J. Phys. Chem. 1995,99, 10354-10358
10354
Microstructure in DzOln-Hexaethylene Glycol Monododecyl Ether (C12E6)/C02 Mixtures Determined by Small-Angle Neutron Scattering R. G. Zielinski, E. W. Kaler,* and M. E. Paulaitis Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received: January 31, 1995; In Final Form: April 20, 1995@
Phase behavior and small-angle neutron scattering ( S A N S ) experiments were performed on mixtures of D20/ COzln-hexaethylene glycol monododecyl ether ( C I ~ Eas ~ )a function of temperature (25-3 1 "C), pressure (63.1-90.7 bar), and CO2 composition (0-3.9 wt 9%). The addition of carbon dioxide shifts the liquidliquid miscibility gap present in C12EdD20mixtures to lower temperatures. Parameters extracted from model fits of the S A N S spectra indicate that, while micellar structure remains essentially unchanged, critical concentration fluctuations increase as the phase boundary and plait point are approached. The variations of micelle structure, scattering contrast, and particle volume fraction with pressure, temperature, and carbon dioxide concentration are consistent with only a minimal amount of carbon dioxide entering the micelles under all conditions.
Introduction Ethoxylated alcohol surfactants (CiEj) in mixtures containing water and oil exhibit complex phase behavior that depends strongly on temperature, but, as is the case for most condensed liquids, only weakly on pressure.'-4 Replacing the incompressible oil with a compressible supercritical or near-critical fluid enables the use of pressure as an additional variable to effect changes in phase behavior. For example, a variety of complex phase behavior near the critical point of carbon dioxide (31.1 "C and 73.8 b d ) is observed in ternary mixtures of H2O and C02 with C ~ Eor I CsE3, and in particular, a liquid-liquid-gas three-phase region forms.6 The lower liquid phase is nearly pure water, and the upper liquid phase contains nearly equal mole fractions of H20, C02, and surfactant. The compositions of the water-rich liquid phase and the C02-rich gas phase change little with pressure and temperature, while the composition of the surfactant-rich phase traverses the phase diagram from the water-rich to the C02-rich comer with increasing pressure.6 In addition to this phase behavior, surfactants can aggregate to form a wide array of structures ranging from simple spherical or rodlike micelles to more complex bicontinuous structure^.^ The small-angle neutron scattering (SANS) method is wellsuited to examining both the structure and intermicellar interactions in surfactant-containing solutions because the length scales probed include both the characteristic size of the aggregate and the interaggregate distance. S A N S studies of dilute C12EdD20 solutions indicate that spherical micelles with diameters of approximately 50-60 8, form in these mixtures and that intermicellar interactions and critical fluctuations increase as the phase boundary is a p p r o a ~ h e d . ~The , ~ critical exponents are Ising-like, and it is important to account for polydispersity when fitting models to S A N S spectra.I0 Surfactant microstructures form in mixtures of water and supercritical fluids with low dielectric constants. This opens the possibility that pressure or fluid density could be used to alter surfactant microstructure.' Electrical conductivity measurements show that the structure of microemulsions containing near-critical propane, water, and the ionic surfactant DDAB can
* To whom correspondence should be addressed. @
Abstract published in Advance ACS Abstracts, June 1, 1995.
0022-3654/95/2099-10354$09.00/0
be changed continuously with pressure from one of unconnected water droplets in oil to a bicontinuous ~tructure.'~ In contrast, S A N S measurements of water-in-oil microemulsions of D20, near-critical propane, and the ionic surfactant AOT show that the reverse micelles present do not change appreciably in size or shape with changes in pressure.14 This lack of change in micelle size is attributed to the head group area not changing with pressure because of a strong electrostatic interaction between head groups.I5 The phase boundary, however, does move, and intermicellar interactions vary in response to the change in pres~ure.'~Finally, the existence of bicontinuous structures in the surfactant-rich phase of H20/C~E3/C02solutions is suggested by the high solubility of both nonpolar and polar dyes in this phase.6s'6 Small inverse micelles containing as few as 10 surfactant monomers have been inferred to exist in CO2-rich solutions of H ~ O / C X E ~ / C based O ~ on results from a solvatochromic shift technique using ionic dyes.17 Techniques to probe for surfactant microstructure that use dyes have the disadvantage of possibly causing microstructure to form in solutions where it would not otherwise. Most prior studies of surfactant microstructure in solutions containing supercritical or near-critical fluids have focused on the supercritical fluid-rich comer of the phase diagram' where the effects of pressure on microstructure and phase behavior are expected to be large. Here we use S A N S experiments to examine the effect of carbon dioxide, pressure, and temperature on the interactions, critical fluctuations, and structure of C12E6 mixtures in the water-rich comer of the phase diagram. The scattering spectra are successfully modeled using a polydisperse hard-sphere form factor to determine particle shape and size, together with an Ornstein-Zernike structure factor to quantify the critical phenomena. These approaches to modeling scattering spectra are well e s t a b l i ~ h e d . ~The ~~~'~ variation in micellar structure and interactions with temperature, pressure, and C02 composition are explained in the context of mixture phase behavior and the calculated micellar composition. 1312,14317
Experimental Section The view cell used for the phase behavior study and preparing the sample for transfer to the S A N S cell is based on a prior design.Ix The view cell is a 17.78 cm long, machined sapphire 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 25, 1995 10355
Microstructure in D20/C12EdC02 Mixtures tube (Insaco) with a 1.113 i 0.001 cm i.d. and 1.67 cm 0.d. Liquid-tight sealing was accomplished using Viton O-rings and backing rings mounted on stainless steel end caps. In this configuration, the tube was hydrostatically tested to 55 1 bar. Pressure in the cell was generated with a water-filled syringe pump (High Pressure Equipment Corp. (HIP)) which moved a piston that pressurized the mixture. The piston was doublesealed (Bal-Seal Engineering Co.) to prevent the pressurizing fluid from contaminating the sample. Pressure in the view cell was determined indirectly by measuring the pressure of the pressurizing fluid using a Bourdon tube gauge (Heise, f0.5bar). In a separate experiment at 159 bar, the pressure drop across the piston was determined to be at most i 3 bar by simultaneously measuring water pressure on both sides of the piston using separate gauges. The temperature of the view cell was controlled to f0.001 "C by immersion in a high-precision bath from Hart Scientific. The bath was custom-built to include a window for phase behavior observations. The cell contents were mixed by manually rocking the view cell. The high-pressure SANS cell is made entirely of machined sapphire (Insaco Inc.) to facilitate measuring at large (30") scattering angles. The scattering cell has a path length of 2 mm and a total volume of 1.6 mL and is thermostated by an aluminum heat transfer jacket. Temperature was measured with a platinum RTD (Newport Electronics, iO.1 "C) placed inside the scattering cell. Pressure was assumed to be equal to the view cell pressure. Liquid-tight sealing at the ends of the S A N S cell was accomplished with Viton O-rings and backing rings mounted on stainless steel end caps. Samples for the view and S A N S cells were prepared by first weighing Cl2E6 into the view cell and then evacuating the cell and surfactant. Due to the low vapor pressure of the surfactant, negligible surfactant was lost during evacuation. D20 was either weighed in before evacuation or, if previously degassed (to prevent surfactant degradation in experiments lasting for more than a day), metered into the cell with a calibrated syringe pump (HIP). Carbon dioxide was added from a preweighed highpressure bomb. Because of C02 sorption into the sealing material and errors in syringe pump calibration, sample composition is estimated to be known to &5%. The sample was transferred to the S A N S cell at near-constant pressure by first pressurizing the S A N S cell with nitrogen to approximately 63 bar. The syringe pump and piston moved the sample to the scattering cell while the displaced nitrogen was bled out of a self-venting regulator. The sample was allowed to equilibrate thermally for 10 min after the transfer was completed. Small-angle neutron scattering was performed using the 30 m spectrometer at the National Institute of Standards and Technology (NIST) in Gaithersburg, MD. Neutrons with a 5 8, wavelength (M/A = 0.15) gave q values from 0.007 to 0.22 where q, the magnitude of the scattering vector, is defined as q = (4n/A) sin(W2) and 6' is the scattering angle. Data were put on absolute scale using a silica standard and data handling software supplied by NIST and corrected for scattering from the empty cell and the D20 solvent. C12E6 (Nikko, >98% pure) and C02 (Matheson, Coleman, grade '99.99% pure) were used as received. Low-conductivity D20 was obtained from Cambridge Isotopes with a stated isotopic purity of 99.9% and was either used as received or degassed prior to use by repeated freeze, pump, and thaw cycles. SANS Modeling
To model the S A N S spectra, we assume there is no correlation between particle size and interactions. For this case, the effects
of particle shape (form factor) and interactions (structure factor) on the measured intensity can be determined independently. The model intensity as a function of q can be written as
= (Ae>24v(P(q))~(4)+ B
(1)
where is the product of contrast and volume fraction of particles, Vis the volume of a micelle, (P(q))is the form factor normalized by 1 / p , S(q) is the structure factor, and B represents the incoherent scattering background. Because of the shape of the scattering curves and the proximity of the sample composition, pressure, and temperature to the phase boundary, a modified Omstein-Zemike structure factor together with a form factor for polydisperse spheres was chosen to model the data. The form factor assumes a Schultz distribution for the particle radii and includes particle radius and the Schultz width parameter (a measure of the degree of polydispersity) as parameter^.'^ The use of a form factor that accounts for polydispersity together with a structure factor that assumes a monodisperse population of aggregates is a good approximation for polydisperse hard spheres when the ratio of polydispersity to radius is less than 0.3.20 The modified Omstein-Zemike structure factor is2'
S(0) is equal to ItpkbTKt, where up is the particle number density,
is the isothermal osmotic compressibility, and 6 is the correlation length. Due to an unknown technical difficulty in determining the absolute scaling factors, a scale factor of 2.35 was used to reconcile measured and modeled absolute intensities. This value was determined by calculating (A@)2@ for solutions with no added carbon dioxide and matching it to the fitted value. This scale factor agrees with that found by measuring an identical sample on another spectrometer. All of the spectra have the same error in absolute scaling, so the value for the scale factor was kept constant for all data analysis. Due to a lack of data at the highest values of q, the background incoherent scattering (B) was also kept constant through all the fitting at a value of 0.06 cm-I. A bootstrapping technique was used to give some quantitative estimate of the size of the error bars on the model parameter^.^^-^^ Bootstrapped data sets were generated by resampling from the normal error distribution with a standard deviation equal to twice the calculated error in intensity and then adding this resampled error to the intensity. One hundred bootstrapped data sets were regressed, and the standard deviation for each parameter is shown in Table 1. K~
Results and Discussion Phase boundaries between one- and two-phase regions for mixtures of D ~ O / C O ~ / Cwere I~E~ determined at constant pressure and composition by measuring the temperature at which the mixture became turbid. Figure 1 shows the temperatureCO2 concentration phase diagrams at 63.1 and 90.7 bar for a constant D20 to C12E6 weight ratio of 12.8 to 1. Carbon dioxide at small concentrations depresses the coexistence curve in Cl2Ed D20 mixtures by more than 20 "C at 4.3 wt % C02. The phase boundary changes little from 63.1 to 90.7 bar, increasing a maximum of 0.52 "cat 4.3 wt % c02. This observation agrees qualitatively with the small pressure effect (an increase of 20 "C from 1 to 3500 bar) observed for the C12Em20 solution phase boundary.25 S A N S measwements were made on mixtures of C I ~ EC02, ~, and D20 in the one-phase region in the water-rich comer of the phase diagram (7.5 wt % C12E6 on a CO2-free basis)
10356 J. Phys. Chem., Vol. 99, No. 25, 1995
Zielinski et al.
TABLE 1: Parameters from SANS AnalysiP
0 0
25 31
63.1 63.1
24.6 f 0.1 24.2 f 0.1
82.2 f 1 71.3 f 4
0.35 f 0.01 0.49 f 0.01
23.7 f 0.1 23.6 f 0.1 23.8 f 0.1 23.6 f 0.1 23.7 f 0.1
4.8 f 0.0 5.2 f 0.0 5.4 f 0.1 5.4 f 0.0 5.5 f 0.0 5.6 f 0.1 5.6 f 0.0
1.7 1.7 1.7 1.7 1.7
25 25 31 31 31
76.9 90.7 63.1 76.9 90.7
111 f 4 115f7 77.2 f 3.9 78.4 f 4.0 82.2 f 4.2
23.4 f 0.1 23.3 f 0.2 22.7 f 0.2 22.9 f 0.1 23.0 f 0.1 23.1 f 0.1
5.8 f 0.1 5.9 f 0.0 6.2 -f. 0.1 6.1 f 0.1 5.8 f 0.0 5.9 f 0.1
61.6 f 1.1 63.2 f 1.1 75.2 f 1.3 90.2 f 1.3 98.1 f 1.2 110% 1
0.47 f 0.02 0.44 f 0.03 0.48 f 0.02 0.48 f 0.02 0.51 f 0.02 1.42 f 0.02 1.42 f 0.04 2.14 f 0.03 3.43 f 0.04 5.15 f 0.06 5.80 f 0.07
3.9 3.9 3.9 3.9 3.9 3.9
25 25 28 31 31 31
76.9 90.7 63.1 63.1 76.9 90.7
1.20 f 0.01 1.21 f 0.00 1.14 f 0.00 1.14 f 0.00 1.13 f 0.01 1.13 f 0.01 1.14 f 0.00
5.63 5.16
0.80 f 0.00 0.81 f 0.01 0.77 f 0.00 0.75 f 0.00 0.73 f 0.00 0.75 zk 0.00
3.22 3.07 2.43 1.99 2.09 2.37
4.38 4.28 4.16 4.24 4.15
r is the micelle radius. Polydispersity is the root-mean-squared deviation from the mean radius (% polydispersity = polydispersity/radius). 5 is the correlation length. S(0) is related to the osmotic compressibility. (Ae)2c$ is the product of scattering contrast and particle volume fraction. The error bar is the standard deviation of each parameter value from fitting the 100 bootstrapped data sets. See text for more explanation. 103-
'
'
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Figure 1. Temperature-composition phase diagrams for D20/C02/ C I ~ mixtures E ~ at a constant D20/C12E6 weight ratio of 12.8 to 1. Open circles are data at 90.7 bar, and the filled circles represent data at 63.1 bar. Crosses show the SANS operating conditions. containing varying amounts of carbon dioxide. The compositions of the samples examined by S A N S are represented by the crosses in Figure 1. SANS experiments were performed at 63.1, 76.9, and 90.7 bar and temperatures of 25, 28, and 31 "C in order to span the carbon dioxide critical pressure near its critical temperature (31.1 "C and 73.8 bar5). Scattering spectra and model descriptions (solid lines) are shown on log-log scales in Figures 2-5 as plots of neutron scattered intensity on an absolute scale as a function of the magnitude of the scattering vector, 4. For clarity of presentation, some of the spectra are multiplied by 2 or 4 (shown as (x2) or (x4) in the figure caption) to be offset from the other spectra. These spectra are distinguished by different degrees of upturn at low q. This feature usually arises from the presence of either attractive interactions between micelles or critical scattering. The high q portions of the spectra change little in shape with changes in temperature, pressure, or C 0 2 composition. This indicates that the micelle structure does not change under these conditions. Figure 2 displays the scattering spectra of CO2-free mixtures. For these samples, the scattering changes little with temperature because their compositions are far ('20 " C ) from the phase boundary. As COz is added, the upturn at low q becomes more pronounced (Figure 3). The effect of increasing pressure at a temperature near the critical point of carbon dioxide is illustrated in Figure 4, where again the upturn at low q becomes more pronounced while the shape of the high q part of the spectra continues to remain unchanged. At lower carbon dioxide
Figure 2. SANS spectra of 7.5 wt % Cl2E&0
solutions at 25 and31 "C (x2) and 63.1 bar. Samples are approximately 20 "C from the phase boundary, and the spectra show little change with temperature. Lines represent model fits to the data.
1
CO ,concentration (wt%)
T=3 l°C P=63.1 bar
r
0.01 0.01
0.1
9
Figure 3. SANS spectra of solutions at 31 "C and 63.1 bar containing constant CO2 concentrations of 0, 1.7 (x2), and 3.9 wt % ( x 4 ) CO2 and constant D20/C12E6weight ratio of 12.3 to 1. There is a large intensity increase at low q at the highest C02 concentration. Lines represent model fits to the data.
concentrations there is a negligible effect of pressure on the scattered intensity (Figure 5 ) . The values for the five fitted parameters-radius ( I ) , polydispersity, correlation length (E), S(O), and (Ag)2$J-were determined by minimizing the x2 value between the model fit and the experimental data. The fits of the five-parameter model
J. Phys. Chem., Vol. 99, No. 25, I995 10357
Microstructure in D20/Cl~EdC02Mixtures 1000'
'
'
" "
1 Pressure (bar)
3.9 wtW
co,
CiEj
E
1
0.01
0.1
0.01 q
Figure 4. SANS spectra of 3.9 wt 8 C02 (DZO/C& weight ratio of 12.3 to 1) solutions at 31 "C and pressures of 63.1, 76.9 (x2), and 90.7 bar (x4). There is a small increase in intensity at low q with increasing pressure. Lines represent model fits to the data. Figure 6. Schematic representation of a H20/CiE,/C02 phase diagram showing the change in the plait point location when pressure is below the C02 critical pressure (top) and when it is above the critical pressure (bottom). The plait point is shown as a filled circle. SANS operating conditions are shown as crosses. See text for more explanation.
IO
I
0.1
0.01
q(
0.1
A3 Figure 5. SANS spectra of 1.7 wt % COz (D20/C& weight ratio of 12.3 to 1) solutions at 31 "C and pressure of 63.1, 76.9 (x2), and 90.7 bar (x4). There is no change in intensity with changes in pressure. Lines represent model fits to the data.
to the data are excellent except at the highest values of q (Table 1). The poor fit at the highest q for some spectra reflects the assumption that the incoherent background remains constant through all of the fitting. From bootstrapping, the error in the parameter values (Table 1) as a result of deviations in scattered intensity is, in most cases, less than 1% and is largest for and
e
S(0). The scattering contrast difference between the micelle and the solvent dominates any intramicellar contrast difference, so the measured radius is the total size of the micelle. The reported polydispersity is a measure of the root-mean-squared deviation from the average radius. Deviations of less than 10% in radius (22.9-24.6 A) and 30% in polydispersity (4.8-6.2) indicate that pressure and carbon dioxide concentration have a limited effect on structure over the entire range of operating conditions. The radii of the particles in the C12Em20 solutions are similar to those reported elsewhere for model fits using the OmsteinZemike structure factor m ~ d e l . ~That , ~ structure does not depend on carbon dioxide concentration also agrees with the qualitative observation that the shapes of the high q portions of the spectra are similar regardless of carbon dioxide concentration, pressure, or temperature. The correlation length and S(0)show the greatest change for the 3.9 wt % C02 solutions. ,The increases in 6 and S(0) with temperature are consistent with an increase in critical fluctuations as the phase boundary is approached. Also, no
(e)
change in S(0)was observed for both the 1.7 wt % C02 solutions and the solutions containing no C02, a result consistent with their relatively large distances from the phase boundary. However, the increase in 6 and S(0)with increasing pressure at constant temperature (31 "C) and composition (3.9 wt % C02) is not consistent with the phase boundary moving closer to the SANS operating conditions because, as shown in Figure 1, the phase boundary in fact moves to slightly higher temperatures with increasing pressure. More careful consideration of the phase behavior is necessary to explain the increase in and S(0) with increasing pressure for the 3.9 wt % C02 sample. Phase behavior measurements of H20/CgE3 or Cfil/CO2 temary mixtures show that the surfactant-rich phase in the liquid-liquid-gas three-phase region moves from the water-rich side of the phase diagram to the CO2-rich side as pressure increases.6 This movement will also cause the plait point of the two-phase region to rotate toward the CO2-rich comer of the phase diagram, as sketched in Figure 6. Measurements of the relative phase volumes of samples containing 4.1 wt % CO2 with a D20 to CI& weight ratio of 12.8 to 1 (a composition just inside the two-phase region) show that the D20-rich phase is the minority phase. Thus, the compositions of interest in the one-phase region are on the surfactant-rich side of the plait point, as shown by the crosses in Figure 6. Consequently, increasing pressure causes the plait point to move closer to the composition of the S A N S sample, and this approach of the plait point to the sample composition is responsible for the observed increase in both 5 and S(0)with increasing pressure. The product of contrast and particle volume fraction decreases by 40% with increasing carbon dioxide concentration but depends little on pressure or temperature. The values of (A&$ were used to determine carbon dioxide partitioning between the water and the micelles. To calculate at different compositions and carbon dioxide densities the following assumptions were made: there are 1.5 waters of hydration per surfactant molecule detected by SANS,8 all components mix ideally, water and surfactant have a constant density, and there is negligible free surfactant monomer. The volume of the surfactant molecule was computed using the volumes of the substituent groups determined by Hayter.26
10358 J. Phys. Chem., Vol. 99, No. 25, 1995 0
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with COz density for different percentages of added C02 being contained in the micelles at an overall concentration of 3.9 wt % C02 (lines). Solid symbols represent the experimental variation of (A@)2qi
Plots of calculated (divided by the scale factor) versus carbon dioxide density are shown in Figures 7 and 8. Each line on these plots represents a different fraction of carbon dioxide entering the micelles. The (he)*@ values calculated for the two extremes of C02 partitioning are very different. This large variation allows a comparison of the fitted and calculated results to determine how much carbon dioxide enters the micelles. The variation in ( A Q )for ~ ~the 3.9 wt % CO2 samples with carbon dioxide density (Figure 7) is consistent with no more than 7% of the added carbon dioxide entering the micelles. A similar plot for the 1.7 wt % COz samples (Figure 8) shows no more than 18% of the added carbon dioxide entering the micelles. The large fraction of C02 in the water is not surprising, since the highest concentration of C02 studied is 4.4 wt % on a surfactant-free basis, which is below the C02 solubility limit in water of 5.8 wt % at 31.04 "C and 76 bar.27 That little, if any, C02 is incorporated into the micelles means that the micellar structure is not affected by C02 density or concentration.
Conclusions S A N S measurements on the system D20/C02/C12& in the water-rich corner of the phase diagram indicate the presence of spherical micelles 50 8, in diameter. These micelles are similar in dimension to those formed in mixtures of D20 and CI& alone. Micelle structure does not change over the range of pressures, temperatures, and compositions studied. The observed changes in S(0) and 6 are consistent with the presence of critical concentration fluctuations near a plait point and phase boundary. The variation of the product (Ae)2d as a function of carbon dioxide density and concentration indicates that little or no carbon dioxide partitions into the micelles when the carbon dioxide in solution is below the solubility limit of carbon dioxide in water.
Acknowledgment. We are grateful for financial support from NASA grant NAG3-1424. We acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing the facilities used in this experiment. The assistance of John Barker and Charlie Glinka
. 0
C 0 2 Density (glcc)
Figure 7. Calculated variation of (A@)%$ (divided by the scale factor)
1
0.00015-
0
0.2
0 0 0.4 0.6 0.8 C 0 2 Density (g/cc)
0
5 1
1.2
Figure 8. Calculated variation of (Ag)24 (divided by the scale factor) with C02 density for different percentages of added COz being contained in the micelles at an overall concentration of 1.7 wt % C02 (lines). Solid symbols represent the experimental variation of (A@)2+.
during the S A N S experiments is gratefully acknowledged, as are helpful discussions with Steve Kline.
References and Notes (1) Kahlweit, M.; Strey, R.; Firman, P.; Haase, D. Langmuir 1985, I , 281. (2) Kahlweit, M.; Strey, R.; Firman, P.; Haase, D.; Jen, J.; Schomacker, R. Langmuir 1988, 4, 499. (3) Kahlweit, M.; Strey, R.; Busse, G. J. Phys. Chem. 1990, 94, 3881. (4) Kahlweit, M.; Strey, R.; Busse, G. Phys. Rev. E 1993, 47, 4197. (5) Carbon Dioxide International Thermodynamic Properties of the Fluid State-3; Angus, S . , Armstrong, B., de Reuk, K. M., Eds.; Pergamon Press: Oxford, 1976. (6) Ritter, J. M.; Paulaitis, M. E. Langmuir 1990, 6, 934. (7) Micelles, Membranes, Microemulsions, and Monolayers; Gelbart, W. M., Ben-Shaul, A., Roux, D., Eds.; Springer-Verlag: New York, 1994. (8) Triolo, R.; Magid, L. J.; Johnson, J. S.; Child, H. R. J. Phys. Chem. 1982, 86, 3689. (9) Douglas, C. B.; Kaler, E. W. Langmuir 1994, 10, 1075. (IO) Wilcoxon, J. P.; Schaefer, D. W.; Kaler, E. W. J. Chem. Phys. 1989, 90, 1909. (11) Gale, R. W.; Fulton, J. L.; Smith, R. D. J. Am. Chem. SOC.1987, 109, 920. (12) Fulton, J. L.; Smith, R. D. J. Phys. Chem. 1988, 92, 2903. (13) Tingey, J. M.; Fulton, J. L.; Matson, D. W.; Smith, R. D. J. Phys. Chem. 1991, 95, 1443. (14) Kaler, E. W.; Billman, J. F.; Fulton, J. L.; Smith, R. D. J. Phys. Chem. 1991, 95, 458. (15) Peck, D. G.; Johnston, K. P. J. Phys. Chem. 1991, 95, 9549. (16) Ritter, J. M. Ph.D. Thesis, University of Delaware, 1989. (17) McFann, G. J.; Johnston, K. P.; Howdie, S. M. AIChE J. 1994,40, 543. (18) Ritter, J. M.; Palavra, A. M. F.; Kao, C. P. C.; Paulaitis, M. E. Fluid Phase Equilib. 1990, 55, 173. (19) Kotlarchyck, M.; Chen, S. H. J. Chem. Phys. 1983, 79, 2461. (20) Griffith, W. L.; Triolo, R.; Compere, A. L. Phys. Rev. A 1987,35, 2200. (21) Chen, S. H. Annu. Rev. Phys. Chem. 1986, 37, 351. (22) Efron, B.; Tibshirani, R. Stat. Rev. 1986, 1, 54. (23) Leger, C.; Politis, D. N.; Romano, J. P. Technomerrics 1992, 34, 378. (24) Full, A. P. Ph.D. Thesis, University of Delaware, 1994. (25) Nishikido, N.; Yoshimura, N.; Tanaka, M.; Kaneshina, S. J. Colloid Interface Sci. 1980, 78, 338. (26) Hayter, J. B. In Physics of Amphiphiles: Micelles, Vesicles, Microemulsions; Digiorgio, V., Corti, M., Eds.; North-Holland: New York, 1985; p 59. (27) Wiebe, R. J. Am. Chem. Soc. 1940, 62, 815. JP9503270
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