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S. K. Ghosh et al.
Bull. Chem. Soc. Jpn. Vol. 82, No. 6 (2009)
667
Table 2. Characteristic Scale Length D, ², and Disordered
Parameter 1/¬², Extracted from the Best Fit to the
Teubner-Strey Theory (eq 1) of the Observed Data
(298 K), for the Fresh Samples (B: Negative Coefficients
in Relative Units and Subscript: 1, Disordered
Microemulsion)
5
4
3
2
1
0
X = 3.7
X = 9.5
X = 20.1
X = 27.0
X
D1/¡
²1/¡
B
1/¬²
1
3.7
9.5
20.1
27.0
83.20
120.48
157.81
178.30
25.99
43.91
72.51
80.64
¹0.13
¹0.15
¹0.24
¹0.25
0.51
0.44
0.35
0.35
also shown in Figure 2 (solid lines) and the values of D1, ²1,
and 1/¬² are listed in Table 2. The parameters D1 and ²
1
1
0.02 0.04 0.06 0.08 0.1 0.12 0.14
increase with increasing X, implying that an increase in the
amount of solubilized water induces an ordered structure in the
q /Å-1
ternary system. Since a larger value of 1/¬² corresponds to a
1
Figure 3. Observed SAXS profiles of the aged samples and
calculated curves (solid lines) of best fit to the Teubner-
Strey model (eq 4).
more disordered structure, a decrease in the value of this
parameter implies an increase in the extent of ordering in the
system. An increase in X brings about an increasingly ordered
structure in the reversed micelles (Table 2), indicating that
polydispersity decreases with increasing X.
micelle and the peak at high q to the first-order peak coming
from the stacking structure of a lamellar. The second-order
peak was not observed, probably suggesting that there is no
long range correlation between fluctuations of the surfactant
concentration or the scattering from fluctuation of the surfactant
concentration was so small that it was not possible to separate it
from the background scattering. A sharp Bragg peak at high q
allows calculation of the repeat distance of a lamellar for each
sample: assuming a repeat distance (D1) of 2³/q, D1 = 76 ¡
for X = 9.5 and D1 = 90-105 ¡ for X = 20.1 and 27.0.
The Teubner-Strey model21 has also been applied to a
comparison of the extent of ordering in the aggregational
systems for the aged and fresh samples. It is emphasized that
the same theoretical model has been used so as to ensure
validity of the comparison.
Teubner and Strey21 suggested that their model may explain
the ubiquitous appearance of the lamellar phase in the vicinity
of the microemulsion. Vonk, Billman, and Kaler24 presented a
model in which the microstructure of a bicontinuous micro-
emulsion is taken as that of a distorted lamellar structure
with alternating water and oil layers separated by surfactant
monolayers. Indeed, the lamellar repeat distance, calculated
using this model, is almost exactly equal to the periodicity,
D, of the domain size extracted from the Teubner-Strey
model.10 Therefore, when we use the Teubner-Strey model
to analyze the Bragg peak arising from a lamellar, the
extracted periodicity, D, may be used as an indicator of the
repeat distance between the two water or oil domains in a
lamellar structure.
The hydration number (X) of an AOT molecule is 2-13,
depending on the method used for its determination: IR
and NMR studies: 2-322a and 3.5,22b differential scanning
2
calorimetry, ESR spin labelling, and H NMR: 2-13,22c and
2H NMR spin-lattice relaxation study: 6.18 We assume that the
hydration number of SDOleS having the same polar groups as
AOT is 3-4.
Thus, for the fresh sample with X = 3.7, water molecules are
probably bound on the polar heads (SO3 Na+) in the reversed
¹
micelles, while for that with X = 9.5, water molecules other
than bound water may form a very small water pool within a
small aggregate in decane. In these microemulsions, SDOleS
molecules probably form a small reversed micelle,23a,23b made
up of only a few monomers. The broad SAXS profiles of low
intensity for these samples suggest the existence of poly-
dispersed small reversed micelles and the absence of any long-
range correlations among the reversed micelles.
For the samples with X = 20.1 and 27.0, solubilization of
excess water into the polar region induces formation of the
droplet with a water core, whose domain size depends upon the
X value, probably reflecting the SAXS profiles of these fresh
samples.
The SAXS profiles of the aged samples are shown in
Figure 3. For the sample with X = 3.7, we see only a single
weak and broad Bragg peak at q = 0.08-0.12 ¡¹1. This
observation implies that the average size of the water-
solubilized reversed micelles changes with aging of the sample.
The X = 9.5 sample shows a broad peak at q = 0.062 ¡¹1 and a
sharp, strong peak at q = 0.082 A¹1, while the samples with
The function chosen to fit the SAXS data of aged samples
was
¹1
X = 20.1 and 27.0 furnish a Bragg peak at q = 0.063 ¡
together with a broad peak at 0.047 ¡¹1. These facts indicate
that the self-assembly system, responsible for the appearance of
the peak at high q, coexists with reversed micelles in these
samples. Comparison of these data with those obtained in
SAXS studies of the AOT-decane-water systems13-15 allows
us to assign the Bragg peak at low q to a droplet-type reversed
1
1
IðqÞ ¼
þ
ð4Þ
A þ Bq2 þ Cq4 A0 þ B0q2 þ C0q4
where A > 0, C > 0, and B < 0, thus providing eqs 2 and 3,
and A¤ > 0, C¤ > 0, and B¤ < 0. Figure 3 (solid lines) shows
the curves of best fit, and the agreement is excellent. From the