Counterion Binding and Regulation of Interactions between Charged

Oct 3, 1996 - Constant potential interactions apply to an unpolarizable surface whose .... was measured using the beam-line at LURE, Université Paris...
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J. Phys. Chem. 1996, 100, 16268-16274

Counterion Binding and Regulation of Interactions between Charged Bilayers Heather N. Patrick and Gregory G. Warr* Department of Chemistry, The UniVersity of Sydney, NSW 2006, Australia ReceiVed: April 22, 1996; In Final Form: July 8, 1996X

Interactions between didodecyldimethylammonium (DDA) bilayers were measured using osmotic stress in the presence of bromide and chloride as mixed electrolyte. DDA bromide exhibits a discontinuity in its force curve, corresponding to a coexistence region in the DDAB/water phase diagram, whereas DDA chloride has a continuously repulsive interaction profile. Mixed electrolyte systems, interacting at constant electrolyte chemical potential, also display demixing. The selective binding of bromide and chloride in lamellar phases has been measured as a function of interlamellar separation and compared with selective binding to the air/ solution interface. A site-binding model was used to interpret the selective binding and osmotic stress results and suggests that these bilayers interact at constant potential.

Introduction The interaction between charged surfaces in aqueous solution is the central problem of colloid chemistry. Analysis of colloidal interactions is usually done using the DLVO theory which accounts for the effects of formation of an electrical doublelayer and dispersion force interactions.1,2 For like surfaces these two effects are of opposite sign, repulsive electrostatics being opposed by attractive dispersion forces. DLVO descriptions of the electrostatic interaction between charged surfaces usually employ one of two approximations: constant surface potential or constant surface charge as a function of surface separation. These convenient boundary conditions apply in principle to different types of surface. Constant potential interactions apply to an unpolarizable surface whose surface potential is set by the concentration of a potentialdetermining ion, as is the case for silver iodide sols.3 The constant charge interaction should apply to surfaces where the density of charged groups is fixed. However, this situation can never really arise, as it leads to a divergence in the osmotic pressure between the surfaces as their separation approaches zero. Nevertheless, it is a convenient upper limit for the strength of the electrostatic interaction between surfaces of known (isolated) surface charge density. For oxides and other ionizable surfaces, the hydrolysis reactions which give rise to surface charge have been considered as a mechanism for “charge regulation” as two surfaces approach.4 In any real chemical system the effect of ion binding or condensation should be considered, and hydrolysis in oxides may be regarded as a particular case of an ion binding equilibrium. In this work we are concerned with the binding of counterions to charged surfaces and the effect that competition between two counterions has on interactions between such surfaces. Two experimental techniques are widely used to measure interactions between like surfaces. These are surface force measurements using cleaved mica sheets and osmotic stressing. Recent work has demonstrated the equivalence of these two techniques for determining interactions between dihexadecyldimethylammonium acetate bilayers.5 The interactions between dihexadecyldimethylammonium acetate bilayers could be described by the equations of DLVO theory using the same parameters whether the bilayers were adsorbed on mica (measured using the surface force apparatus) or unsupported X

Abstract published in AdVance ACS Abstracts, September 1, 1996.

S0022-3654(96)01157-4 CCC: $12.00

(measured by osmotic stressing). Osmotic stressing showed additionally that strong hydration forces occur between planar bilayers below 8 Å surface separations, but this was not evident in the crossed cylinder geometry of the surface force apparatus. Lamellar phases, consisting of periodically spaced, stacked bilayers of surfactant, thus provide an ideal model system for investigating the interactions between planar surfaces and the effects of counterion binding. This work is concerned with the effect of ion binding and ion exchange equilibria on the interactions in didodecyldimethylammonium bromide and chloride lamellar phases. The behavior of didodecyldimethylammonium bromide (DDAB) in water is well characterized.6-11 Phase diagrams show the formation of two lamellar phases at room temperature separated by a broad coexistence region. Osmotic stressing experiments have demonstrated that the stability of charged bilayers in the lamellar phase at high water concentrations is governed by electrostatic forces which scale as expected with added electrolyte. Didodecyldimethylammonium chloride (DDAC) has been studied less often than the bromide salt. However, in common with other counterions and valencies (hydroxide or sulfate), only a single lamellar phase occurs in the DDAC/water system.12-14 A simple electrostatic treatment is obviously insufficient to understand this phenomenon. Counterion-specific effects must be implicated. In fact, the coexistence of lamellar phases is rare. Coexisting lamellar phases have been observed previously for bis(2ethylhexyl) sulfosuccinate in the presence of two counterions, sodium and calcium,15 in the binary system sodium dodecyl5-p-benzenesulfonate in water,16 and in lecithin.17 Ion-specific effects in the interactions between bilayers have been seen previously. When bromide ions are added to adsorbed dihexadecyldimethylammonium bromide bilayers, they behave as though their surface charge density is substantially reduced.18 However, osmotic stressing provides particular insight in that it allows the unusual phenomenon of coexisting lamellar phases to be studied. There are several ways to apply osmotic stress to aqueous samples, as described by Parsegian et al.19 Our chosen method is that used by Dubois and Zemb,8 in which poly(ethylene glycol) solutions are allowed to equilibrate with a lamellar phase sample across a semipermeable membrane. The final equilibrium interlamellar separations have been measured using a convenient proton NMR technique which was later confirmed © 1996 American Chemical Society

Counterion-Specific Interactions between Bilayers with small-angle X-ray scattering measurements. A unique feature of this work is that the bilayers are equilibrated against a reservoir containing known concentrations of two competing counterions, chloride and bromide. The reservoir is in excess and does not change in ionic strength during equilibration. Thus, the chemical potentials of the counterions are fixed, and the effect of competitive ion binding on equilibrium spacing can be determined. In addition, individual ion concentrations in the stressing solution and lamellar phase are measured directly to determine the effect of surface separation on ion exchange equilibrium. This is not possible in the surface force apparatus, as the adsorbed bilayers are immersed in the equilibrium solution. The singular behavior of bromide with the didodecyldimethylammonium ion leads us to study ion-specific effects. We are interested in the role of counterion condensation or specific binding in the behavior of lamellar phases. DDAB and DDAC have different phase behavior, and it is not known how they behave when mixed. Their ternary phase behavior has been studied and competition inside the lamellar phase examined in the osmotic stressing experiment. Experimental Section Chemicals. Didodecyldimethylammonium bromide (DDAB, Eastman) was recrystallized twice from a diethyl ether/acetone mixture. Didodecyldimethylammonium chloride (DDAC) was prepared by ion exchange using Amberlite IRA-400 ion exchange resin (Aldrich) in the hydroxide form. DDAB was dissolved in a warm water-methanol (10:90 v/v) solution and the resin was added, stirred, allowed to stand, and then filtered. Hydrochloric acid (5 M) was added to the filtrate until neutralization was detected by pH measurements. The resultant solution was evaporated and then freeze-dried to yield a white powder. Ion chromatography indicated there was less than 2% bromide content. Optical Microscopy. Identification of a lamellar phase was made by polarizing optical microscopy and inspection through crossed polarizing filters. These are described elsewhere.8 The lamellar phase is clear, viscous, and optically birefringent and gives a characteristic “Maltese cross” pattern in the polarizing optical microscope. The two-phase region is turbid. To study phase behavior, samples were kept at 20 °C in sealed test tubes and progressively diluted. Osmotic Stressing. Osmotic stressing of the lamellar phase was achieved by equilibration at 20 °C of surfactant samples inside dialysis membranes against reservoirs of known osmotic pressure. The reservoirs contained poly(ethylene glycol) (PEG, Sigma Chemicals, MW 8000). The applied osmotic pressure was calculated from the mass of polymer used and the following relation:20

Π (atm) ) -1.29G2T + 140G2 + 4G where G ) (mass of PEG)/(mass of water), 0 e G e 0.8 and 5 < T < 40 °C. The chemical potential of salt inside the lamellae was set by the ionic strength of the reservoir solution. The salts used were potassium bromide and potassium chloride (Merck, AR). Equilibration of the samples took several weeks during which the reservoirs were changed regularly. The final equilibrium repeat spacings of the lamellae were determined by proton NMR spectroscopy. Ion concentrations inside the lamellae and in the reservoirs were determined by ion chromatography. In order to ensure that equilibrium was reached in mixed ion systems, lamellar phase samples of differing initial compositions were used. For example, 1:1 KBr:KCl solutions were equilibrated against solid DDAB, weight percent DDAB, and 4:1 solid DDAB:DDAC.

J. Phys. Chem., Vol. 100, No. 40, 1996 16269 Proton NMR Spectroscopy. A proton NMR technique was developed to measure interlamellar spacings. The integrated proton resonances of both the surfactant hydrocarbon chain and those of water were used to determine the ratio of surfactant to water. Acetone-d6 was used as a lock signal. About 0.2 g of the sample was diluted in the NMR tube with about 0.4 mL of acetone (AR, Merck), before 0.05 mL of acetone-d6 (Cambridge Isotope Laboratories) was added. Dilution was necessary to break up the viscous lamellar phase. The amount of water present in the acetone was negligible. Spectra were recorded on a Bruker AC200 NMR spectrometer operating at a proton resonance frequency of 200 MHz. Samples were analyzed at 300 K for 128 scans and a zero relaxation delay. Fifty-two of the 56 surfactant proton resonances were integrated due to the large acetone resonance obscuring some of the signal. Acetone was chosen over ethanol since it had only one singlet resonance. The ratio of surfactant to water allowed the volume fraction of surfactant to be calculated from molar volumes. Previous studies9 of the lamellar phase has shown a relationship between the repeat spacing, D*, and the volume fraction of surfactant, φ:

D* ) t/φ

(1)

where t is the thickness of the bilayer. The thickness was taken to be 24 Å10 although it has been seen to vary slightly at pressures above 106 Pa. (Zemb, T., personal communication). The relationship between the repeat spacing and volume fraction was confirmed in our SAXS studies. Small-Angle X-ray Scattering. Small-angle X-ray scattering was measured using the beam-line at LURE, Universite´ ParisSud. The monochromator was Ge 111, and the sample to detector distance was 113 cm. The accessible q range was 0.01-0.26 Å-1. Small-angle X-ray scattering was used to confirm the repeat spacings measured by the proton NMR technique as well as refine the phase boundaries observed for the ternary DDAB-DDAC-water system. Samples were studied at 21 °C. Samples of pure DDAB and DDAC and mixed samples in water were studied. Single-phase samples gave a characteristic peak and at least one second-order peak. Two-phase samples gave two peaks, with their intensities in proportion to the amount of that phase present. Ion Flotation. Ion flotation was used to determine the selectivity of one ion over another at an isolated surfactant solution/air interface. The surfactant solution (900 mL) and added salt were foamed inside a glass flotation column by the injection of nitrogen gas through a porous frit at the base. As the experiment progressed, foam was produced and expelled from the top of the column. The bulk solution was sampled with a syringe and hollow needle. The ion concentrations of these samples were determined by ion chromatography. Selectivity coefficients were determined using21 Br log[Br-] ) KCl log[Cl-] + C

(2)

where C depends on initial concentrations. Details of the apparatus and analysis are presented elsewhere.21 The concentration of DDAB was 5 × 10-5 M, which is below the cmc. Equimolar potassium chloride was present in the bulk solution. The data were rendered as a log-log plot of bromide and chloride concentrations. The slope obtained by linear regression gives the selectivity coefficient for bromide Brover chloride, KCl - , at 25 °C. Ion Chromatography. Ion concentrations in the stressing reservoir and inside the lamellar phase were determined by ion chromatography. The samples of bulk solution from the flotation experiments, lamellar samples, and stressing reservoir

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Patrick and Warr

Figure 1. Ternary phase diagram of DDAB/DDAC/water at 20 °C, showing the lamellar phase, LR, and a two-phase region with tie lines determined from experimental selectivity coefficients. The dashed line indicates the general shape of the phase boundary which could not be determined precisely at low water contents.

solutions were analyzed using a Dionex DX-100 ion chromatograph fitted with AS-4 analytical anion exchange columns and a Hewlett-Packard integrator. The detector response was linear in the concentration range studied. Samples from ion flotation were injected directly onto the column. Stressing reservoir samples were diluted and filtered (Centriflo concentrators, 3000 MW cutoff, Amicon) prior to injection. Lamellar phase samples were also diluted prior to injection with potassium nitrite added as an internal standard.

Figure 2. Osmotic pressure, Π, versus interlamellar separation, D, at 20 °C for DDAB/water with KBr in the reservoir at two concentrations: (a) 1 × 10-3 and (b) 1 × 10-2 M. Open symbols are from ref 10. (s) Calculated constant potential interaction for a fully ionized film. (- -) Interaction for a 90% neutralized film. (- - -) Interaction for a 90% neutralized film using A ) 7 × 10-20 J.

Results and Discussion Ternary-Phase Behavior. The isothermal ternary-phase behavior of the system DDAB/DDAC/water was investigated by optical methods and by SAXS at 20 °C, and the results are shown in Figure 1. The binary DDAB/water phase behavior is described along the right-hand water/DDAB axis. Above 75 wt %, a single concentrated lamellar phase forms with spacings below 7 Å. Between 28 and 75 wt %, the system is biphasic, with coexisting lamellar phases separated by 65 and 7 Å. Below 28 wt %, a (swollen) lamellar phase exists. The separation between these lamellae increases as the surfactant concentration decreases. Upon dilution of this phase a maximum swelling is eventually realized at 3 wt %.8 Below this concentration a twophase region consisting of bilayer vesicles dispersed in an aqueous DDAB solution is formed. The maximum concentration of DDAB achievable in water without bilayer formation is approximately 5 × 10-4 M. The behavior of DDAC in water is shown along the lefthand water/DDAC axis. A single lamellar phase forms over the concentration range 18-90 wt %13,14 with separations decreasing from 300 to 7 Å as the surfactant concentration increases. DDAC does not form a two-phase region, nor do DDA+ bilayers with the counterions hydroxide, acetate, or sulfate.12-14 Below 18 wt %, DDAC forms a vesicle dispersion, that is, a lamellar phase which coexists with a dilute solution of fully dissolved DDAC. Light scattering experiments indicate that the maximum concentration for this solution is 0.18 mM.12 The lower axis of Figure 1 represents the fraction of DDAB in the DDAB/DDAC mixture. Addition of chloride to the DDAB/water system is represented by moving across the diagram toward the DDAC/water axis. The two-phase coexistence region forms a lobe which extends out into the ternaryphase diagram from the DDAB/water axis. This region shrinks abruptly as chloride is added until only a single lamellar phase is observed once the DDAC to DDAB ratio exceeds 1.5. This value approximately corresponds to the mole ratio of chloride to bromide.

Figure 3. Osmotic pressure, Π, versus interlamellar separation, D, at 20 °C for DDAC/water with no added salt. (s) Calculated constant potential interaction for a fully ionized film. (- -) Interaction for a fully ionized film with A ) 7 × 10-20 J.

There is clearly some specific effect in the behavior of bromide and chloride manifest in the phase behavior which is beyond electrostatics. At the interlamellar separations where demixing occurs, the major interaction is electrostatic, and hence an ion-specific adsorption effect is most probable. In the following sections we detail the counterion binding behavior of the two competing ions. Force-Distance Isotherms. 1. The DDAB and DDAC Systems. Figures 2 and 3 show the osmotic stressing isotherms for DDAB and DDAC lamellar phases in various electrolytes. DDAB was examined with added potassium bromide in the reservoir at two concentrations, 1 × 10-3 and 1 × 10-2 M, while DDAC was stressed with no added salt. The DDAB data show a discontinuity between separations of 8 and 65 Å, indicated by the shaded region. This corresponds to two-phase coexistence in DDAB/water systems (see Figure 1). In the osmotic pressure isotherm, compression of the lamellae above a critical pressure causes them to jump from a swollen state to a smaller spacing, i.e., the concentrated lamellar phase. This behavior is observed in DDAB equilibrated with both 1 × 10-3 and 1 × 10-2 M KBr as well as in water but is

Counterion-Specific Interactions between Bilayers

J. Phys. Chem., Vol. 100, No. 40, 1996 16271

Figure 4. SAXS spectrum of 4 wt % DDAB at 20 °C showing four orders of peaks.

not present in DDAC at any of the pressures examined. The osmotic pressure isotherm shows a continuous, repulsive interaction at all spacings. Also shown in Figure 2 are the data of Dubois et al. at lower pressures10 for DDAB lamellae with the spacings measured by SAXS. The overlap between the two sets of results shows good agreement between spacings measured by SAXS and the NMR technique. Total pressure is modeled as a sum of three contributions. In addition to the conventional DLVO description as the sum of electrostatic and van der Waals contributions, we include a short-range hydration repulsion. A hydration interaction has often been shown to be necessary to describe effects in lamellar phases at small spacings and is necessary here to describe phase separation even qualitatively.5,22

Πtot ) Πelec + ΠvdW + Πhyd

(3)

The interacting surfaces are assumed to be perfectly flat, charged plates, with the ions treated as point charges. The osmotic pressure, Π, is taken as the derivative of the interaction potential per unit area, V, with respect to the separation D:

Π ) dV(D)/dD The other interactions often included in descriptions of bilayers are membrane elasticity effects. Most important among these are membrane compressibility23 and the fluctuation force.24 SAXS results exhibit several orders of diffraction indicating a high degree of order in DDAB and DDAC lamellar phases. An example is shown in Figure 4. This, together with previous work showing excellent agreement between surface force apparatus measurements on supported bilayers and osmotic stressing results for similar systems,5 leads us to conclude that fluctuation interactions are not significant. The hydration force is described by5

Πhyd ) 108.32e-D/λ

(4)

where λ ) 2.6 Å is the decay length of the interaction. This has been determined for numerous bilayer systems,5 and we assume that it is the same for both DDAB and DDAC. The attractive contribution for thin films separated by water is

ΠvdW )

{

1 -A 1 2 + 6π (D* - t)3 D*3 (D* + t)3

}

The electrostatic interaction between two charged, flat plates was calculated using a numerical solution to the nonlinear Poisson-Boltzmann equation. (For this we used a program kindly provided by D. Y. C. Chan, University of Melbourne.28) The calculated osmotic pressures for surfaces interacting at constant potential are shown as solid lines in Figures 2 and 3. The reasons for using this boundary condition are discussed below. The DDAC/water system is well described using a surface charge density of 1/68 Å2 per charge, corresponding to full ionization of the surfactant film (Figure 3). The surface charge density was obtained from the molecular area of DDAB, determined from X-ray diffraction data.10 The Debye length (78 Å) corresponds to an ionic strength of 1 × 10-3 M, giving an isolated surface potential of 245 mV. The results are relatively insensitive to this concentration, which, although higher than the expected monomer concentration,12 is a reasonable estimate of background electrolyte concentration. The behavior of the DDAB systems (Figure 2) also seems to be well described by treating them as fully ionized surfactant films. (The line goes through the data points.) At large separations, the fit is consistent with the expected Debye lengths for these systems: 78 Å for 1 × 10-3 M and 30 Å for 1 × 10-2 M. However, this model produces a fully repulsive compression curve inconsistent with the observed demixing. In previous work on the DDAB system, Dubois et al. regarded the surface charge density as substantially reduced by counterion binding.10 This is consistent with earlier work by Pashley et al. using the surface force apparatus to examine the effect of added bromide on the interactions between dihexadecyldimethylammonium bilayers adsorbed onto mica. They found that the forces could be described by a constant charge interaction with the surface charge approximately 90% neutralized by bound bromide ion.18 Figure 2 shows the calculated interactions for the DDAB system with the surface charge density reduced to 1/680 Å2, or 90% surface neutralization by bound bromide. For the DDAB/ water/KBr system, surface potentials were correspondingly reduced to 119 mV for 1 × 10-3 M salt and 73 mV for 1 × 10-2 M salt. As Figure 2 demonstrates, this makes little difference to the quality of the fit to the 1 × 10-3 M data at large separations. The electrostatic interactions are relatively insensitive to surface charge density at such high surface charge densities. The key feature that reducing the charge density attempts to model is the demixing, which requires an attractive component to the overall interaction. Reduction of the surface charge density does make the dispersion attraction more significant, but not enough to cause demixing. This may be seen in Figure 2 (dashed line) which shows a continuously repulsive Πtot(D) at both ionic strengths. In order to achieve demixing, Zemb et al. contrived a stronger attraction by inflating the Hamaker constant from 5 × 10-21 5,18,26,27 to 7 × 10-20 J.9 This successfully predicts the observed demixing into two lamellar phases reasonably well according to a Maxwell construction

∫DD (Πtot - Π*) dD ) 0 2

1

(5)

where A is the unretarded Hamaker constant1 and t ) 24 Å the thickness of the surfactant bilayers.10 A is taken to be 5 × 10-21 J, based on calculations for a C12 hydrocarbon chain interacting across water.25 This value is similar to that used for dihexadecyldimethylammonium bilayers,18,5 monoglyceride bilayers,26and egg lecithin bilayers.27

where Π* is the demixing pressure and D1 and D2 are the lamellar spacings of the coexisting phases. Calculated Πtot(D) using the inflated Hamaker constant are shown for DDAB in Figure 2. It can be seen that phase separation would occur in both 1 × 10-3 and 1 × 10-2 M electrolyte cases. It was mentioned above that the elastic energy associated with bilayer compressibility has been neglected in modeling the

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Patrick and Warr

Figure 5. Osmotic pressure versus interlamellar separation for DDAB/ water with the reservoir at a concentration of 1 × 10-3 M. Different symbols correspond to different KBr:KCl ratios in the reservoir.

Figure 6. Osmotic pressure versus interlamellar separation for DDAB/ water with KBr:KCl ) 1 in the reservoir at a concentration of 1 × 10-2 M.

osmotic stress data. Although not a component of the conventional DLVO interaction, lateral compressibility has been shown to be important in understanding didodecyl phosphate lamellar phases.23 In particular, a re-entrant phase transition between lamellar phases with liquidlike (LR) and crystalline (Lβ) chains has been reported, although without a coexistence region on the scale of the present systems. If such effects were present in the DDAB/DDAC systems, then two-phase coexistence at a critical osmotic pressure would also be observed, yielding an apparent attraction between the surfaces. A recent detailed statistical mechanical model of bilayers incorporating alkyl chain elasticity does predict demixing into dilute and concentrated phases.29 How such effects may couple to counterion binding is not yet understood. Although the origin of the attraction is still not known, these results identify the demixing as being a consequence of the strong binding of bromide ions to the charged surfactant bilayers. Figure 3 shows this clearly, where even the large Hamaker constant does not cause a net attraction between fully ionized bilayers, consistent with the experimental observation of a single lamellar phase. The difference between DDAB and DDAC is, in this interpretation, just a difference in counterion binding. 2. Mixed Bromide + Chloride Systems. The effect of ion competition was examined by equilibrating lamellar phases against a stressing solution containing a known concentration of mixed electrolyte, KCl and KBr. Force versus distance isotherms for various Br:Cl ratios at total electrolyte concentrations of 1 × 10-3 and 1 × 10-2 M are shown in Figures 5 and 6, respectively. Mixed counterion systems show the same sequence of phases in the osmotic stressing experiments as the binary DDAB/water systems. As can be seen, the behavior of all systems containing bromide is very similar to that of the pure bromide systems (Figure 2). Moreover, a two-phase region was found for all samples containing bromide. The concentration region of the existence of two phases was reduced in size on the addition of salt and was also reduced when more chloride was added. The two-phase regions for different concentrations are shown as a discontinuity in the interlamellar spacing in Figures 5 and 6. The striking feature of these isotherms is that bromide/ chloride mixtures which lie within the single-phase region of the DDAB/DDAC/water ternary-phase diagram exhibit demixing. This provides strong evidence for selective uptake of bromide into the lamellar phase from the reservoir, and therefore indirect evidence of selective binding of bromide to DDA+ films, supporting the results of Pashley et al.18 and aspects of Dubois’ interpretation of ion binding.10 Measurement of Selective Counterion Binding. In the osmotic stressing experiment, a sample of the surfactant is allowed to equilibrate across a semipermeable membrane with an aqueous polymer solution, in this case poly(ethylene glycol). The polymer prescribes the osmotic pressure in the lamellar

phase. For our purposes this stressing solution also contains one or two electrolytes at known concentrations and hence fixed chemical potentials. We can define and measure a selectivity coefficient that describes the relationship between the concentrations of two counterions in the bulk reservoir and in the lamellar phase as follows. The electrochemical potentials of counterions in the lamellar phase and in the bulk reservoir must be equal for equilibrium. For the counterion bromide we have -

-

µ˜ LBrR ) µ˜ Br aq

(6)

where LR represents the lamellar phase and aq the reservoir. At equilibrium, the electrochemical potential of bromide at any point in the lamellar phase is -

-

+ RT ln[Br-]LR - Fψ µ˜ LBrR ) µL°,Br R

(7)

where ψ is the electrical potential. In the reservoir -

-

µ˜ LBrR ) µ°aq,Br + RT ln[Br-]aq

(8)

Setting these two equations to be equal gives

[Br-]aq °,Br ) RT ln µ + Fψ µL°,Br aq R [Br-]LR

(9)

Similarly, for chloride

[Cl-]aq °,Cl - µ°,Cl ) RT ln + Fψ µLR aq [Cl-]LR

(10)

The standard free energy change for the exchange of bromide and chloride between the reservoir and the lamellar phase is therefore

∆G° ) RT ln

[

]

[Cl-]aq[Br-]LR

[Cl-]LR[Br-]aq

(11)

Experimentally we measure the concentrations of both chloride and bromide in the lamellar and reservoir phases. These can be used to calculate a selectivity or ion exchange Br , for bromide and chloride: coefficient, KCl

K)

[Cl-]aq[Br-]LR [Cl-]LR[Br-]aq

(12)

This quantity describes whether one ion or the other is Br selectively taken up by the lamellar phase. In principle, KCl

Counterion-Specific Interactions between Bilayers

J. Phys. Chem., Vol. 100, No. 40, 1996 16273 specifically bound ions, there is a nonspecific diffuse layer of charge in solution between the bilayers, and the selectivity coefficient reports an average uptake over specifically and electrostatically bound ions. This has been discussed more fully elsewhere.30 Specific binding of bromide and chloride to DDA+ bilayers can be described by a site-binding model involving the formation of a 1:1 complex between surfactant and counterion, similar to a Langmuir adsorption isotherm.

A-aq + S+ ) ASsurface -

B-aq + S+ ) BSsurface

Br + Figure 7. Determination of KCl monolayer at - for an isolated DDA the air/solution interface from ion flotation (at 25 °C).

may be affected by interactions between adjacent charged bilayers and hence a function of separation of the lamellae. Once the lamellar surfaces are at a large separation, say greater than 2κ-1 apart, we may treat them as noninteracting. We then assume each to behave similarly to an isolated surfactant monolayer. A surfactant-coated air/water interface is an example of such an isolated interface, and ion selectivity can be determined using ion flotation.21 The selectivity coefficient in this case is defined in terms of an exchange of two monovalent counterions between the bulk and the interface as follows.

Br-bulk + Cl-interface ) Br-interface + Cl-bulk This is identical to the situation in a highly swollen lamellar phase, in that the surface excess of each counterion must electrically neutralize the charge on the surfactant film. The selectivity coefficient for this exchange process is expressed in terms of the bulk concentration and the surface excess, Γ, as BrKCl -

)

ΓBr-[Cl-] ΓCl-[Br-]

(13)

The equilibrium constants for ion binding are

KAeeψ0/kT )

-

, KBeeψ0/kT )

[A ]ΓS+

ΓBS [B-]ΓS+

(14)

where Γ denotes surface concentration of the surfactant ion or surfactant-counterion complex, and the concentrations refer to the equilibrium concentrations in the reservoir. Ψ0 is the surface potential, and the Boltzmann factor is necessary to relate the reservoir concentrations to those at the bilayer surface. The equilibrium constant (eq 12) is calculated by integrating the ion concentrations in the diffuse layer. Γ, the total surface concentration of one ion in the lamellar phase, is made up of two contributions:

ΓA- ) ΓAS + ∫0 [A-]eeψ(x)/kT dx D/2

(15)

The integral out to D/2 arbitrarily assigns the ion to its nearest surfactant layer. The experimentally measured selectivity coefficient may therefore be written in terms of site-binding equilibria as

KAB )

Br-

A KCl- value greater than 1 indicates that bromide is found adsorbed at the interface more so than chloride. Ion flotation was used to determine the selectivity coefficient for competing bromide and chloride ions at the isolated DDA+ interface using eq 2. The selectivity coefficient was found to be 3.10 ( 0.77, as shown in Figure 7. This agrees with measurements using cetyltrimethylammonium with bromide and chloride anions, Br21 where KCl - was found to be 3.05 ( 0.15. The selectivity coefficient for the lamellar phase and reservoir was determined using eq 12 by direct measurement of bromide and chloride ion concentrations in the lamellar phase and reservoir by ion chromatography. Figure 8 shows the selectivity coefficient as a function of the separation between the lamellar surfaces, determined for a wide range of Br-:Cl- ratios in the reservoir. Also shown for comparison is the value obtained by ion flotation. The value of the selectivity coefficient is close to that at an isolated surface and is independent of interlamellar separation or on reservoir composition. The mean value for K over all interlamellar separations was 3.05 ( 2.50. The selectivity constants found both in the swollen lamellar phase and in the condensed lamellar phase samples are identical within experimental uncertainty. There is, therefore, no difference in Br-:Cl- ratio between coexisting swollen and condensed lamellar phases. The tie lines shown in Figure 1 illustrate this: Br-:Cl- is equal in the two coexisting phases. The selective uptake of ions into the lamellar phase is not a direct measure of specific binding. In addition to

ΓAS

)

[A-]ΓBΓA-[B-] KBeeψ0/kT + C/ΓS+ KAeeψ0/kT + C/ΓS+

(16)

where C is the Boltzmann term describing the electrostatic surface excess,

C ) ∫0 eeψ(x)/kT dx D/2

and ΓS+ is the surface density of surfactant ions (surface charge density). It is equivalent to express ions in the lamellar phase either as a ratio of concentrations or surface concentrations, as KAB is dimensionless. However, surface concentration is more convenient for this model. Electroneutrality requires that the surface excesses of counterions exactly balance the (uncomplexed) surfactant ions:

ΓS+ ) C([A-] + [B-])

(17)

C/ΓS+ ) ([A-] + [B-])-1 ≡ I-1

(18)

Hence

where I is the ionic strength (in the reservoir). This eliminates the need to determine the surface charge density or to know the potential distribution. Equation 8

16274 J. Phys. Chem., Vol. 100, No. 40, 1996

Patrick and Warr selectively adsorbed into the lamellar phase, causing demixing even at quite low bromide content. The binding of bromide, and the competitive binding of bromide and chloride, are consistent with a site binding model which predicts a selective binding constant independent of Brsurface separation. The constant value of KCl - ) 3.1 at all separations suggests that these surfaces interact effectively at constant surface potential. The measured binding constant in the lamellar phase agrees with a determination of binding to an isolated film at the air/solution interface.

-

Br Figure 8. The dependence of the selectivity coefficient, KCl - , on interlamellar separation for DDA+ and the counterions Br- and Cl-, Brat 20 °C. The solid line with shading shows KCl - ) 3.10 ( 0.77 for an + film determined from ion flotation experiments. isolated DDA

becomes, in the site binding model,

KAB )

IKBeeψ0/kT + 1 IKAeeψ0/kT + 1

(19)

The measured selectivity coefficient depends on ionic strength in the reservoir, which is constant for a particular compression isotherm, and on surface potential. If the surfaces interact at constant surface potential, as we have assumed in Figures 2 Brand 3, then KCl - will be independent of interlamellar separation, D. This agrees with our experimental observation (Figure 8). Previous work has concluded that adsorbed bilayers interact with constant surface charge density.18 Although this is reasonable for the nonbinding acetate counterion, it is inconsistent with counterion binding. Both chloride and bromide ions do bind to surfactant films to some extent.31 This site binding model is similar in construction to a surface which generates charge by an acid-dissociation mechanism. Such surfaces have been used to develop charge regulation descriptions of electrostatic interactions.4,32 Previous work has shown that these systems behave more like constant potential than constant charge surfaces because, as the two surfaces approach, compaction of the diffuse layer tends to increase the degree of counterion binding. In the present system this lowers ΓS+ and hence the surface charge density, σ0. Both competing ions condense more onto the surfactant film as the surfaces approach each other, but the measured selectivity coefficient is only little affected. This simple model is sufficient to describe experimental ion selectivities and interactions between bilayers in mixed bromide/ chloride systems. Conclusions The interactions between didodecyldimethylammonium bilayers are dominated by the strong binding of bromide ions to the surfactant bilayers. Although we have not identified the source of the attraction which causes phase separation, it is the binding of bromide which attenuates electrostatic repulsion enough for demixing to occur. In mixed systems, bromide is

Acknowledgment. This work was funded by the Australian Research Council. The authors thank Dr. Pierre Lesieur of LURE for his assistance with SAXS experiments and also Prof. Derek Chan for providing the algorithm used to model the osmotic pressure data. References and Notes (1) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (2) Derjaguin, B. V.; Landau, L. Acta Physicochim. URSS 1941, 14, 633-662. (3) Hunter, R. J. Foundations of Colloid Science; Oxford University Press: Melbourne, 1986; Vol. 1. (4) Healy, T. W.; Chan, D.; White, L. R. Pure Appl. Chem. 1980, 52, 1207-1219. (5) Tsao, Y.-H.; Evans, D. F.; Rand, R. P.; Parsegian, V. A. Langmuir 1993, 9, 233-241. (6) Warr, G. G.; Sen, R.; Evans, D. F.; Trend, J. E. J. Phys. Chem. 1988, 92, 774-783. (7) Fontell, K.; Ceglie, A.; Lindman, B.; Ninham, B. Acta Chem. Scand. 1986, A40, 247-256. (8) Dubois, M.; Zemb, T. Langmuir 1991, 7, 1352-1360. (9) Zemb, Th.; Belloni, L.; Dubois, M.; Marcelja, S. Prog. Colloid Polym. Sci. 1992, 89, 33-38. (10) Dubois, M.; Zemb, T.; Belloni, L.; Delville, A.; Levitz, P.; Setton, R. J. Chem. Phys. 1992, 96, 2278-2286. (11) Gazeau, D.; Zemb, T.; Dubois, M. Prog. Colloid Polym. Sci. 1993, 93, 123-129. (12) Kunieda, H.; Shinoda, K. J. Phys. Chem. 1978, 82, 1710-14. (13) Kang, C.; Khan, A. J. Colloid Interface Sci. 1993, 156, 218-228. (14) Khan, A.; Kang, C. Prog. Colloid Polym. Sci. 1993, 93, 146-149. (15) Khan, A.; Jo¨nsson, B.; Wennerstro¨m, H. J. Phys. Chem. 1985, 89, 5180-5184. (16) Ockelford, J.; Timini, B. A.; Narayan, K. S.; Tiddy, G. J. T. J. Phys. Chem. 1993, 97, 6767-6769. (17) Knoll, W.; Schmidt, G.; Sackmann, E. J. Chem. Phys. 1983, 79, 3439-3442. (18) Pashley, R. M.; McGuiggan, P. M.; Ninham, B. W.; Brady, J.; Evans, D. F. J. Phys. Chem. 1986, 90, 1637-1642. (19) Parsegian, V. A.; Rand, R. P.; Fuller, N. L.; Rau, D. C. Methods Enzymol. 1986, 127, 400-416. (20) Michel, B. E. Plant Physiol. 1983, 72, 66-70. (21) Morgan, J. D.; Napper, D. H.; Warr, G. G.; Nicol, S. K. Langmuir 1994, 10, 797-801. (22) Parsegian, V. A.; Rand, R. P.; Fuller, N. L. J. Phys. Chem. 1991, 95, 4777-4782. (23) Fang, Y.; Rand, R. P.; Leikin, S.; Kozlov, M. M. Phys. ReV. Lett. 1993, 70, 3623-3626. (24) Helfrich, W. Z. Naturforsch. 1978, 33A, 305-315. (25) Hough, D. B.; White, L. R. AdV. Colloid Interface Sci. 1980, 14, 3-41. (26) Pezron, I.; Pezron, E.; Bergensta˚hl, B.; Claesson, P. M. J. Phys. Chem. 1990, 94, 8255-8261. (27) Parsegian, V. A.; Fuller, N.; Rand, R. P. Proc. Natl. Acad. Sci. U.S.A. 1979, 76, 2750-2754. (28) McCormack, D.; Carnie, S. L.; Chan, D. Y. C. J. Colloid Interface Sci. 1995, 169, 177-196. (29) Tsuchiya, M.; Tsujii, K.; Maki, K.; Tanaka, T. J. Phys. Chem. 1994, 98, 6187. (30) Warr, G. G. Langmuir, in press. (31) Morgan, J. D. P. Ph.D. Thesis, The University of Sydney, 1994. (32) Ninham, B. W.; Parsegian, V. A. J. Theor. Biol. 1971, 31, 405-428.

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