Langmuir 1986,2,417-423 possible to obtain qualitatively similar structures. Examination of the data presented above, albeit even if only for a small number of carboxylic acid adsorbates, demonstrates another important, though poorly recognized, characteristic of the self-assembly of closest-packed layers; these systems are strongly limited by kinetic constraints.ll Further, the simplest interpretation as to the nature of this barrier is that it is largely steric in origin. In solution adsorption experiments, this significant feature is less apparent (temperature and concentration being easily manipulated). In UHV,22 even for the simple adsorbates addressed herein, this limitation is pronounced and restricts the general preparative utility of gas-phase adsorption. The final point of interest we wish to note has to do with the thermal stability of the high-coverage adsorption state. There is a qualitative suggestion in the data we have obtained that the stability of this phase is enhanced-that (22) We have documented kinetic barriers to closest-packed aaeembly in solution experimenta in several system, most notably carboxylic acids on All1 and Ag2I substrates and dialkyl disulfides on A u ~ .All these systems form closest-packed assemblies under appropriate conditions, thus the conclusion that the problem is not one of thermodynamic instability but, rather, the kinetics which characterize the approach to equilibrium. In UHV, the problem is maintaining a high flux of reactanta at high surface temperatures. Clearly, absorbing a multilayer is a highflux experiment. The problem, however, is that multilayer8 are stable in UHV only at extremely low temperatures. (23)Nuzzo, R.G.;Allara, D. L., unpublished results. Whitesides, G. M., personal communication.
417
is, it persists to higher temperatures-as the length of the carbon chain increases. If this is correct, it is possible to imagine a critical chain length for a high-coverage phase which would be persistent at ambient temperature. Does such a process as this account for the minimum chain length dependences (typically CI0-Cl2,T 25 "C) which have been extensively reported in the solution literature for closest-packed adsorption of carboxylic acid monol a y e r ~ ? ~ * 'We ~ * 'simply ~ do not know on the basis of the data available, but such a suggestion remains attractive to us.24 The final answer to this question may not reside in additional UHV studies of the type reported herein. Rather, an examination of the influence of temperature on the stability and nature of surface phase formation by adsorption from dilute solution might help address fundamental issues such as these.
Acknowledgment. We thank C. Chidsey for a critical reading of this manuscript prior to publication. Jh&StV NO. C1,64-18-6;Ct, 64-19-7;CB, 79-09-4; Cq, 107-92-6; Ce, 142-62-1; CU, 7440-50-8. (24) We note for clarity that, in the case of solution experimenta, it is important to differentiate between the nature of the monolayer while immersed in an adsorbate-containing solution and that which is found to persist after ita removal. It is this latter state that is most easily compared to OUT UHV experimenta. Any desorption processes in either environment are irreuer8ibk. The solution environment on the other hand, presents the true equilibrium condition where desorption is reversible.
Structure of Microemulsions in the Brine/Aerosol OT/Isooctane System at the Hydrophile-Lipophile Balance Temperature Studied by the Self-Diffusion Technique J. 0. Carnali,*t A. Ceglie,i B. Lindman, and K. Shinodas Physical Chemistry 1, Chemical Center, Lund University, S-221 00 Lund, Sweden Received October 8, 1985. In Final Form: February 13, 1986 At the hydrophile-lipophile balance (HLB) temperature, the brine/isooctane/aerosol OT (AOT) system displays a large L2 phase which extends to very low AOT concentrations. At 5 wt %/system AOT, the self-diffusion of isooctane and water has been measured at isooctane weight fractions ranging down to 0.25. The system is oil-continuous and brine-discontinuous at low brine contents but becomes bicontinuous as the amounts of oil and brine become comparable. In this region, the self-diffusion of isooctane and water is high, and it is reasoned that each component can form temporary, continuous layers. A highly flexible oil/brine interface must exist under these conditions. At isooctane weight fractions under 0.25, it is necessary to go above or below the HLB temperature to obtain a microemulsion. The system is brine-continuous above the HLB temperature, but the isooctane self-diffusion is fairly large, indicating that the interfaces remain flexible. However, as the temperature is increased further, this flexibility is lost. The conclusion is made that the oil/brine interface possesses a large degree of flexibility at the HLB temperature.
Introduction Microemulsions are mixtures of oil, water, and surfactant characterized by being a single, isotropic, and thermodynamically stable The microscopic of Permanent address: Department of Chemistry, Lehigh University, Bethlehem, PA 18015. Permanent address: Dipartimento di Chimica, Universitl degli Studi di Bari, Via Amendola 173, 701 26 Bari, Italy. *Permanent address: Department of Chemistry; Faculty of Engineering, Yokohama University, Tokiwadai, Hodogayaku, Yokohama 240, Japan.
*
0743-7463/86/2402-0417$01.50/0
phase has been the subject of considerable interest and several models have been Originally, Hoar and fM"n2described these systems as an extension of the familiar emulsion systems to very small droplet sizes. For oil-rich systems, they pictured spherical droplets of water surrounded by a monolayer of surfactant. The droplets were dispersed in an oil-continuous phase. The roles of oil and water were interchanged if the systems were water rich. This model has withstood experimental studies by (1)Danielsson, I.; Lindman, B. Colloids Surf. 1981, 3,391. (2) Hoar,T. P.; Schulman, J. H. Nature (London) 1943, 152, 102.
0 1986 American Chemical Society
418 Langmuir, Vol. 2, No. 4, 1986
Carnali et al.
ultra~entrifugation,~~~ static light scattering,5v6 dynamic light scattering,' neutron scattering,&1° dielectric spectroscopy,'lJ2 and other techniques. It has also been the basis for theoretical work on microemulsion stability.13J4 The above model is not consistent, however, with selfdiffusion studies which have been made on several microemulsion systems.16J6 The self-diffusion coefficients for water and oil have been found to be simultaneously high in systems rich in both components. These results do not suggest a dispersed-phase/continuous-phase structure. Further, the phase diagrams of many systems show a single microemulsion phase connecting the water-rich region with the oil-rich region."J8 For such a system, it is difficult to visualize a transition from water-continuous to oil-continuous domains without some sort of transitional structures. These transitional structures were anticipated by Wins0r19 and have been discussed frequently by Shinoda.20p21 In the latter author's preaentation, note is made of nonionic surfactant-water-oil systems which show phase transitions as a function of temperature. At low temperature, a water-continuousmicroemulsion exists in equilibrium with an excess oil phase. At high temperature the identities of the microemulsion and excess phases exchange while at an intermediate temperature, termed the HLB temperature (for hydrophile-lipophile balance), a separate surfactant phase forms. The HLB temperature coincides with the average of the two critical points in the surfactant/ water/oil system and indicates a condition in which the hydrophilicity and the lipophilicity of the surfactant are optimally balanced for maximal solubilization of oil and water into the surfactant phase. For ionic surfactants, an analogous condition can be reached by varying the ionic strength or by blending a hydrophilic surfactant with a lipophilic one.= The interfacial tensions between the oil, water, and surfactant phases are mutually low near the HLB temperature leading to a sandwichlike structure being postulated for the surfadant phase. The alternating oil and water layers in this phase were viewed as being bound between surfactant monolayers whose curvature varies randomly throughout space.21
(3) Bowcott, J. F. L.; Schulman, J. H. Z. Electrochem. 1959,59, 283. (4) Eicke, H. F.; Rehak, J. Helu. Chim. Acta 1976,59, 2883. (5) Schulman, J. H.; Friend, J. A. J. Colloid Sci. 1949, 4, 497. (6) Cazabat, A. M.; Langevin, D.; Pouchelon, A. J. Colloid Interface Sci. 1980, 73, 1. (7) Brunett, S.; Roux, D.; Bellocq, A. M.; Fourche, G.; Bothorel, P. J. Phys. Chem. 1983,87, 1028. (8) Ober, R.; Taupin, C. J.Phys. Chem. 1980,84, 2418. (9) Cebula, D. J.; &tewill, R. H.; Ralston, J. J.Chem. Soc., Faraday Trans. 1981, 77, 2585. (10) Kotlarchyk, M.; Huang, J. S.; Chen, S. H. J. Phys. Chem. 1985, 89, 4382. (11) Chou, S. I.; Shah,D.0. J.Phys. Chem. 1981,85, 1480. (12) Peyrelasse, J.; Boned, C. J. Phys. Chem. 1985, 89, 370. (13) Ruckenstein, E.; Krishnan, R. J.Colloid Interface Sci. 1980,75, 476. (14) Oakenfull, D. J. Chem. Soc., Faraday Trans I 1980, 76, 1875. (15) Lindman, B.; Stilbs, P.; Moaeley, M. E. J. Colloid Interface Sci. 1981, 83, 669. (16) Lindman, B.; Stilbs, P. In 'Microemulsions"; Friberg, S., Bothorel,
P., Eds.;CRC Press: in press. (17) Heil, J.; Clauase, M.; P e y r e h e , J.; Boned, C. Colloid Polym. Sci. 1982,260, 93. (18) Kahlweit, M.; Reinhard, S. Angew. Chem., Int. Ed.Engl. 1985, 24, 654. (19) Winsor, P. A. Trans. Faraday SOC.1948,44, 376, 382, 387, 390. (20) Saito, H.; Shinoda, K. J . Colloid Interface Sci. 1970, 32, 647. (21) Shinoda, K. Progr. Colloid Polym. Sci. 1983, 68, 1. (22) Shinoda, K.; Kunieda, H.; Arai, T.;Saijo, H. J.Phys. Chem. 1984, 88, 5126.
Recently, the transitional structures have been modeled quantitatively. Striven= introduced the notion that they might be equilibrium, bicontinuous structures whose surfactant-coated, oil/water interfaces are periodic, minimal surfaces. Such structures resemble fused polyhedra and have no preferred curvature. Another model is that of Talmon and PragerN in which the volume of the microemulsion is subdivided into space-filling, Voronoi polyhedra which are then randomly filled with oil or water. This model allows the statistical mechanics of the system to be worked out and phase diagrams can be qualitatively predicted.% Whatever the structure of the microemulsion, DeGennes and Taupin have pointed out that the oil/water interface must be extremely flexible.26 Experimental studies of microemulsionsrich in both oil and water are numerous but the techniques employed are usually not sensitive to the subtle differences between the proposed models. The X-ray scattering from the Voronoi polyhedra model can be calculated and compared well with data obtained from a microemulsion containing equal amounts of oil and water.27 A very similar system was studied by Auvray et al.28using neutron scattering with contrast variation. These workers were able to demonstrate for the fiist time that the mean curvature of the oil/water interface is zero. They emphasize that this is a condition which exists only on the average. Fluctuations in the curvature must exist locally on short time scales as was foreseen by Friberg et al.29 In the present work, we have measured the self-diffusion coefficients of oil and water in a microemulsion as the composition is varied from the water-rich to the oil-rich domain. The microemulsion chosen is the system aerosol OT (AOT)/brine/isooctane,studied previously by Kunieda and Shinoda.30 To extract some structural information, we have extended the interpretation of the self-diffusion coefficients to include the obstruction effect felt by a species when inaccessible volumes block its diffusion path.31132 This effect is dependent on the shape of the inacessible volumes and has been calculated for spherical, cylindrical, and lamellar obstruction^.^^ We are thus able to follow the structural changes occurring in the system as its composition moves into the region where transitional structures are anticipated.
Experimental Section Materials. AOT (sodiumbis(2-ethylhexyl)sulf~uccinate)from Fluka AG, Switzerland, was purified according to the procedure recommended by Kunieda and S h i n ~ d a . ~The ~ isooctane (2,2,4-trimethylpentane), from EGA-Chemie, West Germany, and the sodium chloride, from BDH Chemicals Ltd., England, were of reagent grade. The heavy water was of 99.8% 2Hfrom Norsk Hydro, Rjukan, Norway, and the 'HzO was twice-distilled. Sample Preparation. Samples were prepared by weighing the Components directly into 5-mm NMR tubes or into glass ampules. Both types of sample containers were then sealed and
'
(23) Scriven, L. E. Nature (London) 1976,263, 123. (24) Talmon, Y.; Prager, S. Nature (London) 1977, 267, 333. (25) Talmon, Y.; Prager, S. J. Chem. Phys. 1978, 69, 2984. (26) DeGennes, P. G.; Taupin, C. J.Phys. Chem. 1982,86, 2294. (27) Kaler, E. W.; Bennett, K. E.; Davis, H. T.; Scriven, L. E. J. Chem. Phys. 1983, 79, 5673.
(28) Auvray, L.; Cotton, J. P.; Ober, R.; Taupin, C. J. Phys. Chem. 1984,88, 4586. (29) Friberg, S.; Lapczynska, I.; Gillberg, G. J. Colloid Interface Sci. 1976, 56, 19. (30) Kunieda, H.; Shinoda, K. J.Colloid Interface Sci. 1980, 75, 601. (31) Nilsson, P. G.; Lindman, B. J. Phys. Chem. 1984,88,4764. (32) Nilsson, P. G.; Lindman, B. J. Phys. Chem. 1983,87,4756. (33) Jansson, B.; WennerstrBm, H.; Linse, P.; Nilsson, P. G. Colloid Polym. Sci. 1986, 264, 77. (34) Kunieda, H.; Shinoda, K. J. Colloid Interface Sci. 1979, 70,577.
Langmuir, Vol. 2, No. 4, 1986 419
Microemulsion Structure in the BrinelAOTlIsooctane System
70
iso-octane
t
i
45t iso-octane
.1
.2
.3
.4
.5
.6
.7
.8
weight fraction iso-octane
Figure 1. Phase diagram for the system 0.46 wt % NaCl brine, isooctane and 5 wt %/system AOT as functions of temperature
and the isoodane/(brine + isooctane)weight fraction. The water used in the brine is a 22.51775 weight ratio mixture of H20and DzO,respectively. The symbols are identified as 24 = two-phase isotropic region, 14 = one-phase isotropic region, and LC = liquid-crystalline phase containing region. equilibrated in a thermostated water bath. In the phase diagram determination, crossed polaroids were used to check for optical anisotropy. Self-DiffusionMeasurements. The self-diffusioncoefficients of water (HDO) and isooctane were obtained by using the FT pulsed-field gradient spin-echo t e c h n i q ~ e . ~ A ~JEOL . ~ FX-60 spectrometer operating in the lH mode at 60 MHz was employed. A field-frequency lock was provided by internal D20 and the temperature of the measurements was controlled to within f0.5 OC as determined by a calibrated copper/constantan thermocouple. The spin-echo peak amplitude for a given NhfR line (A) follows the equation A = f exp(-y2g2D62(A -6/3))
iso-octane
(1)
where f is constant for a given set of experimental conditions. y is the magnetogyric ratio of a proton, D is the self-diffusion coefficient of the species responsible for the NMR signal, and g is the strength of the applied field gradient. A and 6 are time parameters in the pulse sequence. A is the time between the 90" and 180" pulses and was kept constant at 140 ms for reasons put forth in ref 36. 6, the length of the field gradient pulse, was varied over the range 1-99 ms so as to observe the decay of the spin echo. The decay of A as a function of 6 was fit, by a nonlinear leastsquares routine, to eq 1. The random error limits on D were determined as in ref 35 and correspond to 80% confidence intervals. These errors were generally less than 5% of the determined self-diffusion coefficient. The magnitude of g, needed in the above fitting procedure, was determined from the known self-diffusionof trace HDO in D20.37 At most of the experimental temperatures, it was necessary to extrapolate the data in ref 37 to obtain D(HD0). Then the decay of A with 6 was fit to eq 1 to determine g. The self-diffusion coefficient of neat isooctane was determined on a Bruker 322-9 pulsed NMR spectrometer using 'H NMR at 60 MHz. In this case, the pulsed field gradient technique was employed as described in ref 38. A value of 3.06 X lo4 m2/s was obtained for isooctane at 50 O C . For the neat water the corresponding value mz/s (cf. ref 39 and 40). would be around 3.3 X (35) Stilbs, P.; Moseley, M. E. Chem. Scr. 1980, 15, 176. (36) Stilbs, P. J. Colloid Interface Sci. 1982, 87, 385. (37) Mills, R. J. Phys. Chem. 1973, 77,685. (38) Nilsson, P. G., WennerstrBm, H.; Lindman, B. J . Phys. Chem. 1983,87,1377. (39) Krynicki, K.; Green, C. D.; Sawyer, D. W. Faraday Discuss. Chem. SOC.1978,66, 199.
, brine
\
\
90
80
\ 70
\
60
AOT
Figure 2. Partial three-componentphase diagramsfor the system 0.5 wt % NaCl brine, isooctane, m.dAOT at temperature 3.6 OC below (a), at (b), and 8.3 OC over (c) the HLB temperature.
Single-phase, isotropic regions are defined by dotted lines and all compositionsare expressed in weight percents. These regions are continuous with the L2 phase, an organic solution of AOT, which lies along the isooctane/AOT axis.
Results Figure 1 is the phase diagram for the system 0.46 w t % NaCl brine, isooctane, and 5 w t %/system AOT as a function of temperature and weight fraction of isooctane. The water used in the brine is a 22.5177.5 weight ratio mixture of H 2 0 and DzO, respectively. At temperatures below 44 "C or above 64 O C we observe that the system separates into two isotropic phases. At intermediate temperatures a single isotropic phase is found. Over a 2-deg interval, centered near 52 OC, this single-phase region extends from an isooctane weight fraction of unity down (40) Harris, K. R.; Woolf, L. A. J. Chem. Soc., S. Faraday Trans. 1 1980, 76, 377.
420 Langmuir, Vol. 2,No. 4, 1986 r o ~ FRACTION ~ n ~
BRINE O 0.5
O
0
0
-
-
0.2
0.1
-
0.05
-
00
a
-
0.02
-
0.01
25
35
.45
d E I G H T FFACTlGk
.55
65
75
85
ISO-OCTANE
Figure 3. Self-diffusion ratio (self-diffusioncoefficient in the microemulsion/self-diffusioncoefficient of the neat species) for water ( 0 )and boctane (A)as a function of the isooctane weight fraction at the HLB temperature (lower wale, see Figure 1). The upper scale shows the corresponding volume fractions of brine in the system.
to one of about 0.2. At lower fractions a liquid crystalline phase was encountered whose texture was determined to be mosaic lamellar by polarized light microscopy. This central temperature of 52 "C can be identified as an average HLB temperature for this s y ~ t e m . ~ ~ . ~ ' The nature of the single-phase region at the HLB temperature can be better understood by considering the three-component phase diagram for this system. Figure 2b shows the brine-rich portion of this phase diagram. The phase cut by a line at 5 wt %/system AOT is a direct continuation of the organic solution of AOT, L2, present along the isooctane/AOT axis.42 The self-diffusion coefficients of water and isooctane were determined a t the HLB temperature as a function of the weight fraction of isooctane. The results are shown in Figure 3 where we have plotted DIDo,the diffusion coefficient in the microemulsion divided by that of the neat component a t the same temperature. The trends in the oil and water diffusion are nearly mirror images of one another, with each component diffusing faster as ita weight fraction in the system increases. The trends cross at an oil weight fraction of 0.4 where both components diffuse at about one-half the rate of the neat species. The symmetry in the diffusion ratios breaks down, however, at high (41) Shinoda, K.;S 'tani, H.J. Colloid Interface Sci. 1978, 64, 68. (42) Ekwall, P.;hd? ell, L.;Fontell, K.J. Colloid Interface Sci. 1970, 33, 215.
and low oil contents. At the oil-rich end of the region, the water self-diffusion is reduced to of that the bulk water while the ratio for oil is over 0.8. In contrast, the oil self-diffusion at the brine-rich end of the one-phase region is over ll4that of the neat component and the diffusion ratio for water is only 0.66. As is shown in Figure 1,one-phase isotropic regions exist at oil weight fractions under 0.2 but at temperatures above or below the HLB temperature. The nature of these phases is clarified in Figure 2a,c. Below the HLB temperature, as shown in Figure 2a, the single-phase region moves away from the brine/isooctane axis. The narrow one-phase channel which connects the L2 region with the brine corner changes slope, moving to compositions richer in AOT. It is this channel that is sampled by a line drawn at 5 wt 7 ' 0/system AOT. With decreasing temperature, the intersection with the channel occurs at higher brine contents. Self-diffusion measurements in this channel below the HLB temperature show that DID, is in the range 0.4-0.5 for isooctane and 0.29-0.34for water. Above the HLB temperature, as shown in Figure 2c, the single-phase region is again reduced in its extent compared to the pase at the HLB temperature. The L2 phase is restricted from the brine-rich region except for the narrow channel connecting it with the brine corner. This channel extends along a line at nearly constant AOT/isooctane weight ratio and the ratio increases with temperature. Thus the channel moves symmetrically about the HLB temperature with i b AOT/isooctane weight ratio decreasing as this temperature is approached from either direction. Above the HLB temperature the channel component composition at 5 wt %/system AOT again becomes richer in water as the temperature is increased. The results of self-diffusion experiments in this channel are now shown in Figure 4. DID,for water is in the range 0.7-0.8 for the range of isooctane contents investigated. The isooctane self-diffusion, on the other hand, showed order-of-magnitude variations, not with composition but rather with temperature. Over the approximately 3-deg range of existence of the isotropic phase, the isooctane D/Doratios changed from being on the order of 0.1 at lower temperatures to being on the order of 0.01 at higher temperatures. These variations were strongest in the middle of the com-
Microemulsion Structure in the BrinelAOTlIsooctane System position range investigated. It should be noted that the temperature control in the self-diffusion experiments was not sufficient to allow reliable measurements to be made at the one-phase temperature boundaries. Thus the range of DIDo ratios shown in Figure 4 represent measurements made below the upper temperature limit and the above the lower temperature limit. A larger variation in D / D o might exist. Such strong temperature variations were not observed for water nor for water and isooctane at the compositions represented in Figure 3.
Langmuir, Vol. 2, No. 4, 1986 421
magnitude of Dwaterand Doilin a wide composition range up to the highest brine volume fractions accessible at the HLB temperature. Of particular interest is the behavior at the highest brine volume fractions. Below the HLB temperature, Dwaterand Doildiffer only moderately while above this temperature Doildecreases dramatically with temperature to values orders of magnitude below those of water. With the above as background, we can now turn to the interpretation of the data in Figures 3 and 4. In their calculation of the obstruction due to colloidal particles of the self-diffusion of small molecules, Jonsson et ala3found Discussion that The ionic surfactant AOT has well-balanced hydrophilic/lipophilic properties and so forms a surfactant phase D = ADO (2) as a function of ionic strength and temperature without Here Do is the self-diffusion coefficient of the small the necessity of blending with any other surfactant.30 In molecule in the absence of colloidal particles. A is an the present case, the system 0.46 wt % NaCl aqueous obstruction factor which, in the absence of specific molesolution/isooctane containing 5 wt %/system of AOT cule/particle interactions, depends on the volume fraction shows a single phase which extends from brine-rich to of obstructing colloidal particles and on their shape as is oil-rich compositions as is shown in Figure 1. The HLB shown in Figure 4 of ref 33. These calculations may be temperature is approximately 52 "C for the system made compared with Figure 3 where D / D o is plotted vs. the up with the H20/D20mixture. This temperature reprevolume fraction of brine in the system. For this comsents a 7 OC increase from the HLB temperature for the parison, the correct abscissa in Figure 3 is the volume same system made up with H2OaWThis isotropic shift has fraction of the dispersed phase, brine, plus AOT on the been observed in many other systems when D20 is suboil-rich side of the plot, isooctane plus AOT plus bound stituted for H 2 0 for the purpose of study by NMR or water on the water-rich side. This change would compress neutron ~ c a t t e r i n g . ~ ~ our plot only slightly toward the center and does not affect The three-component phase diagram (Figure 2b) reveals this discussion. We also note that specific interactions that the single phase occurring in this system at the HLB between water or isooctane and any colloidal particles are temperature is directly linked to the L2 phase. The selfnot expected to influence the measured self-diffusion more diffusion data for this phase appears in Figure 3. Before than ca. 10% because of the low concentration of AOT in presenting our interpretation of this data, we would do well the present system. to briefly review the use of the self-diffusion technique as As shown in ref 33, the obstruction factor for the cona structural tool. tinuous phase can range from unity to 2/3, depending upon Confinement of molecules within closed domains drathe volume fraction of the dispersed phase and its geommatically influences their translational mobility over suetry (spherical, prolate, or oblate). The corresponding pradomain distances. This is the simple basis for the use obstruction factor for the dispersed phase would typically of self-diffusion measurements as a structural tool, inter be under 0.1 or a factor of 10 less than that of the conalia for microemulsions as reviewed recently.16 The intinuous phase as outlined above.44 Based on these simple terpretation of molecular self-diffusion coefficients is considerations we infer a distinct droplet-type structure relatively straightforward, and it is possible from a in two ranges of the phase diagram. At the HLB temstructural model of microemulsions to predict the selfperature there is a water-in-oil droplet structure at low diffusion characteristics. Let us start with qualitative brine volume fractions (Dou/Dwater is in the range 10-100). predictions for three clear-cut limiting cases: A waterAt isooctane contents below ca. 0.2 and temperature above in-oil droplet structure would give Dwater(!= Ddroplet)
