n-Octane-in-D2O

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Langmuir 2000, 16, 10106-10114

Effect of Pressure on Microstructure of C12E5/ n-Octane-in-D2O Microemulsions S. Ferdinand,† M. Lesemann,‡ and M. E. Paulaitis* Department of Chemical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218 Received June 23, 2000. In Final Form: October 23, 2000 Forced Rayleigh scattering was used to measure the self-diffusion coefficients of oil droplets dispersed in the water-continuous L1 phase of the C12E5/n-octane/D2O microemulsion. A single microemulsion composition of 3.7 wt % surfactant, 4.3 wt % alkane, and 92.0 wt % water was studied at atmospheric pressure as a function of temperature from 17.3 to 24.5 °C and at 26.2 °C as a function of pressure from 100 to 534 bar. Droplet self-diffusion coefficients were found to decrease by a factor of ∼2 with increasing temperature from the emulsification failure boundary to the phase boundary for this L1 phase and the lamellar phase. This decrease is attributed to a transition from spherical to larger nonspherical oil droplets in water, i.e., a decrease in the spontaneous curvature of the oil/water interface with increasing temperature. The effect of increasing pressure, like decreasing temperature, in this region of the phase diagram is to increase the oil droplet self-diffusion coefficients by a factor of ∼2-3 between 220 and 540 bar. This increase is likewise attributed to a transition from nonspherical to smaller spherical oil droplets in water or an increase in the spontaneous curvature of the oil/water interface with increasing pressure. We conclude that the spontaneous curvature of the oil/water interface is sensitive to pressure, with increasing curvature corresponding to increasing pressure. This conclusion is consistent with the pressure-induced 2 hf3f2 sequence of phase transitions observed for mixtures of CiEj surfactants, liquid alkanes, and water. Our results demonstrate the utility of forced Rayleigh scattering as a complementary experimental technique to small-angle neutron, X-ray, and light scattering in experimental studies of microemulsion microstructures at high pressures.

I. Introduction Microemulsions are isotropic, microstructured equilibrium phases containing two dissimilar fluids, usually water and a nonpolar liquid hydrocarbon, stabilized by surfactant. The oil and water reside in distinct domains separated by an interfacial layer rich in surfactant. Microemulsions dilute in either water or oil are usually droplet dispersions of the minor component in a continuum of the major component. Increases in volume fraction of the minor component at sufficient surfactant concentrations lead to the formation of bicontinuous microemulsions, i.e., sample spanning paths of both oil and water. Microemulsions also form with water, surfactant, and compressible near-critical or supercritical fluids, which opens the possibility of exploiting pressure to control microstructure and modulate the strength of interdroplet interactions in these systems.1 The number of experimental studies of pressure-induced structural changes in microemulsions is limited. Smallangle neutron scattering (SANS) is particularly well-suited for studying the microstructure of such systems because the range of length scales that can be probed with this technique includes both the characteristic droplet size and interdroplet spacing. It is not surprising, therefore, to find that most experimental studies of microstructure in microemulsions at high pressures involve SANS measurements,2-8 although a few high-pressure small-angle † Current address: RY818-C306, Merck & Company, P.O. Box 2000, Rahway, NJ 07065. ‡ Current address: FCC Research, W. R. Grace & Company, 7500 Grace Drive, Columbia, MD 21044.

(1) Gale, R. W.; Fulton, J. L.; Smith, R. D. J. Am. Chem. Soc. 1987, 109, 920. (2) Nagao, M.; Seto, H. Phys. Rev E 1999, 59, 3169. (3) Nagao, M.; Seto, H.; Okuhara, D.; Matsushita, Y. J. Phys. Chem. Solids 1999, 60, 1363.

X-ray and dynamic light scattering experiments have been reported as well.6,9-11 The system of choice in almost all of these studies is sodium bis(2-ethylhexyl) sulfosuccinate (AOT)/alkane/water (or brine) water-in-oil microemulsions at ambient temperatures. In one study, comparisons were made to nonionic surfactant/alkane/water microemulsions, but the measurements were not extensive and the observed effect of pressure on the nonionic microemulsion was inconclusive.7 These high-pressure studies show that increasing pressure leads to an increase in curvature of the oil/water interface toward the oil phase.12 Bicontinuous or lamellar phases are, therefore, favored at high pressures over single-phase dispersions of water droplets in an oilcontinuous phase.2,4 Similar effects are observed for micellar systems where the application of pressure stabilizes bicontinuous phases over inverse micelles.13-16 (4) Nagao, M.; Seto, H.; Okuhara, D.; Okabayashi, H.; Takeda, T.; Hikosaka, M. Physica B 1998, 241-243, 970. (5) Kotlarchyk, M.; Chen, S.-H.; Huang, J. S.; Kim, M. W. Phys. Rev. A 1984, 29, 2054. (6) Eastoe, J.; Young, W. K.; Robinson, B. H.; Steytler, D. C. J. Chem. Soc., Faraday Trans. 1990, 86, 2883. (7) Eastoe, J.; Steytler, D. C.; Robinson, B. H.; Heenan, R. K. J. Chem. Soc., Faraday Trans. 1994, 90, 3121. (8) Gorski, N.; Kalus, J.; Schwahn, D. Langmuir 1999, 15, 8080. (9) Kim, M. W.; Gallagher, W.; Bock, J. J. Phys. Chem. 1988, 92, 1226. (10) Kim, M. W.; Bock, J.; Huang, J. S. Phys. Rev. Lett. 1985, 54, 46. (11) Nagao, M.; Okuhara, D.; Seto, H.; Komura, S.; Takeda, T. Jpn. J. Appl. Phys. 1 1999, 38, 951. (12) We adopt the usual convention of designating curvature toward the oil phase as positive and toward the water phase as negative. (13) Duesing, P. M.; Seddon, J. M.; Templer, R. H.; Mannock, D. A. Langmuir 1997, 13, 2655. (14) Wong, P. T. T.; Mantsch, H. H. J. Chem. Phys. 1983, 78, 7362. (15) Casal, H. L.; Wong, P. T. T. J. Phys. Chem. 1990, 94, 777. (16) Gorski, N.; Kalus, J.; Kuklin, A. I.; Smirnov, L. S. J. Appl. Crystallogr. 1997, 30, 739.

10.1021/la0008840 CCC: $19.00 © 2000 American Chemical Society Published on Web 11/29/2000

C12E5/n-Octane-in-D2O Microemulsions

For oil/water microemulsions stabilized by nonionic alkyl poly(ethylene glycol) ether (CiEj) surfactants, Kahlh f 3 f 2 sequence of phase weit et al.17 predicted the 2 transitions18 with increasing pressure. This sequence of phase transitions corresponds to an increase in the spontaneous curvature of the surfactant film with the application of pressure. In their analysis, the pressure dependence of the phase behavior for the ternary mixture results from the oil/surfactant binary mixture upper critical solution temperature (UCST) rising faster with increasing pressure than the water/surfactant binary mixture lower critical solution temperature (LCST). A higher UCST implies lower mutual solubilities of the oil and the surfactant tailgroups and, as such, lower oil penetration into the tailgroups with increasing pressure. Thus, the phase behavior suggests an energetic driving force for increasing the spontaneous curvature of the surfactant film with increasing pressure that is related to interactions between the oil and the surfactant tailgroups. Pressure-induced 2 h f 3 f 2 phase transitions have been confirmed for several CiEj surfactant/liquid alkane/water (brine) mixtures.9,19-23 It is interesting to note that the reverse sequence of phase transitions (2h f 3 f 2) is obtained with increasing pressure for microemulsions containing low molecular weight alkanes, such as propane, consistent with the known relative pressure dependence of the water/surfactant LCST and the alkane/ surfactant UCST for these mixtures.21,22,24 In this work, we determined the effect of pressure on a nonionic surfactant/oil-in-water microemulsion consisting of 3.7 wt % pentaethylene glycol monododecyl ether (C12E5), 4.3 wt % n-octane, and 92.0 wt % D2O at 26.2 °C and pressures up to ∼500 bar. For comparison, we also determined the effect of temperature on microstructure for the same system and in the same region of the phase diagram. The temperature-composition phase diagram at atmospheric pressure for the C12E5/deuterated n-octane/ D2O microemulsion is shown in Figure 1.25 The 2 f L1 phase boundary (the so-called emulsification failure boundary) at lower temperatures marks the limit of complete oil solubilization in the water-continuous L1 phase, since a slight decrease in temperature causes the formation of an excess oil phase. The temperature corresponding to the emulsification failure (EF) boundary for the composition of interest is 21.5 °C.26 It is argued, on the basis of experimental evidence25,27-34 and theory,35-40 that these droplets are spherical at the EF boundary but (17) Kahlweit, M.; Strey, R.; Firman, P.; Haase, D.; Jen, J.; Schoma¨cker, R. Langmuir 1988, 4, 499. (18) This notation describes the change in surfactant solubility from more oil-soluble (2 h , water-in-oil microemulsion, Winsor type II) to more water-soluble (2h , oil-in-water microemulsion, Winsor type I) with an intermediate three-phase, liquid-liquid-liquid equilibrium. (19) Sassen, C. I.; Gonzalez, C.; de Loos, Th. W.; de Swaan Arons, J. Fluid Phase Equilib. 1992, 72, 173. (20) Sassen, C. I.; de Loos, Th. W.; de Swaan Arons, J. J. Phys. Chem. 1991, 95, 10760. (21) Rudolph, E. S. J.; Bavendeert, M. J.; de Loos, Th. W.; de Swaan Arons, J. J. Phys. Chem. B 1998, 102, 200. (22) Eastoe, J.; Robinson, B. H.: Steytler, D. C. J. Chem. Soc., Faraday Trans. 1990, 86, 511. (23) Sassen, C. I.; Filemon, L. M.; de Loos, Th. W.; de Swaan Arons, J. J. Phys. Chem. 1989, 93, 6511. (24) McFann, G. J.; Johnston, K. P. Langmuir 1993, 9, 2942. (25) Strey, R.; Glatter, O.; Schubert, K.-V.; Kaler, E. W. J. Chem. Phys. 1996, 105, 1175. (26) Since the mole fraction of n-octane in this microemulsion is small, the substitution of n-octane for deuterated n-octane is not expected to have a large effect on the phase behavior. (27) Olsson, U.; Schurtenberger, P. Langmuir 1993, 9, 3389. (28) Leaver, M. S.; Olsson, U. Langmuir 1994, 10, 3449. (29) Leaver, M. S.; Olsson, U.; Wennerstro¨m, H.; Strey, R. J. Phys. II 1994, 9, 515. (30) Leaver, M. S.; Furo´, I.; Olsson, U. Langmuir 1995, 11, 1524.

Langmuir, Vol. 16, No. 26, 2000 10107

Figure 1. Temperature-water volume fraction phase diagram of the C12E5/C8D18/D2O system at ambient pressure and an oil/ surfactant volume fraction of 1.37, taken from ref 25. The arrow indicates the composition studied in this work. L1 ) single phase, oil-in-water microemulsion; LR ) lamellar phase; L3 ) bicontinuous phase; L1′ ) water-rich phase.

then grow and elongate with increasing temperature to form a lamellar phase at higher temperatures, the L1 f LR phase transition in Figure 1. For the composition of interest here, the temperature corresponding to the L1 f LR phase transition is 25.0 °C. The structural transition from spherical oil droplets in water at the EF boundary to a lamellar phase at higher temperatures is thought to be a general property of CiEj/oil-in-water microemulsions.30,31,33,41 The transition from spherical to cylindrical droplets of n-octane in the water-continuous L1 phase with increasing temperature has been confirmed for C12E5/ deuterated n-octane/D2O microemulsions at atmospheric pressure using SANS.25 Since entropy favors the formation of smaller oil droplets at the expense of larger aggregates, it follows that droplet growth and elongation in nonionic CiEj surfactant/oil-inwater microemulsions must be an energy-driven process. Indeed, the decrease in spontaneous curvature of the surfactant film with increasing temperature leading to these structural transitions is predicted from bending energies calculated for the different microstructure shapes.36,37 Two molecular mechanisms explain qualitatively the observed decrease in the spontaneous curvature (31) Gradzielski, M.; Langevin, D.; Farago, B. Phys. Rev. E 1996, 53, 3900. (32) Kahlweit, M.; Strey, R.; Sottmann, T.; Busse, G.; Faulhaber, B.; Jen, J. Langmuir 1997, 13, 2670. (33) Bagger-Jo¨rgensen, H.; Olsson, U.; Mortensen, K. Langmuir 1997, 13, 1413. (34) Menge, U.; Lang, P.; Findenegg, G. H. Colloids Surf. 2000, 163, 81. (35) Safran, S. A. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum Press: New York, 1984; Vol. 3, p 1781. (36) Turkevich, L. A.; Safran, S. A.; Pincus, P. A. In Surfactants in Solution; Mittal, K. L., Bothorel, P., Eds.; Plenum Press: New York, 1986; Vol. 6, p 1177. (37) Olsson, U.; Wennerstro¨m, H. Adv. Colloid Interface Sci. 1994, 49, 113. (38) Menes, R.; Safran, S. A. Phys. Rev. Lett. 1995, 74, 3399. (39) Kahlweit, M.; Busse, G.; Faulhaber, B.; Jen, J. J. Phys Chem. 1996, 100, 14991. (40) Tlusty, T.; Safran, S. A.; Menes, R.; Strey, R. Phys. Rev. Lett. 1997, 78, 2616. (41) Strey, R. Colloid Polym. Sci. 1994, 272, 1005.

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of the surfactant film underlying these transitions.41,42 The first is the dehydration of surfactant headgroups with increasing temperature. The second is enhanced solubility of the surfactant tailgroups in the oil phase when raising the temperature, which increases oil penetration into the tailgroups. It is thought that the first mechanism dominates for nonionic CiEj surfactants because ethylene oxide-water interactions are strongly temperature-dependent.37 In contrast, the application of pressure would favor the formation of small, spherical oil droplets, since the oil is more compressible than water, and spherical droplets have the smallest volume-to-surface area ratio. In addition, the effect of pressure on the oil/surfactant UCST suggests an energetic driving force for increasing the spontaneous curvature of the surfactant film with increasing pressure, as discussed above. Thus, while increasing temperature and decreasing pressure influence the spontaneous curvature of the surfactant film in the same way, their effects may involve intrinsically different molecular mechanisms: temperature through surfactant headgroup-water interactions and pressure through surfactant tailgroup-oil interactions. Viewed in this light, we might anticipate noncongruent effects of temperature and pressure on microstructure in nonionic surfactant microemulsions. II. Experimental Section The technique used to probe microstructure is forced Rayleigh scattering (FRS). FRS experiments were carried out on the oilin-water microemulsion over a range of temperatures between 17.3 and 24.5 °C at atmospheric pressure and at a constant temperature of 26.2 °C and pressures from 100 to 534 bar. These experimental conditions span the L1 region of the phase diagram up to the L1 f LR phase transition. The FRS experiment measures the tracer or self-diffusion coefficient of a dye molecule in both its stable and photoactive states in the microemulsion. The dye we selected is hydrophobic and therefore soluble in the oil but not in the water-continuous phase of the microemulsion. Consequently, the self-diffusion coefficients we measure correspond to diffusion of the dispersed oil droplets themselves in the watercontinuous phase. These diffusion coefficients provide insights into the size and shape of the oil droplets. An overview of the FRS technique and our high-pressure FRS apparatus is presented below. Detailed descriptions have been given elsewhere.43,44 In FRS, the diffusivity of a photoactive dye molecule is measured by monitoring the relaxation of a “forced” gradient in the dye concentration. At sufficiently low dye concentrations, the measurement yields a tracer or self-diffusion coefficient. The FRS experiment involves a writing process to create the dye concentration gradient and a reading process to monitor the time evolution of that concentration gradient. During the writing process a sinusoidal light intensity interference pattern is temporarily established in the sample by crossing two mutually coherent laser beams. The spatial period of that interference pattern, d ) λ/2 sin(θ/2), is determined by the crossing angle between the beams, θ, and the wavelength of the laser light, λ. Dye molecules in the path of the crossing laser beams undergo a photoisomerization to produce the photoactive form of the dye from the thermodynamically stable isomer. Since the extent of the photoisomerization depends on the intensity of the excitation light, two sinusoidal concentration profiles (gratings) are created, one for each form of the dye. These gratings are 180° out of phase, mimic the periodicity of the light intensity interference pattern, and relax at independent rates as the isomers diffuse due to thermal motion. For Fickian diffusion, the spatial distribution of each concentration grating remains sinusoidal, while its (42) Langevin, D. Annu. Rev. Phys. Chem. 1992, 43, 341. (43) Chapman, B. R. Probe Diffusion in CO2-Plasticized Glassy Polystyrene across the Glass Transition by Forced Rayleigh Scattering. Ph.D. Thesis, University of Delaware, 1997. (44) Chapman, B. R.; Gochanour, C. R.; Paulaitis, M. E. Macromolecules 1996, 29, 5635.

Ferdinand et al. amplitude decays exponentially in time. If the lifetime of the photoactive isomer is comparable to the time scale for diffusion, thermal reconversion to the stable isomer also contributes to the relaxation process. The dye concentration profiles produce corresponding periodic profiles in the optical properties of the sample or an optical diffraction grating. The amplitude of that grating can be monitored using a nonexciting laser beam, the reading beam, directed at the Bragg angle. In the general case, when both dye concentration profiles contribute to the optical grating, the time dependence of the diffracted signal intensity is given by the following “dual grating” or “complementary grating” expression45-50

Id ) {A1 exp(-t/τ1) - A2 exp(-t/τ2) + Ccoh}2 + Cinc2 (1) where

1/τ1 ) q2D1

and

1/τ2 ) q2D2 + κ

(2)

and τi is the characteristic relaxation time for the concentration grating of isomer i, Ai is a preexponential factor for each isomer which depends on a number of experimental parameters, Di is the tracer or self-diffusion coefficient of isomer i, q ) 2π/d is the magnitude of the grating wave vector, κ is the rate constant for thermal reconversion, and Ccoh and Cinc are small coherent and incoherent scattering contributions, respectively. Each diffusion coefficient is obtained from eq 2 as the slope of a linear plot of 1/τi vs q2. If the two isomers have identical diffusivities, singleexponential decay is observed. However, while these diffusivities are often similar, they are rarely identical due to differences in the molecular size and shape of the two isomers, as well as differences in their interactions with the local environment. The result is a nonexponential time dependence for relaxation and, under certain conditions, nonmonotonic decay of the diffracted signal intensity.45 The writing laser is a polarized CW argon ion laser (Lexel) tuned to 488.0 nm. Using a plate beam splitter, the initial beam is split into two beams of nearly equal intensity that are redirected by mirrors to cross within the sample volume. The crossing angle can be adjusted to allow grating spacings of approximately 0.4512 µm, with an estimated uncertainty of less than 1% over this entire range. An electronic shutter controls the duration of the writing pulse. For these experiments, writing times of 10-100 ms and intensities of 6-200 mW were used. The reading beam from a polarized 10 mW, 632.8 nm He-Ne laser (Melles-Griot) is directed into the sample volume at an angle that satisfies the Bragg condition for the grating spacing. The diffracted signal intensity is monitored using a monolithic photodiode (Burr-Brown OPT211). An electronic shutter controls the exposure time for the reading beam, while neutral-density filters reduce the initial beam intensity to a value of 1 mW or less. An iris diaphragm and 632.8 ( 3 nm band-pass filter placed in front of the detector minimize the contributions from stray light and the writing beam. A data acquisition board (National Instruments) in a Macintosh computer controls the timing of the experiment, digitizes the photodiode voltage output, and stores the diffracted intensity vs time signal. The uncertainty in the data acquisition timing is (1 ms, the resolution of the on-board timer; the uncertainty in the digitized signal is less than 0.1% of the measured value, the precision of 12 bit A/D conversion with a variable gain. For these experiments, the reading beam remains on continuously while collecting data. (45) Huang, W. J.; Frick, T. S.; Landry, M. R.; Lee, J. A.; Lodge, T. P.; Tirrell, M. AIChE J. 1987, 33, 573. (46) Miles, D. G.; Lamb, P. D.; Rhee, K. W.; Johnson, C. S., Jr. J. Phys. Chem. 1983, 87, 4815. (47) Terazima, M.; Okamoto, K.; Hirota, N. J. Phys. Chem. 1993, 97, 5188. (48) Rhee, K. W.; Gabriel, D. A.; Johnson, C. S., Jr. J. Phys. Chem. 1984, 88, 4010. (49) Wang, C. H.; Xia, J. L. J. Chem. Phys. 1990, 92, 2603. (50) Park, S.; Sung, J.; Kim, H.; Chang, T. J. Phys. Chem. 1991, 95, 7121.

C12E5/n-Octane-in-D2O Microemulsions The custom-built, high-pressure optical cell is constructed of a stainless steel body, sapphire windows, and Teflon seals and has a nominal pressure rating of 550 bar. The distance between the windows sets the sample path length of 2 mm. The cell is housed in a stainless steel jacket which is temperature controlled with a circulating fluid from a constant-temperature bath. The temperature at the outer edge of the cell is monitored using a thermocouple accurate to (0.5 °C and found to be within (0.2 °C of that measured inside the cell. We estimate the uncertainty in reported temperatures to be less than 1 °C and the stability to be (0.1 °C over the course of an experiment. The pressure in the cell is measured to (0.1 bar using a pressure transducer (Viatran model 345, (1 psi sensitivity). The microemulsion sample is introduced into the cell through a single filling port using a syringe. The pressure generator is filled separately with the microemulsion solution before the entire system is pressurized. Preliminary experiments revealed a systematic decrease in the measured diffusion coefficient when the sample remained in the cell over a period of 2 days. This decrease is attributed to degradation of the surfactant in contact with the stainless steel cell, a phenomenon observed previously by others.51 To minimize this undesirable effect, all experiments were carried out within 9 h after loading the microemulsion into the cell. For the FRS experiments carried out at atmospheric pressure, the sample is placed in a glass spectrophotometer cell (Spectrocell) with a 1 mm path length. The cell is housed in a similar custombuilt temperature jacket, which is temperature controlled using the same circulation system and constant-temperature bath. The photochromic dye, methyl yellow, undergoes a lightinduced, thermally reversible trans f cis isomerization that is characteristic of azo-dyes,52

Although neither isomer absorbs strongly at the reading wavelength, both isomers make contributions to the net refractive index of the sample.53 Methyl yellow is hydrophobic and therefore soluble in the oil droplets but not in the water-continuous phase of the microemulsion. Moreover, the two dye isomers have very different dipole moments: the trans isomer has almost no permanent dipole, and the cis isomer has a dipole moment of 3.2 D.54 FRS signals from azo-dyes exhibit nonexponential, nonmonotonic decays in a variety of systems.45,55,56 For methyl yellow, we observe relaxation kinetics that is always “growth decay”, indicating a measurable difference in isomer mobilities.57 The thermal reconversion rate for methyl yellow is on the order of 10 s in organic media.58 Decay times for our experiments vary from 0.5 to 6 s, depending on the value of q2. Plots of 1/τ vs q2 have near-zero intercepts, indicating that thermal reconversion has a negligible effect on the relaxation kinetics relative to that of diffusion. Pentaethylene glycol monododecyl ether (C12E5, >98% purity) was purchased from Nikko Chemicals. The nonionic surfactant was apportioned into 2.5 mL aliquots in a glovebox and then stored at -15 °C until used. D2O (99.9% purity) was purchased from Aldrich Chemicals. p-(Dimethlyamino)azobenzene (methyl yellow) and n-octane (99+% purity) were purchased from Sigma Chemicals. All reagents were used without additional purifica(51) Schubert, K.-V., personal communication. (52) Ross, D. L.; Blanc, J. In Techniques of Chemistry: Photochromism; Brown, G. H., Ed.; Wiley-Interscience: New York, 1971; Vol. III, Chapter 5. (53) Fouassier, J.; Rabek, J. Lasers in Polymer Science and Technology Applications III; CRC Press: Boca Raton, FL, 1990. (54) McClellan, A. Tables of Experimental Dipole Moments; W. H. Freeman & Company: New York, 1963; Vol. 1. (55) Landry, M. R.; Gu, Q.; Yu, H. Macromolecules 1988, 21, 1158. (56) Lee, J.; Park, K.; Chang, T.; Jung, J. C. Macromolecules 1992, 25, 6977. (57) Lodge, T. P.; Chapman, B. R. Trends Polym. Sci. 1997 5, 122. (58) Wang, L. Transport Properties of Polyelectrolytes in Various Media. Ph.D. Thesis, University of WisconsinsMadison, 1988.

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Figure 2. Typical FRS data for the microemulsion sample (92.0 wt % D2O, 4.3 wt % dye/octane, 3.7 wt % C12E5) at 26.2 °C, a pressure of 121 bar, and q2 ) 0.511 µm-2. Points represent the recorded voltage as a function of time. The line is the leastsquares regression fit to the data using eq 1: A1 ) 4.75, A2 ) 6.51, τ1 ) 0.115 s, τ2 ) 0.306 s, and Cinc ) 0.021. tion. The dye was added to the microemulsion as a saturated solution of methyl yellow in n-octane. Although the precise concentration of the dye in this saturated solution is unknown, it was estimated to be less than 1 mol of dye per 100 mol of octane. Assuming spherical oil droplets with a diameter of ∼190 Å,25 this concentration corresponds to fewer than three dye molecules per oil droplet in the microemulsion. Solutions containing ∼10 g of 92.0 wt % D2O, 4.3 wt % octane/dye solution, and 3.7 wt % C12E5 were prepared by weight and allowed to equilibrate overnight at room temperature.

III. Results A typical plot of “growth-decay” relaxation kinetics observed for the diffracted light intensity in a single FRS experiment is shown in Figure 2. The points are the experimental data, and the line is the least-squares fit of the data to eq 1. In the regression analysis, Ccoh is set to zero, and A1, A2, τ1, τ2, and Cinc are determined using a Levenberg-Marquardt nonlinear curve-fitting algorithm.59 Allowing Ccoh to be an additional adjustable parameter improves slightly the overall fit of the data but does not significantly affect the values obtained for τ1 and τ2. The fit in Figure 2 follows closely the experimental data for times up to nearly 1 s but deviates at longer times when the voltage is less than 0.2 V or ∼2.5% of the maximum voltage measured. At long times, this intensity should correspond to background scattering (Cinc). Some fluctuation in background scattering intensity is expected, though, due to noise in the photodiode circuit and temporal variations in the intensity of the reading beam, which would explain the systematic positive deviations from the curve fit at longer times. The experiments at atmospheric pressure were run at four different d spacings, ranging from 7.81 to 17.56 µm, (59) Press, W. H.; Flannery, B. P.; Vetterling, W. T.; Teukolsky, S. A. Numerical Recipes in C, The Art of Scientific Computing; Cambridge University Press: New York, 1992.

10110


Figure 3. Plots of 1/τ1 vs q2 from fits of FRS decays recorded for the microemulsion sample at ambient pressure and several temperatures. Each point is the mean value of 1/τ1 from 10 independent experiments. Error bars represent the standard deviation of the data for the 10 runs. The absence of an error bar indicates a value smaller than the point. Lines are fits of the data through the origin yielding the diffusion coefficient D1 as the slope.

Figure 4. Plots of 1/τ2 vs q2 from fits of FRS decays recorded for the microemulsion sample at ambient pressure and several temperatures. Each point is the mean value of 1/τ2 from 10 independent experiments. Error bars represent the standard deviation of the data for all 10 runs. The absence of an error bar indicates a value smaller than the point. Lines are fits of the data through the origin yielding the diffusion coefficient D2 as the slope.

and at 13 different temperatures between 17.3 and 24.5 °C. For each temperature and d spacing, the experiment was repeated 10 times at a fixed position in the sample. The values of τ1 and τ2 calculated from independent fits of each of these experiments were used to construct plots of 1/τ vs q2. In this analysis, τ1 is always assigned to the faster relaxation time. Representative plots at selected temperatures are shown in Figures 3 and 4. In both cases, a linear relationship is obtained, indicating that grating relaxation is governed by Fickian diffusion according to eq 2. Fits of the 1/τ2 data to a line with nonzero intercept

Ferdinand et al.

Figure 5. Temperature dependence of calculated diffusion coefficients D1 (open circles) and D2 (filled circles). Data are for the microemulsion sample (92.0 wt % D2O, 4.3 wt % dye/octane, 3.7 wt % C12E5) at ambient pressure. Error bars represent the error in value of the slope of the straight line fitted to the 1/τ vs q2 data, calculated by Kaleidagraph 3.08. Inset: temperature dependence of the ratio of D1 to D2 as calculated from FRS experiments on the microemulsion sample at ambient pressure.

(i.e., κ * 0) resulted in intercepts that were zero within experimental uncertainty. We concluded, therefore, that thermal reconversion has no significant impact on the relaxation kinetics in our experiments and neglected this contribution in our analysis. The linear fits in Figures 3 and 4 include the origin. The temperature dependence of D1 and D2 at atmospheric pressure is shown in Figure 5. The ratio D1/D2 is also plotted as a function of temperature in the figure inset. The two diffusion coefficients are essentially independent of temperature between 17.3 and ∼20 °C and then gradually decrease with increasing temperature up to ∼24 °C. The ratio D1/D2 remains constant and equal to unity over this entire temperature range. The value of D1 ≈ D2 ) 1.5 × 10-7 cm2/s corresponding to the plateau at low temperatures is within the range expected for the diffusion coefficients of oil droplets in water.60,61 The diffusion coefficient for similar azo-dyes in organic solvents at room temperature is on the order of 10-5 cm2/s, or roughly 2 orders of magnitude greater than this plateau value.62 Thus, diffusion of free dye molecules within the oil droplets occurs on time scales much faster than those probed in our FRS experiments. Moreover, diffusion of the dye molecules between the dispersed oil droplets is unlikely due to the high-energy penalty associated with the transfer of methyl yellow from the oil into the watercontinuous phase. Above ∼24 °C, D1 increases dramatically with respect to D2 as the temperature is raised, such that at 24.5 °C, D1 is more than 5 times D2. This increase in D1 relative to D2 coincides with the observation of a slightly cloudy but homogeneous microemulsion, which becomes even more cloudy at higher temperatures. Since the FRS technique requires optically transparent, homogeneous (60) Chatenay, D.; Guering, P.; Urbach, W.; Cazabat, A. M.; Langevin, D.; Meunier, J.; Le´ger, L. Lindman, B. In Surfactants in Solution; Mittal, K. L., Bothorel, P., Eds.; Plenum Press: New York, 1986; Vol. 6, p 1177. (61) Cazabet, A. M.; Chatenay, D.; Langevin, D.; Meunier, J.; Le´ger, L. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum Press: New York, 1984; Vol. 3, p 1729. (62) Lee, J. A.; Lodge, T. P. J. Phys. Chem. 1987, 91, 5546.


Figure 6. Plots of 1/τ1 vs q2 from fits of FRS decays recorded for the microemulsion sample at 26.2 °C and various pressures. Each point is the mean value of 1/τ1 from 10 independent experiments. Error bars represent the standard deviation of the data in all 10 run. The absence of an error bar indicates a value smaller than the point. Lines are fits of the data through the origin yielding the diffusion coefficient D1 as the slope.

Figure 7. Plots of 1/τ2 vs q2 from fits of FRS decays recorded for the microemulsion sample at 26.2 °C and various pressures. Each point is the mean value of 1/τ2 from 10 independent experiments. Error bars represent the standard deviation of the data in all 10 runs. The absence of an error bar indicates a value smaller than the point. Lines are fits of the data through the origin yielding the diffusion coefficient D2 as the slope.

samples, the experiment could not be carried out at temperatures above 24.5 °C since the sample became too cloudy to make reliable measurements. We note that this temperature is near the L1 f LR phase transition in Figure 1. The high-pressure FRS experiments were run at the same four d spacings. In all cases, “growth-decay” kinetics were observed for the time dependence of the diffracted signal intensity, which were fit individually to eq 1. Representative plots of 1/τ vs q2 at four different pressures are shown in Figures 6 and 7. As before, linear relationships are obtained, consistent with a Fickian diffusive mechanism for grating relaxation. Linear fits of the 1/τ2 data to eq 2 using a nonzero intercept led to widely varying

Langmuir, Vol. 16, No. 26, 2000 10111

Figure 8. Pressure dependence of calculated diffusion coefficients D1 (open circles) and D2 (filled circles). Data are for the microemulsion sample (92.0 wt % D2O, 4.3 wt % dye/octane, 3.7 wt % C12E5) at 26.2 °C. Error bars represent the error in value of the slope of the straight line fitted to the 1/τ vs q2 data, calculated by Kaleidagraph 3.08. Inset: pressure dependence of the ratio of D1 to D2 as calculated from FRS experiments on the microemulsion sample (92.0 wt % D2O, 4.3 wt % dye/octane, 3.7 wt % C12E5) at ambient pressure at 26.2 °C.

values for κ that correlated with variations in the data at the lowest q value (q2 ) 0.128 µm-2). Neglecting these results gave linear fits through the remaining data with near zero intercepts. On the basis of our analysis of the data at 1 atm leading to the results in Figure 5, thermal reconversion is not expected to make significant contributions at 26.2 °C and the elevated pressures considered here. The data at q2 ) 0.128 µm -2 may have larger experimental uncertainties due to our initial inexperience with the high-pressure FRS technique. The experiments at this q value were the first carried out at high pressure. With these considerations in mind, the fits in Figures 6 and 7 include the data at all four q values as well as the origin. Plots of D1, D2, and the ratio D1/D2 as a function of pressure are shown in Figure 8. At atmospheric pressure and 26.2 °C, the microemulsion is cloudy and scatters all light from the writing and reading beams. From the phase diagram in Figure 1, we expect the system to be in the LR phase at these conditions. As pressure is raised, the microemulsion becomes more transparent and is completely clear at ∼120 bar. The two diffusion coefficients, which are widely different at low pressures, converge with increasing pressure at 138 bar and then decrease to a minimum at 224 bar, before increasing at higher pressures. Unlike the behavior at low temperatures, D1 and D2 do not reach a plateau at the highest pressures studied here. Excluding the results below 138 bar, the diffusion coefficients range from 5.7 × 10-8 to 1.4 × 10-7 cm2/s as a function of pressure, which is nearly identical to the range of diffusion coefficients shown in Figure 5. The one obvious difference between the temperature dependence in Figure 5 and the pressure dependence in Figure 8 is the minimum in D1 and D2 as a function of pressure in the D1 ≈ D2 region near the point at which the two diffusion coefficients diverge from one another. The divergence also involves abrupt changes in both D1 and D2 in opposite directions, while only D1 diverges with increasing temperature in Figure 5. It is not clear, however, whether this behavior

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is intrinsic to the microemulsion or an artifact of the FRS measurements. IV. Discussion From the phase diagram in Figure 1, the temperatures corresponding to the EF boundary and the L1 f LR phase transition at atmospheric pressure are 21.5 and 25.0 °C, respectively. We note, however, that the oil phase in our microemulsion is a solution of n-octane and the FRS dye, while Figure 1 is the phase diagram for a C12E5/deuterated n-octane/D2O microemulsion of the same composition. Thus, the phase transition temperatures for the microemulsion studied here are expected to be slightly different from those given in Figure 1. An estimate of this difference for the L1 f LR phase transition can be made by assuming this transition occurs at the temperature corresponding to the large increase in D1 relative to D2 in Figure 5. The justification for this assumption is given on physical grounds, recognizing that the cis and trans isomers of the hydrophobic FRS dye have much different dipole moments. The trans isomer is nonpolar and therefore more likely to partition into the oil phase of the microemulsion, while the polar cis isomer is more likely to partition into the interfacial region. In the L1 phase, discrete oil droplets exist, surrounded by a surfactant film, and FRS measures identical diffusion coefficients for the two isomers, corresponding to the Brownian motion of the oil droplets in water. In the lamellar phase, however, different diffusion coefficients are obtained due to differences in the diffusivities of the trans isomer, which is primarily in the oilcontinuous phase, and the cis isomer, which is primarily in the interfacial region. Indeed, NMR self-diffusion measurements29,30 give diffusion coefficients for decane that are a factor of ∼5 greater than those for C12E5 in the C12E5/decane/D2O microemulsion as diffusion of both decane and the surfactant is followed across the L1 f LR phase transition. From Figure 5, D1 ≈ D2 at 23.9 °C and D1 . D2 at 24.4 °C, which suggests the L1 f LR phase transition temperature is ∼24 °C. This temperature is only ∼1 °C less than that obtained from Figure 1 for the L1 f LR phase transition at the composition of interest. The temperature dependence of the droplet diffusion coefficients in Figure 5 does not yield the EF boundary for the microemulsion, most likely because the volume of the excess oil phase at temperatures just below the EF boundary is too small, and we do not probe diffusion in the excess oil phase. However, we can use the results in Figure 5 to calculate the hydrodynamic radius of the oil droplets in water at the EF boundary identified in Figure 1, where we assume spherical droplets. We then compare this radius to the droplet radius obtained independently from SANS measurements at the same conditions. Using the Stokes-Einstein expression for the diffusion coefficient of a spherical droplet at infinite dilution in water,63

D° )

kT 6πηRH

(3)

where kT is the thermal energy and η is the viscosity of D2O, the hydrodynamic radius, RH, is 110 Å at 22 °C. This result is in good agreement with SANS experiments on the C12E5/deuterated n-octane/D2O microemulsion that found the oil droplets to be spherical with a radius of 95 Å at 22 °C.25 The radius obtained from SANS is expected to be slightly smaller than the hydrodynamic radius. (63) We correct for the finite concentration at which the diffusion coefficients were measured following the procedure described in ref 28 for the C12E5/decane/water microemulsion.

The decrease in the droplet diffusion coefficient by a factor of ∼2 from 22 to 24 °C is attributed to a transition from spherical to larger nonspherical oil droplets in the water-continuous L1 phase approaching the L1 f LR phase transition. From the SANS experiments,25 the oil droplets are spherical at 22 °C and cylindrical at 23 °C for the C12E5/deuterated n-octane/D2O microemulsion at the composition of interest. Following Leaver et al.,30 we evaluate this shape change using the Stokes-Einstein equation for a prolate droplet,

D°prolate )

kT F(F) 6πηb

(4)

where D°prolate is the droplet diffusion coefficient at infinite dilution, b is the minor axis of the droplet, F is the ratio of the major axis to the minor axis of the droplet, and

F(F) )

ln(F + xF2 - 1)

(5)

xF2 - 1

for prolate droplets. Since the surfactant and oil volume fractions are fixed in these experiments, the surface areato-volume ratio is fixed as well, independent of the droplet shape. Therefore, eq 4 can be rewritten in terms of the hydrodynamic radius of the spherical oil droplets at 22 °C, near the EF boundary,

D°prolate )

kT 6πηRH

2 ln(F + xF2 - 1)

x(F2 - 1)/F2 + F arcos

1 F

()

(6)

with RH ) 110 Å at 22 °C. Using the average value of the two measured diffusion coefficients at 24 °C from Figure 5, and correcting as before for the finite concentration at which these diffusion coefficients were measured, the axial ratio calculated from eq 6 is 5.7 at 24 °C. This structural transition from spherical to elongated oil droplets over such a small temperature interval is expected and, indeed, is considered a distinguishing characteristic of CiEj surfactant/oil/water microemulsions.30,31,41,64,65 The effect of pressure on the measured diffusion coefficients at 26.2 °C, presented in Figure 8, has many of the same qualitative features seen in Figure 5, recognizing, of course, that increasing pressure correponds to decreasing temperature. The two diffusion coefficients diverge at low pressures, approaching the L1 f LR phase transition, but are essentially equal to one another at all pressures above this point of divergence. At the higher pressures studied, the diffusion coefficients increase significantly over a relatively modest pressure range of ∼300 bar, which we attribute to a decrease in droplet size and a change in shape from nonspherical to spherical oil droplets in the water-continuous L1 phase. This shape change has been observed as well in preliminary highpressure SANS experiments at 26.2 °C on this microemulsion.66 The shape change from nonspherical to spherical oil droplets corresponds to an increase in surfactant film curvature with increasing pressure that is also consistent with the pressure-induced 2h f 3 f 2 (64) Anderson, D.; Wennerstro¨m, H.; Olsson, U. J. Phys. Chem. 1989, 93, 4243. (65) Kahlweit, M.; Strey, R.; Firman, P. J. Phys. Chem. 1986, 90, 671. (66) Ferdinand, S. Pressure-Induced Changes in Microstructure of Oil-In-Water Microemulsions. M.S. Thesis, The Johns Hopkins University, 2000.


sequence of phase transitions observed for mixtures of CiEj surfactants, liquid alkanes, and water.9,19-23 Simple geometric arguments would dictate the formation of spherical oil droplets with increasing pressure, as discussed above, since n-octane is more compressible than water, and a spherical geometry gives the smallest droplet volume for a fixed surface area (fixed surfactant volume fraction). In addition, the pressure-induced 2h f 3 f 2 sequence of phase transitions implies a lower mutual solubility of n-octane and the surfactant tailgroups (higher alkane/surfactant UCST) and, therefore, lower n-octane penetration into the tailgroups at higher pressures. This energetic driving force for an increase in spontaneous curvature of the surfactant film favors the formation of small spherical oil droplets over larger nonspherical ones with increasing pressure. The entropy of mixing also favors a larger number of small droplets over a smaller number of large ones. All three factors contribute to the shape change from nonspherical to spherical oil droplets as pressure is raised. However, the compression of n-octane is not large enough at these pressures to account for a significant portion of the observed increase in the droplet diffusion coefficients with increasing pressure. For example, using density data for pure n-octane at high pressures67 and assuming spherical droplets, we calculate a change in the droplet radius of less than 1% over the pressure range from 220 to 550 bar at 26.2 °C. We can discount, therefore, the higher compressibility of n-octane relative to water as a major contribution to a pressure-induced shape change. In addition, the entropy of mixing is not expected to have a strong pressure dependence, if any, which leads us to conclude that the favorable energetic contribution due to an increase in spontaneous curvature of the surfactant film with increasing pressure must be significant. For the shape change from spherical to nonspherical oil droplets with increasing temperature, we note that the entropy of mixing and the bending energy associated with the spontaneous curvature of the surfactant film oppose one another with increasing temperature, and it is the strong temperature dependence of the ethylene oxide-water interactions reflected in decreasing spontaneous curvature at higher temperatures that dominates. The observed decrease in the droplet diffusion coefficients from 140 to 220 bar in Figure 8 is behavior that cannot be explained on the basis of our current understanding of the effect of pressure on microstructure for this microemulsion. Nonetheless, it is not possible to discount the observed behavior as an artifact of the FRS measurements for several reasons. First, the reliability of the data regression was checked rigorously in this pressure range. We found that the relaxation times and hence the diffusion coefficients obtained from them were independent of the imposed initial guesses for all fitting parameters, which were varied over a wide range of values. Indeed, we found that the data regressions of the highpressure FRS measurements were more robust than the regressions of the atmospheric pressure FRS measurements as a function of temperature. Second, it has been shown in previous work43-45 that even though individual relaxation times from different successful fits of the data can vary substantially, the average relaxation time, 0.5(τ1 + τ2), is insensitive to the regression,. Clearly, a plot of the droplet diffusion coefficient derived from just the average values of τ1 and τ2 as a function of pressure would show the same anomalous behavior. Third, visual inspec(67) Eduljee, H. E.; Newitt, D. M.; Weale, K. E. J. Am. Chem. Soc. 1951, 73, 3086.

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tion of the diffracted signal intensity profiles shows unambiguously the qualitative trends in the relaxation kinetics corresponding to the minimum in the diffusion coefficients as a function of pressure. Fourth, no discernible differences in the linearity of the 1/τ vs q2 plots were noticed to suggest additional relaxation mechanisms applied at different pressures. Finally, the microemulsion sample appeared to be transparent at all pressures above ∼120 bar, suggesting that the observed behavior is not connected with a phase transition. V. Conclusions We determined self-diffusion coefficients for oil droplets in the water-continuous L1 phase of the C12E5/n-octanein-D2O microemulsion as a function of temperature and pressure at a composition of 3.7 wt % surfactant, 4.3 wt % alkane, and 92.0 wt % water. For the temperature dependence, we found that the self-diffusion coefficients decrease by a factor of ∼2 with increasing temperature from the EF boundary to the L1 f LR phase transition. This decrease is attributed to a transition from spherical to larger nonspherical oil droplets in water with increasing temperature across the L1 phase. The droplet size and shape as a function of temperature were derived from the measured self-diffusion coefficients, assuming spherical oil droplets at the EF boundary. The calculated spherical droplet radius near this boundary is in good agreement with that obtained from independent SANS experiments. In addition, the nature of the structural changes with increasing temperature derived from our measured droplet diffusion coefficients (spheres f ellipsoids) is in agreement with the SANS results (spheres f cylinders). We conclude, therefore, that the FRS self-diffusion measurements provide a reliable characterization of the microstructure, as well as the temperature-dependent changes in microstructure observed for CiEj/liquid alkane-in-water microemulsions in the L1 region of the phase diagram. The FRS measurements for the oil droplet self-diffusion coefficients as a function of pressure represent new experimental findings. We observe that increasing pressure, like decreasing temperature, produces an increase in the self-diffusion coefficient by a factor of ∼2-3 between 220 and 540 bar at 26.2 °C. If we reasonably attribute this increase to a shape change from nonspherical to spherical oil droplets in water, we conclude that the spontaneous curvature of the surfactant film is sensitive to modest changes in pressure in this region of the phase diagram, with increasing film curvature corresponding to increasing pressure. This conclusion is consistent with the pressureinduced 2h f 3 f 2 sequence of phase transitions observed for mixtures of CiEj surfactants, liquid alkanes, and water. Supporting experimental evidence is found as well in our preliminary high-pressure SANS measurements on this microemulsion at 26.2 °C. We believe the underlying molecular mechanism for a pressure-induced increase in spontaneous curvature of the surfactant film is a favorable energetic contribution due to the effect of pressure on n-octane/C12E5 surfactant tailgroup interactions, although favorable entropic contributions are implicated as well from the entropy of mixing and the packing entropy associated with the higher compressibility of n-octane relative to water. We also note that an effect of pressure not seen in the temperature dependence of the selfdiffusion coefficients is the observed decrease in oil droplet diffusion coefficients with increasing pressure just above the LR f L1 phase transition. This behavior cannot be explained on the basis of our current understanding of the effect of pressure on microstructure for this micro-

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emulsion, nor can it be discounted as an artifact of the FRS measurements. Until additional independent measurements of microstructure in this pressure range are completed, this observation must remain unresolved.

National Aeronautics and Space Administration (NAG31954). Helpful discussions with Dr. Dobrin Bossev, Dr. Kai-Volker Schubert, Dr. Bryan Chapman, and Professor Ulf Olsson are also gratefully acknowledged.

Acknowledgment. This work was supported by the National Science Foundation (CTS-9815520) and the

LA0008840

n-Octane-in-D2O

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