Lamellar Miscibility Gap in a Binary Catanionic Surfactant−Water

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J. Phys. Chem. B 2007, 111, 13520-13526

Lamellar Miscibility Gap in a Binary Catanionic Surfactant-Water System Bruno F. B. Silva,† Eduardo F. Marques,*,† and Ulf Olsson‡ Centro de InVestigac¸ a˜ o em Quı´mica, Department of Chemistry, Faculty of Sciences, UniVersity of Porto, Rua do Campo Alegre, n° 687, P-4169-007 Porto, Portugal, and Physical Chemistry 1, Centre for Chemistry and Chemical Engineering, Lund UniVersity, P.O. Box 124, SE-221 00 Lund, Sweden ReceiVed: August 7, 2007; In Final Form: September 17, 2007

The coexistence of two lamellar liquid-crystalline phases in equilibrium for binary surfactant-water systems is a rare and still puzzling phenomenon. In the few binary systems where it has been demonstrated experimentally, the surfactant is invariably ionic and the miscibility gap is thought to stem from a subtle balance between attractive and repulsive interbilayer forces. In this paper, we report for the first time a miscibility gap for a catanionic lamellar phase formed by the surfactant hexadecyltrimethylammonium octylsulfonate (TASo) in water. Synchrotron small-angle X-ray scattering, polarizing light microscopy, and 2H NMR unequivocally show the coexistence of a dilute (or swollen) lamellar phase, L ′, and a concentrated R (or collapsed) lamellar phase, LR′′. Furthermore, linear swelling is observed for each of the phases, with the immiscibility region occurring for 15-54 wt % surfactant. In the dilute region, the swollen lamellar phase is in equilibrium with an isotropic micellar region. Vesicles can be observed in this two-phase region as a dispersion of LR′ in the solution phase. A theoretical cell model based on combined DLVO and short-range repulsive potentials is presented in order to provide physical insight into the miscibility gap. The surfactant TASo is net uncharged, but it undergoes partial dissociation owing to the higher aqueous solubility of the short octylsulfonate chain. Thus, a residual positive charge in the bilayer is originated and, consequently, an electrostatic repulsive force, whose magnitude is dependent on surfactant concentration. For physically reasonable values of the solubility of the octyl chain, assumed to be constant with surfactant volume fraction, a fairly good agreement is observed between the experimental miscibility gap and the theoretical one.

I. Introduction The coexistence of two lamellar phases in equilibrium has been reported for a number of surfactant systems, which can be globally divided between binary or ternary systems. For ternary systems of the type surfactant-surfactant-water or polymer-surfactant-water, the phenomenon is relatively common because miscibility differences between the surfactants1-4 or between the surfactant and the polymer5-7 may give rise to individual lamellar phases in equilibrium. However, for binary surfactant-water systems, this is an extremely rare event and to some extent, a still puzzling one. It has been observed only for very few systems,8-12 with the didodecyldimethylammonium bromide (DDAB)-water system probably being the most well investigated one.9,13-17 Subtle changes in the DDAB molecule, such as the substitution at the headgroup level of a methyl group by an allyl group10 or the substitution of bromide by nitrate still results in a lamellar-lamellar coexistence.8 With chloride as the counterion, however, there is no phase separation in the lamellar region.18 The [bis((2-((n-dodecylcarbonyl)oxy)ethyl)carbamoyl)methyl]di-methyl[2-(methacryloyl oxy)ethyl]ammonium bromide (DLMDAB)-water12 and sodium dodecyl-5-pbenzenesulfonate (Na5-C12BS)-water11 systems have also been found to possess this type of miscibility gap. The fact that ternary systems form two coexisting lamellar phases is understood easily if the different bilayer components have different interactions across the water layers, as analyzed * Corresponding author. E-mail: [email protected]. † University of Porto. ‡ Lund University.

in detail by Noro and Gelbart.19 Generally, the forces behind this phase separation are of repulsive origin, usually electrostatic or undulation Helfrich-type forces.20 In a binary system, however, a composition degree of freedom is lost, and only the simultaneous occurrence of two opposing forces, an attractive and a repulsive one, can explain the formation of two lamellar phases, with different periodicities, in equilibrium. The nature and origin of the two competing forces is not yet fully understood. In the DDAB-water system, the two-phase coexistence is attributed to a difference in the degree of counterion binding to the lamellar phases,14,17 which adds an attractive force that balances the short-range repulsive and electrostatic forces. The attraction will predominate on the collapsed lamellar phase, preventing it from continuing to swell, while the other lamellar phase forms with a higher swelling. In the AOT-water system, exchanging a fraction of monovalent ions (Na+) for divalent ones (Ca2+) changes the system from a binary to a ternary one, but two forces are also suggested to come into play.21,22 The divalent ions create an attractive force that balances the regular repulsion, originating two lamellar phases in coexistence: (i) one where the Ca2+ cations are repelled from the interbilayer regions and only the repulsive force operates, promoting higher swelling; and (ii) one where the Ca2+ cations are in between the lamellae, attracting them and preventing them from swelling continuously. By means of theoretical considerations and a mean-field potential with an attractive van der Waals force and a repulsive thermal undulation force, Wennerstro¨m gave a qualitative description of the unbinding transition in lamellar phases (from

10.1021/jp076321f CCC: $37.00 © 2007 American Chemical Society Published on Web 11/10/2007

Lamellar Miscibility Gap

Figure 1. Chemical structure of the catanionic surfactant hexadecyltrimethylammonium octylsulfonate, here designated as TASo.

collapsed/bound to the swollen/unbound state).23 A first-order transition with the consequent occurrence of a two lamellar phase coexistence region between these two states was predicted by the model. Two lamellar phases have also been reported in some nonionic surfactant binary (and pseudo-binary) systems.24-26 However, in these systems, the two lamellar phases are not connected and, thus, do not coexist in any region. Therefore, for the moment, all of the systems found to possess lamellar phase coexistence are charged and possess inorganic counterions that have a predominant role in the justification of the attractive force. In the present work, we report for the first time to our knowledge a lamellar phase coexistence in a binary catanionic surfactant-water system, where inorganic counterions are absent. Catanionic surfactants are amphiphiles that result from the equimolar mixture of two oppositely charged ionic surfactants, with counterion removal.27 Thus, these compounds are net uncharged, resembling zwitterionic surfactants, with the fundamental difference that the two individual charges are not covalently linked. They are also sometimes designated as ionpair amphiphile,28,29 and another suggestive designation would be hydrophobic salts. Typically, they are insoluble at room temperature and swell at higher temperatures, as shown by the pioneering work of Jokela, Khan et al.30-34 Furthermore, they have been shown to yield unusual crystalline aggregates such as regular icosahedra and disks, as shown by Zemb, Dubois et al.35,36 When the molecules are made asymmetric, in terms of chain length or number of chains of the ionic counterparts, a complex sequence of thermotropic liquid crystalline phases appears, very much dependent on headgroup nature.37,38 In the present work, it is found that the compound hexadecyltrimethylammonium octylsulfonate, designated here as TASo (Figure 1), is soluble at room temperature over the full composition range. A phase diagram of TASo in water is presented at 25 °C, focusing mainly on the concentrated region (3-80 wt % surfactant). A combination of data by small-angle X-ray scattering, deuterium NMR, and polarizing microscopy shows that in water this surfactant swells linearly over a wide concentration range but has a miscibility gap; that is, it forms two lamellar phases with different periodic distances. Another peculiar feature is that in the dilute regime TASo forms an isotropic solution region (with large micelles), which coexists with the dispersed swollen lamellar phase, appearing in the form of vesicle aggregates. In the last section, cell model calculations, based on combined DLVO and short-range repulsive potentials, are presented, accounting for the miscibility gap and providing insight into its physical origin. II. Experimental Section The surfactants hexadecyltrimethylammonium bromide (CTAB) and sodium octylsulfonate (SOSo), both purchased from Sigma, were used to prepare the catanionic compound hexadecyltrimethylammonium octylsulfonate (TASo), according to the procedure described previously.38 Elemental analysis and sodium atomic absorption show that the compound is pure and coun-

J. Phys. Chem. B, Vol. 111, No. 48, 2007 13521 terion-free. Unless otherwise indicated, all samples were prepared by weight, with TASo and high-purity Millipore water. Samples for 2H NMR were prepared with deuterated water (Armar Chemicals). All of the samples were mixed and equilibrated carefully for several weeks to months at 25 °C before any measurements were carried out. Surface tension measurements in dilute solutions were performed with a DCAT21 tensiometer from DataPhysics (Wilhelmy plate method). Conductivity was measured with an Inolab condutimeter calibrated with a 0.1 M KCl standard solution. A polarizing light microscope BX51 from Olympus, with differential interference contrast lenses, was used for phase assignment and visualization of aggregates. The phase penetration technique described in detail elsewhere39 provided initial valuable data on the phase behavior of the surfactant. Synchrotron radiation small-angle X-ray scattering (SAXS) was used to study the dilute lamellar phase and the coexistence region, while conventional SAXS was performed on the concentrated lamellar phase. SAXS experiments were performed at Max-Lab (Lund), at beam-line I711. A wavelength of 1.08 Å and beam spot-size of approximately 79 mm were used. For data collection, a Mar165 area CCD detector from Mar Research was used with a sample-to-detector distance of 1456 mm. The treatment of the data was performed using the Fit2D software application. SAXS data were also collected by a Kratky compact small-angle system, equipped with a position-sensitive detector (OED 50M from MBraun) containing 1024 channels of width 53.0 µm. The generator was a Seifert ID-300 X-ray, operating at 55 kV and 40 mA. A monochromator with a nickel filter was used to select the Cu KR radiation (λ ) 1.542 Å). The distance between the sample and the detector was 277 mm. The SAXS structural data was obtained according to the following equation

q1 )

φs φ s as 2π ) 2π ) π d δ Vs

(1)

where q1 is the scattering vector from the first-order Bragg peak; d is the repeat distance; δ is the bilayer thickness; Φs is the volume fraction of surfactant; as is the average area per polar headgroup; and Vs is the molecular volume of the surfactant in the bilayer. This latter value was obtained from density measurements of the solid compound. Further data on phase assignment and equilibria were obtained from deuterium quadrupolar splitting NMR.40-42 Within a twosite discrete exchange model, the 2H splitting in a liquid crystalline phase is given by equation

∆ν ) ∆ν0

XS Xw

(2)

where ∆ν is the deuterium quadrupolar splitting; ∆ν0 is the proportionality constant (which includes the quadrupolar coupling constant, hydration number, and the local order parameter); and XS/Xw is the surfactant-to-water molar ratio. The measurements were recorded at 25 °C with a Bruker DMX200 spectrometer, operating at a deuterium resonance frequency of 30.701 MHz. III. Results and Discussion 1. Phase Behavior and Miscibility Gap: Experimental Observations. The catanionic surfactant has a Krafft temperature around 16 °C and is thus soluble at room temperature, yielding clear solutions up to a concentration of 0.3 wt %.

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Figure 2. Surface tension (a) and conductivity (b) curves for the TASo surfactant at 25 °C. The CMC is 0.074 mM (0.0035 wt %), and the corresponding surface tension is 26 mN‚m-1. The CMC value from conductivity is 0.082 mM.

Surface tension measurements at 25 °C, shown in Figure 2a), yield a CMC for TASo of 0.074 mM (0.0035 wt %), a value much lower than the CMCs for CTAB (0.80 mM43) and SOSo (153 mM44) and comparable to that of a nonionic surfactant with a dodecyl chain (e.g., C12E8, with 0.071 mM at 25 °C44). The surface tension value at the CMC, 26 mNm-1, a somewhat low value compared with some common surfactants, indicates that this amphiphile is highly surface active. The conductivity of TASo solutions (Figure 2b) is small but still measurable, showing a CMC break at 0.082 mM (0.0039 wt %), in good agreement with the surface tension value. If the limiting equivalent conductivity of TASo (λTASo ) 47 S cm2 mol-1) is compared with the sum of the values for CTA+ (λCTA+ ) 20 S cm2 mol-1)45 and for So- (λSo- ) 28.6 S cm2 mol-1, our value), then one concludes that before the CMC the surfactant is practically fully dissociated. The ionization degree at the CMC, R0, for a conventional surfactant can be estimated from the ratio of the slopes of the conductivity plot before and after the CMC, respectively;46,47 however, in our case, because of the amphiphilic nature of the counterion (So-), the slope before the CMC has to be multiplied by a λSo- /(λSo- + λCTA+ ) factor. The ionization degree thus obtained for TASo is about 11%. An illustrative phase penetration scan performed on the polarizing light microscope is shown in Figure 3. From left to right in Figure 3a, there is a gradient of increasing surfactant concentration because of the slow water diffusion across the surfactant film. An isotropic (black) region is followed by a birefringent texture with oily streaks and myelin-like patterns39 (Figure 3b), clearly showing the existence of a swollen lamellar liquid crystalline phase. Toward the right, another texture is seen with a more undefined coarse mosaic nature, separated from the first by a non-birefringent “band” (C in Figure 3a).

Silva et al.

Figure 3. Phase penetration scan in the polarized light microscope, with the surfactant concentration increasing from left to right. (a) An isotropic region (A) is followed by a lamellar texture (B), an intermediate band (C), a second lamellar texture (D), and hydrated crystals (E). (b) In the boundary regions between A and B, vesicular aggregates spontaneously detach from the swollen bilayers. Bars: 200 µm (a) and 50 µm (b).

Hydrated crystals are seen on the right-hand side. In Figure 3b, it is possible to observe the spontaneous detachment of vesicular aggregates into the solution in what appears to be a dispersion of the dilute lamellar phase into the isotropic solution. Individual equilibrated samples also observed between crossed polarizers appear as one-phase, birefringent, and very viscous above 55 wt % TASo, whereas in the 15-55 wt % range they are fluid and acquire a milky appearance reminiscent of an emulsion. In the 2.6-15 wt % range, the samples look as one-phase again and show high viscosity and strong static birefringence. Below 2.6 wt %, only flow birefringence is observed. Overall, from these optical observations one could suspect the occurrence of two independent lamellar phases, with a coexistence region between them. This coexistence is indeed confirmed by SAXS measurements (Figure 4 and Table 1). Figure 4a shows two individual lamellar patterns seen for 15 and 55 wt % surfactant, and their superimposition in a 20 wt % sample, unambiguously proving the coexistence. Analysis of the full data allows us to set the coexistence region in the range of 15-54 wt % TASo, as suspected from the ocular inspection of the samples. The obtained d spacings are plotted versus the reciprocal surfactant volume fraction in Figure 4b. Linear swelling is observed for both phases, only interrupted by the miscibility gap. Despite this discontinuity, the two phases display identical slopes. This means that the lamellar thickness δ (2.7 nm) and molecular area as (0.59 nm2) are identical for both lamellar phases.

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Figure 4. SAXS results. (a) Examples of diffractograms for TASo in water at 15, 20, and 55 surfactant wt%. The superposition of both lamellae peaks in the 20 wt % sample is clearly observable. (b) The d values for both lamellar phases. At Φs ) 0.20 and 0.25 (1/Φs ) 5 and 4, respectively), two d values are obtained for the coexisting lamellar phases. The first two values of the graph depart from the linear swelling (Φs > 0.80). From the linear slope, the lamellar thickness δ is 2.7 nm and the area per molecule, as, is 0.59 nm2.

TABLE 1: d Spacings for the Lamellar Phases as Obtained from the SAXS Diffractograms TASo/wt %

d/nm

2.9 3.5 4.0 5.0 8.0 10.0 12.1 15.2 19.7 25.0 30.0 40.0 50.0 54.7 59.6 65.0 70.4 74.2 79.7 84.5

84 75 67 56.1 33.1 27.3 22.3 18.1 17.9; 5.02 14.7; 5.01 4.96 5.04 5.08 4.86 4.45 4.31 3.87 3.66 3.53a 3.46a

phases LR′

LR′ + LR′′ Figure 5. Deuterium quadrupolar splitting NMR spectra for 10, 33, and 65 surfactant wt% samples.

LR′′

a Values from the region where the swelling of the collapsed lamellar phase is no longer linear.

The dilute lamellar phase, henceforth termed LR′, has a huge swelling, with an apparent limiting d spacing of 84 nm at 2.9 wt % surfactant (Figure 4b). By visual inspection, the phase boundary between LR′ and the biphasic region is tentatively set at 2.6 wt % because static birefringence is no longer observed below this value (only flow birefringence). By extrapolation,

the expected value of d for the 2.6 wt % sample would be 102 nm. On the high concentration side, beyond 80 wt %, the swelling is no longer linear (Table 1), and at some point the lamellar phase is expected to coexist with the crystalline solid. Thus, the upper limit of the concentrated lamellar phase, henceforth termed LR′′, is tentatively attributed to 80 wt % surfactant. Figure 5 shows some illustrative 2H NMR spectra for investigated samples, yielding further evidence for the two-phase region. Typical powder spectra with large splitting values are obtained for the concentrated phase, whereas the splitting is much narrower for the dilute phase. In the coexisting region, a broad singlet was obtained for most of the samples, probably because of the mixing of the two phases in some sort of fine dispersion. The latter is extremely stable with time, but for some samples it was possible to observe the appearance of splitting

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Figure 6. Phase behavior at 25 °C for the TASo-water system. L1, isotropic solution; LR′, swollen lamellar phase; LR′′, collapsed lamellar phase.

Figure 7. Schematic representation of the lamellar cell, where d is the periodic distance, δ is the bilayer thickness and A is the bilayer area.

from the collapsed lamellar phase, along with a nonresolved broad peak from the swollen lamellar phase. Further investigations above room temperature are out of the scope of this paper, but we can point out that at high enough temperatures the two coexisting phases coalesce to yield a single lamellar phase, a behavior reminiscent of that for the DDAB-water and (Na5C12BS)-water systems, where an upper consolute temperature was found.11,14,16 The phase behavior observations at 25 °C can be summed up in the phase map displayed in Figure 6. Going from the more concentrated to the more dilute side (right to left in Figure 6), a collapsed lamellar phase (LR′′) is found immediately after the hydrated crystals, followed by the two-phase region, and then by the swollen lamellar phase (LR′). Afterward, a two phaseregion LR′ + L1 is found in which large vesicles (unbound lamellae from the LR′ phase) seem to be dispersed in an isotropic viscoelastic solution. The viscoelasticity strongly suggests that large micelles are present. Upon further dilution, the characteristic bluish color of vesicle dispersion vanishes and a single L1 phase is found. The aggregation behavior and phase boundaries in this part of the phase diagram are under current investigation and will be reported in detail in a forthcoming paper. 2. Theoretical Modeling. From previous works on catanionic surfactants, it is clear that compounds with similar chain lengths of the two ionic counterparts are typically insoluble at room temperature, displaying a single lamellar phase with limited swelling at higher temperature. That is the case for the symmetric compounds studied by Jokela et al.30-34 and also some asymmetric ones (in both chain length and number of chains) with relatively long chains.48-55 However, in this particular case, TASo is soluble at room temperature, yielding a micellar solution and a lamellar phase with a miscibility gap. In order to gain deeper insight into the origins of this miscibility gap, we have developed a theoretical model. The key basis of this model asserts in the intuitive observation (supported by conductivity measurements) that above the chain melting temperature, and owing to the difference in aqueous solubility of the short and long chains, the short anionic chain will partially dissociate from the bilayer, leaving it with a residual positive charge. Let us then consider a lamellar phase with periodicity d and thickness δ, formed by a catanionic surfactant of the type S+S-, in water (Figure 7). Because of the fact that the catanionic is highly asymmetric, with S+ () CTA+) as the long chain and S- () So-) as the short chain, the aqueous solubility of S- is significantly higher than that of S+, resulting in a net positive bilayer charge and a long-range electrostatic repulsion. Upon

Figure 8. Calculated bilayer charge density, σ, and dissociation degree, for constant [So-]aq ) 5 mM, as a function of TASo concentration. Note the logarithmic scale: both quantities are strongly dependent on concentration (in accordance with eq 6).

increase of the water layer volume, more So- is dissolved and concomitantly the bilayer charge density increases. Thus, the charge density, and consequently the electrostatic repulsion force (ER force), will be dependent on the volume fraction of surfactant in water. Assuming that (i) the solubility of CTA+ in water is zero; (ii) the solubility of So-, [So-]aq, is independent of ΦS, which is a good approximation if the chemical potential varies only weakly with ΦS; (iii) the lamellar cell has an aqueous volume V ) A(d - δ), where A is a given area and (d - δ) is the thickness of the water layer, where there are on average n Somolecules; then, the solubility [So-]aq can be written simply as

[So-]aq )

n A(d - δ)

(3)

The bilayer charge density σ is then given by

σ)

1n 1 ) [So-]aq(d - δ) 2A 2

(4)

where the factor 1/2 accounts for the fact that the molecules of So- dissolved in one water layer come from two surfactant bilayers. The periodic distance in the lamellar phase is given by

d)

δ ΦS

(5)

Combining eqs 4 and 5, one finally obtains

(

1 1 σ ) [So-]aq δ -1 2 ΦS

)

(6)

where σ has the dimensions of number of unit charges per unit area, and [So-]aq always has to be smaller than the total surfactant concentration [TASo]total for each lamellar spacing. If [So-]aq g [TASo]total, then the surfactant is fully dissociated and eq 6 does not apply. In this case, the charge density value is truncated for a constant value (1/as), as expected for a fully dissociated (ionic) surfactant. An illustration of the use of eq 6 is shown in Figure 8.

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Having calculated the charge density σ for a given solubility [So-]aq and for each lamellar spacing (determined experimentally), the electrostatic osmotic pressure in the lamellar phase can be computed with a Poisson-Boltzmann cell model. Here we have used the PBCell program, developed by Bengt Jo¨nsson at Lund University,56 that solves the Poisson-Boltzmann equation and also includes the attractive van der Waals force.57 For a given solubility [So-]aq, the osmotic pressure has been calculated for different bilayer concentrations. Different contributions to the osmotic pressure are assumed to be additive, and a short-range repulsive (SRR) force is also included. The overall pressure is then given by

Π ) ΠvdW + ΠER + ΠSRR

(7)

where the short-range repulsive force is expressed as

ΠSRR ) a e-(d-δ)/λ

(8)

Here a is the force amplitude, generally between 106 and 108 N‚m-2; d - δ is the water layer thickness; and λ is the decay length, generally between 0.15 and 0.3 nm. This force is still not understood completely, but it is thought to arise from an entropy loss of the headgroups when two bilayers come into close distance.58 Hence, at short d values the SRR force is extremely high and usually dominant over all others. The Hamaker constant has been maintained as 6 × 10-21 J, a reasonable value for lipid or surfactant bilayers. The values for a and λ (SRR force) are 4.33 × 107 N‚m-2 and 0.3 nm, respectively, and have been chosen in order to set the LR′′ phase lower limit at 54 wt %, as observed experimentally. In Figures 9 and 10, the results of the calculations are shown, for constant [So-]aq ) 5 mM, as an example. At high dilutions, the electrostatic force is dominant because of the high bilayer charge density (Figure 9a); hence, the swollen LR′ phase is stabilized. However, as the concentration increases, the charge density decreases and the ER force becomes weaker. In a completely ionized lamellar phase, the electrostatic repulsion is expected to increase abruptly with concentration. As shown in Figure 10, when [So-]aq is raised significantly (e.g., 50 and 100 mM), there is a dramatic influence on the total osmotic pressure and the curves tend to the ionic surfactant case. For lower [So-]aq values, the electrostatic force does not increase as much as that in the ionic case, and when the bilayers come closer, there is a region of d where the attractive van der Waals force is higher than the repulsive electrostatic force; consequently, phase-separation is promoted. The reason that LR′′ does not completely collapse is due to the fact that at small interlamellar distances (below 2.3 nm), the short-range repulsive force predominates over the van der Waals attraction. Hence, in the force curve, a van der Waals loop is observed, which signifies the coexistence of the two lamellar phases. The phase boundaries of this two-phase region can then be calculated through a Maxwell construction23 (Figure 9b). As pointed out previously, by changing the water solubility of octylsulfonate, the electrostatic force is changed drastically, which will change the osmotic pressure curve significantly (Figure 10). The results of the calculated miscibility gap for different TASo solubilities are also presented in Table 2. By adjusting the hydration force to a maximum swelling of the collapsed lamellar of ca. 54 wt % (observed experimentally), reasonable values are obtained for the two-phase region boundaries, if solubilities above 5 mM are assumed for octylsulfonate. Optimal values (compared to experimental) are obtained for [So-]aq ) 20 mM. Such solubility values are

Figure 9. (a) Contribution of the repulsive and attractive forces to the total pressure curve. Note that the symmetric values of the vdW pressure are plotted, for easier visualization. (b) Maxwell construction to calculate the limits of the coexistence region. The used values in the calculation are: H ) 6 × 10-21 J; A ) 3 × 107 N‚m-2; λ ) 0.3 nm; [So-]aq ) 5 mM.

Figure 10. Total osmotic pressure curves for different solubilities of the octylsulfonate chain of TASo. From top to bottom: [So-]aq ) 100, 50, 20, 10, 5, and 3 mM.

physically realistic if one takes the CMC of sodium octylsulfonate (153 mM44) as a reference. The key assumption of a constant solubility for sulfonate [So-]aq is also reasonable on the basis of the following consideration: the chemical potential varies along with concentration, and the solubility of sulfonate at higher concentrations is expected to decrease; however, in the regime where this effect could be more pronounced (very high concentrations), the SRR force is dominant, making inaccuracies in the ER force calculation negligible.

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TABLE 2: Lower and Upper Limits for the Miscibility Gap lower

upper

[So-]aq/mM

TASo wt %

d

TASo wt %

d

3 5 10 20 50 100

4.76 6.53 9.86 14.5 23.0 31.4

56.9 41.5 27.5 18.7 11.8 8.64

54.4 54.3 54.3 54.0 53.5 52.4

4.98 4.99 4.99 5.02 5.07 5.17

A relevant comparative discussion of the TASo and the DDAB binary systems is elucidative at this point. Although DDAB is an ionic surfactant, one expects the ER force to be strong enough to swell the lamellar phase continuously. Nonetheless, because the Br- ion is slightly hydrophobic, it adsorbs on the bilayer surface, decreasing its charge density, and in turn, also decreasing the magnitude of the ER force; a miscibility gap is then originated. In contrast, TASo should behave as a globally uncharged surfactant (like a zwitterionic one) and show limited swelling, derived only from the SRR force. However, because charge originates from the short-chain dissociation, the lamellar phase is stabilized in a larger extension. Since this ER force is of medium magnitude (compared to a totally dissociated/ionic lamellar phase), it will fail to overcome the attractive dispersion forces at lower d values; a miscibility gap occurs as well. IV. Concluding Remarks It has been shown experimentally that the asymmetric chain length catanionic surfactant hexadecyltrimethylammonium octylsulfonate, which forms micelles at low concentration, exhibits a lamellar phase with a miscibility gap at higher concentration. The latter type of phenomenon is extremely rare in binary surfactant-water systems. The physical essence of the lamellarlamellar coexistence can be reasonably captured by cell model calculations, where a fine balance of attractive and repulsive forces give rise to a van der Waals loop in the osmotic pressure curve, at intermediate d values. The key to this model is the generation of an electrostatic force stemming from the partial solubilization of the short-chain counterpart of the compound. Acknowledgment. We are grateful for financial support from the Portuguese Science Foundation (FCT), Portugal, and FEDER Funds, through the research project POCTI/QUI/44296/2002 and from the Swedish Research Council (VR). Centro de Investigac¸ a˜o em Quı´mica - linha 5 is also acknowledged for financial support. B.B.S. is grateful to F.C.T. for the Ph.D. grant SFRH/ BD/24966/2005. References and Notes (1) McGrath, K. M. Langmuir 1997, 13, 1987. (2) Montalvo, G.; Khan, A. Langmuir 2002, 18, 8330. (3) Ricoul, F.; Dubois, M.; Belloni, L.; Zemb, T.; Andre´-Barre`s, C.; Rico-Lattes, I. Langmuir 1998, 14, 2645. (4) Wang, X.; Quinn, P. J. Biochim. Biophys. Acta 2002, 1567, 6. (5) Deme´, B.; Dubois, M.; Zemb, T.; Cabane, B. Colloids Surf., A 1997, 121, 135. (6) Rong, G.; Yang, J.; Friberg, S. E.; Aikens, P. A.; Greenshields, J. N. Langmuir 1996, 12, 4286. (7) Bryskhe, K.; Schille´n, K.; Lo¨froth, J.-E.; Olsson, U. Phys. Chem. Chem. Phys. 2001, 3, 1303. (8) Brotons, G.; Dubois, M.; Belloni, L.; Grillo, I.; Narayanan, T.; Zemb, T. J. Chem. Phys. 2005, 123, 024704. (9) Fontell, K.; Ceglie, A.; Lindman, B.; Ninham, B. Acta Chem. Scand. 1986, A40, 246. (10) McGrath, K. M.; Drummond, C. J. Colloid Polym. Sci. 1996, 274, 316.

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