pubs.acs.org/Langmuir © 2010 American Chemical Society
A New Approach for the Characterization of Reverse Micellar Systems by Dynamic Light Scattering Jean-Luc Lemyre, Sebastien Lamarre, Ariane Beaupre, and Anna M. Ritcey* D epartement de chimie and CERMA, Universit e Laval, Qu ebec, Canada Pavillon Alexandre-Vachon, 1045 avenue de la M edecine, Qu ebec, Canada G1V 0A6 Received February 5, 2010. Revised Manuscript Received March 23, 2010 This paper reports the use of dynamic light scattering (DLS) to study reverse micelles formed by the water/Igepal CO520/cyclohexane system over a large range of global compositions. A novel approach for data analysis is presented, based on the realization that micelles of a given size must be in equilibrium with free surfactant of a fixed concentration. Compilation of the DLS data into sets of fixed micelle size but differing global compositions therefore allows for the determination of parameters such as free surfactant concentration, micellar molar composition, surfactant interfacial area, and aggregation numbers. Importantly, this method gives access to the variation of each of these parameters with micelle size, as is essential for the characterization of reverse micelles formed by nonionic surfactants. This approach constitutes a significant complement to other available characterization methods. The analysis also provides insight into the primary factors controlling the equilibrium distribution of surfactant within the system and the relative stability of the micelles.
I. Introduction Reverse microemulsions are complex systems. Despite a relatively large body of existing scientific literature, many important systems remain poorly characterized, and the models used to describe them are often oversimplified. Additional data and new perspectives are therefore still very relevant. Reverse microemulsions are self-assembled dispersions of surfactant-stabilized water in a nonpolar solvent. They are thermodynamically stable and optically transparent, being heterogeneous at the nanometer scale. Water/surfactant/oil systems have very rich phase diagrams and can adopt a variety of morphologies.1,2 This paper, however, focuses on the reverse micelles present in the L2 phase. The coexistence of water and oil within this single phase is rendered possible by the important reduction of the interfacial tension by the surfactant. Unlike normal micelles, the formation of reverse micelles is enthalpydriven.3,4 Reverse micelles are of interest in many fields, ranging from the fundamental sciences to technological applications. They have numerous applications such as in the synthesis of inorganic nanoparticles,5-8 as models for biological systems,9 for the *Corresponding author: Ph 418-656-2368; Fax 418-656-7916; e-mail anna.
[email protected]. (1) Hellweg, T. Curr. Opin. Colloid Interface Sci. 2002, 7(1-2), 50. (2) Sager, W. F. C. Microemulsion Templating. In Nanostructured Soft Matter; Zvelindovsky, A. V., Ed.; Springer: Dordrecht, 2007. (3) Myers, D. Surfaces, Interfaces, and Colloids: Principles and Applications, 2nd ed.; Wiley-VCH: New York, 1999; p 389. (4) Liveri, V. T. Controlled Synthesis of Nanoparticles in Microheterogeneous Systems; Springer: New York, 2006; p 167. (5) Lemyre, J.-L.; Ritcey, A. M. Chem. Mater. 2005, 17(11), 3040. (6) Eastoe, J.; Hollamby, M. J.; Hudson, L. Adv. Colloid Interface Sci. 2006, 128-130, 5. (7) Pileni, M.-P. Nat. Mater. 2003, 2(3), 145. (8) Destree, C.; Nagy, J. B. Adv. Colloid Interface Sci. 2006, 123-126, 353. (9) Van Horn, W. D.; Ogilvie, M. E.; Flynn, P. F. J. Am. Chem. Soc. 2009, 131 (23), 8030. (10) Mathew, D. S.; Juang, R.-S. Sep. Purif. Technol. 2007, 53(3), 199. (11) Krishna, S.; Srinivas, N.; Raghavarao, K.; Karanth, N. Reverse Micellar Extraction for Downstream Processing of Proteins/Enzymes. In History and Trends in Bioprocessing and Biotransformation; Springer-Verlag: Berlin, 2002; p 119.
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extraction and purification of biomolecules,10,11 in drug delivery,12 and as enzymatic reaction media.13-15 In all cases, the efficient use of reverse micelles requires a sound knowledge of the basic physicochemical properties of the specific system. For example, in order to model the distribution of various chemical species within the system, parameters such as reverse micelle size, aggregation number, and free surfactant concentration must be known. In general, a better understanding of reverse micelles could lead to better performance or even widen the scope of possible applications. Reverse micelles are traditionally pictured as being small spherical water droplets wrapped in a monolayer of surfactant.8,9,16-18 Their true nature is significantly more complicated in many cases. This is particularly true for nonionic surfactants. By far the most widely studied reverse micellar system is that formed by the ionic surfactant known as AOT (sodium bis(2-ethylhexyl) sulfosuccinate). Nonionic surfactant reverse micelles, on the other hand, have been less studied despite the fact that they are commonly used. Nonionic surfactant systems can differ significantly from ionic surfactant reverse micelles, and extending the general conclusions reached for ionic systems to nonionic ones must be done with caution. The specific nonionic surfactant studied here is polyoxyethylene(5)nonylphenyl ether, better known under the commercial name of Igepal CO-520. Our particular interest in reverse micelles is for their use in the synthesis of inorganic nanoparticles. The synthesis of nanoparticles in these systems proceeds through the mixing of reagents sequestered within the micelles during micellar collisions. This method has proved to be very effective for the synthesis of nanoparticles with exceptionally sharp, in fact, essentially monodisperse, (12) M€uller-Goymann, C. C. Eur. J. Pharm. Biopharm. 2004, 58(2), 343. (13) Biasutti, M. A.; Abuin, E. B.; Silber, J. J.; Correa, N. M.; Lissi, E. A. Adv. Colloid Interface Sci. 2008, 136(1-2), 1. (14) Miyake, Y. Colloids Surf., A 1996, 109, 255. (15) Volkov, A. G. Interfacial Catalyisis; Marcel Dekker: New York, 2003. (16) Langevin, D. Annu. Rev. Phys. Chem. 1992, 43(1), 341. (17) Sedgwick, M. A.; Crans, D. C.; Levinger, N. E. Langmuir 2009, 25(10), 5496. (18) Uskokovic, V.; Drofenik, M. Adv. Colloid Interface Sci. 2007, 133(1), 23.
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However, the ratio of these two parameters can be simply replaced by the ratio of their global concentrations, leading to r ¼
Figure 1. Schematic representation of (a) an ionic reverse micelle, (b) a small nonionic reverse micelle with confined hydrophilic chains, and (c) a nonionic reverse micelle large enough to permit chain extension into the hydrophilic core.
size distributions.5,19-21 Furthermore, particle size can be easily controlled by modifying the water and surfactant content of the reaction mixture. Although several models have been proposed6-8,21-23 to explain the exquisite control over particle size associated with this method, the exact mechanism of particle formation remains unknown. Since the resulting particles are typically much larger than the micelles, the contents of many micelles are required to produce a single particle. Monte Carlo simulations24,25 have been used to model the mass distribution of the micelle contents during random collisions and particle growth. The testing of such models, as well as their use for predicting the appropriate conditions for obtaining a desired particle size, however, requires knowledge of characteristic parameters such as the aggregation number and the quantity of free surfactant. The most common representation of reverse micelles found in the literature is as a small water pool surrounded by a monolayer of surfactant molecules, as sketched in Figure 1a. Assuming that the micelles are spherical, this model is supported by the wellknown relation between the radius of the encapsulated water pool and the water to surfactant molar ratio:21 r ¼
k½H2 O ½Surf:
ð1Þ
where k is a proportionality constant. Equation 1 arises from a simple geometrical analysis of the system, through the following relation between radius, surface area, and volume: r ¼
3V S
ð2Þ
The core volume, V, is considered to contain only water and can therefore be replaced by the number of water molecules per micelle times the molecular volume of water, VH2O. The surface area, S, on the other hand, is governed by the surfactant content and can be expressed as the aggregation number times the area, σ, occupied by a single surfactant molecule at the water-oil interface. In general, the average number of water molecules per reverse micelle and the aggregation number are not known. (19) Boutonnet, M.; Kizling, J.; Stenius, P.; Maire, G. Colloids Surf. 1982, 5(3), 209. (20) Capek, I. Adv. Colloid Interface Sci. 2004, 110(1-2), 49. (21) Pileni, M. P. J. Phys. Chem. 1993, 97(27), 6961. (22) Lopez-Quintela, M. A. Curr. Opin. Colloid Interface Sci. 2003, 8(2), 137. (23) Koetz, J.; Kosmella, S. Water-in-Oil Microemulsions: Preparation of Nanoparticles. In Encyclopedia of Surface and Colloid Science; Somasundaran, P., Hubbard, A., Eds.; Taylor & Francis: London, 2009. (24) Ethayaraja, M.; Dutta, K.; Bandyopadhyaya, R. J. Phys. Chem. B 2006, 110(33), 16471. (25) Ethayaraja, M.; Dutta, K.; Muthukumaran, D.; Bandyopadhyaya, R. Langmuir 2007, 23(6), 3418.
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3VH2 O ½H2 O σ½Surf:
ð3Þ
This is a more explicit form of eq 1 with k = 3VH2O/σ. Equation 1 has been experimentally validated for a few reverse micellar systems.21 The applicability of this simple model depends on three important assumptions: (1) that the concentration of free surfactant is negligible, (2) that the interfacial area occupied by a surfactant molecule is independent of micelle size, and (3) that the volume occupied by the surfactant within the polar core is negligible. As illustrated in this paper, these assumptions are not valid for the Igepal/water/cyclohexane system. This is probably also the case for most other nonionic reverse micellar systems. In this article we describe a new approach to the analysis of dynamic light scattering (DLS) data that leads to the evaluation of free surfactant concentration and the molar composition of the micelles as a function of micelle size. A new geometrical model that is better suited to nonionic reverse micellar systems is also elaborated, allowing for the determination of aggregation number and surfactant interfacial molecular area. The originality of this work resides in the fact that all of these parameters are found solely by relatively simple DLS measurements. Importantly, the method proposed here allows the investigation of reverse micelles over a wide range of global compositions within the L2 phase, instead of being restricted to the solubilization boundary. This method certainly constitutes a significant complement to other characterization methods, particularly for the evaluation of the free surfactant concentration which is difficult to obtain by other means. This analysis also provides insight into the primary factors controlling the equilibrium distribution of surfactant within the system and the relative stability of the micelles.
II. Experimental Section All chemicals were supplied by Aldrich and used as received without further purification. Water was first deionized and then purified to 18.2 MΩ 3 cm by a Barnstead NanoPure II purification system. Microemulsions were prepared by mixing varying amounts of water, the surfactant Igepal CO-520 (polyoxyethylene(5)nonylphenyl ether), and 15 mL of cyclohexane. Homogeneous microemulsions were obtained by mixing with a magnetic stirrer followed by 10 min in an ultrasonic bath. The maximum water solubilization boundary has been determined by visual titration of the maximum water uptake as a function of the surfactant concentration. Surfactant solutions were kept in sealed glass vessels immersed in water at 25 °C. Water was added in small increments with a syringe through a septum. The reverse microemulsion was briefly mixed with a magnetic stirrer and then left at rest at constant temperature for 24 h. Water addition was repeated until persistent turbidity, as judged by the naked eye, was reached. Further surfactant was then added, and the titration continued. Dynamic light scattering (DLS) measurements were performed at 25 °C with a Malvern Zetasizer Nano ZS. This instrument can perform size measurements on highly concentrated dispersions by observing backscattered light. Dynamic viscosities used for the calculation of micelle size from the DLS measurements were obtained at 25 °C with a an Ubbelohde type viscometer to measure kinematic viscosities and a pycnometer to measure densities. The Newtonian character of the samples was verified with a TA Instruments ARES 100-FRT rheometer. A KSV 3000 Langmuir-Blodgett trough was used to determine the surfactant molecular area at a planar water/air interface. DOI: 10.1021/la100541m
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Figure 2. Hydrodynamic diameter of reverse micelles as a function of water volume for (b) 0.5, (O) 0.75, (1) 1, (4) 1.5, (9) 2, (0) 3, and ([) 4 g of surfactant in 15 mL of cyclohexane. Lines have been added to guide the eye.
III. Results and Discussion Dynamic Light Scattering Results. The hydrodynamic diameters of Igepal CO-520 reverse micelles dispersed in cyclohexane at various concentrations of surfactant and water contents are provided in Figure 2. Because these systems cannot be diluted without provoking a change in micelle size, DLS measurements were necessarily performed directly on the relatively concentrated microemulsions. In DLS measurements, particle size is determined from the translational diffusion constant. In concentrated solutions, however, diffusion is restricted due to a reduction of the free volume within which the particles can diffuse. For the range of samples studied here, the dispersed phase corresponds to 7-13% of the total volume, and multibody interactions cannot be neglected. It has, however, been empirically demonstrated that, in the case of Newtonian fluids, restricted diffusion can be compensated for by employing the viscosity of the actual medium in the Stokes-Einstein equation for the calculation of particle size.26 By using the actual viscosity of concentrated suspensions, particle sizes independent of the sample concentration could be obtained.26 This approach was employed here for the evaluation of hydrodynamic diameters. It should be noted that inadequate compensation of restricted diffusion by use of the medium viscosity would lead to the overestimation of hydrodynamic diameters. From the data presented in Figure 2, it can be seen that micelle size varies linearly with water content only for microemulsions at lower surfactant concentrations. At higher surfactant concentrations (above about 1.5 g per 15 mL of solvent), the hydrodynamic diameter appears to be initially independent of water content but then increases sharply as more water is added to the system. This observation suggests that at high surfactant and low water contents there is a significant amount of free surfactant available to form new micelles as more water is added. The water added at this stage therefore serves to create new reverse micelles, with little change in size, rather than to swell existing ones. Figure 3 presents the evolution of reverse micelle size as a function of water/surfactant molar ratio at different total water contents. This graph clearly demonstrates that while the linear relationship predicted by eq 1 holds for a given water content, the slope shows a strong dependence on the global composition of the mixture. In fact, a given water/surfactant ratio can result in very (26) Sun, Z.; Deluca, T.; Mattison, K. Am. Lab. 2005, 37(12), 8.
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Figure 3. Hydrodynamic diameter of reverse micelles as a function of the water/surfactant molar ratio for (b) 0.1, (O) 0.25, (1) 0.5, (4) 0.75, and (9) 1 mL of water in 15 mL of cyclohexane. Horizontal dashed lines have been added to emphasize that many global compositions lead to the same micelle size.
Figure 4. Hydrodynamic diameter of reverse micelles as a function of the reciprocal surfactant concentration for (b) 0.1, (O) 0.25, (1) 0.5, (4) 0.75, and (9) 1 mL of water in 15 mL of cyclohexane.
different hydrodynamic diameters, depending on the overall concentration of the system. It is therefore more appropriate to state that reverse micelle size is inversely proportional to surfactant concentration at constant water content. This is illustrated in Figure 4. Most literature reports of the linear dependence of reverse micelle size on the water/surfactant ratio do not include an explicit consideration of the total water content. Some authors27,28 correctly apply the relationship only at the solubilization boundary by adjusting the temperature to achieve maximum water uptake and the natural curvature of the surfactant monolayer. The behavior illustrated in Figures 3 and 4 clearly indicates that the free surfactant concentration cannot be neglected in this system. In the case of negligible free surfactant, the overall water/surfactant ratio is equal to the average water/surfactant ratio within the micelles or to what can be referred to as the micellar composition. It is the micellar composition, rather than the global composition, that determines micelle size. In this study, (27) Fletcher, P. D. I.; Horsup, D. I. J. Chem. Soc., Faraday Trans. 1992, 88(6), 855. (28) Lipgens, S.; Schubel, D.; Schlicht, L.; Spilgies, J.-H.; Ilgenfritz, G.; Eastoe, J.; Heenan, R. K. Langmuir 1998, 14(5), 1041.
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for a given overall water/surfactant ratio, micelle size decreases with increasing total concentration. As the global concentration is increased, by adding more water and surfactant to a fixed volume of cyclohexane, there is a shift in the fraction of surfactant molecules that participate in micelle formation. It is important to note that neither micelle size nor free surfactant concentration remains constant during the accompanying reorganization of the system. At higher overall compositions, the micellar surfactant/ water ratio increases, resulting in smaller micelles according to the geometric reasoning presented in the Introduction. The reason why this effect is so striking for the current system is that the fraction of free surfactant is very high, as demonstrated later in this text. High free surfactant concentrations have also been previously reported for other nonionic alkyloxyethylene surfactants.16 Free Surfactant Concentration, cμc, and Micellar Composition. Igepal CO-520 is soluble in cyclohexane, and as discussed above, a significant amount of free surfactant is certainly present in the reverse microemulsions. The exact nature of this free surfactant is, however, less clear since it has been previously shown that, in the absence of water, poly(oxyethylene) nonylphenols predominantly dimerize in nonpolar solvents.29 While it is important to keep the possibility of dimer formation in mind, it does not have a direct impact on the analysis presented below. Because of the negligible solubility of water in cyclohexane, it can be assumed that all of the water present in the system is located within the micelles, and nH2O,total/nH2O,per micelle thus corresponds to the number of micelles. The total quantity of surfactant, nsurf,total, can then be expressed by following simple equation: nsurf , total ¼ nsurf , free þ N
nH2 O, total nH2 O, per micelle
ð4Þ
where nsurf,free is the amount of free surfactant, N is the aggregation number, and nH2O, per micelle is the amount of water within a single reverse micelle. Importantly, N/nH2O,per micelle defines the molar ratio of surfactant to water within the micelle or what can be referred to as the micellar composition. Figures 2, 3, and 4 indicate that reverse micelles of identical apparent size can be obtained by a number of different sets of surfactant and water concentrations. This is illustrated, for example, by the dashed horizontal line at a diameter of 10 nm shown in Figure 3, which intercepts the plots corresponding to different global concentrations at different water/surfactant ratios. If it is assumed that the micellar composition (N/nH2O,per micelle) is constant within a series of given micelle size, a plot of nsurf,total against nH2O,total should be linear with a slope corresponding to the micellar composition and intercept equal to free surfactant concentration. It must again be emphasized that each plot must be based on a data set composed of global compositions that all result in reverse micelles of the same apparent size. The data presented in Figure 3 can be used to identify the various global compositions necessary to reach any given size within the experimental range of 4-14 nm. These parameters can then be fitted by linear regression to eq 4 to estimate the micellar composition and free surfactant concentration as a function of reverse micelle size. Figure 5 shows examples of these linear plots at five different micelle sizes. Since data can be extracted from Figure 3 at an infinite number of sizes within the experimental range of 4-14 nm, the results are plotted in subsequent figures as continuous curves rather than as a collection of discrete points. (29) Sheih, P. S.; Fendler, J. H. J. Chem. Soc., Faraday Trans. 1 1977, 73, 1480.
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Figure 5. Examples of linear regressions based on eq 5. The mass of surfactant is plotted as a function of water volume, in 15 mL of cyclohexane, for global compositions that produce reverse micelle with diameters of (b) 14, (O) 9, (1) 6, (4) 5, and (9) 4 nm.
The hypothesis that micellar composition (N/nH2O,per micelle) is constant within a series of given apparent micelle size requires some discussion. It is important to note that identical hydrodynamic diameters do not necessarily imply identical micelles since micelle shape may vary as a function of global composition. In particular, the formation of cylindrical micelles has been reported30 and must be considered. Blokhuis and Sager31 have presented an elegant theoretical treatment of the sphere-tocylinder transition in microemulsion systems. Their theory predicts the coexistence of spheres and cylinders with the volume fraction of cylinders increasing with surfactant concentration at fixed water-to-oil ratio. One very important premise of the theory is that the total interfacial area within the emulsion is determined by the amount of surfactant. This essentially corresponds to an assumption that the concentration of free surfactant is negligible. In fact, it is the geometric constraint imposed by the requirement of accommodating the increasing quantity of surfactant that drives the transition to cylinders. This situation clearly does not apply to the system presented in our study. In the case of significant solubility of the surfactant in the continuous phase, this constraint is not present, and the transition to cylinders may not occur. Kahlweit32 has indeed pointed out that whether it is the bending energy or the interfacial tension which plays the decisive role in determining micelle shape depends on the ratio between the bending energy and the energy of transfer of the monomers between the interfacial layers and the bulk. The linearity of the plots presented in Figure 5 tends to support the hypothesis that the micellar composition remains constant within a given series of global compositions, resulting in constant micelle size. This implies that although the overall water/surfactant ratio varies with global composition, all micelles of a given apparent size are identical and thus composed of a fixed water/surfactant ratio. Surfactant molecules present in the reverse micelles are in dynamic equilibrium with free surfactant molecules, and the two species must therefore have equal chemical potentials. Consequently, all of the different combinations of surfactant and water contents that produce the same reverse micelle size must also have the same free surfactant concentration. (30) Strey, R.; Glatter, O.; Schubert, K.-V.; Kaler, E. W. J. Chem. Phys. 1996, 105(3), 1175. (31) Blokhuis, E. M.; Sager, W. F. C. J. Chem. Phys. 2001, 115(2), 1073. (32) Kahlweit, M. Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 1999, 95, 89.
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Figure 6. Micellar composition as a function of reverse micelle size as evaluated from the slope of plots such as those provided in Figure 5.
Figure 6 presents the micellar composition as a function of reverse micelle size evaluated from the slopes of plots such as those presented in Figure 5. The discontinuity observed around 10.5 nm is due to an experimental restriction and is not physically meaningful. It arises because larger micelles are not observed at low water content and fewer points were available for the linear regressions above this size, resulting in a larger uncertainty in the evaluation of the slope. (This is illustrated, for example, by the horizontal line at 14 nm in Figure 3 that only intersects four of the five global composition plots.) This discontinuity is propagated in some of the following graphs, which are generated from the same data set. The results presented in Figure 6 indicate that even the smallest micelles (those with a diameter of 4 nm) contain more than 20 water molecules per surfactant molecule. If it is assumed that two water molecules can hydrogen bond to each ether group,17 10 water molecules would be sufficient to fully hydrate the hydrophilic part of the surfactant molecule. For the entire size range studied here, the surfactant can thus be considered to be fully hydrated and comixed with any excess water. The presence of a distinct water pool within the smaller reverse micelles would, however, require phase separation between water and the oxyethylene chains, which is unlikely given their miscibility at room temperature. An encapsulated water pool is, however, to be expected in reverse micelles for which the polar core is larger than twice the length of the oxyethylene chain, estimated to be about 1.8 nm, since the surfactant is confined to the interface. The presence of a water pool free of oxyethylene groups in Igepal reverse micelles has been recently deduced from 51V NMR line width experiments using decavanadate as a water-soluble probe.17 Line widths comparable to those obtained in aqueous solution were taken to indicate an environment viscosity equivalent to that of pure water and thus indicative of the presence of a water pool. Although micelle size was not specified, the results are in agreement with the arguments presented here in that probe mobility decreased in global compositions that lead to smaller micelles. In any case, the geometric model presented here is not affected by the presence or absence a water pool. The volume of the spherical polar core is considered to be the sum of the volumes of water and the surfactant hydrophilic tail whether they are mixed or phase separated. The fraction of total surfactant that exists as free surfactant is plotted in Figure 7 as a function of micelle size for various global compositions. The concentration of free surfactant is far from negligible. In systems containing the smallest amounts of water, 95-100% of the surfactant is not involved in micelle formation. Even at the highest water content employed here, 45-60% of the 10528 DOI: 10.1021/la100541m
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Figure 7. Free surfactant fraction (with respect to total surfactant) as a function of reverse micelle size for (solid) 0.1, (dotted) 0.25, (short dash) 0.5, (dots dash) 0.75, and (long dash) 1 mL of water in 15 mL of cyclohexane. The fraction of free surfactant was evaluated from the intercept of plots based on eq 5.
Figure 8. Total amount of free surfactant as a function of reverse micelle size for a fixed volume of 15 mL of cyclohexane.
surfactant exists as free molecules, depending on the exact micelle size. The fraction of free surfactant decreases slightly with increasing micelle size, but this variation is relatively small compared to the effect of water addition. For a given micelle size, the fraction of free surfactant depends strongly on the amount of water present. This dependence is due to an increase in the number of micelles as water is added and not to a change in free surfactant concentration. As noted above, the concentration of free surfactant in equilibrium with micelles of a given size is constant. The free surfactant concentration, expressed as the mass dissolved in a fixed volume of the cyclohexane continuous phase, is plotted in Figure 8 as a function of micelle size. Figure 8 shows that free surfactant concentration increases sharply as micelle size is reduced. This increase in concentration is indicative of a corresponding increase in chemical potential, and it can thus be concluded that the chemical potential of the surfactant in a small micelle is higher than that in a larger micelle. Figure 8 furthermore indicates that the free surfactant concentration reaches a plateau at larger micelle diameters. This limit, equal to 0.45 g/15 mL in the present case, corresponds to the minimum free surfactant concentration and may be considered as the critical micellar concentration (cμc) of the system. The concept of a cμc can be confusing for reverse micelles as it is sometime assumed to be equal to a constant free surfactant concentration. Langmuir 2010, 26(13), 10524–10531
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Figure 9. Maximum volume of water incorporated in micelles as a function of the quantity of surfactant for a fixed volume of 15 mL of cyclohexane.
Figure 10. Molecular interfacial area of the surfactant as a func-
Binary micellar systems, such as those typical of normal (as opposed to reverse) micelles, exhibit a constant free surfactant concentration above the cmc. In such systems, the addition of surfactant simply produces more micelles of the same size while maintaining a constant concentration of the solution. However, the addition of surfactant to a tertiary micellar system, such as is the case for reverse micelles, cannot simply lead to an increase in the number of micelles without also provoking a change in the composition of both the continuous and the micellar phases. This alteration in composition of the micellar phase changes the chemical potential of the surfactant in this phase, thus displacing the position of the equilibrium with the free surfactant in solution. While reverse micellar systems can be characterized by a cμc, it is important to note that this cμc is not necessarily equal to the free surfactant concentration. The critical micellar concentration for a reverse system is defined as the minimum surfactant concentration at which reverse micelle formation is possible. This is also the minimum surfactant concentration for any significant water solubilization.33 It is important to keep in mind that the free surfactant concentration is equal to the cμc only at the maximum water solubilization boundary and may be higher when in equilibrium with less stable reverse micelles. The cμc is generally found by simple visual titration of the maximum water uptake as a function of surfactant concentration.27,34 This is a useful and simple method even if its accuracy is questionable due to the imprecision of human eye observation and the subtlety of the exact onset of phase separation. The results of the visual titration of the current system are presented in Figure 9. A cμc of 0.2 g surfactant per 15 mL of cyclohexane is obtained from the y-intercept of the plot. This can be compared to the 0.45 g evaluated from DLS measurements and the value 0.32 g previously reported in the literature.35 The values are in acceptable agreement considering the scatter of the points in Figure 9. Modified Geometric Model. In order to adequately describe nonionic systems, the model for reverse micelle size presented in the Introduction must be modified to allow for the presence of significant free surfactant. This model also fails to take into account other molecular characteristics of this type of surfactant. Specifically, the model assumes that the polar end of the surfactant occupies a negligible volume of the hydrophilic micelle core and that the interfacial area occupied by a single molecule is
independent of micelle size.28 The hydrophilic segment of typical nonionic surfactants is composed of poly(oxyethylene) oligomers, and this structural unit can be expected to occupy a considerable portion of the hydrophilic core, particularly in small micelles. In fact, at low water/surfactant ratios, the hydrophilic core would be better depicted as water-swollen oxyethylene chains rather than as a water pool surrounded by a surfactant monolayer. Even at high water/surfactant ratios, molecular dynamics simulations indicate that the hydrophilic part of the surfactant significantly penetrates into the water core.36 Finally, the model must be modified to allow the molecular interfacial area of the surfactant to vary with micelle size. Experimental evidence that this is indeed the case is presented later in this paper (Figure 10). The primary reason for the variation of the molecular interfacial area is the dependence of the conformation of the anchored surfactant chains on the radius of curvature. Within small reverse micelles, the oxyethylene chains are highly confined and forced to fold upon themselves, occupying more area at the surface as illustrated by the sketch of Figure 1b. As micelle size is increased, the oxyethylene chains can progressively extend into the hydrophilic core, lowering the interfacial molecular area, as illustrated in Figure 1c. The features of nonionic surfactants outlined in the previous paragraph make it impossible to predict the size of reverse micelles from a model using the global concentration as the only system parameter. Nevertheless, a simple geometrical model can be developed to include the particularities of nonionic surfactants, namely, the volume occupied by the surfactant within the hydrophilic core, the free surfactant concentration, the variable surfactant molecular interfacial area, and the effective length of the hydrophobic tail of the surfactant. The model assumes the polar core of the reverse micelles to be spherical and filled with water and the hydrophilic oxyethylene part of the surfactant, with a negligible volume of mixing. The effective length of the hydrophobic part of the surfactant molecule is added to the radius of this sphere to enable facile comparison with the experimental hydrodynamic radii obtained from DLS measurements. This models lead to following equation:
(33) Aveyard, R.; Binks, B. P.; Fletcher, P. D. I. Langmuir 1989, 5(5), 1210. (34) Aveyard, R.; Binks, B. P.; Fletcher, P. D. I.; Ye, X. J. Chem. Technol. Biotechnol. 1992, 54(3), 231. (35) Ghosh, S. K.; Khatua, P. K.; Bhattacharya, S. C. J. Colloid Interface Sci. 2004, 279(2), 523.
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tion of reverse micelle size. Upper and lower dashed lines are calculated with lhphobe equal to lmax and lliq state, respectively.
rDLS
! 3 VH2 O, total ¼ þ Vsurf , hphile þ lhphobe σ nsurf , in micelles
ð5Þ
where rDLS is the hydrodynamic reverse micelle radius as obtained by DLS, σ is the surfactant molecular interfacial area, VH2O,total is (36) Allen, R.; Bandyopadhyay, S.; Klein, M. L. Langmuir 2000, 16(26), 10547.
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Figure 11. Aggregation number as a function of reverse micelle size. Lower and upper dashed lines are calculated with lhphobe equal to lmax and lliq state, respectively.
the total volume of water, nsurf,in micelles is number of surfactant molecules in all of the micelles, Vsurf,hphile is the volume occupied by the hydrophilic part of a surfactant molecule, and lhphobe is the effective length of the hydrophobic chain of the surfactant. The derivation of eq 5 can be found in the Supporting Information. This equation differs from previous literature by taking into account the volume occupied by the surfactant in the hydrophilic core. Surfactant Molecular Interfacial Area. Once the micellar composition has been established, eq 5 can be used to determine the molecular interfacial area of the surfactant if the volume occupied by the hydrophilic part of a surfactant molecule (Vsurf, hphile) and the effective length of the hydrophobic chain of the surfactant (lhphobe) are known. The volume of the oxyethylene portion of the surfactant can be estimated from the bulk density of poly(ethylene oxide) as being 0.35 nm3/molecule. The maximum length (lmax) of the surfactant hydrophobic chain can be evaluated as 1.4 nm. The effective length (leff) is, however, somewhat less than this since the alkyl chain is probably not fully extended at room temperature. At this temperature, n-nonane contains about 33% gauche conformations.37 Furthermore, Monte Carlo simulations indicate that the end-to-end distance for n-nonane and n-decane at 25 °C is around 90% of the all-trans conformation.38 By applying a similar reduction to the surfactant alkyl chain and adding the rigid phenyl, the effective length can be estimated as 1.3 nm. In should be noted that effective length may be slightly higher in the reverse micelles than in the pure liquid state because of osmotic stretching of the anchored chains. For the reason, we have used an effective length 1.35 nm, chosen to be intermediate between the maximum length and the liquid state effective length. This exact value of this parameter influences the results obtained for the surfactant interfacial molecular area and the aggregation number. In order to put the implications of this somewhat arbitrary value in perspective, curves calculated from the two boundary values are also included in Figures 10 and 11. The repercussions on the calculated results are also discussed in the appropriate sections. The molecular interfacial area of the surfactant is plotted in Figure 10 as a function of micelle size. Clearly, the interfacial area is not constant. A limiting value is reached for micelles larger than 10 nm, but the interfacial area climbs sharply for smaller reverse micelles. This increase in the interfacial area can be attributed to the conformation of the confined oxyethylene chains as discussed (37) Snyder, R. G.; Kim, Y. J. Phys. Chem. 1991, 95(2), 602. (38) Thomas, L. L.; Christakis, T. J.; Jorgensen, W. L. J. Phys. Chem. B 2006, 110(42), 21198.
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above and illustrated in Figure 1b. This effect reaches a critical limit for reverse micelles with diameters of 4 nm. In the case of very small aggregates, the number of surfactant molecules in the micelles becomes so low that any assumption about the spherical nature of the interface is no longer valid, and the corresponding large molecular areas probably do not have true physical significance. A limiting minimum interfacial area of about 1.1 nm2 per surfactant molecule is found for micelles with diameters above 10 nm. In large micelles, the hydrophilic surfactant chains can stretch into the core, thus relieving the steric repulsions at the interface. The limiting curves in Figure 10 indicate that the exact choice of the effective length of the hydrophobic tail only has a minor influence on the calculated area. The divergence is maximal for smaller micelles but in no way affects the overall description of the system. For the same surfactant, a molecular area of 0.84 nm2 was found at the planar air/water interface by measurements with a Langmuir film balance. It is reasonable that the molecular area at a planar surface is smaller than that found at a curved interface. A molecular area of 0.45 nm2 has been previously reported for the same surfactant28 but was evaluated with model that assumed a constant surface area and using the free surfactant concentration equal to the cμc of C12E5 in hexane. Molecular areas reported in the literature28,30,39 for other nonionic surfactants are typically of the order of 0.45-0.70 nm2 and, as such, significantly smaller than what is observed here. This difference may be explained by the higher interfacial curvature of the relatively small micelles found for the Igepal/water/cyclohexane system. This again may be a manifestation of the high surfactant solubility in the continuous phase which renders removal of molecules from the interface energetically more favorable than the formation of a densely packed surface layer. Aggregation Number. It is also possible to employ geometric considerations to establish a relationship between reverse micelle radius and the aggregation number. For example, the following equation has been previously reported:27,40 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½H2 O 3 3N VH2 O þ Vsurf r ¼ 4π ½Surf:
ð6Þ
where N is the aggregation number and [H2O], [Surf], VH2O, and Vsurf are the water and surfactant concentrations and molecular volumes, respectively. This equation is based on a model that considers the micelle as a compact sphere and neglects the presence of solvent molecules between the surfactant hydrophobic tails. In accordance with the model developed above, we have modified this equation to arrive at the following expression:
rDLS
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! u u V 3 3N H O , total 2 ¼t þ Vsurf , hphile þ lhphobe 4π nsurf , in micelles
ð7Þ
where rDLS is the hydrodynamic radius obtained by DLS, N is the aggregation number, and the other parameters are as defined for eq 5. The complete demonstration of eq 7 can be found in the Supporting Information. In this model, the reverse micelle is considered to be a hairy ball rather than a compact sphere. The radius of the micelle is obtained by adding the effective length of the hydrophobic tail to the radius the hydrophilic core. This geometric model was employed to calculate the aggregation number as a function of micelle size. The results are presented (39) Sottmann, T.; Strey, R.; Chen, S.-H. J. Chem. Phys. 1997, 106(15), 6483. (40) Clark, S.; Fletcher, P. D. I.; Ye, X. Langmuir 2002, 6(7), 1301.
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in Figure 11. As was the case for the surfactant interfacial area, the specific choice of an effective length for the hydrophobic tail has only a minor influence on the calculated aggregation number. As can be anticipated, the aggregation number increases with micelle size. It would be interesting to compare the aggregation numbers obtained here with those obtained by time-resolved fluorescence quenching measurements. The DLS based method is certainly experimentally simpler and does not require the addition of probe molecules that may modify the relevant equilibrium parameters. Micelle Shape. The geometrical model employed for the evaluation of the surfactant interfacial area and aggregation number is based on the hypothesis that the reverse micelles are spherical in shape. As mentioned above, cylindrical micelles have been reported in a number of nonionic systems, and the assumption of spherical shape thus requires further justification. While not constituting unequivocal proof, the small size of the micelles, as determined by DLS, supports the hypothesis of their spherical or near-spherical shape. Bernheim-Groswasser et al.41 studied micelle formation in aqueous solutions of C12E5 through a combination of DLS measurements and cryo-TEM. At 24 °C and 0.1% surfactant, cryo-TEM revealed only short cylindrical micelles, of a few tens of nanometers in length. The corresponding hydrodynamic diameter, as evaluated from DLS, was found to be 30 nm. All of the micelles in the present study exhibit hydrodynamic diameters below 30 nm, thus excluding the presence of long cylindrical structures. Additional evidence for spherical nature of the micelles comes from viscosity measurements. Within a series of global compositions resulting in micelles of identical hydrodynamic diameter, the viscosity is found to increase smoothly with increasing water content (see Supporting Information). Importantly, within a given series, samples with higher surfactant-to-water ratio are less viscous than those with lower surfactant-to-water ratios. The shape transition from spheres to cylinders, on the other hand, is predicted to occur upon increasing surfactant to water ratios. An increase in the cylinder population is clearly inconsistent with the observed decrease in viscosity under these conditions. The observed increase in viscosity with water content, at constant micelle size, is, however, consistent with the increase in the number of micelles dispersed in the fixed volume of continuous phase. Despite these considerations, the spherical shape of the micelles has not been strictly proven. It is therefore important to keep the limitations of the model in mind in interpreting the absolute values of the parameter reported in Figures 10 and 11. Thermodynamic Interpretation. The results presented in this article are based on the key realization that micelles of a given size and shape must be in equilibrium with free surfactant of a fixed concentration. This, coupled with the compilation of data into sets of fixed micelle size but differing global compositions, allowed for the evaluation of several important parameters characterizing the reverse micelle system from simple DLS measurements. Of particular interest is the striking increase in free surfactant concentration with decreasing micelle size. This concentration increase indicates a corresponding increase in surfactant chemical potential that can be associated with a decrease in micelle stability. The formation of nonionic reverse micelles is driven by the formation of hydrogen bonds between (41) Bernheim-Groswasser, A.; Wachtel, E.; Talmon, Y. Langmuir 2000, 16(9), 4131.
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water and the oxyethylene chains. Our experimental results suggest that the surfactant within the reverse micelles is fully hydrated at all of the sizes studied, permitting the formation of the maximum number hydrogen bonds even at the lowest water contents. It is thus unlikely that the change in stability of reverse micelles with size is related to a change in hydrogen bonding. The reduction of the hydrophilic core volume also forces the oxyethylene chains to adopt less favorable conformations and thus reduces the surfactant entropy. Comparison of Figures 8 and 10 illustrates a striking correlation between the variation free surfactant concentration (chemical potential) and the variation of surfactant molecular area, both as a function of micelle size. The surfactant chemical potential and the surfactant interfacial area both reach a minimum at the same micelle size, around 10 nm. The decrease of micelle stability with decreasing size can therefore be attributed to the steric crowding of the hydrophilic segment of the surfactant and the resulting perturbation of its preferred conformation. This is consistent with the fact that the surfactant monolayer curvature is the most stable near the solubilization boundary.27
IV. Conclusions Dynamic light scattering measurements were used in conjunction with a new geometric model for nonionic reverse micelles to characterize the water/Igepal CO-520/cyclohexane system. Data analysis based on the assumption that micelles of a given apparent hydrodynamic diameter must be of the same composition allows for the evaluation of free surfactant concentration and micellar molar composition. Importantly, this method gives access to these parameters as a function of micelle size and over a large range of global compositions, including those far from the solubilization limit. In the system considered here, the quantity of free surfactant is found to be relatively high, exceeding 50% of the total surfactant content for the majority of the compositions considered. By assuming a spherical shape for the micelles and applying a geometric model that includes the contribution of surfactant to the volume of the hydrophilic core, the surfactant interfacial area and aggregation number can be obtained. The variation of these parameters with micelle size indicates that the decrease in micelle stability with decreasing size can be attributed to the steric confinement of the hydrophilic oxyethylene chains. The interfacial molecular areas obtained here are significantly larger than those previously reported in the literature for similar nonionic surfactants. This difference can be attributed to the high solubility of the surfactant in the organic phase which facilitates the removal of surfactant from the interface upon increasing geometric confinement. Finally, although not unequivocally proven, the hypothesis of spherical micelles is supported by micelle size and viscosity measurements. Acknowledgment. The authors acknowledge NanoQuebec, le Fonds Quebecois de la recherche sur la nature et les technologies (FQRNT), and the National Sciences and Engineering Research Council of Canada (NSERC) for financial support. Supporting Information Available: Definitions of all symbols, derivation of eqs 5 and 7, measured reverse micelle sizes, tables of calculated data and the viscosities of the microemulsions. This material is available free of charge via the Internet at http://pubs.acs.org.
DOI: 10.1021/la100541m
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