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Spontaneous Transformations between Surfactant Bilayers of Different Topologies Observed in Mixtures of Sodium Octyl Sulfate and Hexadecyltrimethylammonium Bromide L. Magnus Bergström,*,† Sara Skoglund,† Katarina Edwards,‡ Jonny Eriksson,‡ and Isabelle Grillo§ †

School of Chemical Science and Engineering, Department of Chemistry, Surface and Corrosion Science, KTH Royal Institute of Technology, , SE-10044 Stockholm, Sweden ‡ Department of Chemistry - BMC, Uppsala University Box 579, SE-75123 Uppsala, Sweden § Institut Laue Langevin, DS/LSS, 6 rue Jules Horowitz, B.P. 156, 38042 Grenoble Cedex 9, France S Supporting Information *

ABSTRACT: The influence of adding salt on the self-assembly in sodium octyl sulfate (SOS)-rich mixtures of the anionic surfactant SOS and the cationic surfactant hexadecyltrimethylammonium bromide (CTAB) have been investigated with the two complementary techniques, small-angle neutron scattering (SANS) and cryo-transmission electron microscopy. We are able to conclude that addition of a substantial amount of inert salt, NaBr, mainly has three effects on the structural behaviors: (i) the micelles become much larger at the transition from micelles to bilayers, (ii) the fraction of bilayer disks increases at the expense of vesicles, and (iii) bilayer aggregates perforated with holes are formed in the most diluted samples. A novel form factor valid for perforated bilayer vesicles and disks is introduced for the first time and, as a result, we are able to directly observe the presence of perforated bilayers by means of fitting SANS data with an appropriate model. Moreover, we are able to conclude that the morphology of bilayer aggregates changes according to the following sequence of different bilayer topologies, vesicles → disks → perforated bilayers, as the electrolyte concentration is increased and surfactant mole fraction in the bilayer aggregates approaches equimolarity. We are able to rationalize this sequence of transitions as a result of a monotonous increase of the bilayer saddlesplay constant (k̅bic ) with decreasing influence from electrostatics, in agreement with theoretical predictions as deduced from the Poisson−Boltzmann theory.

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INTRODUCTION Aqueous mixtures of an anionic and a cationic surfactant have been extensively studied during the past decades, among other things because these systems exhibit a comparatively rich diversity of different structures that depend on surfactant concentration and composition, including micelles of different size and shape and unilamellar vesicles.1,2 Catanionic systems are also interesting because of the fast dynamic processes taking place and, as a consequence, the different aggregates that form are believed to be thermodynamically equilibrated structures. This property is particularly interesting for the various bilayer structures usually observed in mixtures of an anionic and a cationic surfactant, in striking contrast to bilayer aggregates formed by, for instance, phospholipids. As a result, oppositely charged surfactant mixtures constitute a suitable model system for the study of equilibrium morphologies of bilayers. A substantial proportion of earlier studies of anionic/cationic surfactant mixtures has been carried out using cryo-transmission electron microscopy (cryo-TEM) and was mainly focused on the formation of unilamellar vesicles in the dilute isotropic part of the phase diagrams.1,3−6 In a more recent study, however, it was demonstrated, by means of combining small-angle neutron scattering (SANS) and cryo-TEM, that vesicles coexist with geometrically open bilayer disks in © 2014 American Chemical Society

mixtures of the anionic surfactant sodium octyl sulfate (SOS) and the cationic surfactant hexadecyltrimethylammoinium bromide (CTAB) in the absence of added salt.7 A conspicuous discrepancy between cryo-TEM and scattering techniques was observed for this particular system, in the sense that only micelles were seen in a few samples with cryo-TEM, although scattering indicated the presence of bilayers and the sample appeared bluish to the bare eye. It was argued that this discrepancy between the techniques appears as a result of the comparatively large fraction of surfactant adsorbed at interfaces of the thin film created during the cryo-TEM sample preparation. In the present paper, we follow up our work in ref 7 and report novel discoveries on the structural behaviors of bilayer aggregates in dilute mixtures of SOS and CTAB, as induced by the addition of salt. Although mixtures of oppositely charged surfactants have been frequently studied in the past, including the effect of adding salt,8,9 this is, to our knowledge, the first systematic investigation of the influence of composition and Received: August 7, 2013 Revised: March 5, 2014 Published: March 24, 2014 3928

dx.doi.org/10.1021/la4042259 | Langmuir 2014, 30, 3928−3938

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Δρm is the difference in scattering length per unit mass solute between particles with a homogeneous core and solvent, Mw is the mass of a single particle, and P(q) is the form factor. The average excess scattering length density per unit mass of solute (i.e., scattering length density divided by density of 10 solute12) for SOS in D2O, Δρm cm/g, was SOS = −4.52 × 10 calculated using the appropriate molecular volume v̂SOS = 302 Å3 and molecular weight MSOS = 232.27 g/mol7,13−15 and for 10 3 CTAB,15 Δρm CTAB = −6.66 × 10 cm/g, v̂CTAB = 607 Å , and MCTAB = 364.45 g/mol. The scattering length density (in units of centimeters/molecule) of mixed micelles has been set to Δρ = xΔρSOS + (1 − x)ΔρCTAB, where the mole fraction of SOS in the aggregates x is calculated, according to a procedure described in ref 7. Throughout the data analysis, corrections were made for instrumental smearing. For each instrumental setting, the ideal model scattering curves were smeared by the appropriate Gaussian resolution function when the model scattering intensity was compared with the measured absolute scale intensity in least-squares model fitting data analysis.16,17 The parameters in the model were optimized by means of conventional least-squares analysis and the quality of the fits was measured in terms of the reduced chi-squared parameter (χ2).12,18 In consideration of the high quality of our SANS data and large number of data points, the agreements between models and data are exceptionally good with a reduced chisquared always below χ2 = 5. The errors of the parameters were calculated by conventional methods.12,18 The different form factors and models employed in the least-squares model fitting data analysis are given in the Supporting Information. Cryo-Transmisson Electron Microscopy. The cryo-TEM measurements were carried out at Uppsala University, Uppsala, Sweden using a Zeiss EM 902A Transmission Electron Microscope (Carl Zeiss NTS, Oberkochen, Germany) with a resolution 15 Å/pixel. Analysis was performed under cryoconditions, and the microscope was operating at 80 kV and in a zero-loss bright-field mode. Digital images were recorded under low dose conditions (approximately 10 electrons per Å2) with a BioVision Pro-SM Slow Scan CCD camera (Proscan GmbH, Scheuring, Germany) and iTEM software (Olympus Soft Imaging System, GmbH, Münster, Germany). In order to visualize as many details as possible, an underfocus of approximately 2 μm was used to enhance the image contrast.19

electrolyte concentration on the morphology of bilayer aggregates in mixtures of an anionic and a cationic surfactant.

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MATERIALS AND METHODS

Materials. Sodium octylsulfate (>95%, GC) and hexadecyltrimethylammonium bromide (>98%, GC) were obtained from Sigma and sodium bromide (>99.5%, GC) from Fluka. All surfactants were used without further purification. Deuterium oxide (D2O) with 99.9 atom % D was purchased from Aldrich Chemical Company. Sample Preparation. Stock solutions containing sodium octylsulfate (SOS) and hexadecyltrimethylammonium bromide (CTAB) with surfactant compositions equal to y ≡ [SOS]/ ([SOS] + [CTAB]) = 0.90 and 0.95 were prepared in aqueous solutions with [NaBr] = 0, 0.1, and 0.3 M, by simply mixing the surfactants with sodium bromide and ultrapure Milli-Q water (H2O with resistivity of 18.2 MΩ cm−1) (cryo-TEM) or deuterium oxide (D2O) (SANS). The final samples were obtained by means of diluting the stock solutions with solvent to obtain a range of total surfactant concentration ([SOS] + [CTAB]) from 10 to 160 mM ([NaBr] = 0) and 5−80 mM ([NaBr] = 0.1 and 0.3 M) at ambient temperature (23 °C). Due to the higher critical micelle concentration (cmc) of SOS in the absence of added salt (cf. further below), we have measured the corresponding samples at higher surfactant concentrations. All samples were equilibrated at least 48 h before measured. Deuterium oxide was chosen as the solvent in the small-angle neutron scattering experiments in order to minimize the incoherent background from hydrogen and obtain a high scattering contrast.10 Samples with total surfactant concentrations equal to 80, 60, 40, 20, 10, and 5 mM at y = 0.90 and 0.95 were also investigated with static light scattering using H2O as the solvent. With SLS, we are able to distinguish between small micelles, large micelles, and bilayers7 and the results are given in Tables S1−S4 of the Supporting Information. Small-Angle Neutron Scattering. The small-angle neutron scattering (SANS) experiments were carried out at the D11 and D33 SANS instruments at Institut Laue-Langevin (ILL), Grenoble, France. At D11, a range of scattering vectors, q, from 0.002 to 0.44 Å−1 was covered by three sample-todetector distances (d = 1.2, 8, and 39 m) at the neutron wavelength λ = 4.6 Å. The measurements at D33 were carried out with the three settings (d = 2 m, λ = 4.6 Å), (d = 12.8 m, λ = 4.6 Å), and (d = 12.8 m, λ = 12 Å), giving a range of scattering vectors 0.002−0.29 Å−1. The settings (d = 8 m, λ = 4.6 Å) and (d = 12.8 m, λ = 4.6 Å), respectively, were used as the reference setting for the absolute scale. The wavelength resolution was 10% (full width at half-maximum value). The samples were kept in quartz cells (Hellma) with path lengths 1 or 2 mm. The raw spectra were corrected for background from the solvent, sample cell, and other sources by conventional procedures.11 The SANS data were set to absolute scale units and normalized by means of dividing with the concentration in (g mL−1) of solute (SOS and CTAB), giving the unit (mL g−1 cm−1) for the normalized scattering crosssection, that is dσm(q) 1 dσ(q) ≡ = Δρm2 M wP(q) dΩ cagg dΩ

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RESULTS AND DISCUSSION Dilution paths have been investigated for the surfactant compositions in solution y = 0.90 and 0.95 in [NaBr] = 0.1 and 0.3 M. Examples of SANS data with model fits for samples with y = 0.95 in the presence of [NaBr] = 0.3 M are shown in Figure 1. The results from the model fitting data analysis of samples in the presence of [NaBr] = 0.1 and 0.3 M are given in Tables 1 and 2, respectively. The assigned models in Tables 1 and 2 are based on which model generates best agreement with SANS data. For the sake of comparison, we will also discuss the corresponding results in the absence of adding salt, which were recently presented in ref 7. Along with the fitting results, we have also included the mole fraction of SOS in the aggregates (denoted x) in Tables 1 and 2. These values were obtained by means of carrying out detailed calculations based on the Poisson−Boltzmann (PB) mean field theory as described in ref 7. In accordance, we have been able to demonstrate that the structural changes in mixtures of an anionic and a cationic surfactant are driven by a change in

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calculated from the PB theory, are tabulated in the Supporting Information. On the basis of the model that gives the best agreement with SANS data (for samples in D2O) as well as on static light scattering (SLS) of samples in H2O (cf. Tables S1−S4 in the Supporting Information), we have constructed predominance diagrams for the three cases [NaBr] = 0 (Figure 2), [NaBr] = 0.1 M (Figure 3), and [NaBr] = 0.3 M (Figure 4), showing in which regions small ellipsoidal micelles, large polydisperse rodlike or wormlike micelles, perfect (that is without holes) bilayer disks and vesicles, and perforated bilayers disks and vesicles predominate for the two dilution paths, y = 0.90 and 0.95, respectively. SANS and SLS give identical results with respect to whether small micelles (monodisperse ellipsoids), large micelles (polydisperse rods), or bilayers are present in a particular sample, indicating that the choice of either D2O or H2O has only a small influence (if any at all) on the appearance of the diagrams. Coexisting micelles and bilayers was observed with SANS for the samples (y = 0.95, 80 mM, [NaBr] = 0) and (y = 0.90, 60 mM, [NaBr] = 0.1 M), indicating the point of transition from micelles to bilayers in the corresponding diagrams. For the remaining transitions, we have roughly set the point of transition in between two nearby measured samples, where different aggregate types are observed. The main differences between the samples containing a substantial amount of NaBr and those prepared in the absence of added salt may be summarized as follows. (i) The micelles appear to be much larger at the micelle-to-bilayer transition. (ii) In samples with bilayers, the fraction of disks is considerably higher and vesicles lower. (iii) Perforated bilayers form spontaneously in the most diluted samples. These issues will be further discussed in more detail below.

Figure 1. Normalized scattering cross section as a function of the scattering vector q for mixtures of SOS and CTAB in deuterium oxide in [NaBr] = 0.3 M for a given mole fraction of SOS in solution y = 0.95. The overall surfactant concentration of the samples are [SOS] + [CTAB] = 80 mM (○), 60 mM (□), 40 mM (△), 20 mM (▽) and 10 mM (◇). Symbols represent SANS data, and the solid lines represent the best available fit with a model for general ellipsoids (○ and □), polydisperse wormlike micelles with an elliptical cross-section (△), coexisting perfect bilayer disks and vesicles (▽), and coexisting perforated disks and vesicles (◇). The results of the fits are given in Table 2. The quality of the fits as measured by χ2 is 1.9 (○), 1.6 (□), 4.7 (△), 2.2 (▽), and 2.3 (◇).

composition and surface charge density in the aggregates, as a consequence of the fact that an appreciable amount of free surfactant in excess (SOS) always coexists with micelles or bilayer aggregates.7 The corresponding compositions as well as concentrations of aggregates and free surfactant monomers, as

Table 1. Results from Least-Square Model Fitting Analysis of SANS Dataa [NaBr] = 0.1 M

80 mM

60 mM

20 mM

10 mM

5 mM

y = 0.90

polydisperse rodlike micelles

micelles + perfect bilayers

perfect bilayers

perforated bilayers

perforated bilayers

fd = 0.74 f v = 0.26 ξ = 14.3 Rv = 240 σv/Rv = 0.5 x = 0.59

fd = 0.68 f v = 0.32 ξ = 15.0 Rv = 160 σv/Rv = 0.8 Rdh = 100 f dh = 0.01 Rvh = 60 f vh = 0.11 Nvh = 2.7 x = 0.56 perforated bilayers fd = 0.80 f v = 0.20 ξ = 14.7 Rv = 400 σv/Rv = 0.6 Rdh = 165 f dh = 0.05 Rvh = 65 f vh = 0.07 Nvh = 10 x = 0.57

fd = 0.90 f v = 0.10 ξ = 15.8 Rv = 130 σv/Rv = 0.7 Rdh = 220 f dh = 0.03 Rvh = 50 f vh = 0.10 Nvh = 2.8 x = 0.53 perforated bilayers fd = 0.94 f v = 0.06 ξ = 12.8 Rv = 480 σv/Rv = 0.5 Rdh = 145 f dh = 0.02 Rvh = 60 f vh = 0.04 Nvh = 11 x = 0.54

a = 16.1 b = 22.1 ⟨L⟩ = 290 *σL/⟨L⟩ = 0.95 x = 0.73

y = 0.95

ellipsoidal micelles a = 17.8 b = 23.2 c = 31.4 x = 0.77

f m = 0.14 fd = 0.60 f v = 0.26 rc = 20.6 ξ = 13.1 Rv = 470 σv/Rv = 0.4 x = 0.69

polydisperse rodlike micelles a = 16.7 b = 21.9 ⟨L⟩ = 540 σL/⟨L⟩ = 0.18 x = 0.73

perfect bilayers fd = 0.85 f v = 0.15 ξ = 14.3 Rv = 320 σv/Rv = 0.2 x = 0.60

Dimensional properties (a, b, c, ξ, ⟨L⟩, Rv, Rd, ls, Rdh and Rvh) are given in units of Ångström (Å). Denotations for the different quantities are defined in Appendix A. *Parameters that have been fixed in the model fitting analysis. a

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Table 2. Results from Least-Square Model Fitting Analysis of SANS Dataa [NaBr] = 0.3 M

80 mM

60 mM

40 mM

20 mM

10 mM

y = 0.90



a = 15.9 b = 23.8 ⟨L⟩ = 32.2 σL/⟨L⟩ = 0.7 x = 0.79

a = 16.7 b = 21.0 ⟨L⟩ = 404 σL/⟨L⟩ = 0.5 x = 0.75



perforated bilayers fd = 0.63 f v = 0.37 ξ = 14.4 Rv = 330 σv/Rv = 0.7 Rdh = 200 f dh = 0.02 Rvh = 120 f vh = 0.03 Nvh = 0.9 x = 0.70 polydisperse rodlike micelles a = 17.3 b = 21.9 ⟨L⟩ = 2900 lp = 120 *σL/⟨L⟩ = 0.95 x = 0.73

perforated bilayers fd = 0.72 f v = 0.28 ξ = 15.0 Rv = 350 σv/Rv = 0.7 Rdh = 220 f dh = 0.03 Rvh = 125 f vh = 0.03 Nvh = 1.1 x = 0.63 perfect bilayers fd = 0.49 f v = 0.51 ξ = 15.2 Rv = 300 σv/Rv = 0.7 x = 0.64

perforated bilayers fd = 0.97 f v = 0.03 ξ = 14.9 Rv = 330 σv/Rv = 0.4 Rdh = 185 f dh = 0.02 Rvh = 55 f vh = 0.10 Nvh = 15 x = 0.58 perforated bilayers fd = 0.87 f v = 0.13 ξ = 15.2 Rv = 230 σv/Rv = 0.7 Rdh = 120 f dh = 0.02 Rvh = 45 f vh = 0.10 Nvh = 9.6 x = 0.59

y = 0.95

Dimensional properties (a, b, c, ξ, ⟨L⟩, Rv, Rd, Rdh, and Rvh) are given in units of Ångström (Å). Denotations for the different quantities are defined in Appendix A. *Parameters that have been fixed in the model fitting analysis. a

Figure 2. Diagrams showing surfactant concentrations where small ellipsoidal micelles, large polydisperse rodlike or wormlike micelles, perfect bilayer disks and vesicles (= perfect bilayers), and perforated bilayer disks and vesicles (= perforated bilayers) predominate for the dilution series y = 0.90 and 0.95, in the absence of added salt.

Figure 3. Diagrams showing surfactant concentrations where small ellipsoidal micelles, large polydisperse rodlike or wormlike micelles, perfect bilayer disks and vesicles (= perfect bilayers) and perforated bilayer disks and vesicles (= perforated bilayers) predominate for the dilution series y = 0.90 and 0.95 in [NaBr] = 0.1 M.

Influence of Adding Salt on Micelles. The samples with the highest concentration that were measured at y = 0.95 (80 mM at [NaBr] = 0.1 M and 60 and 80 mM at [NaBr] = 0.3 M) were best fitted with a model for fairly small monodisperse triaxial ellipsoidal micelles. As the samples are diluted, the micelles grow in size as well as becoming considerably polydisperse and the corresponding SANS data could only be fitted with a model for polydisperse rods. An obvious effect of increasing the concentration of added salt is that the concentration of free surfactant becomes reduced. Since the amount of free surfactant virtually

completely consists of the surfactant in excess (SOS in our case), increasing the electrolyte concentrations has a significant impact on the mole fraction of SOS in the aggregates (x) which, as a consequence, is increased [cf. the tabulated values in Supporting Information]. This explains why comparatively large rods are observed in the sample [y = 0.95 and 80 mM] at [NaBr] = 0.1 M (x = 0.73), whereas smaller ellipsoidal micelles form as the concentration of NaBr is increased to 0.3 M (x = 0.80). This effect is also manifest in the predominance diagrams of Figures 3 and 4, where it is seen that the region of micelles increases at expense of the bilayers (see further below), and the 3931


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wormlike micelles with a persistence length equal to about lp = 120 Å. Upon further dilution of the samples, there is an abrupt transition from rodlike or wormlike micelles to considerably larger bilayer aggregates. As evident from the predominance diagrams in Figures 2−4, the surfactant concentration at the micelle-to-bilayer transition is found to decrease with an increasing amount of added salt. In accordance, the transition occurs between 40 and 20 mM (y = 0.95) and 60−40 mM (y = 0.90) in [NaBr] = 0.3 M and between 60 and 40 mM (y = 0.95) and at about 60 mM (y = 0.90) in [NaBr] = 0.1 M, as compared to 100−80 mM (y = 0.90) and 80 mM (y = 0.95) in the absence of added salt. However, according to the theoretical calculations based on the PB theory, these transitions correspond to roughly the same mole fraction of SOS in the aggregates x ≈ 0.7 (cf. Tables 1 and 2 and tabulated values in Supporting Information). Notably, an abrupt transition from micelles to bilayers may be predicted from a theory based on bending elasticity to occur as the spontaneous curvature equals H0 = 1/4ξ, where ξ is the thickness of the self-assembled monolayer interface (equivalent to half bilayer thickness).21,22 The following critical micelle concentrations (cmc) for SOS cmc1 = 133 mM in the absence of added salt,23,24 cmc1 = 102 mM in [NaCl] = 0.1 M, and cmc1 = 69 mM in [NaCl] = 0.3 M were employed as input values in the calculations.24 The corresponding values for CTAB is cmc2 = 0.9, 0.45, and 0.2 mM.25−27 The cmc in deuterium oxide is usually found to be slightly lower than in H2O [i.e., about 2.5% lower for sodium dodecyl sulfate (SDS) and sodium decyl sulfate (SDeS)]28 (two surfactants with identical headgroup as SOS) and 0.7 mM for CTAB.27 This difference in cmc between H2O and D2O is smaller than the difference in cmc as obtained with different experimental techniques and correcting for it has negligible impact on calculated values of x. The cmc values for SOS and CTAB were confirmed with static light scattering measurements (i.e., cmc1 ≈ 130, 100, and 70 mM and cmc2 ≈ 1, 0.5, and 0.2 mM in [NaBr] = 0, 0.1, and 0.3 M, respectively, in both H2O and D2O). Influence of Adding Salt on Bilayers. Samples with bilayers were best fitted with a model for coexisting vesicles and disks.7 The vesicles have a radius roughly equal to Rv = 300 Å, irrespective of the concentration of NaBr, whereas the disks are too large in the presence of brine for their size to be determined with SANS. The insensitivity of vesicle size on concentration of added salt may be due to the large structural changes of the bilayer aggregates and the increase in fraction of disks at the expense of vesicles, with an increasing electrolyte concentration. The vesicle size as obtained with SANS qualitatively agrees very well with what is observed with cryo-TEM (cf. Figure 6B). As previously observed, vesicles formed in mixtures of an anionic and a cationic surfactant are rather small in magnitude.2 However, the anionic vesicles we observe in the SOS/CTAB system are found to be considerably larger than, for instance, vesicles formed in mixtures of sodium dodecyl sulfate (SDS) and didodecyldimethyl ammonium bromide (DDAB). The latter vesicles were found to be as small as 10− 20 nm in average diameter.29,30 Most interestingly, the SANS data for samples containing bilayers appear very different, depending on whether NaBr is present or not. In Figure 5, we have plotted typical SANS data, together with model fits, for one sample in absence of added salt and one in presence of [NaBr] = 0.3 M. The comparatively large amount of vesicles in the former case is evident from the

Figure 4. Diagrams showing surfactant concentrations where small ellipsoidal micelles, large polydisperse rodlike or wormlike micelles, perfect bilayer disks and vesicles (= perfect bilayers), and perforated bilayer disks and vesicles (= perforated bilayers) predominate for the dilution series y = 0.90 and 0.95 in [NaBr] = 0.3 M.

region of ellipsoidal micelles increases at the expense of polydisperse rods, as the amount of NaBr is increased from 0.1 to 0.3 M. A similar effect in which micelles become favored at the expense of bilayer vesicles upon adding salt to mixtures of oppositely charged surfactants has previously been demonstrated in model calculations by Yuet and Blankschtein.20 In their calculations, several contributions related to both head groups and tails were considered, and the physical origin of the effect was thus unclear. In our present calculations, however, it becomes evident that this is entirely an electrostatic effect that can be accurately accounted for by the Poisson−Boltzmann theory. From the calculated values of x, it is evident that ellipsoidal micelles form above about x = 0.8. However, whether rather small and monodisperse ellipsoidal micelles or long polydisperse rods are present in the samples also depends on the concentration of aggregated surfactant, since micelles are expected to grow in size with increasing surfactant concentration, for a given surfactant composition in the aggregates. For instance, ellipsoidal micelles are observed in the sample (y = 0.95, 80 mM, [NaBr] = 0.1 M) for which x = 0.77, whereas polydisperse rods are found in (y = 0.90, 80 mM, [NaBr] = 0.3 M), where x = 0.79 and the surface charge density in the micelles is approximately equal. The PB calculations reveal that the concentration of surfactant aggregated in micelles is substantially larger in the latter case (cmic = 37 mM as compared to 18 mM), which may explain why considerably larger micelles are observed despite the fact that the aggregate mole fraction of the surfactant in excess is about the same (or slightly higher) (cf. the tabulated values in the Supporting Information). The longest micelles observed close to the micelle-to-bilayer transition are rods with an average length ⟨L⟩ = 500 ± 15 Å in absence of added salt and ⟨L⟩ = 540 ± 20 Å in [NaBr] = 0.1 M, whereas wormlike micelles as long as ⟨L⟩ = 2900 ± 175 Å were observed in [NaBr] = 0.3 M. As a result of the micelles being considerably larger in [NaBr] = 0.3 M, they also become flexible, and the data for the sample (y = 0.95, 40 mM, [NaBr] = 0.3 M) were best fitted with a model for polydisperse flexible 3932


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Figure 5. Scattering intensity (in arbitrary units) as a function of the scattering vector q for mixtures of SOS and CTAB for a given mole fraction of SOS in solution y = 0.90 in deuterium oxide, in absence of added salt (○) and in [NaBr] = 0.3 M (□). The overall surfactant concentration for both samples is [SOS] + [CTAB] = 20 mM. Symbols represent SANS data and solid lines represent the best available fit with a model for coexisting bilayer disks and vesicles. The quality of the fits as measured by χ2 is 4.1 (○) and 2.2 (□). The two curves have been separated on the horizontal scale to make them appear clearer.

oscillation appearing at about q = 0.01 Å−1. In the presence of large amounts of salt, the oscillation is less clear, indicating that the fraction of vesicles is significantly lower in [NaBr] = 0.3 M as compared to solutions in the absence of added salt. This trend is also supported by cryo-TEM, which shows an increased amount of open structures and disks present at [NaBr] = 0.1 M, as compared to the case of no added salt [cf. Figure 6]. Notably, several of the disks seen in the cryo-TEM image in Figure 6B are substantially smaller (diameter about 500 Å or slightly less) than suggested by the SANS data analysis (average diameter about 2000 Å in the absence of added salt and too large to determine the size in brine). This discrepancy might be due to the sample treatment in cryo-TEM, in which a thin film ( 90.1 Å−1 between perfect and perforated bilayers for the egg lecithin/CTAC/Brine system. In contrast to these earlier studies, which are all based on indirect arguments considering differences in density of the bilayers and may be the result of several possible causes, we are, in the present investigation, able to directly determine the presence of perforated bilayers by means of investigating the geometrical structure as inherent in the form factor of the small-angle scattering data. Notably, there seems to be a discrepancy between cryo-TEM and SANS with respect to which particular samples of bilayers are perforated [cf. Tables S1−S4 in the Supporting Information for a comparison between the techniques]. For instance, the cryo-TEM image for the sample [y = 0.90, 20 mM, 0.1 M NaBr] shows perforated vesicles coexisting with disks, whereas perfect vesicles and disks are present according to SANS data. Likewise, coexisting wormlike micelles and perforated vesicles are seen with cryo-TEM for the sample [y = 0.90, 20 mM, 0.3 M NaBr] and perfect vesicles and disks with SANS. As a matter of fact, only perforated, and no perfect vesicles, are seen with cryo-TEM in samples with 0.1 or 0.3 M NaBr. We have previously reported an analogous discrepancy with respect to whether micelles or bilayers are present in SOS/CTAB mixtures in absence of added salt, and we were able to conclude that the presence of a comparatively large fraction of surfactant adsorbed at interfaces in the thin film (thickness < 0.5 μm), created during the sample preparation, may influence the structure of bulk aggregates as observed in cryo-TEM.7 Nevertheless, it is clear from our cryo-TEM study that both disks and perforated bilayers are favored at the expense of vesicles as a substantial amount of inert salt, NaBr, is added to our samples (cp. Figure 6, panels A and B). A similar effect may also influence the structure of bilayers (that is whether they are perforated or not), where the bulk aggregates present at total surfactant concentrations close to the transition from perfect to perforated bilayers (as observed with SANS), in average, may have a lower (i.e., negative) curvature than the planar adsorbed surfactant monolayers, provided that the holes are sufficiently small. As a consequence, the distribution of the two surfactants among bulk aggregates and adsorbed monolayers may lead to a depletion of SOS in the bulk aggregates observed with cryo-TEM. This may cause the formation of perforated bilayers in the thin cryo-TEM film to occur at higher surfactant concentrations as compared to a more voluminous sample where the adsorbed amount of

increases. As expected, all form factors coincide in the limit of low q values and assume their proper value of unity. In Figure 9, we have plotted SANS data for three different concentrations at y = 0.90 in [NaBr] = 0.1 M. For the sample

Figure 9. Scattering intensity (in arbitrary units) as a function of the scattering vector q for mixtures of SOS and CTAB for a given mole fraction of SOS in solution y = 0.95 in deuterium oxide in [NaBr] = 0.1 M. The overall surfactant concentrations for both samples are [SOS] + [CTAB] = 20 mM (○), 10 mM (□), and 5 mM (△). Symbols represent SANS data, and the solid lines represent the best available fit with a model for coexisting perfect bilayer disks and vesicles (○) and coexisting perforated bilayer disks and vesicles (□ and △). The results from the least-squares model fitting analysis are given in Table 2. The quality of the fits as measured by χ2 is 4.7 (○), 3.6 (□), and 2.1 (△). The curves have been separated on the horizontal scale to make them appear clearer.

[SOS] + [CTAB] = 20 mM, the data were fitted with a model for coexisting perfect vesicles and disks, but at the more dilute concentrations the data could only be fitted by assuming both disks and vesicles to be perforated. The presence of holes is evident from the decrease in scattering intensity at about 0.01− 0.02 Å−1, making it impossible to fit the data with a model for perfect bilayers. The fraction of disks is found to increase from fd = 0.68 to fd = 0.90, and the fraction of holes in disks increases from 1% to 3%, as the surfactant concentration decreases from 10 to 5 mM. The fraction of holes in vesicles is equal to about 10% for both samples with perforated bilayers. The presence of holes is most evident in samples with surfactant concentrations equal to or below 10 mM in the presence of [NaBr] = 0.1 and 0.3 M. In these samples, the fraction of holes in vesicles (4−11%) is always higher than the fraction of holes in disks (1−5%). The holes in the disks in these samples are always larger in size, with a radius in the range Rdh = 100−220 Å, than the holes in vesicles (Rvh = 45−65 Å). The latter quantity corresponds to, on average, 1−15 number of holes in the vesicles [cf. Tables 1 and 2]. Hence, it is indicated that some of the perforated structures may consist of vesicles with one single or just a few holes. As a matter of fact, vesicles opening up to form a single large hole is seen in a few of our cryo-TEM images, for instance in Figure 6A. In addition, the quality of the model fits for some of the more concentrated samples (i.e., [SOS] + [CTAB] = 20 and 40 mM at y = 0.90 and [NaBr] = 0.3 M) could be significantly improved using the model for perforated bilayers. As a consequence, we do not see any perfect bilayers at y = 0.90 and [NaBr] = 0.3 M (cf., Figure 4A), which indicates the strong 3935


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zero for disks and −4πNHk̅bic for a perforated disk with NH number of holes. Consequently, it follows that increasing values of k̅bic = 2k̅c − 8ξkcH0 is expected to generate an increase in g, as a response to a minimization of the curvature free energy, giving rise to the sequence of transitions, vesicles → disks → perforated bilayers, in agreement with our experimental observations. The following expression

surfactant is negligible. It is also possible that the fact that the cryo-TEM samples were prepared in plain water (H2O), whereas SANS were measured using deuterium oxide (D2O) as a solvent, may have an influence on the concentration where a transition from perfect to perforated bilayers are seen to occur.

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TOPOLOGICAL CHANGES IN SURFACTANT BILAYERS In earlier investigations, perforated bilayers have mainly been reported from investigations using cryo-TEM. On the basis of these studies, it has been suggested that perforated bilayers usually form as an intermediate structure in-between branched long wormlike micelles and (perfect) bilayer vesicles,31 in agreement with some theoretical predictions.42 Also in the present study, perforated bilayers seem to appear at comparatively high surfactant concentrations, not far from the micelle-to-vesicle transition, according to the cryo-TEM measurements. Our SANS results, on the other hand, clearly demonstrate that bilayers are becoming perforated in the very dilute regime at high electrolyte concentrations (i.e. far beyond the micelleto-bilayer transition). We may summarize the structural behavior of mixed SOS/CTAB bilayers, as observed with SANS, with the following sequence of changing aggregate structure, vesicles → disks → perforated bilayers, as the surfactant mole fraction in the aggregates approaches equimolar composition and the electrolyte concentration is increased. As a matter of fact, this sequence of changes in bilayer morphology corresponds to a systematic change in aggregate topology and may be theoretically rationalized in terms of bending elasticity. The bilayer interfacial tension as a function of the mean and Gaussian curvatures may be written as43 bi

γbi(H , K ) = γ0 + 2kcbi(H − H0bi)2 + kc̅ K

bi

kc̅ = −

(6)

has been derived from the Poisson−Boltzmann theory by Mitchell and Ninham49 for an infinitely thin charged interface, where D1(x) ≡

∫x

0

t dt e −1 t

(7) −1

is the Debye function. κ is the Debye screening length, the Bjerrum length equals lB = 7.15 Å for water at room temperature, and ap is the area per surfactant in a planar layer. The saddle-splay constant, according to eq 6, is a monotonously decreasing function when plotted against κ−1, which means that k̅bic is expected to increase with decreasing influence of electrostatics. Equation 6 may be modified in order to take into account effects due to finite thickness of the surfactant layer50 and, in accordance, the spontaneous curvature H0 of a single monolayer may also influence k̅bic and enhance the increase of k̅bic as the influence from electrostatics decreases. As a result, the behavior of k̅bic , as predicted by the Poisson− Boltzmann theory, may explain our observations of a transition from vesicles to disks and subsequently to perforated bilayers as equimolar aggregate composition is approached and the electrolyte concentration is increased. Comparison between the Micelle-to-Bilayer Transition and Topological Transitions of Bilayers. In mixtures of oppositely charged surfactants, including the system studied in the present work, an abrupt transition from micelles to bilayers may be observed as the surfactant composition is changed beyond a certain value.7,51 This transition is characterized by a particularly narrow range of compositions where micelles and bilayer aggregates coexist. It has previously been demonstrated that this transition is expected to occur as the spontaneous curvature equals H0 = 1/4ξ.21,22 As a consequence of this transition only depending on (monolayer) spontaneous curvature H0, the difference in micelle size that is observed at the micelle-to-bilayer transition in absence and presence of added salt, respectively, cannot be rationalized as the result of a difference in spontaneous curvature. Accordingly, we have previously argued that larger and more elongated micelles do form in the presence of large amounts of electrolyte mainly as a result of a lower bending rigidity (kc) together with higher values of the saddle-splay constant (k̅c), in agreement with predictions as deduced from the Poisson−Boltzmann theory.52 The transition between bilayer aggregates with different topologies (vesicles → disks → perforated bilayers) is, on the other hand, mainly driven by changes in the saddle-splay constant (k̅c). This type of transition appears to be very different from the micelle-to-bilayer transition in the sense that it is gradual and diffuse rather than abrupt. It also covers comparatively broad ranges of compositions, where two or more different structures coexist. As a matter of fact, vesicles

(4)

where the spontaneous curvature Hbi0 = 0 for a symmetrical bilayer, the bending rigidity kbic = 2kc, and the saddle-splay constant k̅bic = 2k̅c − 8ξkcH0 may be expressed in terms of the corresponding quantities of a surfactant monolayer (H0, kc, and k ̅ c).44−46 The free energy of a bilayer aggregate is obtained by means of integrating the interfacial bilayer tension γbi over the entire interfacial area A [i.e., E = ∫ γbi(H, K) dA]. All interfacial shapes that may be generated from one another by twisting and stretching, without breaking the interface, belong to the same topology.47 Different topologies are characterized with the quantity genus (g), which represents the number of handles or holes present in the self-assembled aggregate. In accordance with the Gauss-Bonnet theorem, g is directly related to the integral over the Gaussian curvature K, that is

∫ KdA = 4π(1 − g )

⎡ −1 ⎤ 2κ −1 ⎢ ⎛⎜ πlBκ ⎞⎟⎥ D1 ln⎜ πlB ⎢⎣ ⎝ a pq ⎟⎠⎥⎦

(5)

which implies that the corresponding contribution to the curvature free energy, E = 4π(1 − g)k̅bic , depends on g as well as on the saddle-splay constant, k̅bic . With regard to the surfactant bilayer as the surface to be considered, vesicles consist of one geometrically closed surface giving a genus, g = 0; disks have the same topology as a vesicle with one hole giving g = 1, whereas for a perforated disk, g = NH + 1, where NH is the number of holes in the disk.47,48 This means that the Gaussian contribution to the curvature free energy depends on g and becomes equal to 4πk̅bic for vesicles, 3936


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rc

and bilayer disks coexist in all samples with bilayers that have been investigated in the present work, whereas micelles and bilayers (vesicles + disks) only coexist in two of our samples.

Radius of cylindrical micelle Thickness of self-assembled monolayer in bilayer disks ξ and vesicles (half bilayer thickness) σL/⟨L⟩ Relative standard deviation with respect to length of polydisperse rodlike micelles σv/Rv Relative standard deviation with respect to radius of polydisperse vesicles

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CONCLUSIONS The self-assembly in dilute aqueous mixtures of the anionic surfactant SOS and the cationic surfactant CTAB in the presence of [NaBr] = 0.1 and 0.3 M has been investigated with small-angle neutron scattering and cryo-transmission electron microscopy. Adding an inert salt, NaBr, has three major effects on the self-assembly in mixtures of SOS and CTAB. First, the micelles are found to be at least six times larger at the micelleto-bilayer transition in [NaBr] = 0.3 M, as compared to the case of the absence of added salt. Second, bilayer disks appear to be favored at the expense of vesicles upon adding a substantial amount of salt. As a result, unilamellar vesicles are found to be the predominant bilayer structure in absence of added salt whereas, mainly disks are present in the presence of [NaBr] = 0.1 and 0.3 M. The fraction of bilayer disks is found to significantly increase, and the amount of vesicles decrease, as samples prepared in brine are diluted and the surfactant mole fraction in the aggregates approaches 0.5. Third, the bilayers are found to become perforated in the most dilute solutions in the presence of NaBr. Accordingly, we observe the following sequence of transitions, vesicles → disks → perforated bilayers with increasing ionic strength as well as decreasing surface charge density, which implies a gradual change in topology. This sequence of transitions may be rationalized as a result of a monotonously increasing saddle-splay constant with decreasing influence from electrostatics, as predicted from the Poisson− Boltzmann theory. This is the first report of a quantitative characterization of the spontaneous formation of holes in bilayer aggregates as evaluated from a small-angle scattering experiment. Most interestingly, our results have generated a completely novel view with respect to the conditions for hole formation in bilayers, since they indicate that perforated bilayers do form, in mixtures of SOS and CTAB, beyond the regime where perfect bilayers are present, and not in connection with the transformation from micelles to bilayers as has previously been suggested.

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S Supporting Information *

Comparison of results from the different experimental techniques, models employed in the least-square fitting data analysis, normalized scattering cross section figures, and calculations of the surfactant mole fraction in micelles. This material is available free of charge via the Internet at http:// pubs.acs.org.

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fm fv f dh f vh ⟨L⟩ Rd Rv Rdh Rvh

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +46 8 790 99 21. Fax: +46 8 20 82 84. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Institut Laue Langevin (ILL) is acknowledged for allocated SANS beam time (Proposals 9-10-1181 and 9-10-1255). K.E. was supported by the Swedish Research Council (VR).

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REFERENCES

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APPENDIX A

List of Symbols of Fitting Parameters Present in Tables 1 and 2

a b c fd

ASSOCIATED CONTENT

Half axis related to thickness of ellipsoidal micelles Half axis related to width of ellipsoidal micelles Half axis related to length of ellipsoidal micelles Mass fraction of bilayer disks coexisting with bilayer vesicles Mass fraction of micelles coexisting with bilayer disks and vesicles Mass fraction of bilayer vesicles coexisting with bilayer disks Area fraction of holes in disks Area fraction of holes in vesicles Volume-averaged length of polydisperse rodlike micelles Disk radius Volume-averaged vesicle radius Radius of holes in disks Radius of holes in vesicles 3937


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