison to that obtained with sodium. Therefore, the system cannot pass from Winsor III to Winsor II type system. 3.2. Water Uptake. 3.2.1. Parameter EValuation. The procedure for evaluation of the parameters used in eq 20 is

Rabie and Vera

Figure 5. Dissociation fraction as a function of logarithm of water uptake: initial organic phase, 0.1 M Na(AOT) or K(AOT); initial aqueous phase, NaCl or KCl. The water uptake data of Na(AOT)NaCl system are from literature37 and those of K(AOT)-KCl are from present work.

Figure 6. Dissociation fraction as a function of logarithm of water uptake: initial organic phase, 0.1 M AOT; initial aqueous phase, chloride salt. The water uptake data are from literature.37

explained below. As it was done in Figure 2, the dissociation fraction of the AOT-NaCl system is calculated using the experimental water uptake data. When these results are plotted as a function of the logarithm of water uptake data, as shown in Figure 5 for Na(AOT)-NaCl, a linear relation is obtained. This figure also contains the results of K(AOT)-KCl which are discussed below. The slope of the line is 1/R, and the intercept of this line with the x axis gives the value of w0•,i for sodium. The values of these parameters are R ) 7.53 and w0•,Na ) 6.5 moles of water per mole surfactant. As mentioned earlier, the value of R is assumed to be the same for any counterion and the value of w0•,i corresponds to the water uptake of an organic phase, in contact with a highly concentrated salt solution, when the dissociation fraction approaches zero. However, making such an electrolyte solution may be impossible for many salts because of the limit imposed by the salt solubility in water. Figure 6 shows the values of the dissociation fraction of Na(AOT) for a system in which different cations are added. This figure also contains the results for sodium shown as a solid line. The dissociation fraction for different monovalent and divalent cations approached that of sodium at higher water uptakes, which corresponds to lower salt concentrations. Under this condition, the system contains smaller amounts of added counterion and most of the surfactant head groups are engaged with sodium, the original surfactant counterion, either in bound or dissociated forms. Therefore, the behavior of the system approaches that of the Na(AOT)-NaCl system. The deviation from linearity for these cations is due to the presence of more than one counterion in the system. The values of w0•,i listed in

Counterion Binding

Figure 7. Water uptake as a function of equilibrium equivalents of cations in the aqueous phase for different cations: initial organic phase, 0.1 M AOT; initial aqueous phase, chloride salt. The data are from literature.37

Table 1 for different cations were obtained with a least-squares fit of eqs 20 and 21 to the results of Figure 6 and the ion distribution data. In principle, the value of w0•,i for any cation could have been obtained using a method similar to that of Figure 5 with the surfactant in the form of that cation instead of sodium. We performed experiments with the potassium form of surfactant to verify the assumption of having the same R for any counterion. As shown in Figure 5, the dissociation fraction results of K(AOT)-KCl as a function of the logarithm of water uptake also follows a linear relation with a slope very close to that obtained for Na(AOT)-NaCl, which validates our assumption. The values of the parameters R and w0•,K then were obtained as 7.67 and 4.63 from the results of the K(AOT)KCl system. It is interesting to note that the value of w0•,K ) 4.63 is also very close to the value (4.7 in Table 1) obtained from the results of the Na(AOT)-KCl system. 3.2.2. Water Uptake Predictions. At this stage, having determined the water uptake parameters, the complete set of equations, including eqs 20 and 21, can be used to calculate the dissociation fraction and the water uptake. Thus, there is no need to use the experimental water uptake data for prediction of the dissociation fraction. The calculated and experimental water uptake results are presented in Figure 7 for some monovalent and divalent cations. The calculated results shown as solid lines reproduce the experimental results within 0.52%. Since the water uptake is well represented by the model, the results we obtained for the dissociation fraction, using the complete set of equations, followed closely the results of Figures 2 and 3 for the different cations. The results of Figures 2 and 3 were obtained using the experimental water uptake data. It is interesting to note that poorest predictions shown in Figure 7 are for Ba, which, in turn, has the lowest water uptake. In fact, the assumption of a head group area As of 55 Å2 for AOT may be questionable at such a low water uptake. The predictions of the present model were compared with the previously published37 results of water uptake for the system of AOT-isooctane-NaCl-KCl-water for different conditions of the initial surfactant, NaCl, and KCl concentrations and of the initial volume ratio of the phases. An excellent agreement was obtained. For the sake of comparison, two sets of results are shown in Figure 8. This figure shows the water uptake as a function of surfactant concentration for different KCl concentrations. No NaCl was added initially, and the initial volume ratio was unity. The predictions of the model, shown as solid lines, are in a very good agreement with the experimental data. It was previously found29,37 that the water uptake (in moles of

J. Phys. Chem. B, Vol. 101, No. 49, 1997 10301

Figure 8. Water uptake as a function of surfactant concentration for different initial KCl concentration: initial organic phase, AOT; initial aqueous phase, KCl. The lines are the predictions of the present model. The data are from literature.37

Figure 9. Radius of the water pool as a function of equilibrium equivalents of cations in the aqueous phase for different cations: initial organic phase, 0.1 M AOT; initial aqueous phase, chloride salt. The lines are the predictions of the present model. The points are the calculations from literature.31

water per mole of surfactant) does not change with the AOT concentration in the presence of sodium salt. However, as shown in Figure 8, the water uptake is not constant and increases with the surfactant concentration for any initial KCl concentration. It is important to note that this system is a mixedcounterion system of sodium and potassium, since sodium is the original surfactant counterion. Owing to the ion exchange of potassium with the sodium of the surfactant, changing the surfactant concentration causes a redistribution of cations between the two phases. Thus, some of the surfactant molecules at the reverse micellar interface are in potassium form and some in sodium form. Therefore, the nature of the surfactant is changed, and this determines both the dissociation fraction and water uptake. 3.3. Size of the Reverse Micelles. The reverse micellar sizes calculated from eq 21 with the numerical results of water uptake shown in Figure 7 are presented in Figure 9. The calculated results shown in Figure 9 are in close agreement with the calculated results of Leodidis and Hatton,31 shown as solid circles in Figure 9. 4. Conclusions A simple model has been developed to predict the fraction of surfactant dissociated at the reverse micellar interface, the water uptake, and the size of the reverse micelles. The results of the model showed that the dissociation fraction and the water uptake had no effect on the overall ion distribution between

10302 J. Phys. Chem. B, Vol. 101, No. 49, 1997 the two phases. Therefore, the ion distribution calculations can be done assuming that all the surfactant molecules at the reverse micellar interface are bound to either the original surfactant counterion or other counterions. The present model predicts accurately the experimental results of water uptake and gives a good representation of the size of the reverse micelles. Acknowledgment. The authors are grateful to the Natural Sciences and Engineering Research Council of Canada for financial support. References and Notes (1) Haering, G.; Luisi, P. L.; Hauser, H. J. Phys. Chem. 1988, 92, 3574. (2) McFann, G. J.; Johnston, K. P. J. Phys. Chem. 1991, 95, 4889. (3) Johnnsson, R.; Almgren, M.; Alsins, J. J. Phys. Chem. 1991, 95, 3819. (4) Jolivalt, C.; Minier, M.; Renon, H. In Downstream Processing and Bioseparation; Hamel, J. F. P., Ed.; ACS Symposium Series 419; American Chemical Society: Washington, DC, 1990. (5) Lang, J.; Lalem, N.; Zana, R. J. Phys. Chem. 1991, 95, 9533. (6) Jada, A.; Lang, J.; Zana, R.; Marhloufi, R.; Hirsch, E.; Candau, S. J. J. Phys. Chem. 1990, 94, 387. (7) Verbeeck, A.; Voortmans, G.; Jackers, C.; De Schryver, F. C. Langmuir 1989, 5, 766. (8) Sjo¨blom, J.; Skurtveit, R.; Saeten, J. O.; Gestblom, B. J. Colloid Interface Sci. 1991, 141, 329. (9) Eastoe, J. Langmuir 1992, 8, 1503. (10) Lang, J.; Mascolo, G.; Zana, R.; Luisi, P. L. J. Phys. Chem. 1990, 94, 3069. (11) Ninham, B. W.; Chen, S. J.; Evans, D. F. J. Phys. Chem. 1984, 88, 5855. (12) Jolivalt, C.; Minier, M.; Renon, H. J. Colloid Interface Sci. 1990, 135, 85. (13) Krei, G. A.; Hustedt, H. Chem. Eng. Sci. 1992, 47, 99. (14) Brandani, V.; Giacomo, G. D. Process Biotechnol. 1993, 28, 411. (15) Hano, T.; Ohtake, T.; Matsumoto, M.; Kitayama, D.; Hori, F.; Nakashio, F. J. Chem. Eng. Jpn. 1991, 24, 20. (16) Wang, W.; Weber, M. E.; Vera, J. H. J. Colloid Interface Sci. 1994, 168, 422. (17) Rabie, H. R.; Weber, M. E.; Vera, J. H. J. Colloid Interface Sci. 1995, 174, 1.

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