The surface physico-chemical properties of surfactants in ethanol

Colloids and Surfaces
A: Physicochemical and Engineering Aspects 155 (1999) 339 – 348
www.elsevier.nl/locate/colsurfa
The surface physico-chemical properties of surfactants in
ethanol–water mixtures
J.-B. Huang *, M. Mao, B.-Y. Zhu
Institute of Physical Chemistry, Peking Uni6ersity, Beijing 100871, PR China
Received 26 August 1998; received in revised form 21 December 1998; accepted 23 December 1998
Abstract
The surface physico-chemical properties of various kinds of surfactants (including cationic, anionic, nonionic and
catanionic surfactants) in mixed ethanol–water solvents were investigated. In different surfactant systems, ethanol
content influences the cmc and gcmc differently. It is found that the varying tendency of gcmc induced by ethanol
addition can be predicted according to their saturation adsorption and gcmc values in water. For the systems with
bigger saturation adsorption and smaller gcmc values in aqueous solutions without ethanol, their gcmc values rise with
ethanol addition. For the systems with smaller saturation adsorption and bigger gcmc values in aqueous solutions, the
ethanol effect on gcmc is opposite. On the other hand, for the influence of ethanol addition on the cmc of surfactant
systems, the type of surfactant is important. In ionic surfactant systems, ethanol addition makes the cmc decrease
followed by an increase. However, in the systems of nonionic or catanionic surfactants, ethanol addition just makes
the cmc go up. © 1999 Elsevier Science B.V. All rights reserved.
Keywords: Surface adsorption; Micellization; Surface tension; Ethanol – water mixture
1. Introduction
In comparison with the amount of work done
on the physical and chemical properties of surfactants in water and apolar solvents, the study of
surfactants in polar non-aqueous solvents and
their mixture with water is a rather limited field.
Attention was drawn to this topic rather early [1],
and micellization was found in a range of solvents
including ethylene glycol [2], glycerol, formamide,
various diols, formic acid [3] amides and DMSO
[4], hydrazine [5], and low-melting fused salts [6].
* Corresponding author.
However, there have been rather few systematic
investigations on the correlation of solvent properties and surfactant aggregation. One early attempt trying to correlate the formation of micelles
for a nonionic surfactant with a number of properties of some 20 different solvents was reported
by Ray [3] with limited success. Efforts to follow
the change in surfactant aggregation behavior
when gradually and completely exchanging the
water for a polar solvent are even more rare [4,7].
During the last 10 years, interests in studying the
aggregation of surfactants in non-aqueous, polar
solvents and mixed aqueous solutions have increased considerably. Several interesting papers
0927-7757/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 7 - 7 7 5 7 ( 9 9 ) 0 0 0 0 3 - 5
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J.-B. Huang et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 339–348
about surfactants in polar solvents and the mixtures of them with water have been published
[8–10]. Most previous studies in mixed solvents
were mainly on the surfactant micellization, however, it would be important to generalize and
explain the surface physico-chemical properties
and micellization phenomena of surfactants in
mixtures of water and polar solvents for exploring
the regularity and nature of the effect of polar
solvent addition.
The objective of this study was to investigate
the influences of ethanol — a very popular polar
solvent, on surface adsorption and micellization
of various kinds of surfactant systems. The values
of cmc, saturation adsorption(Gmax), minimum
area per surfactant molecule (Amin), and surface
tension at cmc (gcmc) of various surfactants in
different ratios of ethanol – water mixtures were
reported in this work. Regularity and explanation
for the effects of ethanol addition on cmc and gcmc
were discussed.
Fig. 2. Surface tension of C10COONa system (pH 9.2, I = 0.13
mol kg − 1) in ethanol/water mixture with various volume
ratios. (a) 0:1, (b)1:19, (c)1:5, (d)1:4, (e)1:2.
2. Materials and methods
2.1. Materials
Fig. 1. Surface tension of C11COONa system (pH 9.2, I= 0.13
mol kg − 1) in ethanol/water mixture with various volume
ratios. (a) 0:1, (b)1:19, (c)1:9 (d)1:4, (e)1:2.
Sodium alkylcarboxylates (Cn COONa, n=
9,10,11) were prepared by neutralizing the corresponding carboxylic acid (Cn COOH) with NaOH
in ethanol, then the solvent was removed and
Cn COONa was vacuum dried. C9COOH was
double distilled and C11COOH was recrystallized
five times from an ethanol–water mixed solvent
(m.p. 43–44°C). C10COONa was recrystallized
three times from ethanol. Alkyltrimethyl ammonium bromides (Cm N(CH3)3Br m=8,10,12) were
synthesized from n-alkyl bromide and tri-methyl
amine. The crude products were recrystallized five
times from an ethanol–acetone mixture. Sodium
dodecyl sulfate (SDS) was the product of Beijing
Chemical (A.R. grade) recrystallized five times
from
pure
ethanol.
Decylmethylsulfoxide,
C10H21SOCH3 was synthesized and purified in the
same way as used in reference [11]. The purity of
all the surfactants was examined by surface ten-
J.-B. Huang et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 339–348
341
sion measurement using drop volume method [12]
and no surface tension minimum was found in
their surface tension curves (g – log C). Ethanol
was refluxed with magnesium scraps and iodine
more than 2 h to remove the trace of water and
then distilled. Deionized water was treated with
KMnO4 and distilled. Other reagents were products of Beijing Chemical, A.R. grade.
2.2. Methods
Surface tension measurements were made using
the drop volume method [12]. The density of the
ethanol–water mixtures needed for calculating the
surface tension were measured with a DMA45
densitometer (Anton Paar K.G.A-8054, GRAZ,
Australia). All the mixed ratio in ethanol–water
mixture is volume ratio. The temperature of the
experiments was kept at 309 0.05°C.
Fig. 4. Surface tension of C10N(CH3)3Br system in ethanol/water mixture with various volume ratios. (a) 0:1, (b)1:19, (c)1:9,
(d)1:4, (e)1:2.
The pH values in the Cn COONa systems were
controlled to 9.2 (by Na2B4O7·10H2O, 0.01 mol
dm − 3) or 13 (by NaOH). The ionic strengths (I)
in both of the Cn COONa and Cm N(CH3)3Br systems were controlled to 0.13 mol kg − 1(by NaBr
or NaOH, respectively) to obtain the adsorption
results. In 1:1 Cn COONa and Cm N(CH3)3Br systems, the pH values were controlled to 9.2 (by
Na2B4O7·10H2O, 0.01 mol dm − 3) or 13
(NaOH). No pH or ionic strength adjustments in
other surfactant systems were made.
3. Results
Fig. 3. Surface tension of C12N(CH3)3Br system in ethanol/water mixture with various volume ratios. (a) 0:1, (b)1:19, (c)1:9,
(d)1:4, (e)1:2, (f)1:1.
The surface tension(g) versus logarithm of concentrations (log C) curves of various surfactants
in ethanol–water mixtures are shown in Figs.
1–7. The values of critical micelle concentration
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(cmc), and surface tension at cmc (gcmc) of these
systems can be determined from the inflection
points in the g– log C curves. The adsorption of
surfactants (G) was calculated according to the
Gibbs adsorption equation G = −dg/RT d ln C,
since the ionic strength and pH for Cn COONa
systems were kept constant. For calculating the
saturation adsorption(Gmax) the slopes of the
straight parts of g – log C curves were taken for
the dg/d ln C values in Gibbs equation. Then the
minimum area per surfactant molecule (Amin) was
obtained from the saturation adsorption by
Amin =1/Gmax. The values of cmc, gcmc, Gmax and
Amin are shown in Tables 1 – 8. The surface tensions in all the surfactant systems, in which the
volume ratio of mixed solvents is 1:1, do not vary
with the surfactant concentrations.
Fig. 6. Surface tension of C10H21SOCH3 system in ethanol/water mixture with various volume ratios. (a) 0:1, (b)1:19, (c)1:7,
(d)1:4, (e)1:2.
Fig. 5. Surface tension of C11COONa system (pH 13, I =0.13
mol kg − 1) in ethanol/water mixture with various volume
ratios. (a) 0:1, (b)1:19, (c)1:9, (d)1:4, (e)1:1.
Fig. 7. Surface tension of 1:1 C11COONa – C12N(CH3)3Br
system (pH 9.2) in ethanol/water mixture with various volume
ratios. (a) 0:1, (b)1:9, (c)1:4, (d) 1:2, (e)1:1.
J.-B. Huang et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 339–348
343
Table 1
The surface physico-chemical properties of C11COONa (pH 9.2, I =0.13 mol kg−1) in ethanol–water mixtures
C2H5OH/H2O volume ratio
cmc (mol dm−3)
gcmc (mN m−1)
106 Gmax (mol m−2)
Amin (nm2)
0:1
1:19
1:9
1:5
1:4
7.38×10−3
1.26×10−2
7.19×10−3
6.05×10−3
8.00×10−3
25.5
29.9
32.0
31.6
31.2
4.70
3.45
2.15
1.66
1.42
0.35
0.48
0.77
1.00
1.17
Table 2
The surface physico-chemical properties of C10COONa (pH 9.2, I =0.13 mol kg−1) in ethanol–water mixtures
C2H5OH/H2O volume ratio
cmc (mol dm−3)
gcmc (mN m−1)
106 Gmax (mol m−2)
Amin (nm2)
0:1
1:19
1:9
1:5
1:4
2.90×10−2
2.09×10−2
1.78×10−2
1.45×10−2
2.90×10−2
29.8
33.4
33.2
32.7
31.4
4.25
3.08
2.11
1.83
0.90
0.39
0.54
0.79
0.91
1.84
Table 3
The surface physico-chemical properties of C12N(CH3)3Br in ethanol–water mixtures
C2H5OH/H2O volume ratio
cmc (mol dm−3)
gcmc (mN m−1)
106 Gmaxa (mol m−2)
Amina (nm2)
0:1
1:19
1:9
1:4
1:2
1.66×10−2
1.38×10−2
1.58×10−2
3.31×10−2
4.37×10−2
38.4
37.1
33.9
32.5
28.7
3.45
2.53
2.01
1.08
–
0.48
0.66
0.83
1.54
–
a
The ionic strength was controlled to I = 0.13 mol kg−1 to obtain the adsorption data.
4. Discussion
4.1. Effect of ethanol on gcmc
From Figs. 1 – 4 and Tables 1 – 4, we can find
that the influences of ethanol addition on gcmc
values in Cn COONa (pH 9.2, I =0.13 mol kg − 1)
systems and Cm N(CH3)3Br systems are different.
In Cn COONa (pH 9.2, I =0.13 mol kg − 1) systems, ethanol addition makes the gcmc go up,
whereas, in Cm N(CH3)3Br systems, ethanol addition makes the gcmc decrease with the increase of
the adding ethanol amount. However, ethanol
addition makes gcmc decrease in both C11COONa
(pH 13, I =0.13 mol kg − 1) and SDS systems (see
Tables 5 and 8). The difference in ethanol effects
on gcmc cannot be ascribed to the difference of
surfactant types—anionic or cationic surfactants,
since SDS is a kind of anionic surfactant, but
after ethanol addition the gcmc changes similarly
with that of the Cm N(CH3)3Br systems. Furthermore, even for the same surfactant C11COONa,
the variation of pH (from 9.2 to 13) in the system
makes the gcmc change oppositely after ethanol
addition. Comparing the results in Tables 1–8, we
can divide these systems to two groups. For group
A, including C10H21SOCH3, 1:1 C11COONa–
C12N(CH3)3Br and Cn COONa (pH 9.2, I=0.13
mol kg − 1) systems, ethanol addition makes the
gcmc go up. On the other hand, for group B
including Cn COONa (pH 13, I= 0.13 mol kg − 1),
SDS and Cm N(CH3)3Br systems, the gcmc values
decrease with the increase of the ethanol content
(see Fig. 8). It can be seen that all the surfactants
J.-B. Huang et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 339–348
344
Table 4
The surface physico-chemical properties of C10N(CH3)3Br in ethanol–water mixtures
C2H5OH/H2O volume ratio
cmc (mol dm−3)
gcmc (mN m−1)
106 Gmaxa (mol m−2)
Amina (nm2)
0:1
1:19
1:9
1:4
1:2
5.75×10−2
5.50×10−2
7.24×10−2
7.94×10−2
1.70×10−1
39.8
35.6
34.4
32.0
29.8
3.63
3.12
2.33
1.64
0.86
0.46
0.53
0.71
1.01
2.08
a
The ionic strength was controlled to I = 0.13 mol kg−1 to obtain the adsorption data.
Table 5
The surface physico-chemical properties of C11COONa (pH 13, I= 0.13 mol kg−1) in ethanol–water mixtures
C2H5OH/H2O volume ratio
cmc (mol dm−3)
gcmc (mN m−1)
106 Gmax (mol m−2)
Amin (nm2)
0:1
1:19
1:9
1:4
9.33×10−3
6.92×10−3
7.08×10−3
7.24×10−3
35.8
34.6
31.8
30.0
3.68
3.45
2.76
1.38
0.45
0.48
0.60
1.20
Table 6
The surface physico-chemical properties of C10H21SOCH3 in ethanol–water mixtures
C2H5OH/H2O volume ratio
cmc (mol dm−3)
gcmc (mN m−1)
106 Gmax (mol m−2)
Amin (nm2)
0:1
1:19
1:7
1:4
1:2
1.70×10−3
2.40×10−3
3.02×10−3
3.80×10−3
6.31×10−3
24.5
24.6
25.4
26.2
28.5
5.37
4.37
3.88
2.73
–
0.31
0.38
0.43
0.61
–
in group A have bigger Gmax ( \4.25 ×10 − 6 mol
m − 2) and lower gcmc ( B 34 mN m − 1) in water,
and all the systems in group B have smaller Gmax
and bigger gcmc in their aqueous solution without
ethanol. for the systems investigated.
Ethanol addition effect on gcmc of surfactant
systems may come from two sides. Firstly, ethanol
influences gcmc of surfactant systems by changing
the property of solvents. The increase of ethanol
content would reduce the average interaction between molecules of solvent, which would make
the surface tension of the mixed solvents decrease
(the surface tensions at ethanol/water volume ratio of 1:19, 1:9, 1:4, 1:2 and 1:1 are 61.3, 49.0,
39.5, 32.0 and 28.4 mN m − 1, respectively). This
effect must induce a reduction of surface tension
of the system, hence the gcmc values in surfactant
systems tend to go down while ethanol content in
the mixed solvents increases.
Secondly, ethanol as a kind of surface active
matter will adsorb at the air/solvent interface and
compete the positions of surface layer with surfactants. Moreover, with increase of ethanol content,
hydrophobic interaction between the hydrophobic
groups of surfactants would be reduced, inducing
weaker adsorption tendency of surfactants. Both
of them make the adsorption of surfactant in
ethanol–water mixture lower. This is really the
situations for every system investigated. However,
situations are not all the same for various surfactant systems. There are differences in composition
and structure of surface phase between the two
groups of surfactant systems. It is well known,
surfactant molecules keep orientation in saturated
J.-B. Huang et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 339–348
345
Table 7
The surface physico-chemical properties of 1:1C11COONa–C12N(CH3)3Br (pH 9.2) system
C2H5OH/H2O volume ratio
cmc (mol dm−3)
gcmc (mN m−1)
106 Gmax (mol m−2)
Amin (nm2)
0:1
1:9
1:4
1:2
6.80×10−4
7.90×10−4
2.34×10−3
1.00×10−2
22.2
23.5
26.2
26.9
5.21
4.60
2.59
1.81
0.32
0.36
0.64
0.91
Table 8
The gcmc values (mN m−1) of surfactant systems in different ethanol–water volume ratio
Systems
0:1
1:19
1:9
1:4
1:2
SDS
C12N(CH3)3Bra
C10N(CH3)3Bra
C9COONa–C10N(CH3)3Brb
C11COONa–C8N(CH3)3Brb
C10COONab
38.6
36.6
40.4
23.5
25.0
28.5
38.4
35.0
37.1
24.8
36.3
32.8
33.3
25.3
28.3
32.0
33.3
30.9
31.1
25.9
29.0
33.2
29.6
29.8
29.0
30.9
28.5
a
b
The ionic strength was controlled to I = 0.13 mol kg−1 to obtain the adsorption data.
pH was controlled to 9.2 (by Na2B4O7·10H2O, 0.01 mol dm−3).
adsorption layer, forming an area of polar group
near water phase and an apolar area towards air.
For the aqueous solutions of surfactants in group
A, their Gmax are larger and Amin smaller than the
counterparts of the surfactants in group B. It
means that comparing with systems in group B, in
the surface phases of systems in group A, water
contents are smaller, the area ratios occupied by
water to surfactants in the layers of polar group
are smaller; and in the apolar part the outmost
area ratio occupied by methyl to mythylene are
larger. Surface tension of a liquid is mainly determined by the atoms and atomic groups forming
the outmost layer of surface [13] and the contribution of CH3 to surface energy is less than that of
CH2 and much less than that of water [14]. Therefore, systems in group A shows lower gcmc in
water than that in group B. Schematic diagrams
for the structures of surface phase of systems in
groups A and B were shown in Fig. 9(a) and Fig.
10(a), respectively.
As alcohol molecules partake in the surface
layer, they would occupy the empty position of
adsorption layer, i.e. that belonging to water originally, as well as substitute some of adsorbed
surfactants. The first effect would decrease, while
the second increase, the surface tension of solution for the reason explained in previous paragraph. In adsorption layer of the systems in group
B, the area ratios occupied by water are larger,
and the surfactant molecules compact more
loosely than those in group A. Therefore, the first
effect of ethanol addition on adsorption layer
may be predominant for the systems in group B
(see Fig. 9). In addition of the ethanol effect
decreasing the surface tension of the solvent, it is
understandable that the gcmc values decrease with
the increase of ethanol content.
On the other hand, the situation of systems in
group A is different. Comparing with systems in
group B, water contents in the surface phases of
systems in group A are smaller, implying that the
main mechanism for ethanol entering adsorption
layer would be to compete the positions of surface
layer with surfactants as surface active matter.
Therefore, as the ethanol concentration goes up,
more ethanol molecules participate in the interface layer displaying absorbed surfactants and the
average area per surfactant molecule increase. Accordingly the area ratio occupied by mythylene to
methyl in the outmost layer will gradually increase (see Fig. 10). Since the contribution of
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J.-B. Huang et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 339–348
Fig. 10. Schematic diagram for the structure of surface phase
of system in group A (a) without (b)with the participation of
ethanol molecules in adsorption layer.
Fig. 8. gcmc of the various surfactant systems as a function of
x ethanol (ethanol mole fraction) in mixed solvents. (a)
C10N(CH3)3Br, (b)SDS, (c) C12N(CH3)3Br, (d) C11COONa
(pH 13, I= 0.13 mol kg − 1), (e) C10COONa (pH 9.2, I =0.13
mol kg − 1), (f) C11COONa (pH 9.2, I= 0.13 mol kg − 1), (g)
C10H21SOCH3, (h) 1:1 C11COONa–C12N(CH3)3Br (pH 9.2).
smaller saturation adsorption and higher gcmc values in aqueous solutions, the effect of ethanol
addition is opposite (see Fig. 8). A convincing
example is the different effects of ethanol addition
on the systems of the same surfactant C11COONa
but at different pH (9.2 and 13). At pH 9.2, the
saturation adsorption of C11COONa is 4.70×
10 − 6 mol m − 2, and gcmc is 25.5 mN m − 1 and the
system belong to group A according to the effect
of ethanol addition. While the pH value increased
to 13, the saturation adsorption down [15] to
3.68× 10 − 6 mol m − 2, and gcmc is 35.8 mN m − 1.
and the system changes from group A to group B,
based on the effect of ethanol addition.
methylene group to surface tension is larger than
that of methyl group, this effect must result in a
higher gcmc for the systems of group A.
According to the facts provided above, it is
obvious that the variation of gcmc is not determined by the types of surfactants (cationic, anionic, nonionic or catanionic surfactants), but
their saturation adsorption and gcmc values in
aqueous solutions. For the systems with bigger
saturation adsorption and smaller gcmc values in
aqueous solutions, their gcmc values rise with the
addition of ethanol. As for the systems with
Fig. 9. Schematic diagram for the structure of surface phase of
system in group B (a) without (b)with the participation of
ethanol molecules in adsorption layer.
.
Fig. 11. Cmc of the ionic surfactant systems as a function of x
ethanol (ethanol mole fraction) in mixed solvents. (a)
C10COONa (pH 9.2), (b) C10N(CH3)3Br, (c), C10COONa (pH
9.2, I =0.13 mol kg − 1), (d) C12N(CH3)3Br.
J.-B. Huang et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 339–348
347
addition may influence the gcmc values very little or
make them go down in this kind of systems.
4.2. Effect of ethanol on the cmc
Fig. 12. Cmc of the nonionic and 1:1 surfactant systems as a
function of x ethanol (ethanol mole fraction) in mixed solvents. (a) C10H21SOCH3, (b) 1:1 C11COONa–C12N(CH3)3Br
(pH 9.2).
From Fig. 8 and Tables 1, 2, 6 and 7, we can see
that there is still a small difference among the
systems in group A. In C10H21SOCH3 and 1:1
C11COONa – C12N(CH3)3Br systems, ethanol addition makes the gcmc gradually increase. However,
in Cn COONa (pH 9.2, I = 0.13 mol kg − 1) systems,
the gcmc values increase very much while the
ethanol concentration is low, but change little (or
a little goes down) while the ethanol concentration
is big. This may come from the effect of ethanol
addition on the dielectric constants of mixed solvents. The dielectric constants of the mixed solvents will decrease with the ethanol concentration
increase, which will enlarge the electrostatic forces
between ions, resulting in that the hydrolysis equilibrium Cn COO − /H + =Cn COOH, in the
Cn COONa systems move to more Cn COOH produced and the ratio of Cn COOH in adsorption
layer will increase. This effect will increase the
saturation adsorption and have a tendency to
lower the gcmc at higher ethanol – water volume
ratio. Therefore, it is reasonable that more ethanol
.
It is seen in Tables 1–7, ethanol addition influences the cmc of various surfactant systems also
differently. In this case, the type of surfactants is
very important. In ionic surfactant systems, the
cmc values decrease then increase with the increase
of ethanol concentration (see Fig. 11). This may be
because that the ethanol addition has two effects:
one on electrostatic interaction and the other on
the property of solvent. When its concentration is
relatively low, ethanol molecules will predominantly enter the polar area of micelle. This may
lower the surface charge density of micelles, decrease the electrostatic repelling force between the
ionic heads of surfactants in micelle and be advantageous to the micelle formation [16], resulting in
smaller cmc values. However, when the ethanol
concentration increases, the dielectric constants of
the mixtures become lower and lower, as a result,
the electrostatic force of the ionic head groups in
micelle would increase. Furthermore, with the
increases of ethanol concentration, the hydrophobic interaction between hydrophobic groups of
surfactants was gradually reduced [3], i.e. the
micellization potential decreases. These two effects
must result in a higher cmc for ionic surfactant in
mixed solvent of higher ethanol concentration.
Thus, with the increase of ethanol content, the cmc
values in ionic surfactant systems would have a
minimum value versus the ethanol concentration.
As for the nonionic or 1:1 mixed catanionic
surfactant systems, similar to their adsorption
layer, the surfactant molecules compact very close
in micelles. Penetration of ethanol molecules into
the micelles would be less, and the influence of
ethanol on the formation of surfactant micelle
through this mechanism would be limited. On the
other hand, with the increase of ethanol content,
the hydrophobic interaction between the hydrophobic part of surfactants will become weaker,
which making cmc larger. As a whole, ethanol
addition in these systems will make the cmc go up
gradually (see Fig. 12). The results in 1:1
C11COONa–C8N(CH3)3Br
and
C9COONa–
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J.-B. Huang et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 155 (1999) 339–348
C10N(CH3)3Br systems also support this
conclusion.
Since there are many interactions such as hydrolysis equilibrium, mixed micellization and
mixed solvent effect existing in the Cn COONa
systems, The ethanol effect on the cmc of
Cn COONa systems is very complex as shown in
Tables 1, 2 and 5.
Acknowledgements
This project (29773004) was supported by National Natural Science Foundation of China.
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