Langmuir 1994,10, 3449-3454
3449
Viscosity of a Nonionic Microemulsion near Emulsification Failure M. S. Leaver* and U.Olsson Physical Chemistry 1, Chemical Center, Lund University, P.O. Box 124, S-221 00 Lund, Sweden Received December 29, 1993. In Final Form: July 27, 1994@ The viscosity of a water-rich microemulsion phase composed of C1&, water, and decane has been measured. Attention has been focused on the concentration dependence of the viscosity along the emulsification failure boundary, where the microstructure of the system is that of oil-swollen spherical micelles. At high dilution, the concentration dependence of the relative viscosity is consistent with the behavior of a suspension of spheres, with an effective micellar size characterized by its hydrodynamic radius. At higher concentrations, where interactions are important, a good correlation with colloidal hard-sphere systems is obtained if the apparent micellar size is characterized by the hard-sphere radius. With increasing temperature away from the emulsification failure boundary, a significantincrease in the viscosity is observed. The observed temperature dependence ofthe viscosity correlateswith results obtained previously from 2H NMR relaxation and self-diffusion experiments and is consistentwith a micellar growth with increasing temperature.
Introduction Nonionic surfactants have an interesting and rich phase behavior when mixed in polar so1vents.’s2 They are also capable of forming balanced microemulsions in ternary mixtures with 0 i 1 . ~ - ~ It is because of this rich phase behavior that these types of systems have attracted considerable attention as model systems for self-assembly and structured liquids. In connection with various formulations, particular attention has been focused on the ability of these types of surfactant to form microemulsion phases. A microemulsion is a thermodynamically stable, microstructured fluid phase of water and oil, stabilized by surfactant. If the surfactant is insoluble in both solvents, it will reside at the interface of the two immiscible liquids, forming a dividing surface between water and oil. Many studies on the structure of microemulsions have shown that, as a function of either temperature or composition, the structure can vary from discrete swollen micelles in solution to disordered bicontinuous network^.^,^*^ Since many of the properties of the fluid will depend on the microstructure, it is essential to characterize and be able to monitor such structural changes. In theoretical analyses of the various self-assembly microstructures of nonionic surfactant-water-oil systems, the flexible surface model, using the curvature energy concept,lO has been found to be very useful.l1-l8 Here, the relative stability of a given phase and microAbstract published in Advance A C S Abstracts, September 1, 1994. (1)Strey,R.;Schomacker,R.;Roux,D.;Nallet,F.;Olsson,U. J.Chem. SOC.Faraday Trans. 1990,86,2253-2261. (2)Mitchell, D. J.; Tiddy, G.J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J . Chem. SOC.Faraday Trans. 1 1983,79,975. (3)Kahlweit, M.; Strey, R. Angew. Chem. Int. Ed. Engl. 1985,24, 654-668. (4)Kahlweit, M.; Strey, R.; Busse, G. J.Phys. Chem. 1990,94,38813894. (5)Olsson, U.;Shinoda, K; Lindman, B. J . Phys. Chem. 1986,90, 4083-4088. Shinoda, K. J . Dispersion Sci. Technol. 1982,3,233. (6)Kunieda, H.; (7)Shinoda, K. Progr. Colloid Polym. Sci. 1983,68,1-7. (8)Olsson, U.;Nagai, K.; Wennerstrom, H. J . Phys. Chem. 1988,92, 6675-6679. (9)Olsson, U.;Jonstromer, M.; Nagai, K.; Soderman, 0.;Wennerstrom, H.; Klose, G. Progr. Colloid Polym. Sci. 1988,76,75-83. (10)Helfrich, W. 2.Naturforsch. 1973,28c,693-703. (11)Safran, S. A. J . Chem. Phys. 1983,78,2073-2076. @
structure results from an interplay of the curvature energy of the surfactant film and entropy. The local curvature energy density, g,, is often expressed to second order in the curvatures as
g , = 2K(H -
+ EK
(1)
Here H is the mean curvature, HO the spontaneous curvature, K the Gaussian curvature, and K and iz. the bending and saddle splay moduli, respectively. One particular case which can be described within the flexible surface model concerns the limiting solubility of, for example, oil in a water-rich microemulsion, and the limiting microstructure at the solubility limit. This problem was discussed theoretically by Safran and coworkers more than a decade a g ~ , ~while ~ Jexperimental ~ , ~ ~ studies in this direction have been performed only r e ~ e n t l y . ~ Here l - ~ ~the flexiblesurface model predicts that the microstructure should approach that of spherical droplets as one approaches the solubility limit.lg The incomplete solubilization, occurring above the saturation limit, has been termed “emulsification failre".'^^^^ Here spherical droplets having a radius
are predicted to coexist with excess oil. To eq 2 one may (12)Safran, S. A.In Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution; Chen, S., Huang, J. S., Tartaglia, P., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1992. (13)Golubovic, L.; Lubensky, T. C. Phys. Reu. A 1990,41,43434366. (14)Anderson, D.; Wennerstrom, H.; Olsson, U. J . Phys. Chem. 1989, 93,4243-4253. (15)Wennerstrom, H.; Olsson, U. Langmuir 1993,9,365-368. (16)Porte, G.;Appell, J.; Bassereau, P.; Marignan, L. J . Phys. Fr. 1989,50,1335-1347. (17)Pieruschka, P.; Safran, S. A.Europhys. Lett. 1993,22,625-630. (18)Pieruschka, P.; Marcelja, S. Langmuir 1994,10, 345-350. (19)Safran, S. A.; Turkevich, L. A.; Pincus, P. A. J . Phys. Lett. 1984, 45,L69. (20)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,pp 1177-1191. (21)Olsson, U.; Schurtenberger, P. Langmuir 1993,9,3389-3394. (22)h a v e r , M.; Olsson, U.; Strey, R.; Wennerstrom, H. J.Phys. II Fr. 1994,4,515-531. (23)Sicoli, F.; Langevin, D.; Lee, L. T. J . Chem.Phys. 1993,99,47594765.
0743-7463/94/2410-3449$04.50/00 1994 American Chemical Society
3450 Langmuir, Vol. 10, No. 10, 1994
Leaver and Olsson
emulsion phase is compared with previous results from also add a concentration-dependent term, resulting from zH spin relaxation and self-diffusion experiments. the entropy of mixing. However, experimentally one often finds the concentration dependence to be negligible. When Experimental Section the oil content or HOat constant composition is decreased, The nonionic surfactant C& was purchased from Nikko the model predicts a transition to nonspherical shapes. This scenario has also been found experimentally.z1~zz~z4 Chemicals in Japan and was used without further purification. The decane (99.9%)was purchased from Sigma and also used The advantages ofthe nonionic surfactant systems in these without further treatment. The samples were prepared using kind of studies are numerous: (i) The various low millipore filtered water. curvature phases can be formed without addition of The samples for the viscosity experiments (-10 mL total cosurfactant,z5-z7(ii) the spontaneous curvature can be sample volume)were prepared by weighing the components into conveniently tuned by varying the t e m p e r a t ~ r e , ~ J ~ *a~ suitable ~ > ~ ~ container and then immediately sealing. These and (iii) the systems can be tailor-made by combining samples were then homogenized by heating the samples in a suitable lengths of the hydrocarbon and oligo(ethy1ene temperature-controlled water bath to the lamellar phase and gently agitating the container regularly. When mixed, the oxide)chains in the surfactant and the chain length of the oi1.3P30 samples were cooled and kept in the microemulsion phase prior to the experiments. The phase diagram from ref 21, which was This paper deals with the water-rich microemulsion could be reproduced characterized for samples made using 2Hz0, phase formed upon the addition of pentaethylene glycol using the above samples, allowing for the expected -2 "C increase dodecyl ether (C12E5)to decane and water. The surfactant in the transition temperatures upon substitution of water for (as) to oil (ao) volume fraction ratio has been kept constant, 2HzO.35 Here the samples were heated in the water bath and the at a value of @&Do= 0.815, so that we study a fixed cut phase transitions monitored between crossed Polaroid sheets, to of the phase prism. The phase diagram of this particular detect any optical birefringence of the phases. The viscosity of the samples was measured by measuring the cut of the full phase prism has been published previously.21 time taken for 10 mL of the microemulsion to flow through a 0.5 In this system the microemulsion phase is stable over a mm capillary viscometer. The temperature was maintained, to limited temperature range and is bounded at higher an accuracy of kO.1 "C, with a Haake F3 circulating water bath. volume fractions, @ (= QS Q0), by the formation of liquid The sample was pipetted into the viscometer, and then it was crystalline phases. In previous publicationszl,zzit has been left to equilibrate for at least 15 min at the experimental shown that the phase boundary between the single temperature. The sample was also left t o equilibrate for 15 min microemulsion phase and one in coexistence with excess between each experiment during the temperature-dependence oil, which occurs at lower temperatures, can be described study. The time taken for the sample to empty was then in terms of emulsification failure. The microemulsion measured at least 5 times to ensure reproducibility. The relative viscosity of the sample was calculated by consists of spherical oil dropletsz1~zz~31 along the phase measuring the water time through the capillary at various boundary, and results from static and dynamic light temperatures. Before and after each experiment, the capillary scattering and self-diffusion experimentsz1 along this was cleaned by rinsing the equipment with millipore water a phase boundary have furthermore shown the system to number of times and then drying thoroughly. Water times were be behaving in good agreement with predictions for hard then recorded at a specific temperature and the resultant viscosity spheres. In an NMR study, the results indicated that as compared with reference values for water at that temperature the temperature was increased, these micellesfirst showed to ensure the cleanliness of the equipment prior to the introduccharacteristics of growth and then finally crossed over to tion of the next sample. a bicontinuous structure a t higher temperatures and Measurements of the zero shear viscosity were carried out on a Carri-Med CSL rheometer. The rheometer is fitted with a concentrations.z2 Peltier PtlOO temperature control system, which is effective in Here we have performed viscosity experiments along the temperature range -15 to 100 "C, with an accuracy and the emulsification failure boundary and as a function of stability of f O . l "C. The measurements were carried out using temperature for some selected samples. Thus, we have a cone and plate measuring system, with the dimensions of the extended the study of this microemulsion phase to include measuring system chosen to optimize the accuracy ofthe results. an additional technique, viscosity, which is sensitive to In all the experiments, results have been obtained from a 6 cm interactions and allows for a comparison with the welldiameter 1"cone, operating with a 23pm gap between the center studied colloidal model hard-sphere system^.^^-^^ The of the measuring geometry and the plate. The rheometer was operated in the variable shear mode. In the temperatureobject of the study has been to investigate further, by this dependence experiments, a solvent trap is used to ensure no complementary technique, the resemblance between the solvent evaporation during the course of the experiment. The oil-swollen micelles and the colloidal hard-sphere systems. relative viscosities were obtained by measuring the water The results will be presented as follows. Along the viscosities at the corresponding temperatures. In all the experiemulsification failure boundary, where the system forms ments, the runs were repeated a number of times to ensure spherical oil-swollen micelles, the results are compared reproducibility. with those from colloidal hard-sphere system^.^^-^^ The Some additional viscosity measurements (corresponding to the results presented in Figure 5) were carried out on a Bohlin variation of the viscosity with temperature in the micro-
+
(24)Olsson, U.; Wennerstrom, H.Adu. ColloidInterfieSci.,accepted
for publication. (25)Shinoda, K.;Arai, H.J.Phys. Chem. 1964,68, 3485. (26)Saito, H.;Shinoda, K. J. Colloid Interface Sci. 1970,32,647. (27)Shinoda, K.;Kunieda, H.; Arai, T.; Saijo, H. J. Phys. Chem. 1984,88,5126-5129. (28)Strey, R. Colloid Polym. Sci., in press. (29)Kahlweit,M.; Strey, R.; Firmin, P. J. Phys. Chem. 1986,90, 671-677. (30)Kahlweit, M.;Lessner, E.; Strey, R. J.Phys. Chem. 1983,87, 5032-5040. (31)Bagger-Jorgensen,H.; Olsson,U,; Mortensen,K. In preparation. (32)de Kruif, C.G.; van Iersel, E. M. F.; Vrij, A.; Russel, W. B. J. Chem. Phys. 1986,83,4717-4725. (33)van der Werff, J. C.; de Kruif, C. G. J.Rheol. 1989,33,421-454. (34)Jones, D.A.R.; Leary, B.; Boger, D. V. J.Colloid Interface Sci. 1991,147,479-495.
VOR Rheometer System, kindly put at our disposal by the division of Food Technology, Chemical Center. Aconcentric cylinder (C25; inner radius 12.5 mm) was connected to a torque element with a moment of 0.329 mNm and a shear rate of 14.6 s-l. Increasing the shear rate by an order of magnitude did not alter the measured viscosity. The viscosity at each temperature was measured twice to ensure reproducibility. The temperature was controlled within 10.1 "C.
Microemulsion Droplets along the Emulsification Failure Boundary Before the viscosity data are presented we will briefly summarize the existing knowledge of the present micro(35)Strey,R.;Winkler, J.; Magid, L. J.Phys. Chem. 1991,95,75027507.
Viscosity of a Nonionic Microemulsion
Langmuir, Vol. 10, No. 10, 1994 3451
with n being the number of surfactant molecules per micelle and UEO the volume per ethylene oxide chain. The subscript i in eq 4 represents either H or HS. For the C12E5 surfactant, UEO x 4 2 , and the aggregation number, n, is obtained by dividing the total interfacial area by the area per surfactant molecule: Figure 1. Schematic representation of the oil-swollen micelles present at the emulsification failure in the system. Here we define Rhc as the hydrocarbon radius, RH as the hydrodynamic radius, andRHs as the effective “hard-sphere”radius. The polar/ apolar interface associated with Rhc encloses the oil and the hydrocarbon tails of the surfactant.
emulsion. Light scattering,21self-diffusion,21922 and NMR relaxation22 results obtained along the lower phase boundary are consistent with a microstructure of spherical oil-swollen micelles, as also predicted from theoretical considerations.12*20 Spherical oil-swollen micelles have also been found in other ternary microemulsions with nonionic surfactant under similar conditions. Hence, the viscosity results from the lower phase boundary should be compared with the predictions for suspensions of spheres. The oil-swollen micelles can be considered as sterically stabilized oil droplets coated by “end-grafted” pentaethylene oxide chains as illustrated in Figure 2. The “graftin density” corresponds to approximately one chain per 45 which is the area per surfactant molecule, a,, at the polar/apolar i n t e r f a ~ e . ~ l * This ~ ~ B ~interface is defined so as to enclose the oil and the alkyl tails of the surfactant. In the case of C12E5, the alkyl chain and oligo(ethylene oxide) blocks have approximately the same volumes. Thus for a spherical micelle, the radius associated with the polar/apolar interface, which we denote the hydrocarbon radius, R h c , is given by
I;,
(3) where I , is the surfactant length, which is defined as u$as, where the volume of the surfactant, us,has a value of 702 A3.36In addition to R h c , the micelles are characterized by a hydrodynamic radius, RH,and a hard-sphere radius, R H s . The latter characterizes the intermicellar interactions. The different characteristic dimensions of the aggregates are illustrated in Figure 1. From static light scattering and small-angle neutron scattering the hydrocarbon radius was determined as R h c = 78 RHwas determined from collective and selfdiffusion coef‘ficientsto be 94 The hard-sphere radius was determined by static light scattering to be RHS= 88
(5) The aggregation number for spherical micelles has been calculated to be ~ 1 6 0 0 Through . the use of eqs 3 and 5, it is possible to express eq 4 as
From the known values of R h c , RH,and RHS, we obtain, using eq 4, aH = 1.36 and aHs = 1.14, respectively.
Colloidal Hard-Sphere Systems Below we will compare the viscosities from the microemulsion with those obtained from the colloidal model hard-sphere systems studied by de Kruif et a1.32,33These are sterically stabilized silica particles dispersed in an organic solvent. The stabilizing layer of the silica particles is small compared to the overall particle radius. Hence they are characterized by Q ~ H= @HS = Qi. Viscosity along the Emulsification Failure Boundary Lower Concentrations. The relative viscosity qr (which is defined as q/qo, where q is the viscosity of the solution and q o is the solvent (water) viscosity) of a dilute solution of spherical colloidal particles increases weakly with increasing particle concentration. At a finite concentration, qr > 1due to the obstruction of solvent flow by the presence of colloidalparticles. The effective particle dimension in this case is the hydrodynamic radius. Hence, when we compare with the colloidal hard-sphere systems, we should plot qr as a function of @H. This is illustrated in Figure 2 for the more dilute samples where the data points from the microemulsion were measured with a capillary viscometer. The results from the microemulsion are shown as filled circles, and we compare with results from three different silica dispersions, which are shown as open symbols.33 In Figure 2 we also compare with the relation of Sait6: 37,38
A.21731
(7)
A.
Expressing the volume fraction of surfactant plus oil as Qio allows us to define a hydrodynamic volume fraction, QiH, and a hard-sphere volume fraction, @HS, as Q ~ H= aHQiH and @HS = aHsQi, respectively. The proportionality constants aH and aHs can be calculated from the ratios RH/& and RH&?hc, respectively, and @$ao: Qi = Qi,
+
describing the concentration dependence of qr in dilute solution where interactions are negligible. The Sait8 relation is shown in Figure 2 as a solid line. As can be seen in Figure 2, there is a good correlation between the microemulsion data and colloidal hard-sphere
~~
(36)Olsson, U.;Wurz, U.; Strey, R. J . Phys. Chem. 1993,97,45354539.
(37)Saito, N.J . Phys. SOC.Jpn. 1950,5,4. (38)Saito, N.J . Phys. SOC.Jpn. 1952,7 , 447.
Leaver and Olsson
3452 Langmuir, Vol. 10,No.10,1994
100 1.4
1I ' ~
0
e A
microemulsion s':P,o
1
emulsion capillary
Ac
I
ck
0.05
0.1
10
0
0.15
0.3
0.2
0.1
0.4
0.5
0.6
@H s
Figure 2. Low volume fraction dependence of the microemulsion relative viscosity at 25 "C, plotted as a function of the ~ text). The experimenhydrodynamic volume fraction 4 , (see tally determined viscosities from the microemulsion are represented by the filled symbols. We compare these results with data from the colloidal hard-sphere systems of van de Werf€ and de Here, the open symbols correspond t o the viscosity obtained from suspensions of various silica sphere radii particles published in ref 33, and we use their nomenclature for these systems using the followingsymbols: (0)SJ14, ( 0 )SSF1, (A) SJ18. The solid line is calculated using eq 7.
Figure 3. Full concentration dependence ofthe microemulsion relative viscosity at 25 "C, plotted as a function of the hardspherevolume fraction, (PHS(seetext). Here, the experimentally determinedviscosities from the microemulsion are represented by the filled symbols. Filled spheres correspond to capillary viscometry measurements and filled trianglesto cone and plate measurements of the limiting viscosity at low shear rates. Data from colloidal hard-sphere systems of van de Werff and de KruiP3 are again represented by the open symbols exactly as in Figure 2. The solid line is calculated according t o eq 8, using CP, = 0.63.
I 1 data at lower concentrations, and also, both the colloidal 40 hard-sphere and microemulsion viscosity data are well described by the SaitG formulaup to (PHw 0.07. At higher concentrations the experimental data increase faster with 30 the concentration than is predicted by the SaitG formula, signifying that interactions are becoming important. However, what also occurs at these higher concentrations i 20 is that the microemulsion data begin to depart from the colloidal hard-sphere data. The viscosity in the colloidal hard-sphere system increases faster with (PHthan in the 10 microemulsion system. This deviation is consistent with the fact that (PHoverestimatesthe effective volume fraction in the microemulsion as the concentration is increased from the very dilute regime. Hence, we should seek a different effective concentration parameter in the micro23 24 25 26 27 28 29 30 31 emulsion system when we compare with the colloidal hardT ("C) sphere systems at higher concentrations. Figure 4. Temperature dependence of the microemulsion Higher Concentrations. The low shear viscosity of relative viscosity for four different samples. The samples are, a concentrated hard-sphere dispersion is characterized with decreasing amounts of surfactant and oil, given by 4, = by a divergence at a volume fraction of approximately 0.230 (0),0.117(HI, 0.056 (A), and 0.025 (+), respectively. The 0.63,which is referred to as the maximum packing fraction, solid line at 25 "C signifies the emulsification failureboundary. When the packing of the particles is considered, it As an insert is shown the temperature dependence of the observed 2Hrelaxation rate difference (taken from ref 22) is clear that it is the hard-sphere volume fraction, (PHs, through the microemulsion phase of the studied system. which is the relevant concentration parameter, with the Comparison of the AR temperature dependence with that of hard-sphere radius, RHS,being the relevant effective the relative viscosity clearly indicates that the techniques are micellar size. Thus we have chosen to plot the relative sensitive t o the same temperature-induced effects. The solid viscosity from the whole concentration range as a function line represents the emulsification failure boundary. of (PHS. This is done in Figure 3, where we have plotted the high concentrations, has been given by Q ~ e m a d a : ~ ~ microemulsion data together with the colloidal hardsphere data of van der Werff and de K r ~ i f In . ~this ~ plot we have also included data points from the microemulsion (8) obtained a t low shear rates with a cone and plate rheometer, which agrees well with the results from the Here, (Pm is the maximum packing fraction, at which the capillary viscometer. As seen in Figure 3, a very good viscosity diverges. This relation is shown in Figure 4 as correlation is obtained between the microemulsion and a solid line, where we have used (Pm = 0.63.32 the colloidal hard-sphere systems over the whole conThe highest volume fraction studied here corresponds centration range, where the microemulsion data reach up to @HS = 0.58. At this concentration the temperature of to (PHS= 0.58.39 A simple expression, which has been f o ~ n dto~ ~ * the ~ ~emulsification failure boundary has begun to drop significantly and become dependent on the concentration. describe well the divergence of the relative viscosity at
-
(39) Note that the slight discrepancy in the dilute regime where the behavior is characterized by &is invisible on this scale.
I
I
I
1
I
I
I
(40) Quemada, D. E. In Lecture Notes in Physics: Stability of Thermodynamic Systems; Cases-Vasquez, J.,Lebon, J., Eds.;Springer: Berlin, 1982; pp 210-247.
Viscosity of a Nonionic Microemulsion It is of course of interest to follow the behavior of the microemulsion further. The microemulsion phase extends up to a concentration which is very close @HS = 0.64,41 when expressed in terms of a hard-sphere volume fraction. However, it is yet unclear whether the micellar aggregates remain spherical at these higher concentrations or whether they become slightly elongated. This is ofinterest also in the context of the cubic phase formation at higher concentrations, and work is progressing in this area.
Langmuir, Vol. 10, No. 10, 1994 3453
501 40
F-
30 20
Temperature Dependence The variation ofthe relative viscositywith temperature was measured for four different concentrations, @ = 0.025, 0.056,0.117,and 0.230, respectively, in the microemulsion phase. The results are presented in Figure 4. At high dilution, the viscosity is essentially independent of the temperature in the whole temperature range. However, at higher concentrations, a temperature effect is clearly observed. Here, we can identify two distinct temperature dependencies. Close to the emulsification failure boundary, the viscosity is essentially temperature independent. The viscosity was also measured for samples cooled a few degrees below the emulsification failure boundary, where the micelles are metastable, in order to clearly demonstrate the temperature-independent lower temperature plateau. Above a certain temperature, the viscosity increases as the temperature is raised. The particular temperature above which vr begins to rise from its minimum value decreases with increasing concentration but remains above the emulsification failure boundary, 25 "C. The temperature dependence of the relative viscosity presented in Figure 4 shows a strong similarity with the temperature dependence of the relaxation rate difference, AR, observed in a recent 2H spin relaxation study, using selectively deuterium labeled C12E5, ofthe same system.22 Here, AR (= Rz - R1) is the difference between the transverse (Rz) and longitudinal (R1)relaxation rates, which is a strongly increasing function of the micellar size.22,42-44 As an insert in Figure 4, we have plotted AR, from ref 22, as a function of temperature for samples with similar concentrations. When the figures are compared, one observes a strong similarity between the temperature dependencies of vr and AR. In particular, we note the low-temperature plateau observed with both techniques and also the onsets of increases in both qr and AR occur at the same temperature. The increase in AR with increasing temperature can be attributed to micellar growth. From the strong correlation with the spin relaxation data, we may conclude that the increase in viscosity observed with increasing temperature is at least partly due to an increase of the micellar size. An increasing viscosity with increasing temperature has also been observed in a reverse micellar system with the AOT s u r f a ~ t a n t . ~ In~that , ~ ~ study the effect was attributed to attractive interactions, while the micellar size was assumed to remain constant. In the present system it is likely that attractive intermicellar interactions are present at higher temperature^.^^ This is indicated by a critical point on the upper phase boundary of the microemulsion phase and is also thought to play a role for the observed micellar to bicontinuous structural transi(41)Leaver, M. S.;Olsson, U. Unpublished results. (42)Halle, B.; Wennerstrom, H. J . Chem. Phys. 1981,75,1928. (43)Lindman, B.; Soderman, 0.;Wennerstrom, H. In Surfactant Solutions New Methods ofZnvestigation.; Zana, R., Ed.; Marcel Dekker: New York, 1987;pp 295-357. (44)Skurtveit, R.;Olsson, U. J . Phys. Chem. 1992,96,8640. (45)Bedeaux, D.; Koper, G. J. M.; Smeets, J. Physica A 1993,194, 105-113. (46)Smeets, J.;Koper, G. J. M.; Ploeg, J. P. M. v. d.; Bedeaux, D. Langmuir 1994,10,1387-1392.
10
0 15
25
17
19 21 23 Temperature ("C)
25
1
F-
a
0-
"
-
I
20
21
22 23 24 Temperature ("C)
25
26
Figure 6. Temperature dependence of the relative viscosity for two other microemulsions. (a) In the ternary ClzEdwater/ hexadecane system. The composition in weight percent is 14% C12E4,73%water, and 13%hexadecane. (b)In the quaternary CIzEs/water/cyclohexane/hexadecanesystem. The composition in weight percent is 7.0% ClZE6,83.4%water, and 9.6% oil. The weight ratio of cyclohexane to hexadecane is unity.
t i ~ n The . ~strong ~ ~ correlation ~ between the viscosity and AR data as a function of temperature indicates that the increase in viscosity is dominated by the micellar growth effects, since AR is less affected by interactions. We stress once again that the relative viscosity of a particle suspension depends on a number of factors such as the particle size and shape and concentration and interactions. To evaluate the individual effects, additional information from complementary experimental techniques has to be invoked. This is particularly important for complex systems such as microemulsions, where the microstructure can vary with the composition and the temperature. Finally, we note that the particular temperature dependence of the viscosity can also be observed in other microemulsions with the same or similar nonionic surfactants under comparable conditions. In Figure 5 we show the temperature dependence of the relative viscosity for two samples in different microemulsion systems, which have been characterized previously by self-diffusion and 2H spin relaxation experiment^.^,^ In these systems the experiments have clearly indicated a transition from oilswollen spherical micelles to a bicontinuous structure with increasing temperature as in the system studied in this paper. For these two samples the viscosity was measured with a Bohlin VOR Rheometer System. In Figure 5a, the sample composition in weight percent is 14% C12E4, 73% water, and 13% hexadecane. In Figure 5b, the sample composition, again in weight percent, is 7.0% C12E5,83.4%water, and 9.6% oil, where the oil is an equal weight mixture of hexadecane and cyclohexane. Analogous to the data of Figure 4, the viscosity decreases
Leaver and Olsson
3454 Langmuir, Vol. 10, No. 10, 1994 to a plateau value close to emulsification failure, consistent with the 2H relaxation and self-diffusion result^.^,^
demonstrated, although a very recent publication has shown reasonable agreement with solid sphere behavior for the water/AOT/isooctane system.46 Spherical micelles are formed along the emulsification failure boundary, allowing for a wide dilution range of invariable aggregates. The size of the aggregates can be varied by varying the surfactant to oil ratio or, alternatively, the surfactant to water ratio in the case of an oil dilution line together with a corresponding change in the spontaneous curvature (eq 2). For small micelles the ratio of RHand RHSto the droplet radius will be significantly larger than unity. With increasing micellar size, these ratios are expected to decrease. The ratios may also be varied by varying, for example, the oligo(ethy1eneoxide) length of the surfactant. Increasing the temperature away from the emulsification failure boundary results in an increase in the relative viscosity. Here, the results show a striking correlation with previously obtained NMR relaxation data from the same system. From this correlation, the viscosityincrease can be attributed to a micellar growth.
Concluding Remarks The viscosity measurements of a nonionic microemulsion along the emulsification failure boundary presented here show a quantitative agreement with the behavior of colloidal hard-sphere systems. An important property of the microemulsion droplets is that they are described by two radii, rather than a single radius. This is a consequence of the relatively thick stabilizing "end-grafted" surfactant ethylene oxide polar chains at the surface of the droplets. This results in a significant difference between the observed hydrodynamic (RH) and hard-sphere (RHs)radii. However in the colloidal silica and latex systems, used for comparison purposes here, the droplet size is much larger than the stabilizing layer; hence the hydrodynamic and hard-sphere radii are considered to be equivalent. The high dilution viscosity results from the studied system follow the SaitB relation, where the effective micellar size is given by the hydrodynamic radius, RH.At higher concentrations, where interactions become imAcknowledgment. We are grateful to Anders Carlsportant, very good quantitative agreement with results son for his help with the viscositymeasurements presented from colloidal hard-sphere systems is obtained when the in Figure 5. Valuable discussion with Bengt Jonsson are effective micellar size is given by the hard-sphere radius, kindly acknowledged. This work was supported by the RHS. Microemulsion viscosity, with reference to hard-sphere Swedish Natural Science Research Council. M.S.L. systems, has been reported previously in the l i t e r a t ~ r e . ~ ' - ~ ~acknowledges a grant from the Swedish Institute. However, quantitative agreement over an extensive concentration range has, to our knowledge, not been (49)Gradzielski, M.;Hoffmann, H. Adu. Colloid Interface Sci. 1992, ~~
(47)Majolino, D.;Mallamace, F.; Venuto, S.; Micali, N. Phys. Rev. A 1990,42, 7330-7339. (48)Attwood, D.:Currie, L. R. J.: Elworthv, P. H. J . ColloidInterface Sci. 1974,46, 261-265.
~
~
~~~~~
42. ._ , 149 (50) Berg, R. F.; Moldover, M. R.; Huang, J. S. J . Chem. Phys. 1987, 87,3687-3691. (51) Quemada,. D.:. Lanpevin. . D. J . Mec. Theor. Avvl. .. 1986. numero special, 201-237.
