Synthesis of two biofriendly anionic surfactants (N-n-decanoyl-L-valine and N-n-decanoyl-L-leucine) and their mixed micellization with nonionic surfactant Mega-10 in Tris-buffer medium at pH 9

Article abstract of DOI:10.1039/c3ra44677h

Two biofriendly anionic amino acid surfactants (AAS), N-n-decanoyl-l-valine (C₁₀-val) and N-n-decanoyl-l-leucine (C₁₀-leu) were synthesized and mixed micellization of them with nonionic surfactant N-decanoyl-N-methyl-glucamine (Mega-10) was investigated by tensiometry and fluorimetry in 50 mM Tris-buffer (pH = 9) medium at 298 K. The critical micelle concentration (cmc), surface properties, e.g., Gibbs surface excess (Γ_max), area of exclusion per surfactant monomer (A _min) and surface pressure at cmc (Π_cmc) were determined. Gibbs free energy of micellization (ΔG0m) and Gibbs free energy of adsorption (ΔG0ads) were also determined. Both the free energy values are negative indicating the spontaneity and stability of the mixed micelles. The size of the micelles was determined by dynamic light scattering (DLS) measurements. The deviation of mixed micelles from the ideal behavior was discussed on the basis of Clint, Motomura, Rubingh (regular solution theory), Rosen and Maeda's theory. Rubingh-Holland theory was applied on the ternary systems made by these three surfactants. The compositions of mixed micelle, the activity coefficients and the corresponding interaction parameters were evaluated from these theories. The interaction parameters (β) are negative, indicating attractive interaction between the ionic and nonionic surfactants. The micellar aggregation number (N_agg) and micropolarity were evaluated using steady state fluorescence measurements and the packing parameter (P) was determined on the basis of Israelachvili's theory. The standard free energy changes associated with the transfer of surfactant tail due to micellization of pure, binary and ternary combinations of surfactants were determined from Nagarajan's model. We report for the first time in detail the binary and ternary combinations using amino acid based surfactants.

Full text of DOI:10.1039/c3ra44677h

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Synthesis of two biofriendly anionic surfactants
(N-n-decanoyl-L-valine and N-n-decanoyl-L-leucine)
and their mixed micellization with nonionic
Cite this: RSC Adv., 2014, 4, 12275
surfactant Mega-10 in Tris-buffer medium at pH 9†
*
Sibani Das, Susmita Maiti and Soumen Ghosh
Two biofriendly anionic amino acid surfactants (AAS), N-n-decanoyl-L-valine (C10-val) and N-n-decanoyl-
L-leucine (C10-leu) were synthesized and mixed micellization of them with nonionic surfactant N-decanoyl-
N-methyl-glucamine (Mega-10) was investigated by tensiometry and fluorimetry in 50 mM Tris-buffer
(pH ¼ 9) medium at 298 K. The critical micelle concentration (cmc), surface properties, e.g., Gibbs
surface excess (Gmax), area of exclusion per surfactant monomer (Amin) and surface pressure at cmc
(Pcmc) were determined. Gibbs free energy of micellization (DG0m) and Gibbs free energy of adsorption
(DG0ads) were also determined. Both the free energy values are negative indicating the spontaneity and
stability of the mixed micelles. The size of the micelles was determined by dynamic light scattering (DLS)
measurements. The deviation of mixed micelles from the ideal behavior was discussed on the basis of
Clint, Motomura, Rubingh (regular solution theory), Rosen and Maeda's theory. Rubingh–Holland theory
was applied on the ternary systems made by these three surfactants. The compositions of mixed micelle,
the activity coefficients and the corresponding interaction parameters were evaluated from these
theories. The interaction parameters (b) are negative, indicating attractive interaction between the ionic
and nonionic surfactants. The micellar aggregation number (Nagg) and micropolarity were evaluated
using steady state fluorescence measurements and the packing parameter (P) was determined on the
basis of Israelachvili's theory. The standard free energy changes associated with the transfer of surfactant
tail due to micellization of pure, binary and ternary combinations of surfactants were determined from
Nagarajan's model. We report for the first time in detail the binary and ternary combinations using amino
acid based surfactants.
Received 26th August 2013
Accepted 13th January 2014
DOI: 10.1039/c3ra44677h
www.rsc.org/advances
aggregates is a result of a delicate balance of two opposing
forces: attractive hydrophobic interaction between the tails and
Introduction
electrostatic repulsion between the head groups. Amino acid
surfactants (AAS) nd manifold applications in food, pharma-
ceutical, detergent and cosmetic industries as they are surface
active, mild, nonirritating to human skin, low toxic and
biocompatible.4–7
Surfactants are widely used in everyday life on a large scale,
which can affect aquatic environment. So, biodegradability and
biocompatibility are important parts which require function-
ality of the desired surfactant. There is a pressing need for
producing biofriendly surfactants. Amino acid surfactants are
widely studied for this purpose as they mimic the structure of
natural amphiphiles.1–3 The spontaneous self-assembly
of molecules into supramolecular architectures is a result of
various noncovalent interactions such as hydrophobic,
hydrogen-bonding, electrostatic, dipole–dipole, and van der
Waals interactions. The geometry of the supramolecular
The solution properties of mixed surfactants are oen more
interesting than those of individual surfactants and have a wide
range of applications in industrial preparation, pharmaceutical
and medical formulations, enhanced oil recovery process, etc.
Extensive investigations on binary mixtures of cationic–
cationic,8–11 cationic–anionic,11–14 cationic–nonionic,11,15–20
anionic–anionic,11,21,22 anionic–nonionic11,23–25 and nonionic–
nonionic11,20,26,27 surfactants have been reported and analyzed in
the light of Clint,28 Rubingh,29 Rosen,30 Motomura31 and Mae-
da's32 theories to understand the synergism and antagonism of
binary compositions. A theoretical approach of a regular solu-
tion and molecular thermodynamic theory has been applied on
a ternary mixture to determine the cmc and other micellar
Centre for Surface Science, Department of Chemistry, Jadavpur University,
Kolkata-700 032, India. E-mail: gsoumen70@hotmail.com; Fax: +91 33 24146266
† Electronic supplementary information (ESI) available: Plots of composition
dependent cmc and area minimum values for ternary systems and different
surface and thermodynamic properties of binary combinations of surfactants.
Different theoretical treatments and their corresponding data are also available
in the ESI. See DOI: 10.1039/c3ra44677h
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interaction parameters, shape and size of the mixed micelles. acetate and petroleum ether) were purchased from Merck,
Such approach on ternary combinations is limited.8,20,33
India. The solvents were freshly distilled before use. Decanoyl
AAS are widely used as low-molecular-mass organogelators chloride (purity, 98%) and N-decanoyl-N-methyl-glucamine
(LMOG). The interfacial and bulk properties of the amino acid (Mega-10, 99.8%) are products of Aldrich. Tris(hydroxy-
amphiphiles have been studied by many groups,34–36 but their methyl)aminomethane (Tris-buffer) was purchased from
mixed micellar behavior has not been amply explored. Mega-10 is Merck. Cetylpyridinium chloride (CPC, purity ¼ 99%) and
an alkylpolyglucoside. It has a hydrophilic sugar moiety and a pyrene were purchased from Aldrich. Pyrene was recrystal-
hydrophobic alkanoyl chain. With increase in temperature, it lised before use.
cannot be clouded in aqueous solution. Mixed micellization
of Mega-10 with cationic (alkyltrimethylammonium bromides,
ATABs), anionic (sodium dodecylsulfate, SDS) and nonionic
(poly(oxyethylene)alkyl ethers) have been reported earlier.18,26,37,38
Performance limitations of conventional surfactants have
initiated an interest to alternate surfactant structures. From an
environmental perspective, it is desirable to select biofriendly
surfactants. We have therefore, synthesized two amino acid
amphiphiles (C10-val and C10-leu) and for the rst time per-
formed tensiometric measurements on their various binary and
ternary combinations with Mega-10 in Tris-buffer (50 mM)
medium (pH ¼ 9) to learn about the inuence of amino acid
surfactants on the micellization of nonionic surfactant, Mega-
10. Detailed fundamental studies of multicomponent biocom-
patible surfactants are limited. The mutual interaction among
the surfactants arises from the difference of the type and length
of the amphiphile tail and the electrostatic and steric interac-
tions between the head groups. In our study, the tails of all the
surfactants are the same (constituting 10 carbon atoms in the
linear chain), but they differ in the type and size of the head
groups; there is a glucamide moiety (secondary amide linkage)
in Mega-10; there are primary amide linkages at the juncture of
the polar head and non-polar tail in both C10-val and C10-leu.
We can systematically control the head group because surfac-
tants derived from different amino acids have different head
groups. Attempts have been taken to investigate the thermo-
dynamics and interfacial adsorption parameters from tensio-
metric measurements, the aggregation number and polarity
index of the micellar media from uorimetry. In addition, the
shape of the micelle can be predicted from the packing
parameter and dynamic light scattering (DLS) measurements.
The micellar compositions, critical micelle concentration (cmc)
and interaction parameters for the binary systems were
analyzed in the light of Clint's theory, Rubingh model based on
the regular solution theory and Rosen and Motomura models.
Stability and excess free energy of micellization of ionic–
nonionic systems have been explained using Maeda's theory.
The mixed micellar properties of the ternary system were
analyzed on the basis of Rubingh–Holland theory. Nagarajan's
model was applied to calculate the different contributions to the
standard free energy due to micellization.
Synthesis
Two amino acid amphiphiles, N-n-decanoyl-L-valine (C10-val)
and N-n-decanoyl-L-leucine (C10-leu) were synthesized, puried
and recrystallised by following the procedure reported by
Miyagishi et al.39,40 Scheme 1 for the synthesis is given below.
Preparation of L-amino acid methyl ester hydrochloride
L-Amino acids (35 mmol) were added to 50 ml of ice cold
methanol. Then thionyl chloride was added to it dropwise until
the amino acid was completely dissolved and stirred for 24 h.
The excess solvent was evaporated under reduced pressure and
the white solid of L-amino acid methyl ester hydrochloride
(31.85 mmol) was obtained.
Preparation of N-n-decanoyl-L-amino acid methyl ester
N-n-Decanoyl-L-amino acid methyl ester hydrochloride (17.91
mmol) was separately dispersed in 25 ml chloroform. 39.2
mmol NEt3 was added dropwise to the ice cold solution and
stirred. Then 10 ml chloroform solution of n-decanoyl chloride
was added to it dropwise and the mixture was stirred at rt for 6
h. Aer completion of the reaction (checked from TLC), the
reaction mixture was diluted with 50 ml chloroform and acidi-
ed with 1 (N) HCl. The organic layer was extracted with 0.5 (M)
NaHCO3 solution and nally with brine solution. The organic
layer was taken on anhydrous Na2SO4 and shaken vigorously
and ltered. Then the solvent was evaporated and the product
was obtained as white powder.
Preparation of N-n-decanoyl-L-amino acid
N-n-Decanoyl-L-amino acid methyl ester (10.52 mmol) was dis-
solved in 15 ml THF–MeOH (1 : 1) and 1 (M) NaOH (10 ml) was
added to it under ice cold conditions. The reaction mixture was
stirred for 2 h and then acidied with 1 (N) HCl and extracted
Experimental
Materials and methods
Thionyl chloride (purity, 98%), sodium hydroxide, sodium
sulfate, triethylamine (purity, 98%), L-valine (purity, 99%) and
L-leucine (purity, 99%) were purchased from SRL, India and
solvents (methanol, chloroform, tetrahydrofuran, ethyl Scheme 1 Synthetic path of amino acid amphiphiles.
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with ethyl acetate. The organic layer was collected over anhy-
drous Na2SO4, shaken vigorously and ltered. Then the solvent
was evaporated. White crystallized solid (7.57 mmol) was
obtained aer recrystallization of the crude product from ethyl
Dynamic light scattering. DLS measurements were taken in a
Malvern Zetasizers Nano-zs apparatus with a He-Ne laser (l ¼
632 nm) at 298 K. Before the experiment, the surfactant solu-
tions were ltered through cellulose acetate paper of pore size
0.45 mm.
ꢀ
ꢀ
acetate–petroleum ether (40 C–60 C).
Characterization
Results and discussion
Critical micelle concentration (cmc)
N-n-Decanoyl-L-valine. Yield 2.1 g, 7.57 mmol, 72%; 1H-NMR
(CDCl3, 300 MHz): d (ppm): 0.80–0.89 (t, terminal CH3, 3H),
0.91–1.02 (t, CH3, b to Ca, 6H), 1.25 (bs, (CH2)6, 12H), 1.55–1.70
(m, CH2, b to –CONH, 2H), 2.17–2.3 (m, CH2, a to –CONH, 2H
and CH, attached to Ca, 1H), 4.56–4.65 (q, CH, –NHCH, 1H),
6.17–6.26 (d, –CONH, 1H), 9.4 (bs, –COOH, 1H). 13C-NMR
(CDCl3, 300 MHz): d (ppm): 14.05, 17.68, 18.94, 22.63, 25.78,
29.20, 29.23, 29.28, 29.42, 31.05, 31.83, 36.62, 57.06, 174.36,
175.17. IR (KBr): n (cmꢁ1) ¼ 3312.20, 2920.80, 2852.78, 1707.23,
1605.09, 1555.0.
In aqueous solution, the surfactants are preferentially adsorbed
at the air–water interface and decrease the surface tension (g) of
water owing to their amphiphilic character. The surfactant
monomers are aggregated with the help of attractive hydro-
phobic interaction in the tail aer a threshold concentration of
the surfactant. There is an equilibrium between the surfactant
monomer and aggregates. These aggregates are called micelles
and the corresponding threshold concentration is called critical
micelle concentration (cmc). The corresponding surface tension
is known as gcmc. Actually, gcmc is the measure of efficiency of
the surfactant to populate the air–water interface. The cmc
values of individual surfactants (structures of three surfactants
are shown in Scheme 2) and different combinations of binary
(C10-val/Mega-10, C10-leu/Mega-10 and C10-val/C10-leu) and
ternary mixtures (C10-val/C10-leu/Mega-10) in the Tris-buffer
medium (pH ¼ 9) have been determined from the plot of g vs.
log[surfactant] (Fig. 1). The nonionic surfactant, Mega-10 has a
smaller cmc value compared to the two ionic surfactants. The
values are reported in Tables 1 and S1.† Mixed micellization
processes of such binary and ternary combinations have not
been reported earlier. In case of binary and ternary mixtures,
the cmc values increase gradually with increasing composition
of the ionic surfactants. These are similar to the reports on
binary and ternary combinations of the following: sodium
dodecylsulfate (SDS), polyoxyethylenesorbitan monolaurate
(Tween-20) and polyoxyethylene lauryl ether (Brij-35);33 cetyl-
pyridinium chloride (CPC), polyoxyethylenesorbitan monop-
almitate (Tween-40) and polyoxyethylene cetyl ether (Brij-56).20
Tables 1A and S1† shows that the cmc values of the binaries lie
between the individual values of the surfactants. From Table 1B,
it was observed that the cmc values of the ternaries increase
systematically with increasing proportion of C10-val in the
mixture. The dependence of cmc on the different combinations
of the ternary mixture of C10-val/C10-leu/Mega-10 is illustrated
in Fig. S1† in three dimensions. The base points of the prism
N-n-Decanoyl-L-leucine. Yield 2.08 g, 7.2 mmol, 70%; 1H-
NMR (CDCl3, 300 MHz): d (ppm): 0.77–0.91 (t, terminal CH3,
3H), 0.95–1.04 ((t, CH3, b to Ca, 6H), 1.25 (bs, (CH2)6, 12H), 1.54–
1.77 (m, CH2, b to –CONH, 2H, CH2 a to Ca, 2H and CH, b to Ca,
1H), 2.23–2.36 (t, CH2, a to –CONH, 2H), 4.64–4.77 (q, CH,
–NHCH, 1H), 6.27–6.33 (d, –CONH, 1H), 9.19 (bs, –COOH, 1H).
13C-NMR (CDCl3, 300 MHz): d (ppm): 14.07, 21.84, 22.64, 22.81,
24.9, 25.69, 29.17, 29.24, 29.3, 29.43, 31.85, 36.34, 41.11, 51.0,
174.55, 176.26. IR (KBr): n (cmꢁ1) ¼ 3337.71, 2926.76, 2863.63,
1700.0, 1622.53, 1557.35.
Tensiometry. Tensiometric measurements were taken with a
¨
¨
du Nouy tensiometer (Kruss, Germany) using the platinum ring
detachment method. 5 ml of Tris-buffer solution (50 mM and
pH ¼ 9) was taken in a double-wall jacketed container and
connected with a thermostated water bath (accuracy, ꢂ0.1 K) at
the requisite temperature of 298 K. Then individual and mixed
surfactant solution of known concentration was added
progressively. During such measurements, 15 min time interval
for equilibration was allowed aer the surfactant addition and
thorough mixing. The cmc values were estimated from the
break points in the surface tension-log [surfactant] plots. The
determined surface tension (g) values were accurate within
ꢂ0.1 mN mꢁ1
.
Fluorimetry. Fluorescence measurements were taken using
Perkin Elmer LS55 uorescence spectrophotometer. The
temperature was kept at 298 K using a water-ow thermostat
connected to the cell compartment. In all cases, the concen-
tration of surfactant was used above the cmc. Pyrene was excited
at 332 nm and its emission was recorded at 373 and 384 nm,
which corresponded to the rst and third vibrational peaks,
respectively. The excitation and emission slits were 9 and 4 nm,
respectively. A scan speed of 250 nm minꢁ1 was used. The
aggregation number (Nagg) was determined by a uorescence
quenching study of pyrene by cetylpyridinium chloride (CPC).
The pyrene solution was added to the individual and mixed
micellar solutions of surfactants. The probe concentration was
kept low enough to avoid eximer formation. The quencher was
added progressively and the intensity was recorded for data
analysis.
Scheme 2
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The value of n in the binary mixtures of the surfactants was
obtained from the following relation,
P
n ¼ pXi
(2)
where Xi is the stoichiometric mole fraction and p is the number
of species. Assuming complete monolayer formation at cmc, the
minimum area per surfactant molecule at the air–water inter-
face (Amin) was calculated from the equation:
1018
Amin
¼
(3)
NAGmax
where NA is Avogadro's number. The Gmax and Amin values for the
binary and ternary combinations are presented in Tables 1A, B
and S1,† respectively. For the binary mixtures, the Gmax values
gradually decrease with increasing concentration of ionic
surfactants in the mixtures except for the C10-val/C10-leu
combinations. In the latter case, the Gmax value is almost
constant. The Amin values of the mixtures are in the reverse order.
The Amin of ionic surfactants are greater than that of Mega-10 due
to the presence of electrostatic repulsion between the ionic head
groups. The structural differencein the head group region affects
the interaction between the surfactants. C10-leu has an isobutyl
group near the head group which requires a greater area of
exclusion (0.95 nm2 per molecule) than C10-val (0.79 nm2 per
molecule), which contains an isopropyl group. The head group
areas of the binary mixtures were in between those of pure
components. The C10-val/C10-leu combinations have a higher
area than that of other binary mixtures indicating an antago-
nisticor repulsive interaction betweenthe head groups of the two
anionic amphiphiles. For the ternary mixtures, both Gmax and
Amin are independent of the sample compositions. The depen-
dence of Amin on the composition of the ternary system is dis-
played in 3-D form in Fig. S2.† The base points of the prism
represent the compositions of the surfactants on triangular
coordinates and the heights show the corresponding Amin values.
Like in Fig. S1,† here a multifold prole has also been obtained.
The surface pressure, Pcmc was calculated from
Fig.
1 (A) Determination of the cmc of binary combinations of
C10-val/C10-leu at different mole fractions ( , XC10-val ¼ 0.1 and
XC10-val ¼ 0.9) at 298 K. Inset: (a) C10-val/Mega-10 ( , XC10-val ¼ 0,
XC10-val ¼ 0.9, , XC10-val ¼ 1) and (B) C10-leu/Mega-10 ( , XC10-leu ¼ 0,
,
,
,
XC10-leu ¼ 0.9, , XC10-leu ¼ 1). (B) Determination of the cmc of ternary
combinations of C10-val/C10-leu/Mega-10 at different mole fractions ( ,
XC10-val/C10-leu/Mega-10 ¼ 0.125/0.25/0.625, , 0.25/0.625/0.125 and , 0.625/
0.125/0.25) at 298 K.
represent the compositions of the surfactants on triangular
coordinates and the heights show the corresponding cmc
values. A multifold prole is obtained; the trend of the molec-
ular interaction dependent micellization process of the ternary
mixture is complex and non-ideal in nature.
Pcmc ¼ gsol ꢁ gcmc
(4)
where gsol and gcmc are the surface tension of the solvent without
surfactant and the surface tension of the solvent including
surfactant at the cmc respectively. All interfacial properties (Gmax
Amin and Pcmc) are presented in Tables 1 and S1.†
,
Adsorption at the air–water interface
Surfactants orient at the air–water interface and the interfacial
adsorption per unit area of the surface at different concentra-
tions can be evaluated using Gibbs adsorption equation. The
efficiency of the surfactant molecule to populate the air–water
interface in the form of monolayer can also be predicted from
the Gibbs surface excess (Gmax).
Thermodynamics of micellization and interfacial adsorption
The standard free energy of micellization per mole of monomer
unit, DG0m for the binary and ternary mixtures can be calculated
from the regular solution theory using
ꢀ
ꢁ
1
dg
DG0m ¼ RT ln Xcmc
(5)
Gmax ¼ ꢁ
(1)
2:303 nRT d log C
where R and T are the universal gas constant and absolute where Xcmc is the cmc of the solutions in a mole fraction unit.
temperature, respectively, C is the concentration of surfactant The values of DG0m obtained using the above equation is given in
taken and n is the effective number of species present in the Tables 1 and S1.† The free energy of micellization (DG0m) is
solution. The C10-val and C10-leu produced two species each. negative indicating the spontaneity of micelle formation and
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Table 1 (A) Surface and thermodynamic properties of binary mixtures of C10-val/Mega-10 in Tris-buffer medium (pH ¼ 9) at 298 K. (B) Surface
and thermodynamic properties of different ternary mixtures in Tris-buffer medium (pH ¼ 9) at 298 K
A
106
Amin nmꢁ2 per Amin nmꢁ2 per gcmc
Pcmc
mNꢁ1 mꢁ1 kJꢁ1 molꢁ1 kJꢁ1 molꢁ1
ꢁDG0m
ꢁDG0ads
i
cmc
XC10-val
/
XC10-leu cmc/(mM) Gmax molꢁ1 mꢁ2 molecule
molecule
mNꢁ1 mꢁ1 pC20 C20
0
4.63
4.86
5.33
5.71
7.44
4.27
3.18
2.99
2.90
2.85
2.25
2.11
0.39
0.52
0.56
0.57
0.58
0.74
0.79
—
27.9
25.7
26.8
25.6
24.9
25.6
29.4
3.47 13.7
3.43 13.01 37.8
42.4
23.3
23.2
22.9
22.8
22.1
21.1
20.1
33.2
35.1
37.4
38.2
38.0
40.5
39.5
0.1
0.3
0.5
0.7
0.9
1
0.57
0.59
0.61
0.63
0.68
—
3.56 19.4
3.43 15.4
3.24 12.9
3.12 14.8
2.80 10.7
43.2
44.6
45.2
43.8
40.9
11.3
16.9
B
106
Amin nmꢁ2 per
molecule
gcmc
mNꢁ1 mꢁ1
Pcmc
mNꢁ1 mꢁ1
ꢁDG0m
ꢁDG0ads
cmc
C20
XC10-val/
cmc/(mM)
Gmax molꢁ1 mꢁ2
pC20
kJꢁ1 molꢁ1
kJꢁ1 molꢁ1
C10-leu/Mega-10
0.125/0.25/0.625
0.125/0.625/0.25
0.25/0.125/0.625
0.25/0.625/0.125
0.333/0.333/0.333
0.625/0.125/0.25
0.625/0.25/0.125
5.15
6.58
4.88
7.84
5.91
6.58
9.18
2.99
2.40
3.30
2.48
2.87
2.70
2.17
0.56
0.69
0.50
0.67
0.58
0.61
0.76
25.1
22.5
24.3
25.1
24.3
23.0
25.9
3.35
3.25
3.41
3.26
3.31
3.30
3.24
11.5
11.7
12.3
14.3
12.1
13.1
16.0
40.7
41.1
44.1
45.0
43.9
44.0
42.7
23.0
23.1
23.1
22.0
22.7
22.4
21.6
36.6
40.2
36.5
40.1
38.0
38.7
41.3
becomes less negative with increasing concentration of the
ionic surfactant in the binary mixture except for that of C10-val/ values indicate that Mega-10 is more surface-active than the
10-leu mixtures where there are almost constant values of DG0m ionic surfactants. Generally, the efficiency of adsorption of
C10-val and C10-leu as 3.47, 2.80 and 3.03, respectively. The
C
i.e., equal spontaneity of micellization is obtained. The DG0m nonionic surfactant is much greater than in ionic surfactants
values of binary ionic mixtures are slightly lower than those of with the same number of carbon atoms in the hydrophobic
ionic/nonionic combinations. Ternary mixtures also show equal group. Because in the adsorption of ionic surfactants, the
spontaneity of micellization. A similar type of observation is electrical repulsion between the ionic head groups of surfactant
also obtained in previous works.20
The standard free energy of interfacial adsorption at the air– oncoming surfactant ions increase the positive free energy of
ions is already at the interface and the similarly charged
water interface was calculated from the following equation
transfer of the hydrophilic head from the interior of the bulk
cmc
phase to the interface. The
ratio is considered as a measure
Pcmc
DGa0ds ¼ DGm0
ꢁ
(6)
C20
Gmax
of the tendency of the surfactant to adsorb at the interface
The higher the negative value of DG0ads, the higher is the
efficiency of the surfactant to be adsorbed at the surface. The
results are presented in Table 1 and S1.† The magnitude of
DG0ads is more negative than DG0m, indicating that adsorption at
relative to its micellization tendency. The values of pC20 and
cmc
for the different binary and ternary compositions are close
C20
to each other and are shown in Tables 1 and S1.†
air–water interface is more spontaneous than micellization. C10
-
Aggregation number (Nagg) and micropolarity
leu is more surface-active than C10-val. In the case of C10-val/
Mega-10 and C10-leu/Mega-10 systems, DG0ads increase with
increasing concentration of ionic surfactant in the mixture,
whereas in the C10-val/C10-leu mixtures, equal values of DGa0ds
are obtained. The values of DG0m and DGa0ds for ternary mixtures
are comparable with binary systems.
The aggregation numbers of the individual surfactants and the
binary and ternary mixtures (C10-val/Mega-10, C10-leu/Mega-10,
C
10-val/C10-leu and C10-val/C10-leu/Mega-10) were determined
using the steady state uorescence quenching method where
pyrene was used as a uorescence probe. This method is based
on the quenching of the uorescence probe by a known
concentration of the quencher. The aggregation number of
Another physical parameter pC20 is dened as pC20
¼
ꢁlog C20, where C20 is the molar concentration of the surfactant
which is required to decrease the surface tension of the solvent
by 20 mN mꢁ1. The parameter pC20 is the measure of surface
activity of a surfactant. The higher the pC20 value, the more
efficiently the surfactant can adsorb at the air–water interface
and reduces the interfacial tension or the surface tension.24
From Tables 1 and S1† we obtained the pC20 values of Mega-10,
surfactants was determined using the equation
ꢂ ꢃ
I0
I
Nagg½Qꢃ
ln
¼
(7)
½Sꢃ ꢁ cmc
where I0 and I are the uorescence intensities of the surfactant
in absence and presence of quencher, respectively. [S] and [Q]
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are the concentrations of the surfactant and quencher (CPC),
respectively. The aggregation number, Nagg, is obtained from
the tting of uorescence intensity data at various concentra-
tions of a quencher. The aggregation numbers of C10-val, C10-leu
and Mega-10 are 84, 52 and 91, respectively.
The Stern–Volmer equation was used to calculate the equi-
librium constant (KSV) for the interaction between uorescence
probe and quencher.
I0
¼ 1 þ KSV½Qꢃ
(8)
IQ
In the present study, a good linear plot (Fig. 2) was obtained
and KSV was found from the slope of the plot of (I0/IQ) vs. [Q].
The values of Nagg and KSV were listed in Tables 2 and S2.† The
aggregation number of the C10-leu/Mega-10 and C10-val/C10-leu
systems decreases with increasing concentration of C10-leu and
this is reasonable. The aggregation number of C10-val/Mega-10
and ternary combinations is independent of the composition of
amphiphiles. Nagg can be calculated by following the mixing
rationale
P
calcd
agg
i
N
¼
XiNagg
(9)
i
where Nagg is the individual aggregation number of the ionic
and nonionic surfactants and Xi is the stoichiometric mole
Table
2 Values of aggregation number, Stern–Volmer constant,
micropolarity, hydrodynamic diameter and diffusion coefficients of
different (A) binary and (B) ternary mixtures in tris-buffer medium
(pH ¼ 9) at 298 K
obs
XC10-val
XC10-leu
/
N
N
/
104 KSV/Lꢁ1
Dh/nm
(PDI)
D0 ꢄ
agg
molꢁ1
I1/I3
1011 m2 sꢁ1
cal
agg
0
91
2.35
2.43
2.05
1.53
1.73
1.72
1.67
0.84
0.82
0.79
0.77
0.77
0.73
0.72
6.30 (0.28) 7.78
3.60 (0.24) 13.6
2.90 (0.36) 16.9
2.70 (0.31) 18.2
2.70 (0.23) 18.2
2.70 (0.35) 18.2
2.60 (0.21) 18.9
0.1
0.3
0.5
0.7
0.9
1
93/87
76/79
69/71
63/64
60/56
52
XC10-val
XC10-leu
XMega-10
/
/
obs
N
N
/
104 KSV Lꢁ1
Dh/nm
(PDI)
D0 ꢄ
agg
molꢁ1
I1/I3
0.79
0.76
1011 m2 sꢁ1
cal
agg
0.125/0.25/ 79/80
0.625
0.125/
0.625/
0.25
2.07
2.07
2.32 (0.34) 21.1
2.38 (0.36) 20.6
77/66
0.25/0.125/ 78/84
0.625
0.25/0.625/ 77/65
0.125
2.04
2.17
2.21
2.42
0.80
0.77
0.76
0.78
2.33 (0.21) 21.1
2.38 (0.28) 20.6
2.67 (0.33) 18.7
2.33 (0.32) 21.1
Fig. 2 (A) Plot of ln(I0/I) vs. [Q] for C10-val/Mega-10 (XC10-val ¼ 0.5).
0.333/
82/76
Inset: corresponding basic spectrum. (B) Plot of ln(I0/I) vs. [Q] for C10
-
-
0.333/0.333
0.625/
leu/Mega-10 (XC10-leu ¼ 0.7). (C) Plot of ln(I0/I) vs. [Q] for C10-val/C10
90/82
leu (XC10-val ¼ 0.7). Inset: corresponding basic spectrum. (D) Plot of
0.125/
0.25
ln(I0/I) vs. [Q] for C10-val/C10-leu/Mega-10 ( , XC10-val/C10-leu/Mega-10
¼
0.125/0.625/0.25 and , XC10-val/C10-leu/Mega-10 ¼ 0.625/0.125/0.25).
0.625/0.25/ 67/77
0.125
1.95
0.77
2.34 (0.23) 21.1
Inset: corresponding basic spectrum.
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Fig. 3 Variation of the hydrodynamic diameter (Dh) with mole frac-
tions of surfactants (X) Inset. Representative plot for the size distribu-
tion of C10-leu/Mega-10 (XC10-leu ¼ 0.3).
fraction. Good agreement is found between the observed and
calculated aggregation number (Tables 2 and S2†).
The microstructures of the micelles are oen explained by the
important micro environmental property, called micropolarity.
It is obtained from the ratio of rst and third vibronic peak of
pyrene (I1/I3). The micropolarity values range from z1.9 in polar
solvent to z0.6 in hydrocarbon. The experimentally obtained
values of micropolarity are within 0.72 to 0.84 which is close to
0.6; i.e., pyrene is preferentially solubilized in the hydrophobic
region.41 Thus, the polarity sensed by the probe could give
information on thepolarity inthis micellar region. FromTables 2
and S2,† it is observed that the polarity index decreases with
increasing concentration of ionic surfactant in the mixture of
Fig. 4 (A) Variation of the ideal and experimental cmc with mole
fraction for C10-leu/Mega-10 binary mixture. Inset: variation of the
ideal and experimental cmc with mole fraction for C10-val/Mega-10
binary mixture. (B) Variation of the ideal and experimental cmc with
mole fraction for C10-val/C10-leu binary mixture.
C
10-val/Mega-10 and C10-leu/Mega-10, indicating that pyrene
senses more hydrophobic environment. The decrease of micellar
diameter is more prominent than the decrease of aggregation
number from Mega-10 to ionic surfactants. As a result, more
compact micelles are formed with increasing concentration of
ionic surfactant, that is, hydrophobicity increases. Penetration of
solvent in Mega-10 micelle is easier than the micelle of ionic
surfactants. So, pyrene senses more hydrophobicity in ionic
surfactants than in Mega-10 and the polarity decreases with
increasing concentration of ionic surfactants.
measures the diffusion coefficient (D0) of micellar systems and
evaluates the hydrodynamic diameter (Dh) in term of the Stoke–
Einstein equation
kT
D0 ¼
(10)
6phRh
where k is the Boltzmann constant, T is the absolute temper-
ature, h is the viscosity of solution and Rh (¼ Dh/2) is the
hydrodynamic radius. The D0 values are reported in Tables 2
and S2.† For binary mixtures, an increasing tendency of D0
with increasing the mole fractions of ionic surfactant is
observed; although in a few cases, constant values of D0 are
also obtained. For ternary mixtures, constant values of D0 are
obtained. The hydrodynamic diameter of the micelle of Mega-
10 is quite higher (6.30 nm) than that obtained from two ionic
surfactants (2.33 nm for C10-val and 2.6 nm for C10-leu). The
corresponding polydispersity index (PDI) values (in the
Hydrodynamic diameter (Dh) and diffusion coefficient (D0)
The hydrodynamic diameters of all binary and ternary systems
were determined using DLS measurement. The instrument
Table 3 Micellar compositions (XM/XR/XIs), interaction parameters
(bR/bs), activity coefficients (fR) and cmc's of binary mixtures at 298 K
by Motomura, Rubingh and Rosen methods at different stoichiometric
compositions (Xi) of C10-val/Mega-10
cmc/mM
XC10-val XM/XR/XIs
bR/bs
f CR10-val f RMega-10 obsd/Clint parenthesis) are also reported in Tables 2 and S2.† The
hydrodynamic diameters of all binary and ternary composi-
0.1
0.3
0.5
0.7
0.9
0.02/0.05/0.46 ꢁ0.69/ꢁ9.39 0.54
0.22/0.17/0.51 ꢁ0.88/ꢁ6.94 0.54
0.23/0.31/0.55 ꢁ1.25/ꢁ5.85 0.55
0.27/0.43/0.61 ꢁ0.98/ꢁ4.40 0.73
0.78/0.66/0.73 ꢁ0.80/ꢁ2.61 0.91
1.00
0.97
0.89
0.83
0.70
4.86/4.99
5.33/5.92
5.71/7.27
7.44/9.42
11.3/13.4
tions are close to each other. The hydrodynamic diameter of
pure and mixed surfactants indicates a spherical shape of
the micelle. The low PDI value for all combinations indicates
monodispersity of the solution. The variations of the
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hydrodynamic diameter with the mole fraction of surfactant parameters of the mixed micelles (bR) are calculated iteratively
for three binary combinations are shown in Fig. 3.
using the equations:29
2
XR ln½CmX1=C1XRꢃ
¼ 1
(14)
2
ð1 ꢁ XRÞ ln½Cmð1 ꢁ X1Þ=C2ð1 ꢁ XRÞꢃ
Mutual interaction of surfactants in micelles
where C1 and C2 are the critical micelle concentrations of
surfactants 1 and 2, respectively, and Cm is the cmc of the mixed
micelle.
Mixed micelles can be both ideal and nonideal. The ideal
behavior of the mixed micelles can be explained by the
equation28
The interaction parameter (b) can be calculated from the
following equation
n
X
1
Xi
¼
(11)
Cm
fiCi
i¼1
lnðCmX1=C1XRÞ
bR
¼
(15)
2
where Ci and Cm denote the critical micellar concentrations of
the ith component and the mixture, respectively; Xi is the stoi-
chiometric mole fraction of the ith component in solution and fi
is the activity coefficient. For ideal mixed micelle, fi ¼ 1 and eqn
(11) becomes Clint's equation and it is
ð1 ꢁ XRÞ
b is an indicator of the degree of interaction between two
surfactants in mixed micelles relative to the self-interaction of
two surfactants under two similar conditions before mixing and
accounts for deviation from ideality.
n
X
1
Xi
Ci
¼
(12)
The activity coefficients of components fR1 and fR2 in a mixed
micelle can be calculated from the following equations
Cm
i¼1
In the case of eqn (11), the value of fi is necessary to deter-
mine cmc, but eqn (12) is straightforward for evaluating the
cmc. The cmc of the binary and ternary mixtures can be pre-
dicted from the knowledge of cmc of the individual surfactants.
This is useful for a comparison between ideal and nonideal
mixtures. The ideal cmc values of the binary mixtures using eqn
(12) were reported in Tables 3 and S3.† The calculated values for
the binary systems, C10-val/Mega-10 and C10-leu/Mega-10 are
higher than that obtained experimentally (Fig. 4A). There is
more deviation of cmc observed at a higher ionic mole fraction
indicating the presence of non-ideality due to mutual interac-
tion of amphiphiles in the micelle. But the experimental cmc
values for the system C10-val/C10-leu are very close to the ideal
cmc value (Fig. 4B).
Different theoretical treatments of Motomura, Rubingh,
Rosen and Maeda have been used to explain the molecular
interactions in mixed micelles of binary combinations.
According to Motomura, the mixed micelles are considered
as macroscopic bulk phase. The related energetic para-
meters can be obtained from the excess thermodynamic
quantities. The micellar mole fraction of a surfactant in the
mixed micelle (XM) can be calculated from the following
equation
2
1
fR ¼ exp½bRð1 ꢁ XRÞꢃ
(16)
(17)
ꢄ
ꢅ
2
2
fR ¼ exp bRXR
The values of XR, bR and activity coefficients (fR) for the
binary mixtures are listed in Tables 3 and S3.† The values of
XR are lower than the stoichiometric mole fraction. The
activity coefficients of Mega-10 are higher than the ionic
surfactants (except at XC10-val and XC10-leu
¼
0.9), i.e.,
adsorption of nonionic surfactant at the interface is higher
than the nonionic surfactants. The values of fRC
and
10-val
10-leu
fRC
in a binary combination of C10-val/C10-leu are almost
equal and close to unity, indicating that both surfactants
have nearly the same surface activity. Here different molec-
ular activity characteristics have been manifested in the ionic/
nonionic and ionic/ionic mixed micelles containing surfac-
tants with similar tails but dissimilar head groups. The bR
values are negative for both C10-val/Mega-10 and C10-leu/
Mega-10 systems, indicating an attractive interaction between
the surfactants, the more negative the bR value, the greater
will be the attraction. The phenomenon of attractive inter-
action in a mixed micelle is called synergism. For the system
!
ꢂ
ꢃ
C
10-val/C10-leu, some of the bR values are positive (small
^
vCm
^
^
^ ^
XM ¼ X1 ꢁ X1X2=Cm
(13)
value), indicating low repulsive interaction between the
surfactants. Such behavior has also been observed for CPC–
CTAB systems.42
^
vX1
P;T
The interaction parameters (bs) at the air–water interface for
the mixed monolayer formation and mole fraction of the
The values of XM for binary mixtures are presented in Tables
3 and S3.† For all binary combinations, the XM values are lower
than the stoichiometric mole fractions; similar types of obser-
vation are reported for CPC/Bj-56 (ref. 20) and CTAB/Bj-56.42
Motomura's model does not depend on the nature of the
surfactants and their counterions. It helps to predict the
micellar composition only.
The experimental results were interpreted on the basis of
Rubingh's theory based on the regular solution theory. The
micelle mole fraction of the surfactants (XR) and interaction
s
surfactants (X1 ) can be calculated from Rosen's model.30,43 The
equation is given below
ꢆ
ꢇ
ꢆ
ꢄ
ꢅꢇ
2
s
s
X1
ln X1 ln ð1 ꢁ X1ÞCm0 =X1 C10
¼ 1
(18)
ꢆ
ꢇ
ꢄ
ꢆ
ꢇ
ꢅ
2
s
s
1 ꢁ X1
ln ð1 ꢁ X1ÞCm0 = 1 ꢁ X1 C20
where X1 is the stoichiometric mole fraction of the ionic
surfactant 1 and C01, C20 and C0m are the molar concentrations of
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surfactants 1, 2 and their mixtures in the solution phase, where
s
respectively, at a constant g value. The values of X1 for all the
B0 ¼ ln XCN
(22)
(23)
binary systems are higher than that obtained from Rubingh and
Motomura's models except for X1 ¼ 0.9 indicating the higher
surface activity toward micellization. Using the value of X1s, the
interaction parameter (bs) was calculated from the following
equation
ꢂ
ꢃ
XC
XC
I
B1 þ B2 ¼ ln
N
B2 ¼ ꢁb
(24)
ꢆ
ꢇ
s
ln X1Cm0 =X1 C10
bs ¼
:
(19)
ꢆ
ꢇ
2
s
XCN and XCI are the cmc values of nonionic and ionic
surfactants, respectively, in mole fraction units. B1 is related to
the standard free energy change associated with the introduc-
tion of ionic species into a nonionic micelle coupled with the
release of nonionic species from the micelle. B2 (ꢁb) is the
interaction parameter in the micellar phase. The interaction
parameter can be obtained from Rubingh model. R and T have
their usual meanings. The values of DG0m, B0, B1 and B2 are given
in Table 4. Here, the B0 value is constant. For both systems, B1
and B2 values show opposite trend with increasing mole frac-
tion of ionic surfactant. The positive value of B1 denotes the
major role of the attractive interaction in the stability of the
mixed micelle. The DG0m values obtained from Maeda's model
are very close to those obtained from Gibbs adsorption equation
which are almost constant.
1 ꢁ X1
The bs values obtained from Rosen's model for all binary
compositions are negative, indicating an attractive interaction
between the surfactants. The bs values are highly negative,
particularly at a lower mole fraction of ionic surfactants, prob-
ably due to the synergistic electrostatic interaction between the
hydrophilic groups of the anionic amphiphilic molecule and
the glucamide molecule. The values of bs are more negative
than bR, indicating a greater tendency toward population of the
surface than towards micellization. The ideal area minimum
(Amini) values for binary combinations are calculated with the
help of the micellar mole fractions (X1s) obtained from Rosen’s
model and Amin values for pure surfactants, using the following
equation
The excess free energy of the ionic–nonionic mixed micelle
(gex) was calculated from another theoretical model of Maeda,44
based on Gibbs–Duhem equation considered by Hall.45 The
equation is
i
s
1
2
Amin ¼ X1 Amin + (1 ꢁ X1s)Amin
(20)
The Amin values of ionic/nonionic combinations are very
close to the ideal area minimum (Amini) values. The divergence
is maximum for the mixture containing fewer ionic surfactants.
Maeda's model32 is applicable for ionic/nonionic mixed
micelles where the ionic head group repulsion decreases in the
presence of nonionic surfactant in the mixture. This model is
applicable for solutions with a moderately high ionic strength.
The proposed equation for the standard free energy change due
to the micellization process as a polynomial function of the
ionic mole fraction in the micellar phase, XI, is
gex ¼ XmI ln fI + (1 ꢁ XmI)ln fN
(25)
The detailed calculation of XmI, fI and fN was given in the
ESI.† b can be calculated from
gex
b ¼
(26)
Xm ð1 ꢁ Xm
Þ
I
I
Table 4 shows that micellar mole fractions of both systems
are lower than the corresponding stoichiometric mole fractions.
The values of the activity coefficients of ionic and nonionic
DG0m ¼ RT(B0 + B1XI + B2XI2)
(21)
Table 4 Free energy and interaction parameters from Maeda's model
ꢁDG0m
XC10-val/XC10-leu
ꢁB0
B1
B2
kJꢁ1 molꢁ1
d ln Cm/d X1
Xm1
f1
fN
gex
b
C10-val/Mega-10
0.1
0.3
0.5
0.7
0.9
9.39
0.61
0.42
0.05
0.32
0.50
0.69
0.88
1.25
0.98
0.80
23.1
22.8
22.4
21.5
20.6
0.46
0.40
0.83
1.70
2.07
0.06
0.21
0.29
0.34
0.71
0.48
0.45
0.58
0.90
0.84
1.00
1.02
0.87
0.73
0.89
ꢁ0.04
ꢁ0.15
ꢁ0.25
ꢁ0.24
ꢁ0.16
ꢁ0.71
ꢁ0.90
ꢁ1.21
ꢁ1.07
ꢁ0.78
C10-leu/Mega-10
0.1
0.3
0.5
0.7
0.9
9.39
0.39
0.46
0.34
0.24
0.17
0.70
0.63
0.75
0.85
0.92
23.2
22.8
22.4
21.8
21.0
0.52
0.48
0.74
1.23
1.41
0.05
0.2
0.31
0.44
0.77
0.70
0.58
0.68
0.83
0.81
0.98
1.01
0.91
0.83
0.89
ꢁ0.04
ꢁ0.10
ꢁ0.18
ꢁ0.19
ꢁ0.19
ꢁ0.84
ꢁ0.63
ꢁ0.84
ꢁ0.77
ꢁ1.07
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Table 5 Micellar compositions (XRH), activity coefficients (fRH) and cmcRH in ternary mixtures of C10-val/C10-leu/Mega-10 at 298 K by Rubingh–
Holland (RH) method at different stoichiometric compositions (Xi)
RH
C10-val
RH
C10-leu
RH
Mega-10
RH
XC10-val/XC10-leu/XMega-10
X
=X
=X
f
=f RH =f RH
cmc/mM RH/obs/Clint
C10-val C10-leu Mega-10
0.125/0.25/0.625
0.125/0.625/0.25
0.25/0.125/0.625
0.25/0.625/0.125
0.333/0.333/0.333
0.625/0.125/0.25
0.625/0.25/0.125
0.071/0.156/0.772
0.074/0.422/0.504
0.144/0.079/0.778
0.164/0.476/0.360
0.194/0.219/0.586
0.385/0.088/0.527
0.425/0.198/0.377
0.566/0.636/0.959
0.765/0.827/0.822
0.567/0.637/0.958
0.863/0.913/0.718
0.714/0.780/0.866
0.768/0.829/0.820
0.866/0.915/0.714
5.48/5.15/5.77
7.68/6.58/8.60
5.52/4.88/5.87
9.57/7.84/10.6
7.06/5.91/8.17
8.01/6.58/9.65
9.97/9.18/11.8
amphiphiles follow the same trend in the case of both C10-val/
Theoretical evaluation of cmc of multicomponent surfactant
Mega-10 and C10-leu/Mega-10 systems. For C10-val/Mega-10 mixture is limited. Rubingh–Holland theory is applicable for
combination, gex and b values follow the same trend, but this is evaluating the micellar composition, activity coefficient and
not true in the case of other systems. In both systems, negative cmc of the ternary surfactant mixture.
values of b signify synergism. The activity coefficients of
According to the Rubingh–Holland46 (RH) method for a
nonionic surfactant (fI) is higher than the ionic surfactants (fN). multicomponent system, the activity coefficients fi, fj, fk, . of
Table 6 Parameters obtained from the models of Nagarajan and Israelachvili
!
!
!
!
P
Dm0g
Dm0g
Dm0g
Dm0g
ꢁDG0m
ꢁ
2
Surf/XC10-val/XC10-leu
ae (A)
P
kꢁ1/A
kJꢁ1 molꢁ1
cmc/(mM)
˚
˚
kT
kT
kT
kT
T
I
H
Pure surfactants
Mega-10
57.4
55.8
56.2
0.36
0.38
0.37
13.0
11.7
12.0
16.6
21.8
22.0
7.01
6.83
6.88
—
6.80
6.88
0.057
0.057
0.057
23.5
20.0
20.4
4.28
17.7
14.8
C10-val
10-leu
C
C10-val/Mega-10
0.1
0.3
0.5
0.7
0.9
57.3
57.1
56.9
56.7
56.3
0.37
0.37
0.37
0.37
0.37
13.0
13.0
12.8
12.7
12.3
16.8
17.4
18.2
18.8
20.0
7.00
6.98
6.96
6.94
6.90
0.34
1.17
2.13
2.96
4.54
0.057
0.057
0.057
0.057
0.057
23.3
22.9
22.3
21.9
21.0
4.56
5.46
6.76
8.08
11.4
C10-leu/Mega-10
0.1
0.3
0.5
0.7
0.9
57.4
57.2
57.0
56.8
56.6
0.37
0.37
0.37
0.37
0.38
13.0
12.9
12.9
12.7
12.5
16.9
17.5
18.3
19.1
20.3
7.01
6.99
6.97
6.95
6.92
0.41
1.24
2.20
3.17
4.68
0.057
0.057
0.057
0.057
0.057
23.3
22.9
22.5
22.1
21.4
4.58
5.32
6.33
7.55
9.94
C10-val/C10-leu
0.1
0.3
0.5
0.7
0.9
56.1
56.1
56.0
55.9
55.8
0.37
0.37
0.37
0.37
0.37
12.0
11.9
11.9
11.8
11.8
22.0
22.0
21.9
21.9
21.8
6.88
6.87
6.86
6.85
6.84
6.88
6.87
6.86
6.85
6.84
0.057
0.057
0.057
0.057
0.057
20.3
20.3
20.2
20.1
20.0
15.1
15.6
16.2
16.9
17.6
!
!
!
!
P
Dm0g
Dm0g
kT
Dm0g
kT
Dm0g
XC10-val/XC10-leu
XMega-10
/
ꢁDG0m
ꢁ
2
ae (A)
P
kꢁ1/ A
kJꢁ1 molꢁ1
cmc/(mM)
˚
˚
kT
kT
T
I
H
0.125/0.25/0.625
0.125/0.625/0.25
0.25/0.125/0.625
0.25/0.625/0.125
0.333/0.333/0.333
0.625/0.125/0.25
0.625/0.25/0.125
57.0
56.8
57.1
56.5
56.8
56.7
56.5
0.37
0.37
0.37
0.37
0.37
0.37
0.37
12.9
12.8
13.0
12.6
12.8
12.8
12.8
17.7
19.3
17.8
20.0
18.7
19.0
19.9
6.97
1.55
0.057
0.057
0.057
0.057
0.057
0.057
0.057
22.7
21.9
22.6
21.4
22.1
21.8
21.4
5.82
8.02
5.72
9.77
7.46
8.27
10.1
6.94
6.98
6.92
6.94
6.93
6.91
3.41
1.53
4.39
2.83
3.24
4.26
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micelle forming amphiphilic species i, j and k, . can be pre- contribution arising out of the repulsive interaction between
!
Dm0g
sented in the form
the head groups at the aggregate surface and (d)
is the
jꢁ1
n
n
kT
X
X
X
ꢆ
ꢇ
P
ln fi ¼
bijxj2
þ
bij þ bij þ bij xjxk
(27)
contribution of the packing of a monomer within the core of
k¼1
!
j ¼ 1
j ¼ 1
Dm0g
ð jsiÞ
isjsk
the aggregate. Thus, the total contribution to
given by
can be
(29)
kT
where bij denotes the net interaction between the component i
and j, and xj is the mole fraction of the jth component in the
micelle; bik, bjk and xk have similar signicance.
Eqn (27) is valid at the cmc
!
!
!
!
!
Dm0g
Dm0g
Dm0g
Dm0g
Dm0g
¼
þ
þ
þ
H
kT
kT
kT
kT
kT
T
I
P
xi ¼ XiCjfjXj/(CiXjfi)
(28)
Thus, Gibbs free energy of micellization can be determined
from the following equation:
The cmcs of ith and jth components are represented by Ci
and Cj, respectively. The mole fractions of ith and jth compo-
nents are represented by Xi and Xj. The interaction parameter
(bR) obtained from Rubingh's theory for the binary composi-
tions was used in eqn (27) to calculate the activity coefficients
for a ternary system using the method of “successive substitu-
tion” with the help of a computer. The results are presented in
Table 5. The mole fractions of the individual surfactants in
the mixed micelles are different from the stoichiometric
"
!
!
!
Dm0g
Dm0g
Dm0g
DGm0 ¼ exp
þ
þ
I
kT
kT
kT
T
H
! #
Dm0g
þ
ꢄ 55:55
(30)
kT
P
The detailed calculation for the four free energy contribu-
tions to the standard free energy is given in ESI.† Four contri-
butions to the standard free energy and other parameters
obtained from Nagarajan's model are presented in Table 6. The
micellar mole fractions obtained from Rubingh's theory for
binary systems (XR) and Rubingh–Holland theory for ternary
mixtures were considered to calculate the contributions of four
compositions: both XCRH
and XCRH
are much lower than
10-leu
10-val
RH
XC10-val and XC10-leu, but X
is fairly higher than XMega-10.
Mega-10
This indicates that nonionic component dominates in the
mixed micelle. Similar types of results are observed for the CPC/
Tween-40/Brij-56 (ref. 20) and CPC/CTAB/Brij-56 (ref. 42)
systems. The activity coefficients are high and comparable
among three surfactants. But in case of CPC/Tween-40/Brij-56,20
!
!
!
!
Dm0g
Dm0g
Dm0g
Dm0g
free energies [
,
,
and
] to the
fTween-40 was moderately high and fBrij-56 was close to unity, while
fCPC was very low. In case of CPC/CTAB/Brij-56,
kT
kT
kT
kT
T
I
H
P
42
f
and fCTAB
CPC
total free energy. The total free energy change, critical micelli-
zation concentration and packing parameters for the pure
surfactants and their binary and ternary mixtures are also
shown in Table 6. The values of the packing parameters show a
slight tendency for non-spherical micelles. There is a good
correlation between the experimental data and those obtained
from Nagarajan's model.
were very low whereas fBrij-56 was high and close to unity. Both
the calculated (RH method) and experimental cmc values are
lower than the cmcClint denoting the nonideal nature of the
mixed ternary micellar system. The value of cmcRH is higher
than the experimental results; the maximum difference is
observed for the fourth composition, the deviation of cmcRH
from cmcobs can attribute to the discrepancy of the RH theory
whereas the contributions of the molecular parameters of the
component surfactants have been le out of consideration.
In Nagarajan's model,47,48 the standard free energy change
Conclusions
!
A study of binary and ternary combinations of two ionic
surfactants (C10-val and C10-leu) with nonionic surfactant Mega-
10 has not been conducted before. The tails of the three
surfactants are same but the head groups are different. The
binary (C10-val/Mega-10, C10-leu/Mega-10 and C10-val/C10-leu)
and ternary (C10-val/C10-leu/Mega-10) combinations have lower
cmc values than that obtained from Clint's model. That
combinations show nonideal behavior. This nonideality arises
from the interaction between the head groups of the surfac-
tants. The interaction parameters (b) obtained from Rubingh,
Rosen and Maeda are negative, indicating an attractive inter-
action between the system C10-val/Mega-10 and C10-leu/Mega-
10. The mole fractions obtained theoretically are not the same
with the stoichiometric composition. Both DG0m and DGa0ds are
negative, indicating the spontaneity of micelle formation and
DG0m becomes less negative with increasing concentration of
Dm0g
associated with the formation of micelle of a surfactant
kT
from its innitely dilute state in water to an aggregate of size g
!
Dm0g
(aggregation number) has four contributions: (a)
,
kT
T
which is a negative free energy contribution arising from
transfer of surfactant tail from solution to the more favorable
aggregate core, (b) the aggregate core–water interfacial free
!
Dm0g
energy contribution
is a positive quantity, which
kT
I
accounts for the allowance of the penetration of water mole-
!
Dm0g
cules to the aggregate core, (c)
is a positive
kT
H
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ionic surfactant in the binary mixture. DG0m values for binary 19 A. A. Dar, G. M. Rather, S. Ghosh and A. R. Das, J. Colloid
systems obtained from Maeda's model are lower than those Interface Sci., 2008, 322, 572.
obtained from the regular solution theory. The magnitude of 20 S. Ghosh, J. Colloid Interface Sci., 2001, 244, 128.
DG0ads is more negative than DG0m, signifying that adsorption at 21 G. Basu Ray, I. Chakraborty, S. Ghosh and S. P. Moulik,
the air–water interface is more spontaneous than micellization.
Colloid Polym. Sci., 2007, 285, 457.
From the study of the polarity index of all binary compositions, 22 J. F. Scamechorn, in Mixed Surfactant Systems, ed. P. M.
we can say that the surface area per head group decreases with
decreasing concentration of Mega-10 and more compact
Holland and D. N. Rubingh, Washington, DC, 1992, ch. 27,
p. 329, ACS Symposium Series 501, J. Am. Chem. Soc..
micelles are formed with increasing concentration of ionic 23 S. Ghosh, A. Das Burman, G. C. De and A. R. Das, J. Phys.
surfactant, which resists the penetration of the solvent.
Chem. B, 2011, 115, 11098.
24 S. Ghosh and T. Chakraborty, J. Phys. Chem. B, 2007, 111,
8080.
25 J. J. Lopata, K. M. Werts, J. F. Scamehorn, J. H. Harwell and
B. P. Grady, J. Colloid Interface Sci., 2010, 342, 415.
Acknowledgements
S.D. thanks CSIR, Govt. of India, for senior research fellowship,
Prof. S. C. Bhattacharya, Department of Chemistry for using 26 S. B. Sulthana, P. V. C. Rao, S. G. T. Bhat, T. Y. Nakano,
DLS facility and Jadavpur University for laboratory facilities.
G. Sugihara and A. K. Rakshit, Langmuir, 2000, 16, 980.
´
27 K. Szymczyk and B. Janczuk, Langmuir, 2007, 23, 4972.
28 J. H. Clint, J. Chem. Soc., Faraday Trans. 1, 1975, 71, 1327.
29 D. N. Rubingh, in Solution Chemistry of Surfactants, ed. K. L.
Mittal, Plenum, New York, 1979, vol. 1, p. 337.
30 M. J. Rosen and M. Dahanayake, Industrial Utilization of
Surfactants, Principles and Practice, AOCS Press,
Champaign, IL, 2000, pp. 28–29.
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12286 | RSC Adv., 2014, 4, 12275–12286
This journal is © The Royal Society of Chemistry 2014