Effect of Asymmetric Dimeric Zwitterionic Surfactants on Micellization Behavior of Amphiphilic Drugs

Article abstract of DOI:10.1007/s10953-015-0338-9

Abstract The micellization process in mixtures of amphiphilic drugs and asymmetric dimeric zwitterionic surfactants have been investigated tensiometrically. The drugs used are from two families: imipramine hydrochloride (IMP) - a tricyclic antidepressant and ibuprofen (IBF) - a nonsteroidal antiinflammatory drug, whereas zwitterionic dimeric surfactants are heterogemini surfactants that contain quaternary ammonium and phosphate groups as heads. The results show that the cmc of drug-surfactant mixtures decreases with the increase in stoichiometric mole fraction of surfactants (α ₁), suggesting attractive interaction among the two components. This is supported by the values of cmc _id (critical micelle concentration values for ideal mixing) which are always greater than experimental cmc values. Also, the decrease in magnitude is more in IBF-dimeric surfactant mixed systems than in IMP-dimeric surfactant mixed systems. Micellar mole fraction values, obtained using Rubingh's (Formula presented.) and Motomura's (Formula presented.) models, are lower than the micellar mole fraction for ideal mixing (Formula presented.). The micellar interaction parameter (β^m) follows the order: 8(-)-2-16(+) > 10(-)-2-16(+) > 10(-)-2-14(+) > 8(-)-2-14(+). The results are explained on the basis of difference in tail lengths. Interfacial mole fraction (Formula presented.) values, evaluated using Rosen's model, are higher than (Formula presented.) values for IMP-10(-)-2-16(+) and IMP-10(-)-2-14(+) systems while for all other systems (except 8(-)-2-14(+)) the values are smaller than (Formula presented.). The interaction parameter at the interface (β^σ) is negative and (Formula presented.) values are greater than (Formula presented.) in magnitude. All the results indicate that the dimeric surfactants are mostly in cationic form.

Full text of DOI:10.1007/s10953-015-0338-9

J Solution Chem (2015) 44:1292–1309
DOI 10.1007/s10953-015-0338-9
Effect of Asymmetric Dimeric Zwitterionic Surfactants
on Micellization Behavior of Amphiphilic Drugs
Sahar Noori1 Andleeb Z. Naqvi1 Wajid H. Ansari1
Kabir-ud-Din1
•
•
•
Received: 19 August 2014 / Accepted: 9 January 2015 / Published online: 29 May 2015
Ó Springer Science+Business Media New York 2015
Abstract The micellization process in mixtures of amphiphilic drugs and asymmetric
dimeric zwitterionic surfactants have been investigated tensiometrically. The drugs used
are from two families: imipramine hydrochloride (IMP)—a tricyclic antidepressant and
ibuprofen (IBF)—a nonsteroidal antiinflammatory drug, whereas zwitterionic dimeric
surfactants are heterogemini surfactants that contain quaternary ammonium and phosphate
groups as heads. The results show that the cmc of drug-surfactant mixtures decreases with
the increase in stoichiometric mole fraction of surfactants (a1), suggesting attractive in-
teraction among the two components. This is supported by the values of cmcid (critical
micelle concentration values for ideal mixing) which are always greater than experimental
cmc values. Also, the decrease in magnitude is more in IBF–dimeric surfactant mixed
systems than in IMP–dimeric surfactant mixed systems. Micellar mole fraction values,
obtained using Rubingh’s (X1m) and Motomura’s (X1m) models, are lower than the micellar
mole fraction for ideal mixing (X1id). The micellar interaction parameter (bm) follows the
order: 8(-)-2-16(?) [ 10(-)-2-16(?) [ 10(-)-2-14(?) [ 8(-)-2-14(?). The
results are explained on the basis of difference in tail lengths. Interfacial mole fraction (X1r)
values, evaluated using Rosen’s model, are higher than X1m values for IMP-
10(-)-2-16(?) and IMP-10(-)-2-14(?) systems while for all other systems (except
8(-)-2-14(?)) the values are smaller than X1m. The interaction parameter at the interface
(br) is negative and bmav values are greater than barv in magnitude. All the results indicate
that the dimeric surfactants are mostly in cationic form.
Keywords Asymmetric dimeric zwitterionic surfactants Á Imipramine HCl Á Ibuprofen Á
Micellization Á Surface tension
Electronic supplementary material The online version of this article (doi:10.1007/s10953-015-0338-9)
contains supplementary material, which is available to authorized users.
&
Andleeb Z. Naqvi
naqviaz@gmail.com
1
Department of Chemistry, Aligarh Muslim University, Aligarh 202 002, India
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1 Introduction
Solubility of drugs is a point of concern for pharmaceutical companies and formulators. This
problem is becoming even more serious nowadays as formulators are searching for newer
therapeutic agents. Most of the newly developed drugs are either poorly soluble or insoluble in
water. This limits their oral bioavailability by affecting dissolution rates and/or the maximum
amounts that can be dissolved intra-lumenally and, hence, hamper their use [1]. Even those
drugs which are water soluble can be administered by targeted delivery systems. In conven-
tional delivery, such as oral or intravascular, the drug is distributed throughout the body and
only a small portion of it reaches the affected organ. This requires high dosage to be given
frequently. However, in targeted delivery systems the concentration of drug is high in some
parts of the body in comparison to others. This increases the effect of drug while reducing the
concentration in normal tissues and provides a protected drug interaction with the diseased
tissue. Thus, a targeted delivery system has many advantages, including reduction in the
frequency of the dosage taken, more uniform drug effect, and reduction in side effects [2, 3].
In solution, the drugs exist as a mixture of different types of species, like monomers,
soluble as well as insoluble aggregates and if the carrier is an amphiphile, then they may
exist as carrier–drug mixed micelles. Hence, the carrier may interact with the drug and may
change the drug’s activity as well as its availability at the target site.
There are different types of drug carriers, including micelles, liposomes, nano-particles,
dendrimers, etc. An ideal drug carrier must be non-toxic, biocompatible, biodegradable and
must avoid the host’s defence mechanism [4, 5]. Surfactant micelles carry drugs by either
solubilizing them into their micellar core or by forming mixed micelles with them. For this
the size of the micelles should be between 10 and 80 nm and the loading capacity should
be between 5 and 25 % [3]. Also, the critical micelle concentration, cmc, of the surfactant
(i.e., carrier) should be in the millimolar region or lower. When introduced in the body the
surfactant–drug mixed system may get diluted. If the cmc of the surfactant or the mixed
system is high and the system undergoes large dilution, precipitation of the transported
drug may occur. This precipitation may have very serious consequences. Therefore, the
carriers should be of very low cmc. High concentrations of surfactants may also decrease
drug absorption by decreasing the chemical potential of the drug.
Gemini surfactants have very low cmcs [6, 7]. These are surfactants having two (or more)
hydrophobic tails and two (or more) head groups joined together by a linker (or spacer). These
surfactants can be considered as conventional surfactant monomers joined at the head group by
a linker. The hydrophobictails maybeofany lengthandheadgroupsmaybeionic, non-ionicor
may be of different polarities for a single molecule (e.g., zwitterionic). Spacers may be rigid or
flexible, hydrophobic or hydrophilic. Due to their special structure these surfactants have high
tendencies to micellize. Hence, these surfactants are considered as potential candidates for use
as carrier. They are now gaining wide attention in gene therapy also [8, 9].
Keeping the above facts in mind, we have synthesized four asymmetric dimeric zwitte-
rionic surfactants and studied their interactions with two amphiphilic drugs of different
classes and structures. The zwitterionic surfactants contain quaternary ammonium and
phosphate groups as heads. The spacer length was kept constant with 2 –(CH2)2– for all the
four dimerics and the two tails were paired as 8–14, 8–16, 10–14 and 10–16. In this way we
were able to study the effect of variation of bothtails, one at a time, onthe interactions with the
drugs. The chosen drugs are imipramine hydrochloride (IMP), a cationic phenothiazine, and
the sodium salt of ibuprofen (IBF), an anionic drug. These drugs are different from each other,
both chemically and therapeutically. IMP is an antidepressant and IBF belongs to the class of
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nonsteroidal antiinflammatory drugs (NSAIDs). It is used for treating mild and moderate
pain, headache and fever. Also, as zwitterions, the dimeric surfactants contain both positive
and negative charges on the head groups, and thus it would be interesting to study the effect of
an anionic and a cationic drug on the mixing behavior.
2 Experimental Section
2.1 Chemicals Used
The cationic drug IMP (98 %, Sigma Aldrich, St. Louis, USA), anionic drug ibuprofen
sodium salt (99 %, Sigma, USA), phosphoryl chloride (99 %, Otto, Mumbai, India),
ethylene glycol (C99 %, Sigma Aldrich, USA), 1-octanol (C99 %, Merck, Hohenbrunn,
Germany), 1-decanol (99 %, Otto, Mumbai, India), N,N-dimethyltetradecylamine (C95 %,
Aldrich, USA), and N,N-dimethylhexadecylamine (C95 %, Fluka, France) were used
without further purification.
The asymmetric dimeric zwitterionic surfactants (designated as n(-)-2-m(?)) were
synthesized with slight modification in the procedure given in the literature [10, 11].
The synthesis was carried out in two steps (Scheme 1): In the first step, a solution of
phosphoryl chloride (0.025 mol) was added to a cooled (0 °C) solution of ethylene glycol
(0.03 mol) in dry benzene. After the addition, the reaction mixture was stirred for 5 min
and to the cyclic ethylene chlorophosphate 1 formed was added the solution of alkylalcohol
(0.025 mol) in dry benzene. The reaction mixture was stirred continuously for 4 h at room
temperature. The solvent was then removed under reduced pressure to get the precursor 2.
In the second step, N,N-dimethylalkylamine (0.025 mol) was added to a solution of pre-
cursor 2 in 2-propanol and heated to 65–70 °C with stirring for 2 days. After removal of the
solvent under diminished pressure, the desired dimeric surfactant 3 was obtained. The
dry benzene
(as solvent)
O
O
POCl3
+
HOCH2CH2OH
O
5 min, 0 oC
P
Cl
(1)
CH
O
O
O-
3 CH3
O
CnH2n+1OH
O
O
(CH3)2NCmH2m+1
2 days, 65-70 0C
P
P
N
4 h, room temperature
O
O
CmH2m+1
(3)
2- propanol
(as solvent)
CnH2n+1
CnH2n+1
(2)
where n=8 and 10,
m=14 and 16.
Scheme 1 The synthesis route for asymmetric dimeric zwitterionic surfactants
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J Solution Chem (2015) 44:1292–1309
1295
compound was finally purified by recrystallization with acetone. The structures of the sur-
factantswereascertainedby1HNMRspectralstudies(Figs. 1S–4Sofsupportinginformation).
2.2 Tensiometric Measurements
The air/solution interfacial tension was measured using a SD Hardson tensiometer em-
ploying the ring detachment method. The Pt–Ir ring was thoroughly cleaned by washing
Fig. 1 Variation of a surface
(a)
60
55
50
45
40
35
30
25
tension with the logarithm of
concentration of drugs; b specific
conductivity of IBF with drug
concentration
IBF
IMP
0.0
0.5
1.0
1.5
2.0
2.5
log10 C
(b)
0.08
0.06
0.04
0.02
0.00
0
50
100
150
200
250
300
350
-3
-3
conc (10 mol•dm )
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Table 1 Micellization parameter values for binary mixtures of drug and zwitterionic dimeric surfactants in
aqueous solution
2
Dcmc
cmcid
˚
a1
cmc 0.01
(10-3 molÁdm-3
cmcid
(10-3 molÁdm-3
Cmax
1
Amin (A ) Aid pC20 KT 0.5
2
(A )
)
)
107 (molÁm-2
)
(°C)
˚
8(-)-2-14(?) ? IMP
0
45.20
1.053
0.916
0.678
0.506
0.354
0.061
–
–
14
–
117
–
8
–
–
–
–
–
–
–
2.18
3.94
4.35
4.03
4.23
4.25
5.65
–
–
–
–
–
–
–
0.025
0.050
0.075
0.100
0.125
1
2.350
1.205
0.810
0.610
0.490
–
0.552
0.240
0.163
0.170
0.276
–
–
–
–
–
–
–
–
–
24
70
4
8(-)-2-16(?) ? IMP
0.025
0.050
0.075
0.100
0.125
1
0.460
0.310
0.160
0.120
0.092
0.057
2.180
1.116
0.750
0.565
0.452
–
0.789 17
0.722 17
0.786 25
0.785 31
0.796 34
122 30 92
94 10 92
3.68 15.0
4.79 15.5
4.26 16.0
4.88 17.0
4.68 17.5
5.76 19.0
67
54
48
70
3
2
2
4
91
91
91
–
–
24
10(-)-2-14(?) ? IMP
0.025
0.050
0.075
0.100
0.125
1
1.710
1.189
0.520
0.458
0.358
0.071
2.670
1.374
0.925
0.700
0.560
–
0.359
0.134
0.438
–
–
–
–
–
3.20
3.72
–
–
–
–
–
–
3.75 1.0
4.12 2.0
4.26 2.5
5.32 5.0
0.331 42
0.358 42
39
40
49
1
1
3
54
54
–
–
33
10(-)-2-16(?) ? IMP
0.025
0.050
0.075
0.100
0.125
1
1.205
0.760
0.430
0.137
0.111
0.041
1.600
0.812
0.544
0.410
0.330
–
0.245
0.064
0.209
0.665
–
–
–
–
–
–
4.25 15.0
3.52 15.5
3.91 16.5
4.36 16.5
4.56 17.0
5.37 21.5
–
–
–
–
–
–
0.661 43
38
53
2
2
61
–
–
31
8(-)-2-14(?) ? IBF
0
90.365
6.136
–
–
10
161 23
–
1.93
–
–
–
–
–
–
–
0.001
36.719
28.315
23.041
19.423
16.787
–
0.833 28
0.806 31
0.838 34
0.838 34
0.828 40
59
53
50
49
42
70
2
2
3
2
2
4
115 2.80
111 3.08
110 3.21
109 3.36
109 3.43
0.0015 5.482
0.002 3.740
0.0025 3.137
0.003
1
2.890
0.061
–
24
–
5.65
8(-)-2-16(?) ? IBF
0.001 3.192
0.0015 2.489
0.002 1.803
35.004
26.796
21.706
18.241
0.909 24
0.907 25
0.917 31
0.930 33
71
65
54
51
5
4
2
2
128 3.31
126 3.35
124 3.46
124 3.34
0.0025 1.273
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Table 1 Micellization parameter values for binary mixtures of drug and zwitterionic dimeric surfactants in
aqueous solution
2
Dcmc
cmcid
˚
a1
cmc 0.01
(10-3 molÁdm-3
cmcid
(10-3 molÁdm-3
Cmax
1
Amin (A ) Aid pC20 KT 0.5
2
(A )
)
)
107 (molÁm-2
)
(°C)
˚
0.003 0.610
0.057
15.730
–
0.961 38
24
44
70
1
4
122 3.89
1
–
–
5.76 19.0
10(-)-2-14(?) ? IBF
0.001 5.114
39.683
30.992
25.424
21.552
18.704
–
0.871 26
0.889 26
0.891 29
0.917 29
0.931 31
65
63
58
57
53
49
4
3
3
2
2
3
108 3.47
106 3.59
104 3.68
103 3.60
102 3.89
–
–
0.0015 3.442
0.002 2.766
0.0025 1.791
0.003 1.288
1
0.071
–
33
–
5.32 5.0
10(-)-2-16(?) ? IBF
0.001 2.899
28.354
21.111
16.815
13.972
11.951
–
0.898 36
0.904 40
0.899 41
0.919 47
0.919 38
46
41
40
35
44
53
1
2
1
1
1
2
106 3.10
103 3.35
102 3.62
100 3.47
101 3.79
0.0015 2.026
0.002 1.698
0.0025 1.138
0.003 0.969
1
0.041
–
31
–
5.37 21.5
with doubly distilled water and dried by heating in an alcohol flame before each mea-
surement. Solutions of different mole fractions of mixed systems were prepared from stock
solutions of the dimeric surfactants and drugs. Small volumes of the concentrated solutions
were added to double distilled water and readings were taken after thorough mixing and
temperature equilibration for 10 min. The solution concentration was varied by additions
made using a Hamilton-Bonaduz, SCHWEIZ microsyringe. The cmc values were deter-
mined by noting inflections in the plots of c against logarithm of surfactant concentration
(C) isotherms (Fig. 1). The error in the measurements was 0.5 mNÁm-2
.
2.3 Conductometric Measurements
An ELICO conductivity meter (model CM 180) equipped with a cell with platinized
electrodes was used to perform the experiments. A known amount of water (double-
distilled) was taken in a cell. Temperature control was achieved by circulating water
through the jacketed cell holding the solution under study. The experimental error in
temperature was minimized to 0.5 °C. A dip-type conductivity cell of cell constant
1.026 cm-1 (this value was provided with the cell and checked with 0.1 molÁdm-3 KCl
solution) was inserted into the water. The conductivity runs were carried out by adding
aliquots of concentrated surfactant stock solution into the thermostated solvent with a
micropipette (Hamilton, India, accuracy 0.01 mL) and thoroughly mixing, followed by
measurement of the conductance. A similar process was repeated each time an addition of
drug solution was made. The precision of the measurements was within 0.0001 mSÁcm-1
(Fig. 1).
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J Solution Chem (2015) 44:1292–1309
Fig. 2 Variation of surface
tension with the logarithm of
concentration of a pure
surfactants; b IMP-
8(-)-2-14(?) mixtures; and
c IBF-8(-)-2-14(?) mixtures
60
55
50
45
40
35
30
25
(a)
8(-)-2-14(+)
8(-)-2-16(+)
10(-)-2-14(+)
10(-)-2-16(+)
-3.0
-2.5
-2.0
-1.5
-1.0
log10
C
(b)
55
50
45
40
35
30
25
IMP- 8(-)-14(+)
0.025
0.050
0.075
0.100
0.125
-1.5
-1.0
-0.5
0.0
0.5
log10
C
(c)
60
50
40
30
20
IBF-8(-)-14(+)
0.001
0.0015
0.002
0.0025
0.003
-1.5
-1.0
-0.5
0.0
C
0.5
1.0
log10
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2.4 Krafft Temperature Measurements
The Krafft points (KT) of the synthesized dimeric surfactants and their mixtures with
.
amphiphilic drugs were found by taking mixture concentration as 50 9 10-3 molÁdm-3
The transparent solutions were kept in a refrigerator for a day, so that solid surfactant-
hydrate crystals became visible. The samples were then taken out and the temperature was
increased gradually with continuous stirring until the solutions became transparent. The
temperature at this point was taken as the Krafft temperature. The procedure was repeated
three times to check the accuracy of the measurements. The approximated error was
within 0.5 °C.
3 Results and Discussion
Surface tension (c) values for solutions of single and binary mixtures of drugs and sur-
factants at different mole fractions were measured for concentration ranges well above and
below the cmc. The slope of c versus log10 conc curve in low concentration region was
used to calculate various surface parameters, which are provided in Table 1.
Values of cmc for pure surfactants and IMP are in good agreement with those reported
in the literature [10–12]. However, for IBF it comes out to be equal to 90 9 10-3
molÁdm-3, which is half of the value reported earlier [13]. We have repeated the ex-
periment thrice and also performed conductometric measurements. The value of around
90 9 10-3 molÁdm-3 was reproduced each time. The tensiometric profiles of both IMP
and IBF are shown in Fig. 1(a) while the conductivity profile for IBF is given as Fig. 1(b).
Figure 2(a) depicts the surface tension profiles for pure surfactants whereas Fig. 2(b) and
(c) show these profiles for IMP–surfactant and IBF–surfactant systems. It is clear from the
breakpoints in the plots in Fig. 1 that the cmc of IMP is lower than that of IBF. This could
be explained on the basis of the structures of these two drugs, shown as Scheme 2. IMP has
three rings in its hydrophobic part whereas IBF has a single ring system and hence IMP is
more hydrophobic than IBF. At the same time, IMP contains an amine group as head group
and IBF has a carboxylic acid group. It is a well known fact that an amine is more
hydrophilic than a carboxylic acid [14]. These two factors oppose each other and, in our
Scheme 2 Structures of the amphiphilic drugs used in the study
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drugs, the first factor dominates and the cmc of IMP is lower than that of IBF. For dimeric
surfactants, the cmc values are lower than those of conventional surfactants. This result is
well known in the literature. Gemini surfactants are considered as novel and green sur-
factants due to their low cmc values [6, 7] and ability to decrease the surface/interfacial
tension to a greater extent [15, 16]. Also, as expected, cmc values decrease with the
increase in tail length of the surfactant. The cmc values of the four surfactants used here are
in the order: 10(-)-2-14(?) [ 8(-)-2-14(?) * 8(-)-2-16(?) [ 10(-)-2-16(?).
The total number of carbon atoms in a molecule (i.e., n ? m) for the four geminis are 22,
24, 24 and 26, respectively, for 8(-)-2-14(?),8(-)-2-16(?),10(-)-2-14(?) and
10(-)-2-16(?). At first sight it seems that the cmc values should be in the order:
8(-)-2-14(?) [ 8(-)-2-16(?) & 10(-)-2-14(?) [ 10(-)-2-16(?). The excep-
tional behavior of 10(-)-2-14(?) can be explained on the basis of the difference in two
tails of the dimeric surfactants. In 10(-)-2-14(?) the difference in the lengths of the two
tails is of 4 CH2 groups while in the other three surfactants the difference is of 6 or 8 CH2
groups. Large differences in the lengths of the two tails makes adjustment in the core
easier, whereas a smaller difference increases crowding in the core and micellization
becomes difficult. Hence, 10(-)-2-14(?) does not forms micelles as easily.
When these surfactants are mixed with drugs, the mixture cmc decreases with the
stoichiometric mole fraction of surfactant (a1). The values, however, remain above the cmc
of pure surfactants. This means that mixed micelles are formed between the two compo-
nents (i.e., surfactants and drugs) and attractive interactions are operating between the
components of the mixture. As the chain length of the tail increases, the cmc value
decreases. The cmc decrease is less for 10(-)-2-14(?) and 10(-)-2-16(?) (from
45.2 9 10-3 molÁdm-3 to 0.358 9 10-3 molÁdm-3 and 0.111 9 10-3 molÁdm-3) in
comparison with 8(-)-2-14(?) and 8(-)-2-16(?) (from 45.2 9 10-3 to
0.354 9 10-3 molÁdm-3 and 0.096 9 10-3 molÁdm-3) for IMP systems; the reverse is
true for IBF systems. Another point, which is clear from the data, is that the decrease is
more in the case of IBF than in IMP. This suggests that the surfactant molecules may be
predominantly in the cationic form and cationic–anionic mixtures result in sharp decrease
in the cmc values.
When two (or more) amphiphiles are mixed together they form mixed micelles, the
mixing may be ideal or non-ideal depending upon the nature of the individual amphiphiles.
Clint [17] proposed a theory to get an idea about ideality/nonideality in the mixtures. The
equation is as follows:
n
X
1
ai
cmci
¼
ð1Þ
cmcid
i¼1
where ai and cmci are the stoichiometric mole fraction and cmc of ith component in the
mixtures. The cmcid is the cmc of the mixture at ideal mixing conditions. When the cmc
value equals cmcid the mixing is ideal, while cmcid [ cmc or cmcid \ cmc indicate at-
tractive and repulsive interactions, respectively. In our systems, the cmcid values are al-
ways greater than the cmc values, indicating attractive interactions between the two
components. To further compare the extent of experimental cmc deviation from cmcid, we
have used another parameter, i.e., equivalent deviation. It is defined as the ratio of
the difference between cmcid and cmc to cmcid (Dcmc/cmcid). For drug–surfactant systems
the equivalent deviation trend is in general: 8(-)-2-14(?)\10(-)-2-14(?)
\ 10(-)-2-16(?) \ 8(-)-2-16(?). Schulz and his co-workers [18, 19] found that the
difference in tail lengths of the two components affects the process of micellization. In our
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1301
Table 2 Various parameters calculated using the Rubingh, Motomura and Rosen models
X1Moto
X1id
a1
X1m
X1r
bm
br
f1m
f2m
f1r
f2r
8(-)-2-14(?) ? IMP
0.025
0.050
0.075
0.100
0.125
0.698
0.823
0.868
0.870
0.828
0.175
0.403
0.813
–
–
–
–
–
–
0.951
0.975
0.983
0.988
0.991
-5.4
–
–
–
–
–
0.610
0.900
0.948
0.942
0.866
0.071
0.103
0.099
0.068
0.035
–
–
–
–
–
–
–
–
–
–
-3.4
-3.1
-3.5
-4.9
–
8(-)-2-16(?) ? IMP
0.025
0.050
0.075
0.100
0.125
0.640
0.676
0.668
0.674
0.676
0.199
0.528
0.535
0.557
0.547
0.553
0.954
0.977
0.985
0.989
0.991
-8.9
-8.7
-8.9
0.314
0.401
0.315
0.314
0.298
0.026
0.018
0.009
0.007
0.005
0.137
0.023
0.067
0.015
0.018
0.083
0.006
0.014
0.002
0.002
0.588
-17.4
-13.7
-20.3
-20.0
–
–
–
-10.5
-10.9
-11.5
10(-)-2-14(?) ? IMP
0.025
0.050
0.075
0.100
0.125
0.751
0.872
0.759
0.801
0.796
0.199
–
0.944
0.972
0.981
0.986
0.989
-3. 5
-2.2
-5.5
-4.9
-5.5
–
0.805
0.964
0.726
0.823
0.797
0.139
0.185
0.041
0.043
0.031
–
–
0.568
–
–
–
–
–
–
–
–
–
–
–
0.934
0.927
-3.3
-3.6
0.981
0.985
0.046
0.058
10(-)-2-16(?) ? IMP
0.025
0.050
0.075
0.100
0.125
0.813
–
0.236
–
0.966
0.983
0.989
0.992
0.993
-3.1
–
–
0.897
–
0.128
–
–
–
0.653
–
–
–
–
0.853
0.713
0.718
–
–
–
–
-4.0
-9.3
-9.5
–
0.917
0.465
0.468
0.054
0.009
0.007
–
–
–
–
–
–
0.887
-5.4
0.934
0.015
8(-)-2-14(?) ? IBF
0.001
0.0015
0.002
0.0025
0.003
0.521
0.545
0.556
0.566
0.576
0.288
0.484
0.945
0.500
0.541
0.549
0.563
0.566
0.594
0.687
0.746
0.786
0.815
-7.2
-6.8
-7.7
-7.9
7.9
-2.6
-2.9
-5.1
-5.3
-6.3
0.191
0.244
0.218
0.224
0.244
0.141
0.132
0.092
0.079
0.074
0.528
0.538
0.354
0.366
0.303
0.528
0.423
0.215
0.189
0.131
–
8(-)-2-16(?) ? IBF
0.001
0.0015
0.002
0.0025
0.003
0.52
0.399
0.769
0.368
0.385
0.409
0.412
0.430
0.613
0.704
0.760
0.799
0.826
-9.7
-9.8
-12.0
-12.4
-14.6
-13.9
-16.7
0.107
0.122
0.115
0.101
0.058
0.073
0.059
0.043
0.031
0.015
0.004
0.008
0.006
0.009
0.008
0.196
0.158
0.087
0.095
0.046
0.537
0.547
0.552
0.549
-10.5
-11.4
-14.0
10(-)-2-14(?) ? IBF
0.001
0.0015
0.002
0.0025
0.003
0.513
0.53
0.364
0.810
0.475
0.495
0.509
0.522
0.524
0.561
0.658
0.719
0.762
0.794
-8.3
-8.9
-8.0
-8.1
-8.8
-7.6
-10.7
0.141
0.138
0.144
0.116
0.099
0.114
0.080
0.067
0.043
0.031
0.110
0.128
0.121
0.177
0.089
0.164
0.139
0.103
0.127
0.053
0.542
0.547
0.551
-9.2
-10.5
-11.5
123

1302
J Solution Chem (2015) 44:1292–1309
Table 2 continued
X1Moto
X1id
a1
X1m
X1r
bm
br
f1m
f2m
f1r
f2r
10(-)-2-16(?) ? IBF
0.001
0.0015
0.002
0.0025
0.003
0.535
0.55
0.328
0.511
0.534
0.544
0.562
0.554
0.687
0.767
0.814
0.846
0.868
-9.4
-4.8
-6.3
-7.8
-6.6
-9.7
0.131
0.134
0.146
0.122
0.123
0.068
0.049
0.042
0.029
0.025
0.316
0.256
0.199
0.281
0.145
0.285
0.167
0.101
0.123
0.051
0.703
-9.9
-10.0
-11.1
-11.4
0.562
0.565
0.571
–
–
–
systems the difference in tails of surfactants and drug is maximum in 8(-)-2-16(?) and
micellization becomes easier. However, the difference is minimum in 10(-)-2-14(?)
but, as both the chains of the surfactant are long, they result in crowding in the micellar
core and micellization with drugs becomes slightly more difficult than with
8(-)-2-14(?). In addition to this, the magnitude of equivalent deviation is greater for
surfactant–IBF mixed systems. As the hydrophobicity of the surfactant molecule increases,
deviation of the mixed system from ideality also increases. The deviation of cmc from
cmcid values also suggests that the zwitterionic surfactants are mostly in the cationic form
and hence cationic–anionic systems (IBF–surfactants) deviate more from ideality than
cationic–cationic systems of IMP–surfactants.
Most of the theories dealing with the mixtures of amphiphiles are based on regular
solution theory and they are applied to the mixtures in order to estimate the interaction
parameter, b. The interaction parameter for mixed micelles can be evaluated by Rubingh’s
equation [20]:
lnðcmca1=cmc1Xm1 Þ
bm
¼
ð2Þ
(1 À X1m)2
where X1m is the micellar mole fraction of surfactant and can be evaluated using the
equation:
2
ðXm1 Þ ln½cmc Á a1=cmc1Xm1 Š
¼ 1
ð3Þ
(1 À X1m)2ln[cmcð1 À a1Þ=cmc2(1 À X1m)]
The X1m values increase with the values of a1 (Table 2). As the mole fraction of sur-
factants in the solution increases, more surfactant molecules participate in mixed micel-
lization. These values are in between 0.52 and 0.58 for IBF–surfactants whereas they are
between 0.64 and 0.88 in IMP–surfactant systems. This suggests that in IBF–surfactant
systems both components participate almost equally in the mixed micellization. As the
structure of IBF is relatively less bulky it can participate in the process of micellization
more readily. IMP, due to its three ring system, causes more steric hindrance and, hence, it
participates less in mixed micelles.
Motomura et al. [21] claimed that Rubingh’s model is questionable as it neglects the
presence of solvent [22] and considers the excess entropy of mixing to be zero. They
proposed a treatment based on excess thermodynamic quantities. The relevant equations
are:
123

J Solution Chem (2015) 44:1292–1309
1303
ða1a2=cmcÞðocmc=oa1ÞT;P
X1M ¼ a1 À
ð4Þ
dcd m1;cm2;d
1 À
m1;cm2:a1þm2;d:m1a2
where
and
viai
ꢀ
ai ¼
ði ¼ 1; 2Þ
v1a1 þ v2a2
ð5Þ
ð6Þ
cmc ¼ ðv1a1 þ v2a2Þcmc
mi is the number of ions dissociated by the ith component, mi = m1 ? m2, where m1 =
m1a ? m1c and m2 = m2b ? m2d (c and d are counterions).
In the above equations, X1M is the micellar mole fraction of surfactant, ai the bulk mole
ꢀ
fraction. dcd is the Kronecker delta, which is equal to 1 for identical counterions (d = c) and
0 for no or different counterions (d = c).
For zwitterionic dimeric-drug systems Eq. 4 reduces to:
ꢀ
ꢁ
ꢀ
ꢁꢀ
ꢁꢀ
ꢁ
3a1
1
3a1
2 À 2a1
a1 þ 2
ocmc
oa1
X1M
¼
À
ð7Þ
a1 þ 2
ða1 þ 2Þcmc a1 þ 2
The values of mole fraction (X1M) were found to be lower than X1m values at all mole
fractions (Table 2) and increase with increasing a1 (for systems where these equations gave
reasonable values of X1M). These values are higher for surfactant–IBF systems. Values of
micellar mole fraction at ideal conditions (X1id) were calculated using the equation:
a1cmc2
X1id
¼
ð8Þ
a1cmc2 þ a2cmc1
X1id values also increase with a1 and are greater than both X1m and X1M values (Table 2).
Ideally, the mixed micelles should contain only surfactants as surfactants are much more
hydrophobic than drugs. However, drugs form mixed micelles with surfactants and X1m
values become less than the X1id value. The values of X1id are smaller for IBF–surfactant
systems than in IMP–surfactant systems. As the hydrophobic part of IBF contains a single
benzene ring in comparison to three ring system of IMP, its micellization with surfactants
is easier than of IMP. Hence, in ideal conditions IBF should participate more in mixed
micelle formation.
Interaction parameter, bm, given by Eq. 2, is also a measure of nonideality in mixed
systems. The magnitude of bm indicates the strength of interactions whereas the sign of bm
indicates the nature of interaction. bm = 0 means no net interaction, i.e., ideality in the mixed
system. Positive and negative bm values mean net repulsive or attractive interactions, re-
spectively. The bm values in our systems are all negative and the magnitudes are quite high
(Table 2). With the increase in a1, bm for the first two or three values decreases and then
increases in IMP systems while in IBF systems it increases for all mole fractions. The
magnitude is higher for IBF–surfactant systems than for IMP–surfactant systems. Hy-
drophobic interactions among tails of the two components as well as head group charge
decide the magnitude of this parameter. For both drugs the order of magnitude of bm is
8(-)-2-16(?) [ 10(-)-2-16(?) [ 10(-)-2-14(?) [ 8(-)-2-14(?).10(-)-2-
16(?) has 26 carbons while 8(-)-2-16(?) and 10(-)-2-14(?) both have 24 carbons
whereas 8(-)-2-14(?) has 22 carbons. Therefore, the first three are expected to have
123

1304
J Solution Chem (2015) 44:1292–1309
stronger hydrophobic interactions than the fourth. Among the first three, although
10(-)-2-16(?) has more carbon atoms, the difference in two tails and the length of the
tails are more compatible in 8(-)-2-16(?) and hence the interaction is the strongest with
8(-)-2-16(?). Higher magnitudes of bm for IBF–surfactant systems support the idea that
dimeric surfactants are predominantly in cationic form.
Rosen [15] modified Rubingh’s model for mixed interfaces. The relevant equations are:
2
ðXr1Þ lnða1conc=conc1Xr1Þ
¼ 1
ð9Þ
(1 À X1r)2lnfconcð1 À a1)/conc2(1 À X1rÞg
and
lnða1conc=conc1Xr1 Þ
br ¼
ð10Þ
(1 À X1r)2
where conc1, conc2 and conc are the concentrations of single surfactant, single drug and
drug–surfactant mixtures required to decrease the surface tension of a solution to a par-
ticular value.
In IMP–surfactant systems Eq. 9 was convergent for only few mixtures and, hence, we
were unable to evaluate X1r and other related parameters. For IMP-8(-)-2-16(?) the X1r
values are smaller than X1m (Table 2). For the other two surfactants, X1r values are greater
than X1m values. For IBF–surfactants these values are always slightly smaller than X1m
values and are also close to 0.5. In IBF–surfactant systems, surfactants and drug participate
almost equally in mixed monolayer formation as in mixed micelle formation. The struc-
tures of drug and dimeric surfactants are compatible with each other and, hence, both
mixed micelles and mixed monolayers have equal contribution of drug and surfactants.
The interfacial interaction parameter, br, is an indicator of the interactions between the
mixed components at an interface. The br values are also negative and the magnitude in most
of the cases increases with a1. The magnitude of br, as of bm, is largest for 8(-)-2-16(?)-
drug systems (Table 2). Average values of bm, bamv, are greater than barv, average values of br.
Difference in tail length of the two components disturbs the surface and interaction among the
components becomes weaker. In mixed micelles, on the other hand, tails come together;
difference in their length makes room for these tails to adjust and increase the hydrophobic
interactions. As a result, bamv are greater than barv values in magnitude.
Activity coefficients of the two components in mixed micelles and mixed monolayers
are given by:
n
o
À
Á
2
f1m ¼ exp bm 1 À X1m
ð11Þ
ð12Þ
n
o
À
Á
2
f2m ¼ exp bm X1m
and
n
o
À
Á
2
f1r ¼ exp br 1 À X1r
ð13Þ
ð14Þ
n
o
À
Á
2
f2r ¼ exp br X1r
These values are less than unity (Table 2), suggesting that the two components are
far away from their standard states. This means that the mixed systems are nonideal. In
123

J Solution Chem (2015) 44:1292–1309
1305
IMP–surfactant systems the f1 values, in some cases, are closer to unity. In mixed systems
of surfactant and IMP, the surfactants have larger contribution and hence they are closer to
their standard state.
When dissolved in water, amphiphiles initially minimize their Gibbs energy by ad-
sorbing at the air/water interface where hydrophilic parts point towards water and hy-
drophobic parts towards air. This decreases the surface tension of water. As per the Gibbs
adsorption equation [23], the slope of surface tension and log10 conc plots gives the amount
of amphiphile adsorbed at the surface (in molÁm-2):
1
Cmax ¼ À
lim ðoc=o log10 CÞ
ð15Þ
C!cmc
2:303nRT
where n is the number of species adsorbed at the interface whose concentration varies with
the amphiphile concentration, Cmax is surface excess concentration and T is the tem-
perature in Kelvin. Values of n were taken as 2 and 1 for drugs and dimeric surfactant,
respectively, whereas for mixtures, n was calculated as [24]: n = n1Xr1 ? n2X2r (n1 and n2
being the values of n for the surfactant and drug, respectively). Reciprocal of Cmax gives
the minimum area occupied by an amphiphile at the interface (Amin).
1020
Amin
¼
ð16Þ
NA Cmax
where NA is the Avogadro number. 1020 is a factor used to convert area into A units. The
max values increase with a1 while Amin follows the opposite trend (Table 1). The values of
˚
C
Amin are comparable for both the drugs and, in most of the cases, are lower than the Amin
values of the single components. The minimum area occupied by a molecule at ideal
condition is given by:
Aid ¼ X1rA1 þ X2rA2
ð17Þ
These values are almost constant for a particular drug–surfactant mixture and are
greater than the Amin values. Also, the differences in Amin and Aid values are greater in IBF–
surfactant systems than in IMP–surfactant systems. This means that the monolayer formed
in IBF systems is more closely packed, as it would be in the ideal state. This can be
understood by the discussion given for cmc and X1 values that surfactant may be in its
cationic form and hence form a more compact interface with anionic IBF.
From the above values, various thermodynamic parameters were evaluated (given in
Table 3) and are discussed below.
The Gibbs energy of micellization, DGomic, was evaluated using:
DGomic ¼ ð1=j)RT lnxcmc
ð18Þ
where xcmc is the cmc in mole fraction unit and j is the number of alkyl chains in the
amphiphile molecule [25]. Hence, j = 1 for drugs and j = 2 for dimeric surfactants and
drug–surfactant mixtures. The data in Table 3 show all the values to be negative. Also, the
magnitudes of DGmꢀ ic are higher for IMP–surfactant systems than for IBF–surfactant sys-
tems. As the amount of surfactant (i.e., a1) in IBF–surfactant systems is smaller than in
IMP–mixed systems, the magnitude of DGꢀmic is lower, i.e., the favorability of the micelle
formation is less than in IMP–surfactant systems.
123

1306
J Solution Chem (2015) 44:1292–1309
Table 3 Thermodynamic parameters for the binary mixed systems
DGꢀad
ÀDGꢀmic
ÀDGꢀad
DHf0
a1
Gmin
(kJÁmol-1
ÀDGmex
DGꢀmic
(kJÁmol-1
)
(kJÁmol-1
)
(kJÁmol-1
)
(kJÁmol-1
)
)
8(-)-2-14(?) ? IMP
0
17.9
13.7
13.9
14.2
14.6
15.1
17.3
41.2
2.30
27.4
–
–
–
–
–
–
–
–
0.025
0.050
0.075
0.100
0.125
1
–
–
–
2.9
1.2
0.9
1.0
1.7
–
–
–
–
–
–
–
–
–
–
–
–
–
50.3
2.91
12.9
8(-)-2-16(?) ? IMP
0.025
0.050
0.075
0.100
0.125
1
14.7
15.2
16.1
16.4
16.8
17.4
32.5
37.7
27.8
30.3
28.6
52.1
2.20
2.47
1.73
1.84
1.70
2.99
34.2
19.8
17.8
9.8
5.2
4.8
5.8
6.0
6.4
–
78.0
78.4
94.4
138.9
184.1
–
8.8
13.2
10(-)-2-14(?) ? IMP
0.025
0.050
0.075
0.100
0.125
1
13.1
13.5
14.6
15.1
15.1
17.1
–
–
–
1.6
0.6
2.5
1.9
2.2
–
–
–
–
–
–
–
–
–
43.7
47.0
58.1
–
24.6
24.6
47.1
1.63
1.63
2.75
7.5
7.6
9.0
10(-)-2-16(?) ? IMP
0.025
0.050
0.075
0.100
0.125
1
13.5
13.9
14.8
16.3
16.5
17.8
–
–
–
1.2
1.4
1.3
4.8
4.9
–
22.5
–
–
–
–
–
–
–
22.5
47.9
52.3
–
–
–
–
–
1.52
2.78
8.0
9.4
49.4
8(-)-2-12(?) ? IBF
0
12.4
12.4
11.5
11.6
12.1
12.3
17.3
25.7
25.7
23.7
25.0
24.9
25.6
50.3
2.07
2.07
2.07
2.15
2.06
2.08
2.91
27.4
12.2
9.9
–
–
–
–
–
–
–
–
0.001
0.0015
0.002
0.0025
0.003
1
4.5
4.3
4.8
4.9
4.8
–
7.9
7.8
4.8
12.9
8(-)-2-16(?) ? IBF
0.001
0.0015
0.002
0.0025
0.003
1
12.3
12.6
13.0
13.5
14.4
17.4
28.9
28.0
27.2
25.3
25.4
52.1
2.35
2.22
2.09
1.88
1.77
2.99
13.8
12.9
8.5
6.1
6.2
6.6
7.1
8.7
–
9.4
8.6
13.2
123

J Solution Chem (2015) 44:1292–1309
1307
Table 3 continued
DGꢀad
ÀDGꢀmic
ÀDGꢀad
DHf0
a1
Gmin
(kJÁmol-1
ÀDGmex
DGꢀmic
(kJÁmol-1
)
(kJÁmol-1
)
(kJÁmol-1
)
(kJÁmol-1
)
)
10(-)-2-14(?) ? IBF
0.001
0.0015
0.002
0.0025
0.003
1
11.7
12.2
12.5
13.0
13.4
17.1
30.2
29.6
30.2
26.5
28.2
47.1
2.58
2.43
2.42
2.03
2.10
2.75
9.7
5. 2
5.6
5.8
6.6
7.1
–
10.9
8.2
10.7
8.0
9.0
10(-)-2-16(?) ? IBF
0.001
0.0015
0.002
0.0025
0.003
1
12.4
12.9
13.1
13.6
13.8
17.8
22.8
23.8
24.8
22.7
25.2
49.4
1.84
1.85
1.89
1.67
1.83
2.78
9.5
7.3
6.2
6.7
6.7
9.4
5.9
6.2
6.2
6.9
7.0
–
Standard deviation = 5.0
Similar is the behavior of the standard Gibbs energy of adsorption, DGꢀad, which was
calculated using the relation [26]:
pcmc
DGꢀad ¼ DGꢀmic
À
ð19Þ
Cmax
where pcmc (c0 - ccmc) is the surface pressure at cmc. These values are larger in magnitude
than DGꢀmic and the ratio of DGaꢀd /DGꢀmic varies between 1.5 and 3.0, which suggests that
adsorption is a primary process and micellization is secondary.
The minimum Gibbs energy of a surface at equilibrium, Gmin, was obtained using the
equation [27]:
Gmin ¼ ccmcAminNA
ð20Þ
The lower the value of Gmin, the more stable is the surface formed. The values are
positive and with both drugs Gmin is lowest for 10(-)-2-16(?) systems. The cmc result
shows that the decrease is slower in this system. Both of these results indicate that this
system gives a more stable surface and 10(-)-2-16(?) is less effective in decreasing the
cmc.
The excess Gibbs energy of mixing, DGmex, was calculated from the values of f1m and f2m
as:
DGmex ¼ RT[X1mlnf1m þ (1 À X1m)lnf2m]
ð21Þ
The values are all negative (Table 3) signifying that the mixed micelles are relatively
more stable than the micelles of the pure components.
The Krafft temperature (KT) is the minimum temperature at which surfactants form
micelles and it can be used to estimate their solubility. Below the KT, micelles don’t form
and in aqueous solution the surfactants remain in crystalline form. The lower the Krafft
point of surfactant, the better is its solubility. Experimental results (Table 1) show that the
123

1308
J Solution Chem (2015) 44:1292–1309
Krafft points of IBF–surfactant systems are below 0 °C, while the Krafft points of some
mole fraction of surfactant–IMP mixtures are above 0 °C. This indicates that dimeric
surfactant–IBF systems have good solubility compared with the surfactant–IMP mixed
systems. Table 1 shows that with the increase in mole fraction of surfactant, KT increases.
As the sum of carbon atoms in the tail increases, KT increases. However, for the same
number of carbon atoms, the larger the difference in tail lengths, the higher is the KT value.
The KT values were used to calculate the heat of fusion of solid surfactant hydrate to liquid
hydrates (DHfꢀ ) as:
ꢂ
ꢃ
TT10
T10 À T
DHfꢀ ¼ ÀR ln X1m
ð22Þ
where T10 and T are the Krafft temperatures of pure surfactant and its mixtures, respec-
tively. The DHꢀ values show large variation with increasing a1 in 8(-)-2-16(?) systems,
again confirming strong synergism in the mixed micelles.
f
4 Conclusions
Results of the tensiometric study on the mixed systems involving two amphiphilic drugs
(IMP and IBF) and four asymmetric dimeric zwitterionic surfactants (n(-)-2-m(?))
indicate formation of mixed micelles. At a particular a1 the cmc decreases with the increase
in chain length of surfactant. The decrease is more with IBF than with IMP. This suggested
that the surfactants are mostly in cationic form. Micellar mole fraction value (X1m) also
supports this: mixed micelles of IBF–surfactants contain equal amounts of both compo-
nents while surfactants participate more in mixed micelles in IMP–surfactant systems.
With both drugs, the interaction parameters at mixed interface (br) and in mixed
micelles (bm) follow the order: 8(-)-2-16(?) [ 10(-)-2-16(?) [ 10(-)-2-14(?) [
8(-)-2-14(?). This indicates that the interactions among the two components in mixtures
depends both upon the total number of carbon atoms in the tails of the surfactant as well as on
the difference in the length of the two tails.
References
1. Dressman, J., Reppas, C.: Drug solubility: how to measure it, how to improve it. Adv. Drug Deliv. Rev.
59, 531–532 (2007)
2. Dalmora, M.E., Dalmora, S.L., Oliveira, A.G.: Inclusion complex of piroxicam with b-cyclodextrin and
incorporation in cationic microemulsion. In vitro drug release and in vivo topical anti-inflammatory
effect. Int. J. Pharm. 222, 45–55 (2001)
3. Torchilin, V.P.: Targeted polymeric micelles for delivery of poorly soluble drugs. Cell. Mol. Life Sci.
61, 2549–2559 (2004)
4. Bertrand, N., Leroux, J.C.: The journey of a drug-carrier in the body: an anatomo-physiological per-
spective. J. Control Release 161, 152–163 (2012)
5. Scott, R.C., Crabbe, D., Krynska, B., Ansari, R., Kiani, M.F.: Aiming for the heart: targeted delivery of
drugs to diseased cardiac tissue. Expert Opinion Drug Deliv. 5, 459–470 (2008)
6. Zana, R., Benrraou, M., Rueff, R.: Alkanediyl-a,x-bis (dimethylalkylammonium bromide) surfactants.
1. Effect of the spacer chain length on the critical micelle concentration and micelle ionization degree.
Langmuir 7, 1072–1075 (1991)
7. Azum, N., Naqvi, A.Z., Akram, M., Kabir-ud-Din: Studies of mixed micelle formation between cationic
gemini and cationic conventional surfactants. J. Colloid Interface Sci. 328, 429–435 (2008)
123

J Solution Chem (2015) 44:1292–1309
1309
8. Wettig, S.D., Verrall, R.E., Foldvari, M.: Gemini surfactants: a new family of building blocks for non-
viral gene delivery systems. Curr. Gene Ther. 8, 9–23 (2008)
9. Mohammed-Saeid, W., Michel, D., El-Aneed, A., Verrall, R.E., Low, N.H., Badea, I.: Development of
lyophilized gemini surfactant-based gene delivery systems: Influence of lyophilization on the structure,
activity and stability of the lipoplexes. J. Pharm. Pharm. Sci. 15, 548–567 (2012)
10. Sun, Y., Feng, Y., Dong, H., Chen, Z., Han, L.: Synthesis and aqueous solution properties of ho-
mologous gemini surfactants with different head groups. Cent. Eur. J. Chem. 5, 620–634 (2007)
11. Ansari, W.H., Noori, S., Naqvi, A.Z., Kabir-ud-Din: Interaction between zwitterionic surfactants and
amphiphilic drug: a tensiometric study. Z. Phys. Chem. 227, 441–458 (2013)
12. Kabir-ud-Din, Rub, M.A., Naqvi, A.Z.: Effect of inorganic salts and ureas on the micellization behavior
of antidepressant drug imipramine hydrochloride at various concentrations and temperatures. Acta Phys.
Chim. Sin. 28, 885–891 (2012)
13. Ridell, A., Evertsson, H., Nilsson, S., Sundelof, L.O.: Amphiphilic association of ibuprofen and two
nonionic cellulose derivatives in aqueous solution. J. Pharm. Sci. 88, 1175–1181 (1999)
14. Lindemuth, P.M., Bertrand, G.L.: Calorimetric observations of the transition of spherical to rodlike
micelles with solubilized organic additives. J. Phys. Chem. 97, 7769–7773 (1993)
15. Rosen, M.J.: Surfactants and Interfacial Phenomena, 3rd edn. Wiley, New Jersey (2004)
16. Kabir-ud-Din, Sharma, G., Naqvi, A.Z., Chaturvedi, S.K., Khan, R.H.: Ion-dipole induced interaction
between cationic gemini/TTAB and nonionic (Tween) surfactants: interfacial and microstructural
phenomena. RSC Adv. 3, 6549–6959 (2013)
17. Clint, J.H.: Micellization of mixed nonionic surface active agents. J. Chem. Soc. Faraday Trans. 1(71),
1327–1334 (1975)
´
18. Schulz, P.C., Rodrıguez, J.L., Minardi, R.M., Sierra, M.B., Morini, M.A.: Are the mixtures of ho-
mologous surfactants ideal? J. Colloid Interface Sci. 303, 264–271 (2006)
19. Schulz, P.C.: Factors affecting mixed aggregation. In: Paul, B.K. (ed.) Statistical science and inter-
disciplinary research. Recent Trends in Surface & Colloid Science, vol. 21. World Scientific Publishers
Pvt. Ltd., Singapore (2012)
20. Rubingh, D.N.: Mixed micellar solutions. In: Mittal, K.L. (ed.) Solution Chemistry of Surfactants.
Plenum, New York (1979)
21. Motomura, K., Yamanaka, M., Aratono, M.: Thermodynamic consideration of the mixed micelle of
surfactants. Colloid Polymer Sci. 262, 948–955 (1984)
22. Aratono, M., Villeneuve, M., Takiue, T., Ikeda, N., Iyota, H.: Thermodynamic consideration of mix-
tures of surfactants in adsorbed films and micelles. J. Colloid Interface Sci. 200, 161–171 (1998)
23. Chattoraj, D.K., Birdi, K.S.: Adsorption and the Gibbs Surface Excess. Plenum, New York (1984)
24. Zhou, Q., Rosen, M.J.: Molecular interactions of surfactants in mixed monolayers at the air/aqueous
solution interface and in mixed micelles in aqueous media: the regular solution approach. Langmuir 19,
4555–4562 (2003)
25. Zana, R.: Critical micellization concentration of surfactants in aqueous solution and free energy of
micellization. Langmuir 12, 1208–1211 (1996)
26. Rosen, M.J., Aronson, S.: Standard free energies of adsorption of surfactants at the aqueous solution/air
interface from surface tension data in the vicinity of the critical micelle concentration. Colloids Surf. 3,
201–208 (1981)
27. Sugihara, G., Miyazono, A., Nagadome, S., Oida, T., Hayashi, Y., Ko, J.S.: Adsorption and micelle
formation of mixed surfactant systems in water II: A combination of cationic gemini-type surfactant
with MEGA-10. J. Oleo Sci. 52, 449–461 (2001)
123