The Journal of
Physical Chemistry
0 Copyright, 1982, by the American Chemical Society
VOLUME 86, NUMBER 17
AUGUST 19, 1982
LETTERS Temperature Dependence of Size and Polydispersity in a Three-Component Microemulsion by Small-Angle Neutron Scattering Mlchael Kotlatchyk,' Sow-Hsln Chen, Nuclear Enginwflng Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02 139
and John S. Huang Emon Research and Engineering Company, Linden, New Jersey 07036 (Received: May 7, 1982; I n Final Form: July 1, 1982)
The temperature dependence of the size and polydispersity of the water core in a pure three-component microemulsion consisting of decane + AOT + D20has been observed by small-angle neutron scattering. A t each temperature, as the molar ratio X = [DzO]/[AOT] is varied from 8 to 49, a linear increase in the radius is observed from about 25 to 90 A. The extrapolated value of the radius at vanishing water concentration is nonzero, indicating substantial water penetration into the charged head group region of the inverted micelle. From the slope and extrapolated radius of this line we can deduce the effective area and volume occupied by the hydrated head group at each temperature. The polydispersity in size is appreciableeven at room temperature and it increases steadily as the temperature is raised. The Q dependence of the intensity distribution does not follow the Ornstein-Zernike form, but instead it can be well described as scattering from a collection of polydispersed spheres as the critical point (37 "C for 6% DzO) is approached.
Introduction Microemulsions have been studied in the past few years with both quasi-elastic light scattering (QELS)ld and (1)R. A. Day, B. H. Robinson, J. H. R. Clarke, and J. V. Doherty, J. Chem. SOC.,Faraday Trans. 1 , 7 5 , 132 (1979). (2) M. Zulauf and H. F. Eicke, J. Phys. Chem., 83, 480 (1979). (3) A. M.Cazabat, D. Langevin, and A. Ponchelon,J.Colloid Interface Sci., 73, 1 (1980). (4) D. J. Cebula, R. H. Ottewill, J. Ralston, and P. Pusey, J. Chem. SOC.,Faraday Tram. 1 , 77, 2585 (1981). (5)J. S.Huang and M. W. Kim, "ScatteringTechniques Applied to Supramolecular and NonequilibriumSystems",S.H. Chen, B. Chu, and R. Nossal, Ed., Plenum Press, New York, 1982,p 809.
small-angle neutron scattering (SANS).68 Because conventional theory predicts that microemulsions are stable near room temperature: most studies have been performed in the neighborhood of T = 298 K, where the temperature dependence of the microemulsion droplet structure is expected to be weak. However, within the past year, re(6)C. Cabos and P. Delord, J. Appl. Crystallogr., 12, 502 (1979). (7)C. Cabos and P. Delord, J. Phys.-Lett., 41, L-455 (1980). (8)M.Dvolaitzky, M. Goyot, M. Lagiies, J. P. Le Pesaut, R. Ober, C. Sauterey, and C. Taupin, J. Chem. Phys., 69,3279 (1978). (9)D. J. Mitchell and B. W. Ninham, J. Chem. Soc., Faraday Trans. 2,77, 601 (1981).
O022-3654/82/2086-3273$0l.25/O0 1982 American Chemical Society
3274 ,.-T-/
The Journal of Physical Chemlsby, Vol. 88, No. 17, 1982 surfactant tails
'C 0"0'
CH
CH2 CH
$4
\CH(
$H3
CH2-CH3
I I!
I
Aerosol
(a1
- OT
( b )
Flgurr 1. (a) Inverted spherical micelle and proflle of the scatterlng length density: p , = 6.342 X ioa Am*,ps = -0.490 X ioa A-2. (b) AerosoCOT molecule.
p ~ r t s ' ~have J ~ emerged on two microemulsions which describe an apparent critical behavior as the temperature approaches cloud points in certain areas of the phase diagram.5 Specifically, for the oil-rich phase of the AOTwater-decane system, QBLS measurementa5J0have shown that the hydrodynamic radius of the inverted micellar droplet increases as
T,- T -*
Rh
= Ro(
T)
where Ro N 12.2 A and v N 0.75. The AOT-wateldecane system is particularly interesting because it forms one of the few pure three-component microemulsions near room temperature. Conveniently, the cloud point is found to be a t about T,= 309.2 K for the oil-rich phase. From light-scattering measurements,10 it is suggested that an increased polydispersity near T,may play an important role in the critical behavior of microemulsions. Conventionaltheory of microemulsion stabili@J2 predicts that the polydispersity of size is on the order of only a few percent, the exact value depending on the magnitude of the oil-water interfacial tension in the presence of surfactant.12 It is known that the interfacial tension decreases substantially upon approaching the critical point.13 This would imply that polydispersity should increase substantially. Experimental data indicating such an increase in polydispersity as a function of temperature have been absent in the literature. One of the main objectives of this Letter is to present experimental evidence for such a behavior. The size range of the inverted micelles and the high contrast between the D20 core and the surrounding surfactant tail and oil phases suggest that the SANS technique should be sensitive for studying the polydispersity in the AOT-water-decane system. Figure l a shows the conventional picture of an inverted swollen micellar droplet, along with the neutron scattering-length density profile. For a complete water penetration of the AOT head (10)J. S. Huang and M. W. Kim, Phys. Rev. Lett., 47, 1962 (1981). (11)R.Dorahow, F. de Buzzaccarini, C. A. Bunton, and D. F. Nicoli, Phys. Rev. Lett., 47, 1336 (1981). (12)J. N. Ieraelachvilli, D. J. Mitchell, and B. W. Ninham, Bioehim. Biophys. Acta, 470, 186 (1977). (13) M. W. Kim, J. S. Huang, and J. Bock, SPE Proceedings, SPE/ DOE 10788,1982.
Letters
group, it is expected that the change in scattering-length density due to the head group should be small and the neutron scatterhg will see a single sharply contrasted sphere of radius R. It is thus possible to study the size of the water core as a function of [D20]/[AOT] ratio at various temperatures. This information, as described below, gives a unique measurement of the effective headgroup area at a specified temperature. Using only a few basic assumptions, one can relate the radius of the water core I? to the molar ratio X = [DzOI/[AOTl: a0 a0 where v D , ~is the specific volume of a D20 molecule, VH is the volume of the water-penetrated portion of a single AOT head group, and a. is the area per AOT head group on the water-core surface. This equation was derived under the following assumptions: Water penetrates into the AOT head-group region; the AOT molecules form a single layer of surfactant on the water-core surface; and a. is constant. Experimental verification of this equation would substantiate the fundamental concept that there is a unique, optimal head-group area at a given temperature and ionic strength. Such a quantity has been operational in the theory of micelles, vesicles, and microemulsions, being derived from the concept of mutually opposing for~es.~J~ Experimental Section Samples. The three-component microemulsion was prepared from 3% (wt/vol) AOT in n-decane containing varying amounts of D20. The molar ratio [D20]/[AOT] was varied from 8 to 49. Our AOT, obtained from American Cyanimide, was twice recrystallized from methanol and the n-decane was a 99%+ gold label product from Aldrich Chemical Co. The heavy water used contained 99.7% D2O and 0.3% H20. SANS Measurement. Small-angle neutron scattering was performed at the high-flux reactor of the Brookhaven National Laboratory. The spectrometer beam was derived from a cold neutron source moderated by liquid hydrogen. The wavelength selected was h = 5.01 A. A 128 X 128 element two-dimensional position-sensitive proportional counter was used for neutron detection. It had a pixel size of 1.59 mm X 1.62 mm. The entrance pinhole of the spectrometer was 12 mm and the sample pinhole was 6 mm, with a mutual distance of 160 cm. The sample-todetector distance was 150 cm. This gave an available Q range of 0.013-0.100 A-l; Q = (4?r/h) sin 8/2, where 8 is the scattering angle. The measured neutron flux at the sample was 8.8 X lo5 neutrons cm-2 s-l. Samples were contained in disk-shaped cells with l-mm thick quartz windows, The sample thicknesses were also 1 mm. Measured transmission of the samples ranged from 50 to 52%. Temperature was controlled by an external waterbath. I t was monitored and stabilized to within f0.1 degree with a solid-state sensor. The counting times ranged from about 20 min for a sample containing 6% D20 (X= 48.96) to about 1h for a sample containing 1%D20 (X= 8.16). Pure n-decane was used both for a detector sensitivity calibration and for incoherent background subtraction. An on-line computer performed a radial average of the two-dimensional array of data, giving values of the relative scattering intensity vs. Q. (14)C. Tanford, 'The Hydrophobic Effect",Wiley, New York, 1973.
The Journal of Physical Chemistry, Vol. 86, No. 17, 1082 3275
Letters
(A) Data, X=4896,T=306,5K
- - _ - ff = 8 9 , 9 A , s : O - R = S 9 , 9 A , # 1.312
(8) IO-
Dato,X=244S,T:3065K
L
t
Flgure 3. Scattered intensity vs. Q 2 for two temperatures at X = 48.96. The solid llnes represent Guinier plots determined by R; = ( 3 / p ( R 2
+
U2)1'*.
TABLE I: Mean Radius (E) and Polydispersity (o/R)of the D,O Core at Various D,O Concentrations and Temperaturesa
-
R (oix)
X 8.16 24.48 32.64 40.80 48.96
T = 298 57 (0.22) 67 (0.22) 7 8 (0.23)
T = 306.5
T = 301.6 24 45 58 70 81
(NF)
26 50 65 78 90
(0.27) (0.24) (0.25) (0.26)
(NF) (0.34) (0.30) (0.31) (0.31)
a N F denotes that no polydispersity fit was obtained due to lack of statistical accuracy in the data.
P(QR) is the form factor for a sphere of radius R, with j , ( x ) being the spherical Bessel function of order one and f(R) is the Gaussian distribution function for mean particle radius R and width parameter u. By using a series expansion for the particle form factor P(QR) = 1 - f/5(QR)' + (4)
*.
in the limit QR
< 1, we can write
Comparing eq 5 to the usual Guinier expression (Z(Q)/Z(O) = e~p(-'/~Q~R,2)) for the scattered intensity at small Q results in R,2 = 3 / ( R 2 ) (6) where R is the effective radius of gyration of the polydispersed sphere. If we assume that R 5 3u and that f(R)
= f(R - R ) is a symmetric function of R - R , it is easy to show that
(R2) = R2
+ u2
(7)
This means that the radius of gyration obtained from the Guinier plot of In Z vs. Q2 will not be equal to (3/5)1/2R. Rather, it will be given by (3/5)1/2(R2 u2)1/2. Instead of making use of only the small Q region to determine particle size, as most other authors have done>!' we used the complete intensity distribution of eq 3 and performed a nonlinear least-squares fit. The fitting procedure consisted of searching R,u space for the minimum value of the variance between the intensity data and the fitted Z(Q) curve. The solid curves in Figure 2 show typical results from the fitting procedure for the best values of R and u. The dashed curves are obtained with the same R but with u set equal to zero. This gives an indication of the substantial effect of incorporating polydispersity into the data analysis. Figure 3 shows examples of two Guinier
+
3278
The Journal of Physical Chemistry, Vol. 86, No. 17, 1982
90r
Letters
Conclusions Our data show that the effective head-group area per surfactant molecule remains constant as X is varied from 28 upward to 49. At T = 298 K, the area is approximately 69 A2, which compared favorably with theoretical estimates by Israelachvilli et al.15 This value decreases as the temperature is raised, signifying a closer packing of the surfactant tails. However, for data taken with X 5 8 as shown in works by Day et al.' and Cabos et al.? the effective area at 293 K seems to decrease to about 38 A2. Since (see eq 2)
/
dR/dX = 3vD,o/ao 0'
I3
I 20
J 30
40
50
X = [DzO]/[AOT]
Figure 4. Mean radius ( R ) vs. molar ratio ( X ) for three temperatures.
TABLE 11: Area ( a o ) and Water-Penetrated Volume (V,) of a Single AOT Head Group for Three Temperaturesa
298.0 301.6 306.5
68.7 64.1 56.9
311 256 236
4.2 3.9 3.8
a rH is the estimated head-group radius based o n a spherical head completely penetrated with water. rH = [ 3 v H / ( 4 R ) l ' '.
plots, using expressions 6 and 7 for determing the radius of gyration. Table I is a summary of the values of R and a / R for a range of values of the molar ratio X at three different temperatures in the vicinity of the cloud point. The values of R increase with both temperature-and molar ratio X. The percentage polydispersity u / R increases as the cloud point (T = 309.2 K) is approached. It is interesting to notice that u / R is approximately constant at each temperature for a wide range of X values. Figure 4 is a graph of R vs. X for the three temperatures measured. The data seem to indicate a linear relationship, as hypothesized by eq 2. Using the value UD@ = 30.15 A3, we were able to estimate a. for each temperature based on the slope of each line. VH could then be estimated on the basis of the R intercept and the previously obtained value of ao. The values of a. and VH are summarized in Table 11. Also included are estimated values of the head-group radius rH, assuming a spherical head-group volume. The values of a. compare favorably with those estimated by other workers.6 The numerical results indicate that the assumptions leading to eq 2 are reasonable ones.
(8)
the increase in slope, as observed by these authors, may signify an increase in the specific volume of D20,rather than a decrease in ao. This is plausible, since at small water-to-surfactant ratios the structure of the water core does not have to follow a bulk water structure. Instead, it could take a more open structure. The aggregation number ri for the inverted micellar drop is determined by fi = 4?rR2/ao. The values obtained (e.g., rt = 113 at T = 301.6 K and X = 8.16) compare favorably with those quoted by other authors.6 The origin of the observed increase in polydispersity as a function of temperature may be understood from the thermodynamic theory of microemulsion ~ t a b i l i t y .Ac~ cording to this theory, the percentage polydispersity is expected to vary as (KBT/y)'12,where y is the interfacial free energy. It is known that y decreases rapidly as the system approaches the critical point and, as a result, the polydispersity increases. We also attempted to fit the intensity data to the Ornstein-Zernike form, such as used by Huang and Kim! For all cases studied, the data do not conform to this form. Thus, we conclude that, as the microemulsion approaches the critical point, it behaves like a collection of polydispersed spheres. It is important to observe that SANS data give the sizes of the inverted micelles to be about a factor of 2 smaller than the hydrodynamic size as measured by QELS. For the Q range probed by QELS, it is possible that the measured hydrodynamicradius is related to the correlation length of clusters of micelles, rather than the size of an individual sphere. If we extend our SANS measurement to include data at smaller Q, eventually we may find a region where the intensity distribution crosses over into the Ornstein-Zernike form. Such an experiment is being planned for the near future. (15) J. N. Israelachvilli,D. J. Mitchell, and B. W. Ninham, J. Chem. SOC.,Faraday Trans. 2, 72, 1525 (1976).
