N. Fatma et al. / Journal of Molecular Liquids 219 (2016) 959–966
965
gemini surfactant mixtures (with the same counter ion), Eq. (5) can be
modified as
Negative ΔGom values were obtained for all the gemini-gemini surfac-
tant mixtures. The ΔGom values increase slowly with the increase of mole
fraction of the gemini of higher hydrophobicity. The negative ΔGom sug-
gests that the gemini surfactants have greater ability to form mixed mi-
celles in solution (Table 2) than to form the single surfactant micelles.
The ΔGom values of the binary mixtures of 16-E2-16 + 14-E2-14 are
slightly higher than the pure geminis. Thus, the mixed surfactant sys-
tems show more propensity towards micellization. The order of abso-
lute ΔGom values is: 16-E2-16+ 14-E2-14 N 14-E2-14 + 12-E2-
12 N 16-E2-16 + 12-E2-12.
!
ꢄ
ꢅꢄ
ꢅ
1
3α1
3−2α1
α1 þ 3
∂CMC
∂α1
ꢄ
ꢅ
ðα1 þ 3Þcmc α1 þ 3
3α1
α1 þ 3
X1M
¼
−
:
ð8Þ
1
1−
3α1 þ 3α2
ðv1 ¼ v1a þ v1c ¼ ð2 þ 1Þ ¼ 3; v2 ¼ v2b þ v2d ¼ ð2 þ 1Þ ¼ 3Þ
The XM1 values are found to increase with the increase in stoichio-
metric mole fraction of the higher homologue for all the mixed systems
(Table 1) and are in line with the micellar mole fraction (Xm1 , evaluated
by Rubingh's model).
3.4.3. Standard free energy of adsorption
Thermodynamic stability of the adsorbed monolayer can be
discussed in terms of the standard free energy of adsorption (ΔadsG)
[22]
3.3. Adsorption at the air/solution interface
πcmc
Γ max
ΔadsG ¼ ΔGom
−
:
ð13Þ
The surface excess (Гmax) and molecular area (Amin) are two impor-
tant interfacial properties. The former is a measure of the extent of ad-
sorption of various components at the interface whereas the latter
provides the idea about close or loose packing of surfactant molecules
at the gas-liquid interface. The two can be calculated using the following
set of equations [22,23]
The ΔadsG values of the surfactant mixtures, thus obtained, are pre-
sented in Table 2. The values show that the cationic gemini surfactants
have greater ability to adsorb at the air-water interface of the mixed sys-
tems. Lower ΔGom than ΔadsG indicates that the adsorption is preferred
more than micellization.
Another thermodynamic quantity used to explain the synergism in
mixed monolayer is the free energy of a given surface at equilibrium
(Gmin), defined by Eq. (14)
ꢄ
ꢅ
1
∂γ
∂logC
Γ max ¼ −
ð9Þ
2:303nRT
C→CMC
1020
NA Γ max
0
:
ð10Þ
Amin
¼
ðNA istheAvogadro snumberÞ
Gmin ¼ γCMCAminNA:
ð14Þ
The calculated values of Γmax and Amin for the single and binary solu-
tions are summarized in Table 2. It is obvious from the above equation
that Amin increases when Γmax decreases. The value of n for the gemini
surfactant is taken as 3 and for the gemini-gemini surfactant mixtures,
n = 4. Amin values of the pure surfactants were smaller than the mix-
tures because of the electrostatic repulsion which requires larger area
per molecule. For 16-E2-16 + 14-E2-14, the lower value of Amin is
caused by the hydrophobic interactions between the alkyl chains of
comparable chain length resulting in dense packing.
Gmin is the free energy accompanied by the transition of surfactant
from bulk phase to the surface of the solution. Lower the Gmin value,
more thermodynamically stable surface is formed, and higher is the sur-
face activity. The Gmin values show the ease of formation of the mixed
monolayers. Gmin increases with the increase of hydrophobicity in the
binary systems as 14-E2-14 + 12-E2-12 b 16-E2-16 + 12-E2-12 b 16-
E2-16+ 14-E2-14.
4. Conclusions
3.4. Energetics of micellization and adsorption phenomena
• Physicochemical properties of binary mixtures of dicationic biode-
gradable gemini surfactants of varied chain length, consisting diester
The major contributions of the gemini surfactants to the thermody-
namic properties of micellization are: the van der Waals interactions be-
tween the alkyl chains, head group repulsion, hydrophobic effect, and
the energetics associated with the changes in configuration of the
spacer and hydrophobic chains. The influences of such forces on the
thermodynamic behavior of the studied systems are discussed below.
bonded
spacer,
ethane-1,2-diyl
bis(N,N-dimethyl-N-
alkylammoniumacetoxy) dichlorides (m-E2-m, m = 12, 14, 16),
were studied by conductivity and surface tension measurements.
• Differential scanning calorimetry reveals phase transition as well as
thermal stability of pure gemini surfactants.
• Various surface and micellar properties were evaluated in the light of
several theoretical models suggested by Clint, Rubingh and
Motomura. All the mixed surfactant solutions showed nonideality as
indicated by the Xm1 , βm, X1ideal, GEm and ΔGom values.
• Order of synergism of the mixed surfactant systems is 16-E2-16 + 14-
E2-14 N 16-E2-16 + 12-E2-12 N 14-E2-14 + 12-E2-12.
• The results of this work show that a careful design of mixed surfactant
systems containing cleavable surfactants can allow for more sophisti-
cated changes in the properties of a surfactant solution.
3.4.1. Gibbs excess free energy
The excess free energy of micellization (GEm) was calculated using
Eq. (11)
h
ꢂ
i
ꢀ
ꢁ
GEm ¼ RT Xm1 ln f m1
þ
X2mÞ ln f m2
:
ð11Þ
The negative values of GEm could be due to the synergistic interac-
tions among the two components in the mixed micelles which suggest
that the mixed micelles are more stable than the pure surfactant mi-
celles. The absolute GEm values follow the order: 16-E2-16 + 14-E2-
14 N 16-E2-16 + 12-E2-12 N 14-E2-14 + 12-E2-12.
Acknowledgements
Manorama Panda acknowledges financial assistance under the De-
partment of Science and Technology, Government of India, Nazish
Fatma is thankful to the University Grants Commission (India) for fel-
lowship and Kabir-ud-Din is thankful to UGC for awarding Faculty Fel-
lowship under its BSR Program.
3.4.2. Free energy of micellization
The standard free energy of micellization (ΔGom), which measures
the tendency to form micelles, was evaluated with the help of Eq. (12)
ΔGom ¼ RT lnXcmc
ð12Þ