Counterion effect on the thermodynamics of micellization of alkyl sulfates

Article abstract of DOI:10.1021/jp0264329

Thermodynamics of micelle formation of anionic surfactants was investigated by using isothermal titration calorimetry (ITC). Highly purified decyl and dodecyl sulfates have been used to analyze the effect of counterions (Li⁺, Na⁺, K⁺, and Cs⁺) on critical micelle concentration (cmc) and enthalpy of micellization (ΔH_mic) determined between 10 and 60 °C. The enthalpy of micellization decreases strongly with increasing temperature and passes trough zero (endothermic to exothermic processes), while the cmc versus temperature exhibits a minimum. At a given temperature and for a fixed chain length, the decrease of cmc and ΔH_mic in the order Li⁺ > Na⁺ > K⁺ > Cs⁺ is related to the increase of the binding of counterions to micelles. The electrostatic repulsions between ionic headgroups, which prevent the aggregation, are progressively screened as the ionic character decreases with the size of the counterion. The heat of dilution of micelles is markedly dependent on temperature and is correlated with the temperature-dependent shape of micelles. The cmc concept has an exact meaning within the so-called phase separation model of micelle formation. Therefore, free energy and entropy were deduced from the cmc and enthalpy of micellation using this model by taking into account the counterion binding. The temperature changes of ΔS_mic indicate that the process of micellization is entropically driven. ΔG_mic is always negative (thermodynamically favored process) and slightly temperature and counterion dependent.

Full text of DOI:10.1021/jp0264329

J. Phys. Chem. B 2003, 107, 5281-5288
5281
Counterion Effect on the Thermodynamics of Micellization of Alkyl Sulfates
M. H. Ropers,* G. Czichocki, and G. Brezesinski
Max-Planck-Institut fu¨r Kolloid- und Grenzfla¨chenforschung, D-14424 Potsdam, Germany
ReceiVed: July 2, 2002; In Final Form: NoVember 15, 2002
Thermodynamics of micelle formation of anionic surfactants was investigated by using isothermal titration
calorimetry (ITC). Highly purified decyl and dodecyl sulfates have been used to analyze the effect of counterions
(Li+, Na+, K+, and Cs+) on critical micelle concentration (cmc) and enthalpy of micellization (∆Hmic
)
determined between 10 and 60 °C. The enthalpy of micellization decreases strongly with increasing temperature
and passes trough zero (endothermic to exothermic processes), while the cmc versus temperature exhibits a
minimum. At a given temperature and for a fixed chain length, the decrease of cmc and ∆Hmic in the order
Li+ > Na+ > K+ > Cs+ is related to the increase of the binding of counterions to micelles. The electrostatic
repulsions between ionic headgroups, which prevent the aggregation, are progressively screened as the ionic
character decreases with the size of the counterion. The heat of dilution of micelles is markedly dependent
on temperature and is correlated with the temperature-dependent shape of micelles. The cmc concept has an
exact meaning within the so-called phase separation model of micelle formation. Therefore, free energy and
entropy were deduced from the cmc and enthalpy of micellation using this model by taking into account the
counterion binding. The temperature changes of ∆Smic indicate that the process of micellization is entropically
driven. ∆Gmic is always negative (thermodynamically favored process) and slightly temperature and counterion
dependent.
Introduction
counterion binding to micelles was measured by different
experimental techniques, including ultrafiltration,5 specific-ion
The formation of a micelle from monomeric ionic surfactants
results from a balance between (attractive) hydrophobic interac-
tions between the hydrophobic tails of the amphiphiles, (attrac-
tive and repulsive) electrostatic interactions between their
hydrophilic charged headgroups, as well as with and between
the counterions. Micelles are more or less spherical and may
adopt prolate (elongated cylindrical) or oblate (large, flat
lamellar) shapes according to the properties of the molecules
and the media involved. In aqueous solutions, where the
hydrophobic chains of the micelle-forming surfactants are
oriented toward the interior of the micelles, the solution-micelle
interfacial region contains the headgroups and the electrical
double layer that is divided into two parts: the Stern layer of
strongly bound counterions and the diffuse layer of counterions.
The strength and importance of the various interactions resulting
in the micelle formation were analyzed by varying externally
controllable factors, such as temperature and ionic strength, or
the properties of the molecules (nature of ions or chain length).
Relations between concentration and structure of the resulting
micelles, in particular association number and shape, were
found.1-4
Many techniques have been applied to analyze the process
of micellization by measuring changes in physical properties
at the critical micelle concentration (cmc).1,2,4 Most commonly,
the breaks in the electrical conductivity, surface tension, and
light scattering have been used for this purpose. Especially the
differences in cmc with respect to the nature of the counterions
as well as the shape of micelles and the surface charge density
have been investigated and appear to reflect the degree of
binding of the counterions to the micelles. The degree of
electrode,6 electric conductivity,7,8 NMR chemical shift,9 and
Corrins-Harkins plot.10 The values usually depend on the
method used; however, they show the same feature. For alkali
alkyl sulfate surfactants, the large hydrated radii and low
polarizability result in lowering the degree of binding and in
increasing the cmc.7,11-15 The decrease of the surface potential
of micelles with decreasing hydrated radius from Li+ to Cs+ is
in agreement with the modification of the counterion binding.16
For a given counterion (Cs+), the analysis of SANS and SAXS
scattering profiles shows that the counterions are more dissoci-
ated in micelles of surfactants with C10 chains than with C12
chains.17 From a structural point of view, the effect of
counterions has been well documented by Missel and co-workers
for dodecyl sulfates in a salty solution of the same alkali-metal
chloride. Quasi-elastic light scattering proves the tendency of
micelles to grow from spherical to long rodlike structures in
the order Li+ < Na+ < Rb+ < Cs+ with a significant change
in the aggregation number with temperature.18 It has been
recently confirmed that the micellar growth of sodium dodecyl
sulfate is larger when the counterion hydration is smaller (from
Na+, K+, to Cs+).19 The same set of alkyl sulfates was used to
analyze the adsorption behavior at the air/water interface by
neutron reflectivity and surface tension measurements.15,20 It
confirms the larger area occupied by the smaller ion and the
larger number of water molecules bound to the interface for
Li+ and Na+ compared to Cs+.15
Among other techniques, calorimetry was mainly used to
analyze the effect of headgroup, chain length, and temperature
on the micellization of alkyl sulfate surfactants4,21-25 but only
rarely to analyze the effect of counterions,12 probably because
this effect was expected to be very small. For alkyl sulfates
and especially sodium dodecyl sulfate, some thermodynamical
* To whom correspondence should be addressed. E-mail: ropers@mpikg-
golm.mpg.de.
10.1021/jp0264329 CCC: $25.00 © 2003 American Chemical Society
Published on Web 05/10/2003

5282 J. Phys. Chem. B, Vol. 107, No. 22, 2003
Ropers et al.
parameters were calculated at discrete temperatures either by
means of calorimetric measurements4,12,25 or on the basis of
theoretical considerations.8,12,13 Between 20 and 55 °C, calori-
metric measurements showed an almost linear variation of the
enthalpy of micelle formation of Li, Na, and K dodecyl
sulfates.12 The Gibbs free energy adopts similar values for all
counterions.12,15
Actually, the improvement of precision and sensitivity in
calorimetric measurements allows the measurement of very
small heat changes. This led us to reconsider the thermodynam-
ics of micelle formation of decyl and dodecyl sulfate surfactants
with different alkali counterions (Li+, Na+, K+, and Cs+) in
pure water over a large temperature range. Our aim is to
complete the understanding of the micellization of alkyl sulfates
with new accurate calorimetric data using highly purified
surfactants.
function of time (Figure 1a). The heat of each injection
determined by integration of the heat flow peak after subtraction
of a linear base line is divided by the injected mole number. It
yields the heat of reaction per mole plotted versus the
concentration of surfactant in the cell (Figure 1b). The heat flow
plot can be divided into two concentration ranges where the
reaction enthalpies are more or less constant. For the first
injections, the final concentration in the sample cell is below
the cmc. The heat change essentially stands for micellar dilution,
demicellization, and dilution of monomers (whatever of these
come from the micelle or from the equilibrium with micelles).
The strong heat change indicates that the cmc in the sample
cell has been reached. If more micelle solution is added, the
micelles are no longer dissolved and the only heat now measured
is caused by the dilution of micelles. This is the second range.
The cmc corresponds to the concentration where the first
derivative displays a minimum or maximum depending on the
temperature (Figure 1c). At this concentration, the enthalpy of
micellization is calculated as the heat difference between the
two extrapolated lines as indicated in Figure 1d. In all systems
investigated, the estimation of the enthalpy of demicellization
is very accurate for temperatures 5 °C below or above the
temperature where the enthalpy change approaches zero. In this
peculiar case, the first derivative does not display a sharp peak
and the determination of the cmc is less accurate or even
impossible. In the present case, we have used a second-order
polynomial function as an empirical relation between cmc and
temperature in order to determine the temperature at which the
cmc goes through a minimum.
Solubility. At a concentration of 10 times the cmc, potassium
decyl and dodecyl sulfate are not completely soluble in water
at room temperature. The solution contains hydrated crystals
dispersed in a micellar phase. Above 28 °C, the potassium decyl
sulfate solution is completely clear. The micellization of KDeS
was thus investigated in the limited range between 30 and 50
°C. In the case of potassium dodecyl sulfate, which has a Krafft
temperature of 34 °C at the cmc,4 it was impossible to
investigate the micellization process since the temperature
leading to a clear solution was too high (50 °C) and KDS
precipitated at the top of the syringe, which is not thermostated.
Although CsDeS has a smaller hydrated radius than KDeS, its
solubility limit is much above the cmc7 and solutions are clear
even at low temperatures down to 10 °C. This solubility gap
encountered for potassium alkyl sulfates has already been
reported.7,30 Missel has quantified this difference in solubility
by measuring the temperature at which the solid phase is in
equilibrium with the micellar phase. This temperature does not
decrease continuously with the size of the counterion but follows
the order LiDS < NaDS < CsDS < RbDS < KDS for the
dodecyl series.18 This confirms our observation that KDeS has
a lower solubility than CsDeS.
Experimental Section
Synthesis. Alkali decyl and dodecyl sulfates (Li+, Na+, K+,
and Cs+) were prepared by sulfation of the long chain alcohol
with chlorosulfonic acid.26 The purity of decyl and dodecyl
alcohol (puriss. grade, SIGMA-Aldrich, St.Louis, MO) was
99.7%, analyzed by GLC.27a Decyl and dodecyl alcohol,
respectively, dissolved in dried diethyl ether (MERCK, Darm-
stadt, Germany) was sulfated with a diethyl ether adduct of
chlorosulfonic acid (synthesis grade, MERCK, Darmstadt,
Germany) at 0 °C. Chlorosulfonic acid was distilled before use
to remove water. The molar excess of chlorosulfonic acid in
the sulfation reaction amounted to 10%. The obtained sulfuric
acid half ester was neutralized with 2 N lithium, sodium,
potassium, and cesium carbonate (synthesis grade, MERCK,
Darmstadt, Germany), respectively, at 10 °C. The solid was
filtered, dissolved in absolute ethyl alcohol (MERCK, Darm-
stadt, Germany), and filtered again to remove inorganic residues.
Finally, the anionic surfactants were recrystallized several times
from ethyl alcohol. The alcohol was purified by heating with a
saturated potassium hydrate solution for 2 h and following
distillation.
The purity of the prepared alkali alkyl sulfates was proved
by a quantitative high-performance liquid chromatography
(HPLC) method to detect traces of alkanols in alkyl sulfates.27b-29
The influence of long chain alcohols in alkyl sulfates on the
adsorption and aggregation behavior in aqueous solution is
generally known. The corresponding homologous alcohols
possess surface activities that are stronger by more than 2 orders
of magnitude compared to those of the alkyl sulfates themselves.
Therefore, the used alkali decyl and dodecyl sulfates were
extremely purified. The residual decyl and dodecyl alcohol,
respectively, in the surfactants used in this work amounts to
less than 0.01 mol %.
In the next sections, we will use the following abbreviations
for the surfactants investigated: LiDeS, NaDeS, KDeS, and
CsDeS for the decyl compounds and LiDS and NaDS for the
dodecyl compounds with Li+, Na+, K+, and Cs+ as counterions.
Isothermal Titration Calorimetry. Critical micelle concen-
tration (cmc) and enthalpy of micellization (heat of micelle
formation) are measured with an isothermal titration calorimeter
(Microcal Inc., Northampton, MA). Experimentally, these values
are determined via the reverse process, i.e., demicellization. A
concentrated surfactant solution (usually 10 times the cmc) is
injected into the thermostated sample cell containing pure water
(2.1 mL) in multiple steps of 2.5-10 µL using a syringe with
a capacity of 250 µL at a constant stirring rate (400 rpm). At
each step, the heat produced or consumed is measured as a
Results and Discussion
cmc and ∆Hmic. cmc and enthalpy of micellization deter-
mined according to the method described in Figure 1 are
presented in Table 1 and Figures 2-5 for each alkyl sulfate
series.
Our values of the cmc, determined by ITC measurements,
are slightly larger than obtained in previous papers with the
same surfactants.7,12,21,24,31 This difference arises mainly from
the purity of surfactants, because the cmc is quite sensitive to
surface active impurities even in trace amounts. They are also
caused from the sensitivity of the methods used. For example,
differences in cmc for alkylbenzenesulfonate are observed

Micellization of Alkyl Sulfates
J. Phys. Chem. B, Vol. 107, No. 22, 2003 5283
Figure 1. Determination of the cmc and enthalpy of micellization for LiDeS. (a) Heat flow versus time caused by 50 injections of 5 µL of LiDeS
into 2.1 mL of water at 10 °C. (b) Heat of reaction versus LiDeS concentration in the sample cell between 20 and 50 °C. (c) First derivative of the
heat of reaction at 10 °C. The cmc is determined from the maximum of this curve. (d) Determination of the enthalpy of micellization at 45 °C.
between calorimetric and electrical conductivity measurements.31
The cmc can differ up to 10% without significant modifications
of the enthalpy as shown in Figure 5 for sodium dodecyl sulfate.
has the lowest cmc of alkali dodecyl sulfates and forms micelles
with a rodlike shape and a large aggregation number.18
The plot of the cmc versus temperature has a parabolic shape,
typical for ionic surfactants.2,33 The cmc decreases, reaches a
minimum and increases again as the temperature raises (Figures
2 and 3). In the range between 10 and 60 °C, the temperature
dependence of the cmc is small (<2 mM) and independent of
the cmc values, even for surfactants with a low cmc such as
alkali dodecyl sulfate surfactants. Several equations were
proposed25,34 to describe the observed symmetrical parabolic
curve, and we have used the following:
At a given temperature, the cmc decreases in the order Li+
> Na+ > K+ > Cs+ as previously obtained by numerous
studies.7,12,15,16 This decrease was explained by considering the
binding of counterions to micelles. The determination of partial
volumes and calculations of the hydration of micelles indicated
a very small change in hydration during micellization.7 This
means that the hydration shell of cations limits the distance of
closest approach. If the size of nonhydrated ions follows the
order Li+ < Na+ < K+ < Cs+, the size of hydrated ions is
however in the reverse order as shown in Table 2.
ln(cmc) ) aT2 + bT + c
The larger the hydrated radius, the further the ion is located
from the surface of the negatively charged surfactant head-
groups. Thus, Li+ having the largest hydrated radius cannot
approach the highly charged surface of the micelle as close as
smaller ions. Therefore, it can neither screen the charge at the
surface of micelles nor reduce the surface potential as effectively
as the smaller ions.16 On the contrary, the hydrated Cs+ cation
has the smallest size and interacts more strongly with the
oppositely charged heads. The smallest size of hydrated Cs+
results in the highest extent of counterion binding comparing
Li+, Na+, K+, and Cs+. The headgroup interactions (repulsive
forces) are more screened, which favors micelle formation.
Consequently, the cmc decreases when the size of the hydrated
counterion decreases while the degree of counterion binding
increases. The effect of counterion must not be reduced to
electrostatic effects but also influences aggregate size and
aggregation number as shown for the dodecyl series.17,18 CsDS
Fitting this equation to the experimental data points enables us
to determine the temperature T0 at which the cmc has a
minimum. The position of this minimum has a thermodynamic
significance. According to the pseudo-phase model, the free
energy ∆Gmic ) RT ln(cmc) is a linear function of temperature.
Therefore, the minimum in cmc leads to a minimum in (∆Gmic
/
T). According to the Gibbs-Helmholtz relation, the enthalpy
of micellization is written as ∆Hmic ) ∆Gmic - Tδ(∆Gmic)/
δ(T) or as ∆Hmic/T2 ) - δ(∆Gmic/T)/δ(T) and has to be zero at
the temperature T0. Since the cmc of KDeS is measured in a
reduced temperature range above 30 °C, the temperature T0 was
only determined from the temperature dependence of the
enthalpy of micellization, using a second-order polynomial
function to describe the dependence of ∆Hmic on temperature
(T0(∆H ) 20.9 °C). All values determined from the cmc and
)
mic
enthalpy plots are presented in Table 3.

5284 J. Phys. Chem. B, Vol. 107, No. 22, 2003
Ropers et al.
TABLE 1: Critical Micelle Concentrations (cmc’s) and
Enthalpies of Micellization of Alkyl Sulfate Surfactants
Determined by ITC in Pure Water as a Function of
Temperaturea
cmc, ∆H, kJ
cmc, ∆H, kJ
surfactant T, °C mM mol-1 surfactant T, °C mM mol-1
LiDeSb 15.2 40.5
18.2 39.1
7.04
5.97
4.92
4.12
35.2 28.1
37.1 28.45 -6.63
-5.92
20.55 38.3
22.9 37.7
25.1 37.4
27.3 37.1
30.1 37.0
32.6 37.0
35.6 37.2 -1.29
40.2 29.1
42.1 29.2
45.4 29.8
10.3 10.48
12.3 10.35
15.9 10.22
17.5 10.12
20.3 10
-7.61
-8.25
-8.92
9.64
8.53
6.50
5.65
4.09
3.06
1.48
3.18
2.23 LiDSb
1.09
0.00
40.2 38.0 -3.39
42.6 38.6 -4.29
45.0 39.4 -5.17
22.2
25.2
27.5
30.5
32.5
35.5
9.95
Figure 2. Logarithm of the cmc as a function of temperature for alkali
decyl sulfates: (9) Li+, (b) Na+, (2) K+, and (1) Cs+.
NaDeS 15.3 37.3
5.22
3.30
2.77
1.51
0.81
0.53
20.3 36.4
22.1 35.9
25.4 36.0
27.1 35.2
9.97 -1.45
9.92 -2.44
9.98 -4.04
37.1 10.05 -4.86
40.1 10.14 -6.21
42.2 10.29 -7.22
45.6 10.51 -8.75
47.5 10.59 -9.52
50.2 10.78 -10.67
52.1 10.92 -11.49
55.3 11.25 -12.69
57.4 11.5 -13.56
30.1 35.3 -0.87
32.1 35.7 -1.38
36.2 36.2 -2.94
40.5 37.15 -4.21
42.1 37.45 -5.04
45.4 38.8 -6.29
47.3 38.5 -6.74
35.1 31.7 -4.45
37.7 32.3 -5.17
40.2 32.8 -6.10 NaDS
42.8 33.4 -6.82
45.2 33.3 -7.94
47.7 34.3 -8.40
50.15 34.5 -9.20
KDeS
60
11.7 -14.29
10.4
15.2
20.2
21.2
25.2
30
35.2
40.2
45.35 10.1
9.68
9.3
6.87
4.55
2.14
0.90
-0.51
9.16
9.13
9.3
9.46 -2.83
9.51 -5.27
9.73 -7.74
Figure 3. Logarithm of the cmc as a function of temperature for alkali
dodecyl sulfates: (9) Li+, (O) Na+, and (1) Na+ (data from Paula et
al.24).
CsDeS 10.3 27.9
12.7 27.7
3.10
2.30
1.40
15.4 27.5
20.3 27.4 -0.54
22.6 27.4 -1.34
25.2 27.5 -2.24
27.6 27.6 -3.23
30.3 27.75 -4.16
-9.72
50.3 10.45 -11.63
55.3 10.95 -13.62
60.6 11.5 -15.49
a cmc values are obtained with an accuracy of (0.1 mM for alkali
decyl sulfate and (0.05 mM for alkali dodecyl sulfate, whereas the
accuracy of the enthalpy values is (0.03 kJ mol-1 k-1 b For LiDeS
.
and LiDS, values correspond to the average of two independent
measurements.
TABLE 2: Ionic Radius of Alkali Ions in a Crystal rcr and
32
in the Hydrated State rhyd
alkali
Li+
Na+
K+
Rb+
Cs+
rcr (Å)
rhyd (Å)
0.59
3.40
0.99
2.76
1.37
2.32
1.52
2.28
1.67
2.28
Figure 4. Enthalpy of micellization as a function of temperature for
alkali decyl sulfates: (9) Li+, (b) Na+, (2) K+, and (1) Cs+.
The values deduced from the cmc and the enthalpy curves
agree well. Using the pseudo-phase separation model, the free
energy of ionic surfactants is written as ∆Gmic ) RT(1 + f)ln-
(cmc) where f is the fraction of counterions bound to micelles.
The Gibbs-Helmholtz relation can thus be rewritten as -
∆Hmic/T2 ) R(1 + f)δ(ln(cmc))/δT + R ln(cmc)δ(1 + f)/δT.
When the enthalpy passes through zero at T ) T0, the minimum
in cmc can occur at a different temperature since the counterion
binding represented as the parameter f may be temperature
dependent. This could lead to a shift in the minimum temper-
ature T0 and explain the larger difference observed for CsDeS.
The temperature T0, at which the enthalpy of micellization
changes sign, shifts to lower temperatures as the size of the
hydrated counterion decreases. The difference in T0 between
Li+ and Na+ remains constant as the chain length increases.
The enthalpy of micellization is markedly temperature
dependent as illustrated in Figures 4 and 5.
The enthalpy of micellization decreases by about 0.4 kJ/K
for decyl surfactants and by about 0.5 kJ/K for dodecyl
surfactants with increasing temperature. The formation of
micelles is an endothermic process at low temperatures and an
exothermic process at higher temperatures. At a given temper-
ature, the enthalpy of micellization ∆Hmic decreases continuously
in the order Li+ > Na+ > K+ > Cs+. Since the process of
micelle formation consists mainly of (i) the destruction of water

Micellization of Alkyl Sulfates
J. Phys. Chem. B, Vol. 107, No. 22, 2003 5285
TABLE 4: Experimental ∆Cmic(exp) and Theoretical Values
of the Heat Capacity Changes (∆Cmic(th) ) -33nH) in J
mol-1 K-1 at 25 °C for the Investigated Surfactantsa
surfactant
LiDS
NaDS
LiDeS
NaDeS
CsDeS
∆Cmic(th)
∆Cmic(exp)
-825
-534
-825
-493
-693
-448
-693
-407
-693
-362
a The error bars are 10 J mol-1 K-1 for dodecyl sulfates and 17 J
mol-1 K-1 for decyl sulfates.
the values should be the same for all counterions investigated
at a given chain length and decrease only with decreasing chain
length. However, the results shown in Table 4, where both
expected values at 25 °C according to the theory and the
experimental ones are presented, indicate that the counterion
plays a certain role.
Figure 5. Enthalpy of micellization as a function of temperature for
alkali dodecyl sulfates: (9) Li+, (b) Na+, and (O) Na+ (data from
Paula et al.24).
Results are in accordance with literature data (∆Cmic(NaDeS)
) -394 J mol-1 K-1 and ∆Cmic(NaDS) ) -516 J mol-1 K-1
at 25 °C37). The large difference between experimental and
calculated values can be partially explained by a different
number of hydrogen atoms exposed to water during micelliza-
tion. If we compare the data for the same counterion but different
chain lengths, the experimentally observed difference is 86 J
mol-1 K-1 instead of 132 J mol-1 K-1. This indicates that the
number of methylene groups which are still in contact with water
molecules in the micelle decreases with decreasing chain length.
The differences within one alkali alkyl sulfate series indicate
an additional influence of the counterion. ∆Cp increases in the
order Li+ < Na+ < Cs+: the effect of the counterion has a
positive contribution to the heat capacity (41 J mol-1 K-1 from
Li+ to Na+ and 45 J mol-1 K-1 from Na+ to Cs+). During the
micellization process, the condensation of ions onto micelles
reduces the number of water molecules in the solvation shell
since the ions can share hydration water with the headgroups
and the heat capacity associated with the dehydration process
of counterions is positive.38 However, as the size of the
counterion increases, the latter binds more strongly to the
headgroups and the number of water molecules expelled from
the headgroups during micellization is smaller than for a smaller
counterion. Consequently, the dehydration contributes positively
to the heat capacity in the reverse order than observed
experimentally. The compensation effect may arise from a
change in aggregation number as suggested based on change
in hydrodynamic radius (Rh(Li+) ) 26.5 Å, Rh(Na+) ) 26.7 Å,
Rh(K+) ) 124.1 Å, and Rh(Cs+) ) 182 Å between 40 and 45
°C with an alkalichloride salt concentration of 0.45 M).18
Heat of Dilution. Below the cmc, the curves of LiDeS shown
in Figure 1a have a constant positive slope, indicating that the
process of demicellization is dependent on the concentration
of monomers already present in solution. This effect tends,
however, rapidly to decrease with increasing hydrated radius,
i.e., the increase in counterion binding and almost vanishes with
increasing the chain length. Above the cmc, the process of
dilution of the micellar solution is endothermic as for all ionic
surfactants2 and the heat of dilution appears to be almost
constant. However, the plot of the heat of dilution versus
temperature at a given concentration above the cmc (for example
at 6-fold the cmc for the decyl sulfate set and twice the cmc
for the dodecyl sulfate set as shown in Figures 6 and 7) shows
a clear dependence of the heat of dilution on temperature.
It decreases with increasing temperature and reaches a
minimum in the case of Li+ and Na+ counterions. It is
noteworthy that the temperature, at which the heat of dilution
has a minimum, seems to be identical for Li+ and Na+ and
independent of chain length. This minimum seems also to occur
for Cs+ at higher temperatures. However, due to the strong
TABLE 3: Temperature T0 (°C) Associated with the
Minimum in Critical Micelle Concentration and Zero
Enthalpy Change
surfactant
LiDS
NaDS
LiDeS
NaDeS
CsDeS
T0 (cmc)
T0 (∆Hmic
28.1
27.6
22.9
23.7
31.2
32.1
29.0
28.5
21.1
19.0
)
structure surrounding the hydrophobic part of surfactant when
it escapes from water and aggregates as a liquid core inside the
micelle and (ii) the dehydration of the polar part and its
electrostatic interaction due to aggregation,12 the decrease in
∆Hmic from Li+ to Cs+ results mainly from the heat required
to overpass the electrostatic repulsion between headgroups. The
electrostatic repulsions between ionic headgroups prevent the
aggregation but are progressively screened as the degree of
ionicity of the SO4-M+ bond decreases with the size of the
counterion and its polarizability. As the counterion binding
decreases in the order Cs+ > K+ > Na+ > Li+ followed by
increased electrostatic repulsions between headgroups, the
energy required to overpass this repulsion is larger, indicating
that the process is then more endothermic. The curves are
regularly shifted to lower values on going from Li+ to K+.
Assuming the same increment for Rb+ and Cs+, the micelli-
zation enthalpy for cesium decyl sulfate is found at values
expected for rubidium decyl sulfate. As indicated in Tables 2
and 3, both the hydrated radius and the minimum temperature
T0 are similar for K+ and Cs+, so that one can expect a much
smaller increment for the bigger ions such as Rb+ and Cs+.
Finally, the characteristics of micellization are as follows: a
change of the counterion for a given chain length is only
accompanied by a vertical shift whereas an increase in chain
length results in a change of the temperature dependence of the
micellization enthalpy. At low temperatures (T < 20 °C), the
chain length has almost no effect on the micellization enthalpy
whereas at higher temperatures, increasing chain length de-
creases more strongly the enthalpy values (Figures 4 and 5).
The heat capacity ∆Cp,mic determined as ∆Cp,mic ) (∂∆Hmic
/
∂T)P is a linear function of T since ∆Hmic is described as a
second-order polynomial function of temperature. From the
variation of ∆Hmic with T (Figures 4 and 5), the heat capacity
was determined for Li+, Na+, and Cs+ counterions. It has been
proposed that ∆Cp,mic is a linear function of the hydrophobic
surface that gets exposed to water during the de-micellization
process according to ∆Cp,demic ) 33nH(J mol-1 K-1) with nH
the number of hydrogen atoms at 25 °C.35,36 If only the
hydrophobic chain would have an influence on the heat capacity,

5286 J. Phys. Chem. B, Vol. 107, No. 22, 2003
Ropers et al.
Figure 6. Heat of dilution of micelles as a function of temperature
above the cmc for alkali decyl sulfates: (0, 65 mM) Li+, (O, 70 mM)
Na+, and (1, 50 mM) Cs+.
Figure 8. Degree of ionization (1 - f) versus the hydrated radius of
the alkali counterion of dodecyl sulfate micelles. Values are taken from
Mukerjee et al.7 except that for K+, which is determined by its hydrated
radius (see Table 2).
Figure 7. Heat of dilution of micelles as a function of temperature
above the cmc for alkali dodecyl sulfates: (0, 18 mM) Li+ and (O, 18
mM) Na+.
Figure 9. Free energy of micellization as a function of temperature
for alkali decyl sulfates: (9) Li+, (b) Na+, (2) K+, (1) Cs+.
exothermicity at temperatures above 45 °C, it was not possible
to measure the heat changes over a larger temperature range.
The strong temperature dependence of the heat of dilution of
CsDeS micelles could result from the dehydration and/or the
change in micelle shape due to dilution, providing the decrease
in monomer concentration with temperature is comparable for
all surfactants. The cation Cs+, having a smaller radius in the
hydrated state than the other ions and thus a smaller hydration
shell, may be more sensitive to dilution than Li+ or Na+ having
a larger hydration shell. The second assumption of a change in
shape agrees with the results of Missel.18 For the dodecyl sulfate
series, the hydrodynamic radii of Li+ and Na+ as determined
by quasi-elastic light scattering varies slightly with temperature,
whereas those of KDS and CsDS decrease strongly with
temperature. If one applies this result qualitatively to the decyl
series, it means that the temperature strongly influences the
growth of CsDeS micelles (sphere-to-rod transition) leading to
a strong temperature dependence of the heat of dilution in
contrast to LiDeS and NaDeS.
surfactants assumes a state of complete dissociation, but not
all counterions are free in the sense of having the same activity
or mobility as those of a simple electrolyte. To take into account
the electrostatic interactions between headgroups, we must
include a term describing the counterion binding. It has been
proposed to use the equation ∆Gmic ) RT(1 + f)ln(cmc), where
the cmc is written in fraction units and f refers to the fraction
of counterions bound to a micelle, assuming it is temperature-
independent.2 The correct evaluation of the counterion binding
is quite difficult since it depends on the method as proved for
NaDS.3 We have here used the values of the ionization degree,
defined as the fraction of counterions not bound to a micelle
(R ) 1 - f), which are determined by electrical conductivity7
for LiDS, NaDS, and CsDS. In Figure 8, the values of the degree
of ionization R are presented for Li+, Na+ and Cs+ versus the
hydrated radius.7 They are valid for dodecyl sulfate surfactants
and vary with the chain length.8,17 Due to the discrepancy in
the literature data even for one method,3 we have considered
those values as depending only on the counterions and not on
the chain length. The value for K+ was deduced using the
hydrated radius given in Table 2. The values of the free energy
and entropy are presented in Figures 9 and 10 for the decyl
sulfate series and in Figures 11 and 12 for the dodecyl sulfate
series as a function of temperature.
Thermodynamical Parameters. From the cmc and the
enthalpy of micellization, the free energy and entropy can be
determined. The entropy of micellization is easily calculated
from the relationship: T∆Smic ) - ∆Gmic + ∆Hmic. The main
problem lies in the determination of the free energy. Assuming
a sufficiently large aggregation number (m > 60), an ideal
behavior of monomers in water and no electrostatic effects, the
pseudo-phase separation model leads to the following equa-
tion: ∆Gmic ) RT ln(cmc). The use of this equation for ionic
The change in counterion from Li+ to Cs+ produces nearly
vertical shifts in the ∆Gmic curves toward more negative values
indicating that the process becomes thermodynamically more
favorable due to a decrease of the electrostatic repulsions

Micellization of Alkyl Sulfates
J. Phys. Chem. B, Vol. 107, No. 22, 2003 5287
Figure 13. Thermodynamical parameters (2) T∆S, (b) ∆H, and (9)
∆G of the micellization process for LiDeS as a function of temperature.
Figure 10. Entropy of micellization as a function of temperature for
alkali decyl sulfates: (9) Li+, (b) Na+, (2) K+, (1) Cs+.
range, the micellization process turns to be entropically driven,
i.e., the entropy is the controlling factor of micellization. From
the large gain in entropy during micelle formation, it has been
qualitatively concluded that the positive variation in entropy
due to the destruction of the water structure around the
hydrophobic part and due to the dehydration of the polar parts
exceed the entropy decrease due to the association of surfactant
molecules in a micelle and due to the binding of counterions to
the micelles1. Assuming the destruction of the water structure
is the same for all compounds of the alkyl sulfate series, the
decrease in entropy T∆Smic on going from Li+ to Cs+ is mainly
associated to the dehydration of polar headgroups. As the
hydration shell decreases from Li+ to Cs+ due to the larger
polarizability of the ions, the change in entropy is smaller for
ions with a smaller hydrated radius.
Figure 11. Free energy of micellization as a function of temperature
for alkali dodecyl sulfates: (9) Li+, (b) Na+.
Conclusion
This study of the effect of counterions (Li+, Na+, K+, and
Cs+) on the micelle formation of decyl and dodecyl sulfates by
isothermal titration calorimetry has shown that counterions affect
the thermodynamics of micellization and their influence can be
recorded by ITC. Critical micelle concentration (cmc) and
enthalpy of micellization (∆Hmic) decrease in the order Li+
>
Na+ > K+ > Cs+ at a given temperature and for a fixed chain
length. This decrease is associated with the decrease of the
counterion binding in the reverse order. The electrostatic
repulsions between ionic headgroups, which prevent the ag-
gregation, are progressively screened with the size of the
counterion and the process of micelle formation is less endo-
thermic and molecules aggregate already at a lower concentra-
tion. The cmc versus temperature reaches a minimum, while
the enthalpy of micellization passes through zero.
The endothermic heat of dilution of micelles in the post-
micellar region is strongly dependent on the temperature for
the cation Cs+ and correlates with the change in micelle shape.
The use of the pseudo-phase separation model including the
counterion binding shows that the variations of enthalpy and
entropy of micellization compensate each other and the free
energy ∆Gmic is only slightly dependent on counterions and
temperature. A decrease in hydrated ionic radius and an increase
in chain length produce nearly vertical shifts in the plot ∆Gmic
versus temperature.
Figure 12. Entropy of micellization as a function of temperature for
alkali dodecyl sulfates: (9) Li+, (b) Na+.
between polar headgroups. Increasing temperature leads to a
similar decrease in ∆Gmic for all the compounds investigated.
∆Gmic plots do not exhibit a pronounced minimum as the cmc
curves (Figures 2 and 3) since the term RT is dominating and
ln(cmc) acts only as a correcting factor. Both the slight
temperature dependence of the free energy and its negative
values result from the dominating influence of the entropy term
as shown in Figure 13 for LiDeS.
The entropy term (T∆Smic) shows the same vertical shifts on
going from Li+ to Cs+ as the enthalpy and the free energy. The
shortening of the chain length leads to a more pronounced
decrease of the entropy term. In the investigated temperature
Acknowledgment. Financial support by the Max-Planck
Society and Centre de la Recherche Scientifique is gratefully
acknowledged. The authors thank S. Schade for helpful coop-
eration.

5288 J. Phys. Chem. B, Vol. 107, No. 22, 2003
Ropers et al.
(20) Warszynski, P.; Lunkenheimer, K.; Czichocki, G. Langmuir 2002,
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