Nonionic Cosurfactants in AOT Reversed Micelles: Effect on

Koper, G. J. M.; Sager, W. F. C.; Smeets, J.; Bedeaux, D. J. Phys. Chem. 1995, 99 ..... Elizabeth M. Corbeil, Ruth E. Riter, and Nancy E. Levinger. Th...
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Langmuir 1996, 12, 6326-6335

Nonionic Cosurfactants in AOT Reversed Micelles: Effect on Percolation, Size, and Solubilization Site Luı´s M. M. Naza´rio,† T. Alan Hatton,‡ and Joa˜o P. S. G. Crespo*,† Departmento Quı´mica, Faculdade Cieˆ ncias e Tecnologia, Universidade Nova de Lisboa, 2825 Monte de Caparica, Portugal, and Chemical Engineering Department, Building 66-309, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received July 15, 1996X The effect of nonionic cosurfactants on AOT reversed micellar interface and micelle/micelle interactions was studied. The change on the percolating temperature induced by these cosurfactants was determined for several water contents, micelle concentration, and cosurfactant type and concentration. Two types of cosurfactants were used, linear chained alkyl alcohols and poly(oxyethylene) alkyl ethers (CiEj). If an alcohol was added to the microemulsion, a shift in percolation to higher temperature was observed. The opposite was observed for the CiEj. The apparent hydrodynamic radius for the same systems was determined using dynamic light scattering. The apparent hydrodynamic radius of the alcohol-containing microemulsions was only slightly dependent on the concentration and chain size of the alcohol. The CiEj had the opposite effect, the apparent hydrodynamic radius increased for bigger head group sizes and higher concentrations. These results were interpreted in terms of a decrease or an increase of the fluidity of the interface layer. A solubilization site for the cosurfactants is proposed based on this interpretation of the results. Using the experimental results and an association model, the clustering enthalpy and entropy were determined. The clustering process was found to be endothermic and entropically driven.

Introduction Reversed micelles, or water-in-oil microemulsions, are generally described as nanometer-sized water droplets dispersed in an apolar solvent with the aid of a surfactant monolayer, forming a thermodynamically stable and optically transparent solution. Some surfactants cannot form reversed micelles on their own and need a cosurfactant (usually an alcohol) for their stabilization, but the ternary systems formed by surfactant, water, and apolar solvent are the simplest and so are the most studied. The interest in these complex fluids arises from the fact that they can be used in oil recovery,1 as solubilizing media for proteins2 or amino acids,3 in enzymatic reactions,4 and in the preparation of monodisperse colloid size particles.5 This array of fields in which reversed micelles can be used is due to the fact that these aggregates possess three solubilization sites: the apolar continuum, the micellar interface, and the intramicellar water pool. One of the most commonly used surfactants is AOT (bis(ethylhexyl) sodium sulfosuccinate) which can form reversed micelles under a wide range of conditions,6 such as: water content (usually expressed in terms of Wo ) [H2O]/[AOT]), temperature, solvent, electrolyte type, and concentration, without the need for a cosurfactant. This * To whom correspondence should be addressed. † Universidade Nova de Lisboa. ‡ Massachusetts Institute of Technology. X Abstract published in Advance ACS Abstracts, December 1, 1996. (1) Neogi, P. In Microemulsions: Structure and Dynamics; Friberg, S. E., Bothorel, P., Eds.; CRC Press: Boca Raton, FL, 1987. (2) Luisi, P. L.; Giomini, M.; Pileni, M. P.; Robinson, B. H. Biochim. Biophys. Acta 1988, 947, 209. Hatton, T .A. In Surfactant Based Processes; Scamehorn, J. F., Harwell, J. H., Eds.; Marcel Dekker, Inc.: New York, 1989; and references therein. (3) Leodidis, E. B.; Hatton, T. A. J. Phys. Chem. 1990, 94, 6400. (4) Yang, F.; Russell, A. J. Biotech. Bioeng. 1994, 43, 232. (5) Robinson, B. H.; Khan-Lodhi, A. N.; Towey, T. In Structure and Reactivity in Reversed Micelles; Pileni, M. P., Ed.; Elsevier: Amsterdam, 1989. (6) Mitchell, D.; Ninham, B. J. Chem. Soc., Faraday Trans. 1981, 77 (2), 601. Kunieda, H.; Shinoda, K. J. Colloid Interface Sci. 1979, 70, 577.

S0743-7463(96)00687-7 CCC: $12.00

property of AOT made it particularly suitable for the present study. Reversed micelles are highly dynamic structures whose components rearrange themselves over time and space through interactions or collisions, coalescing and redispersing. Numerous methods have been used to determine the structure and dimensions of these systems, including ultrasedimentation,7 several scattering techniques8 (light, X-ray, neutron), time-resolved fluorescence,9 and NMR.10 Eastoe et al.11 recently reviewed some of the structural studies of AOT-stabilized microemulsions. Conductivity measurements are a useful technique in obtaining information on micellar interactions.12-19 A microemulsion has a very low conductivity, 10-9-10-7 Ω-1 cm-1, which is already a significant increase if compared to the conductivity of alkanes (ca. 10-14 Ω-1) and is due to the fact that micelles carry charges. A well-known phenomenon occurs when water is added to the system: At a certain volume fraction the conductivity rises sharply over a narrow range and then remains practically unchanged at a considerably higher value than before the transition. A similar behavior is observed if the temper(7) Eicke, H. F.; Rehak, J. Helv. Chim. Acta 1976, 59, 2883. (8) Cazabat, A. M.; Langevin, D. J. Chem. Phys. 1981, 74, 3148. Cabane, B. In Surfactant Solutions. New Methods of Investigation; Zana, R., Ed.; Marcel Dekker: New York, 1987; p 57 and references therein. (9) Atik, S. S.; Thomas, J. K. J. Am. Chem. Soc. 1981, 103, 3543. (10) Chachaty, C. Prog. NMR Spectrom. 1987, 19, 3543. (11) Eastoe, J.; Robinson, B. H.; Steytler, D. C.; Leeson, D. T. Adv. Colloid Sci. 1991, 36, 1. (12) Kim, M.; Huang, J. S. Phys. Rev. A 1986, 34, 719. (13) Maitra, A.; Mathew, C.; Varshney, M. J. Phys. Chem. 1990, 94, 5290. (14) Jada, A.; Lang, J.; Zana, R. J. Phys. Chem. 1989, 93, 10; 1990, 94, 381, 387. (15) Hamilton, R. T.; Billman, J. F.; Kaler, E. W. Langmuir 1990, 6, 1696. (16) Mukhopadhyay, L.; Bhattacharya, P. K.; Moulik, S. P. Colloids Surfaces 1990, 50, 295. (17) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. J. Phys. Chem. 1995, 99, 8222. (18) Ray, S.; Bisal, S. R.; Moulik, S. P. J. Chem. Soc., Faraday Trans. 1993, 89, 3277. (19) Hurugen, J. P.; Authier, M.; Greffe, J. L.; Pileni, M. P. Langmuir 1991, 7, 243.

© 1996 American Chemical Society

Nonionic Cosurfactants in AOT Reversed Micelles

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ature is increased keeping the composition constant. This phenomenon is called percolation. Some authors do not consider it a distinct phenomenon but only a transition from a discrete droplet phase to a bicontinuous one.11 It is usually considered that during percolation the droplets come in contact and ions are transferred by some kind of “hopping” mechanism and/or channels are formed through which micellar contents can be exchanged. Huang and co-workers12 as well as Maitra et al.13 support the charge-hopping model, while the results obtained by Jada et al.14 and Hamilton et al.15 are interpreted in terms of the second model. Mukhopadya et al.16 does not exclude any of the mechanisms but, based on the activation energies of conduction of ions and the activation energies of percolation, find the channel-forming model more likely. Alexandridis et al.17 do not exclude any of the models because both are based on micelle aggregation for the percolating process. Most of the literature involving percolation is related to percolation induced by the addition of water, or in the case of Ray and Moulik18 by the addition of nonaqueous solvents, i.e., volume fraction-induced percolation. Alexandridis et al.17 did a comprehensive study of temperature-induced percolation in AOT water-in-oil microemulsions, studying the effect of solvent, Wo, and micelle concentration. Using an association model, they calculated a clustering enthalpy and entropy. The authors concluded that the percolating temperature decreased with the increase in water content, micelle concentration, and molecular weight of the solvent and also concluded that the percolating process is enthalpically disfavored. The effect of additives on the volume fraction threshold has also been studied. Hurugen et al.19 studied the effect of cytochrome c on the percolating process and concluded that percolation occurs at room temperature in the presence of their solubilizate. Mukhophadya et al.16 also used temperature-induced percolation to study the effect of alcohols, cholesterol, and crown ethers on the percolating temperature. They conclude that alcohols and cholesterol increase the percolating temperature and crown ethers decrease it. They also calculate percolating activation energies for the systems with and without cosurfactant. In a recent paper, Koper et al.20 reviewed some of the experimental results in the literature and proposed a model for the aggregation phenomena based on a thermodynamic approach. Dynamic light scattering (DLS) is a useful technique to obtain structural information without the need for sophisticated equipment that is necessary, for instance, when using small angle neutron scattering (SANS) or small angle X-ray scattering (SAXS). With DLS the translational diffusion coefficient of the micelles in suspension is measured. It can then be related, under certain conditions, to the hydrodynamic radius (i.e., the radius of the micellar water pool plus the length of the surfactant molecule). Assuming that the particles are spherical and that there are no interactions, the diffusion coefficient is inversely proportional to the hydrodynamic radius through the Stokes-Einstein equation, which is given by

D)

kBT 6πµrh

(1)

where kB is the Boltzmann constant, µ is the solvent’s viscosity, and rh is the hydrodynamic radius of the dispersed particles. At a given micelle concentration, if (20) Koper, G. J. M.; Sager, W. F. C.; Smeets, J.; Bedeaux, D. J. Phys. Chem. 1995, 99, 13291.

there are micellar interactions, their diffusion will be altered, and so a radius obtained from the diffusion coefficient will not only include the hydrodynamic radius but also include a contribution due to interparticle interactions. Some authors prefer to call it correlation length or apparent hydrodynamic radius (rha). The usual way of excluding this contribution is to determine the diffusion coefficient (D) along a dilution line (i.e., upon diluting with fresh solvent), and the extrapolated diffusion coefficient (Do) for a zero value of micellar volume fraction can be used in the Stokes-Einstein equation. This method is mathematically illustrated by eq 2:

D ) Do(1 + Rφ)

(2)

where R is an interaction coefficient and φ is the volume fraction of the dispersed phase. In the case of reversed micelles the interactions are usually attractive, so R is normally negative. If the solution is sufficiently concentrated for interactions to be important, through eq 2 it can be seen that the diffusion coefficient would be smaller, and consequently, when applying the Stokes-Einstein equation, the size of the reversed micelle would be overestimated. The detailed theoretical and mathematical analysis of the method can be found in the literature.21-23 Zulauf and Eicke24 studied the AOT/water/isooctane system as function of temperature and water content. They observed that the apparent hydrodynamic radius increases with the increase in temperature and is approximately independent of the surfactant concentration for Wo below 38. Their interpretation of the trend observed for the rha as a function of temperature is based on the fact that the AOT solubility in water increases with temperature and to restore the surfactant monolayer micelles have to coalesce. Nicholson and Clarke25 studied AOT reversed micelles in h-heptane and determined a linear relation between hydrodynamic radius and Wo, which means that all the water added to the system is being taken by the micelles. It is important to note that the determined linear dependence is only valid for 0 < Wo < 30 and that this might only be true for this system. Yan and Clarke26 interpreted their DLS results of AOT reversed micelles in a binary mixture of solvents, in terms of a model that relates size and refractive index polydispersity. Their conclusion is that size polydispersity can be overestimated if this relation is ignored. Gulari et al.27 studied AOT reversed micelles in n-heptane and observed that size polydispersity increased with dispersed phase volume fraction or when the temperature approached a phase separation temperature. Their results also show that droplet size increases as temperature is increased. Gulari et al.27 also conclude that the total interfacial area, for the system studied, is only a function of the surfactant concentration at a given temperature. Ricka et al.28 studied the hydrodynamic radius of AOT microemulsions using decane as solvent for a wide range of Wo (temperature was not kept constant). Their study had the intent of investigating the feasibility of applying (21) Candau, S. J. In Surfactant Solutions. New Methods of Investigation; Zana, R., Ed.; Marcel Dekker: New York, 1987; p 147. (22) Hofer, M. In Neutron, X-ray and Light Scattering: Introduction to an Investigative Tool for Colloidal and Polymeric Systems; Lindner, R., Zemb, Th., Eds.; Elsevier: Amsterdam, 1991; p 301. (23) Hiemenz, P. C. Principles of Colloid and Surface Chemistry; Marcel Dekker: New York, 1993; p 223. (24) Zulauf, M.; Eicke, H. F. J. Phys. Chem. 1979, 83, 480. (25) Nicholson, J. D.; Clarke, J. H. R. In Surfactants in Solution; Mittal, K. R., Lindman, B., Eds.; Plenum Press: New York, 1984; p 1663. (26) Yan, Y. D.; Clarke, H. R. J. Chem. Phys. 1990, 93, 4501. (27) Gulari, E.; Bedwell, B. J. Colloid Interface Sci. 1980, 77, 202. (28) Ricka, J.; Borkovec, M.; Hofmeier, U. J. Chem. Phys. 1991, 94, 8503.

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a charge-coated model to optical properties of microemulsions. The model has only two fitting parameters: δ, which is approximately the thickness of the surfactant layer and is the ratio between the volume of a surfactant molecule and the projected area on the interface, and γ, which is indicative of the radius’ polydispersity, γ ) 〈r2〉/〈r〉2 - 1. The agreement between the experimental data and the theoretical curve is extremely good not only for the dynamic light scattering but also for the static light scattering. Ricka et al.28 consider it to be a validation of the extrapolation to infinite dilution and conclude that the polydispersity is much lower than previously considered. The agreement between the data and the model shows that AOT reversed micelles can be considered as charge-coated spheres under certain conditions. Not many studies have been made using AOT and cosurfactants; Shah and co-workers29 published a paper, about 10 years ago, in which they used dynamic light scattering to study droplet size and interactions. They concluded that the radius increases linearly with water content and that the cosurfactants increased or decreased interactions according to their structure. They made the distinction between short and long alcohols: The former increase interactions, while the latter decrease them. A decrease in interactions was also noticed for Arlacel (a long chain nonionic surfactant). In the present paper, the effect of nonionic cosurfactants on temperature-induced percolation of AOT reversed micelles was determined for several quaternary systems. For percolation to occur micelles must cluster, and any alteration in the process caused by the addition of cosurfactants will be reflected in the percolating temperature. The apparent hydrodynamic radius was determined for the same systems using dynamic light scattering. The advantage of using this technique is that besides the information on the size of the micelles, it is also possible to obtain information on the interactions between them. The results obtained with the two techniques are compared, and a brief discussion of its implications is made. From the interpretation of the results, a solubilization site for the two types of cosurfactants used is proposed. Finally, based on the conductivity of the microemulsions and the apparent hydrodynamic radius, the enthalpy and entropy of clustering for the systems under study are determined. Materials and Methods Materials. All reagents were over 99% pure and used as received. The AOT (sodium dioctyl sulfosuccinate) was purchased from Sigma, and the isooctane was purchased from Merck. The alcohols were hexanol (Fluka), octanol (Malinckrodt), and decanol (Aldrich). The poly(oxyethylene)s purchased from Nikkol were as follows: C10E1 (lot no. 3003), C10E4 (lot no. 0005), C10E6 (lot no. 1054), C10E8 (lot no. 1008), C12E1 (lot no. 1005), C12E4 (lot no. 9010), C12E6 (lot no. 9011), and C12E8 (lot no. 3085). The water was filtered Mili-Q (for dynamic light scattering) or deionized and doubly distilled (conductivity measurements). Methods. Microemulsions. The microemulsions were prepared using the injection method, i.e., to 5 mL of the organic solution (AOT with or without cosurfactant in isooctane) was added the necessary amount of water to obtain the desired Wo (water to surfactant ratio). The resulting solution was vortexed for about 60 s. Conductivity Measurements. The microemulsions’ conductivity was measured as a function of temperature with an Orion 120 microprocessor conductivity meter, an Orion electrode (0.99 cm-1), and an Orion ATC probe. Two test tubes with a certain amount of the sample (prepared as mentioned above), one with the electrode and the other with the ATC, were placed in a BBraun (29) Hou, M. J.; Kim, M.; Shah, D. O. Langmuir 1988, 123, 398.

Naza´ rio et al. Frigomix S cooling bath with a BBraun Thermomix BU heating head (T (0.02 °C). The sample equilibrated for at least 10 min after any temperature change and before any conductivity reading was done; five readings were made for each temperature. All the samples were single phased and optically transparent. Dynamic Light Scattering. For the determination of the hydrodynamic radius a Brookhaven Model BI-200 SM instrument (Brookhaven Instrument Corp., Holtsville, NY) with a Lexel argon laser (8 W, operating at 514 nm) was used. The detection angle was 90°. The signal analysis was done by a BI 9000 AT digital correlator and the software provided by the manufacturer. The temperature control bath was a Neslab RTE-100, and the temperature was kept at 25 °C (unless otherwise stated). The samples (prepared as mentioned above) equilibrated for approximately 14-16 h in a water bath, which would also allow any dust to sediment. Approximately 2 mL of the sample was pipetted into a cylindrical test tube (12 × 75) and placed in the sample holder until the count rate was stable. To reduce the interface of dust particles, measurements were rejected if the measured and calculated baselines were more than 0.1% different (the rejection level was raised to 0.15/0.2% when the Wo of the samples was close to the index matching point). The determinations were repeated three times. The water content was experimentally determined using a Karl-Fisher automatic titrator.

Results and Discussion Temperature-Induced Percolation. Percolation is a known phenomena in which, at a certain volume fraction of the dispersed phase (at constant temperature) or a certain temperature (at constant composition), there is a sharp increase in the usually low conductivity of the microemulsion, which can span 2 or 3 orders of magnitude. This phenomenon is usually envisaged as micelles clustering and aggregating so that charged material can be exchanged between them. As percolation is dependent on the clustering of micelles, anything that might promote or reduce clustering will obviously have an implication on the percolation process. The effect of nonionic cosurfactants on temperature-induced percolation was studied, i.e., their effect on the percolating temperature. This is defined as that temperature at which there is an abrupt change in slope when the logarithm of the conductivity is plotted as a function of temperature and is determined at the intersection of the two straight lines that pass through the nonpercolating state and the percolating state (as shown by the dashed lines in Figure 1). The first system studied was without cosurfactant, so as to serve as a reference for the other systems. The two types of nonionic cosurfactants used are as follows: (i) linear chained alcohols, which allow the study of the effect of the hydrophobic side chain for the same polar head group, and (ii) poly(oxyethyl) alkyl ethers (CiEj), which are commercially available with different hydrophobic side chain (i is the number of methylene groups) and polar head group (j is the number of oxyethylene groups) sizes. Besides the effect of the system’s composition, we also studied the effect of water content (Wo ) 40 and 55) and micelle concentration (expressed in terms of SO ) 28, 38, and 58). The parameter SO ()[IOct]/[AOT]) is convenient to characterize these systems because for a given water content, 1/SO is proportional to the concentration of micelles. To exemplify the effect of the water content on the percolating temperature (Tp), figure 1 shows the results for AOT and two values of Wo. As would be expected the higher the water content the lower the percolating temperature. This is due to a higher water content and to the fact that bigger micelles lead to an increase in interactions (this behavior was obtained for all the systems studied). Figure 2 shows the conductivity data of the

Nonionic Cosurfactants in AOT Reversed Micelles

Figure 1. Conductivity as a function of temperature for AOT/ water/isooctane microemulsions, for various Wo at a given micelle concentration (SO ) 58).

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Figure 3. Conductivity as a function of temperature for AOT/ C10E4/water/isooctane and AOT/decanol/water/isooctane microemulsions for two cosurfactant concentrations at a given micelle concentration (SO ) 58) and water content (Wo ) 40). Table 1. Percolating Temperatures (°C) of the Systems Studied AOT Dec/AOT ) 0.2 Dec/AOT ) 0.4 C10E4/AOT ) 0.2 C10E4/AOT ) 0.4

Figure 2. Conductivity as a function of temperature for AOT/ C10E4/water/isooctane microemulsions, for several micelle concentrations at a given water content (Wo ) 40).

system C10E4/AOT ) 0.4 and demonstrates the effect of micelle concentration on the percolating temperature. Considering that 1/SO is proportional to the micellar concentration, it would be expected that Tp would decrease with the decrease of SO, and this is indeed the case (again this is valid for most of the systems, the only exception is for Dec/AOT in which Tp is approximately constant; see Table 1). The effect of the cosurfactants is illustrated in Figure 3. When an alcohol (decanol) is added to the system, the resulting microemulsion has a higher percolating temperature, and if the concentration of the alcohol is increased, the percolating temperature is again increased. If the cosurfactant added is a CiEj (C10E4), the opposite is observed; there is a decrease in the percolating temperature that decreases further with an increase in concentration.

Wo ) 40 Wo ) 55 Wo ) 40 Wo ) 55 Wo ) 40 Wo ) 55 Wo ) 40 Wo ) 55 Wo ) 40 Wo ) 55

SO ) 58

SO ) 38

SO ) 28

41.6 31.5 53.4 40.3 64.3 49.5 42.0 23.2 33.4 ,0

38.7 27.5 53.3 41.3 66.9 53.4 34.8 18.1 14.7

35.9 26.7 52.5 40.7 67.0 54.9 29.7 15.7 (4.2)

Table 1 shows the percolating temperatures for all the systems studied. It is clear that the trends illustrated in figures 1-3 are extensive to all the systems. For the system C10E4/AOT ) 0.4, Wo ) 55, it was impossible to get an optically transparent microemulsion for the more concentrated solutions (SO ) 28 and 38). For SO ) 58, even though a microemulsion was obtained, it was impossible to determine a percolating temperature because the conductivity was high even for very low temperatures. For C10E4/AOT ) 0.4, Wo ) 40, the percolating temperature is shown in brackets because the increase in conductivity started at the second datum point and so there is some uncertainty in that value. The two types of cosurfactants used have opposite effects on the percolating temperature of plain AOT reversed micelles. As percolation is directly related to micelle clustering and aggregation, one can conclude that while alcohols make clustering more difficult, CiEj make clustering easier. Considering that the cosurfactants are solubilized in the micellar interface (in the case of the alcohols there will be a partitioning between the oil continuum and the interface), their effect on clustering and aggregation is due to the changes they cause to that interface. In view of the percolating temperatures, the resulting conclusion is that alcohols make the interface more rigid and hence make clustering, aggregation, and, consequently, percolation more difficult, while the CiEj have the opposite effect.

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Naza´ rio et al.

Through the conductivity experiments the effect of nonionic cosurfactants on micelle/micelle interactions and on the micellar interface has been related to an increase or decrease of the interfacial rigidity. A change in the fluidity of the interface should also have an effect on size and possibly shape of the individual micelles; an increase in micellar clustering could lead to an increase in the average size of the particles, and an increase in rigidity should make shape fluctuations less favorable. As was mentioned in the Introduction the determination of the hydrodynamic radius can provide important information in addition to the size of the micelles in solution. Interactions can influence the determined hydrodynamic radius, and so the latter can be used to evaluate the former. Determination of the Apparent Hydrodynamic Radius. The apparent hydrodynamic radius (rha) of the AOT microemulsions without any cosurfactant, as a function of the water content (Wo), is shown in Figure 4. The value of SO is constant and equal to 58. These results will also serve as a term of comparison for the other systems in which a cosurfactant is present. The data can be divided into three regions: (i) for Wo < 30 the rha increases linearly with an increase in Wo; (ii) for Wo ) 30 there is a discontinuity due to the index matching point; and (iii) for Wo > 30 there is a steep increase in rha. The fact that rha increases linearly with Wo is expected and has been obtained by other authors. For example, Nicholson and Clarke25 present an equation for the hydrodynamic radius of AOT/water reversed micelles in heptane (Wo < 30); Pileni30 also presents a linear dependence for AOT using SAXS and SANS (Wo < 45). This relation is to be expected because Wo is proportional to the size of the micelle and they are still fairly small for interactions between micelles to be important. The dashed line shown in Figure 4 is based on the linear relations previously mentioned. The optical matching is due to the fact that the index of refraction is an important factor in the polarizability

of any dispersed particle in a solvent. In this case the dispersed phase consist of the micelles, and because AOT has an intermediate index of refraction to that of water and isooctane, there will be a certain micelle composition at which the index of refraction of the dispersed phase is equal to that of the isooctane. Index matching has been referred to by some authors, such as Zulauf and Eicke,24 Yan and Clarke26 (these authors used a binary mixture of solvents to avoid it), and more recently by Alexandridis et al.31 Ricka et al.28 developed a simple model that is able to relate the refractive index to Wo. Using their model for our system the refractive index increment of the microemulsion would be nil for Wo ) 30.9, which is approximately what we observe experimentally. The steep increase in rha for the higher values of Wo may be due to interactions between micelles that would lead to the overestimation of the rha, referred to in the Introduction, or it could be due to the formation of micelle clusters, considering that the micelles are already very big in that region. The rha is obtained from the diffusion coefficient through the Stokes-Einstein equation, which assumes that there are no interactions between micelles. The classical way for avoiding these artifacts is to determine the diffusion coefficient as a function of the volume fraction of the dispersed phase. To study this in more detail, the rh was determined at infinite dilution (rhinf) for seven Wo, using the data of five different micelle concentrations for each Wo. The obtained rhinf values are also plotted in Figure 4. It can be seen that the two sets of data fall together. This result is very important because it means that the data we obtained for SO ) 58 are not being influenced by micelle interactions, i.e., the SO ) 58 is a sufficiently diluted solution (at least for Wo up to 50). The fact that the radii determined through infinite dilution are in agreement with the ones previously obtained not only shows that interactions are negligible but also excludes micelle clustering as the cause for the steep increase in rh shown in Figure 4. This trend can only be due to shape fluctuations of the individual micelles. There could be a contribution from size polydispersity, but its value was found to be small, and so shape fluctuations must be the dominant cause. The water content of the micelle is such that the curvature is sufficiently small so that fluctuations in shape can occur. Again this conclusion is only valid for Wo up to 50, the highest Wo studied at infinite dilution. For higher Wo clustering may also be significant. Even though the rh values were obtained at infinite dilution, they are still referred to as apparent because the spherical assumption made when using the Stoke-Einstein equation may not be valid. The dynamic light scattering results discussed until now were done at 25 °C, which is a lower temperature than that at which percolation was observed for the same system. To study the effect of temperature, the rha of this system, as a function of Wo, was determined at different temperatures (Figure 5). Considering the high Wo range, the results show that for the lower temperatures (15 and 20 °C) no steep increase of rha occurs; that trend is only apparent at temperatures above 21 °C. The change from one to the other is not gradual. There is a transition temperature (between 20 and 21 °C) which is considerably lower than the percolating temperature previously determined for this system. If the data obtained by percolation and dynamic light scattering (Figure 6) are compared, the difference between

(30) Pileni, M. P. In Structure and Reactivity in Reversed Micelles; Pileni, M. P., Ed.; Elsevier: Amsterdam, 1989.

(31) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. Langmuir 1993, 9, 2045.

Figure 4. Apparent hydrodynamic radii of AOT/water/isooctane for various Wo at a given micelle concentration (SO ) 58) and at infinite dilution.

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Figure 5. Apparent hydrodynamic radii of AOT/water/isooctane for various Wo at different temperatures.

Figure 7. Effect of octanol concentration on the apparent hydrodynamic radius of AOT/octanol/water/isooctane microemulsions.

Figure 6. Comparison between the conductivity curves and apparent hydrodynamic radius of AOT/water/isooctane microemulsions and two different water contents.

the phenomena observed by the two techniques is more evident. If the temperature of a certain AOT microemulsion is increased, there will be an increase in the interfacial flexibility that may lead to shape fluctuations (observed by dynamic light scattering); increasing of the temperature further will induce clustering that eventually will lead to percolation resulting in an increase in conductivity. Effect of the Nonionic Cosurfactants on the Apparent Hydrodynamic Radius. The results presented with cosurfactants were not obtained from infinite dilution, and so the size of the reversed micelles is referred to as apparent hydrodynamic radius. Diluting the initial solution would alter the cosurfactant partitioning between the dispersed phase and the oil. Zana and co-workers32 observed that the exchange rate of the alcohol from the (32) Zana, R.; Lang, J. In Microemulsions: Structure and Dynamics; Friberg, S. E., Bothorel, P., Eds.; CRC Press: Boca Raton, FL, 1988.

Figure 8. Effect of alcohol chain length on the apparent hydrodynamic radius.

interface to the continuum changed with increasing oil content. It was also our intention to keep the solvent to surfactant ratio constant. The effect of the alcohol concentration (expressed in terms of ratio between the alcohol and the surfactant) as well as the effect of the hydrophobic tail length were studied. The results are shown respectively in Figures 7 and 8. Both figures show that the presence of the alcohol has a major effect on the rha of the reversed micelles, i.e., the steep increase is no longer observed for the higher Wo. As the concentration of the alcohol in the system is increased the rha decreases, for a certain value of Wo. This decrease does not depend significantly on the concentration when a certain value is reached (the data for 0.2 and 0.4 are very similar). The same observation can be made from the data obtained for hexanol and decanol (results not shown). There is no visible effect of the tail length

6332 Langmuir, Vol. 12, No. 26, 1996

Figure 9. Effect of head group size on the apparent hydrodynamic radius of AOT/C10Ej/water/isooctane microemulsions.

because all the plots for the different alcohols fall practically together. There is only a small effect for small Wo, but the size of the alkyl chain is not important for the reduction of rha for higher water contents. These results imply that the shape fluctuations, which previously existed, are disfavored by the presence of the alcohol. These results are in agreement with what Shah and co-workers29 obtained for what they called big alcohols. Lissi and Engel33 determined partition constants of alcohols and found no effect of the alkyl chain except for small values of Wo. This was to be expected considering the work done by Leodidis and Hatton3 which concludes that the main driving force for solubilization in reversed micelles is the presence of hydrophilic groups. Since the alcohols have the same functional group, their behavior should be the same and relatively independent of the hydrophobic side chain. With the other type of cosurfactant used for this study (poly(oxyethylene) alkyl ethers, CiEj), in addition to the effect of concentration and tail length, the effect of head group size was also studied. This is shown in Figure 9. The figure shows the rha of the C10Ej and decanol (it can be considered as a C10E0). The effect of these cosurfactants is different than that observed for alcohols when j is bigger than 1. For j ) 4, 6, 8 there is a rapid increase in rha with Wo. The rha seems to increase asymptotically toward a certain value of Wo, eventually leading to a phase transition. This limiting value of Wo becomes smaller as the polar head group size increases. The only CiEj that has a similar behavior to the alcohol is C10E1, which only differs from the alcohols by one oxyethylene group. These high values of rha might not be due to a real increase in the size of the micelle but may be due to shape fluctuations as was previously discussed for the plain AOT reversed micelles. In view of the percolating temperatures determined for C10E4, micellar clustering cannot be excluded as part of the explanation for the high values of rha. Complementary studies using other techniques (e.g., SANS because it can provide information on the size of the micellar water pool) should provide more information on the shape of CiEj-containing micelles. The effect of concentration of C10E4 is illustrated in Figure 10: With the increase in concentration, the limiting (33) Lissi, E. A.; Engel, D. Langmuir 1992, 8, 452.

Naza´ rio et al.

Figure 10. Concentration effect of C10E4 on the apparent hydrodynamic radius of AOT/C10E4/water/isooctane microemulsions.

Figure 11. Effect of hydrophobic side chain of CiEj on the apparent hydrodynamic radius of AOT/CiEj/water/isooctane microemulsions.

value of Wo is reached sooner. For small values of Wo there is no difference between the two sets of data, in contrast to what happens for higher water contents in which there is an important difference in the rha for the two concentrations. The effect of the hydrophobic tail length is small but noticeable, unlike the alcohols (Figure 11). The data obtained for C12Ej are consistently below that obtained for C10Ej. From the data presented one can conclude that the addition of CiEj favors shape fluctuations and/or clustering of micelles, while the alcohols disfavor them. Solubilization Site of the Cosurfactants Used. The solubilization site of the cosurfactant is obviously connected with the resulting fluidity of the micellar interface. In the case of the alcohols (in our case long chain alcohols) we have seen that they increase the rigidity of the interface, which can be achieved if the alcohol solubilizes in the

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Figure 12. Schematic representation of the solubilization site of the cosurfactants.

surfactant tail region and so pushes the surfactant head groups together (Figure 12a). This solubilization site also increases the micellar curvature. On the other hand CiEj make the interface more fluid, and so their solubilization will be such that they expand the micellar interface. There are two possibilities for the exact solubilization site: (i) the CiEj might have its polar head immersed in the water pool, or (ii) the CiEj might have it in the surfactant head group region (Figure 12b). Both sites would lead to an expansion of the micellar interface, but the latter would cause a substantial increase in the interfacial area. The fact that for small Wo, when the concentration of C10E4 is increased (Figure 10), the rha does not change seems to indicate that the polar head group would be solubilized in the micellar water pool (at least for that range of Wo). For a definite conclusion on the exact site, more studies will need to be made using other techniques (e.g., SANS, interfacial area of micelles may be obtained when using contrast variation). Interfacial Fluidity and Charge-Coated Sphere Model. The clustering of micelles and the existence of shape fluctuations have been related to the rigidity or fluidity of the interface. Our results lead to the conclusion that alcohols make the micellar interface more rigid because they disfavor clustering and reduce shape fluctuations. On the other hand, CiEj make the interface more fluid and so the opposite occurs. The decrease or increase in temperature has a similar effect as that of the studied cosurfactants. The more rigid the interface is, the more likely an AOT micelle can be considered as a charge-coated sphere. Given the results that have been shown, there are two cases that should be adequately fitted by a model based on such a representation of the micelles: the presence of an alcohol and the decrease in temperature. If we fit the charge-coated sphere model developed by Ricka et al.28 for the rha to our results, we obtain the curve shown in Figure 13. The figure shows that the data for the AOT are not in agreement with the model for Wo above 30, but the data for octanol/AOT ) 0.4 are in very good agreement with the model, substantiating the discussion above. According to the discussion on the effect of the alcohol on the rigidity of the interface and considering that the model is based on a charge-coated sphere conception of the micelles, it would have been expected that only the data for octanol would agree with the model. The parameters obtained through the fitting are δ ) 1.2 nm and γ ) 0.025. Both parameters are slightly higher than those obtained by Ricka et al.28 (δ ) 1 nm and γ ) 0.0144), but the value for the polydispersity index is not as high as has been previously reported (Kotlarchyk et

Figure 13. Fitting of the charge-coated sphere model to the apparent hydrodynamic radius of AOT/octanol/water/isooctane microemulsions.

al.,34,35 γ ) 0.09). The parameters are not directly comparable because ours are for a mixed interface and the others are for AOT only. The results obtained with the AOT system at various temperatures (Figure 5) are also in agreement with what has been said about the fluidity or rigidity of the interface. A decrease in temperature results in a higher rigidity of the interface, while the opposite results in a decrease. If the model proposed by Ricka et al.28 is used to fit the data obtained for AOT at 15 °C (fit not shown), the values obtained for the fitting parameters are δ ) 1.15 nm and γ ) 0.0196. These values can be compared with the ones obtained by Ricka et al.30 (even though the solvent is different) and are quite similar. The surfactant layer length is slightly larger, meaning that the surfactant interfacial area per surfactant molecule would be 53 Å2 (assuming that it is constant) which is not unrealistic, considering that it does vary with Wo. Most authors use the value of 56 Å2, and Eicke and Rehak6 use 54 Å2 for the interfacial area. The polydispersity index is also slightly higher than their value, about 2%, which is still much lower than the values presented by some of the authors previously cited. The data for AOT reversed micelles at 15 °C shown in Figure 5, unlike that of Ricka et al.,28 were not obtained at infinite dilution but are in good agreement with the model. Ricka et al.28 lowered the temperature so that high values of Wo could be reached; the fact that their results had a very good agreement might not have been only due to the dilution procedure but also to the lowering of the temperature and making the interface more rigid. Energy Calculations for Micellar Clustering. Based on the conductivity data, the hydrodynamic radii, and the discussion made on the solubilization site of the different cosurfactants, it is possible to obtain thermodynamic parameters for droplet clustering using the association model that was used by Moulik et al.18 and Alexandridis et al.17 (34) Kotlarchyk, M.; Stephens, R. B.; Huang, J. S. J. Phys. Chem. 1988, 92, 1533. (35) Kotlarchyk, M.; Chen, S. H.; Huang, J. S.; Kim, M. W. Phys. Rev. A 1984, 29, 2054.

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Table 2. Clustering Enthalpy and Entropy for Some of the Systems Studied AOT C10E4/AOT ) 0.2 C10E4/AOT ) 0.4 Dec/AOT ) 0.2

Wo ) 40 Wo ) 55 Wo ) 40 Wo ) 55 Wo ) 40 Wo ) 40

∆H (kJ/mol)

∆S (kJ/mol K)

88.1 103.1 46.7 75.9 18.3 411.8

0.37 0.45 0.25 0.37 0.17 1.35

Conductivity increases when micelles cluster and eventually form a percolating network that spans the system. Due to this concept of percolation a Gibbs free energy can be calculated from the micelle mole fraction at the onset of percolation through the equation:18

∆Gcl ) RT ln Xp

(3)

where Xp is the mole fraction of the micelles at the percolation threshold. Equation 3 is similar to the equation used to calculate the free energy of micellization. The similarity comes from the analogy made between the micellization/demicellization and percolating/nonpercolating processes.36 The mole fraction of micelles can be obtained from the surfactant concentration, the hydrodynamic radius, and the projected area (the expression developed by Eicke and co-workers was used) if a certain solubilization site is assumed. From the free energy and the percolating temperature a clustering enthalpy and entropy can be calculated. Using this thermodynamic framework the enthalpy and entropy for the systems studied were obtained, and the results are shown in Table 2. For the systems with cosurfactants the assumptions made are as follows: (i) the alcohols are solubilized in the surfactant tail region and so by pushing the surfactant heads together will reduce the surfactant’s projected area; (ii) the CiEj was all at the micellar interface; and (iii) the polar head group of the CiEj is immersed in the micellar water pool, and so the only addition to the interfacial area is due to the hydrophobic side chain. From the results we can conclude that the percolation process is endothermic and entropically driven for all the systems. The values for the enthalpy and entropy increase with an increase in Wo and if an alcohol is added to the system. The opposite happens if a CiEj is the cosurfactant. For the alcohol-containing system only the results for Wo ) 40 are presented because the method is extremely sensitive to the percolating temperatures, which are very close and so the errors are extremely large. The energy values are in the same order of magnitude as the ones calculated by Moulik et al.18 and Alexandridis et al.17 Other authors that have published papers referring to this subject also present similar values. The important point to note is that all of the ∆H and ∆S values found in the literature as well as the ones calculated in this paper are positive. Koper et al.20 in a recent paper also refer to the fact that the enthalpy and entropy are positive and refer to the various explanations published so far (mainly based on van der Waals forces or curvature effects). Alexandridis et al.17 suggest that for micelles to aggregate they must deform their interfaces and so a positive ∆H would be needed, although there could also be a contribution from the breaking of the interface so that coalescence can take place. As alcohols increase the curvature and the rigidity, making it more (36) Hunter, R. J. Foundation of Colloid Science; Oxford University Press: New York, 1987; Vol. 1, Chapter 10.

difficult to bend the interface,37 the clustering enthalpy for that system should be higher than the clustering enthalpy of plain AOT micelles, which is indeed the case. The opposite is also true: An increase in the flexibility of the interface should result in a lower energetic penalty, as the calculated values for the CiEj systems show. The fact that ∆H increases with Wo seems to suggest that the flattening of the interface is not the only important aspect because for the bigger Wo the curvature is already less pronounced. Another contribution for the enthalpy may come from the tail packing because it becomes relevant for larger micelles and will also oppose the bending of the interface. If we consider that the CiEj tail is in the surfactant pseudophase, the packing of the AOT double tail will be easier, resulting in a lower enthalpy than that for AOT for the same Wo. The positive ∆S may be due to the volume dissimilarities of the surfactant molecules anchored at the interface and the solvent molecules that are released from the surfactant tail region due to the overlapping of the surfactant tails. The fact that the solvent molecules are no longer “restricted” leads to an increase in entropy. This would also explain why the entropy for the system with decanol is so largeswhen the surfactant tails overlap at the moment of clustering, the solvent and the decanol molecules in that region are excluded leading to an increase in the entropy. Conclusions The effect of nonionic cosurfactants on AOT reversed micelles has been studied using two very different techniques, and the results lead to similar conclusions. Alcohols change the interfacial fluidity making it more rigid, thereby reducing shape fluctuations and clustering. In summary the alcohols used in this study make the micelles more hard spherelike which enables the hydrodynamic results to be explained by a theoretical model based on that assumption and explains the percolating temperature increase observed for those systems. The CiEj have a completely different effect on the micellar interface: They increase the fluidity which will favor interactions and shape fluctuations and facilitate clustering. The rapid increase in the apparent hydrodynamic radius and the lowering of the percolating temperature are due to that effect on the interface. The fact that the cosurfactants affect the fluidity of the interface can also be used to draw some conclusions on their solubilization. Alcohols such as the ones used for this study will solubilize in the surfactant tail region, pushing together the surfactant heads and so increasing the curvature and rigidity. On the other hand, CiEj solubilize next to the surfactant head group region, increasing the interfacial area and decreasing the curvature and rigidity. The exact site is not known, but two sites have been proposed as follows: (i) the oxyethylene groups are immersed in the micellar water pool and (ii) the oxyethylene groups are solubilized in the surfactant head group region. The interfacial area increase in the second case would be much higher. Other techniques might be helpful in clarifying the solubilization site. Among them, the most likely to produce a clearer picture is small angle neutron scattering (SANS) because it can delineate scattering and internal structure by contrast variation of individual micelles (e.g., radius of micellar water pool). Another parameter that can be (37) Lemaire, B.; Bothorel, P.; Roux, D. J. Phys. Chem. 1983, 87, 1023.

Nonionic Cosurfactants in AOT Reversed Micelles

obtained from SANS is the interfacial area of the micellar interface, which would make it possible to determine the solubilization site of the CiEj. The comparison made between the results obtained for rha and conductivity for the AOT system as a function of temperature (Figure 6) showed that the temperature at which the sharp increase in rha occurred was different from the percolating temperature. This difference seems to indicate that as temperature is increased the system goes through several stages before reaching percolation.

Langmuir, Vol. 12, No. 26, 1996 6335

Initially there is an increase in the interfacial flexibility resulting in shape fluctuations and then clustering and percolation. Acknowledgment. L. Naza´rio would like to acknowledge the financial support from JNICT-Junta Nacional de Investigac¸ a˜o Cientı´fica e Tecnolo´gica through Grant BD 330 and Fundac¸ a˜o Luso-Americana para o Desenvolvimento. LA960687U