1532
J. Phys. Chem. 1980, 84, 1532-1535
A Structural Description of Microemulsions. Small-Angle Neutron Scattering and Electrical Conductivity Study M. Dvolaitrky, M. Lagues, J. P. Le Pesant, R. Ober, C. Sauterey, and C. Taupin” Physique de la Mati&-e CondensBe, E.R.A. 542 du Centre National de la Recherche Scientifique, Coll4ge de France, 75231 Paris Cedex 05, France (Received August 1, 1979) Publication costs assisted by DBlBgation G6nBrale 1 la Recherche Scientifique et Technique
We performed a structural study of microemulsions. Both diluted (low water-to-oil volumic ratio) and concentrated systems were studied. The experimental techniques used were as follows: analytical centrifugation, small-angleneutron scattering, viscosity, low-frequency conductivity. Systems with various droplet sizes were examined. The dilute systems are well described by a dispersion of minute water droplets in an oily continuous phase. New information has been obtained about the distribution of the various components in the interior of the droplet. One can defined an hydrodynamical volume, penetrated by the continuous oily phase and a nonpenetrated “hard-sphere’’shell of about 9 A thick. The neutron-scattering technique proved to be very powerful even for concentrated systems;we were able to show that it is possible to fill the space with droplets up to a fraction of 0.64 without changing their internal structure. Above this density, which corresponds to the random packing one, the structure becomes inverted (w/o o/w). Low-frequency conductivity was measured over a wide range of concentration. Its variation exhibits the behavior of a percolating system, the conduction being confined to the interfacial film. Values of the percolation threshold and of the percolation exponents fit satisfactorily with existing theories. The structural inversion is correlated with a break in the conductivity curve.
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Introduction Microemulsions are transparent fluid systems usually composed of amphiphilic molecules and two otherwise immiscible components such as water and oil. The most common idea about these systems is that they are made by an extreme dispersion of one component (water or oil) in the other. This dispersion is very fine (ca. 100 A) to explain the transparency of the system. A film of amphiphilic molecules separates the two phases. It is often necessary to associate two types of amphiphilic molecules, a true one such as sodium dodecyl sulfate (SDS) and a poorer one such as an alcohol (pentanol), to build a microemulsion. One usually considers that the pentanol partitions between the interfacial film and the oily phase. One characteristic feature of microemulsions is their wide domain of existence in the pseudoternary phase diagram (oil-water-amphiphilic molecules). Many theoretical p a p e r P deal with the properties of these systems but only a few experimental studies have been published to describe their structure. This determination is clearly not simple since few physical techniques are useful with these nonorganized systems. Moreover, due to the wide composition domain of existence of these systems, it is necessary to choose a significant path in the quaternary diagram. Since it is known3 that the oil-rich (“diluted”) systems are made by the dispersion of water droplets in an oily continuous phase we chose to study several different diluted systems and then, by maintaining the soap/water ratio constant, to increase the volumic fraction of water. Small-angle neutron scattering and, particularly, the “variable contrast technique” proved to be a good test for the structure of the elementary object during the concentration process. We present here results obtained with water-cyclohexane microemulsions. In the dilute domain, we used viscosity, sedimentation, and small-angle neutron scattering to obtain informations about the water core radius (which is related to the area per polar head of the soap) and the distribution of components in the interfacial film. 0022-3654/80/2084-1532$0 1.OO/O
In the concentrated region, electrical conductivity measurements indicate a percolation behavior followed as the concentration is increased above the random packing fraction density by structural inversion (w/o o/w).
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Oil-Rich Systems Centrifugation. Ultracentrifugation experiments were performed on a Model E Beckman analytical centrifuge, and sedimentation profiles were recorded by the schlieren technique, which records the variation of the refraction index gradient dn/dR vs. the distance R to the axis of rotation. In our case, this index gradient is essentially due to water droplets. The analysis of the experiment is well known. A rigid and spherical droplet of mass M and hydrodynamic radius rh, in a fluid of density p and viscosity 7, is subjected to a driving force Fd due to the centrifugational field u2R:
which is balanced by a frictional force Ff:
Ff = 6?rqrhV where V is the speed of the droplet. Figure 1 presents a typical pattern obtained at 48 000 rpm for two microemulsions of same composition; the upper and lower traces correspond respectively to protonated and deuterated cyclohexane. The replacement of C6H12 by C6DI2modifies the driving force of sedimentation in two different ways: one is the increase of buoyancy by the change of density of the continuous phase and the other is the change of mass of the sedimenting object which is proportional to the fraction of cyclohexane in the interfacial film. The values of the two sedimentation coefficients, for protonated and deuterated microemulsions, associated with the measurement of the viscosity (time of flow through a capillary) permitted us6 to obtain the composition of the “hydrodynamical droplet”. The 0 1980 American Chemical Society
Structural Description of Minoemulsions
m Journal of r n y s i d chern/stry, vol. 84, NO.
12, 1980 1599
TABLE I: Summary of Data for Three Types of Microemulsions (A, B, and C) Corresponding to Increasing Amounts of Solubilized Water
microemulsions soap-water vol ratio
A 0.69
B
C
0.345
0.23
100 9 0.2 3.6 f 0.2
100 18 0.3 2.8 f 0.2
100 39 0.45 2.3 f 0.2
continuous phase
composition (by vol)
C6H,, CAOH H,O
t C
(rh3lrw)
UHracenMfylepatterns obtalned wim two "E type" miuoemulsions (see Table I) wlth the followingdiiutlon: 5 0 1 oil-to-water by volume. On the upper trace the oil is C,H,, and on the lower traau, is C,D,,. In region A (on the iefl of the sedimentation peak). there is c%t,' the omllnuars phase. in region E appoxhiety the inilial &opW concentration. and in region C a high concentration of sedimented droplets.
sedimentation Technique
Ffgure 1.
up
pc
.
Fgw 2. schematic representah of the varfws types of contrast used hhsmabangle neubon SCanedq .-e The lower part of the iigure represents, on the same scale. the model for a droplet. he mean scattering iengmS per unn vohm are in 10'' cmP.
results showed a profound penetration of the continuous phase in the interfacial film and the presence of an excess amount of alcohol in the interface. The study of the width of the sedimentation peak indicates a spread of 5% on the radius of the water droplet. Small-Angle Neutron Scattering. A powerful characteristic of neutron scattering is the poasibdity to enhance selectively the scattering power of various parts of the object by using protonated or deuterated molecules. Moreover, the study of the coherent scattering CIOSS section at zero momentum transfer as a function of variable contrast gives information about the internal structure of the object.' Figure 2 represents the three different types of contrast which we used in these experiments. Scattering length per unit volume (10'O cm-l) is plotted as a function of the distance to the droplet center! Case a where heavy water, pentanol-0-d, and protonated cyclohexane are used permits us to determine the dimension of the water core. As the scattering length of the sulfate part of SDS is not very different from that of heavy
rw, A
rh. A rh- ;w, A
A,
a
34 52 18 52.5
56.5 79.5 23 68
83 110 27 66
Neutron Scattering Technique
rw, A
34.5 46.5 1.25 12
53 62 1.16 9
1.11 9
water, in fact we measure the radius of the (water + polar head) core rv Case b uses the HzO-CPlzsystem, and at first glance one could think that it would give the "total" radius of the droplet, i.e., water plus the interfacial film. In fact one cannot eliminate the possibility of penetration of this film by deuterated cyclohexane, and the radius which is measured with this contrast is the radius of gyration of the protonated core and is related to the discontinuity of composition between the droplet and the continuous phase, corresponding to a radius r,, which is smaller than the hydrodynamical radius r, previously determined. When such measurements are performed at various concentrations, one can deduce the second virial coefficient of the osmotic compressibility. In agreement with light beating spectroscopy measurements on other systems? this coefficient reveals a small attraction between particles. Contrast c uses both DzO and various CBHI1-CsDI1 mixtures; the coherent scattering cross section at q = 0 is plotted as a function of the scattering length of the protondeuteron mixture. Figure 31a shows a typical experimental result. The position of the minimum of intensity is related to the ratio of the scattering volumes, i.e., (rC/rJa. The deepness of the minimum is related to the polydispersity of the system. Description of the Elementary Droplet. Table I summarizes the results obtained with these two different a p proaches, corresponding to two trpes of measurements: (I) viscosity and centrifugation experiments consider the droplet as a hydrodynamic4 object; (11) neutron scattering is sensitive to the differences in chemical composition of the various shells of the droplet. Both methods agree on the size of the water core r.. From r., one can calculate the area A per polar head of the SDS molecule which increases with the water content a t low water content but reaches a limiting value of 66 Azat high water content. The relatively small variation of A, about 20%,when the soap-water ratio x varies by a factor of 3, reveals that this quantity is probably a determining factor in the geometry of the droplets. It is interesting to note that the limiting value for A is not very different from the value of 65 A2 obtained for micelles.'0 With type I measurements one defines a hydrodynamical interface. Information obtained about its composition shows that it contains an important amount of cyclohexane which is approximately independent of the amount of solubilized water. In contrast, the quantity of alcohol in the interfacial film is dependent on the soapwater ratio.
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The Journal of Physical Chemistty, Vol. 84,
No. 12, 1980
Dvolaitzky et at.
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i
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-8-
I
11
Flgure 3. The square root of the extrapolated zero angle scattering intensity is plotted vs. the volume fraction of deuterated compound: (a) CBH1z-CBD1z mixture, (b) H20-D20 mixture; (I) a, = 0.017, (11) @, = 0.38.
When the amount of solubilized water increases the quantity of alcohol increases, reflecting the variation of the area per polar head. The limiting value of the soap-water ratio corresponds to about two molecules of 1-pentanolper SDS molecule. It is reasonable to suppose that the excess alcohol is anchored at the water interface between the SDS molecules. With this model of a mixed film of alcohol and surfactant one can introduce an equivalent thickness rc r, which is given in Table I. This thickness is compatible with the lengths of the SDS and alcohol molecules which are respectively about 21 and 9 A, and decreases when the amount of alcohol increases. On the other hand, these results may be compared to those obtained from a recent light-scattering study on a similar system.’l The authors have determined a “hard-sphere” radius which is different from the water radius by 8-9 A.
Concentrated Microemulsions Structural Inversion. Most of the structural techniques, such as neutron or X-ray scattering give, in the case of concentrated systems, information which is a mixture of elementary particle structure and interparticle correlation effects. As in the case of microemulsions a continuous change of the droplet during the concentration process is not excluded; we had to avoid this difficulty. The variable contrast technique, which uses measurements at constant concentration, proved to be a fine test of the structure of the droplet. Several points should be noted. (a) The range of variation of p , which in our case can be pWahor pail, is usually limited by chemical considerations
and it may not be possible to reach the point of zero contrast (parts Ib and IIa of Figure 3). In this case, the extrapolation of the curve [i0(p)]1/2 still gives the zero contrast value of p, but with a poorer precision. (b) The depth of the minimum is related to polydispersity of the system; a quantitative correlation is difficult to find but qualitative information may be obtained. (c) When the condition of zero contrast is fulfilled, the value of the scattering length of the external phase is necessarily intermediate between the two other values. This provides an easy way to determine the external phase or detect a phase inversion. Figure 31 shows the experimental results obtained for a diluted microemulsion (labeled as type B in ref 6, water-soap ratio of 2.5 by weight) with two different variable contrasts. The two types of contrast, a and b, give the same value for r,,/r,. Figure 311 shows that for water volume fractions 9, greater than 0.34, the aspect of the variable contrast curve is completely different; with the C6H12-C6D12 mixture, one does not reach a minimum. If a C6D12, H20-D20 contrast is used it is possible to reach a minimum. This shows that for these high concentrations the external phase is the aqueous phase, revealing a phase inversion. This phase inversion in microemulsions has been frequently supposed to occur in these systems but without definite experimental proof. It has to be noted that the variable contrast curve of Figure 311 indicates a higher polydispersity of the particles in the inverted phase. Some polydispersity also appears just before the inversion point.
The Journal of Physical Chemistry, Vol. 84, No. 12, 1980 1535
Structural Description of Microemulsions 1
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l d
1-17-17
01
02
03
04
111
Flgure 4. Variatlon of the conductivity of a microemulsion (logarithmic plot) vs. water concentration.
Percolation. Electrical conductivity measurements were performed at 20 k 0.1 “C with a 600-Hz ac current to avoid electrophoresis. Figure 4 presents the variation of the conductivity of the type B microemulsion as a function of water concentration. I t increases steeply (two orders of magnitude) between a, = 0.06 and a, = 0.09; in this concentration range the droplets fill around 15% of the space which is the theoretical value of the percolation threshold for hard spheres.12 This led us to use percolation theory to describe our results. Let us recall that the percolation concept applies to a random spatial distribution of identical objects; above a critical value aCof the volumic concentration of objects, an infinite path appears through them. Various physical properties of the system, for instance, the mean conductivity, vary steeply around the percolation threshold a,, obeying universal laws independent of the detailed physical properties of the system. In the following, we analyze successively the concentration dependence of the conductivity above and below this threshold. (1) In the region above and in the vicinity of the percolation threshold, numerical simulation and theory predict a power law12 of G(@,) = GO(@,
-. @ J t
(4)
where aCis the percolation threshold and the exponent t is around 1.6. The analysis of the data give t = 1.55 f 0.1 and a,, = 0.078 f 0.002. The part of space filled by the droplets is, in fact, due to the water and the corresponding volume of the interphase determined by the “hard sphere’’ radius rc. The volumic fraction filled by the droplet is in fact 0.14 which is in agreement with the value of 0.148 for a fccub paclking.12 This agreement,, especially that of the exponent, confirms the validity of the percolation model. At aP = 0.332, which corresponds to the structure modificatioin observed by neutron scattering, the curve of Figure 4 exlhibits a break and the conductivity increases more rapidlly. The part of space C, filled at aPby the droplets is CP = 0.630, which should be compared with the random packing volume fraction for hard spheres (0.637).13 It has to be noted that at the percolation threshold the aqueous core of the droplets remain completely discon-
nected. Conduction in the interfacial film seems to be the principal mechanism for aW < aV (2) The determination of the exponent (1.2) below the threshold revealed disagreement with both effective medium theory (1.0) and lattice simulation (0.7). It was recently shown by Lagues14that the experimental exponent is found if one takes in account the Brownian motion of the droplets (“stirred percolation” model).14 Concluding Remarks This study lead us to a precise description of the structure of the water droplet in microemulsions. The hydrodynamicvolume is penetrated by the oily continuous phase, but there is a cyclohexane nonpenetrated part of the interfacial film,containing both soap and alcohol which determines the hard-sphere radius of the droplet. The size of the aqueous core is mainly determined by the area per polar head of the soap. It is possible to increase the number of the poorly interacting droplets without changing their structure. At a volume fraction around 0.15 they exhibit a percolative interfacial conductivity and at 0.6 the structure becomes inverted (w/o o/w). The next steps for microemulsion studies seem to us to be a comprehensive study of the interactions between the water droplets and a better understanding of the inverted (o/w) systems.
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Acknowledgment. It is a pleasure to acknowledge the people who contributed to this study which was initiated by a suggestion made by Professor P. G. de Gennes. An important part of the neutron-scattering experiments was performed in the laboratoire Ldon Brillouin at the CEA of Saclay with the participation of J. P. Cotton. This work was also made possible by the allocation of beam time on the D11 apparatus at the Institute Laue-Langevin (Grenoble, France). We are grateful to Dr. Haas, Dr. Goeltz, and Dr. Dianoux for many discussions about the use of the apparatus. Ultracentrifugation measurements were made in the Laboratoire de Biochimie Cellulaire (CollBge de France, Paris) with essential help from Dr. C. Oriol. Many discussions with Professor D. Quemada (Paris) helped us to understand the viscosity measurements. This investigation was supported by a research grant from the Ddldgation Gdn6rale A la Recherche Scientifique et Technique. References and Notes T. P. Hoar and J. H. Schulman, Nature (Paris), 152, 102 (1943). J. H. Schulman and J. B. Montagne, Ann. N. Y . Acad. Scl., 92, 366 (1961). L. M. Prince, “Surfactant Science Series”, Vol. 6, Part I, K. J. Llssant, Ed., Marcel Dekker, New York, 1976, Chapter 3. E. Ruckenstein and J. C. Chi, J . Chem. Soc., Faraday Trans. 2, 71, 1690 (1975). A. Skoulios and D. Guillon, J. Phys. (Paris) Left., 38, L 137 (1977). M. Dvolaltzky, M. Guyot, M. LaguBs, J. P. Lepesant, R. Ober, C. Sauterey, and C. Taupin, J. Chem. Phys., 69, 3279 (1978). H. B. Stuhrmann, J . Appl. Ctysrallogr., 7, 173 (1974). Two experimental points have to be noted. (1) The system contains lablle protons, two per water and one per pentanol molecule. The exchange between D20and pentanol-0-h causes a decrease of the contrast of the water core by a factor of 4 in the diluted systems. To avoid thls, we used pentanol-0-dso that the water core of the droplet remains fully deuterated. (2) The hydrocarbon part of the tensioacthre molecules (SDS and I-pentanol) was always protonated. A. Graciaa, P. Chabrat, J. Lachaise, L. Letamendia, J. Rouch, C. Vaucamps, M. Bourrel, and C. Chambu, J. Phys. (Paris) Lett., 38, L 253 (1977). F. Reiss-Husson and V. Luzzatl, J. Phys: Chem., 88,3504 (1972). W. G. M. Agterof, J. A. J. Van Zomeren, and A. Vrij, Chem. Phys. Lett., 43, 363 (1976). S. Kirkpatrlck, Rev. Mod. Phys., 45, 574 (1973). J. L. Finney, Nature (London), 268, 309 (1977). M. Lagues, J. Phys. Lett., 40, L-331 (1979).
