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Influence of the Structure of the Hydrophobe on the Ideality of Mixing in Micelles in Binary Mixtures of Amphiphilic Tricyclic Drugs
Journal of Colloid and Interface Science 248, 158–162 (2002) doi:10.1006/jcis.2001.8186, available online at http://www.idealibrary.com on
Influence of the Structure of the Hydrophobe on the Ideality of Mixing in Micelles in Binary Mixtures of Amphiphilic Tricyclic Drugs Pablo Taboada,∗ David Attwood,† and V´ıctor Mosquera∗,1 ∗ Grupo de F´ısica de Coloides y Pol´ımeros, Departamento de F´ısica de la Materia Condensada, Facultad de F´ısica, Universidad de Santiago de Compostela, Santiago de Compostela 15706, Spain; and †School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Manchester MI3 9PL, United Kingdom E-mail: [email protected] Received July 9, 2001; accepted December 13, 2001; published online February 21, 2002
The composition of the micelles in binary mixtures of the cationic amphiphilic antidepressant drugs nortriptyline, amitriptyline, and doxepin has been determined from an analysis of the variation of the critical micelle concentration from conductivity measurements, as a function of solution composition. Assessment of the nonideality of mixing in terms of the interaction parameter from the regular solution approximation showed small deviations from ideal mixing, with negative interaction parameters for nortriptyline/amitriptyline systems and positive interaction parameters for mixtures of nortriptyline and doxepin. These differences in nonideality have been attributed to differences in the packing of the drugs in the mixed micelles arising from differences in the structure of the hydrophobe. C 2002 Elsevier Science (USA) Key Words: mixed micelles, antidepressant drugs, critical micelle concentrations.
1. INTRODUCTION
Nonideality of mixing in binary mixtures of amphiphilic compounds may cause synergism in the properties of the mixtures that may be exploited in their application in industrial preparations and pharmaceutical and medical formulations (1). For example, detergent and cleaning formulations often include both anionic surfactants, to maximize solubilization, and nonionic surfactants, to maximize hardness tolerance (2). In skin care applications, synergism in a surfactant mixture can minimize the total surfactant monomer concentration (3), which in turn has been shown to reduce skin irritation (4, 5). Nonideality is mainly influenced by the nature of the charge or differences in molecular structure of the two amphiphilic molecules of the mixture (1). The study of the properties of mixtures of surface-active drugs in solution provides an opportunity to investigate the influence of the molecular structure of the hydrophobe on the nonideality of mixing because of the wide variation in the structure of this moiety in amphiphilic drugs. In our research group, we have pre1
To whom correspondence should be addressed.
0021-9797/02 $35.00
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158
viously studied binary mixtures of some penicillin drugs (6) and have observed ideality of mixing in mixtures of those penicillins whose only structural variation was the number and nature of the substituents on the single phenyl ring of the hydrophobic moiety. In contrast, mixtures of penicillins with structurally different hydrophobic groups presented a slight synergism between the components of the mixture. Moreover, we have also found that binary mixtures of phenothiazine drugs exhibit ideality of mixing (7), as might be expected for the stacking of the structurally similar, rigid tricyclic ring systems of these drugs. We have shown previously (8) that there is appreciable nonideality of mixing in solutions of two antidepressant drugs, clomipramine and imipramine, which differ only in a Cl substituent on the hydrophobic tricyclic ring system of clomipramine. This nonideality was attributed to possible differences in the packing in the micelles of these two drugs. In the present paper we report further on the influence of the structure of the hydrophobe on the ideality of mixing in binary mixtures of combinations of the three antidepressant drugs, nortriptyline, amitriptyline, and doxepin hydrochlorides (see structures below). These drugs are amphiphilic and their association characteristics in water and aqueous electrolyte have been reported (9–13). The variation of the critical micelle concentration of solutions of selected combinations of these antidepressants with changes in the composition of the binary mixture has been used to determine the composition of the mixed micelles by applying the theoretical model proposed by Motomura et al. (14) based on excess thermodynamic quantities. Any ideality of interaction of components of each selected pairs of drugs in the mixed micelles has been quantified using the dimensionless interaction coefficient, β, introduced by Holland and Rubingh (15).
159
BINARY MIXTURES OF AMPHIPHILIC TRICYCLIC DRUGS
Doxepin HCl Amitriptyline HCl Nortriptyline HCl
Y–Z
R1
O–CH2 CH2 –CH2 CH2 –CH2
=CH[CH2 ]2 N[CH3 ]2 =CH[CH2 ]2 N(CH3 )2 =CH[CH2 ]2 NH(CH3 )
2. EXPERIMENTAL
A. Materials Amitriptyline, nortriptyline, and doxepin hydrochlorides of at least 98.5% purity were purchased from Sigma Chemical Co. and used without further purification. Solutions of the antidepressants were prepared with double-distilled and degassed water.
FIG. 1. Specific conductivity, κ, for the binary mixture nortriptyline/ doxepin (0.5 mol fraction nortriptyline) as a function of molal concentration, m, at 298.15 K. The dashed line corresponds to the Gaussian fit of the second derivative. The arrow denotes the cmc.
B. Conductimetric Measurements Conductivities of the binary mixtures were measured at 298.15 ± 0.01 K with a Hewlett Packard 4285A Precision LCR meter equipped with a Hewlett Packard E5050A colloid dielectric probe operating in the frequency range between 200 kHz and 20 MHz. The probe is designed to measure inductances and to avoid the potential problems with polarization of the molecules, which may arise when a plain condenser is used. To obtain the highest precision, the probe was incorporated into a cell designed in-house (16), composed of a cylinder (diameter 8 cm and height 5 cm) with the probe entrance on the side such that the probe head was always surrounded by at least 2 cm of solution. The cell was immersed in a Techne model RB-12A thermostat bath equipped with a Tempunit TU-16A thermostat. Temperature control was monitored using an Anton Paar DT 100-30 thermometer, maintaining the temperature constant to within ±0.01 K. A Variomag 20P shaker was used to homogenize the solution. The probe data were calibrated with aqueous solutions of KCl over the appropriate concentration range using the molar conductivity data of Shedlovsky (17) and Chambers et al. (18). Water was progressively added to concentrated aqueous solutions of antidepressant mixtures of known molality and composition using an automatic pump (Dosimat 665 Metrohm).
and involves the application to the conductivity–concentration data of a combination of the Runge–Kutta numerical integration method and the Levenberg–Marquardt least-squares fitting algorithm. The analytical procedure is designed to enable the determination of the cmc in systems in which there is curvature in the region of the cmc. Such curvature is noted in mixed micellar systems as a consequence of changes in the composition of the mixed micelles at concentrations close to the critical micelle concentration (19), and is a particular problem in the present study because of the low aggregation number of the micelles. Figure 1 illustrates the application of the analytical method to the specific conductivity–molality data for an equimolar binary mixture of nortriptyline and doxepin. Similar plots (not shown) were obtained for mixtures of the two systems, nortriptyline/doxepin and nortriptyline/amitriptyline, at 0.00, 0.25, 0.35, 0.50, 0.65, 0.80, and 1.00 mole fractions of components. The dashed line of Fig. 1 corresponds to the second derivative of the conductivity–concentration curve, the cmc being the concentration at which the second derivative is a minimum. Table 1 shows cmc values determined in this way for the nortriptyline/doxepin and nortriptyline/amitriptyline series; it was
3. RESULTS AND DISCUSSION
TABLE 1 Critical Micelle Concentrations, cmc, (mol kg−1 ) of the Mixed Systems Nortriptyline/Amitriptyline and Nortriptyline/Doxepin at 298.15 K Determined by Conductivity Measurements
Critical micelle concentrations (cmc) for mixed systems of nortriptyline/amitriptyline and nortriptyline/doxepin were determined from plots of specific conductivity, κ, as a function of molality, m, following the method proposed by P´erez-Rodr´ıguez et al. (16). This method is based on the Philips definition of the cmc (20),
d 3κ dm 3
=0 m=cmc
[1]
Mol fraction nortriptyline Nortriptyline/amitriptyline Nortriptyline/doxepin 0.00 0.20 0.35 0.50 0.65 0.80 1.00
0.063 0.057 0.053 0.051 0.048 0.045 0.044
0.069 0.064 0.061 0.058 0.055 0.051 0.044
160
TABOADA, ATTWOOD, AND MOSQUERA
not possible to measure cmc values for amitriptyline/doxepin mixtures due to the similarity of their cmc values. Changes in the distribution of the components of each system between monomeric and micellar phases as a function of the total solution composition were evaluated by analysis of the variation of the cmc with composition using a method proposed by Motomura et al. (14), which is based on excess thermodynamic quantities. This method of estimation of the equilibrium distribution of components in a mixed system has been shown to give values in good agreement with those derived from direct measurement by gel permeation chromatography (21). In this treatment the composition of the mixed aggregate formed by amphiphiles 1 and 2 is derived using the relationship x¯ 2m = x¯ 2 − (x¯ 1 x¯ 2 /cmc)(∂cmc/∂ x¯ 2 )T, p 1 − δdc ν1,c ν2,d (ν1,c ν2 x¯ 1 + ν2,d ν1 x¯ 2 ) ,
[2]
where cmc = (ν1 x1 + ν2 x2 ) × cmc νi xi x¯ i = (i = 1, 2) ν 1 x 1 + ν2 x 2 x¯ im =
νi xim + ν2 x2m
ν1 x1m
FIG. 2. Variation of cmc (cmc = 2 cmc) with the mole fraction of amitriptyline in the nortriptyline/amitriptyline system. The dotted line shows the equilibrium total concentration of the free monomeric drug for a given mole fraction of amitriptyline in the mixed micelle, x¯ 2m , as calculated from Eq. [4]; the solid line gives the mole fraction of amitriptyline in monomeric form, x¯ 2 , in the solution in equilibrium with the micelles.
[3] [4]
(i = 1, 2)
[5]
and x1 and x2 are the mole fractions of amphiphiles 1 and 2 in the binary system; x1m and x2m are the mole fractions of amphiphiles 1 and 2 in the mixed aggregate; ν1 = ν1,a + ν1,c and ν2 = ν2,b + ν2,d ; where ν1,a and ν1,c are the number of anions and cations produced upon dissociation of drug 1, and ν2,b and ν2d are the number produced upon dissociation of drug 2. The drugs under investigation are 1 : 1 electrolytes with identical counterions, so in this case
the monomeric drug for a given composition of the micelles, while the solid line gives the mole fraction of each component in monomeric form corresponding to this equilibrium. It is readily seen that, for a given composition of the system, the antidepressant with the higher cmc has a higher mole fraction in monomeric form in solution; i.e., the micelle is enriched with the drug with a lower cmc. Inspection of Fig. 3 shows that the values of x¯ 2m are close to those of x¯ 2 at low mole fractions of nortriptyline; i.e., the incorporation of this drug into micelles of doxepin is associated with nearly ideal mixing. However, appreciable deviation of the experimental and predicted lines at high mole fractions
ν1,a = ν1,c = ν2,b = ν2,d = 1 and hence cmc = 2cmc. [6] The Kronecker delta, δcd , for the systems investigated here, in which counterions are identical, is 1, and Eq. [5] reduces to
x¯ 2m
x¯ 1 x¯ 2 = x¯ 2 − 2 cmc
∂cmc ∂ x¯ 2
.
[7]
T, p
x¯ 2m was evaluated as a function of cmc by computer analysis of the critical micelle concentration data (see solid lines in Figs. 2 and 3). The upper lines (dotted) in Figs. 2 and 3 show the variation of the cmc with the composition of the mixed micelle as determined by this method. The lower curves show the variation of the experimentally measured cmc with the composition of the system. Figures 2 and 3 may be regarded as phase diagrams, expressing the relationship between the mole fraction of the drug in the mixed micelle and that in the solution in equilibrium with it. The dotted line shows the equilibrium total concentration of
FIG. 3. Variation of cmc (cmc = 2 cmc) with the mole fraction of doxepin in the nortriptyline/doxepin system. The dotted line shows the equilibrium total concentration of the free monomeric drug for a given mole fraction of doxepin in the mixed micelle, x¯ 2m , as calculated from Eq. [4]; the solid line gives the mole fraction of doxepin in monomeric form, x¯ 2 , in the solution in equilibrium with the micelles.
161
BINARY MIXTURES OF AMPHIPHILIC TRICYCLIC DRUGS
of nortriptyline in this system indicates that the incorporation of small amounts of doxepin into nortriptyline micelles is not an ideal process. To quantify the nonideality of mixing in the mixed aggregates we have used the simplified approach proposed by Holland and Rubingh (15). According to this model, the monomer concentration of each component in the micelle mixture, cim , is given by cim = xi cmcm ,
[8]
where xi is the mole fraction of the ith component in the total mixed solute and cmcm the critical micelle concentration of mixed system. For nonideal binary mixtures of surfactants, the activity coefficients are given by f i = xi cmcm xim cmci
(i = 1, 2),
[9]
where cmci is the cmc of the pure component. Using a simple regular solution approximation, the activity coefficients can be expressed as functions of the mole fractions of each of the components in the mixed micelle, xim , and an appropriate interaction parameter β12 that is related to net interaction between drug molecules in the mixed aggregates. The regular solution approximation for the activity coefficients in the mixed micelles gives 2 f 1 = exp β12 1 − x1m 2 f 2 = exp β12 x1m .
[10] [11]
The net interaction parameter β12 can be readily determined when the mixed critical micelle concentration for the binary system is known, by interactively solving for x1m at the critical micelle concentration using a relationship such as
2 x1m
x1 cmcm x2 cmcm m 2 = 1 − x1 ln [12] ln m x1 cmc1 1 − x1m cmc2
obtained from Eqs. [9], [10], and [11]. β12 can then be directly obtained by combining Eq. [9] with Eq. [10] to give β12
ln x1 cmcm x1m cmc1 = . 2 1 − x1m
[13]
Values of the molecular interaction parameter β12 were calculated for nortriptyline/doxepin and nortriptyline/amitriptyline systems (see Table 2) using Eq. [13] and cmc values of the pure components. For the nortriptyline/amitriptyline mixed systems β12 is low and negative, indicating slight attractive electrostatic forces between the antidepressant molecules. This agrees with previous results obtained for the binary mixture of the antidepressant drugs imipramine and clomipramine, for which a mean
TABLE 2 Molecular Interaction Parameters, β12 , for the Systems Nortriptyline/Amitriptyline and Nortriptyline/Doxepin at 298.15 K Mol fraction nortriptyline Nortriptyline/amitriptyline Nortriptyline/doxepin 0.20 0.35 0.50 0.65 0.80
−0.02 −0.13 −0.11 −0.15 −0.37
+0.25 +0.28 +0.35 +0.45 +1.04
interaction parameter β12 of −0.9 was calculated. However, for the system nortriptyline/doxepin β12 values are positive, indicating the existence of a repulsive interaction in mixed micelles. Moreover, β12 becomes more positive as the mole fraction of nortriptyline in the mixed micelles is increased. The difference in behavior of the two systems may be a consequence of differences in the preferred packing within the micelles of each drug as indicated in a previous work (7). In this respect it is interesting to note that the solubility of nortriptyline in mixtures with doxepin was appreciably higher than when mixed with amitriptyline. Since these drugs possess the same hydrophilic charged groups any differences in the extent of solubilization of nortriptyline or in the packing in the mixed micelles in these two binary systems must be associated with the presence of the oxygen atom in the tricyclic ring system of doxepin. The lone pair of electrons on this oxygen atom can undergo resonance with the aromatic rings, giving rise to tautomers with zwitterionic character, thus decreasing the hydrophobicity of the ring system. The tautomeric zwitterions may interact electrostatically with the charged groups of nortriptyline, so facilitating the incorporation of this drug in the mixed micelles and hence enhancing its solubility. In addition, our results suggest that there is also an effect on the packing in the mixed micelle as evidenced by the difference in the interaction parameters of the two mixed systems. Repulsive interaction in mixed micelles in aqueous media is unusual and, for hydrocarbon-chain surfactants, has been reported only in mixtures of long-chain carboxylates and long-chain alkylbenzensulfonates (22). It is more commonly found in mixtures of anionic fluorocarbon-chain and anionic hydrocarbon-chain surfactants (23). We have previously noted this effect in mixed systems of the penicillins nafcillin and either cloxacillin or dicloxacillin where it was thought to be a consequence of structural differences between the hydrophobic groups (6). 4. CONCLUSIONS
The relatively low values of the dimensionless interaction parameter β12 suggest only small deviations from ideality of mixing in mixed micellar solutions of the antidepressant drugs amitriptyline, nortriptyline, and doxepin. However, it is interesting to note the difference in sign of the β12 values for the
162
TABOADA, ATTWOOD, AND MOSQUERA
two mixed systems and the higher β12 values for the nortriptyline/doxepin solutions, which, it is suggested, might be a consequence of structural effects due to differences in the packing of the drug molecules in the small micelles. ACKNOWLEDGMENT The authors thank Xunta de Galicia for financial support.
REFERENCES 1. Holland, P. M., in “Mixed Surfactant Systems” (P. M. Holland and D. N. Rubingh, Eds.), ACS Symposium Series, Chap. 2. Am. Chem. Soc., Washington, DC, 1992. 2. Hill, R. M., in “Mixed Surfactant Systems” (K. Ogino and M. Abe, Eds.), Surfactant Science Series 46, Chap. 11. Dekker, New York, 1993. 3. Garcia, M. T., Ribosa, I., Sanchez Leal, J., and Comelles, F., J. Am. Oil Chem. Soc. 69, 25 (1992). 4. Prottey, C., and Ferguson, T., J. Soc. Cosmet. Chem. 26, 29 (1975). 5. Rhein, L. D., Simion, F. A., Hill, R. L., Cagan, R. H., Mattai, J., and Maibach, H. I., Dermatologica 180, 18 (1990). 6. Taboada, P., Attwood, D., Ruso, J. M., Garc´ıa, M., Sarmiento, F., and Mosquera, V., J. Colloid Interface Sci. 216, 270 (1999). 7. Attwood, D., Mosquera, V., Novas, L., and Sarmiento, F., J. Colloid Interface Sci. 179, 478 (1996).
8. Sarmiento, F., L´opez-Font´an, J. L., Prieto, G., Attwood, D., and Mosquera, V., Colloid Polym. Sci. 275, 1144 (1997). 9. Taboada, P., Attwood, D., Ruso, J. M., Garc´ıa, M., and Mosquera, V., Phys. Chem. Chem. Phys. 2, 5175 (2000). 10. Taboada, P., Attwood, D., Ruso, J. M., Garc´ıa, M., and Mosquera, V., Langmuir 17, 173 (2001). 11. Taboada, P., Ruso, J. M., Garc´ıa, M., and Mosquera, V., Colloids Surf. A 179, 125 (2001). 12. Taboada, P., Ruso, J. M., Garc´ıa, M., and Mosquera, V., Colloid Polym. Sci. 279, 716 (2001). 13. Taboada, P., Mart´ınez-Landeira, P., Ruso, J. M., Garc´ıa, M., and Mosquera, V., Colloids Surf. A 197, 95 (2002). 14. Motomura, K., Yamanaka, M., and Aratono, M., Colloid Poly. Sci. 262, 948 (1984). 15. Holland, P. M., and Rubingh, D. N., J. Phys. Chem. 87, 1984 (1983). 16. P´erez-Rodr´ıguez, M., Prieto, G., Rega, C., Varela, L. M., Sarmiento, F., and Mosquera, V., Langmuir 14, 4422 (1998). 17. Shedlovsky, T., J. Am. Chem. Soc. 54, 1411 (1932). 18. Chambers, J. F., Stokes, J. H., and Stokes, R. H., J. Phys. Chem. 60, 985 (1965). 19. Mysels, K. J., and Otter, R., J. Colloid Interface Sci. 16, 462 (1961). 20. Phillips, J. N., Trans. Faraday Soc. 51, 561 (1955). 21. Attwood, D., and Patel, H. K., J. Colloid Interface Sci. 129, 222 (1989). 22. Rosen, M. J., and Zhu, Z. H., J. Colloid Interface Sci. 133, 473 (1989). 23. Zhao, G. X., and Zhu, B. Y., in “Phenomena in Mixed Surfactant Systems” (J. F. Scamehorn, Ed.), ACS Symposium Series 311, p. 311. Am. Chem. Soc., Washington, DC, 1986.
Influence of the Structure of the Hydrophobe on the Ideality of Mixing in Micelles in Binary Mixtures of Amphiphilic Tricyclic Drugs Pablo Taboada,∗ David Attwood,† and V´ıctor Mosquera∗,1 ∗ Grupo de F´ısica de Coloides y Pol´ımeros, Departamento de F´ısica de la Materia Condensada, Facultad de F´ısica, Universidad de Santiago de Compostela, Santiago de Compostela 15706, Spain; and †School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Manchester MI3 9PL, United Kingdom E-mail: [email protected] Received July 9, 2001; accepted December 13, 2001; published online February 21, 2002
The composition of the micelles in binary mixtures of the cationic amphiphilic antidepressant drugs nortriptyline, amitriptyline, and doxepin has been determined from an analysis of the variation of the critical micelle concentration from conductivity measurements, as a function of solution composition. Assessment of the nonideality of mixing in terms of the interaction parameter from the regular solution approximation showed small deviations from ideal mixing, with negative interaction parameters for nortriptyline/amitriptyline systems and positive interaction parameters for mixtures of nortriptyline and doxepin. These differences in nonideality have been attributed to differences in the packing of the drugs in the mixed micelles arising from differences in the structure of the hydrophobe. C 2002 Elsevier Science (USA) Key Words: mixed micelles, antidepressant drugs, critical micelle concentrations.
1. INTRODUCTION
Nonideality of mixing in binary mixtures of amphiphilic compounds may cause synergism in the properties of the mixtures that may be exploited in their application in industrial preparations and pharmaceutical and medical formulations (1). For example, detergent and cleaning formulations often include both anionic surfactants, to maximize solubilization, and nonionic surfactants, to maximize hardness tolerance (2). In skin care applications, synergism in a surfactant mixture can minimize the total surfactant monomer concentration (3), which in turn has been shown to reduce skin irritation (4, 5). Nonideality is mainly influenced by the nature of the charge or differences in molecular structure of the two amphiphilic molecules of the mixture (1). The study of the properties of mixtures of surface-active drugs in solution provides an opportunity to investigate the influence of the molecular structure of the hydrophobe on the nonideality of mixing because of the wide variation in the structure of this moiety in amphiphilic drugs. In our research group, we have pre1
To whom correspondence should be addressed.
0021-9797/02 $35.00
C 2002 Elsevier Science (USA)
All rights reserved.
158
viously studied binary mixtures of some penicillin drugs (6) and have observed ideality of mixing in mixtures of those penicillins whose only structural variation was the number and nature of the substituents on the single phenyl ring of the hydrophobic moiety. In contrast, mixtures of penicillins with structurally different hydrophobic groups presented a slight synergism between the components of the mixture. Moreover, we have also found that binary mixtures of phenothiazine drugs exhibit ideality of mixing (7), as might be expected for the stacking of the structurally similar, rigid tricyclic ring systems of these drugs. We have shown previously (8) that there is appreciable nonideality of mixing in solutions of two antidepressant drugs, clomipramine and imipramine, which differ only in a Cl substituent on the hydrophobic tricyclic ring system of clomipramine. This nonideality was attributed to possible differences in the packing in the micelles of these two drugs. In the present paper we report further on the influence of the structure of the hydrophobe on the ideality of mixing in binary mixtures of combinations of the three antidepressant drugs, nortriptyline, amitriptyline, and doxepin hydrochlorides (see structures below). These drugs are amphiphilic and their association characteristics in water and aqueous electrolyte have been reported (9–13). The variation of the critical micelle concentration of solutions of selected combinations of these antidepressants with changes in the composition of the binary mixture has been used to determine the composition of the mixed micelles by applying the theoretical model proposed by Motomura et al. (14) based on excess thermodynamic quantities. Any ideality of interaction of components of each selected pairs of drugs in the mixed micelles has been quantified using the dimensionless interaction coefficient, β, introduced by Holland and Rubingh (15).
159
BINARY MIXTURES OF AMPHIPHILIC TRICYCLIC DRUGS
Doxepin HCl Amitriptyline HCl Nortriptyline HCl
Y–Z
R1
O–CH2 CH2 –CH2 CH2 –CH2
=CH[CH2 ]2 N[CH3 ]2 =CH[CH2 ]2 N(CH3 )2 =CH[CH2 ]2 NH(CH3 )
2. EXPERIMENTAL
A. Materials Amitriptyline, nortriptyline, and doxepin hydrochlorides of at least 98.5% purity were purchased from Sigma Chemical Co. and used without further purification. Solutions of the antidepressants were prepared with double-distilled and degassed water.
FIG. 1. Specific conductivity, κ, for the binary mixture nortriptyline/ doxepin (0.5 mol fraction nortriptyline) as a function of molal concentration, m, at 298.15 K. The dashed line corresponds to the Gaussian fit of the second derivative. The arrow denotes the cmc.
B. Conductimetric Measurements Conductivities of the binary mixtures were measured at 298.15 ± 0.01 K with a Hewlett Packard 4285A Precision LCR meter equipped with a Hewlett Packard E5050A colloid dielectric probe operating in the frequency range between 200 kHz and 20 MHz. The probe is designed to measure inductances and to avoid the potential problems with polarization of the molecules, which may arise when a plain condenser is used. To obtain the highest precision, the probe was incorporated into a cell designed in-house (16), composed of a cylinder (diameter 8 cm and height 5 cm) with the probe entrance on the side such that the probe head was always surrounded by at least 2 cm of solution. The cell was immersed in a Techne model RB-12A thermostat bath equipped with a Tempunit TU-16A thermostat. Temperature control was monitored using an Anton Paar DT 100-30 thermometer, maintaining the temperature constant to within ±0.01 K. A Variomag 20P shaker was used to homogenize the solution. The probe data were calibrated with aqueous solutions of KCl over the appropriate concentration range using the molar conductivity data of Shedlovsky (17) and Chambers et al. (18). Water was progressively added to concentrated aqueous solutions of antidepressant mixtures of known molality and composition using an automatic pump (Dosimat 665 Metrohm).
and involves the application to the conductivity–concentration data of a combination of the Runge–Kutta numerical integration method and the Levenberg–Marquardt least-squares fitting algorithm. The analytical procedure is designed to enable the determination of the cmc in systems in which there is curvature in the region of the cmc. Such curvature is noted in mixed micellar systems as a consequence of changes in the composition of the mixed micelles at concentrations close to the critical micelle concentration (19), and is a particular problem in the present study because of the low aggregation number of the micelles. Figure 1 illustrates the application of the analytical method to the specific conductivity–molality data for an equimolar binary mixture of nortriptyline and doxepin. Similar plots (not shown) were obtained for mixtures of the two systems, nortriptyline/doxepin and nortriptyline/amitriptyline, at 0.00, 0.25, 0.35, 0.50, 0.65, 0.80, and 1.00 mole fractions of components. The dashed line of Fig. 1 corresponds to the second derivative of the conductivity–concentration curve, the cmc being the concentration at which the second derivative is a minimum. Table 1 shows cmc values determined in this way for the nortriptyline/doxepin and nortriptyline/amitriptyline series; it was
3. RESULTS AND DISCUSSION
TABLE 1 Critical Micelle Concentrations, cmc, (mol kg−1 ) of the Mixed Systems Nortriptyline/Amitriptyline and Nortriptyline/Doxepin at 298.15 K Determined by Conductivity Measurements
Critical micelle concentrations (cmc) for mixed systems of nortriptyline/amitriptyline and nortriptyline/doxepin were determined from plots of specific conductivity, κ, as a function of molality, m, following the method proposed by P´erez-Rodr´ıguez et al. (16). This method is based on the Philips definition of the cmc (20),
d 3κ dm 3
=0 m=cmc
[1]
Mol fraction nortriptyline Nortriptyline/amitriptyline Nortriptyline/doxepin 0.00 0.20 0.35 0.50 0.65 0.80 1.00
0.063 0.057 0.053 0.051 0.048 0.045 0.044
0.069 0.064 0.061 0.058 0.055 0.051 0.044
160
TABOADA, ATTWOOD, AND MOSQUERA
not possible to measure cmc values for amitriptyline/doxepin mixtures due to the similarity of their cmc values. Changes in the distribution of the components of each system between monomeric and micellar phases as a function of the total solution composition were evaluated by analysis of the variation of the cmc with composition using a method proposed by Motomura et al. (14), which is based on excess thermodynamic quantities. This method of estimation of the equilibrium distribution of components in a mixed system has been shown to give values in good agreement with those derived from direct measurement by gel permeation chromatography (21). In this treatment the composition of the mixed aggregate formed by amphiphiles 1 and 2 is derived using the relationship x¯ 2m = x¯ 2 − (x¯ 1 x¯ 2 /cmc)(∂cmc/∂ x¯ 2 )T, p 1 − δdc ν1,c ν2,d (ν1,c ν2 x¯ 1 + ν2,d ν1 x¯ 2 ) ,
[2]
where cmc = (ν1 x1 + ν2 x2 ) × cmc νi xi x¯ i = (i = 1, 2) ν 1 x 1 + ν2 x 2 x¯ im =
νi xim + ν2 x2m
ν1 x1m
FIG. 2. Variation of cmc (cmc = 2 cmc) with the mole fraction of amitriptyline in the nortriptyline/amitriptyline system. The dotted line shows the equilibrium total concentration of the free monomeric drug for a given mole fraction of amitriptyline in the mixed micelle, x¯ 2m , as calculated from Eq. [4]; the solid line gives the mole fraction of amitriptyline in monomeric form, x¯ 2 , in the solution in equilibrium with the micelles.
[3] [4]
(i = 1, 2)
[5]
and x1 and x2 are the mole fractions of amphiphiles 1 and 2 in the binary system; x1m and x2m are the mole fractions of amphiphiles 1 and 2 in the mixed aggregate; ν1 = ν1,a + ν1,c and ν2 = ν2,b + ν2,d ; where ν1,a and ν1,c are the number of anions and cations produced upon dissociation of drug 1, and ν2,b and ν2d are the number produced upon dissociation of drug 2. The drugs under investigation are 1 : 1 electrolytes with identical counterions, so in this case
the monomeric drug for a given composition of the micelles, while the solid line gives the mole fraction of each component in monomeric form corresponding to this equilibrium. It is readily seen that, for a given composition of the system, the antidepressant with the higher cmc has a higher mole fraction in monomeric form in solution; i.e., the micelle is enriched with the drug with a lower cmc. Inspection of Fig. 3 shows that the values of x¯ 2m are close to those of x¯ 2 at low mole fractions of nortriptyline; i.e., the incorporation of this drug into micelles of doxepin is associated with nearly ideal mixing. However, appreciable deviation of the experimental and predicted lines at high mole fractions
ν1,a = ν1,c = ν2,b = ν2,d = 1 and hence cmc = 2cmc. [6] The Kronecker delta, δcd , for the systems investigated here, in which counterions are identical, is 1, and Eq. [5] reduces to
x¯ 2m
x¯ 1 x¯ 2 = x¯ 2 − 2 cmc
∂cmc ∂ x¯ 2
.
[7]
T, p
x¯ 2m was evaluated as a function of cmc by computer analysis of the critical micelle concentration data (see solid lines in Figs. 2 and 3). The upper lines (dotted) in Figs. 2 and 3 show the variation of the cmc with the composition of the mixed micelle as determined by this method. The lower curves show the variation of the experimentally measured cmc with the composition of the system. Figures 2 and 3 may be regarded as phase diagrams, expressing the relationship between the mole fraction of the drug in the mixed micelle and that in the solution in equilibrium with it. The dotted line shows the equilibrium total concentration of
FIG. 3. Variation of cmc (cmc = 2 cmc) with the mole fraction of doxepin in the nortriptyline/doxepin system. The dotted line shows the equilibrium total concentration of the free monomeric drug for a given mole fraction of doxepin in the mixed micelle, x¯ 2m , as calculated from Eq. [4]; the solid line gives the mole fraction of doxepin in monomeric form, x¯ 2 , in the solution in equilibrium with the micelles.
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BINARY MIXTURES OF AMPHIPHILIC TRICYCLIC DRUGS
of nortriptyline in this system indicates that the incorporation of small amounts of doxepin into nortriptyline micelles is not an ideal process. To quantify the nonideality of mixing in the mixed aggregates we have used the simplified approach proposed by Holland and Rubingh (15). According to this model, the monomer concentration of each component in the micelle mixture, cim , is given by cim = xi cmcm ,
[8]
where xi is the mole fraction of the ith component in the total mixed solute and cmcm the critical micelle concentration of mixed system. For nonideal binary mixtures of surfactants, the activity coefficients are given by f i = xi cmcm xim cmci
(i = 1, 2),
[9]
where cmci is the cmc of the pure component. Using a simple regular solution approximation, the activity coefficients can be expressed as functions of the mole fractions of each of the components in the mixed micelle, xim , and an appropriate interaction parameter β12 that is related to net interaction between drug molecules in the mixed aggregates. The regular solution approximation for the activity coefficients in the mixed micelles gives 2 f 1 = exp β12 1 − x1m 2 f 2 = exp β12 x1m .
[10] [11]
The net interaction parameter β12 can be readily determined when the mixed critical micelle concentration for the binary system is known, by interactively solving for x1m at the critical micelle concentration using a relationship such as
2 x1m
x1 cmcm x2 cmcm m 2 = 1 − x1 ln [12] ln m x1 cmc1 1 − x1m cmc2
obtained from Eqs. [9], [10], and [11]. β12 can then be directly obtained by combining Eq. [9] with Eq. [10] to give β12
ln x1 cmcm x1m cmc1 = . 2 1 − x1m
[13]
Values of the molecular interaction parameter β12 were calculated for nortriptyline/doxepin and nortriptyline/amitriptyline systems (see Table 2) using Eq. [13] and cmc values of the pure components. For the nortriptyline/amitriptyline mixed systems β12 is low and negative, indicating slight attractive electrostatic forces between the antidepressant molecules. This agrees with previous results obtained for the binary mixture of the antidepressant drugs imipramine and clomipramine, for which a mean
TABLE 2 Molecular Interaction Parameters, β12 , for the Systems Nortriptyline/Amitriptyline and Nortriptyline/Doxepin at 298.15 K Mol fraction nortriptyline Nortriptyline/amitriptyline Nortriptyline/doxepin 0.20 0.35 0.50 0.65 0.80
−0.02 −0.13 −0.11 −0.15 −0.37
+0.25 +0.28 +0.35 +0.45 +1.04
interaction parameter β12 of −0.9 was calculated. However, for the system nortriptyline/doxepin β12 values are positive, indicating the existence of a repulsive interaction in mixed micelles. Moreover, β12 becomes more positive as the mole fraction of nortriptyline in the mixed micelles is increased. The difference in behavior of the two systems may be a consequence of differences in the preferred packing within the micelles of each drug as indicated in a previous work (7). In this respect it is interesting to note that the solubility of nortriptyline in mixtures with doxepin was appreciably higher than when mixed with amitriptyline. Since these drugs possess the same hydrophilic charged groups any differences in the extent of solubilization of nortriptyline or in the packing in the mixed micelles in these two binary systems must be associated with the presence of the oxygen atom in the tricyclic ring system of doxepin. The lone pair of electrons on this oxygen atom can undergo resonance with the aromatic rings, giving rise to tautomers with zwitterionic character, thus decreasing the hydrophobicity of the ring system. The tautomeric zwitterions may interact electrostatically with the charged groups of nortriptyline, so facilitating the incorporation of this drug in the mixed micelles and hence enhancing its solubility. In addition, our results suggest that there is also an effect on the packing in the mixed micelle as evidenced by the difference in the interaction parameters of the two mixed systems. Repulsive interaction in mixed micelles in aqueous media is unusual and, for hydrocarbon-chain surfactants, has been reported only in mixtures of long-chain carboxylates and long-chain alkylbenzensulfonates (22). It is more commonly found in mixtures of anionic fluorocarbon-chain and anionic hydrocarbon-chain surfactants (23). We have previously noted this effect in mixed systems of the penicillins nafcillin and either cloxacillin or dicloxacillin where it was thought to be a consequence of structural differences between the hydrophobic groups (6). 4. CONCLUSIONS
The relatively low values of the dimensionless interaction parameter β12 suggest only small deviations from ideality of mixing in mixed micellar solutions of the antidepressant drugs amitriptyline, nortriptyline, and doxepin. However, it is interesting to note the difference in sign of the β12 values for the
162
TABOADA, ATTWOOD, AND MOSQUERA
two mixed systems and the higher β12 values for the nortriptyline/doxepin solutions, which, it is suggested, might be a consequence of structural effects due to differences in the packing of the drug molecules in the small micelles. ACKNOWLEDGMENT The authors thank Xunta de Galicia for financial support.
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