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Articles Transition from Micelles to Vesicles in Aqueous Mixtures of Anionic and Cationic Surfactants Olle So¨derman* Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P. O. Box 124, S-221 00 Lund, Sweden
Kathleen L. Herrington and Eric W. Kaler Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
David D. Miller Eastman Kodak Company, Rochester, New York 14650-2110 Received August 9, 1996. In Final Form: May 19, 1997X Vesicles form spontaneously in a variety of aqueous mixtures of oppositely charged surfactants. Here we report the morphological transition from spherical micelles to vesicles observed in mixtures of dodecyltrimethylammonium chloride (DTAC) and sodium dodecylbenzenesulfonate (SDBS) as probed by the complementary techniques of quasielastic light scattering (QLS), NMR self-diffusion and relaxation measurements, and time-resolved fluorescence quenching (TRFQ) experiments. In these mixtures, there is limited growth of the micelles with changes in composition, and vesicles abruptly begin to form at a characteristic mixing ratio of the two surfactants. As the composition moves further into the vesicle region, the quantity of micelles decreases in proportion to the number of vesicles that form. Thus, in mixtures of DTAC and SDBS, the transition from micelles to vesicles is continuous. This is in contrast to the first-order phase transition exhibited by other aqueous mixtures of oppositely charged surfactants, in which micelles first grow into extended threadlike micelles and samples intermediate to the micellar and vesicle phases separate into two macroscopic phases.
Introduction Vesicles form spontaneously when oppositely charged surfactants are mixed in aqueous solution.1-3 This unexpected finding is a direct consequence of the strong nonideal interactions between oppositely charged head groups in surfactant aggregates. The effective “neutralization” in the head group plane reduces the repulsion between head groups, and as a result, the effective surfactant packing parameter depends on composition.1,2 An additional consequence of this nonideal interaction is that aggregates form in aqueous solution at concentrations far below that of the cmc of either pure surfactant.2-4 In this paper, we explore in more detail the transformation in microstructure that occurs as the content of cationic surfactant is reduced relative to the amount of anionic surfactant. In particular, we explore the transformation of spherical micelles (characteristic of the pure aqueous solutions of each surfactant) into large unilamellar vesicles. The nature of the transition from micelles to vesicles * Corresponding author. X Abstract published in Advance ACS Abstracts, September 15, 1997. (1) Kaler, E. W.; Murthy, A. K.; Rodriguez, B.; Zasadzinski, J. A. Science 1989, 245, 1371. (2) Kaler, E. W.; Herrington, K. L.; Murthy, A. K.; Zasadzinski, J. A. J. Phys. Chem. 1992, 96, 6698. (3) Herrington, K. L.; Kaler, E. W.; Miller, D. D.; Zasadzinski, J. A.; Chirulvolu, S. J. Phys. Chem. 1993, 97, 13792. (4) Holland, P. M.; Rubingh, D. N. J. Phys. Chem. 1983, 87, 19841990.
S0743-7463(96)00790-1 CCC: $14.00
is important in a number of practical applications5,6 and is of fundamental interest as well.7-12 The unilamellar structure of a vesicle mimics the cell membrane; consequently, vesicles have been widely used as model systems for in vitro investigations such as the study of membrane proteins. In these investigations, surfactants are often used to solubilize cell membranes in order to obtain pure samples of membrane proteins. Often, membranes are reformed with the purified proteins by starting with a mixed micellar solution of surfactant and the membraneforming lipid. Removal of the surfactant then induces membrane formation. For proper design of these processes, an understanding of lipid-surfactant interactions and phase transformations is necessary. In general, the solubilization of phospholipid liposomes with added surfactant proceeds in three stages:5,6 (1) incorporation of surfactant into the bilayer, (2) transition from liposomes to mixed micelles, and (3) complete solubilization, often with a decrease in micellar size as the surfactant content in the micelle increases. Protein reconstitution follows the reverse path as bilayers are formed either with dilution or with removal of surfactant by dialysis. In the transition region, micelles (5) Helenius, A.; Simons, K. Biochim. Biophys. Acta 1975, 415, 29. (6) Fendler, J. Membrane Mimetic Chemistry; Wiley: New York, 1983. (7) Fromherz, P.; Ro¨cker, C.; Ru¨ppel, D. Faraday Discuss. Chem. Soc. 1986, 81, 39. (8) Fromherz, P. Chem. Phys. Lett. 1983, 94, 259. (9) Lasic, D. D. Biochim. Biophys. Acta 1982, 692, 501. (10) Lasic, D. D. J. Theor. Biol. 1987, 124, 35. (11) Lasic, D. D. Biochem. J. 1988, 246, 1. (12) Stecker, M. M.; Benedek, G. B. J. Phys. Chem. 1984, 88, 6519.
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and bilayered structures can coexist in a single macroscopic phase, or when extensive micellar growth is favored, samples can separate into phases of rodlike micelles and bilayered structures. The literature about phospholipid membrane solubilization is extensive and often contradictory. This is in part because studies of phospholipid membranes are confounded by use of metastable structures which lead to observations of phenomena that depend on the experimental path rather than on the thermodynamic state. Consequently, some of the observed change in morphology is due to the release of stresses present in the metastable vesicles. In contrast, vesicles formed from oppositely charged surfactants are equilibrium structures, so it is possible to study the microstructural transformation related solely to the micelle-to-vesicle phase transition. Thus, investigation of the micelle-to-vesicle phase transition using vesicles prepared from oppositely charged surfactants can provide insight into biological membrane applications by decoupling the effects due to metastability from those due to the relationship between composition and morphology. Mixtures of dodecyltrimethylammonium chloride (DTAC) and sodium dodecylbenzenesulfonate (SDBS) were selected for a systematic investigation of the morphological transition. The microstructure present in the neighborhood of this transition can be probed using the complementary techniques of quasielastic light scattering (QLS), time-resolved fluorescence quenching (TRFQ) experiments, and NMR self-diffusion and relaxation measurements. Quasielastic light scattering is a standard method for sizing colloidal dispersions, but as discussed elsewhere,13 it alone does not provide an adequate characterization of samples that contain polydisperse populations of various aggregates. The TRFQ technique is a well-established method for determining aggregation numbers of surfactant micelles.14-16 An extension of this technique can detect the presence of small micelles in turbid solutions of vesicles and liposomes.17,18 Such detection using scattering techniques is frustrated by the overwhelming signal from large vesicular or liposomal structures. In the TRFQ method, the quenching of a fluorescent probe is monitored following its instantaneous excitation by a pulse of light. It is possible to differentiate between microstructures on the basis of the observed kinetics of the fluorescence quenching. In micelles, probes see a statistical distribution of quenchers and the fluorescence quenching follows an approximately double exponential decay. On the other hand, vesicles act essentially as batch reactors in which the probes see an average quencher concentration; thus, the fluorescence quenching follows a nearly single exponential decay. NMR tracer self-diffusion and relaxation experiments can provide detailed information on the microenvironment present in complex fluids.19-22 For example, use of a 2Hlabeled surfactant molecule can provide information on the time scale for lateral diffusion of the probe molecule (13) Yatcilla, M. T.; Herrington, K. L.; Brasher, L. L.; Kaler, E. W.; S. Chiruvolu; Zasadzinski, J. A. J. Phys. Chem. 1996, 100, 5874. (14) Almgren, M.; Lo¨froth, J. E. J. Colloid Interface Sci. 1981, 81, 486. (15) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289. (16) Almgren, M. Adv. Colloid Interface Sci. 1992, 41, 9-32. (17) Miller, D. D.; Evans, F. D. J. Phys. Chem. 1989, 93, 232. (18) Miller, D. D.; Magid, L. J.; Evans, F. D. J. Phys. Chem. 1990, 94, 5921. (19) So¨derman, O.; Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 445-483. (20) So¨derman, O.; Olsson, U. Micellar Solutions and Microemulsions. In Encyclopedia of Nuclear Magnetic Resonance; Grant, D. M., Harris, R. K., Eds.; Wiley: Chichester, England, 1996; pp 3046-3057.
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along the aggregate surface.23 In parallel, by measuring the self-diffusion of water, it is possible to detect the presence of enclosed aqueous pockets, as is the case in solutions containing vesicles or reversed micelles. NMR measurements of samples containing heavy water can also identify the presence of two phases in a sample that may be difficult to detect by any other technique (see, for example, refs 24 and 25). This is especially valuable when investigating viscous multiphase samples (e.g. rodlike micelles and liquid crystalline phases). In this case, twophase samples may appear homogeneous and as a single phase for a long period of time, when in fact they are metastable dispersions that are kinetically trapped. NMR measurements easily distinguish between metastable dispersions and true one-phase samples. Deuteron exchange between the two phases is slow relative to the NMR time scale; therefore, the measured NMR spectrum is the superposition of the spectra from each phase in the sample. In the present study we have used two NMR methods in order to characterize the morphological transitions taking place, viz. the NMR self-diffusion method to monitor the water self-diffusion and the 2H NMR relaxation method to monitor the dynamics of specifically 2Hlabeled DTAC. In summary, we feel that the combination of these methods provides an unambiguous view of the evolution of the microstructure in the mixed surfactant system presently under study. Materials and Methods Sample Preparation. Dodecyltrimethylammonium with either bromide (DTAB) or chloride (DTAC) counterions was obtained from Tokyo Kasei and was recrystallized three times from a 1:1 mixture of ethanol and acetone. DTAC, with 2Hlabeled methyl groups in the trimethylammonium head group, was used for selected NMR measurements. The labeled DTAC was obtained from Syntestja¨nst (Lund, Sweden) and was used as received. Hard-type (branched-chain) sodium dodecylbenzenesulfonate (SDBS) was used as received from Tokyo Kasei. Samples were prepared by first making stock solutions of either cationic or anionic surfactant at the desired concentration in deionized water. The stock solutions were equilibrated at room temperature, and then samples were prepared by vortex-mixing the stock solutions at the desired ratio. Samples were equilibrated for at least 1 month in a thermostated bath. Except for vortex-mixing and gravity filtration, the solutions were not subjected to any type of mechanical agitation. All subsequent experiments were performed at 25.0 °C. Phases were examined by eye and between crossed polarizer films to determine the number of phases and the presence of any lamellar or hexagonal liquid crystal phases. Single phases displaying Tyndall scattering were identified as possible vesicle phases, with the presence or absence of vesicle structures ultimately determined by the following methods. Quasielastic Liquid Scattering. Quasielastic light scattering (QLS) measurements were made with a Brookhaven spectrometer (BI-9000) of standard design. All measurements were made at a scattering angle of 90°, and the intensity autocorrelation function was analyzed by the method of cumulants.26 Stock solutions of each pure surfactant were filtered through 0.22 µm Millipore filters prior to preparing samples. (21) Lindman, B.; Olsson, U.; So¨derman, O. Surfactant Solutions: Aggregation Phenomena and Microheterogeneity. In Dynamics of Solutions and Fluid Mixtures by NMR; Delpuech, J.-J., Ed.; John Wiley: Chichester, England, 1995. (22) Lindman, B.; Olsson, U. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 344. (23) Quist, P. O.; Halle, B.; Furo, I. J. Chem. Phys. 1991, 95, 69456961. (24) Monduzzi, M.; Olsson, U.; So¨derman, O. Langmuir 1993, 9, 2194. (25) Marques, E.; Khan, A.; Miguel, M. G.; Lindman, B. J. Phys. Chem. 1993, 97, 4729. (26) Koppel, D. E. J. Phys. Chem. 1972, 57, 4814.
Transition from Micelles to Vesicles Occasionally, solutions for light scattering were also filtered through a 0.22 µm Millipore filter into the scattering cell. Filtering did not alter the measured vesicle sizes. TRFQ. Fluorescently-labeled surfactant solutions were prepared by drying a measured amount of pyrene in cyclohexane onto the walls of a glass vial, adding the desired surfactant solution, and stirring overnight. In all cases, the molar ratio of pyrene to surfactant was less than 0.001. Successive aliquots of the quencher dibutylaniline (DBA) in ethanol were added directly to the surfactant solutions in quartz cuvettes 1-2 h prior to measurement. In no case did the amount of ethanol in the surfactant solution exceed 1 vol %. Time-resolved fluorescence quenching experiments were performed using the LS-100 fluorimeter system of Photon Technology, Inc. (South Brunswick, NJ). Excitation at 337 nm was accomplished using an N2 flash lamp and monochromator. Excitation (lamp) profiles were collected at 337 nm using a nonfluorescent scattering solution (nondairy creamer). Pulse widths were no broader than 5 ns at half-height. Fluorescence emission was collected at 384 nm using 500 channels at 1.5 ns/ channel. Analysis with lamp deconvolution was performed using software provided by IBH Consultants, Ltd. (Glasgow, Scotland). NMR. The 2H NMR relaxation results were obtained on a Bruker MSL100 spectrometer operating at 15.3 MHz. The spinlattice relaxation times T1 were determined by means of the standard inversion recovery technique. The T1 values were evaluated by means of a nonlinear least-squares procedure based on the Unifit package.27 The errors presented in the T1 values correspond to an approximately 80% level of confidence, taking random errors only into account. They were obtained following procedures suggested in ref 28. The transverse relaxation times, T2, were determined from the bandwidths (all of the recorded NMR bands were Lorentzian to within the experimental uncertainty; see also the discussion below) after suitable corrections for the magnetic field inhomogeneties. The errors reported in the T2 values are estimated from repeated experiments. The water self-diffusion coefficients were determined from the same samples as those used in the relaxation studies on a Surrey Medical Imaging Systems Inc. (SMIS) NMR spectrometer, interfaced to a JEOL FX100 electromagnet. An ordinary spinecho sequence was used and parameters were as recommended by Stilbs.29 The field-gradients were generated by a gradient driver of “in-house” design and construction. The actual diffusion coefficients were obtained from the raw data with the Unifit package (see above). Presented errors correspond to an approximately 80% level of confidence, taking random errors only into account.
Results and Discussion Phase Behavior. The phase behavior in cationic-rich mixtures of unlabeled DTAC with SDBS is shown in Figure 1. Micelles form in DTAC-rich mixtures up to a mixing ratio, Y, of about 0.93 (Y ) mol of DTAC/[mol of DTAC + mol of SDBS]), as determined by both QLS and NMR methods (see below). When additional SDBS is added, vesicles form. The single-phase vesicle lobe extends to nearly 1 wt % surfactant in DTAC-rich mixtures of DTAC and SDBS. At higher concentrations, the solution separates into two phases (a vesicle phase and a lamellar phase). For comparison, the phase behavior in cationicrich mixtures of DTAB and SDBS is also shown. When bromide is the counterion, the vesicle phase extends to higher surfactant concentrations (100 mM, compared to 40 mM when chloride is the counterion). The phase behavior in SDBS-rich mixtures with DTAC was not studied. On the basis of these observations, we explored the transition from micelles to vesicles at a fixed overall surfactant concentration of 0.8 wt % (0.8 wt % corresponds to 29 mM DTAC or 23 mM SDBS) as a function of Y. (27) Program No. 307, Quantum Chemistry Program Exchange, Department of Chemistry, Indiana University, Bloomington, IN 47401 (Author: Chandler, J. P. Oklahoma State University, Stillwater, OK). (28) Stilbs, P.; Moseley, M. J. Magn. Reson. 1978, 31, 55. (29) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1-45.
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Figure 1. The partial phase diagram for aqueous mixtures of SDBS with either DTAB or DTAC at 25 °C on a molar basis. The phase boundaries for mixtures of SDBS with DTAC are shown with solid lines and those for mixtures of SDBS with DTAB are shown with dashed lines. Single phase regions are vesicles (V) and micelles (M). At higher concentrations, the vesicle and/or micellar phases are in equilibrium with a lamellar phase of higher surfactant content. The mixing ratio at which vesicles start to appear for mixtures of DTAC and SDBS was found to within (0.005. The long dashed line is the equimolar line.
The surprising effect that counterion identity has on the extent of the vesicle lobe for cationic-rich mixtures is most likely an indication of the important role that intervesicle interactions play in determining the extent of the vesicle phase. As reported elsewhere,2,30 the extent of the vesicle phase appears to be set by the condition of close-packing of the vesicles. When intervesicle interactions are stronger, the vesicles begin to feel crowded at lower surfactant concentrations, and the extent of the vesicle lobe decreases. The observation that the lobe is smaller when chloride is the counterion is in keeping with this rationale. Chloride ions are more highly hydrated than are bromide ions and thus are less effective in shielding the charge of the surfactant aggregate than are bromide counterions. As a result, there is a lower degree of counterion binding in micellar solutions when chloride is the counterion.18 It is likely that this effect is the explanation for the reduced lobe size in mixtures of DTAC and SDBS. QLS Results. The morphology in the neighborhood of the micelle-to-vesicle transition was probed further using QLS. The sharp increase in apparent aggregate radius as the mixing ratio falls below the critical mixing ratio is consistent with the observed increase in scattered light intensity, as shown in Figure 2. On the basis of the QLS measurements, the critical mixing ratio at 0.8 wt % surfactant occurs at Y ) 0.94 for labeled DTAC in mixtures with SDBS and Y ) 0.95 with unlabeled DTAC (Figure 2). This small difference in the mixing ratio that corresponds to the onset of vesicle formation is likely due to the different batches of DTAC used and/or the accuracy of the experiments. TRFQ Results. In micelles, the quenching of fluorescence intensity as a function of time, I(t), from micellesolubilized pyrene by the micelle-solubilized DBA, following an instantaneous pulse of excitation, is described by14-16 (30) Herve´, P.; Roux, D.; Bellocq, A.-M.; Nallet, F.; Gulik-Krzywicki, T. J. Phys. II Fr. 1993, 3, 1255.
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Figure 2. The apparent aggregate radius as a function of the surfactant mixing ratio, Y, in the region of the transition from micelles to vesicles as probed by QLS for samples with a total surfactant concentration of 0.8 wt %. Circles are results for aqueous mixtures of labeled DTAC and SDBS while the symbol × shows the results for mixtures of unlabeled DTAC and SDBS.
I(t) ) I(0) exp[-A2t - A3(1 - exp(-A4t))]
(1)
where A2 and A4 are independent of quencher concentration and represent the unquenched rate constant for pyrene fluorescence and the quenching rate constant, respectively. A3 is the average number of quenchers per micelle, or
A3 )
CDBA N ) ηNagg Cm agg
(2)
where cDBA is the quencher concentration, cm is the concentration of surfactant in micellar form, η is their ratio, and Nagg is the average aggregation number of the micelles. In many cases, cm can be calculated as the total surfactant concentration less the cmc. The complex “exponential inside an exponential” form of eq 1 arises from the statistical (Poissonian) distribution of quenchers in micelles. Thus, some micelle-solubilized probes see no quenchers during their excited-state lifetimes, while others see one, two, or more quenchers. Fluorescence decay curves from micellar systems appear to be of a double-exponential form, with a rapid decay at short times (from micelles containing an excited probe and at least one quencher) followed by a slow, unquenched decay at long times (from micelles containing an excited probe and no quencher). The slow decay time is independent of the quencher concentration. In vesicles and other large aggregates, on the other hand, each probe sees the same average number of quenchers during its excited-state lifetime. Quenching in large aggregates, then, is governed by a modified Stern-Volmer kinetic expression14-16,31,32
I(t) ) I(0) exp[-A5t - A6t1/2]
(3)
where A5 and A6 both depend on quencher concentration. A5 is related to the Stern-Volmer parameter, and A6 is a so-called “diffusion depletion” term.17,18 Decay curves measured for samples containing only large aggregates, (31) Caruso, F.; Grieser, F.; Murphy, A.; Thistlethwaite, P.; Urquhart, R.; Almgren, M.; Wistus, E. J. Am. Chem. Soc. 1991, 113, 4838. (32) Medhage, B.; Almgren, M. J. Fluoresc. 1992, 2, 7.
Figure 3. Normalized value of the parameter A4 as a function of quencher concentration η for various values of Y. Samples have a total surfactant concentration of 0.8 wt %.
such as vesicles, appear as nearly single exponentials with decay times that decrease as the quencher concentration increases. When both micelles and vesicles coexist, the quenching kinetics will be governed by a linear combination of eqs 1 and 3. Unfortunately, the large number of parameters involved in such a combination makes quantitative analysis intractable. As long as the system contains some population of micelles, however, the decay curves will maintain a double-exponential appearance, and the decay at long times will be characteristic of unquenched probe and independent of quencher concentration. As the fraction of the surfactant in micelles decreases (and the fraction in vesicles increases), the quality of the fit to eq 1 decreases (the sum of the squared errors becomes large), and the self-consistency of the parameter estimates disappears (e.g., A4 becomes a strong function of quencher concentration). For a sample with a very large number ratio of vesicles to micelles, it is no longer possible to get a meaningful fit of the data to eq 1, and eq 3 must be used. Hence, TRFQ can be used to detect the presence of small micelles in turbid, vesicle-containing dispersions and to track the transformation of small micelles into vesicles as conditions are changed. TRFQ data for mixtures of DTAC and SDBS at 0.8 wt % and at various values of Y were measured. For samples with Y ) 0.974, 0.944, 0.925, 0.898, and 0.85, the slope of the fluorescence decay at long times is independent of quencher concentration and equal to the slope of the unquenched (η ) 0) decay. This indicates that there are micelles present in these samples, even though the QLS results show a dramatic change in average size around Y ) 0.94. In contrast, the decay curves for Y ) 0.799 are almost monoexponential, and the slopes at long times, for quenched samples (η > 0) are steeper than the slope of the unquenched curve (η ) 0). Thus there are no micelles in this sample. The variation of A4 (obtained by fitting the data to eq 1) with η has been found to be diagnostic for vesicles; the more positive the slope of A4 vs η, the more vesicles are in the sample.18 A4 plotted as a function of η (Figure 3) shows that very few, if any, vesicles are present at Y ) 0.974 and 0.944. Only a small number are present at Y ) 0.925, and a significant number are present at Y ) 0.898. Again, the QLS data show the same trend, but the QLS method is very sensitive to the small vesicle concentrations present around Y ) 0.94. For samples with Y ) 0.85 and 0.799, however, no meaningful fits of
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scale of the experiment is on the order of 100 ms. Thus a fast exchange situation is at hand with regard to exchange from the interior to the exterior of the vesicle. On the other hand, it takes on the order of 10 µs for a water molecule to travel across a vesicle of radius 1000 Å. As a consequence, the water is equilibrated with regard to position during its stay in the vesicle, and the point of exit of a water molecule from a vesicle is not correlated with the point of entry. Thus, a vesicle equilibration condition with regard to the position for the water molecules in the vesicle holds on the time scale of the measurements. For such a situation, the observed diffusion coefficient is a weighted average given by19 Figure 4. The reduced water diffusion coefficient Dr as a function of the surfactant mixing ratio Y for samples with a total surfactant concentration of 0.8 wt %. The horizontal line indicates the value for bulk water while the second solid line is the result of a fit of eq 6 to the data with R ) 2000 Å and the area per polar head group Ahg ) 25 Å2 and the use of the data in Table 1 to obtain the fraction of DTAC and SDBS in the vesicle aggregates. See text for details.
the data to eq 1 could be found. The decay curves for Y ) 0.799 are well fit by the vesicle model (eq 3), but those for Y ) 0.85 do not match either model closely. Micellar aggregation numbers, as calculated from the TRFQ data assuming that all aggregated surfactant is in micellar form, show a slight increase in micellar size with increasing SDBS content. The micelle aggregation number increases from 48 for Y ) 0.974 to 86 for Y ) 0.944. When Y ) 0.925, the fit of the data to the micelle model is not self-consistent, which indicates the coexistence of micelles and vesicles. This mixing ratio represents roughly 8 SDBS molecules for 100 DTAC molecules. At still higher amounts of added SDBS, the data strongly support coexistence of micelles and vesicles, and the fraction of vesicles increases with increasing SDBS concentration. Finally, for values of Y above about 0.799, the quenching data indicate that all mixed micelles have been solubilized and that only vesicles remain. Details of aggregate structure at intermediate compositions (e.g., Y ) 0.85) cannot be determined from the TRFQ data. NMR Water-Diffusion. Figure 4 shows the reduced diffusion coefficients Dr (the actual diffusion coefficients divided by the value for bulk water) as a function of the mixing parameter Y. The value of Dr stays constant and equal to unity in a range of values for the mixing ratio from Y ) 1 down to a value of approximately Y ) 0.93. Below this value of Y, the values drop and show an approximately linear dependence on Y. At the low surfactant concentration present, the effects of micellar obstruction effects and surfactant hydration, both of which could decrease the reduced diffusion coefficients, are negligible. The break in the plot at Y ) 0.93 signals the formation of vesicles. As a consequence, the observed decrease in Dr is caused by a contribution due to the entrapped water, the proportion of which is increasing as Y decreases. Moreover, the linear dependence upon Y also indicates that the transition from micelles to vesicles is a continuous one. This is further corroborated by the NMR relaxation data discussed below. A more quantitative analysis of the diffusion data can be developed as follows. With a limited number of assumptions, this analysis yields an estimate of the vesicle size. The residence time of a water molecule in a vesicle of radius 1000 Å is on the order of 1 ms,33 while the time (33) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain where Physics, Chemistry, Biology and Technology meet; VCH Publishers, Inc.: New York, 1994.
D ) PvesDves + (1 - Pves)Dbulk
(4)
where Pves is the fraction of water entrapped in the vesicle, and is approximately equal to the volume fraction of vesicles, Φves. Dves is the contribution to the observed diffusion from water within the vesicles, and Dbulk is the diffusion coefficient of the bulk water in the vesicle solution. The total rms displacement of water molecules measured by the NMR experiment is on the order of 10-20 µm. As a consequence, the diffusion of water within a vesicle does not contribute to the rms displacement of the water in a vesicle solution. The contribution from diffusion of the vesicle, Dves, may be neglected in eq 4 since, for reasonable size vesicles, this term is small compared to diffusion of the bulk water. Finally, the bulk diffusion coefficient of water can be set equal to the diffusion of pure water D0, slightly reduced by the obstruction effects due to the presence of the vesicles. For spherical aggregates the obstruction effect is given by34
A)
1 1+
Φ 2
(5)
where Φ is the volume fraction of spherical aggregates. With all of these simplifications, eq 4 reduces to
1 - Φves D ) Dr ) D0 Φves 1+ 2
(6)
which can be expanded to first order in the vesicle volume fraction
3 Dr ) 1 - Φves + ... 2
(
)
(7)
where the next term is of the order Φves2. For further analysis we require knowledge of the distribution of the two surfactants in their different environments. Let us assume that the concentration of free DTAC at the point where vesicles start to form is negligible. (A concentration of 0.8 wt % corresponds to 29 mM surfactant, while the cmc for DTAC is 20.3 mM, implying that a fraction of free DTAC close to the cmc is 0.7. However, this number is reduced considerably by the added anionic surfactant.4) Let us further assume that the vesicles have 5 DTAC per SDBS (this value represents the ratio of DTAC to SDBS where the vesicle lobe has its maximum extension; cf. Figure 1). Thus at the critical mixing ratio where vesicles start to form, micelles with a mole fraction with of SDBS of 0.07 (Y ) (34) Jo¨nsson, B.; Wennerstro¨m, H.; Nilsson, P.-G.; Linse, P. Colloid Polym. Sci. 1986, 264, 77-88.
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Table 1. Fraction of DTAC Bound to Vesicles, PDves as a Function of Ya Y PDves
0.9269 0.0167
0.9186 0.0933
0.9103 0.1716
0.9019 0.2516
0.8792 0.4772
0.8294 1.0135
a The values of P Dves have been obtained assuming that (i) there is no free monomeric surfactant, (ii) that the micelles have a mole fraction of 0.07 with respect to SDBS, and (iii) that the vesicle contains 5 DTAC per SDBS.
0.93) are assumed to coexist with vesicles containing 5 DTAC per SDBS. With these assumptions the fraction of DTAC bound to the vesicles, PDves can be calculated, and the results are presented in Table 1. Knowledge of the area per polar head group, Ahg, now allows us to compute the vesicle radius R (assuming that the vesicles are monodisperse in size), since the total area of the vesicle bound surfactant and the value of R determines the value of Φves. We have performed a small angle X-ray scattering investigation of a lamellar sample with composition 13.9/56.1/30.0 wt % SDBS/DTAC/water, corresponding to a molar ratio of DTAC to SDBS of 5:1, i.e., the assumed molar ratio in the vesicles. The average area per polar head group for this sample was 25.3 Å2. Using this value for the area per polar head group (together with the result of Table 1), a value of R ) 2000 Å is obtained for the vesicle size from the reduced diffusion coefficients in Figure 4. The theoretical predictions for Dr using this value for R and eq 6 are included as a solid line in Figure 4. This size is larger than that measured with QLS, which probably reflects the neglect of polydispersity effects and the cost of the somewhat crude assumptions made above as well as the neglect of vesicle interactions in the QLS analysis. We note that neglect of repulsive interparticle interactions (as would be the case for the charged vesicles considered here) in the analysis of QLS data underestimates the particle sizes. In summary, the diffusion data give us the following picture of the micelle to vesicle transition. Vesicles start to form at a rather well-defined mixing ratio. The transition is continuous, in the sense that there is an equilibrium between micelles and vesicles which is gradually shifted toward the vesicle form as the value of Y is decreased. At no point do the vesicles and micelles form separate phases. If the vesicles are described as monodisperse spheres and the area per polar head group is assumed to be 25 Å2 (as obtained from independent experiments), the vesicle radius corresponds to approximately 2000 Å. NMR Relaxation. In addition to the self-diffusion measurements, NMR allows measurement of the surfactant dynamics. The most suitable surfactant-bound nuclei for such studies is the 2H nucleus. Thus we have chosen to perform experiments on DTAC with the three N-methyl groups deuterated. Given in Figure 5 are the transverse 2H relaxation rates (R ) as a function of the mixing ratio 2 Y, with the longitudinal relaxation rates (R1) presented as an insert. The relaxation rates follow the same trends as for the data presented above, with sudden changes taking place at a mixing ratio of roughly 0.93. A very important question is whether vesicles coexist with micelles within a single phase. Although the data presented above provide some insight into this question, the measured NMR DTAC deuterium spectra provide a definite answer. If micelles and vesicles coexist within a single phase, there is the possibility of rapid exchange of surfactant between vesicles and micelles and in such a case, a single NMR signal would be observed. On the other hand, if the two microstructures were in separate phases, the exchange would always be slow, and the NMR
Figure 5. The deuterium spin-lattice relaxation rates R2 (measured at 15.3 MHz) as a function of the surfactant mixing ratio Y for samples with a total surfactant concentration of 0.8 wt %. The estimated errors in R2 are always smaller than the size of the symbol. The insert gives the corresponding longitudinal relaxation rates.
signals from the two phases would overlap. The experimental results for DTAC and SDBS mixtures show (with a high degree of accuracy) a single NMR Lorentzian band with a width that steadily increases with decreasing mixing ratio Y. It should be added that while it is difficult to differentiate between a situation with a sum of Lorentzian bands of not too widely differing bandwidths from that of a single Lorentzian band, the bandwidth of a micellar bound surfactant is much smaller than that of a vesicle (by roughly a factor of 50), which makes it possible to differentiate the two cases. To analyze the relaxation data in more detail, the following background information is needed. The deuterium relaxation rates are given by the coupling between the electric field gradient at the site of the deuterium nucleus and the deuterium quadrupole moments. The relevant expressions for the longitudinal (R1) and the transverse (R2) relaxation rates are35
R1 ) K[2J(ω0) + 8J(2ω0)] R2 ) K[3J(0) + 5J(ω0) + 2J(2ω0)]
(8)
K is given by (3π2/40)χ2, where χ is the quadrupole coupling constant. J(ωo) is the (reduced) spectral density function, and it is in this quantity that the information concerning the surfactant dynamics can be found. The relaxation rates measured for aggregated surfactant systems can be reasonably described by the “two-step” model. In this model, two well-separated time scales account for the surfactant dynamics:19 one is associated with the rapid internal motions within the aggregates (in the present case of a methylene-group such motions would be constituted by rotation around the C3 axis of the methylene-group and of “internal” motions that the surfactant undergoes) while the second motion, which occurs on a slower time scale, is isotropic. Candidates for the slow motion are aggregate tumbling and/or surfactant lateral diffusion over curved aggregate surfaces (often referred to as translationally induced rotation), but also other isotropic motions are possible, such as surfactant exchange between aggregate bound states and monomeric state in the solution. The expression for the spectral density term in this model becomes36 (35) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, England, 1961. (36) Halle, B.; Wennerstro¨m, H. J. Chem. Phys. 1981, 75, 19281943.
Transition from Micelles to Vesicles
J(ω) ) A + S2Js(ω)
Langmuir, Vol. 13, No. 21, 1997 5537
(9)
where A is a constant contribution from the fast motions (which are assumed to be in the extreme narrowing regime), Js(ω) is the spectral density function associated with the slow motion referred to above, and S is the order parameter that quantifies the fraction of the quadrupolar interaction modulated by the slow motion. The order parameter is analogous to the order parameter measured from quadrupolar line splittings in anisotropic phases. Taking the difference between R2 and R1 eliminates the constant term connected with the fast internal motions, so
∆R )
9π2 2 2 s (χ S )[J (0) + Js(ω0) - 2Js(2ω0)] (10) 40
Figure 6 shows the variation of ∆R with Y. As for the other data, there is clearly a marked change taking place at roughly Y ) 0.93. In line with the analysis of the diffusion data, we now have to consider the rate of exchange of the DTAC molecules between the free monomeric state, the micellar state, and the vesicle state. If the exchange rate is rapid with respect to the intrinsic values of R2, then we will record a single NMR signal from the samples. This, as mentioned above, is in fact the result for all samples studied. Thus we may write a relation analogous to eq 4 for ∆R (assuming again that the fraction of free monomeric DTAC is negligible), so
∆R ) PDves∆Rves + (1 - PDves)∆Rmic
(11)
where PDves is the fraction of DTAC bound to vesicles. From the data in Figure 6 (and taking values for PDves from Table 1), we obtain ∆Rves ) 385 s-1. In order to calculate a slow correlation time for the vesicle bound surfactant, we require a value for χS (cf. eq 10 above). This can be obtained from the line splittings measured for anisotropic phases. In the present case we have measured the quadrupolar splitting ∆ to be 2.00 kHz in a lamellar phase of composition 56.1 wt % DTAC, 13.9 wt % SDBS, and 30 wt % water, corresponding to a molar ratio of DTAC to SDBS of 5:1. For a lamellar phase
3 ∆ ) χS 4
(12)
and with this value of χS, the slow correlation time for the vesicle-bound surfactant is calculated to be 12 µs. What is the physical origin of this correlation time? There are two rather obvious candidates for the underlying physcial process. Let us first consider the contributions to Js(ω) from the vesicle tumbling (correlation time τt) and surfactant lateral diffusion (correlation time τd) over the curved vesicle surface. Both of these give rise to Lorentzian spectral density terms:
J(ω) )
2τt,d 1 + ω2τt,d2
(13)
Moreover, as these two motions are independent we may write
τt )
4πηR3 3kT
τd )
R2 6Dlat
Figure 6. The quantity ∆R (measured at 15.3 MHz) as a function of the surfactant mixing ratio Y for samples with a total surfactant concentration of 0.8 wt %. The solid line is a fit of eq 11 to the data, in which we have used the data in Table 1 to obtain the fraction of DTAC in the vesicle aggregates. See text for details.
τs-1 ) τt-1 + τd-1
(14)
To judge the relative contributions from τd and τt, a value for Dlat is required. Based on extensive relaxation studies of DTAC micelles, one of the present authors and his coworkers arrived at a value of 5 × 10-11 m2 s-1 at 27 °C.37,38 With this value of Dlat and for any reasonable value of R, the term connected with the lateral diffusion dominates, and we may therefore write
τs )
R2 6Dlat
(15)
With the values of τs and Dlat given above, we obtain R ≈ 600 Å from eq 15. This value differs by a factor of 3 from the result of the diffusion analysis and by a factor of slightly less than 2 from the QLS results. Even if there is a certain degree of uncertainty in the choice of values for the parameters (such as Ahg, Dlat and χS) necessary for the analysis of both sets of NMR data performed above, it is not possible to reconcile the two data sets by any reasonable choice of parameter values. The inclusion of vesicle size polydispersity cannot account for the differences between the results from the relaxation and diffusion data. The relaxation data are weighed by R to the fourth power (on account of the fact that the correlation time is weighed by R2 (cf. eq 15) and the amount of spins in each vesicle is weighed by the area and hence R2) while the diffusion data is weighed by R to the third power. Hence, the relaxation data would, for a polydisperse situation, report a larger value of R than would the diffusion data. Let us now consider the second candidate for the process underlying the slow correlation time of eq 15. This is constituted by surfactant exchange between vesicles, micelles, and free surfactant. Presumably, such an exchange takes place via monomeric DTAC in the bulk. For such a case the slow correlation time is simply the lifetime of the surfactant in the vesicle aggregate. Given the inconsistency between the vesicle size as obtained from the analysis based on surfactant lateral diffusion and water diffusion and QLS data, we believe that it is the second candidate that is responsible for the (37) So¨derman, O.; Walderhaug, H.; Henriksson, U.; Stilbs, P. J. Phys. Chem. 1985, 89, 3693-3701. (38) So¨derman, O.; Henriksson, U.; Olsson, U. J. Phys. Chem. 1987, 91, 116-120.
5538 Langmuir, Vol. 13, No. 21, 1997
slow correlation time obtained from the relaxation data. Thus we suggest that the lifetime of a DTAC molecule in the vesicle is on the order of 12 µs. Concluding Remarks. The sequence of phases observed in mixtures of DTAC and SDBS as a function of the mixing ratio Y is compatible with that predicted on the basis of geometric packing arguments: small spherical micelles form in binary surfactant-water mixtures, and aggregates of low curvature, such as vesicles or lamellar bilayers, form as equimolar compositions are approached. There is no observable two-phase region separating the phases containing micelles or vesicles in mixtures of surfactants in which there is insignificant growth of micelles. At higher surfactant concentrations, samples do separate into two phases; however, the two phases are an isotropic phase and a lamellar phase. From this observation, it appears that one of the two equilibrium phases contains either vesicles or micelles and the second phase consists of the LR phase. Thus, this two-phase region does not correspond to the transition from micelles to
So¨ derman et al.
vesicles. This behavior is also observed in all SDBS-rich mixtures,2 for mixtures of SDBS with MTAB,2 and in dilute anionic-rich mixtures of CTAB and SOS.13 Aggregate morphology in aqueous mixtures of oppositely charged surfactants is controlled by composition: both the concentration and mixing ratio of the two surfactants participate in determining the equilibrium microstructure. In this paper, we describe a continuous transition between small, spherical micelles and large unilamellar vesicles triggered by the change in the ratio of cationic to anionic surfactant. The change in morphology has been followed using the complementary techniques of QLS, TRFQ, and NMR relaxation and self-diffusion. Acknowledgment. This work received financial support from the Swedish Natural Science Research Council and from the United States National Science Foundation (CTS-9319447). LA960790J
