Micellization properties of cationic gemini surfactants in aqueous solution

Article abstract of DOI:10.1016/j.tca.2013.01.016

The main goal of this work was to investigate the self-assembly process for water solutions of two gemini surfactants, which differ in spacer chain length, at wide range of temperatures. For this reason the aqueous solutions of hexylene-1,6-bis(dimethyl-octylammonium bromide) and dodecylene-1,12- bis(dimethyloctylammonium bromide) have been examined by the calorimetric (DSC) and densimetric methods within the 293-323 K and 288-323 K temperature range, respectively. The analysis of c_p values obtained for the examined systems allowed to propose an alternative way to estimate the region where micellization process can occur. The observed temperature dependence of the c.m.c. for surfactants investigated shows a typical shape for ionic gemini surfactants. This behavior was explained as a resultant of two competing effect: decrease in the hydrophilic properties of the surfactant molecule and decrease in the hydrophobic hydration of the alkyl chain along with the temperature increase. The enthalpy of micellization ΔH_mic and other thermodynamics parameters associated with the micellization process: ΔG_mic, ΔS_mic and ΔC_{p mic} were calculated on the base of the pseudo-phase separation model. As expected, more exothermic enthalpies of micellization are observed with increasing temperature for both the surfactants investigated in this work.

Full text of DOI:10.1016/j.tca.2013.01.016

Thermochimica Acta 558 (2013) 29–35
Contents lists available at SciVerse ScienceDirect
Thermochimica Acta
journal homepage: www.elsevier.com/locate/tca
Micellization properties of cationic gemini surfactants in aqueous solution
∗
K. Łudzik , H. Piekarski, K. Kubalczyk, M. Wasiak
Department of Physical Chemistry, University of Łód ´z , Pomorska 165, 90-236 Łód ´z , Poland
a r t i c l e i n f o
a b s t r a c t
Article history:
The main goal of this work was to investigate the self-assembly process for water solutions of two gemini
surfactants, which differ in spacer chain length, at wide range of temperatures.
Received 19 November 2012
Received in revised form 16 January 2013
Accepted 20 January 2013
For this reason the aqueous solutions of hexylene-1,6-bis(dimethyl-octylammonium bromide) and
dodecylene-1,12-bis(dimethyloctylammonium bromide) have been examined by the calorimetric (DSC)
and densimetric methods within the 293–323 K and 288–323 K temperature range, respectively. The
analysis of cp values obtained for the examined systems allowed to propose an alternative way to estimate
the region where micellization process can occur. The observed temperature dependence of the c.m.c. for
surfactants investigated shows a typical shape for ionic gemini surfactants. This behavior was explained
as a resultant of two competing effect: decrease in the hydrophilic properties of the surfactant molecule
and decrease in the hydrophobic hydration of the alkyl chain along with the temperature increase. The
enthalpy of micellization ꢀHmic and other thermodynamics parameters associated with the micellization
process: ꢀGmic, ꢀSmic and ꢀCp mic were calculated on the base of the pseudo-phase separation model.
As expected, more exothermic enthalpies of micellization are observed with increasing temperature for
both the surfactants investigated in this work.
Available online 21 February 2013
Keywords:
Alkanediyl-␣,␻-
bis(dimethylalkylammonium bromide)
surfactants
Aggregation behavior
Critical micelle concentration (c.m.c.)
Thermodynamics parameters of
micellization
Gemini surfactants
©
2013 Elsevier B.V. All rights reserved.
1
. Introduction
The aqueous solutions of the 8-6-8 surfactant have been studied
by Frindi et al. [8] who found two break points on the concentration
dependence of surfactant solution electrical conductivity. These
authors assigned the second break on the ꢁ = f (Cm) curve at 73 mM
to the c.m.c. of the surfactant, as it corresponds well to the appro-
priate results of fluorescence probing and ultrasonic absorption
examinations. The interpretation of the first break was specula-
tive due to the fact that no characteristic behavior was observed
with other methods within the concentration near to73 mM. In the
case of 8-12-8 surfactant, there is no literature information on the
micellization process of its aqueous solutions.
The main goal of this work was to analyze the influence of
temperature and spacer chain length – s on the micelle formation
process – particularly on the c.m.c. We expected, that the thermody-
namic functions of micellization calculated from the data obtained
together with the appropriate literature data would enable us to
discuss the influence of the factors mentioned above on the behav-
ior of the group of the 8-s-8 type surfactants.
Thermodynamic properties of a system can be commonly used
to gain information on the behavior of surfactant solutions. Among
them the functions based on the volumes and heat capacities of
micellar system have been frequently determined [1–5]. In the
case of surfactant solutions, advantages of these techniques are
their high sensitivity to changes in hydrophobic interactions lead-
ing to micellization or association and, on the other hands, their
relatively low sensitivity to macroscopic changes and electrostatic
interactions [6]. Systems able to form micellar aggregates show
characteristic changes in the concentration dependencies, among
others, of partial molar volume, volume expansion coefficient,
heat capacity and partial molar heat capacity in the composition
range where the association processes occurs [7]. Therefore, in the
present work we used the functions mentioned in order to analyze
the micellization process in aqueous solutions of cationic dimeric
surfactants: hexylene-1,6-bis(dimethyloctylammonium bromide)
(
8-6-8) and dodecylene-1,12-bis(dimethyloctylammonium bro-
mide) 8-12-8.
2
. Experimental
We have examined the aqueous solution of these surfactants
by the calorimetric (cp measurement) and densimetric methods
within a relatively wide range of temperature.
2.1. Materials
The synthesis of hexylene-1,6-bis(dimethyloctylammonium
bromide) (8-6-8) was carried out according to procedure given by
Zana [9]. A solution of 1,6-dibromohexane (0.05 mol, Aldrich) and
N,N-dimethyloctylamine (0.11 mol, Aldrich) in ethanol (100 cm )
∗ Corresponding author. Tel.: +48 42 6355826.
E-mail addresses: kasialudzik@tlen.pl, kasialudzik@o2.pl (K. Łudzik).
3
0
040-6031/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.tca.2013.01.016

3
0
K. Łudzik et al. / Thermochimica Acta 558 (2013) 29–35
0
0
0
0
0
.00034
.00032
.00030
.00028
.00026
0
0
0
0
.00032
.00030
.00028
.00026
0.00
0.05
0.10
0.15
1
0.20
0.00
0.05
0.10
0.15
0.20
-
-1
m /mol kg
m /mol kg
Fig. 2. Dependence of volumetric expansion coefficient on the concentration of 8-
2-8 surfactant at a temperature of 298.15 K.
Fig. 1. Dependence of volumetric expansion coefficient on the concentration of 8-
-8 surfactant at a temperature of 298.15 K.
1
6
III Setaram (France). Measurements were performed within the
temperature range of 292.15–333.15 K. In our experiments the
was heated for 48 h under reflux. Ethanol and unreacted com-
pounds were removed by evaporation under vacuum and the
crude product obtained was purified by crystallization from ethyl
acetate/propan-2-ol (10/1) mixtures (m.p. 488 K, yield 51%).
“continuous with reference” mode was used. The method is based
on the measurement of the differential heat flow between a cell
filled with the solutions and a reference, which occurs during a
continuous increase of temperature. The scanning rate used in our
1
13
The H NMR and C NMR spectra were recorded on a Varian
Gemini 200 BB.
−
1
1
experiments was 0.35 K min . The isobaric heat capacity values
were calculated from cp = f (T) function, by interpolation. As a ref-
erence we used water because of its known heat capacity. Taken as
a base the procedure developed by Góralski et al. [10], the uncer-
tainty in the cp values can be estimated to be lower than 0.25% with
an error on the absolute determination of temperature 0.05 K.
H NMR (200 MHz, D O) 3.34–3.16 (8H, m, N-oct-1-CH2 and N-
2
hex-1,6-CH ), 3.00 (12H, s, N-CH ), 1.84–1.58 (8H, m, N-oct-2 CH
2
3
2
and N-hex-2,5-CH ), 1.46–1.14 (24H, m, N-oct-3,4,5,6,7,-CH2 and
2
N-hex-3,4-CH ), 0.90–0.72 (6H, m, N-oct-8-CH ).
2
3
1
H NMR (200 MHz, D O with addition of DMSO-d6 as a ref-
2
erence) 3.20–3.02 (8H, m, N-oct-1-CH2 and N-hex-1,6-CH ), 2.87
2
(
12H, s, N-CH ), 1.70–1.44 (8H, m, N-oct-2 CH2 and N-hex-2,5-
3
3. Results and discussion
CH ), 1.32–1.04 (24H, m, N-oct-3,4,5,6,7,-CH and N-hex-3,4-CH ),
2
2
2
0
.78–0.62 (6H, m, N-oct-8-CH ).
3
13
3.1. Volumetric functions
C NMR (50 MHz, D O with addition of DMSO-d6 as reference)
2
6
5.9, 65.5, 52.6, 33.0, 30.2, 27.5, 27.0, 24.0, 23.8, 15.5.
Dodecylene-1,12-bis(dimethyloctylammonium
Thermal expansion coefficient, ˛T, and apparent molar volumes,
Vꢂ of 8-6-8 and 8-12-8 surfactants in aqueous solutions at various
temperatures were calculated from the density data by using Eqs.
bromide),
hexylene-1,6-
(
surfactant
8-12-8)
was
prepared
as
bis(dimethyloctylammonium bromide). The crude product
(1) and (2).
obtained was washed with ethyl acetate and dried under vacuum,
m.p. 353–356 K, yield 75%). The 1H NMR and C NMR spectra
13
(
1
∂d
˛
T = −
·
(1)
(2)
were recorded on a Varian Gemini 200 BB or Bruker Avance III
00 MHz.
dT ∂T
6
1
M2
d
1000(d − d)
H
NMR (600 MHz, D O) 3.35-3.24 (8H, m, N-oct-1-CH2
0
2
Vꢂ
=
+
m dd
and N-dod-1,12-CH ), 3.09 (12H,s, N-CH ), 1.76–1.65 (8H, Br s,
2
0
2
3
N-oct-2-CH2 and N-oct-2,11-CH ), 1.50–1.24 (36H, m, N-dod-
2
T
ꢂ
Figs. 1–4 show the trends of ˛ and V values of 8-6-8 and 8-12-
8 surfactant solutions in water as a function of solution molalities
at a temperature of 298.15 K.
The dependences of volumetric expansion coefficient on molal-
ity for the aqueous solutions of 8-6-8 and 8-12-8 surfactants
3
,4,5,6,7,8,9,10-CH2 and N-oct-3,4,5,6,7-CH ), 0.93 (6H, t J = 7.2 Hz,
2
N-oct-8 CH ).
3
13
C NMR (150 MHz, D O) 62.67, 62.60, 51.86, 31.60, 29.12, 28.88,
2
2
8.69, 28.62, 28.57, 25.74, 25.70, 22.51, 22.04, 13.93.
The surfactants synthesized were dried under vacuum at tem-
perature 323 K. All solutions were prepared by weight with a mean
−6
−1
uncertainty in the molality of 2 × 10 mol kg by using double
distilled, freshly boiled water.
4
4
4
94
93
92
2
.2. Experimental methods
Density measurements. Density measurements were carried out
within the temperature range of 293.15–323.15 K for aqueous
solution of 8-6-8 surfactant and 283.15–328.15 K for aque-
ous solution of 8-12-8 using an oscillating U-tube densimeter
Anton Paar 5000. The densimeter was calibrated with degasses
−3
distilled water (d = 0.997043 g cm
at 298.15 K) and dry air
0
0.00
0.05
0.10
0.15
0.20
0.25
−3
(
d = 0.001169 g cm at P = 1 bar). The reproducibility of the den-
-1
−6
−3
m /mol kg
sity measurements was 1 × 10 g cm and the uncertainty was
−6
−3
.
estimated as 7 × 10 g cm
Fig. 3. Apparent molar volume of the 8-6-8 gemini surfactant as a function of sur-
factant molality at 298.15 K. Solid line results from the fit of the experimental data
to Eq. (3).
Heat capacity measurements. Isobaric heat capacities were deter-
mined by means of a differential scanning calorimeter micro DSC

K. Łudzik et al. / Thermochimica Acta 558 (2013) 29–35
31
5
5
5
5
5
96
92
88
84
80
decrease in the hydrophilicity of surfactant molecule which favors
micellization, and on the other hand the increase of temperature
brings about a decrease in hydrophobic hydration of alkyl chains
that hinder micellization. These two effects compete with each-
other. As a result within a lower range of temperature the first effect
dominates in contrast with a higher temperature range where the
second effect prevails [15].
The minimum temperatures of the c.m.c. shifts to the lower val-
ues as the spacer chain length – s increases in homologous series of
surfactants with the same counter ions. Similar observations were
made in the case of other surfactants [16,17]. This relation can
be easily explained taking into account the previously discussed
effects. For surfactants with long hydrophobic spacer length the
self-organized process is hindered at lower temperature than in
case of surfactants shorter chain length. It means that the contribu-
tion of the hydrophobic hydration of alkyl group is more significant
for long chained surfactants. Therefore, the micellization process is
hindered after crossing 303 K for 8-12-8 surfactant whereas for 8-
0.00
0.05
0.10
0.15
0.20
-1
m
/mol kg
Fig. 4. Apparent molar volume of the 8-12-8 gemini surfactant as a function of
surfactant molality at 298.15 K. Solid line results from the fit of the experimental
data to Eq. (3).
6
3
-8 micellization starts to be disfavored only for temperature near
18 K. It is noticeable that the spacer chain length – s, affects on the
0
0
0
0
.070
.065
.060
.055
c.m.c. value weaker than alkyl chain length – m [18]. The explana-
tion of this fact can be connected with the amount of spacer – s an
alkyl chains – m in one molecule of surfactant.
The apparent molar volume function of concentration for aque-
ous solutions of surfactants investigated in this work (Figs. 3 and 4)
have a characteristic shape of most micellar systems [7,8,19,20].
Initially, the apparent molar volume of surfactant remains almost
constant and then rapidly increases. This increase in apparent
molar volumes is caused by the changes in the water structure
in the neighborhood of the surfactant molecule non-polar groups
300
310
T /K
320
(hydrophobic hydration) [20,21] and by the changes in the elec-
trostriction effect connected with the polar groups of surfactant
molecule. As is known, great changes in the solute–solvent inter-
actions in these systems take place in the c.m.c. region where the
micelles formation process begins [7]. A further change in the struc-
ture of micelles is expected to give a tiny change in the course of the
Vꢂ = f (m) function. This trend does not change significantly within
the whole temperature range investigated.
Fig. 5. Temperature dependence of the c.m.c. of 8-6-8 in water. The values of c.m.c.
were obtained as the position of inflection point of function ˛T = f (m), as is shown
in Fig. 2.
have similar shape with a characteristic break point correspond-
−
1
ing to the solution concentrations of 0.070 mol kg for 8-6-8 and
0
−1
.025 mol kg for 8-12-8 at a temperature of 298.15 K. As in our
The volumetric data have been analyzed assuming a pseudo-
phase transition model in order to extract micellization parameters
previous paper, we assume that the inflection point in the curves
under discussion corresponds to the position of c.m.c. [7]. The
temperature dependence of the c.m.c. values of 8-6-8 and 8-12-
[
8,19,20]. According to this model the concentration dependence of
the apparent molar volume of the surfactant can be expressed in
the following form:
8
determined in water are depicted in Figs. 5 and 6 and described
by the second degree polynomial.
For both the surfactants investigated the temperature depend-
ence of the c.m.c. exhibited characteristic shape. Generally, such
a behavior is commonly observed for the aqueous solutions of
ionic surfactants [11–14]. According to Shimizu and co-authors, the
value of c.m.c is a resultant of two effects. The increase in T causes a
c.m.c.
Vꢂ = Vꢂ,M
−
ꢀVꢂ,M
(3)
m
where Vꢂ,M and ꢀVꢂ,M are the adjustable parameters, respectively,
Vꢂ,M represents the value of the apparent molar volume of the sur-
factant in the micellar phase and ꢀVꢂ,M denotes the volume change
in the micelle formation [7,8,19,20]. Based on this equation the
Vꢂ,c.m.c. can be calculated as a difference between Vꢂ,M and ꢀVꢂ,M.
Experimental data for both surfactants were fitted to Eq. (3) using
the c.m.c. values obtained as the position of break point of function
T = f (m), which are collected in Table 1. Due to a lack of experimen-
tal values of c.m.c. of 8-6-8 surfactant based on densimetric data for
93.15 K and 323.15 K temperatures the c.m.c. values obtained by
the calorimetric method were taken into account (Table 1). The
method used to calculate the critical micelle concentrations from
calorimetric measurements is described in the next paragraph (DSC
III). The results of the fitting procedure for aqueous solutions of 8-6-
and 8-12-8 gemini surfactants within the examined temperature
range are presented in Table 2.
0
0
0
.035
.030
.025
˛
2
290
300
310
320
8
T/K
Based on the additivity model presented in the literature
8,9], the apparent molar volume of the surfactant in infinitely
diluted solution is a sum of the contributions made by appropriate
Fig. 6. Temperature dependence of the c.m.c. of 8-12-8 in water. The values of c.m.c.
were obtained as the position of inflection point of function ˛T = f (m), as is shown
in Fig. 3.
[

3
2
K. Łudzik et al. / Thermochimica Acta 558 (2013) 29–35
Table 1
The positions of inflection point of functions: (a) ˛T = f (m) and (b) cp = f (m) for the investigated temperature range.
T (K)
8-6-8
8-12-8
m (mol kg 1) a
−
m (mol kg ) b
−1
m (mol kg ) a
−1
m (mol kg ) b
−1
2
2
2
3
3
3
3
3
88.15
0.035
0.027
0.025
0.024
0.024
0.029
0.031
0.037
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.070
0.063
0.060
0.057
0.055
0.075
0.071
0.065
0.062
0.055
0.052
0.051
0.026
0.025
0.024
0.023
0.024
0.025
0.026
a
Calculated from ˛T = f (m).
Calculated from cp = f (m).
b
Table 2
The apparent molar volume of the surfactant in the micellar phase (Vꢂ,M) and isothermal volume changes (ꢀVꢂ,M) due to micelle formation for 8-6-8 and 8-12-8 surfactants
at various temperatures.
T (K)
8-6-8
8-12-8
ꢀ
Vꢂ,M (cm3 mol−1
)
Vꢂ,M (cm3 mol−1
)
ꢀVꢂ,M (cm3 mol−1
)
Vꢂ,M (cm3 mol−1
)
2
2
2
3
3
3
3
3
88.15
5.3 ± 0.2
4.9 ± 0.2
4.4 ± 0.1
3.9 ± 0.1
2.7 ± 0.1
1.9 ± 0.1
1.3 ± 0.1
0.6 ± 0.03
589.1 ± 0.1
594.5 ± 0.1
594.2 ± 0.1
596.9 ± 0.1
599.6 ± 0.1
601.9 ± 0.1
604.4 ± 0.1
606.7 ± 0.1
93.15
98.15
03.15
08.15
13.15
18.15
23.15
3.7 ± 0.1
3.9 ± 0.1
3.7 ± 0.1
3.9 ± 0.1
3.8 ± 0.1
4.2 ± 0.1
3.4 ± 0.1
492.9 ± 0.1
495.5 ± 0.1
497.8 ± 0.1
500.1 ± 0.1
502.5 ± 0.1
505.1 ± 0.1
506.9 ± 0.1
monomers, groups and atoms. For the examined here 8-s-8 gemini
surfactants the Vꢂ can be presented as (Eq. (4))
Table 3 illustrates also the isothermal volume change due to the
◦
micellization process obtained from the fit of experimental data to
Eq. (3) and literature data [7,8,19]. Variations in the values of ꢀVꢂ,M
are related to changes in the micelle morphology (micellar shape,
size, packing agreement). The changes in these values suggest that
the structural changes occur as the length of the spacer is varied. In
the case of 8-s-8 group of surfactant the values of ꢀVꢂ,M are quite
similar, so a closer conclusion about the influence of the spacer
chain length on the micellization process seems to be risky.
◦
◦
◦
◦
ꢂ
V (8 − s − 8) = 2V (OTAB) + (s − 2)V (CH ) − 2V (H)
(4)
2
ꢂ
ꢂ
ꢂ
◦
where, according to the literature [8,9]: 2V (OTAB)
ꢂ
3
−1 −1
◦ ◦
225.1 cm mol , V (CH ) = 15.8 cm mol and V (H) = 10.7 cm
2
ꢂ ꢂ
3
3
=
mol 1
−
.
Due to the low values of the c.m.c.’s for investigated series of
◦
gemini surfactants it can be assumed that Vꢂ,c.m.c are equal to V .
ꢂ
3
.2. Calorimetric functions
Therefore, the apparent molal volumes at the critical micelle con-
centration can be estimated by using the additivity model. The
◦
It is generally accepted that heat capacities significantly depend
values of V (8 − s − 8) calculated in this way for 8-6-8 and 8-12-
ꢂ
on structural interactions. For that reason, we expected that specific
heat capacity as a function of molality should exhibit characteristic
trend which allows one to determine the range where the micelli-
zation process occurs. As an example the specific heat capacity for
-6-8 and 8-12-8 as a function of surfactant molality at a temper-
ature of 298.15 K are presented in Figs. 7 and 8.
8
surfactants are listed in Table 2 together with the appropriate V
ꢂ
data calculated from Eq. (3) for m = c.m.c. using the data obtained
in this work. For the sake of comparison the analogous data for
8-s-8 surfactants where s = 6,7,8 are also shown in Table 3. The val-
8
ues calculated on the basis of the pseudo-phase model stay in good
agreement with those obtained from the additivity model. As it can
be seen, the increase in the length of spacer (-s-) causes the increase
in Vꢂ,M values for 8-s-8 surfactants.
4
4
4
4
4
.20
.15
.10
.05
.00
Table 3
Calculated and experimental apparent molal volumes and isothermal volume
changes due to micelle formation (ꢀVꢂ) for the 8-s-8 gemini surfactants at 298.15 K.
Vꢂ0 (cm3 mol )a
−1
Vꢂ,c.m.c. (cm3 mol−1
)
ꢀVꢂ (cm3 mol−1
)
b
c
8-3-8
8-6-8
8-7-8
8-8-8
8-12-8
444.6a
492.0a
507.8a
437.0b
11 ± 2 , 8.8 ± 0.6
492 ;491.6e
b
11 ± 2 ; 9.3 3.9
b
c
d
d
507.8
5.2
a
d
d
523.6
523.2
4.4
586.8a
589.8e
3.95
0
4.4 ± 0.1
.00
0.05
0.10
0.15
0.20
0.25
a
b
c
Calculated using additivity method.
From Ref. [8].
From Ref. [19].
From Ref. [7].
Calculated from pseudo-phase model.
-1
m /mol kg
d
e
Fig. 7. Specific heat capacity for 8-6-8 as a function of the surfactant concentration
at a temperature of 298.15 K.

K. Łudzik et al. / Thermochimica Acta 558 (2013) 29–35
33
4
4
4
4
.20
.15
.10
2
1
1
1
000
800
600
400
.05
0
0
.00
0.05
0.10
m /mol kg
0.15
0.20
.00
0.02
0.04
0.06
0.08
0.10
-
1
-1
m /mol kg
Fig. 10. Dependence of apparent molar heat capacity of 8-12-8 surfactant on molal-
ity within the temperature range (293.15–323.15) K. ꢀ, 293.15 K; ᭹, 298.15 K; ꢀ,
Fig. 8. Specific heat capacity for 8-12-8 as a function of the surfactant concentration
at a temperature of 298.15 K.
3
03.15 K; ꢀ, 313.15 K; ꢁ, 323.15 K.
For all the temperatures investigated here, the plot of cp = f (m)
show characteristic course with well visible break point. The sim-
ilar trends are also observed for ˛T = f (m) and the c.m.c. values
obtained stay in good agreement with densimetric results (Table 1).
Moreover, the concentrations which correspond to these points are
close to the concentrations, at which the second break point in the
conductivity curve was reported previously for 8-6-8 surfactant at
functions as well as to those given in the literature [7]. The other
characteristic point on Cp,ꢂ = f (m) for 8-6-8 surfactant, which occurs
at lower concentration (about 0.02 mol kg−1), corresponds to the
break point observed by Zana on the base of conductivity data and
can be ascribed to the formation of ionic pairs or small molecular
aggregates [8,22]. However, according to our knowledge, no Cp,ꢂ
maximum caused by the formation of ionic pairs has been observed
yet. Therefore we suppose that the first maximum observed within
the lower concentration range is connected with formation of small
aggregates similar to those observed in cellosolves solution [23].
It is worth to notice that the shape of the Cp,ꢂ and Vꢂ curves is
almost symmetrical and the position of characteristic points on
both curves are close to each other. The thermodynamic parameters
of the micellization for the systems examined can be calculated on
the basis of the temperature dependence of the c.m.c. of the surfac-
tant investigated and phase separation model [11,15]. According to
this model the free energy of micellization, ꢀGmic, corresponding to
the standard free energy change for the transfer of one amphiphilic
molecule from solution to the micellar phase is expressed by:
2
98 K [8].
On the basis of the experimentally determined specific heat
capacity data, we have calculated the apparent molar heat capac-
ities (Cp,ꢂ) of the surfactants examined in aqueous solutions using
the well known equation:
∗
1
000(cp − c )
p
Cp,ꢂ = M cp +
(5)
2
m
2
(g mol−1) is the amphiphile molecular mass;
where
(
M
m
2
−
1
∗
−1 −1
mol kg ) is the solution molality; cp and cp (J g
K
) are the
specific heat capacities of solution and pure water, respectively.
The dependences of cp,ꢂ on the concentration of solution (molal-
ity) obtained for the compounds under investigation are shown in
Figs. 9 and 10.
The changes in the course of Cp,ꢂ = f (m) function for aqueous
solutions of 8-6-8 and 8-12-8 surfactants are very pronounced. In
ꢀGmic = RT ln Xc.m.c.
(6)
where Xc.m.c. is the critical micellization concentration expressed in
mole fractions units, R is the gas constant and T is the temperature
of the experiment.
In order to obtain the enthalpy of micelle formation, the c.m.c.’s
were correlated by a second-degree polynomial:
the case of 8-6-8 surfactant, C increases up to the concentration
p,ꢂ
−
around 0.02 mol kg 1 then decreases very slowly, and from the con-
−
1
centration near 0.065 mol kg it decreases rapidly. For 8-12-8 the
−
1
biggest decrease in Cp,ꢂ occurs near 0.025 mol kg . The concen-
tration, where a rapid decrease in Cp,ꢂ begins (0.065 mol kg 1 for
−
2
ln Xc.m.c.(T) = a + bT + cT
(7)
8
-6-8 and 0.025 for 8-12-8) reflects the structural changes con-
where a, b and c are constants determined via a nonlinear regression
procedure.
nected with the formation of micelles in solution and its position
corresponds to c.m.c. determined in this work from volumetric
The ꢀHmic values were determined from the van’t Hoff relation:
∂
ln Xc.m.c.
2
1
1
1
1
1
700
600
500
400
300
ꢀHmic = −RT (
)p
(8)
∂T
The TꢀSmic were obtained by using Gibbs–Helmholtz’s equa-
tion:
TꢀSmic = ꢀHmic − ꢀGmic
(9)
All calculated values ꢀGmic, ꢀHmic, TꢀSmic at examined temper-
atures for both the systems investigated are listed in Table 4 and
they are presented as functions of temperature in Figs. 11 and 12
respectively.
At low temperatures, the micellization enthalpy for 8-6-8 and
-12-8 is endothermic and then becomes exothermic as the tem-
perature raises (Table 4). There are numerous papers that explain
this tendency [15,24]. It is well known that the effect of changes
in temperature influences on the water structure. At the high tem-
peratures it breaks down and the water seems to behave similarly
0.00
0.05
0.10
0.15
0.20
0.25
8
-
1
m /mol kg
Fig. 9. Dependence of apparent molar heat capacity of 8-6-8 surfactant on molal-
ity within the temperature range (293.15–323.15) K. ꢀ, 293.15 K; ᭹, 298.15 K; ꢀ,
3
03.15 K; ꢀ, 313.15 K; ꢁ, 323.15 K.

3
4
K. Łudzik et al. / Thermochimica Acta 558 (2013) 29–35
Table 4
Thermodynamic parameters of micellization and ꢀcp mic of the surfactants investigated as function of temperature.
T (K)
c.m.c.
mol kg 1
Xc.m.c.
ꢀGmic
(kJ mol
ꢀHmic
(kJ mol
TꢀSmic
(kJ mol
ꢀCp mic
−
−1
−1
−1
−1 −1
(kJ mol K )
(
)
)
)
)
2
98.15
0.070
0.063
0.060
0.057
0.053
0.001258
0.001133
0.001079
0.001025
0.000989
−16.55
−17.10
−17.50
−17.92
−18.30
−4.35
−14.43
−25.18
−36.60
−48.72
12.20
2.66
−7.67
−18.68
−30.42
−0.108
−0.097
−0.086
−0.076
−0.065
8
8
-6-8
303.15
308.15
313.15
318.15
-12-8
288.15
0.0346
0.0265
0.0245
0.0238
0.0246
0.0283
0.0310
0.0370
0.0006224
0.0004771
0.0004406
0.0004280
0.0004431
0.0005086
0.0005579
0.0006663
−17.68
−18.64
−19.15
−19.55
−19.78
−19.74
−19.82
−19.65
13.88
5.08
−4.35
31.57
23.72
14.80
−1.68
−1.82
−1.95
−2.09
−2.22
−2.35
−2.49
−2.62
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−14.44
−25.18
−36.60
−48.72
−61.55
5.11
−5.39
−16.85
−28.90
−41.90
to an apolar fluid. In consequence the destruction of the structured
water which neighbours on hydrophobic chains is dominated by
the exothermic effect of hydrophobic chains condensation inside
the micelle. Therefore ꢀHmic becomes more negative as a temper-
ature increases.
The ꢀGmic values for both investigated surfactants are negative
what illustrate that micellization process is privileged. The exper-
iment confirms the tendency that surfactant with longer spacer
chain length associate more spontaneously what is reflected in the
more negative ꢀGmic values.
The first derivate of ꢀHmic = f (T) yields the change in heat capac-
ity ꢀCp,mic:
ꢀ
ꢁ
∂
ꢀHmic
ꢀCp mic
=
(10)
∂T
P
As expected for process related to hydrophobic effects, through-
out the whole temperature range ꢀCp,mic values were found to be
negative for both the systems in question (Table 4).
4. Summary
A comparison of the entropy and enthalpy of micellization val-
ues shows that within low temperature range the entropy term
TꢀSmic gives a meaningful contribution to the negative value of the
free energy of 8-6-8 and 8-12-8 surfactant examined.
The study used the densimetric and calorimetric measurements
to investigate the micellization process in the aqueous solutions
of alkanediyl-␣,␻-bis(dimethylalkylammonium bromide) surfac-
tants differing in the spacer chain length. It has been shown that the
inflection point in the curves of the dependence of specific capacity
on molality corresponds to the position of c.m.c. The values of the
critical micelle concentration obtained by this way coincide with
concentration where the rapid decrease in Cp,ꢂ begins and stay in
good agreement with c.m.c. values determined by the densimetric
methods. For that reason the function cp = f (m) can be used to deter-
mine the areas where the aggregate formation begins. The shape
of the Cp,ꢂ and Vꢂ curves for 8-6-8 and 8-12-8 surfactants is almost
symmetrical and the position of characteristic points are very close
to each other.
The analysis of thermodynamics parameters of the micelliza-
tion for the systems investigated here shows that ꢀHmic becomes
more exothermic upon increasing temperature. The ꢀGmic values
for both the 8-6-8 and 8-12-8 surfactants confirm that the micelle
formation occurs easier for surfactants with a longer spacer chain
length. It is worth to emphasizing that the main contribution to
the negative value of the free energy of the surfactant investigated
temperature range examined gives TꢀSmic but only within the low
temperature range.
2
0
0
-
-
-
20
40
60
3
00
310
320
T /K
Fig. 11. Thermodynamic parameters for the micellization of 8-6-8 as a function of
temperature. ꢀ, ꢀHmic; ꢁ, ꢀGmic; ꢀ, TꢀSmic.
2
0
0
References
[
1] G. Perron, J.F. Côté, D. Lambert, J. Pageau, J.E. Desnoyers, Volume heat capac-
ity of model non-aqueous self-assembly systems, J. Solution Chem. 23 (1994)
-
-
-
20
40
60
121–133.
[
2] D. Hetu, C. Camire, G. Perron, J.E. Desnoyers, Volume heat capacity of n-pentanol
in aqueous surfactants: effect of chain length and polarity of the head group,
Langmuir 10 (1994) 4039–4047.
[
[
[
[
3] S.D. Wettig, R.E. Verrall, Thermodynamic studies of aqueous m-s-m gemini
surfactant systems, J. Colloid Interface Sci. 235 (2001) 310–316.
4] J.E. Desnoyers, G. Perron, in: K.S. Birdi (Ed.), Handbook of Surface and Colloid
Chemistry, CRC Press, Boca Raton, FL, 1997, 119-145.
5] J.E. Desnoyers, G. Perron, A.H. Roux, in: R. Zana (Ed.), Surfactant Solutions New
Methods of Investigation, Marcel Dekker, NY, 1986, 22-46.
6] E. Vignola, G. Perron, J.E. Desnoyers, Apparent molar volumes and heat capaci-
ties of various adsorbed additives on polystyrene latexes, Langmuir 18 (2002)
6035–6048.
2
90
300
310
320
T /K
Fig. 12. Thermodynamic parameters for the micellization of 8-12-8 as a function of
temperature. ᭹, ꢀHmic; ꢂ, ꢀGmic; ꢀ, TꢀSmic.

K. Łudzik et al. / Thermochimica Acta 558 (2013) 29–35
35
[
[
[
7] H. Piekarski, K. Łudzik, M. Wasiak, Calorimetric densimetric examinations
of aqueous solutions of heptylene-1,7-bis(dimethyloctylammonium bro-
mide) and octylene-1,8-bis(dimethyloctylammonium bromide), J. Therm. Anal.
Calorim. 104 (2011) 765–770.
8] M. Frindi, B. Michels, H. Levy, R. Zana, Alkanediyl-␣, ␻-bis(dimethylalkyl-
ammonium bromide) surfactants. 4. Ultrasonic absorption studies of
amphiphile exchange between micelles and bulk phase in aqueous micellar
solutions, Langmuir 10 (1994) 1140–1145.
[16] Li-Jen Chen, Shi-Yow Lin, Chiung-Chang Huang, Effect of hydrophobic chain
length of surfactants on enthalpy–entropy compensation of micellization, J.
Phys. Chem. B 102 (1998) 4350–4356.
[17] J.J. Galán, J.R. Rodríguez, Thermodynamic study of the process of micellization,
J. Therm. Anal. Calorim. 101 (2010) 359–364.
[18] R. Zana, M. Benrraou, R. Rueff, Alkanediyl-␣, ␻-bis(dimethylalkylammonium
bromide) surfactants. 1 Effect of the spacer chain length on the critical micelle
ionization degree, Langmuir 7 (1991) 1072–1075.
[19] S.D. Wettig, R.E. Verrall, Thermodynamic studies of aqueous m-s-m gemini
surfactant systems, J. Colloid Interface Sci. 235 (2001) 310–316.
9] R. Zana, Alkanediyl-␣,(-bis(dimethylalkylammonium bromide) surfactants. 10
Behavior in aqueous solution at concentrations below the critical micelliza-
tion concentration: en electrical conductivity study, J. Colloid Interface Sci. 246
[20] E. Fisicaro, C. Compari, E. Duce, C. Contestabili, G. Viscardi, P. Quagliotto,
First evaluation of the thermodynamic properties for spheres to elongated
micelles transition of some propanediyl-␣, ␻-bis(dimethylalkylammonium
(
2002) 182–190.
[
10] P. Góralski, M. Tkaczyk, M. Chor a˛ z˙ ewski, Heat capacities of ␣,␻-dichloroalkanes
at temperatures from 284.15 to 353.15K and a group additivity analysis, J.
Chem. Eng. Data 48 (2003) 492–496.
bromide) surfactants in aqueous solution, J. Phys. Chem.
1744–1749.
B 109 (2005)
[
11] Z. Kirláy, I. Dekány, Thermometric titration study on the micelle formation of
sodium decylsulfate in water, J. Colloid Interface Sci. 242 (2001) 214–219.
12] S. Paula, W. Süs, J. Tuchtenhagen, T.A. Blume, Thermodynamics of micelle for-
mation as a function of temperature: a high sensitivity titration calorimetry
study, J. Phys. Chem. 99 (1995) 11742–11751.
[21] E. Fisicaro, C. Compari, A. Braibanti, Comment on entropy/enthalpy compensa-
tion: hydrophobic effect, micelles and protein complexes, Phys. Chem. Chem.
Phys. 6 (2004) 4156–4166.
[22] R. Zana, Alkanediyl-␣,␻- bis(dimethylalkylammonium bromide) surfactants.
10 Behavior in aqueous solution at concentrations below the critical micelli-
zation concentration: an electrical codductivity study, J. Colloid Interface Sci.
246 (2002) 182–190.
[
[
13] G.C. Kresheck, in: F. Franks (Ed.), Water A Comprehensive Treatise, vol. 4,
Plenum Press, NY, 1975, 9.
[
14] H. Piekarski, K. Łudzik, M. Wasiak, A microcalorimetric titration study on the
micelle formation of alkanediyl-␣, ␻-bis(dimethylalkylammonium bromide)
surfactants at a 283. 15-343.15K temperature range, J. Therm. Anal. Calorim.
[23] H. Piekarski, M. Tkaczyk, M. Wasiak, Heat capacity of aqueous 2-(2
hexyloxyethoxy)ethanol solutions by DSC application of two-point scal-
ing to pseudophases coexistence, J. Therm. Anal. Calorim. 82 (2005)
711–718.
(
2012), http://dx.doi.org/10.1007/s10973-012-2310-x.
[
15] S. Shimzu, R.P. Augusto, O.A. Seoud, Thermodynamics of micellization of
benzyl(2-acylaminoethyl)dimethylammoniumchloride surfactants in aqueous
solutions: a conductivity and titration calorimetry study, Langmuir 20 (2004)
[24] L. Grosmaire, M. Chorro, C. Chorro, S. Partyka, R. Zana, Alkanediyl-alpha,omega-
bis(dimethylalkylammonium bromide) surfactants 9. Effect of the spacer
carbon number and temperature on the enthalpy of micellization, J. Colloid
Interface Sci. 246 (2002) 175–181.
9
551–9559.