Interaction between zwitterionic surfactants and amphiphilic drug: A tensiometric study

Article abstract of DOI:10.1524/zpch.2012.0340

The physicochemical properties, viz, critical micelle concentration (cmc), surface excess concentration (Γ_max), minimum area per head group (A_min) of zwitterionic surfactants (designated as n(-)-2-m(+); n = 8, 10, 12 and m = 12, 14, 16) and their mixtures with amphiphilic antidepressant drug amitriptyline hydrochloride (AMT) were determined by using surface tension measurements. The cmc and ideal cmc (cmc_id) values along with interaction parameters, β^m and β ^α (calculated using Rubingh's and Rosen's models), suggest attractive interactions among the components. The Krafft temperature measurements also indicate strong attractive interactions. Γ_max (or A_min) increases (or decreases) with the addition of gemini surfactant; the values being closer to that of the drug. These values and micellar mole fraction (Xm-calculated from Rubingh's model and X ₁^Moto-calculated from Motomura's model) indicate larger contribution of gemini surfactants in mixed micelles and smaller contribution at air/solution interface (as mole fraction values at interface, X ^σ₁, are slightly smaller than X₁m). The standard Gibbs energy of micellization (ΔG°_mic) and adsorption (ΔG°_ad) as well as excess energy of mixing (ΔG_exm) are all negative. All these results suggest higher stability of the mixed systems. UV absorbance results also suggest that the mixed micelles are stable for several days. by Oldenbourg Wissenschaftsverlag.

Full text of DOI:10.1524/zpch.2012.0340

Z. Phys. Chem. 227 (2013) 441–458 / DOI 10.1524/zpch.2012.0340
© by Oldenbourg Wissenschaftsverlag, München
Interaction between Zwitterionic Surfactants and
Amphiphilic Drug: A Tensiometric Study
∗
∗
By Wajid H. Ansari , Sahar Noori, Andleeb Z. Naqvi , and Kabir-ud-Din
Department of Chemistry, Aligarh Muslim University, Aligarh-202002, India
(Received August 13, 2012; accepted in revised form November 13, 2012)
(Published online January 28, 2013)
Amitriptyline Hydrochloride / Zwitterionic Gemini Surfactants / Surface
Tension / Mixed Micelles
The physicochemical properties, viz, critical micelle concentration (cmc), surface excess con-
centration (Γmax), minimum area per head group (Amin) of zwitterionic surfactants (designated as
n(−)-2-m(+); n = 8, 10, 12 and m = 12, 14, 16) and their mixtures with amphiphilic antidepressant
drug amitriptyline hydrochloride (AMT) were determined by using surface tension measurements.
The cmc and ideal cmc (cmcid) values along with interaction parameters, βm and βσ (calculated
using Rubingh’s and Rosen’s models), suggest attractive interactions among the components. The
Krafft temperature measurements also indicate strong attractive interactions. Γmax (or Amin) increases
(or decreases) with the addition of gemini surfactant; the values being closer to that of the drug.
These values and micellar mole fraction (X1m-calculated from Rubingh’s model and XM1 oto-calculated
from Motomura’s model) indicate larger contribution of gemini surfactants in mixed micelles and
smaller contribution at air/solution interface (as mole fraction values at interface, Xσ1 , are slightly
smaller than Xm1 ). The standard Gibbs energy of micellization (ΔG◦mic) and adsorption (ΔGa◦d) as
well as excess energy of mixing (ΔGmex) are all negative. All these results suggest higher stability
of the mixed systems. UV absorbance results also suggest that the mixed micelles are stable for
several days.
1. Introduction
The aqueous solubility of solid drugs is a major problem and, hence, an important sub-
ject for pharmaceutical scientists. Knowledge of aqueous solubility of drugs helps in
choosing the best solvent for dissolving drugs and designing drug formulation. Drug
solubility affects the pharmacokinetics such as transport, release and absorption [1].
Drugs with low aqueous solubility often show inadequate or variable bioavailability
which hampers their applicability. Two main aspects of successful drug formulation
are its solubility and stability. The solubilizing system must be able to solubilize
the required concentration of the drug. Also, the system must be such that the drug
remains stable in it. Some of the methods used to modify drug solubility are microniza-
tion [2], complexation [3], use of prodrugs [4], cosolvency [5], pH adjustment [6],
* Corresponding authors. E-mail: naqviaz@gmail.com; wajidhusain.chem@gmail.com
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442
W. H. Ansari et al.
Scheme 1. Molecular structures of zwitterionic heterogeminis (A) and AMT (B).
hydrotropy [7] and solubilization in micelles/microemulsions [8,9]. However, many of
these methods have limitations and cannot be used for all active drugs [9–13].
Colloidal drug carrier systems such as micelles and mixed micelles show great
promise in drug delivery as with these systems size of the carrier as well as the amount
of drug loading can be optimized. Also, these systems are easy to prepare, have long
shelf life and low toxicity [14]. The most commonly used surfactants include Cre-
mophor EL, Tween 20, Tween 80 and sodium lauryl sulphate [12,15]. However, Tweens
are known to be toxic, although less than Tritons [16]. Cremophor EL, which is used to
solubilise various drugs like anaesthetics, photosensitizers, immunosuppressive agents,
sedatives, anticancer and antitumor drugs, is reported to have side effects like severe
anaphylactic hypersensitivity reactions, abnormal lipoprotein patterns, hyperlipidaemia
and peripheral neuropathy [17–19].
Gemini surfactants can be 10 to 100 times more surface active than conven-
tional ones and, hence, are gaining wide attention in both academic and industrial
research [20,21]. These surfactants have shown great promise in skin care [22], drug
entrapment and release [23], gene therapy [24] and antibacterial regimens [25] as well
as in various analytical processes [26]. The most widely used gemini surfactants are
the m-s-m type, i.e., symmetrical ones: two hydrophobic chains of equal length con-
nected by a spacer at the level of head groups, with same charge on both heads. Charge
on head groups may be either positive (cationic gemini) or negative (anionic gem-
ini) [27]. Cationic geminis with the same head group but different tails are also reported
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Interaction between Zwitterionic Surfactants and Amphiphilic Drug: A Tensiometric Study
443
in literature [28,29]. Studies on these types of surfactants indicated that unsymmetrical
geometry may give interesting properties to the surfactant self-assembly.
Another type of gemini surfactants is the heterogemini surfactants [30–32] in which
the head groups are of different types. Among these types anionic-cationic ones, also
known as zwitterionic, are the most interesting and important. Presence of a cationic
and an anionic group in the same molecule gives the surfactant a nature intermediate
to ionic and non-ionic ones [33]. Depending upon the type of head groups these sur-
factants may show pH-dependent or pH-independent behavior. These surfactants are
known to be less skin irritating. The zwitterionic geminis contain no counterions and
when mixed with ionic amphiphiles they may produce strong synergism.
In this paper we present results of mixed micellization studies of AMT with
nine zwitterionic surfactants which contain a negatively charged phosphodiester and
a positively charged quaternary ammonium head. The two head groups are sepa-
rated by two methylene groups. The lengths of the two tails vary between 8–12 and
12–16 (Scheme 1A). AMT is an amphiphilic drug which possesses a rigid, almost
planar tricyclic ring system bound to a short alkyl chain with a terminal nitrogen
atom (Scheme 1B). This drug suffers from anticholinergic, cardiovascular and antiar-
rhythemic side effects. However, these side effects can be reduced by using AMT with
a carrier.
Although there exists a few reports on the physicochemical properties of these sur-
factants [30,34–37], this is probably the first detailed study of mixed systems of these
surfactants with a drug.
2. Experimental section
2.1 Materials
The antidepressant drug amitriptyline hydrochloride (98%, Sigma Aldrich, St. Louis,
USA, CAS: 594-18-8), phosphoryl chloride (99%, Otto, Mumbai, India, CAS: 10025-
87-3), ethylene glycol (≥ 99%, Sigma Aldrich, USA, CAS: 107-21-1), 1-octanol
(≥ 99%, Merck, Hohenbrunn, Germany, Cat. No.: 8209311000), 1-decanol (99%, Otto,
Mumbai, India, CAS: 112-30-1), 1-dodecanol (99%, Otto, Mumbai, India, CAS: 112-
53-8), N,N-dimethyldodecylamine (95%, Acros Organics Mumbai, India, CAS: 112-
18-5), N,N-dimethyltetradecylamine (≥ 95%, Aldrich, USA, CAS: 112-75-14), N,N-
dimethylhexadecylamine (≥ 95%, Fluka, France, CAS: 112-69-6) were used without
further purification.
2.2 Synthesis of gemini surfactants (one pot synthesis)
The zwitterionic geminis (designated as n(−)-2-m(+) throughout this text) were syn-
thesized according to the procedure given in literature [30,36].
The synthesis was carried out in two steps: In the first step, a solution of phos-
phoryl 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 this cyclic ethylene chlorophosphate (1) formed was added the solution of alkyl-
alcohol (0.025 mol) in dry benzene. The reaction mixture was stirred continuously for
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444
W. H. Ansari et al.
Scheme 2. Synthesis of the zwitterionic gemini surfactants (n = 8, 10, 12; m = 12, 14, 16).
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 precursor (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 gemini surfactant (3)
was obtained. The compound was finally purified by recrystallization with acetone. The
structures of the geminis were ascertained by 1H NMR spectral studies.
1H-NMR (300 MHz, CDCl3, δ scale); 0.86–0.88 (t, 6H, 2CH3– tail alkyl chains),
1.25–1.34 (m, 28–44H, –CH2– both tail alkyl chains), 1.83 (m, 2H, N+–C–CH2– tail
alkyl chain), 3.00 (t, 2H, N+–CH2–C– tail alkyl chain), 2.82 (s, 6H, N+(CH3)2), 1.65
(m, 2H, O–C–CH2– tail alkyl chain), 3.95 (t, 2H, O–CH2–C– tail alkyl chain), 4.08 (t,
2H, O–CH2–C–N+), 3.78 (t, 2H, N+–CH2–C–O).
2.3 Tensiometric measurements
The tensiometric measurements were performed using a platinum ring by the ring de-
tachment method with a S. D. Hardson tensiometer. Different mole fractions of mixed
systems were prepared from stock solutions of zwitterionic gemini surfactants and
AMT. The instrument was calibrated each time measurements were made. The surfac-
tant concentration was varied by using Hamilton-Bonaduz, SCHWEIZ, microsyringe
and readings were taken after thorough mixing and temperature equilibration. The cmc
values were obtained from surface tension versus logarithm of surfactant concentration
plots.
2.4 Krafft temperature measurements
The Krafft temperature measurements of pure gemini surfactants and their mixtures
with AMT were made at concentration 5 and 50 mM, respectively. The clear experi-
mental solutions were kept in a refrigerator for at least a day, when the precipitation
of solid surfactant-hydrate crystals occurred. The temperature was raised slowly with
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Interaction between Zwitterionic Surfactants and Amphiphilic Drug: A Tensiometric Study
445
Table 1. Solution properties (cmc, Γmax, Amin, pC20, ΔG◦mic, ΔGaod, Gmin and KT )a of pure amphiphiles.
Amphiphiles
cmc
Γmax
1
Amin pC20
(Å2)
ΔG◦mic
(kJ mol−1
ΔG◦ad
(kJ mol−1
Gmin
(kJ mol−1
KT
(K)
(mM) 107 (mol m−2
)
)
)
)
AMT
36.22
0.148
0.061
0.057
0.144
0.070
0.041
0.073
0.041
0.032
21
43
24
24
27
33
31
21
20
44
80 4 1.92 −18.4 0.2 −34.0 0.3 19.1 0.9
38 1 4.71 −32.3 0.3 −41.8 0.4 7.3 0.2
8(−)-2-12(+)
8(−)-2-14(+)
8(−)-2-16(+)
10(−)-2-12(+)
10(−)-2-14(+)
10(−)-2-16(+)
12(−)-2-12(+)
12(−)-2-14(+)
12(−)-2-16(+)
68 3 5.55 −34.5 0.3 −50.2 0.5 12.9 0.5
70 3 5.74 −34.7 0.3 −52.0 0.5 13.2 0.5 292.0
61 2 4.13 −32.3 0.3 −41.2 0.4 16.7 0.6
49 1 5.32 −34.1 0.3 −47.1 0.5
53 2 5.37 −35.5 0.3 −49.4 0.5
8.9 0.2 278.0
9.3 0.3 294.5
77 3 5.77 −34.0 0.3 −53.2 0.5 14.2 0.6
83 4 6.26 −35.5 0.3 −56.3 0.6 15.0 0.7 279.0
38 1 5.22 −35.9 0.4 −45.1 0.4
6.9 0.1 298.0
1
a
−1
equations used for calculation: Γmax
=
(∂γ/∂ log C), Amin = (NAΓmax
)
×1020, pC20 = − log C20,
2.30a3nnRdT Gmin = γcmc Amin NA.
π
ΔG◦mic = RT ln Xcmc, ΔGa◦d = ΔGm◦ ic
−
cmc
Γ
max
continuous stirring until the solution became clear and readings were taken by visual
inspection. The process was repeated three times to check the reproducibility of the
measurements. The estimated error was within 0.5 ◦C.
2.5 Micellar stability
The stability of mixed system was obtained by measuring their absorbance with a UV-
vis spectrophotometer (SHIMADZU-model UV mini 1240). The absorbance of one
mole fraction (0.075) of gemini surfactants with the drug and pure AMT were taken
above the cmc.
3. Results and discussion
On dissolution, an amphiphile first saturates the interface, and then the excess
molecules tend to self-associate in the bulk solution to form micelles and surface ten-
sion becomes constant. This concentration is taken as critical micelle concentration
(cmc, Fig. 1).
3.1 Surface and micellar properties
3.1.1 Critical micelle concentration
Data in Table 1 record the cmc values of pure drug and n(−)-2-m(+) surfactants along
with other parameters. The drug cmc comes out to be 36 mM which agrees well with the
literature value [38–40]. As is clear from Scheme 1, the hydrophobic part of the drug
is short. Hence, its cmc value is very high. As for the heterogemini surfactants com-
pared to conventional ones, their cmc values are remarkably low. This arises mainly due
to the presence of two hydrophobic tails which transfer at the same time from aque-
ous to micellar phase. In agreement with the published values [36], cmc of 0.073 mM
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W. H. Ansari et al.
Fig. 1. Variation of surface tension (γ) vs. log C of pure amphiphiles (A) and 8(−)-2-12(+)-AMT mixed
systems (B) at different mole fraction (α1, indicated) of 8(−)-2-12(+).
for 12(−)-2-12(+) is observed (see Table 1). Dodecyltrimethylammonium bromide
(DTAB), which is the monomeric analog of the heterogemini 12(−)-2-12(+) and sym-
metrical cationic gemini ethylenediyl-α,ω-bis(dimethyldodecylammonium bromide)
(12-2-12), has cmc value (15.3 mM [41]) more than 15 times higher than that of
12-2-12 (cmc value is 0.83 mM [42]), which is again 11 times higher than that of 12(−)-
2-12(+). Mainly two factors affect the process of micellization: effect of tails which
favors micelle formation and effect of head groups which opposes it. Although 12-2-
12 and 12(−)-2-12(+) both contain two equal chains, their cmc values are more than
10 times different from each other. Due to the opposite charges on the head groups of
12(−)-2-12(+), the effect of head group (which opposes the micellization) decreases.
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Interaction between Zwitterionic Surfactants and Amphiphilic Drug: A Tensiometric Study
447
Fig. 2. Variation of experimental (A) and ideal cmc (B) values with mole fraction (α1) of gemini surfac-
tants.
This, in turn, decreases the cmc. Among geminis with the same spacer, the trend in
cmc in the present case is as: with the increase in total number of carbon atoms in
the two tails (i.e., n +m), cmc decreases, the two exceptions being 8(−)-2-14(+) and
8(−)-2-16(+). As the number of –CH2– groups in the tail increases, hydrophobicity of
the molecule also increases and the cmc decreases. For the 8(−)-2-14(+) and 8(−)-
2-16(+) geminis, the chain length difference makes micellization easier. One shorter
chain makes room for the other long chain making tail adjustment in the core much
easier and cmc values decrease remarkably.
Figure 2A exhibits the variation of cmc values of the mixed drug-gemini surfac-
tant systems with the stoichiometric mole fraction of gemini surfactant (α1). The cmc
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448
W. H. Ansari et al.
values decrease sharply as the surfactants are added (at α1 = 0.025, cmc values drop
from 36 mM to ≤ 4 mM). The decrease becomes slower at higher α1 values. All the
values of cmc fall in between the values of single components. This indicates that the
two components form mixed micelles through attractive interactions. The mixing of two
homologous amphiphiles is considered as an ideal mixing. However, amphiphiles with
different structures usually mix nonideally. In order to investigate the ideality in mixed
systems the pseudophase thermodynamic model proposed by Clint [43] can be used.
This model relates the stoichiometric mole fraction of the mixed components (αi ) with
their cmc values (cmci) as
1
α1
α2
=
+
(1)
cmcid
cmc1 cmc2
where 1 and 2 stand for surfactant and drug, respectively, and cmcid is the cmc at ideal
mixing. The difference in experimentally obtained cmc values (cmc) and cmcid gives an
idea about the extent of the nonideality in the solution. cmcid values decrease with in-
crease in α1 (shown in Fig. 2B); the magnitude always remains higher than cmc values.
To further analyse the extent of deviation, we have evaluated another parameter, i.e.,
equivalent deviation which may be defined as the ratio of difference between cmcid and
cmc to cmcid values. The magnitude of Δcmc/cmcid is the highest for 8(−)-2-14(+) and
8(−)-2-16(+) (Table 2). Due to incompatible and unequal tails these two surfactants
make micelles at very low concentration and greatest deviation, as expected, is shown
by these two surfactants.
3.1.2 Surface excess concentration
The surface excess concentration under the condition of surface saturation (Γmax) can be
used as a measure of surface adsorption. Γmax can be calculated using the well known
Gibbs adsorption equation [44].
1
Γmax
=
(∂γ/∂ log C)
(2)
2.303nRT
The value of n, the number of ions whose concentration at the interface changes with
amphiphile concentration, is taken as 1 for gemini, 2 for drug and 3 for drug-gemini
mixtures. The values of pure components and mixed systems are given in Tables 1
and 2. The value of Γmax for AMT is slightly higher than the value found in litera-
ture [45]. Although the Γmax values for mixture are always smaller than that of pure
components, they increase with increase in gemini surfactant content in the mixture.
May be the negative charge on gemini is interacting attractively with the positive one
on the drug resulting in compact surface and increase in Γmax
.
3.1.3 Minimum area per molecule
−1
The minimum area per molecule (Amin) in Å can be calculated by (NA Γmax
)
×1020
(where NA is Avogadro’s number). The trend is opposite of Γmax, i.e., with increase in
α1, Amin decreases. The values of mixture are always greater than single components.
The ideal mixing values, Aid, calculated from the relation Aid = X1σ A1 + X2σ A2 (where
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Interaction between Zwitterionic Surfactants and Amphiphilic Drug: A Tensiometric Study
449
Table 2. Surface parameters of zwitterionic gemini surfactant-AMT mixed systems.
Surfactant
mole frac-
tion (α1)
Γmax
1
Amin
(Å2)
Aid
(Å2)
Δcmc/
cmcid
pC20
βσ
f1σ
f2σ
X1σ
107
(mol m−2
)
8(−)-2-12(+)
0.125
0.10
0.075
0.05
15
14
9
8
7
110
120
181 18
189 19
228 27
7
8
0.179
0.092
0.216
0.065
0.214
3.66
3.61
3.80
3.87
3.39
46
45
44
−4.034
−2.863
−1.291
0.860
0.923
0.976
0.072
0.137
0.382
0.807
0.833
0.863
0.025
8(−)-2-14(+)
0.125
0.10
0.075
0.05
16
10
9
8
7
102 13
156 16
172 19
186 27
229 49
69
0.107
0.145
0.216
0.286
0.584
4.61
4.34
4.22
4.61
4.29
−4.663
0.957
0.022
0.903
70
69
−5.312
−2.565
0.843
0.974
0.027
0.126
0.821
0.898
0.025
8(−)-2-16(+)
0.125
0.10
0.075
0.05
14
13
9
9
9
113
123
178 17
179 17
182 18
7
8
74
74
74
74
75
0.621
0.232
0.334
0.365
0.650
4.22
4.05
4.32
3.43
3.31
−15.315
−12.089
−14.733
−7.978
−7.559
0.054
0.106
0.05
0.213
0.182
0.007
0.019
0.011
0.081
0.124
0.564
0.569
0.549
0.560
0.525
0.025
10(−)-2-12(+)
0.125
0.10
0.075
0.05
11
11
11
6
144 11
146 12
157 12
249 32
277 39
68
65
64
0.600
0.092
0.155
0.234
0.312
3.94
3.32
3.03
3.16
2.65
−10.182
−2.276
−1.293
0.216
0.891
0.949
0.022
0.255
0.437
0.612
0.775
0.800
0.025
6
10(−)-2-14(+)
0.125
0.10
0.075
0.05
15
14
9
13
8
109
114
182 18
123
209 23
6
7
59
58
0.860
0.861
0.733
0.623
0.713
4.80
4.75
3.57
3.68
3.87
−11.752
−10.518
0.335
0.400
0.003
0.005
0.695
0.705
8
0.025
56
−3.909
0.851
0.083
0.797
10(−)-2-16(+)
0.125
0.10
0.075
0.05
13
10
10
14
8
130
156 13
167 15
116
192 19
9
57
58
58
0.568
0.635
0.604
0.411
0.484
4.60
4.75
4.60
3.82
3.80
−5.718
−7.063
−5.790
0.912
0.773
0.856
0.013
0.009
0.017
0.873
0.809
0.836
7
0.025
12(−)-2-12(+)
0.125
0.10
0.075
0.05
9
8
5
4
4
177 17
201 21
310 49
367 66
409 81
0.358
0.125
0.135
0.216
0.282
4.23
4.83
5.31
5.64
5.17
77
78
78
78
−5.828
−10.050
−14.268
−10.378
0.866
0.449
0.172
0.314
0.016
0.007
0.002
0.010
0.843
0.718
0.649
0.666
0.025
12(−)-2-14(+)
0.125
0.10
0.075
0.05
10
9
8
7
6
169 16
181 18
207 23
250 33
285 42
0.075
0.057
0.195
0.176
0.089
4.41
4.81
4.56
3.95
3.16
0.025
12(−)-2-16(+)
0.125
0.10
0.075
0.05
10
7
6
5
8
169 15
231 28
258 28
314 50
207 23
47
50
47
49
0.189
0.289
0.201
0.369
0.393
5.04
5.25
4.78
5.31
3.76
−8.237
−11.841
−7.640
−9.058
0.686
0.359
0.681
0.496
0.006
0.003
0.010
0.009
0.786
0.706
0.776
0.722
0.025
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450
W. H. Ansari et al.
σ
σ
σ
X1 is the mole fraction of surfactant in mixed monolayer and X2 = 1− X1 ) are also
given in Table 2 along with Amin values. Aid values are always smaller than Amin values.
This expansion of area after mixed monolayer formation has been observed by other
researchers also [46,47]. Although the mixed layer formation is due to attractive in-
teractions, the expansion of area as compared to Aid is due to the insertion of gemini
surfactant in the monolayer formed by drug molecules. It is also clear from Table 2
that Amin values are highest for geminis with longest tail attached to the phosphate head
group (i.e., 12(−)-2-m(+)).
3.1.4 Surface activity
It is a measure of surface activity of amphiphile in terms of its concentration required to
decrease the surface tension of the solvent by 20 mN m−1. The values of pC20 (pC20
=
− log C20), given in Tables 1 and 2, indicate that the drug is less active than the gemini
surfactants and the mixtures show intermediate surface activity. This is what we have
expected as the cmc results also suggest similar behavior. As the head groups in all the
surfactants are same, the values of pC20 (or C20) are not very different from each other.
3.1.5 Micellar mole fractions
The results of cmc and cmcid indicate attractive interactions between the components.
To further analyze for the ideality/nonideality of interactions, the regular solution the-
ory is used [48]. In this theory type and extent of interactions are characterized by an
interaction parameter (βm) which is also related to the activity coefficients ( fim) of the
two components. The fundamental equations are:
(Xm1 )2 ln[cmc α1/cmc1 Xm1 ]
= 1
(3)
(1− Xm1 )2 ln[cmc(1−α1)/cmc2(1− Xm1 )]
and
ln(cmcα1/cmc1 Xm1 )
βm =
(4)
(1− Xm1 )2
where Xm1 is the micellar mole fraction of gemini surfactants. Equation (3) is solved
iteratively for Xm1 . These values are then used to calculate f1m values as
ꢀ
ꢁ
f1m = exp βm(1− X1m)2
(5)
(6)
ꢀ
ꢁ
f2m = exp βm(Xm1 )2
Motomura [49] considered mixed micelles as a macroscopic bulk phase and pro-
posed that the energetics of such systems should be evaluated in terms of excess
thermodynamic quantities. The composition of mixed micelles is evaluated by the re-
lationship:
(α1 α2/cmc) (∂cmc/∂α1)T,P
XM1 oto = α1 −
(7)
δdcν1,cν2,d
1−
ν1,cν2 α1 +ν2,d ν1α2
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Interaction between Zwitterionic Surfactants and Amphiphilic Drug: A Tensiometric Study
451
where
cmc = (ν1α1 +ν2α2)cmc
(8)
(9)
and
νiαi
= ν1α1 +ν2α2
αi
(i = 1, 2)
νi is the number of ions dissociated by the ith component, νi = ν1 +ν2, where ν1 = ν1a +
ν1c and ν2 = ν2b +ν2d (c and d are counterions).
In the above equation, XM1 oto is the micellar mole fraction of surfactant, αi the bulk
mole fraction. δdc is Kronecker delta which is equal to 1 for identical counterions (d = c)
and 0 for no or different counterions (d = c).
For zwitterionic gemini-drug systems Eq. (10) reduces to
ꢂ
ꢃ ꢂ
ꢃ
α1 α2
∂cmc
∂α1
XM1 oto = α1 −
(10)
cmc
T,P
Analogous to Rubingh’s theory, Rosen proposed a model for mixed monolay-
ers [47] in which, instead of cmc values, concentrations (of pure components and their
mixtures required to produce a given surface tension value) are used.
Both Xm1 and X1Moto values for mixed systems increase with increase in α1. With the
increase in mole fraction of zwitterionic surfactant in mixed systems, contribution of
surfactants in mixed micelles also increase. It seems that the added surfactant replaces
some of the drug molecules from mixed micelles resulting in some reduction in steric
hindrance in the micellar core. The values obtained for our systems are given in Table 3.
σ
For few systems equation for X1 is non-convergent. In most of the cases, Xm1 values are
slightly higher than Xσ1 . As the surfactants contain two hydrophobic tails, they prefer
to form micelles and, hence, mixed micelles are rich in gemini surfactants. The drug
molecules, on the other hand, due to the rigid hydrophobic moiety, prefer to adsorb on
the air/water interface (as it is difficult for them to accommodate in curved areas). The
mixed monolayer is thus richer in the drug. With the increase in α1, in most of the cases,
Xm1 values increase whereas X1σ values decrease. With the increase in α1, more and
more surfactant contributes in mixed micelles (i.e., Xm1 increases) and its contribution
in mixed monolayer (i.e., Xσ1 ) decreases.
The micellar mole fraction in the ideal mixing state (Xi1d) for the respective mixtures
can be computed using the equation:
α1cmc2
Xi1d =
(11)
(α1cmc2 +α2cmc1)
These values are also given in Table 3. In all the cases, Xi1d > X1m, i.e., the mixed
micelles are poorer in surfactants over their values in ideal mixtures. As the gemini
surfactants are more hydrophobic than the drug, ideally the micelles should contain sur-
factant upto 90–95%. However, mixed micelles contain some drug molecules also, may
be because of the negative charge on one of the head groups of zwitterionic surfactants.
As the length of the two tails of the surfactants increases the behavior of a few systems
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W. H. Ansari et al.
Table 3. Solution properties of gemini surfactant-AMT mixed systems.
Surfactant
mole frac-
tion (α1)
ΔGmex
X1m
XM1 oto
Xi1d
KT
(K)
ΔHf◦
βm
f1m
f2m
(kJ mol−1
)
(kJ mol−1
)
8(−)-2-12(+)
0.125
0.10
0.075
0.05
−0.87
−0.39
−0.95
−0.23
−0.72
0.849
0.892
0.813
0.878
0.747
0.972
0.964
0.951
0.927
0.862
−2.716
−1.616
−2.488
−0.853
−1.524
0.939
0.981
0.916
0.987
0.907
0.141
0.276
0.193
0.518
0.427
0.991
0.317
0.025
8(−)-2-14(+)
0.125
0.10
0.075
0.05
−0.61
−0.78
−1.15
−1.43
−0.3
0.905
0.879
0.838
0.798
0.681
0.988
0.984
0.979
0.968
0.937
−2.807
−2.929
−3.356
−3.534
−5.475
0.975
0.958
0.915
0.865
0.573
0.100
0.104
0.095
0.105
0.079
0.688
0.342
0.151
0.025
8(−)-2-16(+)
0.125
0.10
0.075
0.05
−0.42
−1.32
−1.85
−1.90
−3.56
0.719
0.838
0.792
0.771
0.667
0.989
0.986
0.980
0.971
0.942
289
288.5
288
77.15
35.36
40.76
32.89
−8.243
−3.877
−4.467
−4.273
−6.359
0.521
0.903
0.824
0.799
0.494
0.014
0.065
0.060
0.079
0.059
0.876
0.415
0.192
286.5
0.025
10(−)-2-12(+)
0.125
0.10
0.075
0.05
−3.52
−0.40
−0.64
−0.94
−1.14
0.703
0.893
0.844
0.787
0.714
0.972
0.965
0.953
0.929
0.865
−6.697
−1.666
−1.940
−2.222
−2.227
0.554
0.981
0.954
0.904
0.833
0.036
0.265
0.251
0.252
0.321
0.647
0.196
0.025
10(−)-2-14(+)
0.125
0.10
0.075
0.05
−7.17
−7.04
−4.82
−3.59
−4.02
0.648
0.643
0.673
0.69
0.986
0.982
0.976
0.964
0.929
−12.473
−12.168
−8.701
−6.669
−6.965
0.213
0.212
0.394
0.527
0.413
0.005
0.006
0.019
0.041
0.055
0.853
0.291
0.025
0.644
10(−)-2-16(+)
0.125
0.10
0.075
0.05
−3.89
−4.35
−3.91
−2.31
−2.48
0.739
0.716
0.718
0.764
0.722
0.992
0.989
0.986
0.978
0.957
285.5
23.49
24.54
21.94
16.22
−7.999
−8.498
−7.672
−5.078
−4.916
0.58
0.012
0.013
0.019
0.051
0.077
285
284
283
0.503
0.543
0.753
0.684
0.930
0.273
0.025
12(−)-2-12(+)
0.125
0.10
0.075
0.05
−2.13
−0.69
−0.64
−1.00
−1.16
0.791
0.889
0.875
0.822
0.766
0.985
0.982
0.975
0.962
0.926
−5.108
−2.771
−2.321
−2.708
−2.576
0.800
0.966
0.964
0.918
0.868
0.041
0.112
0.169
0.160
0.220
0.430
0.125
0.025
12(−)-2-14(+)
0.125
0.10
0.075
0.05
−0.46
−0.33
−1.10
−0.92
−0.36
0.93
0.992
0.989
0.986
0.978
0.957
−2.834
−2.375
−3.528
−2.974
−1.452
0.986
0.992
0.928
0.941
0.982
0.086
0.122
0.076
0.112
0.318
0.941
0.855
0.857
0.888
0.783
0.347
0.086
0.025
12(−)-2-16(+)
0.125
0.10
0.075
0.05
−1.28
−1.86
−1.25
−2.12
−2.02
0.869
0.824
0.858
0.783
0.758
0.993
0.992
0.989
0.983
0.966
287
286
285
284.5
9.07
11.43
8.32
−4.480
−5.092
−4.075
−4.962
−4.376
0.925
0.854
0.921
0.791
0.773
0.034
0.031
0.049
0.047
0.081
0.621
0.351
0.097
12.77
0.025
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Interaction between Zwitterionic Surfactants and Amphiphilic Drug: A Tensiometric Study
453
changes: Xm1 decreases which may be due to the overcrowding of chains in the micellar
core.
3.1.6 Interaction parameters
The β parameters measure the interaction between two amphiphiles after mixing rela-
tive to the self-interaction of those amphiphiles before mixing under the same condi-
tions. Negative β values indicate synergism while positive values mean antagonism. β
values close to zero mean almost ideal mixing. In our systems both the interaction pa-
rameters for mixed micelles (βm) and mixed monolayers (βσ ) are negative indicating
synergism in the systems. These values are shown in Tables 2 and 3. The values (both
βm and βσ ) should, however, remain constant for a given amphiphile pair. The non-
constancy of β with composition have been reported previously also [50]. βσ is greater
than βm for the systems in which either the tails are small or the difference in length of
two tails is small.
3.1.7 Activity coefficients
The values of activity coefficients are given in Tables 2 and 3. These values are always
σ
less than unity indicating the mixing to be nonideal. Both f1m and f1 are much greater
than f2m and f2σ and are close to unity which means that surfactants in the mixed systems
are near to their standard state.
3.2 Krafft temperature behaviour
Tables 1 and 3 contain the values of KT for pure surfactant and some mixed systems.
We could not obtain the KT value for some pure as well as mixed systems as they were
below 0 ◦C. With the increase in mole fraction of surfactant KT increases. As the total
number of carbon atom in the hydrophobic tail increases, KT increases, but for the same
number of carbon atoms, the greater the difference in tail lengths the higher is the KT
value. These values were used to evaluate the heat of fusion of solid surfactant hydrate
to liquid hydrates (ΔHf◦) as [51]
ꢄ
ꢅ
TT10
T10 − T
ΔHf◦ = −R ln Xm1
(12)
where T10 and T are the Krafft temperatures of pure surfactant and its mixtures, re-
spectively. The ΔH◦ values show large variation with increasing α1 in 8(−)-2-16(+)
systems, again confifrming strong synergism in the mixed micelles (Table 3).
3.3 Thermodynamics of mixing
3.3.1 Standard Gibbs energy of micellization
The standard Gibbs energy of micellization, ΔG◦mic, was calculated using the well
known equation
ΔG◦mic = RT ln Xcmc
(13)
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W. H. Ansari et al.
Fig. 3. Plots of ΔG◦ad (filled symbols) and ΔGomic (unfilled symbols) vs. mole fraction (α1) of gemini sur-
factants (A) and Gmin vs. mole fraction (α1) of gemini surfactants (B).
where Xcmc is the mixture cmc in the mole fraction units. The values are shown in
Fig. 3A. For pure components, these values are given in Table 1. The values are all
negative confirming that the process of micellization is spontaneous. The magnitude of
ΔG◦mic values varies with the type and mole fraction of the gemini surfactants. The mag-
nitude is smaller for drug in comparison to that of gemini surfactants. Due to its short
hydrophobic portion, the drug is less hydrophobic than the gemini surfactants.
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Interaction between Zwitterionic Surfactants and Amphiphilic Drug: A Tensiometric Study
455
The values for mixtures are intermediate to those of single components. Presence of
a gemini surfactant makes the process of micellization more spontaneous than for pure
drug.
3.3.2 Standard Gibbs energy of adsorption
The standard Gibbs energy of adsorption is given by [52]
πcmc
ΔG◦ad = ΔG◦mic
−
(14)
Γmax
where πcmc is the surface pressure at the cmc. These values are shown in Fig. 3A which
are also negative indicating the process of adsorption to be spontaneous. Moreover, the
absolute values of ΔG◦ad are greater than that ofΔGm◦ ic. This means that the hydropho-
bicity of the molecules leads them towards the air/solution interface and after surface
adsorption, micellization takes place.
3.3.3 Minimum free energy of adsorption
The values of molar free energy at the maximum adsorption attained at cmc, Gmin, are
calculated according to Eq. (15) [53]
Gmin = γcmc Amin NA
(15)
In other words, Gmin is the minimum free energy of the given surface with fully ad-
sorbed amphiphile molecules. The smaller is the value of Gmin, the more stable surface
forms. Hence, as expected, the values of Gmin for surfactants are smaller than that of
drug and for mixtures the values decrease with the increase in gemini surfactant content
in the solution (Fig. 3B).
3.3.4 Excess free energy of mixing
Excess free energy of mixing, ΔGemx, was calculated from the values of f1m and f2m by
ΔGmex = RT[X1m ln f1m +(1− Xm1 ) ln f2m]
(16)
The values are all negative (Table 3) suggesting mixed micelles to be relatively more
stable than the micelles of individual components. Except in one or two cases, the ab-
solute value decreases with the increase in α1. Thus, increasing concentration of gemini
surfactants increases the stability of mixed micelles.
3.4 Stability of mixed micelles
Figure 4 depicts the UV spectra of pure drug as well as its mixtures with zwitterionic
surfactants. The spectra recorded at different time intervals (just after preparation and
after 3, 7 and 15 days) show absorption maxima at around 210 to 260 nm. There is
hardly any change in spectra even after 15 days implying that the mixed micelles are
quite stable for the period.
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W. H. Ansari et al.
Fig. 4. UV-vis spectra of pure AMT (A) and 8(−)-2-12(+)-AMT mixed systems (B) at α1 = 0.075, just
after preparation ( ), 3 ( ), 7 ( ) and 15 ( ) days.
4. Conclusions
We have investigated the interactions among an amphiphilic drug amitriptyline hy-
drochloride (AMT) and nine zwitterionic heterogemini surfactants which have a phos-
phodiester (anionic) and a quaternary ammonium (cationic) polar heads (denoted as
n(−)-2-m(+), n = 8, 10, 12 and m = 12, 14, 16). To the best of our knowledge, this
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Interaction between Zwitterionic Surfactants and Amphiphilic Drug: A Tensiometric Study
457
is the first report dealing with detailed physicochemical investigations on mixed micel-
lization involving AMT and zwitterionic heterogemini surfactants. The mixed systems
have cmc values lower than the individual components and ideal cmc values. The
cmc values and interaction parameters (βm) suggest strong attractive interactions in the
mixed micelles. The results get support from Krafft temperature measurements as ΔHf◦
values (calculated from KT values) show variations. The surface excess (Γmax) increases
and minimum area per head group (Amin) decreases with increasing stoichiometric mole
fraction (α1) of the surfactant. The values are closer to that of the pure drug. Appli-
cation of the Rubingh’s, Motomura’s and Rosen’s theoretical approaches also shows
synergism in all the drug-surfactant systems. Micellar mole fraction (Xm1 ) values indi-
cate larger contribution from surfactants. Micellar mole fraction (XM1 oto) evaluated from
Motomura’s model, are in line with that obtained by Rubingh’s model. Mole fraction
values at mixed interface (Xσ1 ) are slightly smaller than Xm1 which means that the drug
participates more in monolayer formation than in micelle formation. Rigid ring system
of the drug makes easier for it to adjust at the planar air/solution interface. The UV-
spectra of pure drug as well as its mixtures show maxima in absorption at 210 to 260 nm
in all systems that remain constant upto 15 days. This suggests that the mixed micelles
remain stable after long time.
Acknowledgement
Sahar Noori is thankful to MANF for financial support and Kabir-ud-Din thanks the
UGC for awarding BSR-Faculty Fellowship. Andleeb Z. Naqvi acknowledges financial
assistance under DST’s SERC Scheme (SR/FT/CS-82/2011).
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