Mixed Micelle Formation between Amphiphilic Drug Amitriptyline

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J. Phys. Chem. B 2010, 114, 6354–6364

Mixed Micelle Formation between Amphiphilic Drug Amitriptyline Hydrochloride and Surfactants (Conventional and Gemini) at 293.15-308.15 K Kabir-ud-Din,* Malik Abdul Rub, and Andleeb Z. Naqvi Department of Chemistry, Aligarh Muslim UniVersity, Aligarh, 202002, UP, India ReceiVed: January 6, 2010; ReVised Manuscript ReceiVed: March 13, 2010

The micellization of amphiphilic drug amitriptyline hydrochloride (AMT, an antidepressant) and conventional as well as gemini surfactants has been studied conductometrically in pure and mixed states in aqueous solutions at different temperatures to derive various physicochemical properties such as critical micelle concentration (cmc), ideal cmc (cmcid), counterion dissociation (g), standard Gibbs free energy (∆Gm0), enthalpy (∆Hm0), and entropy of micellization (∆Sm0), micellar mole fractions of surfactant (X1, Xm 1 ), mole fraction of surfactant in ideal state (Xid 1 ), interaction parameter (β), activity coefficients (f1, f2), and excess free energy of mixing (∆Gex). All the results indicate synergism and attractive interactions in the mixed systems. 1. Introduction In recent years, much research has been directed toward the study of mixed amphiphile systems.1-6 A mixed amphiphile system can exhibit surface and colloidal properties different from those of the pure individual components. Nonideal mixing of amphiphilic components often causes synergism in the properties of the mixtures that may be exploited in their applications. When a mixed amphiphile system shows lower critical micelle concentration (cmc) values than that of pure components, the system is said to be synergistic. As a result, mixed micelles are commonly used in pharmaceutical formulations, in industries, and in enhanced oil recovery processes.7-9 As compared to the single head, single tail conventional surfactants, gemini (or dimeric) surfactants consist of two amphiphilic monomers connected at the level of headgroups (Scheme 1). Compared to their monomeric counterparts, the geminis have much lower cmc as well as much greater efficiency in reducing the surface tension of water. Cationic gemini surfactants, besides their surface activity, also show antibacterial properties.10,11 It is known that the spacer chain largely influences the physicochemical properties of these surfactants.12 In micelles formed by single head/single tail surfactants, only the thermodynamic equilibrium distance between polar headgroups is considered. For gemini surfactants, however, two headgroup distances control the process of micellization, one corresponding to the single-tail surfactant equilibrium distance and another corresponding to the length and nature of spacer.13 Amitriptyline hydrochloride (AMT) is a drug that belongs to the family of tricyclic antidepressants. It possesses a rigid, almost planar tricyclic ring system and a short hydrocarbon chain carrying a terminal nitrogen atom (Scheme 1). It is amphiphilic and earlier studies have established that aggregates of 6-12 drug molecules are formed in water above the cmc.14,15 AMT suffers from several drawbacks such as anticholinergic, cardiovascular and antiarrhythmic side effects. These undesirable side effects may be reduced if the drug is properly targeted to the organism. Surfactant aggregation gives rise to regions of different physicochemical properties. The headgroup region (of entities * To whom correspondence should be addressed: Tel.: +91 571 2703515. E-mail: [email protected].

SCHEME 1: Structure of (a) Conventional Surfactant, (b) Gemini Surfactant, and (c) Amitriptyline Hydrochloride (AMT)

formed on aggregation, the so-called micelles) provides a highly polar environment while the core provides a low polarity region. These micelles are, hence, capable of encapsulating drugs in their core and improving the drug’s water solubility and bioavailability and protecting them from destructive factors upon parenteral administration.16,17 Keeping the above in view and the fact that surfactant micelles, like many other amphiphilic substances, are potentially important encapsulating/solubilizing agents, we have performed conductometric measurements on AMT-surfactant mixed systems. The approaches of Clint, Rubingh, and Motomura have been utilized to obtain various parameters related to mixed micelles. Also, the effect of temperature is seen on the micellization process, and thermodynamic parameters such as ∆Gm0, ∆Hm0, ∆Sm0 are evaluated. The surfactants used are the so-called alkanediyl-R,ω-bis(dimethylalkylammonium bromide), m-s-m-type cationic geminis

10.1021/jp100123r  2010 American Chemical Society Published on Web 04/27/2010

Micelle Formation between AMT and Surfactants

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with m ) 14 or 16 and s ) 4, 5, 6 and their monomeric counterparts, that is, tetradecyltrimethylammonium bromide (TTAB), and cetyltrimethylammonium bromide (CTAB). 2. Experimental Section Materials. Amitriptyline hydrochloride (AMT, catalogue no. A8404, 98%, Sigma, Germany), tetradecyltrimethylammonium bromide (TTAB, 99%, Sigma, Germany), and cetyltrimethylammonium bromide (CTAB, 99%, Merck, Germany) were used as received. Cationic gemini surfactants were synthesized by refluxing R,ω-dibromoalkane (butane, pentane, or hexane) with a slight excess of N,N-dimethylalkylamine (tetradecyl or cetyl) in dry ethanol for 2-3 days followed by more than four recrystallizations from a mixture of ethanol and ethylacetate.18 All the compounds had satisfactory 1H NMR, IR, and mass spectra. Conductometry. An ELICO conductivity meter (model CM 180) was used to perform the experiments. A 12 mL portion of water (double-distilled) was taken in a cell dipped in a thermostatic water bath. A dip-type conductivity cell of cell constant 1.026 cm-1 was inserted into the water. A known volume of concentrated solution of drug (160 mM) was then added to the water with a pipet (J Sil, India, accuracy of (0.01 mL) and thoroughly mixed, followed by measurement of the conductance. A similar process was repeated each time an addition of drug solution was made. For drug-surfactant mixtures, the surfactant solutions of fixed concentration were used as solvent. The specific conductance (K) was then plotted against drug concentration. The plots showed change in slope above a certain concentration. The break in plot, that is, the point at which slope changes, is considered as the cmc of the solution. Values of the ratio of slopes were used to obtain the degree of counterion dissociation (g), which is the ratio of postmicellar slope to premicellar slope. 3. Results and Discussions Aqueous solutions of amphiphiles behave as simple electrolytes and follow the Onsager equation at low concentrations. Above a certain concentration, however, the behavior deviates from Onsager equation and the conductivity decreases markedly. Plots of specific conductance versus AMT concentration with and without surfactant (16-6-16) at 298.15 K are shown in Figure 1. Figure 2 shows the effect of mole fraction of the added surfactant (R1) and temperature on the cmc of drug-surfactant mixtures (evaluated on the basis of conductance measurements). The cmc values of pure components agree well with the literature.14,19-21 The cmc values, along with other relevant parameters such as ideal cmc (cmcid), degree of counterion dissociation (g), standard Gibbs free energy (∆Gm0), enthalpy (∆Hm0), and entropy of micellization (∆Sm0), mole fraction of surfactant in ideal state (X1id), interaction parameter (β), and activity coefficients (f1, f2), are recorded in Tables 1-3 for AMT and conventional and gemini surfactants in pure and mixed state. As the hydrophobic group of the drug molecule consists of three rings and is rigid, it is difficult for the drug molecules to adjust in the curved area of a micelle. Therefore, the drug forms micelles, but at high concentrations, as compared to the surfactants. An increase in chain length of the hydrophobic part of the surfactant releases more water molecules causing an increase in entropy. Hence, in a homologous series of surfactants cmc decreases with an increase in the length of hydrophobic tail of the surfactant. Similarly, two hydrophobic chains of a gemini surfactant break more water structure and thus increase

Figure 1. Representative plots of specific conductance vs concentration of AMT with (b) and without (O) surfactant (16-6-16) at 298.15 K.

the tendency to form micelles. Thus, the cmc values are lower for gemini surfactants. Figure 3 and Tables 1-3 show that, as the temperature increases from 293.15 to 308.15 K, the two components behave differently. The surfactants behave in the normal way. As the temperature increases, cmc also increases. An increase in temperature increases the thermal agitation in the solution resulting in a decreasing adhesion between monomers. The observance of no minima in the cmc-temperature curve for CTAB and TTAB have been reported in previous literature too.22-25 However, the drug behaves in the opposite manner: its cmc increases when the the temperature increases from 293.15 to 303.15 K and then decreases at 308.15 K. A similar behavior was observed by Lopez Fontan et al.26 for clomipramine hydrochloride. The decrease in cmc indicates that at high temperature, water associated with drug molecules is released and this factor dominates in micelle formation. As surfactants are added to the drug solution, the cmc decreases. It is well-known that drugs form mixed micelles with the surfactants.3,27,28 The cmc values of mixed systems usually fall in between the cmc values of pure components. In our systems too, the cmc values of the mixed systems lie in between the cmc values of pure amphiphiles. It is clear from Figure 2 that the geminis are more effective in reducing the cmc of the drug as compared to conventional surfactants. Clint’s eq 1 is used to calculate the values of ideal cmc (cmcid):

1 ) cmcid

2

R

∑ cmci i

(1)

i)1

where Ri and cmci are the mole fraction and cmc of ith component. Any deviation of experimentally determined cmc from cmcid would account for mutual interactions among amphiphiles. A positive deviation, that is, cmcid < cmc, means antagonism, whereas a negative deviation, cmcid > cmc, indicates synergism. In the present case, cmcid values are found to be greater than the experimental cmc, indicating synergism in the system. In ionic micelles, most of the counterions are bound strongly to the Stern layer. As some of the counterions remain bound to the amphiphile molecules even above the cmc, the ratio of values

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TABLE 1: The Physicochemical Parameters for Conventional Surfactants (Cationic)-AMT Mixed Systems at Various Temperatures (Evaluated on the Basis of Conductance Measurements) R1

cmc (mM)

0 4.49 - 10-6 8.98 × 10-6 13.47 × 10-6 16.17 × 10-6 1.0

29.30 26.29 24.14 22.94 21.59 0.93

0 4.49 × 10-6 8.98 × 10-6 13.47 × 10-6 16.17 × 10-6 1.0

31.23 28.57 27.65 25.89 24.21 0.99

0 4.49 - 10-6 8.98 × 10-6 13.47 × 10-6 16.17 × 10-6 1.0

32.60 30.57 29.01 27.95 26.30 1.04

0 4.49 × 10-6 8.98 × 10-6 13.47 × 10-6 16.17 × 10-6 1.0

29.64 27.75 26.57 25.46 24.0 1.13

0 13.47 26.95 40.42 53.90 1.0

10 10-6 10-6 10-6

29.30 27.60 25.85 22.21 21.85 3.15

× × × ×

10-6 10-6 10-6 10-6

31.23 28.32 26.85 24.75 23.25 3.42

× × × ×

-6

10 10-6 10-6 10-6

× × × ×

-6

0 13.47 26.95 40.42 53.90 1.0 0 13.47 26.95 40.42 53.90 1.0 0 13.47 26.95 40.42 53.90 1.0

× × × ×

-6

10 10-6 10-6 10-6

32.60 29.16 27.38 25.42 24.04 3.61 29.64 27.80 26.40 23.70 22.15 3.93

g

-∆Gm0 (kJ mol-1)

29.30 29.29 29.29 29.29

0.65 0.66 0.68 0.65 0.72 0.29

24.9 25.1 24.8 25.7 24.4 45.7

CTAB, T ) 293.15 K 10.3 49.7 14.5 36.2 17.3 25.8 19.1 22.6 18.0 22.0 15.8 102.0

31.23 31.22 31.22 31.21

0.65 0.67 0.66 0.70 0.72 0.26

25.0 25.0 25.3 24.7 24.5 47.1

CTAB, T ) 298.15 K 10.6 48.2 14.8 34.1 18.2 23.8 18.9 19.3 18.6 19.8 16.7 102.1

32.60 32.59 32.59 32.58

0.69 0.67 0.70 0.68 0.69 0.24

24.5 25.2 24.8 25.2 25.3 48.2

CTAB, T ) 303.15 K 10.7 45.8 15.3 32.5 18.3 21.6 19.9 17.6 19.8 18.3 17.4 101.5

29.64 29.63 29.63 29.63

0.71 0.72 0.72 0.72 0.68 0.30

24.9 24.9 25.0 25.3 26.1 47.1

CTAB, T ) 308.15 K -19.3 143.5 -19.5 144.0 -17.7 138.7 -18.9 143.5 -19.0 146.4 17.5 96.3

29.30 29.29 29.29 29.29

0.65 0.63 0.65 0.69 0.73 0.30

24.9 25.5 25.2 25.0 24.4 40.5

TTAB, T ) 293.15 K 10.3 49.7 5.4 68.6 5.5 67.1 14.0 37.6 8.7 53.6 17.9 77.1

31.23 31.22 31.22 31.22

0.65 0.65 0.67 0.68 0.70 0.31

25.0 25.4 25.1 25.3 25.1 40.7

TTAB, T ) 298.15 K 10.6 48.2 5.5 66.7 5.6 65.4 14.6 35.9 9.1 53.5 18.5 74.6

32.60 32.59 32.59 32.59

0.69 0.67 0.66 0.67 0.72 0.31

24.5 25.3 25.8 25.7 25.0 41.2

TTAB, T ) 303.15 K 10.7 45.8 5.6 65.0 5.9 65.5 15.2 34.9 9.3 51.9 19.1 72.8

29.64 29.63 29.63 29.63

0.71 0.70 0.71 0.71 0.72 0.46

24.9 25.4 25.2 25.7 25.7 37.7

TTAB, T ) 308.15 K -19.3 143.5 -9.8 114.1 -7.4 105.8 -14.3 129.7 -16.5 136.7 17.9 64.1

cmcid (mM)

-∆Hm0 (kJ mol-1)

of slopes gives the degree of counterion dissociation. The degree of dissociation (g) decreases with an increase in electrolyte concentration29 and may decrease with micellar growth.30 Also, with the increase in temperature, cmc values increase and micellar growth decreases. Therefore, we can safely conclude that with the increase in temperature, an increase in g is expected, which is also observed in the case of ionic surfactants (where degree of binding decreases with increase in temperature).31-34 We have obtained a similar trend of g values (Tables 1-3); that is, with the increase in cmc and temperature, g also increases. In ionic amphiphiles, the larger the hydrated radius of the counterion, the weaker the degree of binding or the greater the degree of dissociation. Thus, Br- ions bind more strongly than Cl- ions. Therefore, g values are smaller for CTAB and TTAB than for AMT-surfactant mixtures (Tables 1-3). The values of standard free energy (∆Gm0), enthalpy (∆Hm0), and entropy of micellization (∆Sm0) of mixed systems were

∆Sm0 (J K-1 mol-1)

X1id

β

f1

f2

-∆Gex (kJ mol-1)

0.0001 0.0003 0.0004 0.0005

-7.30 -7.62 -7.67 -7.99

0.0018 0.0022 0.0027 0.0027

0.9648 0.92 0.8918 0.8562

1.2 1.7 2.0 2.3

0.0001 0.0003 0.0004 0.0005

-6.98 -6.75 -7.10 -7.55

0.0021 0.0032 0.0033 0.0031

0.9743 0.9256 0.9256 0.8869

1.0 1.2 1.6 2.1

0.0001 0.0003 0.0004 0.0005

-6.51 -6.68 -6.72 -7.18

0.0027 0.0033 0.0039 0.0036

0.9851 0.9625 0.9443 0.9106

0.8 1.2 1.4 1.8

0.0001 0.0002 0.0004 0.0004

-6.73 -6.77 -6.90 -7.34

0.0023 0.0029 0.0033 0.0031

0.9842 0.9657 0.9447 0.9119

0.8 1.2 1.5 1.9

0.0001 0.0003 0.0004 0.0005

-6.53 -6.93 -8.10 -7.91

0.0026 0.0028 0.0022 0.0027

0.9867 0.9578 0.8715 0.8631

0.7 1.2 2.2 2.3

0.0001 0.0002 0.0004 0.0005

-7.28 -7.29 -7.71 -7.95

0.0017 0.0024 0.0025 0.0027

0.9697 0.9437 0.8984 0.8620

1.1 1.5 2.0 2.3

0.0001 0.0002 0.0004 0.0005

-7.51 -7.57 -7.88 -8.04

0.0015 0.0021 0.0023 0.0026

0.9627 0.9305 0.8885 0.8559

1.3 1.7 2.1 2.4

0.0001 0.0002 0.0003 0.0004

-6.85 -7.02 -7.84 -8.13

0.0020 0.0024 0.0021 0.0023

0.9847 0.9620 0.9026 0.8632

0.8 1.2 2.0 2.4

evaluated using the following relations: ∆Gm0 ) (2 - g)RT ln Xcmc

(

∆Hm0 ) (2 - g)RT2

∆Sm0 )

d ln Xcmc dT

∆Hm0 - ∆Gm0 T

(2)

)

(3)

(4)

For pure gemini surfactants, modified forms of eqs 2 and 3 are used:35 ∆Gm0 ) (3 - 2g)RT ln Xcmc

(5)



TABLE 2: The Physicochemical Parameters for Gemini Surfactants (16-s-16)-AMT Mixed Systems at Various Temperatures (Evaluated on the Basis of Conductance Measurements) R1 0 1.80 2.69 3.59 4.49 1.0

cmc (mM)

cmcid (mM)

g

-∆Gm0 (kJ mol-1)

-∆Hm0 (kJ mol-1)

∆Sm0 (J K-1 mol-1)

29.29 29.29 29.29 29.28

0.65 0.64 0.65 0.65 0.65 0.56

24.9 31.9 31.5 31.7 32.1 67.3

16-4-16, T ) 293.15 K 10.3 49.7 7.6 83.1 9.2 76.1 8.6 78.7 10.3 74.2 32.8 117.6

31.22 31.22 31.22 31.21

0.65 0.66 0.68 0.70 0.68 0.57

25.0 31.4 31.1 30.4 31.1 66.7

16-4-16, T ) 298.15 K 10.6 48.2 7.6 79.7 9.3 73.1 8.4 73.8 10.2 69.9 33.4 111.9

24.5 31.5 30.0 30.2 31.4 70.3

16-4-16, T ) 303.15 K 10.7 45.8 7.8 78.3 9.2 68.8 8.5 71.3 10.5 68.7 36.1 112.9

× × × ×

10-7 10-7 10-7 10-7

29.30 27.50 26.40 25.80 24.90 0.025

× × × ×

10-7 10-7 10-7 10-7

31.23 28.60 27.40 26.90 25.95 0.028

0 1.80 2.69 3.59 4.49 1.0

× × × ×

10-7 10-7 10-7 10-7

32.60 29.95 28.50 27.7 27.1 0.032

32.59 32.59 32.59 32.59

0.69 0.67 0.71 0.71 0.68 0.53

0 1.80 2.69 3.59 4.49 1.0

× × × ×

10-7 10-7 10-7 10-7

29.64 27.95 26.65 26.04 25.1 0.036

29.64 29.63 29.63 29.63

0.71 0.73 0.71 0.72 0.73 0.61

24.9 29.9 31.0 30.7 30.2 65.2

16-4-16, T ) 308.15 K -19.3 143.5 -11.0 132.9 -16.8 154.9 -15.3 149.3 -18.5 158.2 34.3 100.4

0 2.69 3.59 4.49 5.39 1.0

× × × ×

10-7 10-7 10-7 10-7

29.30 25.01 24.30 23.32 22.48 0.027

29.29 29.29 29.29 29.28

0.65 0.63 0.69 0.67 0.65 0.64

24.9 32.8 30.4 31.6 32.3 61.1

16-5-16, T ) 293.15 K 10.3 49.7 13.6 65.3 12.4 61.5 13.5 61.7 15.3 58.1 32.3 98.3

0 2.69 3.59 4.49 5.39 1.0

× × ×

10-7 10-7 10-7 10-7

31.23 27.06 25.95 25.28 24.52 0.031

31.22 31.22 31.22 31.21

0.65 0.68 0.65 0.69 0.69 0.65

25.0 31.2 32.3 31.0 31.2 60.9

16-5-16, T ) 298.15 K 10.6 48.2 13.3 59.9 13.5 63.0 13.6 58.3 15.2 53.7 33.0 93.4

10-7 10-7 10-7 10-7

32.60 27.90 27.06 26.21 25.50 0.035

32.59 32.59 32.59 32.58

0.69 0.70 0.69 0.72 0.70 0.65

24.5 30.5 31.3 30.2 31.2 61.0

16-5-16, T ) 303.15 K 10.7 45.8 13.3 56.8 13.4 59.2 13.5 55.0 15.5 51.8 34.0 89.3

10-7 10-7 10-7 10-7

29.64 25.35 24.61 23.85 23.1 0.040

29.63 29.63 29.63 29.63

0.71 0.68 0.72 0.72 0.72 0.62

24.9 32.2 31.1 31.0 31.2 64.2

16-5-16, T ) 308.15 K -19.3 143.5 -24.7 184.8 -23.5 177.1 -22.1 173.4 -24.4 180.3 36.6 89.3

× × × ×

10-7 10-7 10-7 10-7

29.30 26.50 25.30 24.25 0.22.61 0.036

29.30 29.29 29.29 29.29

0.65 0.69 0.67 0.60 0.72 0.58

24.9 30.2 31.2 34.1 29.5 64.1

16-6-16, T ) 293.15 K 10.3 49.7 12.4 60.8 9.5 74.2 9.2 84.8 12.5 58.2 30.6 114.1

× × × ×

10-7 10-7 10-7 10-7

31.23 28.01 26.50 25.40 24.08 0.041

31.23 31.22 31.22 31.22

0.65 0.70 0.70 0.71 0.71 0.62

25.0 30.2 30.3 30.1 30.3 61.6

16-6-16, T ) 298.15 K 10.6 48.2 12.4 60.8 9.4 70.0 8.3 72.9 13.1 57.7 30.2 105.3

× × × ×

10-7 10-7 10-7 10-7

32.60 29.50 27.40 26.05 25.30 0.045

32.60 32.59 32.59 32.59

0.69 0.69 0.69 0.69 0.69 0.56

24.5 30.8 31.1 31.2 31.3 66.6

16-6-16, T ) 303.15 K 10.7 45.8 13.3 57.8 9.9 70.0 8.8 73.8 13.9 57.6 33.4 109.4

× × × ×

10-7 10-7 10-7 10-7

29.64 26.90 25.60 24.50 23.01 0.051

29.64 29.63 29.63 29.63

0.71 0.63 0.69 0.72 0.72 0.55

24.9 34.0 31.7 30.7 31.0 67.5

16-6-16, T ) 308.15 K -19.3 143.5 -25.3 192.2 -17.3 159.1 -15.0 148.4 -23.2 175.9 34.8 106.3

0 1.80 2.69 3.59 4.49 1.0

0 2.69 3.59 4.49 5.39 1.0 0 2.69 3.59 4.49 5.39 1.0 0 1.80 3.59 5.39 6.29 1 0 1.80 3.59 5.39 6.29 1 0 1.80 3.59 5.39 6.29 1 0 1.80 3.59 5.39 6.29 1

× × × ×

× × × ×

X1id

β

f1

f2

-∆Gex (kJ mol-1)

0.0002 0.0003 0.0004 0.0005

-6.07 -6.37 -6.39 -6.58

0.0041 0.0040 0.0046 0.0046

0.9860 0.9690 0.9586 0.9405

0.7 1.0 1.2 1.4

0.0002 0.0003 0.0004 0.0005

-6.60 -6.80 -6.73 -6.89

0.0030 0.0032 0.0038 0.0040

0.9755 0.9555 0.9466 0.9277

0.9 1.3 1.4 1.6

0.0002 0.0003 0.0004 0.0005

-7.03 -6.95 -6.99 -6.98

0.0023 0.0029 0.0033 0.0037

0.9654 0.9532 0.9388 0.9275

1.2 1.3 1.5 1.6

0.0001 0.0002 0.0003 0.0004

-6.33 -6.79 -6.80 -7.01

0.0031 0.0028 0.0032 0.0033

0.9873 0.9670 0.9561 0.9370

0.7 1.1 1.3 1.6

0.0003 0.0004 0.0005 0.0006

-7.18 -7.19 -7.36 -7.48

0.0027 0.0031 0.0033 0.0035

0.9404 0.9023 0.9023 0.8815

1.5 1.6 1.9 2.1

0.0003 0.0004 0.0005 0.0005

-7.08 -7.25 -7.27 -7.36

0.0027 0.0029 0.0033 0.0035

0.9484 0.9261 0.9121 0.8950

1.4 1.7 1.8 2.0

0.0003 0.0003 0.0004 0.0005

-7.32 -7.35 -7.43 -7.48

0.0024 0.0027 0.0029 0.0032

0.9413 0.9251 0.9075 0.8923

1.5 1.7 1.9 2.0

0.0002 0.0003 0.0003 0.0004

-7.58 -7.60 -7.68 -7.78

0.0019 0.0022 0.0024 0.0025

0.9401 0.9243 0.9069 0.8886

1.6 1.8 2.0 2.2

0.0001 0.0003 0.0004 0.0005

-7.14 -7.04 -7.08 -7.59

0.0020 0.0029 0.0035 0.0031

0.9688 0.9468 0.9248 0.8841

1.1 1.4 1.6 2.1

0.0001 0.0003 0.0004 0.0005

-7.34 -7.33 -7.33 -7.69

0.0017 0.0025 0.0030 0.0029

0.9645 0.9368 0.9144 0.8833

1.2 1.6 1.8 2.1

0.0001 0.0003 0.0004 0.0005

-7.26 -7.49 -7.57 -7.67

0.0018 0.0022 0.0027 0.0028

0.9689 0.9313 0.9035 0.8869

1.1 1.7 2.0 2.1

0.0001 0.0002 0.0003 0.0004

-7.44 -7.41 -7.47 -7.92

0.0015 0.0021 0.0025 0.0023

0.9698 0.9453 0.9224 0.8853

1.1 1.5 1.8 2.2

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Figure 2. Critical micelle concentration (cmc) vs mole fraction of surfactant (R1) in surfactant-AMT mixtures at different temperatures: 293.15 (9), 298.15 (b), 303.15 (2), 308.15 K (1); (a) 16-carbon chain, (b) 14-carbon chain.

∆Hm0 ) (3 - 2g)RT2

(

d ln Xcmc dT

)

(6)

where Xcmc is the cmc expressed in mole fraction units and R and T are gas constant and absolute temperature. The ∆Gm0 values are all negative and show slight variation with temper-

ature as well as with an increase in surfactant concentration (Tables 1-3). The values of ∆Gm0 for pure AMT are similar to those obtained for other antidepressants.36-38 The ∆Gm0 values for conventional surfactants, which also agree well with literature data,39 are more negative indicating that the micellization process is more spontaneous with surfactants than with



TABLE 3: The Physicochemical Parameters for Gemini Surfactants (14-s-14)-AMT Mixed Systems at Various Temperatures (Evaluated on the Basis of Conductance Measurements) R1 0 0.54 1.08 1.62 2.16 1.0

cmc (mM)

cmcid (mM)

g

-∆Gm0 (kJ mol-1)

-∆Hm0 (kJ mol-1)

∆Sm0 (JK-1 mol-1)

29.30 29.29 29.29 29.29

0.65 0.60 0.59 0.63 0.64 0.33

24.9 33.5 34.0 32.6 32.4 73.8

14-4-14, T ) 293.15 K 10.3 49.7 10.3 79.3 11.1 77.9 10.6 74.9 13.3 65.2 23.9 170.0

31.23 31.22 31.22 31.22

0.65 0.68 0.64 0.68 0.67 0.34

25.0 31.1 32.5 31.3 31.8 74.3

14-4-14, T ) 298.15 K 10.6 48.2 9.8 71.4 10.9 72.5 10.4 69.9 13.4 61.7 24.7 166.3

32.60 32.59 32.59 32.58

0.69 0.68 0.69 0.69 0.66 0.38

24.5 31.4 31.0 31.0 32.4 72.5

14-4-14, T ) 303.15 K 10.7 45.8 10.1 70.3 10.6 67.1 10.6 67.4 14.0 60.7 24.6 157.9

0.71 0.67 0.69 0.70 0.69

24.9 32.4 31.7 31.4 32.2

14-4-14, T ) 308.15 K -19.3 143.5 -19.0 166.7 -18.9 164.2 -19.1 163.7 -26.6 190.8

24.9 32.3 33.0 33.6 31.8 71.4

14-5-14, T ) 293.15 K 10.3 49.7 8.3 82.1 7.2 83.7 7.6 88.7 6.4 86.5 28.2 147.5

× × × ×

10-6 10-6 10-6 10-6

29.30 26.30 25.6 25.15 24.04 0.13

× × × ×

10-6 10-6 10-6 10-6

31.23 27.23 26.8 26.5 25.6 0.14

× × × ×

10-6 10-6 10-6 10-6

32.60 28.50 27.90 27.40 26.8 0.15

× × × ×

10-6 10-6 10-6 10-6

29.64 26.50 25.90 25.40 24.15

0 0.63 1.26 1.89 2.52 1.0

× × × ×

10-6 10-6 10-6 10-6

29.30 26.08 25.60 25.01 24.7 0.13

29.30 29.29 29.29 29.28

0.65 0.63 0.62 0.60 0.66 0.37

0 0.63 1.26 1.89 2.52 1.0

× × × ×

10-6 10-6 10-6 10-6

31.23 26.90 26.20 25.75 25.30 0.15

31.23 31.22 31.22 31.21

0.65 0.66 0.65 0.66 0.65 0.38

25.0 31.8 32.1 32.0 32.5 70.9

14-5-14, T ) 298.15 K 10.6 48.2 8.3 78.9 7.2 83.7 7.4 82.4 6.7 86.6 28.7 141.5

0 0.63 1.26 1.89 2.52 1.0

× × × ×

10-6 10-6 10-6 10-6

32.60 27.85 27.01 26.55 26.08 0.16

32.60 32.59 32.59 32.58

0.69 0.67 0.67 0.67 0.69 0.39

24.5 31.8 32.0 32.0 31.4 71.2

14-5-14, T ) 303.15 K 10.7 45.8 8.5 76.9 7.3 81.4 7.6 80.6 6.6 81.8 29.5 137.4

× × × ×

10-6 10-6 10-6 10-6

29.64 26.36 25.80 25.32 25.02 0.17

29.64 29.63 29.63 29.63

0.71 0.69 0.68 0.70 0.70 0.40

24.9 31.6 32.4 31.5 31.4 71.7

14-5-14, T ) 308.15 K -19.3 143.5 -14.0 148.0 -11.9 144.0 -12.0 141.0 -10.1 134.7 30.4 134.2

× × × ×

10-6 10-6 10-6 10-6

29.30 27.15 26.30 25.05 24.5 0.14

29.30 29.29 29.29 29.28

0.65 0.62 0.62 0.59 0.64 0.39

24.9 32.6 32.5 34.0 32.5 69.9

14-6-14, T ) 293.15 K 10.3 49.7 10.8 74.2 11.1 73.1 13.0 71.7 11.5 71.6 30.1 135.7

10-6 10-6 10-6 10-6

31.23 28.75 27.60 26.50 25.75 0.16

31.23 31.22 31.22 31.21

0.65 0.67 0.67 0.64 0.68 0.39

25.0 31.3 31.3 32.8 31.2 70.1

14-6-14, T ) 298.15 K 10.6 48.2 10.6 69.2 10.9 68.4 12.8 66.9 11.3 66.6 31.0 131.0

10-6 10-6 10-6 10-6

32.60 29.60 28.75 27.70 26.90 0.18

32.60 32.59 32.59 32.58

0.69 0.70 0.69 0.68 0.68 0.40

24.5 30.5 30.9 31.6 31.6 70.0

14-6-14, T ) 303.15 K 10.7 45.8 10.6 65.7 11.0 65.7 12.7 62.5 11.7 65.6 31.7 126.3

10-6 10-6 10-6 10-6

29.64 27.35 26.65 25.40 24.80 0.19

29.64 29.63 29.63 29.63

0.71 0.69 0.70 0.72 0.71 0.41

24.9 31.5 31.5 30.8 31.2 70.4

14-6-14, T ) 308.15 K -19.3 143.5 -19.2 164.3 -19.2 164.5 -21.4 169.2 -20.3 167.1 32.6 122.7

0 0.54 1.08 1.62 2.16 1.0 0. 0.54 1.08 1.62 2.16 1.0 0 0.54 1.08 1.62 2.16

0 0.63 1.26 1.89 2.52

0 0.72 1.44 2.16 2.87 1.0 0 0.72 1.44 2.16 2.87 1.0 0 0.72 1.44 2.16 2.87 1.0 0 0.72 1.44 2.16 2.87 1.0

× × × ×

× × × ×

× × × ×

29.64 29.63 29.63 29.63

X1id

β

f1

f2

-∆Gex (kJ mol-1)

0.0001 0.0002 0.0004 0.0005

-7.45 -7.09 -6.86 -7.05

0.0016 0.0026 0.0035 0.0037

0.9645 0.9525 0.9444 0.9204

1.2 1.3 1.4 1.7

0.0001 0.0002 0.0004 0.0005

-7.87 -7.35 -7.03 -7.09

0.0013 0.0023 0.0032 0.0036

0.9504 0.9426 0.9380 0.9196

1.4 1.5 1.5 1.7

0.0001 0.0002 0.0003 0.0005

-7.89 -7.40 -7.17 -7.08

0.0013 0.0022 0.0030 0.0036

0.9504 0.9411 0.9324 0.9211

1.5 1.5 1.6 1.7

0.0001 0.0002 0.0003 0.0004

-7.73 -7.30 -7.10 -7.35

0.0013 0.0021 0.0028 0.0030

0.9620 0.9520 0.9427 0.9152

1.3 1.4 1.5 1.8

0.0001 0.0003 0.0004 0.0006

-7.45 -6.96 -6.80 -6.63

0.0017 0.0029 0.0038 0.0047

0.9605 0.9530 0.9419 0.9363

1.2 1.3 1.4 1.4

0.0001 0.0003 0.0004 0.0005

-7.96 -7.51 -7.25 -7.11

0.0013 0.0022 0.0030 0.0037

0.9426 0.9301 0.9221 0.9132

1.6 1.6 1.7 1.8

0.0001 0.0003 0.0004 0.0005

-8.10 -7.69 -7.42 -7.27

0.0012 0.0020 0.0028 0.0034

0.9377 0.9227 0.9146 0.9056

1.7 1.8 1.8 1.9

0.0001 0.0002 0.0003 0.0004

-7.73 -7.28 -7.07 -6.89

0.0013 0.0022 0.0030 0.0037

0.9595 0.9501 0.9413 0.9359

1.3 1.4 1.5 1.6

0.0002 0.0003 0.0005 0.0006

-6.68 -6.48 -6.68 -6.62

0.0025 0.0038 0.0041 0.0049

0.9802 0.9670 0.9431 0.9321

0.8 1.1 1.4 1.5

0.0001 0.0003 0.0004 0.0006

-6.88 -6.78 -6.85 -6.84

0.0022 0.0032 0.0037 0.0043

0.9771 0.9590 0.9387 0.9238

0.9 1.2 1.5 1.6

0.0001 0.0003 0.0004 0.0005

-7.17 -6.86 -6.88 -6.89

0.0019 0.0030 0.0036 0.0041

0.9705 0.9578 0.9393 0.9241

1.1 1.3 1.5 1.7

0.0001 0.0002 0.0003 0.0005

-7.05 -6.75 -6.96 -6.91

0.0019 0.0029 0.0032 0.0038

0.9778 0.9671 0.9433 0.9311

1.0 1.1 1.5 1.6

6360


Kabir-ud-Din et al.

Figure 3. Effect of temperature on the critical micelle concentration (cmc) of pure and mixed AMT-surfactant systems.

a drug. The ∆Gm0 values for CTAB and TTAB show a slight maximum with an increase in temperature. Similar behavior was observed by Sugihara et al. for dodecylammonium alkanesulfonates also.40 The rigid hydrophobic structure of the drug makes micellization difficult. Gemini surfactants contain two hydrophobic chains and hence micellization is more favorable as compared to single chain analogues (which is evident from the low cmc and more negative ∆Gm0 values of geminis (Tables 2 and 3)). As solutions contain low concentration of surfactants, mixed micelles also contain less surfactant contribution than the drug, and hence ∆Gm0 values of mixed systems are close to those of pure AMT. The ∆Hm0 values of pure surfactants are negative and, as the temperature increases, they become more negative (Figure 4 and Tables 1-3). Thus, the process of aggregation becomes more exothermic with an increase in temperature. However, pure AMT behaves in a different manner. At 293.15 K, ∆Hm0 is -10.30 kJ mol-1, and it becomes more negative as the temperature increases. At 308.15 K, the ∆Hm0 value becomes positive, that is, the process becomes endothermic. A similar trend was observed for drug-surfactant mixtures. At higher temperature, endothermicity may be due to dehydration of nonpolar tails. Although we are not sure about the reason for this reversal in behavior, the release of water molecules from hydrophobic portion may be the cause of endothermicity as well as decrease in cmc at 308.15 K. The ∆Sm0 values for micellization of pure surfactants are positive and decrease with increasing temperature (Figure 5 and Tables 1-3). Also, with the addition of surfactants, the positive entropy values of AMT decrease. This means that in pure components the entropic contribution predominates while in

AMT-surfactant mixtures this entropic contribution decreases. However, in all systems, at T ) 308.15 K, the entropy values increase sharply. Obviously, this is caused by the particular structure of AMT, which is the principal component of the mixed micelles. Seemingly, the key lies in the difference in the hydration between the saturated and aromatic hydrocarbon part of the drug molecule. The high increase in entropy suggests a strong liberation of water, which probably is the water associated with the aromatic ring of AMT. This, in turn, must increase the hydrophobicity of AMT molecules causing reduction of cmc (see Tables 1-3). (We are highly thankful to one of the reviewers for his valuable suggestion to explain the unusual behavior of AMT at 35 °C (308.15 K).) The cmc and cmcid values, as stated earlier, indicate synergism in the mixed systems. Therefore, the cmc values have been used to determine the composition of the mixed micelles and the micellar molecular interaction parameter (β) among the components by applying the phenomenological models given by Rubingh41 and Motomura.42 The fundamental equations of Rubingh’s model are (X1)2 ln(cmc R1/cmc1 X1) (1 - X1)2 ln[cmc(1 - R1)/cmc2(1 - X1)] β)

ln(cmc R1/cmc1 X1) (1 - X1)2

)1

(7)

(8)

where X1 is the micellar mole fraction of surfactant in the mixture. The cmc1 and cmc2 correspond to cmc values of the



Figure 4. Effect of temperature on the enthalpy of micellization (∆Hm0) of pure and mixed AMT-surfactant systems.

respective single systems of components 1 (surfactant) and 2 (AMT). Motomura considered mixed micelles as a macroscopic bulk phase and proposed that the energetics of such systems should be evaluated in terms of excess thermodynamic quantities. The composition of mixed micelles is determined by the following relationship:

Xm 1 ) R1 -

(R1R2 /cmc)(∂cmc/∂R1)T,P δν1,cν2,d 1ν1,cν2R1 + ν2,dν1R2

Xm 1 ) R1 -

(9) Xm 1 )

(10)

(

νiRi ν1R1 + ν2R2

(i ) 1, 2)

R1R2 ∂cmc 2cmc ∂R1

(12) T,P

)

(11)

In the above equation, X1m is the micellar mole fraction of surfactant, Ri is the bulk mole fraction, νi is the number of ions dissociated by the ith component, and δ is the Kronecker delta

(

)(

) ( )

3R1 3R1 2 - 2R1 1 × R1 + 2 (R1 + 2)cmc R1 + 2 R1 + 2 ∂cmc (13) ∂R1

The mole fraction of surfactants in the ideal state was calculated using eq 14

Xid 1 )

and

Ri )

( )( )

for AMT-conventional surfactant systems, whereas for AMT-gemini systems, eq 9 would reduce to

where

cmc ) (ν1R1 + ν2R2)cmc

which is equal to 1 for identical counterions and 0 for different counterions. Equation 9 reduces to

R1cmc2 (R1cmc2 + R2cmc1)

(14)

Both X1 and Xm1 (as well as Xid1 ) values for AMT-conventional surfactants increase with an increase in surfactant concentration and decrease with an increase in temperature (Figure 6 and Tables 1-3). However, for AMT-gemini surfactant mixtures, Xid1 shows the trend similar to that of AMT-conventional systems but X1 values at all mole fractions show a peaked behavior: after increasing up to 303.15 K, X1 decreases at

6362


Kabir-ud-Din et al.

Figure 5. Effect of temperature on the entropy of micellization (∆Sm0) of pure and mixed AMT-surfactant systems.

308.15 K. The X1m values in almost all cases are greater than both X1 and X1id. With the increase in concentration of surfactant in the solution, contributions of surfactants in mixed micelles also increase. In all systems, X1 is always greater than R1. As the concentration of surfactant in the solutions is very small, the micelles in the ideal state should contain less surfactants. It seems that the added surfactant replaces some of the drug molecules from the mixed micelles resulting in some reduction in steric hindrance in the micellar core. Hence, more surfactant is present in mixed micelles as compared to the ideal state. It is clear from Figure 2 that, although the mole fractions of gemini surfactants are lower than that of conventional surfactants (i.e., low concentrations of geminis are used), their contribution in mixed micellization at low R1 values is higher than of single chain surfactants. This is due to the presence of two hydrophobic chains (thus increasing their hydrophobicity) which try to accommodate in mixed micelles. However, excess concentration of gemini (i.e., at higher R1 values) increases steric hindrance in the micelles caused by the drug molecule’s rigid structure, and their concentration in the micelles decreases (i.e., X1 decreases at higher R1) in comparison to that in CTAB-drug mixed micelles. All the results and discussion given above indicate synergistic interactions among the two components of the mixed micelles. As such, the interaction parameter, β, comes out to be negative at all mole fractions (βav values vary between -6 and -8). The values are greater for conventional surfactants, which are in line with the X1 values. Bulky hydrophobic groups of both drug and

gemini surfactants decrease the contributions of geminis as well as interactions between the two components. The activity coefficients of the two components were evaluated from the relations

f1 ) exp{β(1 - X1)2}

(15)

f2 ) exp{βX12}

(16)

The values are always less than unity confirming nonideality in the systems. The f1 and f2 values can also be used to find excess free energy of mixing, ∆Gex, as43,44

∆Gex ) RT{X1 ln f1 + X2 ln f2}

(17)

The values come out to be negative and their magnitudes increase with an increase in surfactant concentration, suggesting that the mixed micelles formed are more stable than the micelles of pure components. 4. Conclusions Conductometric studies were performed on an amphiphilic drug (AMT)-cationic surfactant (conventional and gemini) mixed systems. The results indicate that the drug forms mixed micelles with the surfactants. Ideal cmc values, calculated from



Figure 6. Variations of X1 and Xm 1 vs mole fraction of surfactant (R1) in surfactant-AMT mixtures at different temperatures: 293.15 (9,0), 298.15 (b,O), 303.15 (2,4), 308.15 K (1,3); (a) 16-carbon chain, (b) 14-carbon chain. Filled symbols are for Rubingh’s and open symbols are for Motomura’s model.

Clint’s model, show synergism in the mixed system. The interaction parameter, calculated using Rubingh’s approach, comes out to be negative; again confirming attractive interactions. Values of the micellar mole fraction of surfactants obtained from Rubingh’s and Motomura’s models are greater

than ideal Xid 1 values. Although the stoichiometric mole fraction of conventional surfactants (CTAB and TTAB) is higher than that of geminis in the mixed systems, the contribution of the latter is more than the conventional ones. Seemingly, the drug’s rigid structure resists its contribution in micelle formation.

6364


Acknowledgment. The authors are thankful to the Council of Scientific and Industrial Research, New Delhi, India, for providing a research grant (No. 01 (2208)/08/EMR-II). References and Notes (1) Taboada, P.; Attwood, D.; Mosquera, V. J. Colloid Interface Sci. 2002, 248, 158–162. (2) Oida, T.; Nakashima, N.; Nagadome, S.; Ko, J.; Oh, S.; Sugihara, G. J. Oleo Sci. 2003, 52, 509–522. (3) Rodriguez, A.; Junquera, E.; del Burgo, P.; Aicart, E. J. Colloid Interface Sci. 2004, 269, 476–483. (4) McLachlan, A. A.; Marangoni, D. G. J. Colloid Interface Sci. 2006, 295, 243–248. (5) Fernandez-Leyes, M. D.; Messina, P. V.; Schulz, P. C. J. Colloid Interface Sci. 2007, 314, 659–664. (6) Hu, J.; Zhou, L.; Feng, J.; Liu, H.; Hu, Y. J. Colloid Interface Sci. 2007, 315, 761–767. (7) Holland, P. M. In Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992. (8) Hill, R. M. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Surfactant Science Series, Vol. 46; Dekker: New York, 1993. (9) Ghosh, S.; Moulik, S. P. J. Colloid Interface Sci. 1999, 208, 357– 366. (10) Cross, J.; Singer, E. J. Cationic Surfactants: Analytical and Biological EValuation; Dekker: New York, 1994. (11) Perez, L.; Torres, J. L.; Manresa, A.; Solans, C.; Infante, M. R. Langmuir 1996, 12, 5296–5301. (12) Zana, R. J. Colloid Interface Sci. 2002, 248, 203–320. (13) Danino, D.; Talmon, Y.; Zana, R. Langmuir 1995, 11, 1448–1456. (14) Attwood, D.; Florence, A. T. Surfactant Systems, Their Chemistry, Pharmacy, and Biology; Chapman and Hall: New York, 1983. (15) Taboada, P.; Attwood, D.; Ruso, J. M.; Garcia, M.; Mosquera, V. Phys. Chem. Chem. Phys. 2000, 2, 5175–5179. (16) Jones, M.; Leroux, J. Eur. J. Pharm. Biopharm. 1999, 48, 101– 111. (17) Torchilin, V. P. J. Controlled Release 2001, 73, 137–172. (18) De, S.; Aswal, V. K.; Goyal, P. S.; Bhattacharya, S. J. Phys. Chem. 1996, 100, 11664–11671. (19) Kabir-ud-Din; Fatma, W.; Khatoon, S; Khan, Z. A; Naqvi, A. Z. J. Chem. Eng. Data 2008, 53, 2291–2300.

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Mixed Micelle Formation between Amphiphilic Drug Amitriptyline

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