J . Phys. Chem. 1992, 96, 11018-1 1021
11018
Apparent Molar Enthalpies of Amphiphilic Drugs in Aqueous Solution
D.AtWood,* Department of Pharmacy, University of Manchester, Manchester MI 3 9PL, U.K.
E.Boitard, J.-P. Dub&, and H.Tachoire Laboratoire de Thermochimie, Universite de Provence, F-13331, Marseille Cedex 03, France (Received: May 27, 1992; In Final Form: August 4, 1992)
Apparent molar enthalpies have been determined as a function of concentration by heat conduction calorimetry for aqueous solutions of the amphiphilic drugs chlorpromazine hydrochloride, promethazine hydrochloride, promazine hydrochloride, and imipramine hydrochloride. The concentration dependence of the apparent molar enthalpy could be quantitatively described using a mass-action model of association based on the Guggenheim equations for the activity coefficients of mixed electrolytes. Micellar properties predicted by the application of this theory to calorimetric data were in good agreement with experimental values from light scattering techniques, but the derived values of the monomer-counterion interaction parameters were strongly negative indicative of possible premicellar association.
Introduction Although the self-association of amphiphilic drugs has been widely studied,] few workers have reported the direct measurement of the thermodynamic properties of the drug solutions. Osmotic and activity coefficients have been derived from vapor pres~iure~*~ and freezing point4 measurements on aqueous solutione of several drugs possessing tricyclic hydrophobic moieties. A mass- action model of association proposed by Burchfield and Woolley,s-8 which assumes the single-step formation of micelles at the critical micelle concentration (cmc), quantitatively described the concentration dependence of the osmotic coefficients but yielded counterionmonomer interaction coefficients which were strongly negative suggesting p i b l e premicellar association of monomers. Recent determinations9 of the apparent molar volume of several phenothiazine drugs supported this hypothesis; positive deviation from the DebyeHiickel limiting law indicated continuous association in dilute solution leading to the formation of a stable aggregate at the critical concentration. Application of the technique of heat conduction calorimetry to solutions of the phenothiazine drug, promethazine hydrochloride, containing added electrolyte (0.14.6 mol dm-' NaCl) also showed limited assoCiation below the critical concentration.l"-12 The calorimetric data in this concentration region could be satisfactorily described by an association scheme in which a primary aggregate comprising 3-4 monomers was formed by stepwise association. Molar enthalpies for formation of these aggregates were reported. Such measurements have cast doubts on the validity of the identification of the observed discontinuity of the physicochemical properties of the solutions at the critical concentration, with the cmc of typical surfactants. The recent dem~nstration'~ of additional discontinuities in the light scattering data of several phenothiazine drugs a t higher solution concentrations suggests a complex association pattern for these drugs. We now report the application of the Burchfield and Woolley mass-action model to data derived by heat conduction calorimetry for the phenothiazine tranquilizing drugs, chlorpromazine, promethazine, and promazine and the tricyclic antidepressant drug, imipramine. Values of the thermodynamic parameters derived from this study have been compared with those previously derived from vapor pressure datae2 Experimental Section Materials. The hydrochlorides of chlorpromazine [2-chloro10-(3-(dimethylamino)propyl)phenothiazine], promethazine [ lo-(2-(dimethylamino)propyl)phenothiazine], promazine [ 10(3-(dimethylamino)propyl)phenothiazine], and imipramine [5 (3-(dimethylamino)propyl)- 10,lldihydre5H-dibenz [bJ1azepine] (Sigma Chemical Co.) conformed to the purity requirements of the British Pharmacopoeia and as such contained not less than
TABLE I: Comparison of Micellar Properties As Predicted from Mass-Action Model with Experimental Values from Light Scattering (in Parentheses) c'/mol ka-' n B promethazine" 0.85 (0.73) 0.058 (0.058) 7 (11) promazine" 0.87 (0.83) 0.040 (0.035) 6 (1 1) imipramineb 0.78 (0.77) 0.048 (0.047) 7 (8) chlorpromazine" 0.026 (0.027) 6 (12) 0.72 (0.80)
"Light scattering values from ref 13. bLight scattering values from ref 21. 98.5% of the specified compound. Calorimetric Equipment. Calorimetric measurements were performed at 30 "C on a modified Arion-Electronique conduction calorimeter, the design, operation, and calibration of which have been described previ0us1y.l~ The transfer function of such equipment may lead to signal deformation and, in order to measure the instantaneous power absorbed by the environment of the reaction during the course of the experiment, it is essential to deconvolve the response by compensation of the principal time constants.IsJ6 Deconvolution was achieved by analog filtering"-I9 of the calorimetric output. Continuous monitoring of the calorimetric output enabled the variation of the relative apparent molar enthalpy with molality to be displayed by means of graphs composed of between 350 and 600 data points over the concentration range 0-0.25 mol kg-I. Results We have shown previously" that the relative apparent molar enthalpy, &(m), a t a molality m, may be derived from the continuous measurement of the instantaneous power, P, absorbed during the controlled dilution of a drug solution using where d2 is the rate of addition of drug and P is the average power a t a point in the dilution where the concentration is m, Le.
P = (1/t)
S ' P dt 0
Plots of +L as a function of m (Figures 1 and 2) show clear inflection points at the concentrations, c', given in Table I. Comparison with values of c' from light scattering techniques".2' shows good agreement for all drugs. The drug micelles are assumed to be formed by a single-step association from n cations of drug A+ and no counterions Maccording to the equilibrium nflM- + nA+
M nBAnn(l-W
0022-3654/92/2096-11018$03.00/00 1992 American Chemical Society
(3)
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 11019
Molar Enthalpies of Amphiphilic Drugs
QLO~L, kJ mol
where
and
a mM+mA+mB = i E( m
(g)p
-200
0.1
m/mol k g '
-
1
ln(10)
)-?
L
0.2
Figure 1. Variation of 4Land L, with concentration, m, for promethazine (upper) and chlorpromazine (lower). Data points (350600) for against m plots are within the thickness of lines representing the best-fit curves as calculated using eqs 4-9 and the parameters of Table 11.
@ J ~
-+
mA is the molality of drug in monomeric form, i.e., mA = ( 1 a)m;mBis the molality of drug in micellar form, Le., mB = am/n; mMis the molality of free drug counterions, i.e., mM= (1 - @a)m, where a is the molar fraction of the drug in micellar form; /3 is the fraction of counterions bound to the micelle; n is the aggregation number; A , is the Debye-Hiickel parameter for activity coefficients,Z is the ionic strength, b is an ion-size parameter; B I , and B,,, are the Guggenheim ion interaction parameters for counterion-monomer and counterion-micelle interactions, respectively; and the derivatives of mA, mB,and mMwith respect to temperature, T , at constant pressure P are (am,/aT), = -m(aa/aT)P
(7)
(amB/aT)P = (m/n)(aa/aT)P
(8)
( a m M / a n P= -j3m(aa/anP
(9)
The equilibrium constant for the formation of drug micelle is given by
K=
r
[a/n( 1 - @a)"@(1 - a)nm("b+wl)]
(10)
where
Hence
- 20;
0.1
m/mol kg'
0.2
Figure 2. Variation of 4Land L with concentration,m, for imipramine (upper) and promazine (lower). Data points (350-600) for dL against m plots are within the thickness of lines representing the best-fit curves as calculated using eqs 4-9 and the parameters of Table 11.
Application of the Burchfield and Woolley mass-action models-* for the micellization of ionic surfactants, which uses the Guggenheim activity coefficient expressions for mixed electrolyte solutions derived from the Debye-HBckel theory, gives the following expression for t # ~ ~
log K = log ( a m / n ) - nj3 log (1 - j3a)m - n log (1 - a ) m [2n(Z - m)A,Z1/2/am(l+ b11/2)]+ (nB,, - Bn,)(28a l ) m - Bl,n/3m (1 1) Equation 11 may be used to calculate the fraction of drug in micellar form, a,as a function of molality for given values of the parameters K , 8, n, A,, BI,, and B,,,. The derivative (da/dT), was determined from eq 12 which is derived by means of the van't Hoff equation ( a a / d n p= A , H o , / R p D
+N/D
(12)
11020 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
Attwood et al.
TABLE II: P8mWtem Derived by A p p l l c a h of Mass-Action Model to C8lorlmelrk Data (ConcentratioasRange m 4 0.25 mol kg-* Except %re 1adiatCd)a
std dev aB a T for N kg 1dkl data B , / k mol-' mol-' K-' mol-' K-' mint 4.2 f 0.1 2.23 f 0.01 3.02 f 0.05 -13.4 N = 430 (1.4) -12.3 f 0.2 2.40 f 0.01 7.0 f 0.2 12.0 N = 420 -2.7 f 0.8 1.4 f 0.02 3.23 f 0.4 31.0 (2.70) N=600 -22.3 f 0.01 4.98 f 0.01 2.09 f 0.01 10.3 (4.90) N = 380 -2.07 f 0.1 4.79 f 0.01 3.20 f 0.1 30.4 N = 775 aBl,laTl
A,H8,1kJ
In K mol-' 6 B , , / k a mol-' 7 0.89 f 0.01 33.6 f 0.1 -34.9 f 0.5 0.50 f 0.01 -0.41 f 0.01 (7) (35.5) (0.47) (-1.6) 6 0.84 f 0.01 31.5 0.1 -116.9 f 0.2 0.84 f 0.01 -3.02f 0.02
6
n
promethazine promazine imipramine chlorpromazine chlorpromazine (m 4 0.4 mol @-I)
7 0.76 f 0.02 35.2 f 0.1 -78.3 h 0.2 (8) (35.0) 6 0.81 f 0.01 33.1 0.1 -116.0 f 0.1 (8) (51.8) 6 0.72 f 0.02 32.3 f 0.1 -105.7 f 0.3
*
0.48 f 0.03 (0.45) 0.89 f 0.01 (0.40) 0.90 f 0.01
-2.72 f 0.02 (-0.70) -1.86f 0.05 (0.20) -1.88 f 0.05
~
dVaIuc9in parenthcscs were obtained by application of the model to osmometric data.2 1.0 L
0
O
'
m/moi kdl
0.2
0
0.1
m/moi k$
0.2
y+ (from q la), as a function of concentration, m,for promethazine
Figure 4. Osmotic coefficients, t j ~(from eq 17), and activity coefficients, yt (from eq 16), as a function of concentration, m, for imipramine
(upper) and chlorpromazine (lower).
(upper) and promazine (lower).
where Wmo is the molar enthalpy of the reference reaction and N and D are given by
Values for the relative apparent molar enthalpy were determined from eqs 4-9 with values of a and (aa/aT)pcalculated by means of eqs 11 and 12, respectively. An iterative method of calculation was used in which 8, K, A&,o, BIT,B 6 , (aBl,/aT)B and (aB,pT), were treated as variables with $'= 0.515 kg'/z (BA,/dT), = 8.8804 x lo4 K-I, and b 1. Computations were carried out for a series of values of n,and the best fit to the experimental 4L-m curves was determined for each by a least-squaresmethod. The resultant best fit curves (subject to the constraint that 6 < 1) are shown in Figures 1 and 2 and the corresponding parameters are given in Table 11. Also included on these figures is the concentration dependence of the partial molar enthalpy L of the drug as calculated from eqs 5 and 15.
Figure 3. Osmotic coefficients, (from q 17), and activity coefficients, #J
-
L = - 2 ~ T r ( aIn rl/aT),
where a
. i
n(1
- ,9)262 - (b + 1 )
and 6 is a shielding factor.
The variation of the activity coefficient, vt, and osmotic coefficient, 4, with molality was determined using the best fit parameters of Table I, from the following expressions:s
Molar Enthalpies of Amphiphilic Drugs
--
1
BI, Bn, M A ~ M + log (16) + bZ1I2+ - (2M A + m M )+ -mB 2 m2
A",
Figures 3 and 4 show plots of y+ and 4 as a function of concentration for the four drugs.
Discussion The values of the parameters n, K,6, BI,, and B,,., derived here are compared in Table I1 with values determined by the application of the Burchfield and Woolley mass-action model to osmotic data.2 In general, there is good agreement between values of n and K derived from both experimental techniques and also with the critical concentrations and aggregation numbers from light scattering measurements (see Table I). Comparison of the monomer-counterion interaction coefficients, Bl?, shows poorer agreement, although it should be noted that the mass-action model predicts negative values of this parameter from the experimental data of both techniques. Thus, although, as seen from the graphs of 4Lagainst m (Figures 1 and 2 ) , the mass-action model provides an excellent fit to the experimental data, the negative values obtained for B1,provide a strong indication of possible association of the drug molecules at concentrations below the critical concentration. Limited premicellar association was also reported previously1*'* from calorimetric measurements on promethazine hydrochloride solutions containing added electrolyte and a stepwise association model was used to describe the aggregation behavior in this concentration region. These findings also support the results of a recent studyg of the apparent molal volumes of a seria of phenothiazine drugs in which association at low solution concentrations was indicated from positive deviations of the apparent molar volume from the Debye-Htickel limiting law. The values of BITare determined mainly by the experimental data at low concentrations, and the cause of the discrepancies between the Bl, values from the osmometric and calorimetric techniques is thought to be the lack of precision of the osmometric technique at concentrations below c'. Figures 3 and 4 show nonlinear variations of both 4 and y+ over the concentration range 0 < m < c'. Curvature of similar plots derived from osmometric meas~rements~-~ could not be detected due to the limited amount of data and the uncertainty of measurements in this concentration region. Consequently greater reliability should be placed on the values derived from calorimetric measurements. The value of the micelltcounterion interaction coefficient B,, can be shown to be highly dependent on the concentration range over which the r#JL-mcurve is fitted by the mass-action model. Table I1 shows the appreciable change in the value of this parameter as a result of extending the concentration range to 0 4 . 4 mol kg-'; other parameters show a much smaller dependence on concentration range. The negative values obtained for this parameter may indicate an increase of aggregation number with concentration. If this is so, the less negative values obtained when the concentration range is extended suggest a tendency for the attainment of a more stable micelle at higher concentrations. The sensitivity of this parameter to the concentration range of measurement and, more importantly, to the values of the other variables describing the micellar properties may explain the very large
The Journal of Physical Chemistry, Vo1. 96, No. 26, 1992 11021
differences between values reported here and those reported previously from osmometric measurements. Table I1 shows the influence of molecular structure on the micellar parameters of these drugs. The branching of the side chain of promethazine causes appreciable differences in its properties when compared with promazine in which the only structural difference is the linearity of this side chain. Thus, the standard molar enthalpy of micellization of promethazine is much less exothermic, and this drug may have a lower propensity for premicellar association as indicated by its less negative B I , value. In contrast, the presence of the C1 substituent in the phenothiazine ring system of chlorpromazine, which distinguishes it from the otherwise identical drug, promazine, causes only small changes in Afl and Bly, both values being more negative for chlorpromazine. The comparison of promazine and imipramine highlights the influence of the ring system on the micellar properties, since these two drugs have identical side chains. Imipramine, which is an iminodibenzyl derivative, may have a very strong tendency to associate below cl, as evidenced by its strongly negative B I , value, although its relative apparent molar enthalpy of micellization is less exothermic. Acknowledgment. We thank Professor Earl Woolley for helpful discussions. Registry No. Chlorpromazine hydrochloride, 69-09-0; promethazine hydrochloride, 58-33-3; promazine hydrochloride, 53-60- 1; imipramine hydrochloride, 113-52-0.
Supplementary Material Available: Tables of values of 4Las a function of molality for each drug (13 pages). Ordering information is given on any current masthead page.
References and Notes (1) Attwood, D.;Florence, A. T. SurfacfanfSysrems; Chapman and Hall: London, 1983; Chapter 4. (2) Attwood, D.; Dickinson, N. A.; Mosquera, V.; Perez Villar, V. J . Phys. Chem. 1987, 91,4203. (3) Attwood, D.; Mosquera, V.; Perez W a r , V. J . Chem. SOC.,Faraday Trans. I 1989, 85, 301 1. (4) Attwood, D.; Mosquera, V.; Rey, C.; Vasquez, E. J . Chem. Soc., Faraday Trans. 1991,87, 2971. (5) Burchfield, T. E.; Woolley, E. M. J . Phys. Chem. 1984, 88, 2149. (6) Woolley, E. M.; Burchfield, T. E. J . Phys. Chem. 1984, 88, 2155. (7) Woolley, E. M.; Burchfield, T. E. J . Phys. Chem. 1985, 89, 714. (8) Woolley, E. M.; Burchfield, T. E. Fluid Phase Equilib. 1985, 20, 225. (9) Attwood, D.;Blundell, R.; Mosquera, V.; Garcia, M. J . Chem. Soc., Faraday Trans., submitted for publication. (10) Attwood, D.; Fletcher, P.; Boitard, E.; Dub&, J.-P.; Tachoire, H. T. J . Phys. Chem. 1990, 94, 6034. (11) Attwwd, D.;Fletcher, P.; Boitard, E.; DuMs, J.-P.; Tachoire, H. T. In Surfactants in Solurion; Mittal, K., Ed.; Plenum Press: New York, 1989; Vol. 7, p 265. (1 2) Attwood, D.; Boitard, E.; Dub&, J.-P.; Tachoire, H. T. Colloids Sur/. 1990, 48, 35. (13) Attwood, D.; Doughty, D.; Mosquera, V.; Perez Villar, V. J. Colloid Inferface Sci. 1991, 141, 316. (14) Attwood, D.; Fletcher, P.; Boitard, E.; DuMs,J.-P.; Tachoire, H. T. J . Phys. Chem. 1987, 91, 2970. (15) Navarro, J.; Torra, V.; Macqueron, J. L.; Dub&, J.-P.; Tachoire, H. Thermochim. Acta 1980, 39, 73. (16) Cesari, E.; Torra, V.; Macqueron, J. L.; Prost, R.; DuMs,J.-P.; Tachoire, H. Thermochim. Acta 1982, 53, 1, 17. (17) Dub&, J.-P.; Barr&, M.; Boitard, E.; Tachoire, H. Thermochim. Acta 1980, 39, 63. (18) Dub&, J.-P.; KEchavarz, R.; Tachoire, H. Thermochim. Acra 1984, 79, 15. (19) Cesari, E.; Torra, V.; Macqueron, J. L.; Dub&, J.-P.; KEchavarz, R.; Tachoire, H. Thermochim. Acta 1984, 79, 27. (20) Boitard, E.; DuMs, J.-P.; KEchavarz, R.;Tachoire, H. Thermochim. Acta 1987, 1 16, 1. (21) Attwood, D.; Gibson, J. J . Pharm. Pharmacol. 1978, 30, 176.
