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Branched Worm-like Micelles and Their Networks Z. Lin Miami Valley Laboratories, The Procter & Gamble Company, P.O. Box 538707, Cincinnati, Ohio 45253-8707 Received July 10, 1995. In Final Form: December 6, 1995X Branched worm-like micelles were found in aqueous solutions of alkylamine oxide and alkyl ethoxylate sulfate mixtures by cryo-transmission electron microscopy (cryo-TEM). These branched micelles formed interconnected micellar networks at high solution pH or salt concentrations. The networks are similar to the bilayer structures in the bicontinuous L3 phase reported in the literature, where an infinite multiconnected fluid membrane forms a bicontinuous structure. The rheological properties of these branched worm-like micelles and their networks were also studied. The branched micelle solutions exhibited weak viscoelasticity and an apparent yield stress value. However, no real yield stress value was observed. When a dense micellar network formed, the solution exhibited well-defined Maxwell behavior.
Introduction Surfactant molecules self-assemble into aggregates in aqueous solutions above the so-called critical micelle concentration (cmc). At low concentrations, the aggregates are generally spherical micelles.1 In some surfactant systems, long worm-like micelles form at higher concentrations and/or upon addition of salt or acid. The most extensively studied systems are alkyltrimethylammonium halide and alkylpyridinium halide.2-5 Halide anions associate only moderately with surfactant cations, and micellar growth is gradual. However, with anions that associate strongly with surfactant cations, such as salicylate (Sal-), worm-like micelles grow rapidly with the increase of salt concentrations. Entangled worm-like micellar networks were found in such systems.6,7 The spherical-to-worm-like micelle transition was also observed in cetyltrimethylammonium bromide upon addition of methylsalicyclic acid.6 This transition is not abrupt. Both types of micelles can coexist. When the majority of the surfactant is in worm-like micelles, the rheological behavior exhibited by these systems is viscoelastic as a result of micellar entanglement,6 analogous to that observed in solutions of flexible polymers.6-11 X
Abstract published in Advance ACS Abstracts, March 1, 1996.
(1) Tanford, C. The hydrophobic effect; Wiley: New York, 1973. (2) Imae, T.; Ikeda, S. Sphere-rod transition of micelles of tetradecyltrimethylammonium halides in aqueous sodium halide solutions and flexibility and entanglement of long rodlike micelles. J. Phys. Chem. 1986, 90, 5216-5223. (3) Kern, F.; Lemarechal, P.; Candau, S. J.; Cates, M. E. Rheological properties of semidilute and concentrated aqueous solutions of cetyltrimethylammonium bromide in the presence of potassium bromide. Langmuir 1992, 8, 437-440. (4) Appell, J.; Porte, G. Polymerlike behaviour of giant micelles. Europhys. Lett. 1990, 12, 185-190. (5) Candau, S. J.; Hirsch, E.; Zana, R.; Adam, M. Network properties of semidilute aqueous KBr solutions of cetyltrimethylammonium bromide. J. Colloid Interface Sci. 1988, 122, 430-440. (6) Lin, Z.; Cai, J. J.; Scriven, L. E.; Davis, H. T. Spherical-to-wormlike micelle transition in CTAB solutions. J. Phys. Chem. 1994, 98, 59845993. (7) Clausen, T.; Vinson, P. K.; Minter, J. R.; Davis, H. T.; Talmon, Y.; Miller, W. G. Viscoelastic micellar solutions: microscopy and rheology. J. Phys. Chem. 1992, 96, 474-484. (8) Rehage, H.; Hoffmann, H. Rheological properties of viscoelastic surfactant systems. J. Phys. Chem. 1988, 92, 4712-4719. (9) Cates, M. E.; Candau, S. J. Statics and dynamics of worm-like surfactant micelles. J. Phys.: Condens. Matt. 1990, 2, 6869-6892. (10) Shikata, T.; Hirata, H.; Kotaka, T. Micelle formation of detergent molecules in aqueous media: viscoelastic properties of aqueous cetyltrimethylammonium bromide solutions. Langmuir 1987, 3, 1081-1086. (11) Shikata, T.; Hirata, H.; Takatori, E.; Osaki, K. Nonlinear viscoelastic behavior of aqueous detergent solutions. J. Non-Newtonian Fluid Mechanics 1988, 28, 171-182.
Table 1. Sample Compositions (wt %) for Systems Studied 1 (pH ) 2 (pH ) 3 (pH ) 4 (pH ) 5 (pH ) 12.5) 13.3) 13.3) 8.7) 12.5) C12 amine oxide lauryl ethoxy sulfate NaCl
0.23 1.6
0.71 1.65
0.71 1.65
0.77 1.5
0.77 1.6
2.2
2.2
3.1
2.2
2.2
It has also been reported that rheological properties of worm-like micellar solutions in the system of cetylpyridinium chlorate (CPClO3) in sodium chlorate brine were very different from the systems mentioned above.12a,b A light-scattering study of this system suggested that wormlike micelles were present in the system. However, the viscosity was much lower than for other worm-like micelle systems and its response to stress was Newtonian or weak viscoelastic, depending on the salt concentration.12a,b In order to explain this unusual rheological behavior, Appell et al.12a suggested that a network of branched worm-like micelles that were interconnected could allow for the observed facts as opposed to an entangled network. A multiconnected branched micellar network and an entangled micellar network cannot be distinguished by scattering techniques such as neutron and light scattering. However, the rheological properties could be different. In the viscous flow, the branched micelle can slide the crosslink points along the micelle to response to the flow. This will give a very fluid solution and allow solution to have a faster relaxation of stress than disentanglement or breaking of worm-like micelles. An analogy can be drawn between this branched micellar network and structures in the L3 phase where an infinite multiconnected fluid membrane forms a bicontinuous structure.13 Cryo-TEM is a technique suitable for direct visualization of surfactant aggregates formed in solution.14 There is no staining or drying artifact associated with this technique.15 Recently, cryo-TEM has been used to explore the spherical-to-worm-like micelle transition in cetyltri(12) (a) Appell, J.; Porte, G.; Khatory, A.; Kern, F.; Candau, S. J. Static and dynamic properties of a network of wormlike surfactant micelles (cetylpyridinium chlorate in sodium chlorate brine). J. Phys. II France 1992, 2, 1045-1052. (b) Khatory, A.; Kern, F.; Lequeux, F.; Apell, J.; Porte, G.; Morie, N.; Ott, A.; Urbach, W. Entangled versus multiconnected network of wormlike micelles. Langmuir 1993, 9, 933939. (13) Snabre, P.; Porte, G. Viscosity of the L3 phase in amphiphilic systems. Europhys. Lett. 1990, 13, 641-645. (14) Vinson, P. K.; Bellare, J. R.; Davis, H. T.; Miller, W. G.; Scriven, L. E. Direct imaging of surfactant micelles, vesicles, discs and ripple phase structures by cryo-transmission electron microscopy. J. Colloid Interface Sci. 1991, 142, 74-91.
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Figure 1. Cryo-TEM image of sample 1. Worm-like micelles (w) and spherical micelles (s) coexist in solution.
methylammonium bromide solutions,6 the micellar geometry in the nonionic surfactant hexaethylene glycol monohexadecyl ether,16 and vesicles and micelles in siloxane surfactant solutions.17a,b Cryo-TEM is the only technique available to distinguish branched and unbranched micelles. Cryo-TEM images of branched micelles have been reported in an aqueous solution of cetyltrimethylammonium 3,5-dichlorobenzoate and cetyltrimethylammonium bromide mixtures,18 and in a trimeric quaternary ammonium bromide solution.19 However, images of branched micelles are not widely reported in the literature. In this paper, branched micelles and their network were imaged by cryo-TEM and their rheological properties were also explored. Materials and Methods Surfactants used in this study were dodecyldimethylamine oxide, C12H25(CH3)2NO, and sodium laureth sulfate (n ) 1), C12H25OCH2CH2OSO3-Na+. Solutions were made by adding double-distilled water to weighed quantities of the surfactants and the salt, NaCl. Sodium hydroxide then was added to adjust (15) Kilpatrick, P. K.; Miller, W. G., Talmon, Y. Staining and dryinginduced artifacts in electron microscopy of surfactant dispersions. J. Colloid Interface Sci. 1985, 107, 146-158. (16) Lin, Z.; Scriven, L. E.; Davis, H. T. Cryogenic electron microscopy of rodlike or wormlike micelles in aqueous solutions of nonionic surfactant hexaethylene glycol monohexadecyl ether. Langmuir 1992, 8, 2200-2205. (17) (a) Lin, Z.; Hill, R. M.; Davis, H. T.; Scriven, L. E.; Talmon, Y. Cryo transmission electron microscopy study of vesicles and micelles in siloxane surfactant aqueous solutions. Langmuir 1994, 10, 10081011. (b) Lin, Z.; He, M.; Davis, H. T.; Scriven, L. E.; Snow, S. A. Vesicle formation in electrolyte solutions of a new cationic siloxane surfactant. J. Phys. Chem. 1993, 97, 3571-3578. (18) Vinson, P. K. Cryo-electron microscopy of microstructures in complex fluids. Ph.D. Dissertation, University of Minnesota, 1990. (19) Danino, D.; Talmon, Y.; Levy, H.; Beinert, G.; Zana, R. Branched threadlike micelles in an aqueous solution of a trimeric surfactant. Science 1995, 269, 1420-1421.
the pH of the solutions. The samples were then stirred with a magnetic stirrer rotating at about 2 Hz for about 1 h. The compositions and pH of the samples studied are summarized in Table 1. Cryo-TEM. Cryo-TEM samples were prepared in the controlled environment vitrification system (CEVS), which is described in detail elsewhere.20 A 5-µL drop of the sample solution was placed on a carbon-coated holey polymer support film which was mounted on the surface of a standard 200-mesh TEM grid.21 The drop was blotted with filter paper until it was reduced to a thin film (10-200 nm) spanning the holes (2-10 µm) in the support film. The sample was then vitrified by rapidly plunging it through a synchronous shutter at the bottom of the CEVS into liquid ethane at its freezing point. The vitreous specimen was transferred under liquid nitrogen to the cryo-TEM transfer stage (Model 626, Gatan, Inc., PA), which was inserted into the microscope (Philips CM12, Mahwah, NJ) for direct observation. The temperature was maintained below -170 °C throughout specimen observation. The specimen was imaged at 100 kV and an underfocus of 2-4 µm in order to achieve the phase contrast responsible for image contrast formation. The images were recorded on Kodak SO-163 films that were developed with fullstrength D-19 developer (Eastman Kodak, Co., NY) for 12 min. Rheology. Steady shear and small-amplitude oscillatory shear, i.e., dynamic shear, were performed on a Rheometrics Dynamic Stress Rheometer SR200, which is supported by RHIOS software. Dynamic shear measurements were taken over the frequency sweep from 0.1 to 50. The rheometer has a built-in computer which converts the torque measurements into both G′ (the storage modulus) and G′′ (the loss modulus) in dynamic shear experiments, or viscosity in steady shear experiments. The experiments were carried out in cone-and-plate geometry, with (20) Bellare, J. R.; Davis, H. T.; Scriven, L. E.; Talmon, Y. Controlled environment vitrification technique. J. Electron Microsc. Tech. 1988, 10, 87-111. (21) Vinson, P. K. The preparation and study of a holey polymer film. Proc. 45th Annual Meeting of the Electron Microscopy Society of America; Bailey, G. W., Ed.; San Francisco Press: San Francisco, 1987; pp 644645.
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Figure 2. Cryo-TEM image of sample 2. Worm-like micelles are found in solution. Some worm-like micelles are branched. Arrows point to the branching points. cone plate diameter d ) 40 mm and cone angle β ) 0.0419 rad (2.4°). The gap was set at 0.048 mm throughout the measurements. An environmental control unit was used during the measurements to prevent the evaporation of the solvent.
Results Figure 1 displays a cryo-TEM image of sample 1. Wormlike micelles were found in solution as well as some spherical micelles. The micellar length for the worm-like micelles varied. Some of the shorter ones measured several hundred nanometers in length. No apparent micellar branching or entanglement was detected. Figure 2 shows a cryo-TEM image of sample 2. Long worm-like micelles were found in the solution. A few branching points can be identified, indicating the existence of branched micelles. The main contribution to the image contrast in cryoTEM is so-called phase contrast, which results from the interference of unscattered and elastically scattered electrons. A difference in the mean inner electron potential in the specimen is responsible for forming the phase contrast. Because surfactant molecules have a higher mean inner electron potential than water, micelles appear darker than the surrounding water media as seen in the micrographs. If two micelles are entangled or simply overlap, the entanglement point or overlapping point would appear darker, since this point would have the highest mean inner electron potential. However, if the micelles are branched, the branching point should have the same appearance as the regular micelles. In Figure 2, arrows point to the joints that have the same appearance in darkness as the regular micelles, indicating that the joints have the same mean inner electron potential. The “Y”-shaped joints, in particular, can be identified as branching points of the branched micelles.
When observing apparent entanglements and other features, recall that electron micrographs are twodimensional projections of microstructures confined in three-dimensional specimens. In some cases, this nature causes problems in the determination of micelle length and polydispersity. In Figure 1, because some worm-like micelles can be identified from one end to the other, it is relatively easy to identify the polydispersity of the micelles. However, in Figure 2, because the micelles overlap, it is not possible to identify where they begin and end. Figure 3 shows a cryo-TEM image of sample 3. A micellar network formed by branched micelles was found. This is interconnected, branched micellar network, spanning over a large space. It is analogous to the sponge (L3) phase, where an infinite multiconnected fluid bilayer separates hydrophilic and hydrophobic regions.22 Here, the mesh size of the network, i.e. the micellar length between two branching points, is more important than the actual individual micellar length. Figures 4 and 5 show cryo-TEM images of samples 4 and 5, respectively. These samples were prepared at lower pHs with the same surfactant and salt concentrations. Figure 4 displays a few branched worm-like micelles and Figure 5 displays a branched micellar network. This network is not as dense as the one found in sample 3. Figure 6 shows steady state shear viscosity measurements for all of the samples studied. One can conclude that sample 1 is a Newtonian liquid, since the viscosity does not change with the shear rate. Recall that the cryoTEM image (Figure 1) showed short, worm-like micelles coexisting with spherical micelles in solution. The (22) Roux, D.; Coulon, C.; Cates, M. E. Sponge phases in surfactant solutions. J. Phys. Chem. 1992, 96, 4174-4187.
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Figure 3. Cryo-TEM images of sample 3. Worm-like micelles are found. (a) Many branching points can be identified. (b) These branched micelles form a dense network.
coexistence of spherical and worm-like micelles indicates that it is a transitional regime for the spherical-to-wormlike micelle transition.6 The Newtonian behavior of such a solution has been demonstrated in cetyltrmeth-
ylammonium bromide/methylsalicylic acid systems.6 Samples 2-5 all showed shear-thinning behavior. Sample 3 has the highest zero-shear viscosity and the smallest onset shear rate for shear thinning, which
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Figure 4. Cryo-TEM image of sample 4. Few branched worm-like micelles can be identified.
Figure 5. Cryo-TEM iamge of sample 5. Branched worm-like micelles form some small networks.
indicates that the worm-like micelles in that solution have the longest relaxation time. This corresponds to the
most dense micellar networks imaged by cryo-TEM (Figure 3). The observed trend is that the onset shear
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a
Figure 6. Steady state shear viscosity measurements.
b
Figure 7. Shear stress plots against shear rate.
Figure 8. Shear stress plots against shear rate for sample 2: (a) linear plot, showing an apparent yield stress value; (b) loglog plot, indicating there is no true yield stress value.
rate for shear thinning and zero-shear viscosity increases with an increase in the density of the micellar network in solution. Figure 7 displays plots of shear rate against applied shear stress for all samples. The shear rate increases linearly with an increase of shear stress, further indicating that sample 1 exhibits Newtonian behavior, which is consistent with the cryo-TEM image (Figure 1) and the viscosity measurements (Figure 6). All other samples exhibit pseudoplastic behavior with apparent yield stress values. Sample 3 has the largest apparent yield stress value (about 160 dyn/cm2), which probably is due to the extremely dense branched micellar network as shown in Figure 3. However, by closely examining the results, all of these samples do not have a true yield stress value. Figures 8 and 9 show the sample plots for samples 2 and 3, respectively. Figures 8a and 9a are linear plots, which give an apparent yield stress value. However, by replotting Figures 8a and 9a in log-log plots (Figures 8b and 9b), the stress decreases with a decrease of shear rate. In addition, the fact that zero-shear viscosity exists in
samples 2-5 also indicates that these solutions do not have a true yield stress value. Figures 10-13 show a series of dynamic shear moduli measurements for samples 2-5, respectively. The shear stress was kept at 1 dyn/cm2, except for sample 4, to ensure that the measurements were made in the linear viscoelasticity regime. Sample 4 was measured with shear stress at 10 dyn/cm2. Figure 14 shows a typical dynamic stress sweep measurement. The linear viscoelasticity regime extends to about 10 dyn/cm2. No G′ was detected for sample 1, indicating Newtonian behavior, which is consistent with the steady state measurements. Samples 2-5 all showed viscoelasticity. In Figures 12 and 13, G′ is larger than G′′ throughout the whole frequency range. However, this could be the result of the instrument’s inability to keep the stress constant at higher frequencies, which is common for low-viscosity materials. In any case, the crossing point of G′ and G′′ is out of the measurable frequency range of the instrument if it exists. From Figure 6, there is an onset shear rate for shear thinning at about 10 s-1 for samples 2, 4, and
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5. That indicates that the crossing point of G′ and G′′ should exist, for the onset shear rate for shear thinning and the crossing point of G′ and G′′ both represent the relaxation time of the system. Samples 2 and 3 (Figures 10 and 11) showed typical viscoelasticity for worm-like micelle systems. The fact that G′ decreases when the frequency is lowered confirms that all of these solutions do not have a true yield value. A simple Maxwell element was used to analyze the data for samples 2 and 3. A simple Maxwell element describes the rheological behavior of a system as a single spring connected in series to a viscous dashpot. In shear experiments, this results in
G(t) ) G0e-t/λ
(1)
G′ ) G0ω2λ2/(1 + ω2λ2)
(2)
G′′ ) G0ωλ/(1 + ω2λ2)
(3)
where ω is the frequency, G0 is the plateau modulus, and λ is the relaxation time. The fitted data were also shown in Figures 10 and 11 for samples 2 and 3, respectively. The Maxwell model fits sample 3 very well with G0 ) 195.6 dyn/cm2 and λ ) 0.21 s. The relaxation time is within the range of relaxation times of the worm-like micelle systems reported in the literature3,6 but is shorter than that of some fully entangled micellar systems.7,10,23 Discussion Electron microscopy provides images of the structures in materials and may be used to determine their size and shape. In the case of branched micelles, because branching is a local structural feature, it is difficult for scattering techniques, such as light and neutron scattering, to identify them. Rheological measurements are used to probe the properties of micelles and their networks. Combining electron microscopy and rheology, we can provide insight into these branched micelles and their networks. Surfactant solutions with globular micelles generally exhibit Newtonian behavior. The viscosity of the solution increases linearly with the volume fraction of the micelles according to Einstein’s equation:
η ) ηs(1 + 2.5φ)
(4)
where ηs is the viscosity of the pure solvent and φ is the effective volume fraction which takes into account the hydration of the molecules. Spherical micelles and short, worm-like micelles can fit into this model. This is seen in Figures 1 and 6. It has also been demonstrated that, in the entangled micellar systems, the networking points have only a temporary character with a rather long relaxation time; typical values are of the order of a few hundred seconds.23 As a consequence, these solutions do not have a yield stress value. Vesicle systems, on the other hand, show viscoelastic properties and have a yield stress value. They also have near constant G′ throughout the frequency range. Hoffman et al. attributed the yield stress value to the dense packing of the vesicles.23 The rheological behavior of solutions that contain branched worm-like micelles and their networks is very different from that of vesicle systems. For branched (23) Hoffman, H.; Thunig, C.; Schmiedel, P.; Munkert, U.; Ulbricht, W. The rheological behavior of different viscoelastic surfactant solutions. Systems with and without a yield stress value. Tenside, Surfactants Deterg. 1994, 31, 389-400.
Figure 9. Shear stress plots against shear rate for sample 3: (a) linear plot, showing an apparent yield stress value; (b) loglog plot, indicating there is no true yield stress value.
micelles that did not form large networks (such as samples 2, 4, and 5), the systems showed only weak viscoelasticity with short relaxation times (less than 0.2 s). A dense micellar network, sample 3, behaves like a Maxwell module with a single relaxation time and similar to the entangled micellar systems. In this case, rheology alone cannot distinguish between entangled worm-like micelles and a dense, branched micellar network. Cryo-TEM images, on the other hand, provide clear evidence of branching. The short relaxation time (about 0.2 s for sample 3 and even shorter for samples 2, 4, and 5) could be the result of a different cross-linking mechanism. Although a cross-linking point can slide along the wormlike micelle as proposed in the literature,12 the relaxation time of the system will be determined by the mesh size of the interconnected worm-like micellar network. All of these branched micellar systems exhibit pseudoplastic behavior and have an apparent yield stress value. Such behavior has not been reported for entangled micellar systems. Figures 8b and 9b indicate that the linear region in the log-log plot corresponds to the Newtonian region
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Figure 10. Dynamic shear moduli measurements for sample 2 (shear stress ) 1 dyn/cm2). A simple Maxwell model fitting is also plotted.
Figure 11. Dynamic shear moduli measurements for sample 3 (shear stress ) 1 dyn/cm2). A simple Maxwell model fitting is also plotted.
in the shear viscosity measurement (Figure 6). At shear rates between about 10 and 100 Hz, there is a plateau for the shear stress, which gives an apparent yield stress value. Short relaxation times alone cannot explain this apparent yield stress, as some entangled micellar solutions have even an smaller relaxation time.3 The breakage of interconnected micellar meshes could be responsible for such behavior. Sample 1 has only about one-third of amine oxide as the other samples. The worm-like micelles in sample 1 are much shorter than micelles in the other samples and they are not branched or entangled. Comparing results from samples 2 and 3, the micellar network is observed to develop with an increase in salt concentration. Sample 3 has the highest pH and highest salt concentration among the systems studied. It has the most dense branched micellar network. The salt concentration in sample 3 is
Lin
Figure 12. Dynamic shear moduli measurements for sample 4 (shear stress ) 10 dyn/cm2).
Figure 13. Dynamic shear moduli measurements for sample 5 (shear stress ) 1 dyn/cm2).
0.52 M when it is converted to molar concentration. This high salt concentration to promote branched micelle and branched micellar network formation is consistent with previous studies in the CPClO3 system.12 With pH increases from 8.7 to 13.3, the branched micellar network developed into a dense network (Figures 3-5). The dependence on pH can be attributed to the deprotonation of amine oxide molecules. The degree of protonation of amine oxide molecules has a great effect on the interactions between amine oxide and sodium laureth sulfate molecules. In dilute solutions, where interaggregate interactions can be neglected, the morphology of surfactant aggregates is a function of the degree of curvature of either the surfactant monolayer or bilayer.24,25 For hydrocarbon(24) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. Theory of self-assembly of hydrocarbon amphiphiles into micelles and bilayers. J. Chem. Soc., Faraday Trans. 2 1976, 72, 1525-1568.
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creases. The protonated amine oxide molecules act like cationic surfactant molecules. They interact strongly with anionic surfactant molecules like laureth sulfate. Because of the strong interaction, a is reduced, and thus the packing parameter is increased. This provides favorable conditions for forming cross-links rather than highly curved endcaps to promote branched micelle formation. By adding a large amount of salt to the solution, the ionic head groups of the protonated amine oxide and laureth sulfate molecules are more effectively screened, thus reducing head group repulsion and, therefore, head group area. This also favors the formation of branched micelles. Dery and Cates26 investigated theoretically the formation of cross-links between worm-like micelles. They concluded that the free energy cost for formation of crosslinks is much higher than for forming end-caps. However, Cates27 has also pointed out that, in ionic surfactant solutions, it is known that the end-cap energy increases with salinity. With high salt concentrations in the systems studied here, it is possible to form cross-links instead of end-caps. All of these factors are consistent with the experimental results. Figure 14. Dynamic stress sweep measurements for sample 4 (frequency ) 10 rad/s).
based surfactants, it has been argued that the curvature of the aggregate is strongly influenced by the packing parameter p:
p ) v/la
(5)
where ν is the hydrophobic volume, l is the hydrophobic chain length of the surfactant molecule, and a is the head group area of that molecule. When p is between 1/3 and 1/2, surfactant molecules will packed into cylindrical micelles. When p is between 1/2 and 1, flexible bilayers and vesicles form.24,25 Worm-like micelles correspond to a locally cylindrical geometry with two endcaps that are generally thought to be of semisphere geometry having higher curvature that cylindrical geometry. In the systems studied here, by lowering the pH of the solution, the protonation of amine oxide molecules in(25) Micthell, D. J.; Ninham, B. W. Micelles, vesicles and microemulsions. J. Chem. Soc., Faraday Trans. 2 1981, 77, 601-629.
Summary Branched micelles were imaged by cryo-TEM in mixtures of amine oxide and sodium laureth sulfate solutions. These branched micelles formed an interconnected network at high solution pH and salt concentrations. These micellar networks are similar to structures formed in the L3 phase where an infinite multiconnected fluid membrane forms a bicontinuous structure. The rheological measurements showed that branched micelle solutions exhibit viscoelasticity and an apparent yield stress value. The solutions with a dense branched micellar network exhibit simple Maxwell behavior. Acknowledgment. The author would like to thank Dr. David Githuku for the use of his rheometer. The author is grateful to Prof. Y. Talmon of Technion, Israel, and Prof. R. K. Prud’homme of Princeton University for helpful discussions during the preparation of this paper. LA950570Q (26) Drye, T. J.; Cates, M. E. Living networks: the role of cross-links in entangled surfactant solutions. J. Chem. Phys. 1992, 96, 1367-75. (27) Cates, M. E. Isotropic phases of self-assembled amphilipic aggregates. Phil. Trans. R. Soc. London A 1993, 344, 339-356.
