8732
Langmuir 2007, 23, 8732-8739
Dielectric Model and Theoretical Analysis of Cationic Reverse Micellar
Solutions in CTAB/Isooctane/n-Hexanol/Water Systems
Likun Yang and Kongshuang Zhao*
College of Chemistry, Beijing Normal UniVersity, Beijing 100875, China
ReceiVed March 7, 2007. In Final Form: May 12, 2007
Dielectric relaxation spectra of CTAB reverse micellar solutions, CTAB/isooctane/n-hexanol/water systems with
different concentrations of CTAB and different water contents, were investigated in the frequency range from 40 Hz
to 110 MHz. Two striking dielectric relaxations were observed at about 104 Hz and 105 Hz, respectively. Dielectric
parameters were obtained by fitting the data using the Cole-Cole equation with two Cole-Cole dispersion terms and
the electrode polarization term. These parameters show different variation with the increase of the concentration of
CTAB or the water content. In order to explain the two relaxations systematically and obtain detailed information
on the systems and the inner surface of the reverse micelles, an electrical model has been constituted. On the basis
of this model, the low-frequency dielectric relaxation was interpreted by the radial diffusion of free counterions in
the diffuse layer with Grosse model. For the high-frequency dielectric relaxation, Hanai theory and the corresponding
analysis method were used to calculate the phase parameters of the constituent phases in these systems. The reasonable
analysis results suggest that the high-frequency relaxation probably originated from the interfacial polarization. The
structural and electrical information of the present systems were obtained from the phase parameters simultaneously.
Introduction
It is well-known that surfactant/cosurfactant/water ternary
systems, depending on the amount of each component, form
different structures such as micelles, reverse micelles, hexagonal,
lamellar, and cubic liquid crystals, and other structures.1 Reverse
micelles are nanometer-sized droplets of water or polar solvent,
which are surrounded by a layer of surfactant molecules and
dispersed in a nonpolar solvent or weakly polar solvent.2-4 The
hydrophilic headgroups of the surfactant molecules are directed
toward the core of the micelles, and the hydrophobic groups are
directed toward the bulk organic solvent. The cosurfactant acts
as a “spacer” that minimizes repulsions between the electriferous
surfactant heads.5
The size of a reverse micelle in a suspension is characterized
by W0, the molar ratio of water or polar solvent to surfactant S,
W0 ) [H2O]/[S]; and W0 has been shown to be directly
proportional to the micellar radius, RM ) 3Vs/∑s + 3VWW0/∑s,6
so the increase of water content in the system will cause the
reverse micelles to enlarge. Confined environments in reverse
micelles can be used to carry out a variety of reactions, either
by modifying the properties of the encapsulated liquid or by
bringing reactants into close contact.7,8 Therefore, the properties
of water within the reverse micelles have been extensively
studied by many techniques, such as infrared spectroscopy,9
NMR spectroscopy,10 Raman and inelastic light scattering,11
* Tel: +8601058808283. E-mail: [email protected].
(1) Laughlin, R. G. The Aqueous Phase BehaVior of Surfactants; Academic
Press: London, 1994.
(2) Luisi, P. L., Straube, B. E., Eds. ReVerse Micelles; Plenum Press: New
York, 1984.
(3) Luisi, P. L. Angew. Chem., Int. Ed. Engl. 1985, 24, 439.
(4) Fendler, J. H. Annu. ReV. Phys. Chem. 1984, 35, 137.
(5) Schulman, J. H.; Riley, D. P. J. Colloid Sci. 1948, 3, 383.
(6) Cushing, B. L.; Kolesnichenko, V. L.; O’Connor, C. J. Chem. ReV. 2004,
104, 3893.
(7) Menger, F. M.; Donohue, J. A.; Williams, R. F. J. Am. Chem. Soc. 1973,
95, 286.
(8) Menger, F. M.; Yamada, K. J. Am. Chem. Soc. 1979, 101, 6731.
(9) Temsamani, M. B.; Maeck, M.; El, Hassani, I.; Hurwitz, H. D. J. Phys.
Chem. B 1998, 102, 3335.
(10) Hauser, H.; Haering, G.; Pande, A.; Luisi, P. L. J. Phys. Chem. 1989, 93,
7869.
fluorescence upconversion,12 and molecular dynamics (MD)
simulations.13
Dielectric relaxation spectroscopy (DRS), which measures
permittivity and conductivity as a function of frequency in a
noninvasive way, can detect the structural changes in many
systems in situ and provide insights into structures and electrical
properties on the molecular and macroscopic levels.14 Moreover,
DRS is very sensitive to all kinds of intermolecular interactions
and dipole moment fluctuations,15 so it can be used to investigate
the relaxation processes that originate from different polarization
mechanisms over an extremely wide range of characteristic
frequency (10-6-1011Hz). The information provided by DRS
includes the diffusion of counterions in the compact layer and
the diffuse layer, the size and the distribution of particles estimated
by the relaxation time, and the properties of each phase in the
heterogeneous system obtained by dielectric analysis with the
proper dielectric model. Therefore, DRS is very useful in
analyzing the physical and chemical properties of heterogeneous
systems such as colloidal particles,16,17 micelles,18,19 reverse
micelles,20,21 microemulsions,22 vesicles,23 and biological cell
dispersions.24
The four-component system, CTAB/isooctane/n-hexanol/
water, contains anisotropic structures with a high dielectric
permittivity dispersed in a solvent of low permittivity. It can be
expected that some properties of this system can be disclosed
(11) D’Aprano, A.; Lizzio, A.; Liveri, V. T.; Aliotta, F.; Vasi, C.; Migliardo,
P. J. Phys. Chem. 1988, 92, 4436.
(12) Willard, D. M.; Levinger, N. E. J. Phys. Chem. B 2000, 104, 11075.
(13) Faeder, J.; Ladanyi, B. M. J. Phys. Chem. B 2000, 104, 1033.
(14) Asami, K. Prog. Polym. Sci. 2002, 27, 1617.
(15) Daniel, V. V. Dielectric Relaxation; Academic Press: London, 1967.
(16) Chen, Z.; Zhao, K. S. J. Colloid Interface Sci. 2004, 276, 85.
(17) He, K. J.; Zhao, K. S. Langmuir 2005, 21, 11878.
(18) Yang, L. K.; Zhao, K. S.; Xiao, J. X. Langmuir 2006, 22, 8655.
(19) Shikata, T.; Imai, S. Langmuir 1998, 14, 6804.
(20) Cirkel, P. A.; van der Ploeg, J. P. M.; Koper, G. J. M. Phys. ReV. E 1998,
57, 6875.
(21) Angelico, R.; Palazzo, G.; Colafemmina, G.; Cirkel, P. A.; Giustini, M.;
Ceglie, A. J. Phys. Chem. B 1998, 102, 2883.
(22) Bordi, F.; Cametti, C. J. Colloid Interface Sci. 2001, 237, 224.
(23) Schrader, W.; Halstenberg, S.; Behrends, R.; Kaatze, U. J. Phys. Chem.
B 2003, 107, 14457.
(24) Bai, W.; Zhao, K. S.; Mi, H. L. Bioelectrochemistry 2006, 69, 49.
10.1021/la700665s CCC: $37.00 © 2007 American Chemical Society
Published on Web 07/17/2007
Cationic ReVerse Micellar Solutions
by DRS. However, most of the earlier work on reverse micelles
by DRS only involves the systems which consist of anionic
surfactant or nonionic surfactant,25-27 and the researches have
always focused on the condition of little water content.28,29 The
information obtained is very limited, because most of the previous
studies only rest on the description of the dielectric parameters.
In fact, the most potential application of DRS consists of its
explanation of the experimental data based on the proper model.
Therefore, in this paper, the dielectric spectra of CTAB reverse
micellar solutions, CTAB/isooctane/n-hexanol/water systems,
have been investigated over a frequency range from 40 Hz to
110 MHz. The concentration of CTAB changed from 0.02 to 0.1
mol L-1, and the water content of CTAB reverse micelles changed
from 5 to 40. It is surprising that two dielectric relaxations,
low-frequency relaxation and high-frequency relaxation, have
been observed under all of the conditions in this system. This
is similar to those in the dispersing systems of particles.30,31 This
phenomenon is seldom found in other studies of reverse micelles
except for the soybean lecithin/water/perdeuterated cyclohexane
system.20,21 In order to clarify the two relaxations systematically,
a phenomenalistic electrical model has been considered. The
two relaxations were reasonably explained by the radial diffusion
of free counterions in the diffuse layer with Grosse model32 and
the interfacial polarization with Hanai theory and the corresponding analysis method.33,34 On the basis of the dielectric
parameters, the phase parameters of the high-frequency relaxation
have been calculated, which was consistent with the real system.
Experimental Section
Materials. Cetyltrimethylammonium bromide (CTAB), analytical
grade, purchased from Boao Biologic Science and Technology Ltd
Co. (Shanghai, China), was recrystallized three times from methanol/
ether, and the recrystallized CTAB was without minima in its surface
tension plot. Isooctane and n-hexanol used in the syntheses were
obtained from Bodi Chemical Ltd Co. (Tianjin, China) without further
purification. Highly deionized water possessing specific resistance
higher than 16 MΩ cm-1 was used, which was obtained from an
Aquapro P Series water purification system (Taiwan).
Preparation of Reverse Micelles. Reverse micelles were prepared
by mixing CTAB, isooctane, n-hexanol, and water. Certain quantities
of CTAB were dissolved in a constant volume ratio (9:1) of isooctane
and n-hexanol. Solutions of different concentrations were taken in
different topped conical flasks. Certain volumes of water were added
to the mixed solutions under stirring until they became clear. The
concentration of CTAB ranged from 0.02 to 0.1 mol L-1, and W0
ranged from 5 to 40. These solutions were used for dielectric
measurements.
Dielectric Measurement. Dielectric measurements were carried
out on an HP 4294A Precision Impedance Analyzer with a 16047E
spring clip fixture (Agilent Technologies) over a continuous frequency
range of 40 Hz to 110 MHz. The amplitude of the applied alternating
field was 500 mV, and the measurement temperature was 20 (
0.1 °C. A dielectric measurement cell with concentrically cylindrical
platinum electrodes35 was employed. The volume of the solutions
(25) Gestblom, B.; Sjoblom, J. Langmuir 1988, 4, 360.
(26) Asami, K. Langmuir 2005, 21, 9032.
(27) Middleton, M. A.; Schechter, R. S.; Johnston, K. P. Langmuir 1990, 6,
920.
(28) Peyrelasse, J.; Boned, C. J. Phys. Chem. 1985, 89, 310.
(29) Freda, M.; Onori, G.; Paciaroni, A.; Santucci, A. J. Non-Cryst. Solids
2002, 307-310, 874.
(30) Blum, G.; Maier, H.; Sauer, F.; Schwan, H. P. J. Phys. Chem. 1995, 99,
780.
(31) Roldán-Toro, R.; Solier, J. D. J. Colloid Interface Sci. 2004, 274, 76.
(32) Grosse, C. J. Phys. Chem. 1988, 92, 3905.
(33) Hanai, T.; Koizumi, N. Bull. Inst. Chem. Res. Kyoto UniV. 1975, 53, 153.
(34) Hanai, T.; Koizumi, N.; Gotoh, R. Bull. Inst. Chem. Res. Kyoto UniV.
1962, 40, 240.
(35) Hanai, T.; Zhang, H.-Z.; Sekine, K.; Asaka, K.; Asami, K. Ferroelectrics
1988, 86, 191.
Langmuir, Vol. 23, No. 17, 2007 8733
used in the experiment was 1 mL in order to submerge the electrodes.
The experimental data were corrected for the residual inductance
arising from the terminal leads and measurement cell by using
Schwan’s method.36 The stray capacitance and cell constant were
determined with pure water, ethanol, and air at 20 °C. The permittivity
and conductivity were calculated from the corrected capacitance
and conductance.
Determination of the Relaxation Parameters. DRS determines
the polarization of the sample resulting from an applied electric field
of frequency f. The response of the polarization of the sample is
reflected in terms of the complex permittivity spectrum. In order to
obtain the parameters of dielectric relaxation, such as the limiting
values of low and high frequency of permittivity and conductivity
and the characteristic relaxation frequency, the Cole-Cole empirical
equation37 (eq 1) with two Cole-Cole dispersion terms can be used
to fit the experimental data in the applied frequency range
* ) ′ - j′′ ) h +
l - m
1 + (jωτl)
βl
+
m - h
1 + (jωτh)βh
(1)
where * is the complex permittivity, ′′ ()(κ - κl)/ω0) is the
dielectric loss, ω ()2πf) is the angular frequency, κl is the lowfrequency limit of conductivity, ∆ ()l - h) is the relative
permittivity increment, l and h are the low- and high-frequency
limits of permittivity, respectively, 0 is the permittivity of vacuum
equal to 8.854 × 10-12 F m-1, f0 is the characteristic relaxation
frequency, τ ()(2πf0)-1) is the relaxation time, β (0 < β e 1) is the
Cole-Cole parameter indicating the dispersion of the relaxation
time τ, and j ) x-1.
However, the effect of electrode polarization due to the accumulation of spatial charges on the electrode surface often obscures
the dielectric dispersion when it is measured in the low-frequency
range. To acquire accurate values of the dielectric parameters, the
electrode polarization term is added to the Cole-Cole equation
(eq 1)26
* ) h +
l - m
1 + (jωτl)
βl
+
m - h
1 + (jωτh)βh
+ Aω-m
(2)
where A and m are adjustable parameters, respectively, determined
by fitting the experimental data simultaneously. All the data were
eventually fitted with eq 2. By using this method, the influence of
electrode polarization can be subtracted from the experimental data,
and the real dielectric response of the samples is obtained.
Results and Discussion
Dielectric Relaxation Behavior of CTAB/Isooctane/nHexanol/Water Reverse Micelles. In order to detect the dielectric
relaxation behavior under different conditions, the DRS of CTAB
reverse micelles with different concentrations of CTAB and
different water contents were measured.
Figure 1 shows 3D representations of the dielectric spectra as
the water content W0 of CTAB reverse micelles is 15. It can be
seen that there are two dielectric relaxations in Figure 1a as
shown by the arrows, and two peaks appear in Figure 1b indicating
two relaxations too. The number of relaxations determined by
the relative permittivity in Figure 1a corresponds to the number
of peaks represented by the dielectric loss in Figure 1b. Similarly,
Figure 2 shows 3D representations of the dielectric spectra as
the concentration of CTAB reverse micelles is 0.04 mol L-1.
There are also two relaxations in CTAB reverse micelles as
shown by the arrows in Figure 2a and the peaks in Figure 2b.
Therefore, it can be concluded that there are two relaxations in
this system.
(36) Schwan, H. P. In Determination of Biological Impedance; Physical
Techniques in Biological Research; Nastuk, W. L., Ed.; Academic Press: New
York, 1963; Vol. VI, Part B, p 434.
(37) Cole, K. S.; Cole, R. H. J. Chem. Phys. 1941, 9, 341.
8734 Langmuir, Vol. 23, No. 17, 2007
Figure 1. Three-dimensional representations of the concentration
dependence of (a) the relative permittivity spectrum and (b) the
dielectric loss spectrum of CTAB/isooctane/n-hexanol/water reverse
micelles at W0 ) 15.
In order to investigate the dielectric relaxation change with
increasing the concentration or the water content as shown in
Figures 1a and 2a in detail, the relative permittivity spectra of
four conditions are displayed in Figure 3. The figure shows the
best-fit results simultaneously, which are in good agreement
with the experimental data. Some of the dielectric parameters
obtained by fitting the experimental data with the Cole-Cole
equation (eq 2) are listed in Table 1. The results should be
considered as the dielectric parameters representing the real
properties of the whole system, because the effect of the electrode
polarization has been eliminated. From this table, it can be found
that the two relaxations in CTAB reverse micelles are around
104 Hz and 105 Hz, respectively. Cole-Cole parameters βl and
βh are relatively large, indicating that the dispersion of the
relaxations is single, which is close to Debye-type relaxation.
These results also indicate that it is reasonable to fit the
experimental data with eq 2.
Yang and Zhao
Figure 2. Three-dimensional representations of (a) the relative
permittivity spectrum and (b) the dielectric loss spectrum of CTAB/
isooctane/n-hexanol/water reverse micelles at C ) 0.04 mol L-1
with different water contents.
The dependence of dielectric relaxation parameters, lowfrequency permittivity l, and conductivity κl was shown in Figure
4a,b at a fixed water content. In Figure 4a, the value of permittivity
increases with the concentration of CTAB. Counterions can
dissociate in the water pool in ionic reverse micelles. Some of
them form counterion clouds covering the surface of the water
pool. If the shapes of the counterion clouds deviate from this
symmetry, a dipole moment u0 will be induced. Therefore, the
water pool with counterion clouds can be regarded as a dipole
to some extent. The permittivity which characterizes the
polarization capability of materials is related to the dipole moment
u0 and the molecular number n in unit volume.38 At the beginning
of the relaxation, l is close to the whole permittivity of CTAB
reverse micelles. When the water content is fixed, the number
of the water pool in reverse micelles approximately increases
(38) Skanavi, G. I. Dielectric Physics; National Publishing Institute of
Techno-theoretical Literature, 1949.
Cationic ReVerse Micellar Solutions
Figure 3. Relative permittivity spectra extracted from Figures 1a
and 2a on the condition of two concentrations of CTAB and two
water contents, respectively. The symbols and the solid lines represent
the experimental data and the best fitting curves evaluated from eq
2, respectively.
with the concentration of CTAB, while the size of the water pool
remains constant. If the dipole moment u0 remains almost
invariable as a result of the constant size of the water pool, l
will increase with n. In Figure 4b, the value of κl increases linearly
with the concentration of CTAB. This is with respect to the
concentration of counterions, Br- anions, which increases with
the concentration of CTAB in the water pool.
The dependence of dielectric relaxation parameters, lowfrequency permittivity l and conductivity κl, was shown in Figure
4c,d at fixed concentration of CTAB. In Figure 4c,d, both of l
and κl increase with the water content to reach a peak and then
decrease. When the concentration of CTAB is fixed, the size of
the water pool in the system approximately increases with the
increase in the water content, while the number of the water pool
basically remains constant. CTAB molecules may not dissociate
thoroughly at a relatively small water content. At the primal
stage of the increase of the water content, some undissociated
CTAB molecules dissociated once again, so that l and κl will
increase with the number of Br-. As all of the CTAB molecules
dissociate with the further increase of the water content, the
concentration of Br- will decrease a little as a result of the increase
of the water content. Therefore, l and κl decrease eventually.
Dielectric Relaxation Mechanisms in CTAB Reverse
Micelles. In order to expatiate on the two relaxation processes
shown in Figures 1 and 2 and analyze the inner properties of
CTAB reverse micelles, the structural characterization and the
distribution of counterions are presented in a structural sketch
in Figure 5a. The outermost layer is composed of the bulk
isooctane molecules. The surfactant molecules of CTAB and the
cosurfactant n-hexanol are located together in the surfactant
molecular layer. The dissociated counterions from the surfactants,
Br- anions, and all of the water molecules exist in the water
pool. It can be noticed that there are three components with
different electrical properties in CTAB reverse micelles, which
are the oil phase, the surfactant molecular layer, and the water
phase with counterions, respectively.
Generally speaking, there are two characteristic dielectric
relaxations in a heterogeneous structure of dispersing systems
measured under the usual frequency range (from 1 Hz to 1 ×
108 Hz). They appear at the low-frequency range and highfrequency range, respectively. Both are sensitive to the polarization of the electric double layer of the dispersing particles as well
as the electric properties of the constituent phase. The lowfrequency relaxation occurs below a few kilohertz, caused by the
tangential current of bound counterions in the electric double
layer or the diffusion of counterions in the bulk solution.32 The
high-frequency relaxation appears at several megahertz, originated
Langmuir, Vol. 23, No. 17, 2007 8735
from the Maxwell-Wagner interfacial polarization effect in the
conventional meaning.39,40 The two relaxations in this investigated
system are in accordance with those of the ordinary dispersing
systems of particles. Therefore, it can be speculated that the
diffusion of Br- ions may result in the dielectric relaxation of
low frequency because of the existence of large numbers of Brions in the diffuse layer. Simultaneously, the presence of the
large interface between the reverse micelles and the oil continuous
phase probably causes the other relaxation. In order to analyze
the high-frequency relaxation, a dielectric model is considered
in Figure 5b based on Hanai theory. In this model, the surfactant
molecular layer and the inner water pool are considered as a
whole, which are dispersed in the continuous oil medium. The
radius of the whole sphere is R, which includes the thickness of
the surfactant molecular layer (R - Rw) and the radius of the
water pool (Rw). The apparent complex permittivity of this sphere
is i* and the apparent complex permittivity of the continuous
oil phase is a*. The apparent complex permittivity * of the
whole reverse micellar system is defined as * ) - jκ/ω0.
Low-Frequency Dielectric Relaxation. Low-frequency relaxation was first given a theoretical explanation by Schwarz.41
Subsequently, Dukhin and Shilov42,43 developed a new approach
to this problem based on the concept of a diffuse double layer.
Grosse32 presented a simple model for the dielectric properties
of suspensions of charged particles in an electrolyte solution,
and the Grosse model provides the calculation formula for the
two mean relaxation times as follows, by which we can estimate
the relaxation time in the present system
τ1 ) r2/Dt
( )
( )
p
+2
m
τ2 )
2λs
+2
κm
rκm
(3)
0m
(4)
where Dt is the diffusion coefficient of the counterions; r is the
radius of a spherical particle; m, κm, p, and κp are the permittivity
and conductivity of a medium and a particle, respectively; and
λs is the surface conductivity arising from the tangential motion
of bound counterions.
It is well-known that the value of λs is about 10-9 Ω with
respect to the order of magnitude for many systems;44 therefore,
λs in CTAB reverse micelles can be estimated. The values of τ2
calculated from eq 4 under all conditions are equal to 10-9 s,
which is much less than the experimental values. That is, the
rapid tangential motion of the counterions along the surface of
CTAB reverse micelles is not the natural reason for the dielectric
relaxation.
The diffusion coefficient Dt of Br- anions in the aqueous
solution is about 2.1 × 10-5 cm2 s-1.45 The average radius Rw
of the water pool of CTAB reverse micelle shown in Figure 5a
is about 3 nm.46 So, the relaxation time τ can be estimated with
eq 3, equal to about 5 × 10-9 s. This relaxation time τ is also
less than the low-frequency relaxation time obtained from the
(39) Maxwell, J. C. A Treatise on Electricity and Magnetism, 3rd ed.; Clarendon
Press: Oxford, England, 1891; Chapter 4.
(40) Wagner, K. W. Arch. Elektrotech. (Berlin) 1914, 2, 371.
(41) Schwarz, G. J. Phys. Chem. 1962, 66, 2636.
(42) Dukhin, S. S.; Shilov, V. N. Dielectric Phenomena and the Double Layer
in Dispersed Systems and Polyelectrolytes; Halsted: Jerusalem, 1974.
(43) Shilov, V. N.; Dukhin, S. S. Colloid J. 1970, 32, 293.
(44) Baar, C.; Buchner, R.; Kunz, W. J. Phys. Chem. B 2001, 105, 2914.
(45) Imai, S.; Shikata, T. Langmuir 1999, 15, 8388.
(46) Das, P. K.; Chaudhuri, A. Langmuir 2000, 16, 76.
8736 Langmuir, Vol. 23, No. 17, 2007
Yang and Zhao
Table 1. Partial Dielectric Parameters of CTAB Reverse Micellesa
concn
(mol L-1)
0.04
0.1
W0
l
m
h
∆l
∆h
βl
βh
f0l
(kHz)
f0h
(kHz)
15
25
15
25
1.390
1.414
1.559
1.676
0.882
0.950
0.996
1.148
0.692
0.746
0.928
1.031
0.508
0.464
0.563
0.528
0.190
0.204
0.068
0.117
0.859
0.922
0.863
0.879
0.898
0.913
0.904
0.78
11.1
14.4
31.0
25.6
237.8
372.0
508.8
225.0
a
Permittivity increment of low-frequency dielectric relaxation, defined as ∆l ) l - m, and that of high-frequency relaxation, defined as ∆h
) m - h.
Figure 4. Dependence of two dielectric relaxation parameters evaluated by fitting eq 2 to the observed dielectric spectra. (a,c) Low-frequency
limit of the relative permittivity l; (b,d) low-frequency limit of the conductivity κl. There are two sets of data in all graphs, which are indicated
by squares and circles.
Figure 5. (a) Structural sketch of CTAB/isooctane/n-hexanol/water reverse micelle. (b) Dielectric model of high-frequency relaxation.
experiment (about 8 × 10-6 s). The difference between the
calculated relaxation time and the experimental data is due to
the variation of the microenvironment in the water pool of reverse
micelles compared with the surroundings of the aqueous medium.
The variation of the microenvironment will change the diffusion
coefficient indeed.47-49 For example, the obtained lateral surface
diffusion coefficient of the Br- anion is about 10-9 m2/s, roughly
half of the bulk diffusion coefficient of Br-.47 On the other hand,
the diffusion of the counterions taking place in the inner water
pool is different from the typical model. On this condition, the
(47) Hedin, N.; Furo, I. J. Phys. Chem. B 1999, 103, 9640.
Cationic ReVerse Micellar Solutions
Langmuir, Vol. 23, No. 17, 2007 8737
Table 2. Phase Parameters of W0 ) 15 in CTAB Reverse
Micelles
limits are given by
concn
(mol L-1)
κa (S m-1)
φ
i
κi (S m-1)
V1
0.02
0.04
0.06
0.08
0.1
1.041 × 10-6
2.817 × 10-6
3.901 × 10-6
4.976 × 10-6
5.999 × 10-6
0.1770
0.2257
0.2651
0.2927
0.3165
48.21
48.64
48.87
49.25
49.57
3.803 × 10-5
1.084 × 10-4
1.259 × 10-4
1.610 × 10-4
2.076 × 10-4
0.5577
0.5637
0.5669
0.5721
0.5766
Table 3. Phase Parameters of C ) 0.04 mol
Reverse Micellesa
L-1
κa (S m-1)
φ
i
κi (S m-1)
V1
5
10
15
20
25
30
35
40
4.338 × 10-7
1.280 × 10-6
2.817 × 10-6
2.941 × 10-6
2.806 × 10-6
2.837 × 10-6
1.676 × 10-6
1.585 × 10-6
0.1952
0.2185
0.2257
0.2395
0.2607
0.2618
0.2788
0.2994
42.02
44.80
48.64
49.58
50.77
52.35
54.62
55.94
3.279 × 10-5
9.384 × 10-5
1.084 × 10-5
9.057 × 10-5
9.442 × 10-5
1.051 × 10-4
1.371 × 10-4
6.888 × 10-5
0.4718
0.5104
0.5637
0.5767
0.5932
0.6151
0.6466
0.6649
a The two relaxations are explained by the diffusion of counterions
in the diffuse layer with the Grosse model and the interfacial polarization
with Hanai theory.
diffusion of the counterions is counteracted in the confined space.
Therefore, a considerable amount of bound water existing in the
water pool can lead to the decrease of Dt of Br- ions. As a result,
the term of Dt in eq 3 must be modified by a corrected factor
A, which means the degree of the decrease of Dt, as shown in
eq 5. So, it can be speculated that the radial diffusion of the free
counterions in the water pool is the essential mechanism of the
low-frequency dielectric relaxation in this system. This model
is shown in Figure 5a. From the analysis above, it also can be
concluded that the effect of the variation of the microenvironment
on Dt is very obvious.
τ1 ) r2/(Dt - A)
a
i
()
1/3
)1-φ
(6)
where the subscripts a and i represent the continuous phase
and the dispersed phase respectively, and φ is the volume
fraction of the dispersed phase. The low- and high-frequency
(48) Okamoto, K.; Hirota, N.; Tominaga, T.; Terazima, M. J. Phys. Chem. A
2001, 105, 6586.
(49) Shah, D. M.; Davies, K. M.; Hussam, A. Langmuir 1997, 13, 4729.
(50) Bruggeman, D. A. G. Ann. Phys. (Leipzig) 1935, 24, 636.
1/3
)1-φ
(7)
)
)
l
i
a
a - i
1
3
)3
+
κ l - κi κ l
κa - κi κl - κi
κa
(8)
κh
κi
κa
κa - κi
3
1
)3
+
h - i h
a - i h - i
a
(9)
κl - κi κ a
κa - κi κl
1/3
)1-φ
(10)
Since the dielectric properties of reverse micelles which can
be characterized by the phase parameters are useful for the
application in synthesis, it is necessary to evaluate these
parameters of the inner phases from the dielectric parameters.
On the basis of eq 6, Hanai provides a systematic method to
calculate the phase parameters,51 which has been successfully
applied to many actual systems.52,53 The expressions of the phase
parameters are obtained after the cumbersome mathematical
treatments. For simplicity, a formula has been defined
C≡
()
h
a
1/3
‚(1 - φ)
(11)
From eqs 7, 8, and 10, it can be known that
C)
-Q - xQ2 - 4PR
2P
(12)
where
P)
(5)
High-Frequency Dielectric Relaxation. Different from the
dielectric parameters, the phase parameters refer to a series of
parameters presenting the inner properties of the continuous phase
and dispersed phase, such as the permittivity and conductivity
of the two phases, and the volume fraction of the dispersed phase.
CTAB reverse micelles can be considered as spherical droplets
dispersed in a continuous oil phase. Therefore, Hanai theory and
the relevant analysis method can be applied to the present systems. It has been proven that Hanai theory is appropriate to the
ordinary emulsions,33,34 which are similar to the reverse micelles,
and this theory is an extension of Wagner’s equation40 to
high volume fractions along the Bruggeman’s effective
medium approach.5050 It can be expressed by the following
equation in a complex relative permittivity
* - /i /a
/ - / *
(
(
in CTAB
W0
()
) (
) (
()
h - i a
a - i h
( )
( )
κa
κl
+ 2 lD - 3[hD - a(D - 1)]D +
- 1 aD (13)
κl
κa
Q ) 3[2hD - a(D - 1)] κa
κl
+ 2 D + 3 l - - 1 aD (14)
κl
κa
[( ) ] ( )
R ) 3(l - h)
(15)
and
D)
( )
aκl
hκa
1/3
(16)
Eventually, the function C given by eq 12 is a complicated function
of κa.
Next, eqs 7 and 10 are substituted for eq 9 to eliminate i and
κi. Thus, the following equation is obtained:
[ ( )]
a
C (1 - DC)κh - 3{κl - [κa(D - 1) +
h
h
κl]C}(1 - C) + κa 1 - C(1 - DC) ) 0 (17)
a
J(κa) ≡ 3 - 2 +
( )
(51) Hanai, T.; Ishikawa, A.; Koizumi, N. Bull. Inst. Chem. Res. Kyoto UniV.
1977, 55, 376.
(52) Ishikawa, A.; Hanai, T.; Koizumi, N. Bull. Inst. Chem. Res. Kyoto UniV.
1984, 62, 251.
(53) Zhao, K. S.; Asami, K.; Lei, J. P. Colloid Polym. Sci. 2002, 280, 1038.
8738 Langmuir, Vol. 23, No. 17, 2007
Yang and Zhao
Figure 6. Dependence of several phase parameters calculated by eq 6 on the basis of the dielectric parameters in CTAB reverse micelles.
(a,b) Volume fraction φ of the dispersed phase; (c,d) permittivity i of the dispersed phase; (e,f) conductivity κi of the dispersed phase. There
are two sets of data in all graphs, which are indicated by squares and circles.
If l, h, κl, κh, and a are given through eqs 12 and 16, the
left-hand side of eq 17, which is a formula abbreviated as J(κa),
is a function of κa. Although eq 17 cannot be solved for κa due
to the complicated functional form, computers have made it
possible to search out a root for J(κa) ) 0 numerically. Using
the calculated value of κa in the above way, the values of φ, i,
and κi then can be derived.
φ)1-
1/3
‚C
(18)
h - aC
1-C
(19)
κl - κaDC
1 - DC
(20)
i )
κi )
()
a
h
The permittivity a (0.3) and the conductivity κa (3 × 10-6 S/m)
of the continuous phase, which have been measured in an
individual experiment, are used as a known quantity during all
of the calculations. By using eqs 17-20, the phase parameters
of CTAB reverse micelles were calculated, and the partial results
are listed in Tables 2 and 3, respectively. The information about
microstructure and interface between the oil phase and the water
phase is acquired simultaneously.
From these tables, it can be noticed that, if the water content
is fixed, φ and i increase with the concentration of CTAB; as
the concentration of CTAB is fixed, φ and i also increase with
the water content. These relationships are approximately linear
as shown in Figure 6a-d.
Because the water pool and the surfactant molecular layer of
CTAB reverse micelles are regarded as a whole by Hanai theory,
the volume fraction φ obtained from this theoretical calculation
comprises both the dispersed phase (water) and the CTAB layer
(n-hexanol and CTAB). This model is also shown in Figure 5b.
It is rational that the values of φ in Tables 2 and 3 are much
higher than those of the water content in the experiments.
Following the increase of the water content or the concentration
of CTAB, the value of φ will also increase, as shown in Figure
6a,b. Similarly, since the molecules of water, n-hexanol, and
CTAB are considered simultaneously, the value of permittivity
of the dispersed phase i is much lower than that of the pure
water (80.1 at 20 °C). So, the values of i which are between 42
and 57 in our calculated results are reasonable. As the water
Cationic ReVerse Micellar Solutions
Langmuir, Vol. 23, No. 17, 2007 8739
the concentration of CTAB or the water content, whereas the
extent of the increase is obviously different. When the water
content is fixed, the size of the water pool remains constant with
the concentration of CTAB. So, the increase of V1 is very slow
in Figure 7a, or it can be considered constant compared with
Figure 7b. The concentration of CTAB is fixed; the size of the
water pool increases with the water content. Thus, it can be seen
that the increase of V1 in Figure 7b is very apparent.
From the analysis above, it can be concluded that the highfrequency relaxation is probably ascribed to the interfacial
polarization, which is a result of the accumulation of virtual
charge at the interface between the two phases with different
permittivities and conductivities. The structural and electrical
information about CTAB reverse micelles is obtained by analyzing
dielectric spectra with Hanai theory and the corresponding
method.
Conclusion
Figure 7. Relationship of V1 calculated by eq 16 on the basis of i
in CTAB reverse micelles with the water content (a) or the
concentration of CTAB (b). There are two sets of data in all graphs,
which are indicated by squares and circles.
content or the concentration of CTAB increases, the value of i
increases too, as shown in Figure 6c,d. The concentration of
counterions increases with the concentration of CTAB; therefore,
the value of κi in Figure 6e also increases. However, the value
of κi shows different variational tendency in Figure 6f. Because
the partial counterions continue to dissociate at the beginning of
the increase of the water content, the value of κi also increases.
When the water content increases further, the concentration of
counterions will decrease, resulting in the value of κi decreasing.
These varieties are consistent with the dielectric parameters given
in Figure 4.
According to the phase parameter i of the whole micellar
sphere presented in Tables 2 and 3, the volume ratios of water
distributed in the dispersed phase of CTAB reverse micelles
were approximately evaluated by eq 21 where the subscripts 1
i ) V1i1 + (1 - V1)i2
(21)
and 2 represent the two components of water and the mixture
of n-hexanol and CTAB, and V1 ()Rw3/R3) is the volume ratio
of water in the dispersed phase.
The results of V1 in Tables 2 and 3 are also plotted in Figure
7. The values of V1 are coincident with the literature,46 basically
indicating that the phase parameters calculated on the basis of
the electrical model proposed above are suitable. The relationship
between V1 and the concentration of CTAB or the water content
in CTAB reverse micelles is also presented in Figure 7. From
the figure, it can be seen that V1 increases almost linearly with
In this article, dielectric relaxation spectra of CTAB reverse
micelles were investigated under different concentrations of
CTAB and water contents, and the dielectric spectra characterizing
two relaxation processes were found. The dielectric parameters
reflecting the dielectric relaxation spectroscopy were obtained
by fitting the experimental data with the Cole-Cole equation.
Both of the low-frequency limits of relative permittivity l and
conductivity κl increased with the concentration of CTAB, while
they increased with the water content at first and then gained a
maximum. The properties of the dispersed phase changed
differently with the increase of the concentration of CTAB or
the water content, so the two parameters showed different
variation.
A modified electrical model for explaining systematically the
two relaxations occurring in our investigating systems was
proposed. In light of the model combining the Maxwell-Wagner
interfacial polarization theory and the Grosse model, the relaxation
mechanisms of these two relaxations were interpreted reasonably.
In addition, the phase parameters of the high-frequency relaxation
which is consistent with the real system composed of the micellar
phase and the oil medium were calculated by Hanai theory and
the relevant analysis method. On the basis of the phase parameters,
the structural and electrical information of CTAB reverse micelles
formed under the conditions of varying water content and
concentration of CTAB was obtained.
The present study shows that it is feasible to obtain many local
properties of reverse micelles just by dielectric measurements,
while the acquisition of these properties maybe require more
instruments in general. Furthermore, as another successful
example, it also demonstrates the advantage of DRS in obtaining
inner information of intricate heterogeneous systems once again.
Nevertheless, it should be pointed out that the analysis of dielectric
spectra based on an appropriate model and calculation approach
is essentially indispensable.
Acknowledgment. This work is financially supported by the
National Nature Science Foundation of China (no. 20673014).
LA700665S