Shape, Size, and Structural Control of Reverse Micelles in Diglycerol

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J. Phys. Chem. B 2007, 111, 1664-1671

Shape, Size, and Structural Control of Reverse Micelles in Diglycerol Monomyristate Nonionic Surfactant System Lok Kumar Shrestha,† Takaaki Sato,‡ and Kenji Aramaki*,† Graduate School of EnVironment and Information Sciences, Yokohama National UniVersity, Tokiwadai 79-7, Hodogaya-ku, Yokohama 240-8501, Japan, and DiVision of Physics and Applied Physics, Faculty of Science & Engineering, Waseda UniVersity, Okubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan ReceiVed: NoVember 14, 2006; In Final Form: December 14, 2006

We have investigated the self-organization structures of diglycerol monomyristate (DGM) in different types of organic solvents. Study of phase behavior shows the presence of solid at lower temperature, and upon increasing temperature, the solid phase transforms to lamellar liquid crystal (LR) phase in the surfactant axis in all the DGM/oil systems. In the dilute regions, however, the dispersion of the solid or LR phase is observed, depending on the solvent and temperature. At higher temperatures, the LR phase melts to the isotropic reverse micellar solution phase. GIFT analysis of small-angle X-ray scattering data supported by a complementary modeling method have unambiguously shown that the structure of the DGM reverse aggregates can flexibly be controlled by optimizing the fundamental properties of solvent oils. In aromatic oils, the observed moderate micellar elongation is almost solely governed by the polarity of the aromatic ring, the length of the hydrocarbon side chain group showing no drastic effect. In contrast, when the solvent is replaced with linear-chain hydrocarbon oils, the drastic effects depending on the chain length emerge; by gradually increasing the length from decane to hexadecane, the long cylindrical particles in decane are finally transformed into planar aggregates, whose mechanism may be explained in terms of the transfer free energy of the diglycerol moiety from the hydrophilic environment to the hydrocarbon oils with a different chain length. We have also systematically examined the effects of temperature, the surfactant concentration, and added water.

1. Introduction An amphiphilic molecule undergoes self-aggregation and forms a variety of self-organized structure in water. The aqueous phase behavior and the self-assembled structures of the conventional poly(oxyethylene)-type nonionic surfactant has been extensively studied in the past.1-8 The self-organization of these surfactants is highly influenced by the alkyl chain length, the poly(oxyethylene) chain length, the surfactant concentration, and the temperature. However, when compared to the aqueous phase, much less study has been concentrated on the nonaqueous phase behavior and its self-assemblies in nonpolar organic solvents.9 The poly(oxyethylene) hydrophilic moiety is soluble in many organic solvents, so the surfactant tends to dissolve monomerically in nonaqueous solvents, and hence, it does not form selforganized structures in nonpolar organic solvents, especially in the absence of water. On the other hand, most ionic surfactants are insoluble in many organic solvents, and they tend to precipitate as a solid, except for some special surfactants. Different from the conventional poly(oxyethylene) chains, other hydrophilic moieties, such as sucrose and polyglycerol, are more lyophobic10,11 and, hence, tend to aggregate in nonpolar media, where it is possible for them to form different self-organized structures. The aggregation of the surfactant molecules in nonpolar organic media has been described by the similar concept of * To whom correspondence should be addressed. Phone/fax: +81-45339-4300. E-mail: [email protected]. † Yokohama National University. ‡ Waseda University.

aggregation in aqueous solvents. The aggregates in the nonpolar oils consist of polar head groups of the amphiphile shielded by the hydrophobic environment of the solvents. Since the structure of aggregates in the nonaqeous system is opposite that of the aqueous systems, it is often called inverted micelles or reverse micelles. The solution behavior of the amphiphilic molecules in nonpolar solvents markedly differs from that in aqueous solvents. It is well-known that the physicochemical properties of aqueous surfactant solutions undergo an abrupt change over a narrow concentration range. The concentration at which a sharp change occurs is regarded as the critical micelle concentration (CMC). However, the physicochemical properties of the nonaqueous surfactant solution change gradually with the surfactant concentration without any sharp transition. Therefore, the existence of the micelles was doubtful in the case of nonaqueous solvent systems. Nevertheless, previous experiments have confirmed the aggregation of amphiphilicmoleculesinnonpolaroils,evenatlowconcentration.12-14 However, the aggregation numbers are relatively much smaller as compared to the aqueous solution systems. The small size aggregates with small aggregation number are believed to increase with the total surfactant concentration. Self-aggregation of the amphiphilic molecules in nonpolar media leading to the formation of long cylindrical to flat particles has been very rarely reported so far. In most of the cases, only small aggregates have been observed. In the present contribution, we report on a study of the self-organization of diglycerol monomyristate, hereafter abbreviated as DGM, nonionic surfactant, and structural investigation of reverse micellar aggregates in aromatic and aliphatic cyclic and linear chain hydrocarbon oils. The formation of small to nearly flat

10.1021/jp067546d CCC: $37.00 © 2007 American Chemical Society Published on Web 01/26/2007

Control of Reverse Micelles in DGM Surfactant aggregates via long cylindrical micelles is presented. The structure of the reverse micellar aggregates are confirmed by the small-angle X-ray scattering technique. Furthermore, we have discussed the effect of surfactant concentration, temperature, and added water on the reverse micellar structure.

2. Experimental Section 2.1. Materials. The surfactant diglycerol monomyristate (Sunsoft Q-14D) was kindly provided by Taiyo Kagaku Company, Japan. The surfactant was 92.9% pure by the gas chromatography test, and the main impurities present were the unreacted diglycerol, diglycerol difatty acid esters. The surfactant was used without further purification. The nonpolar organic solvents n-octane, n-decane, n-tetradecane, n-hexadecane, cyclohexane, ethyl benzene, and 1-phenyl octane were purchased from Tokyo Chemical Industry, Japan. All the oils used were 99.5% pure as confirmed by the gas chromatography test. 2.2. Methods. 2.2.1. Sample Preparations. Samples of DGM/ oil mixtures with concentrations of DGM ranging from 1 to 7 wt % were prepared using different organic solvents, such as n-octane, n-decane, n-tetradecane, n-hexadecane, ethyl benzene, 1-phenyl octane, and cyclohexane, in clean, dry glass ampoules. The samples were mixed for 2 h by using a dry thermo bath, vortex mixer, and repeated centrifugation to achieve homogeneity. After mixing, the samples were placed in a temperature-controlled water bath at 50 °C for 2 h before the measurements. 2.2.2. Small-Angle X-ray Scattering (SAXS). We have performed a series of SAXS measurements on 5 wt % DGM/oil systems at 40, 50, 60, and 70 °C to answer the question of how the geometry (shape and size) of reverse aggregates is controlled by changing or optimizing the nature (chain length, polarity, molecular structure, and so on) of oils, temperature, surfactant concentration, and added water. We employed a SAXSess camera (Anton Paar, Austria), which is attached to a PW3830 X-ray generator (PANalytical, Netherlands) with a sealedtube anode (Cu KR wavelength of 0.1542 nm). The generator was operated at 40 kV and 50 mA. The SAXSess camera is equipped with focusing multiplayer optics and a block collimator for an intense and monochromatic primary beam with low background. A semitransparent beam stop enables measurement of an attenuated primary beam for the exact definition of the zero scattering vector and transmission correction. Samples were enclosed in vacuum-tight, reusable thin quartz capillaries to attain exactly the same scattering volume and background contribution. The sample temperature was controlled with a thermostated sample holder unit (TCS 120, Anton Paar). The 2-D scattered intensities recorded on an imaging plate detector were read out by a Cyclone system (Perkin-Elmer, U.S.A.), and were converted via SAXSQuant software (Anton Paar) to one-dimensional scattering curves as a function of the magnitude of the scattering vector, q ) (4π/λ) sin(θ/2), where θ is the total scattering angle. All the intensities were transmission-calibrated by normalizing an attenuated primary intensity at q ) 0 to unity and were corrected for the background scattering from the capillary and the solvents. The absolute scale calibration was made using water as a secondary standard.

J. Phys. Chem. B, Vol. 111, No. 7, 2007 1665 For one-component particle systems having n particles in unit volume, the total (absolute) scattered intensity I(q) can generally be given by

I(q) ) n P(q) S(q)

(1)

where P(q) is the averaged form factor and S(q) is the static structure factor. P(q) is given by the Fourier transformation of the so-called pair-distance distribution function (PDDF), p(r), as

P(q) ) 4π

∫0∞ p(r) sinqrqr dr

(2)

S(q) describes the spatial distribution of the particles and is given by the Fourier transformation of the total correlation function, h(r) ) g(r) - 1, as

S(q) ) 1 + 4πn

∫0∞ [g(r) - 1]r2 sinqrqr dr

(3)

where g(r) is the pair-correlation function. The SAXS data for the reverse micellar solutions were analyzed by the generalized indirect Fourier transformation (GIFT) technique,15,16 whose basic concept is simultaneous determination of P(q) and S(q) with minimal assumptions. P(q) is calculated via the model-free routine as the well-established IFT does, while an interaction potential model for S(q) is to be assumed. We chose the averaged S(q) model,17,18 which is described by the weighted average of Percus-Yevick analytical solutions of the Ornstein-Zernike equation for Gaussiandistributed hard-sphere radii. The detailed theoretical description of the method has been reported elsewhere.19,20 Note that when the particle geometry deviates from an ideal spherical symmetry, the S(q) parameters as the outputs of the GIFT analysis become no longer exact. Nevertheless, the GIFT approach can greatly improve the calculation of p(r), efficiently suppressing the influence of the interparticle interference scattering. 2.2.3. Densimetry. Using a high precision DSA5000 densimeter (Anton Paar, Austria),21 density measurements were carried out on DGM, oils (octane, decane, tetradecane, hexadecane, cyclohexane, ethyl benzene, and 1-phenyl octane), and the mixtures at the same temperature as the SAXS experiments. The DSA5000 instrument is based on the conventional mechanical oscillator method, which measures the natural resonance frequency of a U-shaped glass tube filled with 1 mL of sample. The highly tuned temperature control of the apparatus enables an accuracy of 10 mK in an absolute value. 3. Results and Discussions 3.1. Phase Behavior of DGM/Oils. In Figure 1, we present a temperature-composition diagram for the DGM/hexadecane system. Phase diagrams of surfactant/oil binary systems as a function of temperature and composition for the DGM surfactant in a variety of oils are described.22 The DGM surfactant is practically immiscible with linear chain hydrocarbon-type oils at normal room temperature. However, by changing the oil from a linear chain hydrocarbon to aromatic or cyclic aliphatic oils, the mutual dissolution tendency of the surfactant increases, and there is isotropic solution at normal room temperature, 25 °C. There is surfactant solid at lower temperature, and upon increasing the temperature, the solid-phase transforms to the lamellar liquid crystal phase (LR), which swells a small amount of oils. In the dilute regions, dispersion of the LR phase is observed mainly in the case of linear chain oils, such as in

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Figure 1. Temperature-composition binary phase diagram of the DGM/hexadecane (S ) solid, O ) excess oil, LR ) lamellar liquid crystal, I ) isotropic solution, and II ) two liquid phases). Adopted from ref 22.

octane, decane, tetradecane, and hexadecane. At higher temperature, the LR phase melts to isotropic single or turbid solutions, depending on the nature of the solvents. The turbid solution, which separates into two liquid phases after some time, is observed only in the case of tetradecane and hexadecane systems, and the two-liquid-phase domain is wider in the case of the DGM/hexadecane system. On further increasing the temperature, the turbid solution transforms to a single isotropic liquid phase. Unlike in the water-poly(oxyethylene) type of surfactant system, in which the surfactant becomes less hydrophilic with increasing temperature and the phase separation takes place (cloud point)23,24,25 due to dehydration of the ethylene oxide chain as a result of conformational change with temperature, in the surfactant/oil systems, the miscibility of oil and surfactant increases with an increase in temperature. The penetration of the oil in the surfactant chain is enhanced with increasing temperature, and the packing parameter decreases; that is, planar aggregates transform to either cylindrical or spherical aggregates, depending on the lipophilic chain length of the surfactant and the oils.26 3.2. Reverse Micellar Structures. A number of important interfacial phenomena, such as solubilization, detergency, and so on, depend on the micellization behavior of the amphiphilic molecules. Considering the recent upward trend of utilizing micellar solutions as a template for the preparation of nanomaterials, such as nanocrystals or mesoporous materials,27-33 controlling freely the size and shape of micellar aggregates is of central importance from an application viewpoint because the geometry of micellar aggregates largely affects the structure of the products. The studies on the self-aggregation of amphiphilic molecules have a long history. However, far less is known about the reverse micellar aggregates in nonpolar organic solvents if compared to aqueous systems. It is readily known that when surfactant molecules are added to nonpolar organic solvents, there is a tendency to minimize contact between the solvent and the hydrophilic head group of the amphiphile, and thus, reverse micelles are formed, which is the opposite of the conventional normal micelles in aqueous media. Namely, the micellar aggregates in nonpolar media consist of a head group oriented toward each other in the interior of the structure and the hydrophobic groups oriented toward the nonpolar solvent. In contrast to the aqueous systems, generally, the structure of the nonpolar oils is largely unaltered by the presence of the amphiphile molecules. The interaction of the surfactant hydro-

Shrestha et al. phobic tail with the solvent molecules is just as favored as with other surfactant tails. In such a case, there would be no strong tendency that the formation of large aggregates is favored. However, the dipole-dipole interaction between the hydrophilic head groups may act as one of the driving forces of the formation of reverse micelles in nonpolar media. In addition, as we will later discuss, the transfer free energy of the hydrophilic head group from the hydrophilic environment to oil may provide insights into the mechanism of the reverse micellar formation. SAXS measurements were carried out at 40, 50, 60, and 70 °C in the isotropic single liquid-phase region. We will unambiguously show that contrary to the conventional wisdom, by the optimum choice of the surfactant, the geometry of the reverse aggregates can be flexibly controlled, from spherical or rodlike to planarlike by tuning the properties of oils, surfactant concentration, temperature, and added water. 3.2.1. Effect of the Oils on the Micellar Structure. Most of the previous studies on the micellar aggregates focused on a discussion of the effect of the amphiphilic chain length, head group size, and oil solubilization. However, to our knowledge, the effects of the nature of the solvents on the reverse micellar structure have not been studied in a sufficiently systematic way. We have performed structural investigations of the reverse micellar aggregates in different types of nonpolar solvents, such as aromatic, aliphatic cyclic, and straight-chain hydrocarbon oils. Interestingly, diglycerol monomyristate nonionic surfactant has a potential ability to form a variety of reverse micellar aggregates with different geometries, sharply reflecting the nature of the organic solvents and other outer conditions. The scattering functions, I(q), and the corresponding pair-distance distribution functions, p(r), for the DGM/oil systems are displayed in Figure 2, which compares the effects of aromatic oils, a cyclic aliphatic oil, and straight-chain hydrocarbon oils on the aggregation behavior of the DGM surfactant. As can be seen from Figure 2b, the PDDF curve of 5 wt % DGM in ethyl benzene exhibits a symmetric bell shape, assigned to a typical feature of a nearly spherical micelle, in which the core radius is estimated to be ∼1.5 nm from the maximum dimension, Dmax ∼ 3 nm. A slight elongation of the micellar structure is attained with the cross section diameter virtually unchanged when the 1-phenyl octane replaces ethyl benzene. Ethyl benzene and 1-phenyl octane are aromatic hydrocarbon oils having some degree of polarity. Hence, it is expected that the aromatic ring goes all the way to the hydrophilic/ hydrophobic interface of micelles and a spherical-like micellar aggregate is favored due to a voluminous polar head group. A slight elongation in the case of 1-phenyl octane compared to the ethyl benzene may possibly be caused by the situation that the former oil cannot reach as deep a center of the micelle as the latter does due to a less polar character with the longer alkyl chain. Cyclohexane is less polar than these aromatic oils34-36 so that a more elongated aggregate formation may be expected to be favored. However, the structural behavior of the DGM/ cyclohexane system is not as straightforward as can be explained as a simple counterpart of the aromatic oil-based systems. Judging from the slightly asymmetric shape of the PDDF curve and the lack of a local maximum and minimum, the DGM/ cyclohexane system seems to have a slightly elongated, prolatelike shape with a nearly homogeneous scattering length density distribution inside the core. Dmax is considerably increased as compared to those of the aromatic oil-based systems, accompanied by an increase in the cross-sectional diameter, as

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Figure 2. The X-ray scattered intensities I(q) of 5 wt % DGM/oil systems at higher temperature, 50 °C, in absolute unit and the pair-distance distribution functions p(r) extracted with GIFT analysis. I(q) of the DGM/oil systems in aromatic and cyclic saturated oils (a) and linear-chain hydrocarbon oils (c), and the corresponding p(r) respectively in b and d. Solid and broken lines in panels b and d represent the GIFT fit and the calculated form factor for n particles existing in unit volume, nP(q), respectively. The arrows in panel d indicate the maximum dimension of micelles, Dmax, and the broken line on the inflation point of p(r) on the high-r side of the maximum highlights the core diameter.

can be seen in Figure 2b. Surprisingly, Dmax ∼ 6.5 nm far exceeds twice of the extended hydrophilic chain length of the DGM surfactant. To explain all these features, we have to consider that cyclohexane is dissolved in the hydrophilic core and nearly randomly distributed, despite its nonpolar nature. When straight-chain hydrocarbon oils are used as solvents, the scheme of micellar growth turns out to be fairly different from the cases in aromatic oils; it becomes highly sensitive to the chain length of the oil, leading to the formation of long, cylindrical to, finally, planarlike aggregates. As shown in Figure 2, upon changing oils from octane to hexadecane, we observed the successively increasing scattered intensity, together with an increasing slope in the low-q region, which clearly represents the signature of micellar growth with increasing chain length of oils. The resulting PDDFs in octane and decane systems exhibit typical signs of prolate particles having nearly homogeneous electron density distribution. With tetradecane, in addition to a rapid increase in Dmax, a bump appears in p(r) on the higher-r side of its maximum around r ∼ 8 nm. When the solvent is replaced with the longer-chain hexadecane, the low-q slope of I(q) becomes markedly steeper and reaches ∼q-2. The small bump seen in p(r) of the DGM/tetradecane system grows into a pronounced broad maximum for the DGM/hexadecane, accompanying a drastic increase in Dmax. All these features confirm a planarlike aggregate formation in the DGM/hexadecane system.

It is worthwhile to note that, for instance, tetradecane and 1-phenyl octane have almost equivalent molecular weights; however, SAXS experiments have shown that very long cylindrical particles are produced in the former, whereas in the latter, only slightly elongated particles are present, which highlights the markedly different effects of linear-chain hydrocarbon oils and aromatic oils. In the aromatic oil-based systems, the (subtle) micellar growth is almost solely governed by the polarity of the aromatic ring, which is proven by the fact that the chain length has no major effect on the micellar growth, despite a large difference in hydrocarbon chain length, as confirmed by the comparison between 1-phenyl octane and ethyl benzene. In contrast, as we have shown, there appears to be a drastic effect of the hydrocarbon chain length on the micellar growth when linearchain hydrocarbon oils are used as the solvent, which may be explained in terms of the free-energy landscape. The recent development in the free energy theory approach37,38 has given a convincing explanation to the exponential decrease in the critical micellar concentration with the hydrocarbon chain length and its nonmonotonous temperature dependence for normal micellar systems, such as poly(oxyethylene) alkylethers in aqueous media. These arise essentially from the linear and nonmonotonic trends of the oil-water transfer free energy, respectively, as a function of hydrophobic chain length and temperature. Although we cannot calculate the transfer free energy of our components directly from our SAXS

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Figure 3. The model-free cross-section (core) structure analysis. The cross section PDDFs, pc(r), for the DGM/oil systems with octane, dectane, and tetradecane (a) and the cross section radial electron density profile, ∆Fc(r), deconvoluted from pc(r) (b).

data and, therefore, at moment, we have to limit ourselves to a qualitative postulation, even for reverse-micellar systems, the similar thermodynamic route, that is, the transfer free energy of the hydrophilic part of the surfactant from the hydrophilic environment to oils with different hydrocarbon chain length may be of central importance for the determination of the selforganization behavior of the amphiphile. It is naturally expected that the oil-to-oil transfer free energy of the hydrophobic moiety of DGM will be negligible for hydrocarbon oils of different chain lengths. Considering the highly hydrophilic nature of the diglycerol group, its transfer free energy from the hydrophilic environment to oil will considerably differ depending on the chain length of the hydrocarbon oils, as oil-to-water transfer free energies of different chain length hydrocarbons sensitively do. The unfavorable free energy of the diglycerol moiety with the longer-chain hydrocarbon oil will decrease the cross-sectional area occupied by the surfactant molecule on the hydrophilic/hydrophobic interface to optimize the contact with the solvent oils. The decreasing cross-sectional area increases the critical packing parameter and promotes the formation of cylindrical or disklike lamellar micelles.39 Our postulation explains well the formation of the highly elongated or even planar micelles in the longer chain oils and the sensitivity of micellar geometry to the chain length of oils. The SAXS results are in good agreement with the trend readout from the phase diagrams. The long-chain oil has less degree of penetration to the surfactant chain and tends to separate from the surfactant. The mutual dissolution of surfactant and oil decreases with an increase in the hydrophobicity of the oil, and therefore, hexadecane is the least miscible with the surfactant of all the oils studied. For cylindrical scattering objects as observed in the DGM/ oil systems, for example, with octane, decane, and tetradecane, a model-free analysis of the micellar cross-sectional structure is available, under the assumption that the scattering length density profile of the cross section is simply a function of the radial position. The core diameter for all DGM/oil systems with linear-chain hydrocarbon oils is approximately in the range of 3.0-3.5 nm when using an inflection point of p(r) located on the higher-r side of the sharp maximum as its measure. To confirm this estimation, we used the model-free approach to the cross-section structure. The interplay between the cross

section (core) radial density profile, ∆Fc(r), and the cross section PDDF pc(r) are given by40

pc(r) ) r∆Fc2(r)

(4)

The cross section PDDF can directly be calculated from the experimental scattered intensity I(q) according to

I(q)q ) πLIc(q) ) 2π2L

∫0∞ pc(r)J0(qr) dr

(5)

where J0(qr) is the zero-order Bessel function. The IFT approach based on eq 5 yields pc(r), from which ∆Fc(r) can be deduced via the deconvolution procedure. If judged from Dc,max in pc(r) shown in Figure 3, the DGM/ oil systems with octane, decane, and tetradecane give the nearly identical (maximum) core diameters of ∼3.5 nm, which is quantitatively complementary to that estimated from the inflection point in p(r). 3.2.2. Effect of Surfactant Concentration on the Micellar Growth. The DGM surfactant favors micellar growth with an increase in the surfactant concentration. In Figure 4, we present the scattering functions, I(q), and the resulting PDDFs, p(r), of the DGM/octane system of different surfactant concentrations at 50 °C. As can be seen from Figure 4a, increasing surfactant concentration increases the total scattering intensity, which is more than expected simply from the increasing scattering volume according to WS. In WS < 0.05, the increasing low-q slope of I(q) versus q in Figure 4a is due to one-dimensional growth of the micelles, as can be clearly seen from the real space functions in Figure 4b, where we observed a gradual increase of Dmax in p(r) with WS. Theoretically, the formation of a long cylindrical (homogeneous) particle leads to q-1 behavior in the forward intensity.16 The internal density fluctuation, as expected for the actual systems, also affects the low-q slope. In WS < 0.05, the low-q slope of I(q) is a bit smaller than q-1, although the micellar structure is already elongated. At the highest concentration (WS ) 0.07), the slope of the scattering function I(q), in the low-q region, gets markedly steeper, which exceeds q-1. Simultaneously, p(r) exhibits an additional feature of a pronounced bump on the higher-r side of the peak (around r ∼ 10 nm). These observations indicate the onset of two-dimensional growth of aggregates from cylindrical to planar in shape.41,42 Thus, the presence of flat particles is highly expected at higher surfactant concentrations.

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Figure 4. The scattering curves I(q) of DGM/octane systems at different surfactant concentrations obtained on an absolute scale at 50 °C (a) and the corresponding pair-distance distribution functions p(r) (b). Solid and broken lines in panel a represent the GIFT fit and the calculated form factor for n particles existing in the unit volume, nP(q), respectively.

Figure 5. (a) The X-ray scattered intensities I(q) of 5 wt % DGM/octane system in absolute unit at different temperatures (a) and PDDFs p(r) extracted from these scattering curves with GIFT analysis (b). Solid and broken lines in panel a represent the GIFT fit and the calculated form factor for n particles existing in the unit volume, respectively. Arrows and a broken line in panel b highlight Dmax and the core diameter, respectively.

3.2.3. Effects of Temperature on the Micellar Structure. In Figure 5, we display the scattering functions, I(q), and the resulting PDDFs, p(r), for 5 wt % DGM/octane system at different temperatures. As shown in Figure 5a, the low-q slope of I(q), mainly affected by the micellar elongation, monotonically decreases with increasing temperature without changing the high-q intensities in q/nm-1 > 1.0 related to the local structure of aggregates, such as the cross section of particle. Dmax in the PDDF curves successively decreases from ∼17 to ∼10 nm with increasing temperature from 40 to 70 °C, whereas the position of the characteristic inflection located on the higher-r side of the sharp maximum that gives a measure of the cross-sectional diameter of the hydrophilic core is virtually unchanged (see Figure 5b). The semiqualitatively estimated hydrophilic core diameter ∼3.0-3.5 nm is well-fitted to twice the length of the diglycerol moiety. Unlike aqueous systems, in which the miscibility of the surfactant decreases with temperature so that phase separation takes place at higher temperature, the miscibility of oil and surfactant increases with the temperature. The increased mutual solubility of the surfactant and oils is possibly because an increased thermal agitation increases the space available for the solubilization in the micelle. The observed result with the decreasing trend of the micellar aggregates with the temperature

is quite reasonable and expected behavior of the spontaneous curvature, which is expected to decrease with increasing temperature. 3.2.4. Effects of Added Water on the Micellar Structure. The physical properties of the surfactant solution in nonpolar oils markedly differ from those of aqueous systems and change gradually with the rise of surfactant concentration. Therefore, the existence of a CMC is questionable in nonpolar organic solvents. However, previous investigations have shown that a small amount of water induces micellization in nonaqueous media. The addition of water tends to increase the spontaneous curvature as a result of head group repulsion and favors micellar growth in the nonpolar oil systems. This may also be related to the problem of the transfer free energy, given in the previous section. Moreover, added water that is solubilized in the interior of the micelle core in the nonpolar medium has been shown to cause an increase in the aggregation number.43 In the present SAXS investigation, we have studied the effects of added water on the micellar size and obtained clear evidence for micellar growth by the addition of traces of water. For example, upon addition of 0.6 wt % of water to a 5 wt % DGM/cyclohexane system, a slight increase in the cross section of the hydrophilic core is observed in terms of the slightly shifted inflection point seen on the higher-r side of the maximum in p(r). As can be seen from the I(q) curves, the low-q intensity is

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Figure 6. (a) The X-ray scattering intensities I(q) of 5 wt % DGM/cyclohexane and 5 wt % DGM/cyclohexane with added 0.6 and 1 wt % water obtained in absolute unit at 50 °C (a) and the corresponding pair-distance distribution functions p(r) (b). Solid and broken lines in panel a represent the GIFT fit and the calculated form factor for n particles existing in the unit volume, nP(q), respectively.

Figure 7. The model calculation and fit to the experimental X-ray scattered intensities of 5 wt % DGM/octane (a) and 5 wt % DGM/1-phenyl octane (b) as typical examples. The data were fitted using a model of a homogeneous prolate.

strongly enhanced and the scattering curve in the high-q region shifts toward forward direction upon the addition of water. This indicates that the added water causes simultaneous changes in the maximum dimension and the cross section structure of reverse micellar aggregates. Addition of 1 wt % of water causes a drastic elongation of reverse micelles, as proven by Figure 6b. The Dmax of the micelle nearly doubles that of the system without water. This is in good agreement with the finding of our previous work.44 One can expect phase separation at a higher water concentration when the excess water cannot be incorporated in the micellar core. In the present investigation, we determined the extent of water solubilization at the interior of the micellar core and found that around 4.9 wt % water can be solubilized in the micellar core of the DGM/cyclohexane system, and further addition of water causes phase separation. Note that the surfactant may be contaminated by a small amount of water. It is practically difficult to remove water completely and to measure SAXS data in an absolutely dry state, which makes it difficult to discuss the effect of added water on the micellar shape in the exact manner. For example, the present DGM contains 0.66% water,14 corresponding to ∼0.03 wt % water in the 5 wt % DGM/ cyclohexane solution before the addition of water. Hence, upon addition of water from 0 to 1 wt %, the actual amount in the ternary system is changed from roughly 0.03 to 1.03 wt %. 3.3. Model Calculation of the Scattering Function. We have shown in Figures 2-6 a virtually model-free approach to the

structure of the DGM/oil systems using IFT and its generalized version GIFT and, additionally, the model-free cross section IFT analysis. The greatest advantage of our approach is to be able to give real space and, thus, easy understanding and specific information on the investigated system without imposing any structure model. However, we know that a modeling method involving the fitting of the experimental I(q) with a theoretical function calculated from structure models is still mainline in the field. To check the consistency of the structural pictures derived from a model-free approach and a modeling method and to supply additional qualitative information, for example, the aggregation number, Nagg, we have performed a model calculation for selected systems to test a number of plausible structure models for the investigated reverse micelles. The results are shown in Figure 7. In Figure 7, the symbols represents the experimental SAXS data; the solid lines stand for the scattering function from the model calculation. The calculation was done on the basis of the method reported.45 To fix the scattering length density difference of the micelle, densities of the investigated mixtures, pure surfactant, and oils were measured at the equivalent temperatures of SAXS measurements. Densities of octane, tetradecane, ethyl benzene, and 1-phenyl octane are, respectively, 0.6791, 0.7420, 0.8408, and 0.8338 g/cm3 at 50 °C, giving the electron density difference of the hydrophilic part of the DGM surfactant, ∆Fe ) 167.0, 146.5, 126.6, and 123.1 el/nm3 at 50 °C, respectively, in these oils, in

Control of Reverse Micelles in DGM Surfactant which the partial electron density of the hydrocarbon group of the surfactant was extracted from the literature values.46 The contrast of the hydrophilic core, ∆F, was determined with ∆Fe and the scattering length of electron l ) 0.282 × 10-12 cm for the individual systems and was used as input for the fitting procedure. In addition to the core radius, R, and the total axial length, L, for a cylinder or the short and long axes of a spheroid, a and b, by taking advantage of the absolute scale measurements, the number of particles, n, per unit volume can be obtained. The number of surfactant molecules per unit volume, N, in advance calculated from the density data divided by the extracted n gives the aggregation number, Nagg, in our routine. Note that the estimation of Nagg can be biased not only by the accuracy of the absolute scale calibration (approximately several percent) and the structural parameters in the model used, but also by polydispersity and the neglected internal density fluctuation, which is detected by the cross section analysis shown in Figure 3, so that to say the least, the error bar of Nagg is expected to be greater than 10%. Therefore, we consider that the trend of Nagg upon changing solvents and temperature must be paid attention to over its absolute value. Within the framework of the model calculation outlined above, a Nagg of 360 is estimated for the DGM/octane system at 40 °C, which with the rise of temperature goes down to 197 at 70 °C, and that of 280 at 50 °C is increased up to 449 by replacing oil with tetradecane. In contrast, the DGM/aromatic oil systems show a fairly smaller Nagg value, 55 for ethyl benzene at 50 °C. We have successfully confirmed that all the results from the model calculation are basically consistent with those obtained with GIFT/IFT and the cross section IFT. 4. Conclusion We have investigated the self-organized structure of the diglycerol monomyristate nonionic surfactant in different nonpolar organic solvents, such as n-octane, n-decane, n-tetradecane, n-hexadecane, cyclohexane, ethyl benzene, and 1-phenyl octane. The DGM forms reverse micelles in these organic solvents above solid or LR phase melting temperature in the dilute regions. SAXS data supported by the complementary model calculation showed that the structure of the aggregates could be controlled by solvent properties, concentration of the amphiphiles, temperature, and added water. In aromatic oils, the hydrocarbon chain lengths of the oils do not affect the structure of the micelles and we observed small nearly spherical aggregates. However, in linear chain hydrocarbon oils, the size of the aggregates largely depends on the chain length. With an increase in the chain length from decane to hexadecane, long cylindrical particles finally transform into planar aggregates. The reverse micellar size monotonically increased with an increase in the surfactant concentration. Increasing temperature decreases the Dmax of the micellar structure, and more oils are solubilized at higher temperature, which is in good agreement with the previous results and the present phase behavior. Addition of traces water causes one-dimensional micellar growth and at higher water concentration saturation is reached so that phase separation takes place. The SAXS data and the complementary model calculations clearly show the effect of the chemical structure of the nonpolar solvents on the features of the reverse micelles formed by the DGM. Thus, the present study contributes to obtaining more structural information in the field of reverse micelles, which, indeed, is less known. Acknowledgment. We are thankful to Dr. Tetsuro Iwanaga from Taiyo Kagaku Co., Ltd. Japan for supplying the surfactant.

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