Dielectric relaxation of 1-butyl-3-methylimidazolium tetrafluoroborate/TX-100/toluene microemulsions: Structure transition, percolation mechanism, interfacial polarization and electrical properties of microdroplets

Abstract

The dielectric relaxation spectra of the non-aqueous ionic liquid (IL) microemulsions composed of 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4])/p-(1,1,3,3-tetramethylbutyl)phenoxypolyoxyethyleneglycol (TX-100)/toluene were obtained, the measured frequency is between 1 MHz to 3 GHz. A unique dielectric relaxation located at 10-100 MHz was observed. The direct current (dc) conductivity data were obtained from the total dielectric loss. Near the percolation transition, weight fraction dependence of dc conductivity and static dielectric constant, frequency dependence of permittivity and loss angle all suggest that static percolation occurs in this hydrophilic IL microemulsion. Phase boundaries of IL-in-toluene (IL/O), bicontinuous (B.C.) and toluene-in-IL (O/IL) subregions were determined by the inflection points in the dependent curve of relaxation parameters varied with weight fraction. The mechanism of this dielectric relaxation is attributed to the interfacial polarization of droplets by analyzing relaxation time with Maxwell-Wagner theory. The phase parameters, which reflect the interior properties of the spherical dispersed particle, were calculated by Hanai theory. The dependence of phase parameters on the variation of sample composition was properly explained. For O/IL subregion, the continuous phase should be an IL/TX-100 binary solvent rather than the pure IL. For IL/O subregions, a certain amount of toluene was dissolved in the droplets.

Full text

Journal Pre-proof
Dielectric relaxation of 1-butyl-3-
methylimidazolium tetrafluoroborate/TX-
100/toluene microemulsions: structure transition,
percolation mechanism, interfacial polarization and
electrical properties of microdroplets
Zhen Li, Zhefeng Fan, Zhen Chen, Yiwei Lian
PII: S0927-7757(21)01696-4
DOI: https://doi.org/10.1016/j.colsurfa.2021.127827
Reference: COLSUA127827
To appear in: Colloids and Surfaces A: Physicochemical and Engineering
Aspects
Received
date:
21 August 2021
Revised date: 14 October 2021
Accepted
date:
26 October 2021
Please cite this article as: Zhen Li, Zhefeng Fan, Zhen Chen and Yiwei Lian,
Dielectric relaxation of 1-butyl-3-methylimidazolium tetrafluoroborate/TX-
100/toluene microemulsions: structure transition, percolation mechanism,
interfacial polarization and electrical properties of microdroplets, Colloids and
Surfaces A: Physicochemical and Engineering Aspects, (2021)
doi:https://doi.org/10.1016/j.colsurfa.2021.127827
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Dielectric relaxation of 1-butyl-3-methylimidazolium tetrafluoroborate/TX-
100/toluene microemulsions: structure transition, percolation mechanism,
interfacial polarization and electrical properties of microdroplets
Zhen Li,a,b Zhefeng Fan,a* Zhen Chen,c and Yiwei Lianb
a School of Chemistry and Material Science, Shanxi Normal University, Linfen, Shanxi, 041001, China
b Department of Applied Chemistry, School of Material Science and Engineering, Hebei University of Engineering,
Handan, Hebei, 056038, China
c Department of Applied Chemistry, School of Science, Anhui Agricultural University, Hefei, Anhui, 230036, China
*Corresponding author. E-mail addresses: zhefengfan@126.com
Abstract
The dielectric relaxation spectra of the non-aqueous ionic liquid (IL) microemulsions composed of 1-butyl-3-
methylimidazolium tetrafluoroborate ([bmim][BF4])/p-(1,1,3,3-tetramethylbutyl)phenoxypolyoxyethyleneglycol (TX-
100)/toluene were obtained, the measured frequency is between 1 MHz to 3 GHz. A unique dielectric relaxation located at
10-100 MHz was observed. The direct current (dc) conductivity data were obtained from the total dielectric loss. Near the
percolation transition, weight fraction dependence of dc conductivity and static dielectric constant, frequency dependence of
permittivity and loss angle all suggest that static percolation occurs in this hydrophilic IL microemulsion. Phase boundaries
of IL-in-toluene (IL/O), bicontinuous (B.C.) and toluene-in-IL (O/IL) subregions were determined by the inflection points in
the dependent curve of relaxation parameters varied with weight fraction. The mechanism of this dielectric relaxation is
attributed to the interfacial polarization of droplets by analyzing relaxation time with Maxwell-Wagner theory. The phase
parameters, which reflect the interior properties of the spherical dispersed particle, were calculated by Hanai theory. The
dependence of phase parameters on the variation of sample composition was properly explained. For O/IL subregion, the
continuous phase should be an IL/TX-100 binary solvent rather than the pure IL. For IL/O subregions, a certain amount of
toluene was dissolved in the droplets.
Keywords Waterless microemulsions, bicontinuous structure, loss angle, phase parameters, static dielectric constant
1. Introduction
Ionic liquids (ILs) are electrolytes or salts that are liquid below 100 °C [
1
]. Due to their special physical and chemical
properties, such as high thermal stability, nonflammability, negligible vapor pressure, environmental friendliness, wide liquid
range and can be easily tuned through careful selection of cation-anion combinations, ILs can serve as all kinds of (polar or
nonpolar) solvent and surfactant in colloid dispersion systems [
2
-
6
]. Over the past few years, IL based microemulsions, in
which either the aqueous phase, the oil phase, the surfactant or even two of these components are replaced by ILs, become an
attractive topic [
7
-
38
]. This is because IL microemulsions have both the advantages of ILs and microemulsions, which can
not only overcome solubility limitations of ILs to dissolve a number of chemicals including some hydrophilic and
hydrophobic substances but also provide hydrophobic or hydrophilic nano domains, and thus broaden the utility of ILs.
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The most intensely investigated IL microemulsions are waterless microemulsions in which water has been replaced by an
IL. The advantages of these systems lie in: they are especially useful when water should be avoided; the microemulsion
structure can be maintained over a wider temperature range compared to water [7] and can circumvent the solubility
limitations of ILs in nonpolar solvents. Han et al. reported the first non-aqueous microemulsion with IL as a polar phase in
2004 [8], they characterized 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4])/TX-100/cyclohexane by using
phase diagram, conductivity, dynamic light scattering and freeze-fracture transmission electron microscopy measurements.
Eastoe et al. performed small angle neutron scattering experiment on the same microemulsion, which demonstrated the
formation of surfactant-stabilized dispersed nanodroplets with IL cores [9]. Chakrabarty et al. also studied this microemulsion
and discussed the effect of confinement on rotational and solvation relaxation of probe molecule [10]. No change of IL
([bmim][BF4]) and surfactant (TX-100), by replacing the cyclohexane with toluene, benzene, p-xylene, respectively, the
variety of waterless IL microemulsions is expanded [11-15]. Ghosh et al. [16] also extended IL microemulsions without
water by changing the type of IL, namely, they prepared different microemulsions composed of TX-100, cyclohexane and IL
with the variation of alkyl chain length of the [CnSO4]- anion (n=4,6,8), and they proposed that the long octayl chain of octayl
sulfate allows the anion to align itself along with the TX-100 surfactant which increase the rigidity of the system. Mandal et
al. [17] provided an IL microemulsion that all components were biologically acceptable ([C2mim][C4SO4]/Tween-80/Span-
20/IPM). A wide variety of other ILs are suitable for the preparation of IL-based nonaqueous microemulsion, such as
[bmim][PF6] [18-20], [N3111][NTf2] [21], [C2mim][Tf2N] [22] and [P13][Tf2N] [23]. Researchers have successfully
characterized these systems by using phase diagram, UV–visible spectroscopy, DLS, FTIR, electrical conductivity, small
angle X-ray scattering and diffusion-ordered spectroscopy NMR measurements. In addition, there are numerous other (non-
ionic, cationic as well as anionic) surfactants can form non-aqueous IL microemulsion [24-29]. Even some nonaqueous IL
microemulsions without surfactant have been reported [30,31]. Nonaqueous IL microemulsions have been applied as reaction,
separation, and extraction media, and applied in biocatalysis, polymerization, (nano-)material synthesis, drug delivery etc.
[5].
The understanding of physical and chemical properties of nonaqueous IL microemulsion are supplemented by the
analysis of dielectric behavior recently. Over a wide frequency range, multiple dielectric relaxations were observed in IL
microemulsions such as [bmim][BF4]/TX-100/cyclohexane [32-34], [bmim][PF6]/TX-100/ethyleneglycol [35,36],
[bmim][BF4]/TX-100/benzene [37], [bmim][BF4]/TX-100/p-xylene [38] and [bmim][BF4]/TX-100/triethylamine [
39
]. In
these reports, a theoretical and quantitative analysis of the direct current (dc) conductivity data (obtained from the dielectric
measurement) were carried out, which indicated the static percolation process took place in these systems [32,35,37-39]. In
addition, that conclusion was supported by the quantitative analysis for the frequency dependence of the dielectric constant
[32,39]. However, previous studies only used the conductivity method to discussed the percolation process qualitatively
[8,11-13,19-22,30]. The observed dielectric relaxation around 10-100 MHz was ascribed to an interfacial polarization, which
is a strong evidence that interfaces exist in such systems [33,35,36,39]. The phase parameters represent the individual
electrical properties of the constituent phase were calculated according to Hanai theory [33,35,36,39]. The obvious problem
with the dielectric study of nonaqueous IL microemulsions is that only five such systems have been studied. Compared with
conventional conductivity measurements, dielectric spectroscopy has a major advantage for investigating percolation of
microemulsions, namely, this technique allows the determination of the percolation mechanism by using four different
methods at the same time: concentration dependence of (1) dc conductivity and (2) static dielectric constant, frequency
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dependence of (3) permittivity and (4) loss angle. Method (1) was widely used in many nonaqueous IL microemulsions [32-
39]; in [bmim][BF4]/TX-100/cyclohexane methods (1) and (3) were both used [33]; finally, all four methods have only been
used simultaneously in [bmim][BF4]/TX-100/triethylamine [39]. This shows that the dielectric spectrum method has an
important potential application in judging the percolation mechanism of anhydrous IL microemulsion.
Based on the above considerations, we measured the weight fraction dependent dielectric relaxation spectra of
[bmim][BF4]/TX-100/toluene at a constant temperature. The dielectric behavior (including loss angle and static dielectric
constant) of this system was analyzed in light of the percolation theories and Hanai theory, the structure transition
information, percolation mechanism, dynamics properties (interfacial polarization) and interior electrical properties (the
phase parameters) of IL/O and O/IL droplets were studied. This study expanded the research scope for the dielectric analysis
of nonaqueous IL-based microemulsion, and thus is a supplement to the understanding of the physical and chemical
properties of these systems.
2. Experiment
2.1. Preparation of IL-based microemulsion
Fig. 1. Chemical structure of TX-100, [bmim][BF4] and toluene.
The IL [bmim][BF4] (purity > 99%) was obtained from Shanghai Cheng Jie Chemical Co. Ltd., China. The water was
less than 10000ppm and the residual chlorides was less than 800ppm in the IL sample. TX-100 (p-(1,1,3,3-
tetramethylbutyl)phenoxypolyoxyethyleneglycol) (laboratory grade) was purchased from Sigma-Aldrich LLC. America.
Toluene (analytical grade) was produced by Beijing Chemical Reagent Factory, China. The structural formula of TX-100,
[bmim][BF4] and toluene are shown in Fig. 1. According to the literature [11], by mixing appropriate weight fractions of
[bmim][BF4], TX-100 and toluene, a series of microemulsions of different weight fractions were prepared, the experimental
path is shown in Fig. 2. In these samples, the weight ratio of toluene/TX-100 is fixed at 1:1, and the weight fraction of
[bmim][BF4] ranged from 3.39 wt% to 60.07 wt%, the interval is approximately 3.00 wt%. We prepared other two samples
which are marked as (I) and (II) in Fig. 2; the weight fractions of [bmim][BF4], TX-100 and toluene are 16, 68 and 16 wt%
for (I) and 9, 83 and 8 wt% for (II). For comparison, we prepared two [bmim][BF4]/TX-100/triethylamine samples which
noted as (III) and (IV); the weight fractions of [bmim][BF4], TX-100 and triethylamine are 16, 67 and 17 wt% for (III) and 9,
82 and 9 wt% for (IV). The molar fractions of IL, TX-100 and oil of samples (I) and (III) are both 20, 30 and 50 %, and the
ratio for samples (II) and (IV) are both 15, 50 and 35 %. All mixtures were transparent and were allowed to stand for over
seven days prior to dielectric measurement to equilibrate these systems.
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Fig. 2. Experimental path diagram for [bmim][BF4]/TX-100/toluene systems, which denotes the change of IL content when the weight ratio
of toluene/TX-100 is fixed at 1.
2.2. Dielectric measurement
The dielectric measurements were performed on an RF impedance analyzer (Keysight E4991B, USA) that allows for a
continuous frequency measurement from 1 MHz to 3 GHz. This impedance analyzer was tested and calibrated in accordance
with the procedure recommended by the manufacturer. The complex permittivity were obtained with a coaxial sample cell
[
40
] located at the end of a coaxial line, which is composed of an outer conductor, with an inner diameter of 3.5 mm and a
length of 25 mm, and an inner conductor, with an outer diameter of 2 mm and a length of 10 mm. The temperature of weight
fraction dependent dielectric measurements was 20 ± 0.1 °C. The permittivity and total dielectric loss at every measured
frequency were directly obtained.
3. Method and models
3.1. Dielectric spectra analysis
When a microemulsion with high conductivity is placed in an applied electric field of angular frequency

(
2f


,
f
is the frequency), the dielectric properties of this sample can be generally characterized in terms of the complex
permittivity
*

.
     
* ' "total
j
     

(1a)
   
0
'" l
jj

    
  
(1b)
where
'

is the permittivity,
21j
,
"total

is the total dielectric loss,
"

is the dielectric loss of the sample,
0

is the
permittivity of vacuum,
l

is the dc conductivity (which can be obtained by fitting the part of
 
"total

that has an index
of -1 [
41
,
42
,
43
]).
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If the measured sample presents a dielectric relaxation, the dielectric spectrum can be further characterized by a set of
dielectric parameters. These parameters can be obtained by fitting the experiment data with the empirical function containing
a Cole-Cole term as below [
44
,
45
]
   
*1
hj


   



(2)
where
h

is the high-frequency limit of permittivity,


is the dielectric increment,

is the relaxation time,

(
01


) is the Cole-Cole parameter (indicating the dispersion of the relaxation time). The static dielectric constant is
defined as
sh
  
  
. By using these dielectric parameters, we can not only analyze the relaxation mechanism but also
calculate the phase parameters.
3.2. Percolation models
Fig. 3. Diagrammatic drawing of (a) [bmim][BF4]-in-toluene (IL/O) subregion, (b) bicontinuous (B.C.) subregion, (c) toluene-in-
[bmim][BF4] (O/IL) subregion. Both (a) and (c) can be modeled as spherical droplets dispersed in a continuous phase.
As illustrated in Fig. 3, when the weight fraction of IL increases, the microstructure of the IL microemulsions will
change from a IL-in-oil (IL/O for short; see Fig. 3a for the schematic diagram) droplets to an oil-in-IL (O/IL for short; see
Fig. 3c for the schematic diagram) type, this is the so-called percolation phenomenon. There are two theories to describe the
transition mechanism between IL/O and O/IL. The dynamic percolation model [
46
,
47
] considered that percolation clusters
are formed during the percolation process. The static percolation attributes the percolation to the appearance of a
bicontinuous (B.C.) structure [
48
] as shown in Fig. 3b. Conductivity and dielectric relaxation spectroscopy are the frequently
used techniques to investigate microstructure and structural change on the basis of the percolation theories. Both the dynamic
and static percolation models hold that the percolation transition takes place at a certain threshold
p
c
[46,47,48]. Below and
above
p
c
, the relations between the dc conductivity and the weight fraction of water (or hydrophilic) phase are as below,
respectively:
s
lp
cc



for
p
cc
(3)
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lp
cc



for
p
cc
(4)
Similar with Eq. (3), there is another scaling relation between static dielectric constant and weight fraction of hydrophilic
phase below
p
c
[41,
49
,
50
].
 
s
sp
cc



for
p
cc
(5)
Moreover, s and μ are related to a universal exponent
u
through Eq. (6):
us



(6)
The value of
u
can be obtained directly by
 
'

and
 

curves near
p
c
by using Eqs. (7) and (8), respectively
[41,49,50].
 
1
'u
  


(7)
 
11-
2
pu


(8)
Where
 

is the loss angle of sample and is defined as
     
"/ '
     

. The plateau (or maximum) of
 

provides the asymptotic value
p

of the loss angle, which gives
u
according to Eq. (8). In these equations, s ≈ 1.2 and u ≈
0.61 in dynamic theory [46,47], s ≈ 0.7 and u ≈ 0.73 in static theory [48], and μ ≈ 1.9 both in dynamic and static theory
[46,47,48].
3.3. Calculation of phase parameters (Hanai theory)
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Fig. 4. Diagrammatic drawing of Hanai model: the continuous phase has the permittivity of
m

and the conductivity of
m

, in which the
dispersed phase has the permittivity of
p

and the conductivity of
p

, the volume fraction of the dispersed phase is

.
Relaxation parameters represent the collective properties of microemulsions, while phase parameters represent the
individual electrical properties of constituent phase. As illustrated in Fig. 4, phase parameters include the permittivity of the
dispersed phase
p

, the permittivity of the continuous phase
m

, the conductivity of the dispersed phase
p

, the
conductivity of the continuous phase
m

and the volume fraction occupied by the dispersed phase

. For a system of
spherical droplets as depicted in Fig. 3a and 3c, with high volume fractions dispersed in a continuous phase, according to the
Hanai theory, can be modeled as
1/3
**
**
*=1
*
pm
mp

  
 


(9)
On the basis of this equation, the formulae related to the limiting values of low- and high-frequencies are given by
1/3
=1
hp
m
m p h

  
 


(10)
31
3m p p m
s
l p l m p l p m
   
       
   

   
   
   
  
   
(11)
31
3m l l m
h
h p h m p h p m
   
       
   

   
   
   
  
   
(12)
1/3
=1
lpm
m p l
 
  
 


(13)
where
10hl
   

  
is the high-frequency limit of conductivity. After cumbersome and mathematical treatments, the
phase parameters are calculated from the dielectric parameters. By using the phase parameters, the relaxation time of the
interfacial polarization, according to Maxwell-Wagner theory, can be calculated as below:
 
 
0
2
2
m p m p
MW
m p m p
   

   
   
   
(14)
4. Results and discussion
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Fig. 5. Three-dimensional representations for the frequency dependences of the (a)
'

(permittivity), (b)
"total

(total dielectric loss) and
(c)
"

(dielectric loss of sample) for [bmim][BF4]/TX-100/toluene microemulsions with different IL weight fractions.
Fig. 5a and b show the directly measured frequency dependence of complex dielectric permittivity of microemulsions
[Bmim][BF4]/TX-100/toluene with different IL weight fractions when the weight ratio of toluene/TX-100 is fixed as 1:1. Fig.
5a shows the variation of permittivity as a function of frequency. Fig 5b shows the spectra of total dielectric loss. As an
example, Fig. 6 shows the total dielectric loss
"total

directly measured (open circles) when the IL weight fraction is 11.94
wt%.
"total

depends on frequency with a power of -1 in the low frequency range, which indicates that
"total

includes the
contribution of dc conductivity
0
/
l
  
. Therefore, according to Eq. (1b) we fit the data at low frequency, the fitting result
is represented by the straight line in Fig. 6, thus the dc conductivity
l

of the sample was obtained. Further subtracting
0
/
l
  
from
"total

, the dielectric loss of sample
"

(represented by the solid circles in Fig. 6) can be obtained.
"

and
l

of each measured sample, obtained by this method, are respectively shown in Fig. 5c and Table 1.
Fig. 6. Example of obtaining dc conductivity and dielectric loss of sample from the total dielectric loss at an IL weight fraction of 11.94
wt%.
A remarkable dielectric relaxation was observed in Fig. 5a, which is confirmed from the corresponding peak position of
dielectric loss of sample as shown in Fig. 5c. In addition, as shown by the arrows in Fig. 5a and c, these spectra and the
relaxation they exhibited have three distinct different weight fraction dependence stages. This phenomenon should relate to
that the experimental path spans three different subregions (IL/O, B.C. and O/IL) of the microemulsions.
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Table 1
DC conductivity and dielectric parameters of the relaxations for [bmim][BF4]/TX-100/toluene with different IL weight fractions.
IL
c
(wt%)
Micro-
structure
l

(mS/cm)
h




(ns)

s

3.39
IL/O
0.194±0.001
3.82±0.06
5.10±0.08
2.53±0.06
0.58±0.01
8.92
6.41
IL/O
0.726±0.001
3.85±0.09
7.35±0.04
2.33±0.07
0.63±0.01
11.20
9.22
IL/O
1.364±0.002
3.86±0.08
8.05±0.08
2.24±0.07
0.67±0.01
11.91
11.94
IL/O
2.202±0.002
3.86±0.07
8.81±0.06
1.87±0.08
0.67±0.01
12.67
15.08
IL/O
3.513±0.003
3.87±0.08
9.12±0.06
1.42±0.08
0.66±0.01
12.99
18.25
IL/O
4.964±0.004
3.88±0.08
9.35±0.07
1.29±0.07
0.68±0.01
13.23
20.94
B.C.
6.167±0.005
3.90±0.07
9.38±0.07
1.25±0.08
0.64±0.01
13.28
23.93
B.C.
8.258±0.007
3.91±0.07
9.34±0.08
1.08±0.08
0.64±0.01
13.25
27.15
B.C.
10.43±0.01
3.95±0.07
9.20±0.08
0.978±0.003
0.64±0.01
13.15
29.99
B.C.
15.27±0.02
4.02±0.08
9.25±0.07
0.903±0.003
0.62±0.01
13.27
33.18
B.C.
18.45±0.02
4.05±0.08
9.15±0.06
0.790±0.003
0.64±0.01
13.20
36.00
O/IL
20.58±0.03
4.09±0.09
9.38±0.07
0.767±0.004
0.63±0.01
13.47
39.11
O/IL
21.93±0.02
4.09±0.09
9.5±0.08
0.788±0.004
0.60±0.01
13.59
42.16
O/IL
23.74±0.03
4.10±0.07
9.76±0.08
0.730±0.004
0.60±0.01
13.86
45.14
O/IL
25.31±0.03
4.10±0.07
9.98±0.07
0.739±0.004
0.58±0.01
14.08
47.99
O/IL
26.44±0.05
4.10±0.08
10.00±0.07
0.702±0.005
0.57±0.01
14.10
50.97
O/IL
30.17±0.05
4.11±0.08
10.11±0.08
0.695±0.005
0.58±0.01
14.22
53.80
O/IL
32.60±0.04
4.12±0.08
10.36±0.06
0.679±0.005
0.57±0.01
14.48
56.88
O/IL
34.85±0.05
4.13±0.07
10.51±0.07
0.644±0.005
0.57±0.01
14.64
60.07
O/IL
37.37±0.05
4.14±0.09
10.55±0.08
0.625±0.005
0.59±0.01
14.69
4.1. The percolation in IL-based microemulsion
Fig. 7. Dc conductivity of [bmim][BF4]/TX-100/toluene as a function of IL weight fraction. The arrow points out the percolation threshold
which is obtained from Fig. 9.
As shown in table 1, the dc conductivity of the lowest IL weight fraction is 0.194 mS/cm, and the value is 37.37 mS/cm for
the highest IL weight fraction. That is to say with increasing of IL weight fraction, the dc conductivity of [bmim][BF4]/TX-
100/toluene changed by two orders of magnitude, which is known as an electric percolation [
51
-
53
]. This phenomenon means
that the microstructure of this IL microemulsion changed from [bmim][BF4]-in-toluene droplets (as shown in Fig. 3a) to
toluene-in-[bmim][BF4] droplets (as shown in Fig. 3c) through a transition structure. As introduced in section 3.2, there are
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two models, namely, percolation clusters and bicontinuous structure to describe this transition structure. Theoretical analysis
of dc conductivity and complex permittivity is needed to determine what the structure is. Fig. 7 shows the dependence of dc
conductivity listed in table 1 on IL weight fraction. Neither the inflection points indicating the boundary of different
microregions in this microemulsion nor the percolation threshold can be detected in this curve, due to the high conductivity
of ILs.
Fig. 8. Permittivity of [bmim][BF4]/TX-100/toluene microemulsions vs IL weight fraction for different frequencies.
The dependences of
'

for seven different frequencies on IL weight fraction are shown in Fig. 8. Clearly, there exists an
inflexion which provides the percolation threshold at approximately 27.15-36.00 wt% in this curves. In the case of not only
traditional microemulsion but also IL microemulsions [35,38,39,41,49], the maximum of the dependence of
/
l IL
d dc

on
IL
c
corresponds to the value of the threshold
p
IL
c
. Here, the percolation threshold 29.98 wt% is obtained from the same way
as shown Figure 9 and is pointed by the arrows both in Fig. 7 an Fig. 9. This value falls within the range of the percolation
threshold (27.15-36.00 wt%) shown in Fig. 8, which demonstrates the effectiveness of these two methods.
Fig. 9. The dependence of
/
l IL
d dc

on
IL
c
, the percolation threshold
p
IL
c
(=29.98 wt%) is obtained from the maximum point.
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Fig. 10. Scaling behavior of the dc conductivity below and above the percolation threshold. The line is the scaling fit result of data below
percolation threshold according to Eq. (3).
Figure 10 depicts the variation of dc conductivity as a function of percolation distance divided by the percolation
threshold. Note that the dc conductivity is plotted in logarithmic coordinates. In this figure, the data below percolation
threshold (open circles) can be divided into two linear dependencies. The previous linear relationship was fitted by using Eq.
(3) with the slope of -0.7. The fitting solid line can describe properly the scaling behavior of the dc conductivity data which
having located the percolation process when below the percolation threshold. Thus, s=0.7 i.e. the static percolation process
takes place in the microemulsion.
Fig. 11. Dependence of static dielectric constant on
/
pp
IL IL IL
c c c
, which is plotted in a logarithmic scale. The line is the fitting
result of data below percolation threshold according to Eq. (5).
The static dielectric constant of every measured sample is obtained according to
sh
  
  
, which will be
introduced in section 4.2 as following. The dependence of
log s

on
 
log /
pp
IL IL IL
c c c
is shown in Fig. 11.
According to Eq. (5) with the slope -0.7, we get the fitting line, which can properly describe the scaling behavior of static
dielectric constant in the data range of 49.70 to 78.62 wt%. This phenomenon also indicates that the static percolation process
takes place in this microemulsion, which is consistent with the conclusion obtained from the analysis of dc conductivity data.
The analysis of physical significance for other conductivity and static dielectric constant data are failed, which is possibly
caused by: (1) the higher electrical conductivity of IL microemulsion than that of traditional microemulsion; (2) the
superposition of interfacial polarization and percolation process (this conclusion will be introduced in the second paragraph
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of section 4.3). In above discussions of
l

and
s

, the data which can conform to the theoretical predictions are very limited,
the other exponents μ and u cannot be obtained. These two limitations thus make it is necessary to further decide theoretically
the percolation mechanism by the discussion of frequency-dependent dielectric behavior.
Fig.12. Scaling dependence of permittivity on frequency for the IL weight fraction of 29.98 wt%. The slope of the straight line gives u =
0.73.
Compared with conductivity measurements, dielectric spectroscopy has a major advantage for investigating percolation
of microemulsions, because the universal parameter u can be directly determined by the measured dielectric spectra, namely
via Eq. (7) and (8). The evolution of
log '

with
log f
is shown in Fig. 12. By using the slope of linear part of this curve -
0.27, u is calculated as 0.73, which manifests again the system undergoes a static percolation process. The exponent u is also
accessible from the loss angle following Eq. (8). The variations of

vs frequency for the percolation threshold is shown in
Fig. 13. The horizontal line corresponds to
p

=0.39 and then u=73, which is consistent with the value obtained from Fig. 12.
Fig. 13. Variation of the loss angle

as a function of frequency for IL weight fraction of 29.98 wt%.
In summary, four data curves provide evidence that a bicontinuous structure is formed in this [bmim][BF4]/TX-
100/toluene IL microemulsion during the percolation process. Fig. 3b presents a simplified portrayal of bicontinuous
structure, namely, IL and oil tubes are entangled and crossed with each other, with IL and hydrocarbon regions stretching
over large distances. In addition, the rapid migration of ions in the IL tunnels results in the percolation phenomenon observed
in Fig. 7, which makes the conductivity increase by two orders of magnitude.
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4.2 Structural transition of IL microemulsion
Fig. 14. Variations of
'

(○) and
"

(□) vs
f
, the solid lines are the theoretical curve of Eq. (2),
IL
c
=15.08 wt%.
As an example, Fig. S in the Supplementary Material shows the complex plane plot of [bmim][BF4]/TX-100/toluene at an
IL weight fraction of 20.94 wt%. The situation is much closer to the Cole-Cole Plot (the dotted line is the Debye function), so
we finally used the Cole–Cole function, namely Eq. (2), to fit all of the complex dielectric spectra shown in Fig. 5a and c.
During this process, a satisfactory estimation of the dielectric parameters is obtained by using the nonlinear least-squares
method to minimize the sum of the residuals for the complex permittivity. To manifest the goodness of the fitting process,
Fig. 14 shows the fitting curves (solid lines) are in agreement with the experimental data (open symbols) when the IL weight
fraction in the microemulsion is 15.08 wt%, as an example. The values of dielectric parameters
h

,


,

, and

were
listed in Table 1 and the weight fraction dependence of them are shown in Fig. 15. In Fig. 15, all the data curves have two
inflection points at the same positions, namely, 19.30 and 33.84 wt%. Since section 4.1 has already proved the microstructure
of this IL microemulsion changed from IL/O to O/IL through the bicontinuous state (B.C.), by using these two weight
fractions in Fig. 15, the experimental path is divided into IL/O, B.C. and O/IL subregions. In addition, the positions of these
two inflection points are consistent with the phase boundaries which are reported in the literature [11], which indicates that
the dielectric parameters obtained by our fitting process are reasonable. The dependence of dc conductivity on IL weight
fraction, as shown in Fig. 7, does not have inflection points; meanwhile, platforms cannot be detected in Fig. 7 either, on the
contrary, we can detect two platforms (or slow growth) in both IL/O and O/IL subregions in the curve of
h

vs IL weight
fraction as shown in Fig. 15d. Those all demonstrates that the dielectric parameters are more sensitive to structure of the
system than conductivity data. In summary, two phase transitions are occurring between the data-range we have selected in
Fig. 2.
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Fig. 15. Plot of (a)

(hollow symbols), (b)

, (c)


, (d)
h

against IL weight fraction. In (a), solid symbols represent the relaxation
time of interfacial polarization
MW

of samples.
4.3 Relaxation mechanism
The most direct way to determine the relaxation mechanism for the observed dielectric relaxation is to compare the
experimental and theoretical values of the relaxation time. As introduced in section 3.2, both IL/O and O/IL droplets can be
modeled as spherical droplets dispersed in a continuous phase. In addition, because the dielectric constants of [bmim][BF4],
TX-100 and toluene are significantly different, in the IL microemulsion made up by using these three materials, the electrical
parameter of dispersed and continuous phase should also be different, and the interfacial polarization should be observed in
our measured frequency range, as summarized in section 3.3. On the basis of this idea, we calculated the phase (electrical)
parameters including the relaxation time of interfacial polarization according to Eq. (9-14) by using the dielectric parameters,
the results are listed in Table 2.
For convenient comparison, the dependence of
MW

on IL weight fraction is also shown in Fig. 15a. In this figure, we can
see that not only the theoretical values
MW

(solid circles) for every sample in both IL/O and O/IL subregions are very close
to the experimental values

(hollow circles), but also they have the same weight fraction dependence trend. Thus, we
believe that the dielectric relaxation observed in the [bmim][BF4]/TX-100/toluene microemulsions should be attributable to
the interfacial polarization, which was also observed in other IL-based [33,35,36,39] and traditional [
54
,
55
] microemulsions.
The existence of interfacial polarization indicates that: (1) the previous spherical IL/O and O/IL models is reasonable, which
strongly proves the existence of microdroplet structure coated by surfactant interfacial membrane; (2) the dielectric properties
of continuous phase and dispersed phase are significantly different; (3) in Fig. 15 the two inflection points are taken as the
boundaries between these three subregions (IL/O, B.C. and O/IL) is reasonable. The superposition of these two polarizations
results in only part of the data for
s

in Fig. 10 can match the theoretical prediction. In addition, Maxwell-Wagner
polarization for suspensions is more specifically ascribed to the fluctuation of space charge (arising in solution neighboring
the particle surface) within the Debye length (a measure of the thickness of the double layer characterizing the size of the
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diffuse ion cloud), as reported by O’Brein et al. [
56
,
57
] and Dukhin et al. [
58
,
59
]. This double layer and then the Debye
length may exist not only on the surface of O/IL and IL/O droplets but also on the surface wall of oil and IL channels in the
B.C. subregion. That is why the dicontinuous phase also has a dielectric relaxation and the relaxation time in this sub-region
transitions continuously from IL/O to O/IL microregions, as shown in Fig. 15a. The relaxation time distribution index

is
in the range of 0.65 to 0.70, which deviates from 1, indicating that there are at least two types of relaxation mechanisms in
this observed dielectric relaxation: one is the interfacial polarization which is just identified; the other one is related to the
percolation process introduced in section 4.1 because percolation can be regarded as a polarization process [39,41,50].
As shown in Table 1, the value of dielectric increment falls within the range of a typical interfacial polarization relaxation.
The sum of interface in the system is proportional to the dielectric increment [35,39], thus the weight fraction dependence of
interface can be seen in Fig. 15c through the
 
IL
c


curve: (1) from 3.39 to 18.25wt%, namely, in IL/O subregion, more
and more IL molecules keep inserting into the micelle cores, which induce an increase of interface and is why


increases
from 5.10 to 9.35; (2) from 20.94wt% to 33.18wt%,


is a constant in the B.C. subregion, and the average value of it is
9.26; this phenomenon infers that the interface sum is not change during the formation of IL and oil channels (namely, the
IL/O droplets break at the same time the O/IL droplets form) in this subregion [
60
-
62
]; (3) in O/IL subregion, the volume
fraction of oil droplets increase (as discussed in the fifth paragraph of section 4.4) makes the sum of interface increases, that
is why above 36.00wt%,


still increases.
4.4 Analysis of the phase parameters
Table 2
Phase parameters of [bmim][BF4]/TX-100/toluene with different IL weight fractions.
IL
c
(wt%)
Micro-structure
m

m

(mS/cm)
p

p

(mS/cm)

MW

(ns)
3.39
IL/O
2.40
0.0490
7.50
6.56
0.382
2.20
6.41
IL/O
2.40
0.134
6.32
11.1
0.461
1.51
9.22
IL/O
2.40
0.210
5.76
11.6
0.518
1.28
11.94
IL/O
2.40
0.294
5.44
14.5
0.558
1.06
15.08
IL/O
2.40
0.423
5.25
18.9
0.589
8.37
18.25
IL/O
2.40
0.534
5.06
21.8
0.623
7.54
36.00
O/IL
10.7
4.71
2.40
34.1
0.718
1.17
39.11
O/IL
10.8
4.97
2.40
36.1
0.723
1.13
42.16
O/IL
11.0
5.30
2.40
38.9
0.726
1.08
45.14
O/IL
11.2
5.57
2.40
41.4
0.729
1.04
47.99
O/IL
11.3
5.81
2.40
42.9
0.732
1.02
50.97
O/IL
11.4
6.61
2.40
48.8
0.734
0.909
53.80
O/IL
11.6
7.05
2.40
52.8
0.735
0.859
56.88
O/IL
11.7
7.50
2.40
56.3
0.737
0.818
60.07
O/IL
11.8
8.04
2.40
60.1
0.738
0.774
The IL/O and O/IL microemulsions are both spherical droplets (with a high volume fraction

) dispersed in a continuous
phase as shown in Fig. 4, whose phase parameters can be all calculated according to the Hanai theory introduced in section
3.3. When
m

in the IL/O microregion and
p

in the O/IL microregion are respectively taken as the dielectric constant of
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pure toluene (2.40), other phase parameters of each sample was calculated according to Eqs. (9-13), the results were listed in
Table 2. To better show the weight fraction dependence, the phase parameters of these two subregions listed in table 2 were
plotted in Fig. 16.
Compared with traditional microemulsions, ILs often require more surfactants to form stable microemulsions. In addition,
the range of IL/O and O/IL microregions is narrow in the selected experimental path in this paper, the structural
transformation is rapid. Both of these two factors mean that the measured sample should be a dense system. This prediction
can be illustrated by our calculation, namely, the minimum of the volume fraction is 38.2% for the dispersed phase. This
calculation result also shows that the using of Hanai theory is reasonable.
Fig. 16. Evolution of (a)

, (b)
p

, (c)
m

and (d)
p

as a function of IL weight fraction for IL/O subregions. Plot of (e)

, (f)
m

and (g)
p

against toluene weight fraction for O/IL subregions.
In the IL/O subregion, as shown in Fig. 16a, with increasing IL weight fraction,

also increases because the IL
constantly solubilizes into the micropool of droplets. As shown in Fig. 16b,
p

decreases as the IL weight fraction increases,
and their values are lower than the values of both pure IL (13.06 [33]) and pure TX-100 (7.59 [33]) but higher than the value
of pure toluene 2.40. This means that the dispersed phase should be a mixture of IL, TX-100 and toluene under our
calculation setting. In this subregion, the continuous phase is formed by oil with low conductivity, and the dispersion phase is
formed by ILs with high conductivity, which indicates that, as shown in Figs. 16c and 16d, the calculated result of Hanai
theory, namely, the conductivity of the continuous phase
m

is lower than the conductivity of the dispersed phase
p

, are
reasonable. With the increasing of IL weight fraction, the IL dissolved in the continuous phase (although very little) increases,
and the number of ions in the disperse phase also increases, which is why the calculated values of
m

and
p

both increase.
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In the O/IL subregion, as listed in Table 2, for every sample, only when
m

is taken the value calculated according to the
formula below, can other phase parameters have certain physical significance.
m TX TX IL IL
  
   
(15)
where
TX

and
IL

are the volume fractions of TX-100 and IL, which are both calculated according to the weight ratio of
IL/TX-100 introduced in Section 2.1,
TX

and
IL

are the dielectric constant of TX-100 (7.59) and IL (13.06) [33]. This
shows that the continuous phase consists of the IL mixed with a certain amount of TX-100. There are two possible reasons
for this phenomenon: (1) the stable IL microemulsion needs a large number of surfactants; (2) there is no significant
difference between
TX

and
IL

, thus the contribution of TX-100 to the permittivity of the continuous phase cannot be
ignored. The similar situations have been found in [bmim][BF4]/TX-100/cyclohexane [33] and [bmim][BF4]/TX-
100/triethylamine [39].
In the O/IL microemulsion, with the increase of toluene weight fraction from 20.07 to 31.95 wt%, the volume fraction of
dispersed phase should increase because the oil molecules constantly solubilize into micropool of oil. However, the
calculated volume fraction of dispersed phase

decreased slightly by 2% instead as shown in Fig. 16e, compared to an
increase of nearly 12% in the oil weight fraction. This phenomenon can be explained as: as illustrated in Fig. 3a to Fig. 3c,
when the droplet changing from IL/O to O/IL with increasing IL weight fraction, the orientation of the TX-100 hydrophilic
chain changed from facing inward towards the IL micropool to facing outward towards the IL continuous phase, which
makes more space for the palisade layer to fill with more ILs, as illustrated by Fig. 17. This volume increase effect overcomes
the volume decrease caused by the decrease of oil weight fraction, as a result, the volume fraction of O/IL droplets increases
slightly. The value of

increases until close to the maximum stacking density of spheres 74%, which means that the
spherical microemulsion structure will soon be broken down as the weight fraction of the oil decrease (TX-100 content
decrease at the same time) because the single phase IL microemulsion will break down and become a multiphase system.
Similarly, in the IL microemulsion [bmim][BF4]/TX-100/triethylamine [39], although only the oil phase was different,

also decreases with the oil content increases in the O/IL microemulsion because the same surfactant (TX-100 with a long
hydrophilic chain) constitutes the palisade layer at the interface of oil droplets. In contrast, for IL microemulsion
[bmim][BF4]/ethanol/toluene in our preparation article, although IL and oil are the same,

in the O/IL microemulsion
increases as the oil weight fraction increases because the palisade layer at the interface of oil droplets is ethanol which does
not have a long hydrophilic chain.
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Fig. 17. The volume fraction of dispersed phase

increases slightly, although the oil weight fraction decreases.
In the O/IL droplets, the hydrophilic chain of TX-100 directing towards the outside continuous phase, thus more space
for the palisade layer to fill with ILs, which is also the reason why the electrical conductivity of the dispersed phase
p

further increases with the decrease of weight fraction of toluene (the weight fraction of IL increases) as shown in Fig. 16g. In
the O/IL subregion,
m

(Fig. 16f) is less than
p

(Fig. 16g), possibly because the binary solvent, which contains a large
amount of nonionic surfactant, is used as the continuous phase. The conductivity of the continuous phase of the IL/O
microzone (Fig. 16c) is less than that of the O/IL microzone (Fig. 16f), which is also reasonable, because the continuous
phase of the former is just oil, and the continuous phase of the latter is an IL/TX-100 binary solvent that contains ILs. In
conclusion, according to our calculation results, no matter the O/IL or IL/O subregions, the dispersed phase in the IL based
microemulsion has a higher conductivity than traditional microemulsions. This conclusion is supported by a qualitative report
in the literatures [8,9].
In summary, Hanai theory successfully models IL/O and O/IL microregion as spherical particles with high volume fraction,
and the calculation results is reasonable, thus indicates that: (1) again confirms the phase transition between these three
microregions in our measured experimental path; (2) the concentration ranges chosen for these two spherical microregions
are reasonable; (3) there indeed exists interfacial polarization in these spherical dispersed particle; (4) the large volume of
droplets leads to a small vibration range of them; the large volume fraction of droplets makes them easier to contact each
other and connect together to form a double channel structure; moreover, a large number of surfactants exist, the surfactants
have long hydrophilic chains, the hydrophilic chains interact strongly with the IL, which together make the ions in the
droplets difficult to break through the thick surfactant layer coated in the surface. As a result, the ion is hard to exchange
between the droplets, thus the structure of percolation clusters cannot form; these may be the reasons why the static
percolation occurs in this IL microemulsion.
4.5 Comparison of dielectric spectra of the two kinds of IL microemulsion
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Fig. 18. Comparison of complex dielectric spectra for [bmim][BF4]/TX-100/toluene (○ permittivity □ dielectric loss) and
[bmim][BF4]/TX-100/triethylamine (● permittivity, ■ dielectric loss) with the same molar fraction of IL/surfactant/oil (a) 20, 30 and 50 %,
(b) 15, 50 and 35 %.
The dielectric spectra of sample (I) and sample (III) described in Section 2.1 are placed in Fig. 18a, the hollow circle and
hollow square are the permittivity and dielectric loss data of sample (I), the solid circle and solid square are the permittivity
and dielectric loss data of sample (III). Similarly, dielectric spectra of samples (II) and (IV) are shown in Figure 18b, the
hollow symbols are the data of sample (II), the solid symbols are the data of sample (IV), the circular symbols represent the
permittivity, and the square symbols represent the dielectric loss. As can be seen from Figure 18a, although the oil phase that
compose the microemulsion are different, both the permittivity and dielectric loss spectra are very similar, and there is no
essential difference. Figure 18b even shows the spectra almost overlapping with each other, no matter permittivity and
dielectric loss data. This phenomenon can be explained as: the dielectric constants of the two oil phases, namely toluene (2.40)
and triethylamine (2.44), are very close to each other; and the substances that constitute the interface film (TX-100) and the
polar phase ([bmim][BF4]) are the same. In conclusion, the difference between the dielectric properties of the continuous
phase and the dispersed phase is the main factor for the dielectric relaxation phenomenon in this frequency band, while the
molecular details of the oil phase are the secondary factor.
5. Conclusion
We studied the dielectric properties of three subregions for IL microemulsion [bmim][BF4]/TX-100/toluene. The three
microstructures of this IL-based microemulsion, namely, IL-in-oil, B.C. and oil-in-IL were divided by the weight fraction
dependence of dielectric parameters. Both the conductivity behavior and dielectric behavior indicate that the static
percolation occurs when the phase change from IL/O droplet to O/IL droplet, which infers that a network of IL tubes in an oil
matrix or a network of oil tubes in a IL matrix exist in this system. The only dielectric relaxation observed may be caused by
the interfacial polarization, which indicates that there indeed exists interface in IL/O and O/IL microdroplets caused by the
dielectric difference between the dispersed phase and continuous phase. The conductivity and permittivity of the droplet and
the continuous phase were calculated quantitatively. The electrical conductivity of droplets in the IL microemulsion is much
higher than that of droplets in the traditional microemulsion. The dielectric relaxation is more affected by the static dielectric
constant of each component than by the molecular structural details of oil.
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Acknowledgement
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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CRediT authorship contribution statement
Zhen Li: Conceptualization, Methodology, Formal analysis, Investigation, Resources, Data Curation,
Writing - Original Draft. Zhefeng Fan: Investigation, Resources, Writing - Review & Editing,
Supervision. Zhen Chen: Resources. Yiwei Lian: Resources.
Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal
relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be
considered as potential competing interests:
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Graphical Abstract
The dielectric properties of three subregions, namely, IL-in-toluene, bicontinuous and toluene-in-IL for
non-aqueous ionic liquid microemulsion [bmim][BF4]/TX-100/toluene.
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