Properties of Dilute Aqueous Solutions of Double-Chain Surfactants, Alkyldodecyldimethylammonium Bromides with a Change in the Length of the Alkyl Chains

Article abstract of DOI:10.1246/bcsj.76.1903

A series of cationic surfactants, dialkyldimethylammonium bromides with dodecyl as the primary alkyl chain and with methyl, ethyl, propyl, butyl, hexyl, octyl, and decyl as the second alkyl chain, as well as those with symmetric alkyl chains, dioctyl, didecyl and didodecyl ones, were synthesized, and their properties were investigated through measurements of the conductivity and air-liquid surface tension for their aqueous solutions to determine their critical micelle concentrations (cmc) and surface adsorption parameters in the formulation according to a two-dimensional lattice model in the form of the Frumkin equation. The change in cmc revealed that the free energy to transfer from water to the micelle per methylene unit is significantly small for asymmetric double-chain surfactants with a shorter second alkyl chain, and it approaches as elongating the second alkyl to those for the single-chain and symmetric double-chain surfactants. The free energy to transfer to an air-solution interface decreased approximately linearly with the total length of the hydrocarbon chains for all of the species examined. The lattice area for a symmetric double-chain surfactant molecule decreased with the length of its hydrocarbons. In a series of asymmetric ones, it showed a maximum for that with hexyl in its second alkyl.

Full text of DOI:10.1246/bcsj.76.1903

Ó 2003 The Chemical Society of Japan
Bull. Chem. Soc. Jpn., 76, 1903–1910 (2003) 1903
Properties of Dilute Aqueous Solutions of Double-Chain Surfactants,
Alkyldodecyldimethylammonium Bromides with a Change in the Length
of the Alkyl Chains
ꢀ
Koichi Hiramatsu, Keiichi Kameyama, Ryo Ishiguro, Masaki Mori, and Hisao Hayase
Department of Biomolecular Science, Faculty of Engineering, Gifu University, Yanagido 1-1, Gifu 501-1193
Received March 6, 2003; E-mail: hiramatu@biomol.gifu-u.ac.jp
A series of cationic surfactants, dialkyldimethylammonium bromides with dodecyl as the primary alkyl chain and
with methyl, ethyl, propyl, butyl, hexyl, octyl, and decyl as the second alkyl chain, as well as those with symmetric alkyl
chains, dioctyl, didecyl and didodecyl ones, were synthesized, and their properties were investigated through measure-
ments of the conductivity and air–liquid surface tension for their aqueous solutions to determine their critical micelle
concentrations (cmc) and surface adsorption parameters in the formulation according to a two-dimensional lattice model
in the form of the Frumkin equation. The change in cmc revealed that the free energy to transfer from water to the
micelle per methylene unit is significantly small for asymmetric double-chain surfactants with a shorter second alkyl
chain, and it approaches as elongating the second alkyl to those for the single-chain and symmetric double-chain
surfactants. The free energy to transfer to an air–solution interface decreased approximately linearly with the total length
of the hydrocarbon chains for all of the species examined. The lattice area for a symmetric double-chain surfactant
molecule decreased with the length of its hydrocarbons. In a series of asymmetric ones, it showed a maximum for that
with hexyl in its second alkyl.
Cationic surfactants of the type of quaternary ammonium
salts constitute a major class among various types of
surfactants. Quaternary ammonium surfactants with a single
long alkyl chain, and those carrying two long hydrophobic
chains are widely applied in practical fields, such as fabric
softeners and antimicrobial or antiseptic agents, besides their
common properties as surface-active agents.1,2 The class of
quaternary ammonium surfactants are utilized for a variety
of purposes, since their properties can be selected by control-
ling the chemical structures of their hydrophobic tail groups.
Single-chain surfactants of quaternary ammonium salts have
been studied concerning their micellar structures; namely,
transition phenomena from spherical micelles to rod-like mi-
celles have been observed mostly for this type of
surfactant.3,4 On the other hand, double-chain quaternary am-
monium salts have attracted interest owing to their properties
to form bilayer structures, or vesicles,5–12 and concerning in-
teractions with proteins.13 Such variations in the properties
of these types of surfactants should be correlated with their
chemical structures, which determine the hydrophilic–hydro-
phobic balance, or packing properties, in various types of
molecular assemblies. It is hence important to investigate
the relationship between the chemical structure and the solu-
tion or surface-active properties of the surfactants.
variation in the properties of quaternary ammonium salts, it
seems to be pertinent to study the change in the properties with
the length of the second alkyl chain in a systematic way.
For characterizing the variation of their properties with the
length of the second alkyl chain, we prepared a series of di-
alkyldimethylammonium bromides with various lengths of
the second alkyl chain, of which the primary alkyl is un-
changed to be dodecyl, which is abbreviated as C12CnDMA.
In the present study, the properties of aqueous solutions of
eight kinds of surfactants, namely n ¼ 1, 2, 3, 4, 6, 8, 10,
and 12, of C12CnDMA surfactants, were investigated through
precise measurements of the surface tensions of the air–solu-
tion interfaces as well as measurements of the conductivities
of their aqueous solutions.
Experimental
Synthesis of the Double Chain Cationic Surfactants. Alkyl-
dodecyldimethylammonium bromides were synthesized through a
quaternarization reaction between dodecyldimethylamine and
corresponding alkyl bromides. The reactions were performed
with ethanol as a solvent under a nitrogen stream, and the result-
ing products were extracted by ether. The surfactants were puri-
fied by recrystallization from a mixture of acetone and ethanol.
As a recrystallization solvent, ethyl acetate was occasionally used
for those with hexyl and longer ones as their second alkyl chains.
Measurements of Surface Tension. The surface tension of
the air–liquid interface was measured according to the drop-vol-
ume method16 by using an automatic surface tensiometer, type
YMK98, manufactured by Yamashita Giken Ltd. (Tokushima,
Japan). This instrument is equipped with a photo-sensing drop
counter and a precise monitor of the drop volume. The vessel ac-
While some studies have been reported concerning the
change of the solution properties of those surfactants with a
change in the length of the hydrocarbon chain for double-chain
surfactants with equal lengths of alkyl chains7–10 and for those
with unequal lengths of alkyl chains,11,14,15 the variation in the
properties of the surfactants from single-chain to double-chain
ones has not been explicitly demonstrated. To understand the
Published on the web October 15, 2003; DOI 10.1246/bcsj.76.1903

1904 Bull. Chem. Soc. Jpn., 76, No. 10 (2003)
Properties of Double-Chain Surfactants
commodating the drop counting apparatus was immersed into a
water bath, of which the temperature was controlled to be
25 Æ 0:01 ꢁC. The surface tension (ꢀ) was calculated according to
Table 1. Critical Micelle Concentrations and Related Prop-
erties
Surfactant species
cmc/mol kgÀ1
(Surface tension) (Conductivity)
ꢁ
ꢀ ¼ ðVÁdg=rÞYðr=V1=3Þ:
ð1Þ
C12C1DMA
C12C2DMA
C12C3DMA
C12C4DMA
C12C6DMA
C12C8DMA
C12C10DMA
1:50 Â 10À2
1:42 Â 10À2
1:16 Â 10À2
9:43 Â 10À3
3:99 Â 10À3
1:35 Â 10À3
3:50 Â 10À4
1:55 Â 10À2
1:43 Â 10À2
1:22 Â 10À2
9:16 Â 10À3
3:63 Â 10À3
1:29 Â 10À3
4:35 Â 10À4
0.24
0.32
0.29
0.32
0.50
0.54
0.58
Here, g is the acceleration due to gravity and Ád is the difference
in the density between the solution and humid air, which was ap-
proxmated to the density of water at 25.00 ꢁC. In this equation, r is
the radius of the dropping tip, which was measured with a micro-
gauge for each of the tips used. The compensation factor,
Yðr=V1=3Þ, was calculated according to an approximated quadratic
function proposed by Lando and Oakley17 for a given r and the
measured drop volume (V).
Measurements of Conductivity. The conductivities of the
surfactant solutions at 25 ꢁC were measured by an electric conduc-
tivity meter, CM-1DB (Toa electronics Co., Japan) with elec-
trodes, CG-201PL, supplied by the same manufacturer. The elec-
trodes were equilibrated with each of the surfactant solutions for 5
to 30 min before a measurement.
C8C8DMA
C10C10DMA
C12C12DMA
2:22 Â 10À2
1:50 Â 10À3
7:0 Â 10À5
2:30 Â 10À2
1:55 Â 10À3
1:91 Â 10À4
0.32
0.53
0.71
(n ¼ 3), butyl (n ¼ 4), hexyl (n ¼ 6), octyl (n ¼ 8), decyl
(n ¼ 10) and dodecyl (n ¼ 12) groups plotted against the sur-
factant concentration. For each of the surfactants, the plot
shows a clear deflection, which indicates a change of the spe-
cific conductivity of the solute due to the formation of molec-
ular assemblies. The concentration at the deflection point is
hence the critical micelle concentration (cmc). The thus-deter-
mined values of cmc are given in Table 1.
Results
Conductivities of Aqueous Solutions. Figure 1 shows the
conductivities measured for aqueous solutions of alkyldode-
cyldimethylammonium bromides (C12CnDMA) with the sec-
ond alkyl chain of methyl (n ¼ 1), ethyl (n ¼ 2), propyl
While the increment of the specific conductivity below the
cmc was not varied with the surfactant species, that above
the cmc seemed to increase with the length of the second alkyl
chain. The ratio between the slope below cmc and that above
cmc (ꢁ) can be used as a measure of the degree of the counter-
ion dissociation for the micelle. The thus-calculated values are
given in Table 1. The ꢁ for C12C1DMA is in good agreement
with the previously reported one.14,18 The ꢁ was observed to
increase in an approximately linear way with the length of the
second alkyl chain. This may be ascribed to the change in the
charge density on the micellar aggregates, since the increment
of the conductivity below the cmc was not significantly varied
with the surfactant species.
Surface Tensions of Air–Aqueous Solution Interfaces.
Figure 2 shows the surface tension of the air–liquid interface
measured for aqueous solutions of alkyldodecyldimethylam-
monium bromides (C12CnDMA) with the second alkyl chain
of methyl (n ¼ 1), ethyl (n ¼ 2), propyl (n ¼ 3), butyl (n ¼
4), hexyl (n ¼ 6), octyl (n ¼ 8), and decyl (n ¼ 10) groups
plotted against the logarithm of the concentration.
For all of the surfactant species, the surface tension de-
creased monotonously with the surfactant concentration up
to a deflection point. Assuming this deflection to indicate
the formation of micellar aggregates, the concentration at the
deflection point can be referred to the critical micelle concen-
tration (cmc) of each of the surfactants. Here, we use the term
cmc commonly for describing the concentrations at which an
observed quantity changes deflectively, though the aggregates
formed at the concentration may not be defined as the coven-
tional micelle, as discussed in the Discussion section.
Above the deflection, the surface tension varied very scarce-
ly with the surfactant concentration for those surfactants with a
shorter second alkyl chain (C12C1DMA, C12C2DMA,
C12C3DMA, and C12C4DMA). For those with longer second
chain (C12C6DMA, C12C8DMA, and C12C10DMA), however,
Fig. 1. Conductivities of aqueous solutions of alkyldode-
cyldimethylammonium bromides.
C12C2DMA ( ), C12C3DMA ( ) and C12C4DMA (
C12C1DMA ( ),
)
in (a), C12C6DMA ( ) and C12C8DMA ( ) in (b), and
C12C10DMA ( ) and C12C12DMA ( ) in (c).

K. Hiramatsu et al.
Bull. Chem. Soc. Jpn., 76, No. 10 (2003) 1905
Fig. 4. Critical micelle concentrations of quaternary ammo-
nium bromides plotted against the total number of carbon
atoms in the molecule (nC). Symbols and surfactant spe-
Fig. 2. Surface–tension isotherms for aqueous solutions of
alkyldodecyldimethylammonium bromides. From right
to left, C12C1DMA ( ), C12C2DMA ( ), C12C3DMA
cies:
( ), alkyldodecyldimethylammonium bromides
(C12CmDMA); ( ), symmetric dialkyldimethylammonium
bromides (CnCnDMA), among which the data of C14C14-
DMA (nC ¼ 30) was adopted from Haas and Hoffmann
(1996),11 and ( ), alkyltrimethylammonium bromides of
which data were taken from Aoki et al. (1986).20
(
(
), C12C4DMA ( ), C12C6DMA ( ), C12C8DMA
), and C12C10DMA ( ).
and C10C10DMA was largely the same as that of asymmetric
dialkyl surfactants shown in Fig. 2. In Fig. 3, the results for
C12C4DMA and C12C8DMA are shown for a comparison. Ap-
parently, the surfactants with the same carbon number have a
very similar effect on decreasing surface tension, while the
cmc’s of the symmetric dialkyl surfactants are higher than
those of the asymmetric dialkyl surfactants carrying the same
carbon number. These results suggest that the magnitude of
surfactant adsorption on the air–solution interface is additively
determined by the total length of the hydrocarbon chains in a
surfactant molecule, but the chain length inequality affects the
stability of micellar aggregates (to be discussed later, see
Fig. 4).
In the surface–tension isotherm of C12C12DMA, a second
deflection point could be observed at a rather higher
concentration. Above this point, the surface tension of its so-
lution was observed to be constant with the surfactant
concentration. Solutions of C12C12DMA at these concentra-
tions were slightly turbid, while the dispersion was quite
stable. The second inflection point is hence presumed to be
the boundary between the isotropic micellar solution and the
water–liquid crystal coexisting region.
Fig. 3. Surface–tension isotherms for aqueous solutions of
dialkyldimethylammonium bromides. From right to left,
C8C8DMA ( ), C10C10DMA ( ), and C12C12DMA
( ). The data of C12C4DMA ( ) and C12C8DMA ( ),
are reproduced from Fig. 2 for comparison.
it showed a significant decrease above the deflection concen-
tration.
Discussion
Figure 3 shows surface–tension isotherms for the dialkyl
surfactants with equal lengths of a couple of alkyl chains
(C8C8DMA, C10C10DMA, and C12C12DMA bromides). These
surface–tension isotherms for symmetric double-chain surfac-
tants were mostly in good agreement with the results reported
by Svitova et al.10 at 22 ꢁC, except for C10C10DMA. The
mode of the change of the surface tension for C8C8DMA,
In the present study, we obtained systematic results for qua-
ternary ammonium bromides as double-chain surfactants car-
rying two elongated hydrocarbons, mainly through surface
tensiometry. Here, we discuss some quantitative aspects for
the change in the properties of the surfactant with varying
length of the second alkyl chain.

1906 Bull. Chem. Soc. Jpn., 76, No. 10 (2003)
Properties of Double-Chain Surfactants
Critical Micelle Concentrations. In Table 1, the values of
cmc determined from the deflection points in the surface–ten-
sion isotherm and conductivity measurements are summarized.
The values from the two methods agree well, except for
C12C12DMA. The cmc for C12C12DMA was not precisely de-
termined by a conductivity measurement, since the deflection
in the concentration dependence of the conductivity was very
shallow. For aqueous solutions of this kind of double-chain
surfactant, the presence of two deflection points has been
reported.10–12 The presently reported values of cmc are judged
to be the lower ones in the above reports. Below this (the first)
cmc, the solutions involve soley monomerically dissolved sur-
factants.
hold only for those of which the chain length is very short.
As summarized in the literature,19 shifting the position of a
sulfate group has been shown to increase cmc to shift the log
cmc versus m line for the homologous series of surfactants.
Those changes of cmc are quite similar to the present
results. In the expression of Eq. 2, the difference in the length
of the second chain is reflected by that of the constant, B. This
can be regarded as a change in the properties of the hydrophilic
head group. In the results for RR0CHSO4Na surfactants, the
relation of Eq. 2 has been shown to hold for the length of
one (primary) alkyl chain for each series of surfactants which
has same the length as another (second) chain. This indicates
that the additional second hydrocarbon chain attaching to a
head group acts to modify the original properties of the hydro-
philic group, or generates a new series of surfactants of which
cmc varies systematically with the length of the primary hy-
drocarbon.
For the present series of asymmetric double-chain surfac-
tants, the change in the hydrophilic head group in terms of B
can be estimated, provided that the cmc of each series of sur-
factants with the same length of the second chain changes as
Eq. 2 or Eq. 4 with same slope, A as a function of the chain
length of the primary alkyl. Figure 5 shows the variance in
the intercept (B) with the length of the second chain. In this
result, B changes linearly with the length of the second chain
for carbon numbers up to 4, and further elongation of the chain
has an effect similar to that in the series of symmetric double-
chain surfactants.
In Fig. 4, the cmc obtained in the present study for the dou-
ble chain surfactants are plotted against the total number of
carbon atoms in the surfactant molecule. For ionic surfactants,
the change of cmc with the hydrocarbon chain length is ex-
pressed as follows:19
log cmc ¼ ÀAm þ B;
ð2Þ
where A and B are constants for a homologous series of
surfactant. In particular, the coefficient A is described by
!
A ¼
:
ð3Þ
2:303kTð1 þ KgÞ
Here, m is the number of carbon atoms in the hydrocarbon
chain(s), ! the free energy to transfer one methylene group
from a hydrophobic environment to water, Kg the negative
slope of ln cmc versus the counter-ion concentration, k the
Boltzmann constant, and T the absolute temperature.
Here, the change in cmc for the present double-chain surfac-
tants can be discussed in terms of the balance between their
hydrophilic and hydrophobic contributions to the energetics
of micelle formation. The value of cmc is correlated with
the change in the Gibbs free-energy upon micelle formation,
As shown in the figure, the log cmc for the single-chain sur-
factant decreases linearly with the total number of carbons, or
with the length of its hydrocarbon chain.20 Such a linear rela-
tion is shown to also hold for a series of double-chain surfac-
tants with equal length of the alkyl groups. It is also noted that
the change for the equal-length double-chain surfactants is par-
allel with that for single-chain surfactants. This fact has been
shown by Kunieda and Shinoda7 for those quaternary ammoni-
um chlorides. In this respect, an elongation of the alkyl chain
length additively affects the stabilization of micelle formation
for both types of surfactants. This aspect thus indicates that
both types of surfactants are equivalent in terms of A, but dis-
tincted in B.
ÁGmꢁ. The relation may be assumed to be described by the
ꢀ
following equation for ionic surfactants:24
In the results of the present series of surfactants carrying un-
equal lengths of two alkyl chains, the points are shown to de-
viate from the line of the single-chain species and approach to
that of the equal-length double-chain species as the carbon
number increases. The change of cmc with the hydrocarbon
chain length can be compared with the effect of the position
of the ionic group in a long hydrocarbon chain.21,22 The result-
ing compound can be regarded as a series of double-chain
surfactants of the type of sodium 1-alkylalkyl sulfates
(RR0CHSO4Na).
It has been pointed out that the elongation of the shorter al-
kyl chain in the above type of surfactants carrying another long-
er alkyl chain also linearly decreases ln cmc, but does not do
so as effectively as that of the longer one.23 For the present
results for dialkyldimethylammonium bromides, the linear re-
lation with respect to the second alkyl chain length appears to
Fig. 5. Variation in
B for asymmetric double-chain
surfactants, alkyldodecyldimethylammonium bromides
(C12CmDMA) with the number of carbon atoms in the sec-
ond alkyl group. The dashed line is the level for the sin-
gle-chain surfactants (lower line) and that for symmetric
double-chain surfactants (upper line). The dotted line
shows the line with the slope corresponding to the com-
mon A to the single-chain surfactants and the symmetric
double-chain ones.

K. Hiramatsu et al.
Bull. Chem. Soc. Jpn., 76, No. 10 (2003) 1907
where ꢂ2 and a2 are the chemical potential and the activity of
the solute, respectively. For aqueous solutions of an ionic sur-
factant, its activity is given by a ¼ a a ¼ ðf C Þðf C Þ,
ꢁ
ÁGm ¼ ꢂꢁm À ꢂ1ꢁ ¼ ð1 þ KgÞRT ln Xcmc
;
ð4Þ
ꢀ
where ꢂꢁm and ꢂꢁ1 are the standard chemical potential for the
surfactant species in a micellar environment and that for a
monomeric species in an aqueous environment; Xcmc is the
mole fraction of the surfactant at cmc. Combined with Eq. 2,
the change in the Gibbs free energy can be described as
Æ
þ
À
þ
þ
À
À
where f and f are the activity coefficients for the cation
þ
À
and the anion, respectively. For a monomeric surfactant solu-
tion with a concentration of C2ð1Þ, C ¼ C ¼ Cð1Þ
. In the
present study, regarding each of the activity coefficients to
þ
À
2
be unity, we estimated the surface excess by
T;P
ꢁ
0
ꢀ
ꢀ
ÁGm ðmÞ ¼ À! m þ Gw:
ð5Þ
!
1
@ꢀ
@ ln C2ð1Þ
Here, !0 ¼ 2:303RTAð1 þ KgÞ is the increment of the free
À2 ¼ À
:
ð7Þ
2RT
ꢀ
energy per one mole of methylene group, and Gw
¼
2:303RT½Bð1 þ KgÞ þ ln ꢁwꢂ, where ꢁw is the molality of wa-
ter, and can be regarded as a constant term for a series of sur-
factants carrying the same hydrophilic head group.
The parallel relation for the single-chain species and the
equal-length double-chain ones in Eq. 2 is interpreted as that
both of them have almost the same values for !0, while the for-
The surface excesses thus estimated from the surface–tension
isotherms are shown in Fig. 6 against the logarithm of the sur-
factant concentration.
In a simple theoretical treatment for the surface adsorption
by using the Bragg–Williams approach,25 the following rela-
tion between the surface excess and the solute concentration
in a bulk solution is derived:
ꢀ
mer has a smaller value of Gw than the latter. This indicates
that the formation of micelles by an equal-length double-chain
surfactant is unstabilized compared with that by a single-chain
surfactant carrying the same total carbon number in its tail
group; namely, the former shows a higher cmc than the
latter. This difference is largely ascribed to that in the energet-
ic contribution of their hydrophilic parts upon transfer from
water to the molecular assemblies formed by each of surfactant
species.
A0À2
C2 ¼
expðWA0À2Þ:
ð8Þ
Kð1 À A0À2Þ
Here, A0 is the surface area per lattice site, and W represents
the magnitude of the preferential interaction among the
adsorbed molecules. In the above equation, K is an elementary
binding constant, which is related to the standard free-energy
change per mole of the adsorbed surfactant (ÁGꢁa) by
An elongation of an alkyl chain in a surfactant molecule is
supposed to increase unfavorable interactions between mono-
merically dissolved species and surrounding water molecules,
namely to increase ꢂꢁ1. This usually yields a decrease of cmc,
when the elongation would not alter the micellar state to keep
ꢂꢁm unchanged. In the case of an elongation of the second al-
kyl chain, it should also certainly contribute to the destabiliza-
tion of the monomeric state in water, even for the unequal-
length species. The fact that the elongation yields not so much
depression of cmc implies that the chemical potential in the
micellar state (ꢂꢁm) should be increased concomitantly by an
elongation of the second alkyl chain.
It is to be noted that the initial slope of the plot in Fig. 5
closely coincides with the value of A. This coincidence indi-
cates that the magnitude of the increase in ꢂꢁm is equal to that
of the increase in ꢂꢁ1 by an elongation of the second alkyl
chain. This suggests that the elongated hydrophobic part in
the second chain is scarcely embedded into the internal envi-
ronment of the micellar aggregates, but is mostly protruded in-
to the aqueous environment, especially when the second chain
is relatively short. This could make the micellar state rather
unstable to increase ꢂꢁm. The effect seems less pronounced
with increasing the length of the second alkyl chain. This is
plausible, because some of the hydrophobic part of the second
chain can be hidden from the aqueous medium upon the for-
mation of micellar aggregates.
ÁGꢁa ¼ ÀRT ln K:
ð9Þ
The above formulation is known as the Frumkin equation.26,27
The surface excess empirically estimated as above is known to
change in a discontinuous manner in a region of low bulk
concentration.28,29 Sophisticated treatments have been made
to describe the entire change of the surface tension.30,31 In
the present study, Eq. 8 was applied to the whole concentration
region, while neglecting the discontinuous behavior of the sur-
face adsorption. The empirically estimated À2ðC2Þ was read as
C2ðÀ2Þ, and the parameters in Eq. 8 were evaluated by a non-
linear fitting procedure. The fitting was reasonably well made
except for the discontinuous region. The results are shown as
functions by the smooth lines in Fig. 6, and the thus-estimated
adsorption parameters are given in Table 2. To compare the
variation in the parameters with the surfactant species, those
parameters are plotted against the total number of carbon
atoms of the surfactant molecule in Fig. 7.
In Fig. 7a, the standard free-energy change upon adsorption
(ÁGꢁa) decreases linearly with the number of carbon atoms. A
very similar tendency of this parameter can be found in other
series of compounds having a linear hydrocarbon in the data
reported by Hirte and Lunkenheimer.30 It is noted that the
two symmetric double-chain surfactants, C8C8DMA and
C10C10DMA, show nearly the same values as those for the
asymmetric ones with the same carbon number, C12C4DMA
and C12C8DMA, respectively. This indicates that the free en-
ergy to transfer a hydrocarbon chain from the aqueous phase to
the air–liquid interface is determined additively by the length
of the hydrocarbon chain, even in asymmetric double-chain
surfactants. This change may be compared with the change
in cmc, which varies linearly with the length of hydrocarbon
Properties in Air–Solution Interfaces. According to the
Gibbs equation for a binary solution, the surface excess of the
surfactant (À2) is related to the change in the surface tension
with the activity of the surfactant,
ꢀ
ꢁ
ꢀ
ꢁ
@ꢀ
1
@ꢀ
RT @ ln a2
À2 ¼ À
¼ À
;
ð6Þ
@ꢂ2
T;P
T;P

1908 Bull. Chem. Soc. Jpn., 76, No. 10 (2003)
Properties of Double-Chain Surfactants
Fig. 6. Changes of surface excess (À2) for aqueous solutions of alkyldodecyldimethylammonium bromides with surfactant
concentration. Symbols are C12C6DMA ( ), C12C8DMA ( ), C12C10DMA ( ), and C12C12DMA ( ) in (a), and C12C1DMA
( ), C12C2DMA ( ), C12C3DMA ( ), and C12C4DMA ( ) in (b).
Table 2. Adsorption Parameters
DADMA Br
A0 Â 1016/cm2
K/kg molÀ1
ÁGꢁa/kJ molÀ1
W
C12C1DMA
C12C2DMA
C12C3DMA
C12C4DMA
C12C6DMA
C12C8DMA
C12C10DMA
55.0
55.7
63.4
72.2
87.0
75.5
66.1
1:58 Â 102
2:20 Â 102
5:41 Â 102
9:09 Â 102
3:55 Â 103
1:03 Â 104
4:08 Â 104
À12:5
À13:4
À15:6
À16:8
À20:3
À22:9
À26:3
À2:45
À1:87
À1:13
À1:52
À2:38
À2:41
À1:81
C8C8DMA
C10C10DMA
C12C12DMA
74.4
65.0
48.8
1:05 Â 103
1:93 Â 104
5:19 Â 104
À17:3
À24:5
À26:9
À1:96
À0:750
À3:26
only when the length of the second alkyl chain is very similar
to that of the primary chain. This indicates that the energetics
for transferring a hydrocarbon chain from the aqueous phase to
the air is not identical with that to the interior of a micellar ag-
gregate for those surfactants. The difference evidently indi-
cates that the change of cmc should be affected by the proper-
ties of the micellar or vesicular assemblies formed at the con-
centration reflected by ꢂꢁm in Eq. 4. Upon adsorption to a flat
air–liquid interface, the effect of elongating the chain length
may be totally averaged, so that the lengths of both chains ad-
ditively affect the energetics of the adsorption. These results
also strongly suggest that the mode of the molecular assembly
in the aggregates formed at the critical concentration could
prominently vary as the second alkyl length elongated from
methyl to hexyl.
for example. This may be ascribed to the properties of the hy-
drophilic head group, which exserts significant electrostatic in-
teractions for the present surfactants. The value is shown to
decrease linearly with the alkyl chain length for symmetric
double-chain surfactants. This change appears to be inconsis-
tent with the change in the molecular size. The magnitude of
A0 is considered to correlate rather better with the properties of
the hydrophilic head group of a surfactant molecule than its
overall molecular size. It is presumably correlated with the
magnitude of interactions among the molecules set in an array
on the interface. The present results hence suggest that a
change in the hydrophobic tail group significantly affects the
properties of the head group interacting at the surface. The in-
teractions among the molecules on the interface should involve
a repulsive one due to an ionic interaction, and an attractive
one due to van der Waals interaction between neighboring
molecules. The decrease in A0 with the length of the hydrocar-
bon chains can be rationalized, since the latter is generally en-
hanced for elongated hydrocarbon chains. The correlation be-
tween A0 and the size of the adsorbent molecule does not seem
The values of A0 for the present single-chain surfactant
(C12C1DMA), 55 Â 10À16 cm2, is similar to the reported value,
49 Â 10À16 cm2.32 The value for the ionic surfactant is rather
large compared with nonionic surfactants having the same
length of alkyl chain, 36 Â 10À16 cm2 for dodecylglucoside,33

K. Hiramatsu et al.
Bull. Chem. Soc. Jpn., 76, No. 10 (2003) 1909
leads directly to the stabilization of micellar aggregates, due
to an increase in the chemical potentials of the monomerically
dissolved state. This reflects in a shift of the linear correlation
between ln cmc and the chain length. For asymmetric double-
chain surfactants with a shorter second alkyl, however, the
elongation does not contribute very much to the micellar state
to lead a destabilization effect of the micellar state.
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