9586
J. Phys. Chem. B 1997, 101, 9586-9592
Calorimetric Study of the Influence of Electrolyte on the Micellization of Phenothiazine Drugs in Aqueous Solution D. Attwood* School of Pharmacy and Pharmaceutical Sciences, UniVersity of Manchester, Manchester M13 9PL, U.K.
E. Boitard, J.-P. Dube` s, and H. Tachoire Laboratoire de Thermochimie, UniVersite´ de ProVence, F-13331 Marseille Cedex 3, France ReceiVed: July 3, 1997; In Final Form: September 8, 1997X
Apparent molar enthalpies have been determined as a function of concentration by heat conduction calorimetry for aqueous solutions of the phenothiazine drugs chlorpromazine hydrochloride, promethazine hydrochloride, and promazine hydrochloride in the presence of added electrolyte (0.025-0.10 mol dm-3 NaCl). 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 for mixed electrolytes. Derived values of the monomer-counterion interaction coefficient became increasingly negative with increase of salt concentration, suggesting that electrolyte addition promoted association at concentrations below the critical micelle concentration (cmc). Calculations of the fraction of each drug in the form of micelles as a function of concentration further confirmed the tendency for premicellar association. Significant differences in properties were observed between promethazine and the other two drugs. The micellization of this drug became increasingly exothermic with increase of electrolyte concentration, whereas the micellization of both chlorpromazine and promazine became increasingly endothermic. Moreover, the premicellar association of promethazine was more pronounced, the predicted fraction of drug in micellar form at the cmc increasing from 2.6% in water to 65% in 0.1 mol dm-3 NaCl.
Introduction The phenothiazine tranquillizing drugs have interesting association characteristics which derive from their rigid, tricyclic hydrophobic groups.1 A recent NMR study has indicated a vertical concave-to-convex stacking of molecules within the micelles.2 The occurrence of several discontinuities in the light scattering data for aqueous solutions of these drugs in the absence of added electrolyte3 suggests a complex association pattern. In a previous paper 4 we determined apparent molar enthalpies of several phenothiazine drugs by heat conduction calorimetry in the concentration region of the first critical concentration (hereafter referred to as the critical micelle concentration, cmc). The concentration dependence of apparent molar enthalpy could be quantitatively described using a mass action model of micellization proposed by Burchfield and Woolley5,6 which assumes the single-step formation of micelles at the cmc. Micellar properties predicted by the application of this theory to the calorimetric data were in good agreement with experimental values from other techniques. However, the derived values of the monomer-counterion interaction coefficients were strongly negative, indicative of possible limited association at concentrations below the cmc. Similar conclusions were reported from an application of the mass action theory to vapor pressure data;7 from the deviations of the apparent molar volume from the Debye-Hu¨ckel limiting law in very dilute solution;8 and from emf measurements.9 In the presence of high concentrations of added electrolyte (0.2-0.6 mol dm-3 NaCl), the association at concentrations above the cmc was continuous and data from both light scattering10 and calorimetric techniques11,12 could be simulated using models that assumed micellar growth by the stepwise addition of monomers to the primary micelle formed at the cmc. Moreover, the X
Abstract published in AdVance ACS Abstracts, November 1, 1997.
S1089-5647(97)02186-X CCC: $14.00
analysis of the calorimetric data revealed evidence of limited association at concentrations below the cmc, leading to the formation of the primary micelle. We now report the application of the Burchfield and Woolley mass action model to data derived by heat conduction calorimetry for solutions of the phenothiazine drugs chlorpromazine, promethazine, and promazine in dilute electrolyte solution (molarity e 0.1 mol dm-3). Micellar properties derived from this study are compared with previously reported values from static light scattering.13 Experimental Section Materials. The hydrochlorides of chlorpromazine [2-chloro10-(3-dimethylaminopropyl)phenothiazine], promethazine [10(2-dimethylaminopropyl)phenothiazine], and promazine [10(3-dimethylaminopropyl)phenothiazine] (Sigma Chemical Co.) conformed to the purity requirements of the British Pharmacopoeia and as such contained not less than 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 previously.14 The transfer function of such equipment may lead to signal deformation, and 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.15,16 Deconvolution was achieved by digital inverse filtering17-19 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 400 and 900 data points over the concentration range 0-0.30 mol kg-1. © 1997 American Chemical Society
Micellization of Phenothiazine Drugs
J. Phys. Chem. B, Vol. 101, No. 46, 1997 9587 TABLE 1: Comparison of Critical Micelle Concentrations, c′ , Micellar Aggregation Number, n, and Degree of Counterion Binding, β, As Predicted from Mass Action Model with Experimental Values (Given in Parentheses) NaCl/mol dm-3 0.000
0.050
0.100
0.040 (0.04010) 9 (1122) 1.016 (0.8022)
0.033 (0.031,27 0.0343) 10 (12,131910) 1.008 (0.8613)
Chlorpromazine c′/mol kg-1 0.026 0.018 0.013 (0.027,22 0.02213) (0.01810) (0.01410) n 6 8 9 (123) (1522) (2622) β 0.710 0.910 0.985 (0.80,3 0.8327) (0.8122) (0.8522)
0.008 (0.008,3 0.00713) 12 (35,13,27 403) 0.981 (0.81,27 0.9013)
c′/mol kg-1 0.059 (0.05822,27) n 7 (113,10) β 0.801 (0.733)
c′/mol kg-1 0.041 (0.03522) n 6 (113,10) γ 0.798 (0.833)
0.025 Promethazine 0.048 (0.04510) 6 (1022) 1.036 (0.7622)
Promazine 0.032
0.023
9
9
0.914
0.954
0.019 (0.01927) 11 (2110) 0.982
The equilibrium constant for micelle formation in the presence of added electrolyte21 is given by: Figure 1. Variation of the relative apparent molar enthalpy, Lφ, with molality, m, for (A) promethazine, (B) promazine, and (C) chlorpromazine in (s) water and (•••) 0.025, (•-•-•) 0.050, and (o-o-o) 0.100 mol dm-3 NaCl. Data points (400-1000) are within the thickness of the lines representing the best-fit curves as calculated using mass action theory.
Results We have shown previously20 that the relative apparent molar enthalpy, Lφ(m), at 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
Lφ(m) ) (P h /d2)m - (P/d2)∞
(1)
h is the average where d2 is the rate of addition of drug and P power at a point in the dilution where the concentration is m, i.e.
P h ) (1/t)
∫o P dt t
(2)
Plots of Lφ as a function of m (Figure 1) show inflection points at the critical micelle concentrations, c′, given in Table 1. Comparison with literature values shows good agreement for all drugs. For promethazine, Lφ decreases with m in water and at all salt concentrations with the consequence that the thermal effects associated with micelle formation of this drug are negative. For the other two drugs, the thermal effects are negative only in water and 0.025 mol dm-3 electrolyte; a pronounced increase of Lφ is observed for both drugs in 0.100 mol dm-3 electrolyte. In the Burchfield and Woolley mass action model5,6,21 the drug micelles are assumed to be formed by a single-step association from n cations of drug A+ and nβ counterions Maccording to the equilibrium
nβM + nA h MnβAn -
+
+n(1-β)
(3)
K ) [R/n(r - βR)nβ(1 - R)nm(nβ+n-1)](γB/γMnβγAn) (4) where γB, γM, and γA are the activity coefficients for species [MnβAn+n(1-β)], M-, and A+, respectively, r ) 1 + mx/m with mx ) molality of counterion, β ) fraction of counterions bound to the micelle, R ) the fraction of drug in micellar form, and n ) the aggregation number. The activity coefficients are given by the Guggenheim equations as
log γB ) -{(n2(1 - β)2δ2AγI1/2)/(1 + bBI1/2)} + BnγmM (5) log γA ) -{AγI1/2/(1 + bAI1/2)} + B1γmM
(6)
log γM ) -{AγI1/2/(1 + bMI1/2)} + B1γmA + BnγmB + Bxγmx (7) log γx ) -{AγI1/2/(1 + bxI1/2)} + BxγmM
(8)
where Aγ is the Debye-Hu¨ckel coefficient, B1γ, Bnγ, and Bxγ are the interaction parameters for counterion-monomer, counterion-micelle, and ions of added electrolyte respectively, δ is a “screening factor” for the micellar charge, and the ion-size parameters bA, bB, bM, and bx are assumed to be equal to 1. I is the ionic strength of the solution given by I )(amR/2) + mr, where a ) n(1 - β)2δ2 - (1 + β). Replacing mA, mB, mM, and mx with their expressions in terms of m, R, β, and r in eqs 5-8 gives the following expression for the micellar equilibrium constant:
log Kmic ) log(Rm/n) - nβ log(r-Rβ)m - n log(1-R)m 2n(I - mr)AγI1/2/Rm(1 + bI1/2) + (2βR - r)(nB1γ Bnγ)m - nβ[(B1γ - Bxγ) + rBxγ]m (9) Equation 9 may be used to calculate the fraction of drug in micellar form, R, as a function of m if values of the parameters Kmic, β, n, Aγ, B1γ, Bnγ, and Bxγ are known. Similarly, the
9588 J. Phys. Chem. B, Vol. 101, No. 46, 1997
Attwood et al.
mean ion actiVity, γ(, of the drug MA and the electrolyte MX, the osmotic coefficient, φ, the relatiVe apparent molar enthalpy, Lφ, and the relative partial molar enthalpy, LMA, may be calculated from eqs 10, 11, 12, 13, and 14, respectively.
log γ((MA) ) - AγI1/2/(1 + bI1/2) + B1γ(r - βR + 1 R)m/2 + BnγRm/2n + Bxγ(r - 1)m/2 + (1/2)log(r - βR)(1 - R)/r (10) log γ((MX) ) - AγI1/2/(1 + bI1/2) + B1γ(1 - R)m/2 + BnγRm/2n + Bxγ(2r - βR - 1)m/2 + (1/2)log(r - βR)/r (11) φ ) 1 - [R(1 + β - 1/n)/2r] [ln(10)AγI3/2σ(bI1/2)/3rm] + [ln(10)m(r - βR)/2r][B1γ(1 - R) + BnγR/n + Bxγ(r - 1)] (12)
[(
2
Lφ ) -2RT
)
∂ ln γ((MA) + ∂T p ∂ ln γ((MX) ∂φ -r (r - 1) ∂T p ∂T
( (
LMA ) -2RT2
∂ ln γ((MA) ∂T
p
p
(13)
(14)
where
( ) [ ( ) ( ) ( ) ( ) ( ) ] ( )
(
)
1/2 ∂ ln γ((MA) ln(10) ∂ AγI ) -ln(10) + (mA + 1/2 ∂T ∂T 1 + bI p 2 p ∂B1γ ∂Bnγ ∂Bxγ ∂mA + + mB + mX + mM) ∂T p ∂T p ∂T p ∂T
∂mB mAmM ∂mM 1 ∂ B1γ + Bnγ + ln ∂T p ∂T p 2 ∂T rm2
(15)
p
and
(
)
(
)
1/2 ∂ ln γ((MX) ∂ AγI ) -ln(10) + ∂T ∂T 1 + bI1/2 p p ∂B1γ ∂Bnγ ∂Bxγ ln(10) mA + mB + (mX + mM) + 2 ∂T p ∂T p ∂T p
( ) [( ) ( ) ( ) ( ) ( ) ] ( ) ∂mA ∂mB ∂mM mM 1 ∂ B + B + B + ln ∂T p 1γ ∂T p nγ ∂T p xγ 2 ∂T rm
p
(16) and
()
(
)
1 ∂(mM + mA + mB) ∂φ ) ∂T p 2rm ∂T p ∂B1γ ln(10) ∂ ln(10) (AγI3/2σ(bI1/2)) + mM mA + 3rm ∂T p 2rm ∂T p ∂Bnγ ∂Bxγ ∂mA ∂mM + mX + B1γ mM + mA + mB ∂T p ∂T p ∂T p ∂T p ∂mB ∂mM ∂mM + mB + BxγmX (17) Bnγ mM ∂T p ∂T p ∂T p
( ( )
)
( [ ( ) ( )] [ ( ) ( )] [ ( ) ( )] ( ))
The derivatives of mA, mB, and mM with respect to temperature, T, at constant pressure P are
(18)
(∂mB/∂T)p ) (m/n)(∂R/∂T)p
(19)
(∂mM/∂T)p ) -βm(∂R/∂T)p
(20)
The derivative (∂R/∂T)p was determined from eq 21, which is derived by means of the van’t Hoff equation,
(∂R/dT)p ) ∆micH°m/RT2D + N/D
(21)
where ∆micH°m is the molar enthalpy of the reference reaction; N and D are given by
( ) [( ) ( ) ] [( ) ( ) ( ) ]
∂B1γ naI1/2 ∂Aγ + (r - 2βR)m n N ) ln(10) 1/2 ∂T ∂T p 1 + bI ∂Bnγ ∂B1γ ∂Bxγ ∂Bxγ + nβm +r (22) ∂T p ∂T p ∂T p ∂T p D ) (1/R) + n
) ( )] )
(∂mA/∂T)p ) -m(∂R/∂T)p
(
)
1 β2 + r - βR 1 - R
ln(10)
[
2
na mAγ
4I1/2(1 + bI1/2)2
]
+ 2βm(nB1γ - Bnγ) (23)
The parameters characterizing the micellization process were determined from the best fit to the curves of Figure 1. Values for the relative apparent molar enthalpy were determined from eq 13 with values of R calculated from eq 9, (∂R/∂T)p from eq 21, (∂ ln γ((MA)/∂T)p from eq 15, (∂ ln γ((MX)/∂T)p from eq 16, and (∂φ/∂T)p from eq 17. An iterative method of calculation was used in which β, Kmic, ∆micH°m, B1γ, Bnγ, Bxγ, δ, (∂B1γ/ ∂T)p, (∂Bnγ/∂T)p, and (∂Bxγ/∂T) were treated as variables with Aγ ) 0.515 kg1/2 mol-1/2, (∂Aγ/∂T)p ) 8.8804 × 10-4 kg1/2 mol-1/2 K-1, and b ) 1. Computations were carried out for a series of values of n, and the best fit to the experimental Lφ(m) curves was determined for each by a least-squares method. The resultant best fit curves are shown in Figure 1, and the corresponding parameters are given in Table 2 together with data derived from a previous calorimetric study of the association of these drugs in water.4 Since the values of several of the parameters predicted by the mass action theory, notably ∆micH°m and Bnγ, have been shown to be dependent on the concentration range of the analysis, we have reanalyzed the curves from this previous study over the concentration range used here to allow a more meaningful comparison with the data in electrolyte solutions. The derived values of ln Kmic for each drug increase with increase of electrolyte concentration as expected. Values of the counterion-monomer interaction coefficient B1γ derived from the data-fitting procedure are negative, indicative of association below the critical concentration, and, in general, become increasingly negative as salt concentration increases, suggesting that electrolyte addition promotes the association in this concentration region. The simulation of osmometric7 and freezing point depression22 data using the Burchfield and Woolley model has also yielded negative values of B1γ for these drugs in water and salt concentrations up to 0.05 mol kg-1. Inspection of the computed parameters of Table 2 shows interesting differences in properties of promethazine micelles and those of the other two drugs. B1γ values of promethazine are significantly more negative at all electrolyte concentrations, suggesting a greater degree of premicellar association (as will be discussed below). In addition, Bnγ values are very much larger than for the other two drugs, indicating a more pro-
5.3 N ) 550 36.7 N ) 875 33.0 N ) 865 34.3 N ) 865 (5411 ( 1) × 10-6 (460 ( 1) × 10-5 (3144 ( 1) × 10-6 0.0292 ( 0.0002 0.691 ( 0.001 1.65 ( 0.02 1.28 ( 0.02 1.420 ( 0.005 1.156 ( 0.005 0.696 ( 0.005
Figure 2. Relative partial molar enthalpy, LMA, from eq 14 as a function of molality, m, for (A) promethazine, (B) promazine, and (C) chlorpromazine in (s) water and (•••) 0.025, (•-•-•) 0.050, and (o-o-o) 0.100 mol dm-3 NaCl.
Values recalculated from the data of ref 4 over a similar concentration range. a
6 9 9 11 0.000 0.025 0.050 0.100
0.798 ( 0.004 0.914 ( 0.001 0.954 ( 0.001 0.982 ( 0.002
29.6 ( 0.1 57.10 ( 0.01 59.24 ( 0.01 73.7 ( 0.05
-99 ( 1 -64.70 ( 0.05 89.3 ( 0.5 101 ( 5
0.842 ( 0.001 0.918 ( 0.001 0.956 ( 0.001 0.787 ( 0.001
0.72 ( 0.01 -2.820 ( 0.001 -2.939 ( 0.003 -2.392 ( 0.004
Promazine 1.16 ( 0.05 12.280 ( 0.002 8.64 ( 0.01 4.35 ( 0.02
(244 ( 1) × 10-4 (144 ( 1) × 10-4 (330 ( 5) × 10-5 -(420 ( 1) × 10-5
10.5 N ) 450 32.9 N ) 880 33.7 N ) 750 9.2 N ) 870 (423 ( 2) × 10-5 (4495 ( 1) × 10-6 (3065 ( 1) × 10-6 (166 ( 2)10-4 0.53 ( 0.03 1.09 ( 0.05 5.651 ( 0.001 (498 ( 1) × 10-4 (348 ( 1) × 10-4 (405 ( 1) × 10-5 -(238 ( 1) × 10-5 1.643 ( 0.002 1.09 ( 0.01 0.724 ( 0.001 Chlorpromazine -1.82 ( 0.01 -24.9 ( 0.3 -1.40 ( 0.03 19.7 ( 0.5 -2.19 ( 0.02 5.22 ( 0.03 -1.244 ( 0.002 15.008 ( 0.005 0.956 ( 0.001 0.781 ( 0.001 0.989 ( 0.001 0.726 ( 0.001 -112.0 ( 1 -93 ( 2 65.0 ( 0.5 908 ( 4 30.3 ( 0.1 53.52 ( 0.01 64.19 ( 0.01 88.80 ( 0.01 6 8 9 12 0.000a 0.025 0.050 0.100
0.710 ( 0.005 0.910 ( 0.003 0.985 ( 0.001 0.981 ( 0.001
14.5 N ) 485 7.9 N ) 750 6.2 N ) 550 18.7 N ) 750 (6273 ( 5) × 10-6 (4467 ( 2) × 10-6 (3000 ( 1) × 10-6 3.02 ( 0.05 -0.582 ( 0.001 -2.01 ( 0.01 -3.440 ( 0.005 (2227 ( 1) × 10-5 (927 ( 2) × 10-5 (407 ( 3) × 10-5 (369 ( 2) × 10-5 1.47 ( 0.03 1.25 ( 0.05 0.86 ( 0.01 7 6 9 10 0.000a 0.025 0.050 0.100
0.801 ( 0.005 1.036 ( 0.001 1.016 ( 0.001 1.008 ( 0.001
31.6 ( 0.1 42.36 ( 0.01 72.73 ( 0.04 96.78 ( 0.05
-66.6 ( 0.3 -84.2 ( 0.1 -267 ( 1 -721 ( 2
0.49 ( 0.01 0.968 ( 0.001 0.89 ( 0.01 0.79 ( 0.01
-0.69 ( 0.02 -3.82 ( 0.01 -5.46 ( 0.05 -8.18 ( 0.01
Promethazine 2.90 ( 0.03 27.38 ( 0.01 43.9 ( 0.2 45.67 ( 0.05
∂Bnγ/∂T/10-2 kg mol-1 K-1 ∂B1γ/∂T/10-2 kg mol-1 K-1 Bxγ/kg mol-1 Bnγ/kg mol-1 B1γ/kg mol-1 δ ∆micH°/kJ mol-1 ln K°mic n
β
J. Phys. Chem. B, Vol. 101, No. 46, 1997 9589
NaCl mol dm-3
TABLE 2: Parameters Derived by Application of Mass Action Model to Calorimetric Data (Concentration Range 0 < m < 0.30 mol kg-1)
∂Bxγ/∂T/10-2 kg mol-1 K-1
std dev for N data points
Micellization of Phenothiazine Drugs
nounced micelle-counterion interaction, and predicted δBnγ/ δT for promethazine become increasingly negative at higher electrolyte concentration in contrast to the increasingly positive values for the chlorpromazine and promazine. A comparison of the micellar properties derived from the application of the mass action theory to the calorimetric data with experimental values is given in Table 1. Although the simulation of the calorimetric data yields values of n that show the expected increase with increase of electrolyte concentration, the predicted values are consistently lower than equivalent experimental values from light scattering, the discrepancy being most apparent in the case of chlorpromazine. Although the mass action theory is clearly overestimating the extent of counterion binding to the drug micelles (β > 1 for promethazine), the rank order of the predicted values in Table 1 is in agreement with the Bnγ values which also show a greater involvement of counterions with the micelles of promethazine than with the other two drugs. The results are also in agreement with reported values of zeta potential23 and calculated values of surface charge from the application of DLVO theory to dynamic light scattering data for phenothiazines,13 both of which show a lower micellar charge for promethazine compared with chlorpromazine. Comparison is made in Table 1 with literature values of β derived from static light scattering data by application of the Anacker and Westwell equations for ionic surfactants.24 Experimental values for the degree of counterion binding to micelles of promethazine in dilute electrolyte solution have also been reported from emf measurements using a drug selective electrode and from the variation of cmc with salt concentration;9 both methods gave a β value of 0.65 for electrolyte concentrations up to 0.2 mol dm-3.
9590 J. Phys. Chem. B, Vol. 101, No. 46, 1997
Attwood et al.
Figure 4. Osmotic coefficients, φ, from eq 12 as a function of molality, m, for (A) promethazine, (B) promazine, and (C) chlorpromazine in (•••) 0.025, (•-•-•) 0.050, and (o-o-o) 0.100 mol dm-3 NaCl.
Figure 3. Mean ion activity coefficients, γ((MA), from eq 10 as a function of molality, m, for (A) promethazine, (B) promazine, and (C) chlorpromazine in (s) water and (•••) 0.025, (•-•-•) 0.050, and (o-o-o) 0.100 mol dm-3 NaCl.
Using the calculated parameters of Table 2, the concentration dependence of mean ion activity coefficient of the drug, the osmotic coefficient, the relative partial molar enthalpy, and the fraction of drug in micellar form were determined from eqs 10, 12, 14, and 9, respectively (see Figures 2-5). There is further evidence from these plots for significant association of promethazine below c′. Plots of LMA vs m for promethazine (Figure 2) show evidence of an inflection below the critical concentration which becomes more pronounced with increase in the concentration of added electrolyte. In addition, the mean ion activity coefficient γ( decreases markedly with drug molality at low concentrations for this drug (Figure 3), which supports the suggestion of premicellar association. The most convincing evidence for association of promethazine below the critical concentration is seen in the variation of R with concentration (Figure 5), from which it is clear that a significant fraction of
drug is in the form of aggregates at concentrations well below c′. This fraction increases with increase of concentration of added electrolyte from a value of 2.6% in water to 65% in 0.1 mol dm-3 NaCl. Emf measurements of Wan-Bahdi et al.9 using membrane electrodes selective for the promethazine cation have shown marked deviation from Nernstian behavior for solutions of promethazine at electrolyte concentrations below 0.05 mol dm-3, which has been attributed to premicellar association. No significant association was detectable, however, in the premicellar region at higher electrolyte concentration, in conflict with the results presented here and those of a previous calorimetric study12 in which the association characteristics of promethazine were examined at much higher salt concentrations (0.2-0.6 mol dm-3). Calorimetric data for promethazine at these higher salt concentrations could be simulated using theoretical models that assumed the formation of a primary unit of 3-4 monomers below the critical concentration and its subsequent growth at higher drug concentrations by stepwise addition of monomers. Table 3 shows that the predicted fraction of monomers involved in aggregate formation at low concentrations for the remaining drugs is appreciably lower. Other workers have determined the free monomer concentration at c′. Analysis of elution curves from gel permeation chromatography of chlorpromazine at a higher salt concentration than the present study (0.154 mol dm-3 NaCl)25 yielded the monomer concentration as a function of
Micellization of Phenothiazine Drugs
J. Phys. Chem. B, Vol. 101, No. 46, 1997 9591 TABLE 3: Thermodynamic Parameters for Micellization per Mole of Monomer, and Fraction, r, of Drug in Micellar Form at the cmc As Predicted from the Mass Action Model NaCl (mol dm-3)
Figure 5. Variation of the fraction, R, of monomers involved in aggregate formation at the cmc, from eq 9, as a function of molality, m, for (A) promethazine, (B) promazine, and (C) chlorpromazine. Cmc’s are denoted by (+).
total drug concentration from which approximately 60% of chlorpromazine is seen to exist as free molecules at c′. Funasaki and co-workers interpreted these data in terms of dimerization of drug at concentrations below c′. Similarly, analysis of NMR chemical shift data for chlorpromazine in D2O at concentrations below the critical concentration using a stepwise association model with equal equilibrium constants for each dissociation step2 indicated that about 45% of drug existed in aggregated form at c′, a value appreciably higher than that reported here, possibly as a consequence of the difference in association models adopted for these calculations. Although it should in principle be possible to detect differences in static and dynamic light scattering data for these drugs in the vicinity of c′ arising from differences in the fraction of monomer in aggregated form, the
∆micH°m/n (kJ mol-1)
∆micG°m/n (kJ mol-1)
∆micS°m/n (J K-1 mol-1)
R
6.3 12.5 -30.7 -157.3
0.03 0.38 0.59 0.65
0.000 0.025 0.050 0.100
-9.5 -14.0 -29.7 -72.1
Promethazine -11.4 -17.8 -20.4 -24.4
0.000 0.025 0.050 0.100
-18.7 -11.6 7.2 75.7
Chlorpromazine -12.7 -16.9 -18.0 -18.6
-19.8 17.5 83.1 311.1
0.07 0.10 0.14 0.16
0.000 0.025 0.050 0.100
-16.5 -7.2 9.9 9.2
Promazine -12.4 -16.0 -16.6 -16.9
-13.5 29.0 22.1 25.4
0.05 0.09 0.10 0.12
published light scattering data on the phenothiazines in water and dilute electrolyte (see for example ref 13) show no evidence of this effect, possibly reflecting the difficulties of precise measurement of these weakly aggregating systems in very dilute solution. The thermodynamic parameters per mole of monomer for micellization of the three drugs are given in Table 3. In view of the sensitivity of ∆micH°m to the concentration range of analysis (see above) comparison with literature values is not meaningful. Nevertheless, the results of this study, which have all been analyzed over the same concentration range, clearly show that the micellization of promethazine becomes increasingly exothermic with increase of electrolyte concentration, whereas the micellization of both chlorpromazine and promazine becomes increasingly endothermic. ∆micG°m values show the expected increase with increase of electrolyte concentration and the greater hydrophobicity of chlorpromazine compared to promazine, which is a consequence of the ring-substituted -Cl. Values of ∆micS°m calculated from these two thermodynamic properties become progressively more negative with increase of added electrolyte concentration in the case of promethazine and increasingly positive for chlorpromazine and promazine. Nusselder and Engberts26 have stressed the importance of the London dispersion forces as the main attractive force for micellization. The negative ∆micH°m values of promethazine suggest that these dispersion forces play the major role in micellization of this drug, while the positive values of both ∆micH°m and ∆micS°m for the other two drugs suggest the greater importance of hydrophobic interactions. The origin of this difference in driving force for these structurally similar molecules with identical counterions remains unclear. In summary, the simulation of calorimetric data using the mass action theory has highlighted a difference between the micellization characteristics of promethazine and those of chlorpromazine and promazine. Although all three drugs show evidence of limited association at concentrations below the critical concentration, the counterion-monomer interaction coefficients B1γ of promethazine are significantly more negative than those of the other drugs at equivalent electrolyte concentrations. Moreover, analysis of the data predicts a much higher fraction of this drug in aggregated form at the critical concentration in solutions containing added electrolyte. The micellization of this drug became increasingly exothermic with increase of concentration of added electrolyte, in contrast to that of chlorpromazine and promazine, which became increasingly endothermic.
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