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Langmuir 2006, 22, 9860-9865
Effect of Mixing on the Morphology of Cylindrical Micelles Nily Dan,*,† Karin Shimoni,‡ Veena Pata,†,§ and Dganit Danino*,‡ Department of Chemical and Biological Engineering, Drexel UniVersity, Philadelphia, PennsylVania 19104, Department of Biotechnology and Food Engineering, and the Russell Berrie Nanotechnology Institute, TechnionsIsrael Institute of Technology, Haifa, Israel 32000, and Laboratory of Cellular and Molecular Biophysics, National Institute of Child Health and Human DeVelopment, Bethesda, Maryland 20892-2425 ReceiVed May 5, 2006. In Final Form: September 1, 2006 Increasing the spontaneous curvature of an amphiphile can lead to a first-order morphology transition from threadlike micelles to a branched network. The two morphologies were linked to entropy-driven topological defects; networks are dominated by Y-junctions, while linear threadlike structures are dominated by spherical end-caps. In this paper we investigate the effect of mixing on the morphological transitions in nonionic amphiphilic systems. We find that mixed equilibrium structures are obtained within seconds; these mixed cylindrical structures display comparable numbers of end-caps and branch points, resulting in a novel ‘short armed’ branched (SAB) morphology. Quite surprisingly, the probability of either defect (end-caps or branch points) is independent of composition, so that neither a first-order nor a second-order morphological transition is observed. A possible explanation may be local demixing of the two amphiphilic components, which adds a degree of freedom and thus enables the formation of a unique morphology that cannot be obtained in single-component systems. We further find that within a relatively large composition range phase equilibrium exists between vesicles, SAB micelles, and spherical micelles.
Introduction Self-assembled cylindrical micelles have recently been identified in a variety of biomedical and biomaterial systems. For example, the transition from vesicle to threadlike micelles in phosphatidylcholine-sphingomyelin-cholesterol mixtures may be related to bile and intestinal lipid processing.1 Huntingtonexon 1, a marker of Huntington’s disease progression, has been shown to form self-assembled cylindrical aggregates.2 The formation of cylindrical micelles in some lipid-detergent mixtures affects the reconstitution of membrane proteins,3 while cylindrical diblock copolymer micelles were found to solubilize drugs more effectively than spherical aggregates.4 The “packing parameter”, defined as the ratio between the volume of the hydrophobic tail and the area per headgroup times the tail length, defines the amphiphile spontaneous curvature.5,6 The spontaneous curvature, in turn, defines the local curvature at which the amphiphile interfacial energy is optimized. Cylindrical micelles are formed by amphiphiles with moderate spontaneous curvature, namely, where the effective size of the headgroup is somewhat larger than that of the tail. The aggregate energy is minimized by the formation of infinitely long, rodlike * D.D. address: Department of Biotechnology and Food Engineering, TechnionsIsrael Institute of Technology, Haifa, Israel 32000. Phone: (9724) 829-2143. Fax: (972-4) 829-3399. E-mail:
[email protected]. N.D. address: Department of Chemical and Biological Engineering, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104. Phone: (215) 895-6624. Fax: (215) 895-5837. E-mail:
[email protected]. † Drexel University. ‡ TechnionsIsrael Institute of Technology. § National Institute of Child Health and Human Development. (1) Moschetta, A.; Frederik, P. M.; Portincasa, P.; van Berge-Henegouwen, G. P.; van Erpecum, K. J. J. Lipid Res. 2002, 43, 1046-1053. (2) Burke, M. G.; Woscholski, R.; Yaliraki, S. N. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 13928-13933. (3) Knol, J.; Sjollema, K.; Poolman, B. Biochemistry 1998, 37, 16410-16415. (4) Crothers, M.; Zhou, Z.; Ricardo, N. M.; Yang, Z.; Taboada, P.; Chaibundit, C.; Attwood, D.; Booth, C. Int. J. Pharm. 2005, 293, 91-100. (5) Israelachvili, J. N. Intermolecular and surface forces: with applications to colloidal and biological systems; Academic Press: London, 1985. (6) Safran, S. A. Statistical thermodynamics of surfaces, interfaces and membranes; Addison-Wesley: Reading, MA, 1994.
micelles, where the interfacial curvature is uniform everywhere. However, the entropy of such a system is proportional to the number of micelles and is therefore relatively low. Topological defects increase the entropy of the cylindrical micelles; spherical end-caps shorten the length of linear micelles, thereby increasing their number, while Y-junction points increase branching and randomness. However, both types of defects (end-caps and branch points) are associated with an energetic penalty resulting from the formation of regions with nonoptimal curvature.7-9 In single-component nonionic amphiphilic suspensions, the type of preferred defect is set by the spontaneous curvature of the amphiphile:7,8 The energetic penalty associated with the formation of spherical end-caps is moderate for molecules with relatively high spontaneous curvature. Therefore, such amphiphiles will form finite-length threadlike, linear micelles, whose length decreases with increasing density of end-cap defects. The density of end-caps increases and the length of the cylindrical micelles decreases with increasing amphiphile spontaneous curvature, until a transition to spherical micelles occurs.7,8 The penalty associated with the formation of Y-junctions is moderate for amphiphiles with lower spontaneous curvature, where the degree of hyperbranching (and thus the size of the network) increases with increasing junction density. The two types of cylindrical morphologies (linear or branched) differ significantly in their solution properties: systems of threadlike micelles are characterized by a viscoelastic behavior similar to that of linear homopolymer suspensions.10 Percolation in branched micelles can lead to phase separation11 and rheological behavior similar to that of a cross-linked gel.12 The transition between the two types of morphologies was found to be of first order, induced by changes in the amphiphilic spontaneous curvature.7-11 The (7) Tlusty, T.; Safran, S. A. J. Phys. Condens. Matter 2000, 12, A253-A262. (8) Zilman, A.; Safran, S. A.; Sottmann, T.; Strey, R. Langmuir 2004, 20, 2199-2207. (9) Dan, N.; Safran, S. A. AdV. Colloid Interface Sci. In press. (10) Hoffman, H. ACS Symp. Ser. 1994, 578, 2-31. (11) Strey, R.; Glatter, O.; Schubert, K.-V.; Kaler, E. W. J. Chem. Phys. 1996, 105, 1175-1188. (12) Voit, A. V.; Shchipunov, Y. A. Colloid J. 2000, 62, 424-430.
10.1021/la061254m CCC: $33.50 © 2006 American Chemical Society Published on Web 10/19/2006
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methodology by which the spontaneous curvature was adjusted (temperature,11 weight fraction of the hydrophilic group13) was not found to affect the nature of the transition. Many of the cylindrical micelle systems of biological and/or technological interest contain more than one type of amphiphile.1-4 However, although the morphology of cylindrical micelles in single-component systems is well understood,7-9 less is known about the morphology of mixed cylindrical micelles. Previous studies of nonionic amphiphilic mixtures found that the contour length of cylindrical micelles increases (i.e., end-caps are reduced) with the mole fraction of the low interfacial curvature component,14,15 with temperature,16,17 or with a decrease in the spontaneous curvature of one of the components.14,15 Since all these reduce the average spontaneous curvature of the mixture, these observations are consistent with the single-amphiphile case, where reducing the spontaneous curvature of the amphiphile reduces the probability of end-cap formation. However, to the best of our knowledge, the nature of the morphological transition in mixed systems has not been established.9 The goal of this study is to investigate the effect of mixing on the morphology of cylindrical micelles. Most indirect methods cannot distinguish between linear micelles, branched micelles, or networks, so that generally the structure is deduced indirectly from measurements of the aggregate hydrodynamic radius, turbidity, or viscosity.8-12,14-17 Direct observation is more effective in determining the exact type of structures formed and can yield much more detailed information, especially in cases where coexistence between different structures may take place. Therefore, we employ digital cryo-transmission electron microscopy (cryo-TEM), a method that has been shown to be effective in studying a variety of self-assembled systems, including cylindrical morphologies in single, nonionic amphiphiles.13,18-20 Combining it with light microscopy, we could probe the structures on length scales ranging from few nanometers (cryo-TEM) to many micrometers (light microscopy). The direct microscopy study is complemented by indirect dynamic light scattering measurements. Several criteria led to our choice of system: to ensure that cylindrical structures are indeed composed of both components, the pure amphiphiles should not be known to form any type of cylindrical micelles. Also, the structures formed by the individual amphiphiles should be insensitive to their concentration in solution, so that the spontaneous curvature of the mixture would vary only as a function of the mixture composition and not the absolute amphiphile concentration. These criteria eliminate such components as the nonionic alcohol ethoxylate (oligo oxyethylene-n-alkyl ether) surfactants, CiEj, or ionic amphiphiles, since their aggregation behavior is known to be sensitive to their concentration and the system temperature.11,21 Our system is composed of a moderate MW, vesicle-forming diblock copolymer (polybutadiene-co-ethylene oxide, PBD-PEO) and a surfactant that forms spherical micelles (Triton X-100). Both components are nonionic and have not been found to form anything but vesicles (diblock copolymer, as shown below) or spherical micelles (surfactant),22 regardless of system conditions. (13) Jain, S.; Bates, F. S. Science 2003, 300, 460-464. (14) Acharya, D. P.; Kunieda, H. J. Phys. Chem. B 2003, 107, 10168-10175. (15) Acharya, D. P.; Hossain, M. K.; Jin-Feng; Sakai, T.; Kunieda, H. Phys. Chem. Chem. Phys. 2004, 6, 1627-1631. (16) Kwon, S. Y.; Kim, M. W. Phys. ReV. Lett. 2002, 89: Art. No. 258302. (17) Kwon, S. Y.; Kim, M. W. Langmuir 2001, 17, 8016-8023. (18) Talmon, Y. Ber. Bunse-Ges. 1996, 100, 364-372. (19) Bernheim-Groswasser, A.; Wachtel, E.; Talmon, Y. Langmuir 2000, 16, 4131-4140. (20) Danino, D.; Talmon, Y.; Zana, R. J. Colloid Interface Sci. 1997, 186, 170-179. (21) Svenson, S. Curr. Opin. Colloid Interface Sci. 2004, 9, 201-212.
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Thus, any observed cylindrical micelle must contain some fraction of both components. Materials and Methods The diblock copolymer P2903-BDEO (Polymer Source, Inc.) has a total MW of 3800 g/gmol and the MPEO of 1300 g/gmol, the volume fraction of EO block is 0.34, and the polydispersity is 1.04. The block copolymer contains 46 BD units and 30 EO units. Phosphatebuffered saline (PBS, Biological Industries) and Triton X-100 (BioLab) were used as received. Above the critical micelle concentration, which is 0.2-0.3 mM,22 Triton X-100 forms spherical micelles of ∼4 nm in diameter. Polymer vesicles were prepared by film rehydration. Briefly, a given amount of polymer was solubilized in chloroform, dried with nitrogen, and kept under vacuum for 4 h. Rehydration of the polymer film with PBS, followed by incubation at 60 °C in an oven for 48 h, led to spontaneous formation of vesicles. To study the solubilization of the block copolymer-based aggregates, stock micellar solutions of Triton X-100 were prepared, and calculated amounts were mixed with the block copolymer vesicular solutions to yield the final concentrations required. Light Microscopy (LM). A small (5 µL) drop was placed on a glass slide, covered with a cover slide, and examined at 25 °C by an Olympus BX51 light microscope, operated with Nomarski differential interference contrast (DIC) optics. Images were recorded digitally with an Optronixs LE-digital camera connected to the light microscope. Cryogenic-Transmission Electron Microscopy (cryo-TEM). For cryo-TEM studies, specimens were prepared in a controlled environment vitrification system (CEVS)23 at a controlled temperature of 25 °C and at saturation to avoid loss of volatiles. A drop of the examined solutions was placed on a TEM grid covered with a perforated carbon film using two preparation procedures: (1) ‘conventional’ procedure, in which the examined diblock copolymer/ surfactant solutions were mixed in the tube, and a drop of the mixture was applied to the grid; (2) on-the-grid-processing (OTGP) procedure, in which the components were mixed on the grid, resulting in contact times of only a few seconds.24 In both procedures, the drop was blotted with a filter paper to form a thin liquid film (100-250 nm thick). The thinned sample was immediately plunged into liquid ethane at its freezing temperature (-183 °C) to form a vitrified specimen and then transferred to liquid nitrogen (-196 °C) for storage, until examination. The vitrified specimens were examined in a Philips CM120 or an FEI Tecnai 12 transmission electron microscopes operating at an accelerating voltage of 120 kV. We used an Oxford CT3500 cryo-specimen holder that maintained the vitrified specimens below -175 °C during sample transfer and observation. Specimens were examined in the low-dose imaging mode to minimize beam exposure and electron-beam radiation damage. High magnification images were recorded digitally on a cooled Gatan MultiScan 791 CCD camera or a Gatan Ultrascan 2kx2k cooled CCD camera, using the DigitalMicrograph software. Dynamic Light Scattering (DLS). DLS measurements of 4 mg/ mL block copolymer solutions and Triton X-100 concentrations of up to 10 mM (1 mM Triton X-100 is equivalent to 0.65 mg/mL) were done using a Brookhaven laser light scattering system (BIC, BI-200SM Research Goniometer System). Experiments were conducted with a diode-pumped solid-state 300 mW laser at a wavelength of 532 nm, at a constant temperature of 25 °C. The scattered light was detected at an angle of 90° by a photomultiplier tube. The hydrodynamic radii, RH, of pure polymer-based assemblies and of the assemblies that formed after the addition of Triton X-100 were determined from the Stokes-Einstein equation. The intensityautocorrelation function was measured with a BI-9000AT digital signal processor and analyzed using the Contin method.25,26 (22) Jones, N. M. Int. J. Pharm. 1999, 177, 137-159. (23) Bellare, J. R.; Davis, H. T.; Scriven, L. E.; Talmon, Y. J. Electron Microsc. Tech. 1998, 10, 87-111. (24) Danino, D.; Talmon, Y.; Zana, R. Colloid Surf. A 2000, 169, 67-73. (25) Pronencher, S. W. Comput. Phys. Commun. 1982, 27, 217-227. (26) Pronencher, S. W. Comput. Phys. Commun. 1982, 27, 229-242.
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Figure 1. Cryo-TEM images of pure diblock copolymers in aqueous solutions: (a) 4 mg/mL copolymer and (b) 10 mg/mL. In both concentrations we observe only bilayer structures in the form of unilamellar and multilamellar vesicles. Identical structures were observed after 3 months (not shown), indicating vesicle stability. Bars ) 100 nm.
Results In Figure 1 we show a cryo-TEM micrograph of the pure copolymer in water. The average number of hydrophobic BD monomer repeat units, NBD, is 46 and that of hydrophilic EO, NEO, is 30. As may be expected from this ratio,13 the pure copolymer forms only bilayer structures (vesicles), either single or multilamellar, whose thickness is ∼20 nm. Only vesicles were observed over the entire range of concentration examined (0.81 to 10 mg/mL) and over long periods of time (up to 3 months), thereby suggesting high structural stability. Multiple Structure Coexistence. Mixing the high spontaneous curvature surfactant with the low spontaneous curvature copolymer enables control of the average spontaneous curvature, similar to the use of temperature8 or modification of the amphiphile head and/or tail group (i.e., synthetic methodologies).13 To relate the mixture composition to the spontaneous curvature we use the average weight fraction of the hydrophilic headgroups:5,6 The weight fraction of the hydrophilic (PEO) copolymer segment is 0.34, while the weight fraction of the headgroup in Triton X-100 is approximately 0.68. Thus, mixing them in different ratios allows the average head weight fraction to be varied between those two values. In Figure 2 we compare representative light micrographs of the polymeric vesicle solution (4 mg/mL or ∼1 mM) taken in the absence (Figure 2a) and presence of 1.2 mM (Figure 2b) Triton X-100. We see that the density of large (micrometer and up) vesicles decreases upon the addition of the nonionic surfactant, suggesting that mixing leads to a reduction in large structures and, presumably, an associated increase in small structures. The density of the large structures apparently decreases monotonically with increasing Triton X-100 concentration. This is consistent, qualitatively, with our DLS measurements (see Table 1), which show that the size of the larger structures (presumably the large vesicles) decreases with increasing surfactant concentration, and the width of the structure size distribution becomes narrower. This is also consistent with the results of Pata et al.,25 where the intensity peak of polymeric vesicles decreased, and that of smaller structures increased, upon mixing with Triton X-100.
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Figure 2. Light microscopy micrographs of 4 mg/mL P29 vesicles in the absence (a) and in the presence of 1.2 mM (b) Triton X-100. Upon addition of surfactant, the number of large vesicles continuously decreased. Table 1. DLS Measurements of the Mean Diameter of P29 Vesicles, and the Mixed P29-Detergent Complexes as a Function of the Triton X-100 Concentration
Triton X-100 concentration [mM]
range of diameters [nm]
mean diameter, by intensity [nm]
mean diameter, by number [nm]
0 0.6 1.2 2 4 10
96-4000 135-1350 49-1227 43-1227 34-752 11-28
1650 1023 467 428 301 16.3
204 184 57.5 53.8 44.9 12.9
The DLS data (Table 1) and the light micrographs suggest that, as expected, mixing the vesicles with a high spontaneous curvature surfactant leads to vesicle dissolution. Our DLS data shows that the size of the self-assembled structures in the mixed polymer/surfactant systems ranges between ∼10-1000 nm. However, these measurements cannot yield detailed information regarding the nature and characteristics of the mixed structures. Cryo-TEM is an ideal method to directly visualize structures on such length scales: In Figure 3 we show a sequence of cryoTEM micrographs taken after mixing the copolymer (4 mg/mL or ∼1 mM) with increasing amounts of the nonionic surfactant Triton X-100. As expected, we find coexistence between cylindrical micelles and intact vesicles in the mixed systems. This coexistence is observed in surfactant concentrations ranging from 0.6 to 4 mM. The diameter of the cylindrical micelles is about 20 nm in all mixture compositions, similar to the width of the diblock copolymer bilayers. The structure of the cylindrical micelles is insensitive to the surfactant concentration (as discussed in detail below). However, in the cylindrical/vesicle coexistence regime, we also observe spherical micelles. The diameter of the spherical micelles, ∼15 nm, is somewhat smaller than that of the cylindrical ones (∼20 nm), but it is much bigger than that of the pure surfactant micelles (∼4 nm). Thus, we conclude that these
Mixed Cylindrical Micelles
Figure 3. Cryo-TEM images of diblock copolymer/surfactant mixtures in aqueous solutions, taken at least 10 min after mixing the component solutions. All systems are based on a copolymer concentration of 4 mg/mL, which translates to 1 mM. Surfactant concentrations correspond to (a) 0.6 mM, namely, polymer to surfactant molar ratio of 5:3, (b) 1.2 mM, polymer-to-surfactant ratio of 5:6, (c) 2 mM, polymer-to-surfactant ratio of 1:2, and (d) 4 mM, polymer to surfactant molar ratio of 1:4. Bars in all panels equal 100 nm. Throughout this range of compositions we see cylindrical micelles with a diameter of ∼20 nm, similar to the bilayer thickness. The structures display Y-junctions with ‘short armed’ branches’ (SAB) whose characteristic length is of the order of 2-5 times the micelle diameter (white arrows). The number of junction points roughly corresponds to the number of end-caps observed in all micrographs, regardless of the surfactant concentration. Coexistence of vesicles, SAB cylinders, and spherical mixed micelles (∼15 nm in diameter) was observed throughout this composition range.
spherical micelles must be composed of a mixture of copolymer and surfactant. Coexistence of vesicles, cylindrical micelles, and spherical micelles is observed for detergent compositions ranging from 0.6 to 4 mM. At 10 mM surfactant, namely, 1:10 polymer-tosurfactant and 0.65 head weight fraction, only mixed spherical micelles and small pure surfactant micelles are found (not shown), and threadlike aggregates and vesicles are no longer observed. The coexistence between the three different morphologies (lamellar, cylindrical, and spherical) indicates that in our mixed system the free energy difference between these structures is low. Formation of ‘Short Armed’ Branched (SAB) Structures. Once branched threadlike micelles form, increasing the spontaneous curvature (or surfactant content) further is expected to induce a morphological transition from branched to linear threadlike micelles.7-13 The nature of the transition between the two cylindrical micelle forms may be first-order as given by coexistence between branched and linear micelles, where the fraction of branched structures decreases with increasing spontaneous curvature, i.e., surfactant content.9 Alternately, the transition may be second-order, where the degree of branching decreases and the number of end-caps increases uniformly with the surfactant concentration. In our mixed system, cylindrical micelles are observed in the presence of 0.6 to 4 mM of Triton X-100, corresponding to molar copolymer-to-surfactant ratios that vary from 5:3 (excess of copolymer) up to 1:4 (excess of surfactant) and to average
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Figure 4. Effect of time on mixing in copolymer/surfactant systems. The system contains 4 mg/mL block copolymer and 1.2 mM Triton X-100, namely, about 50% mol of each component. Bar is identical for all panels, equals 100 nm. (a, b) Images taken 3 min after mixing the copolymer and surfactant solutions. (c, d) Images taken two weeks after mixing the solutions. We see that regardless of the equilibration time, the cylindrical micelles display SAB morphology, and these SAB structures coexist with vesicles and mixed spherical micelles. We do not see, at any time point, coexistence between hyperbranched structures and linear micelles (although a few threadlike micelles are sometimes seen). Also, the ratio of end-caps to junction points is similar in all cases. White arrows point to junctions, the black arrow to an end-cap, and the white arrowhead to a spherical micelle.
hydrophilic headgroup weight fractions ranging between 0.47 and 0.61. The weight fraction of the PEO segment of our diblock copolymer is 0.34. The weight fraction of the headgroup in Triton X-100 is approximately 0.68. Thus, mixing any ratio of polymer to surfactant should lead to an average head weight fraction that is larger than 0.34 and lower than 0.68. Jain and Bates13 found that PB-PEO diblock copolymers with MWs of the order of 3-5 kg/mol (similar to the one used in this study) form some type of cylindrical micelles at PEO weight fractions ranging from approximately 0.36 to 0.64. The range of mixture compositions at which we find cylindrical micelles is in agreement with previous studies. However, contrary to expectations from the single-component systems, we do not observe branched and/or threadlike morphologies. As shown in Figure 3, over the entire composition range at which we find cylindrical micelles, both Y-junctions and end-caps are found, leading to a composite morphology of ‘short armed’ branched structures (SAB). The SAB micelles display two striking features. First, the length of many of the arms is relatively short, of the order of 2-5 times the cylinder diameter. Second, we see no evidence of a first-order morphological transition between different types of cylindrical micelles, namely, coexistence of linear and branched structures. Nor do we find a second-order type transition, where the number (or density) of branch points decreases, and the number of end-caps increases, with increasing surfactant content. In fact, the overall number of end-caps is found to be similar to that of Y-junction points, regardless of the surfactant concentration. While this statement cannot be taken to be quantitative, due to the limitations of cryo-TEM as a quantitative sampling method, it clearly supports the lack of a trend in the ratio of branch points to end-caps as a function of surfactant concentration. Kinetics of the Structural Transitions. One possible explanation for SAB micelles is that they are not equilibrium
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structures. Indeed, the kinetics of surfactant/bilayer mixing from stock solutions (containing preformed aggregates) may be surprisingly slow, even in systems where the bilayer component is a small molecule.27,28 Diblock copolymers require even longer relaxation times.29 As shown in Figure 4a,b, SAB-type cylindrical micelles are observed within 1 min after mixing the copolymer and surfactant suspensions, thereby indicating rapid exchange between the diblock copolymer bilayers and the surfactant micelles. Identical structures are found when the mixture is allowed to equilibrate over periods ranging from 24 h to 14 days (Figure 3c,d). We did not observe regions of predominantly linear or mostly hyperbranched structures in any of the surfactant/ copolymer compositions (namely, 0.6-4 mM surfactant/4 mM copolymer), regardless of the equilibration time. (Similar structures have been observed by Jain and Bates29 in mixtures of nonionic diblock copolymers that were molecularly mixed before the introduction of the aqueous solvent, thereby ensuring equilibration.)
Discussion and Conclusions In this paper we examine the effect of increasing the spontaneous curvature on the self-assembled structures formed by mixing a low spontaneous curvature, vesicle-forming component (the copolymer) with a high spontaneous curvature, spherical micelle-forming component (Triton X-100 surfactant). We find that, as may be expected,30 the population of vesicles decreases and that of mixed structures increases with increasing mole fraction of the surfactant. However, contrary to previous studies, which find coexistence between vesicles and cylindrical micelles, we find coexistence between vesicles (lamellae), cylindrical micelles, and mixed spherical micelles over a wide range of mixture compositions. Moreover, our data indicates that cylindrical micelles composed of two nonionic amphiphiles differ significantly from singlecomponent systems. In the single-component system, there is a first-order transition from Y-junction dominated branched structures to end-cap dominated linear, threadlike arrays. This transition is induced by increasing the spontaneous curvature.7,8 However, in our mixed system we find coexistence of both topological defects in the form of SAB micelles. The coexistence between the two types of defects does not indicate a secondorder transition, since the relative number of junction points to end-caps is insensitive to surfactant concentration. To understand this conclusion we must review the underlying causes for the formation of topological defects. Topological defects in cylindrical micelles form to increase the assembly entropy.6-9 The entropic gain associated with either type of defect (end-cap or Y-junction) is similar, a constant that is independent of amphiphile properties.7,8 In a single-amphiphilic system, the entropy gain associated with a defect is reduced by an energetic penalty due to the formation of a region with nonoptimal interfacial curvature. Thus, the type of defect favored in the single-component system depends on the defect that incurs a lower interfacial bending penaltyshighly curved end-caps for amphiphiles with relatively high spontaneous curvature, and low curvature Yjunction points for amphiphiles with low spontaneous curvature.8 Changing the spontaneous curvature leads to a first-order transition between the two defects, and thus, between the micelle morphologies.7-11 (27) Schnitzer, E.; Kozlov, M. M.; Lichtenberg, D. A. Chem. Phys. Lipids 2005, 135, 69-82. (28) Lichtenberg, D. A.; Schnitzer, E.; Kozlov, M. M. Biophys. J. 2004, 86, 174A-174A, Part 2, Suppl. S. (29) Jain, S.; Bates, F. S. Macromolecules 2004, 37, 1511-1523. (30) Pata, V.; Ahmed, F.; Discher, D. E.; Dan, D. Langmuir 2004, 20, 38883893.
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In a system containing a mixture of amphiphiles with different spontaneous curvatures, the energetic penalty for the formation of a topological defect may be mitigated by local segregation of the components: regions of end-caps will be enriched in the high curvature component (in our case, the surfactant), while Y-junctions will be enriched with the low curvature component (the diblock). This local segregation reduces the interfacial bending penalty associated with the formation of defects, but at some entropic cost due to demixing. It is interesting to note that the formation of one type of defect, enriched in one component (e.g., end-caps/surfactant), must be associated with the formation of a neighboring region depleted by that component, thus more likely to form the other type of defect (junction points enriched by copolymer). As a result, both types of defects are likely to occur within the same cylindrical micelle, in similar numbers, and (likely) within a short distance from each other. Unfortunately, we are not aware of an analytical model that can describe mixed, nonionic amphiphilic micelles (most models31-33 are based on expansions in interfacial curvature, applicable only to low curvature structures such as bilayers). However, we can qualitatively enumerate the different energetic and entropic contributions to the formation of topological defects. The gain in entropy associated with defect formation is similar whether the micelle composition remains uniform (as in the singlecomponent case) or segregates into regions of different composition. However, the penalties associated with defect formation in the two cases are different. In the uniform, or one-component, case, formation of defects whose curvature differs from that of the micelle incurs a penalty whose magnitude is proportional to the bending stiffness of the amphiphile(s) times the area of the defect.8 In the case of local segregation (assuming that spontaneous curvature of the mixture in the area of the defect matches the defect curvature), the penalty is due to loss of entropy arising from demixing. Thus, the parameters determining whether an amphiphilic mixture will remain uniformly mixed (and thus exhibit either end-caps or Y-junctions, but not both) or segregate (and thus exhibit both types of defects) are the interfacial bending stiffness and the size of the segregation area (defect). If the stiffness is low when compared to the mixing entropy, we will observe suspensions of either threadlike, linear micelles or hyperbranched networks. If the bending stiffness is high when compared to the mixing entropy, then we expect segregation and formation of structures characterized by both defects simultaneously, i.e., SAB micelles. It should be emphasized that the formation of SAB micelles applies only to mixtures where one amphiphile has a low spontaneous curvature and the other has a high spontaneous curvature. In mixtures of moderate cylinder-forming amphiphiles with high curvature ones, end-caps will be favored over branch points regardless of which mechanism (segregation or uniform deformation) takes place, and the length of the cylindrical micelle should decrease (namely, the number of end-caps increases) with the fraction of the high curvature component. In mixtures of cylindrical forming amphiphiles with low curvature (bilayer forming) amphiphiles, we expect that junction points will be favored over end-caps. The density of branch points should increase with increasing fraction of the bilayer-forming component. In Table 2 we summarize our predictions for the morphologies formed by different types of mixtures. The bending moduli of (31) Dan, N.; Safran, S. A. Macromolecules 1994, 27, 5766-5772. (32) Harries, D.; BenShaul, A. J. Chem. Phys. 1997, 106, 1609-1619. (33) Yuet, P. K.; Blankschtein, D. Langmuir 1996, 12, 3819-3827.
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Table 2. Effect of Mixture Characteristics on Preferred Cylindrical Micelle Morphology category
amphiphile 1 (mol fraction ) x)
amphiphile 2 (mol fraction ) 1 - x)
bending penalty
linear cylindrical micelles branched cylindrical micelles branched cylindrical micelles bilayers
low or high low high low or high
A B C D
spherical micelles spherical micelles spherical micelles branched cylindrical micelles
E F
spherical or linear cylindrical micelles bilayers spherical or linear cylindrical micelles bilayers
nonoionic amphiphilic molecules tend to increase with molecular weight. Thus, we expect that mixtures containing at least one macromolecular/polymeric amphiphile would fall into the ‘high’ bending penalty group, while those of small molecules will be described by a low bending penalty. Zheng and Davis34 investigated mixtures of a nonionic (linear), cylindrical micelleforming small molecule amphiphile with a spherical micelleforming diblock copolymer, thereby falling into the A category. They found, in all compositions, only spheroidal micelles.34 Jain and Bates29 investigated various mixtures of diblock copolymers: in systems of type C they found short armed branched micelles (except for one system where the spherical component was 50% of the mix). Mixtures of type F were also found26 to form SAB micelles. Uddin et al.35 examined mixtures of type D and found that most mixtures displayed a cloud point, namely, they formed a phase-separating percolating network. The agreement of so many different systems with our qualitative predictions, as summarized in Table 2, suggests that, indeed, our analysis is valid and not limited to any particular mixed amphiphile system. In conclusion, we examine here the topological defects determining the morphology of mixed, nonionic cylindrical (34) Zheng, Y.; Davis, H. T. Langmuir 2000, 16, 6453-6459. (35) Uddin, Md. H.; Morales, D.; Kunieda, H. J. Colloid Interface Sci. 2005, 285, 373-381.
low high
preferred morphology linear micelles; length decreases with x branched at low x, linear at high x short armed branched micelles over most x. branched networks; degree of hyperbranching decreases with x linear micelles at low x, branched micelles at high x. short armed branched micelles at all x (where cylindrical micelles form)
micelles. We find that although the types of defects (Y-junctions and end-caps) are similar in single- and mixed-component micelles, the resulting morphologies differ significantly. While in single-component systems increasing the spontaneous curvature leads to a first-order transition from junction dominated branched networks to end-cap dominated linear micelles,7-11 in mixed systems both types of defects coexist to form a ‘short armed’ branched (SAB) structure. Quite surprisingly, the shape of the SAB micelles (i.e., short armed branched micelles with comparable numbers of end-caps and branch points) is independent of the mixture composition (or spontaneous curvature ratio). The coexistence of these two types of defects may result from local desegregation of the amphiphilic components. Our observations are generalized, in a qualitative analysis, and found to agree with the behavior of a large number of different nonionic amphiphile mixtures. Acknowledgment. The collaboration was supported by The Louis and Bessie Stein Family Fellowship. The cryo-TEM work was performed at the Cryo-TEM Hannah and George Krumholz Laboratory for Advanced Microscopy, at the Technion. D.D. acknowledges the generous support of the Matilda Barnett Recoverable Trust and the Israel Science Foundation of the Israel Academy of Sciences and Humanities (Grant No. 9059/03). LA061254M
