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Langmuir 2002, 18, 3650-3654
Solute and Solvent Structure Effects on the Volume and Compressibilities of Some Colloidal Penicillins in Aqueous Solution Manuel Gutie´rrez-Pichel,† Pablo Taboada,† Luis M. Varela,† David Attwood,‡ and Vı´ctor Mosquera*,† Grupo de Fı´sica de Coloides y Polı´meros, Departamentos de Fı´sica de la Materia Condensada y Fı´sica Aplicada, Facultad de Fı´sica, Universidad de Santiago de Compostela, E-15706 Santiago de Compostela, Spain, and School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Manchester M13 9PL, U.K. Received October 30, 2001. In Final Form: February 1, 2002 The apparent molal volumes and adiabatic compressibilities of aqueous solutions of the sodium salts of the amphiphilic anionic penicillins cloxacillin, dicloxacillin, and nafcillin have been determined from density and ultrasound velocity measurements at 298.15 K. Critical concentrations were obtained from both techniques, confirming the existence of a second critical concentration for dicloxacillin, as had been previously reported. Positive deviations of the concentration dependence of the apparent molal volumes of cloxacillin and dicloxacillin from that predicted by the Debye-Hu¨ckel limiting law in dilute solution provide evidence for limited association at concentrations below the first critical concentration. Isentropic apparent molal adiabatic compressibilities of the aggregates formed by the drugs, calculated by combining the ultrasound velocity and density data, were typical of those for a stacked aggregate.
Introduction Many drugs exert their activity by interaction with biological membranes.1 This membrane affinity is a measure of the hydrophilic-hydrophobic interactions in the molecule and can be related to the surface activity at the air/solution interface. A detailed understanding of the solution behavior of amphiphilic drugs requires information on a variety of thermodynamic parameters. The volumes and compressibilities are two important thermodynamic properties, which can be helpful in the identification of solvent-solute, as well as solute-solute, interactions. Moreover, these parameters are useful as complementary information to the data obtained by such characterization methods as laser diffusion and NMR techniques. Interest in the colloidal properties of penicillin dates from the late 1940s with the early studies of McBain and co-workers,2 Hauser et al.,3 and Few and Schulman.4 These early investigations, mainly on penicillin G, were adversely affected by surface active impurities. The colloidal properties of amphiphilic drugs are largely determined by the nature of the aromatic ring systems of their hydrophobic moieties, and such drugs are useful in probing the relationship between molecular architecture and physicochemical properties.1 These substances owe their physicochemical properties to the presence of aromatic rings in their molecular structure that determine their hydrophobic character and consequently their self-association * To whom correspondence should be addressed. E-mail:
[email protected]. † Universidad de Santiago de Compostela. ‡ University of Manchester. (1) Attwood, D.; Florence, A. T. Surfactant Systems; Chapman and Hall: London, 1983. (2) McBain, J. W.; Huff, H.; Brady, A. P. J. Am. Chem. Soc. 1949, 71, 373. (3) Hauser, E. A.; Marlow, G. J. J. Phys. Colloid Chem. 1950, 54, 1077. (4) Few, A. V.; Schulman, J. H. Biochim. Biophys. Acta 1953, 10, 302.
colloidal behavior. In different previous studies5-11 we have investigated the physicochemical properties of aqueous solutions of some synthetic penicillins in water and electrolyte solution and have shown the existence of weak aggregation behavior. These drugs form aggregates of very low aggregation number in water at a critical concentration, which can be detected by a discontinuity of the concentration dependence of the physicochemical properties of the solution. The presence of substituents on the hydrophobic core or variations of the hydrocarbon chain length results in modifications of the behavior of these drugs in solution, altering their physicochemical properties and pharmacological activity. The importance of investigating the aggregation characteristics of penicillin drugs was stressed by Funasaki and co-workers12 in a discussion of the effects of self-association on their bacterial activity and chemical stability. In the present study we have examined the apparent molal volumes and adiabatic molal compressibilities of three penicillin drugs at 298.15 K from density and ultrasound velocity measurements, with particular emphasis on the effect of the substituents on the association behavior of these drugs. Two of the penicillins, sodium cloxacillin (X ) H) and sodium dicloxacillin (X ) Cl), are structurally related compounds differing only in the number and nature of the substituents on the aromatic (5) Taboada, P.; Attwood, D.; Ruso, J. M.; Sarmiento, F.; Mosquera, V. Langmuir 1999, 15, 2022. (6) Taboada, P.; Attwood, D.; Ruso, J. M.; Garcı´a, M.; Sarmiento, F.; Mosquera, V. J. Colloid Interface Sci. 1999, 216, 270. (7) Taboada, P.; Attwood, D.; Ruso, J. M.; Garcı´a, M.; Sarmiento, F.; Mosquera, V. J. Colloid Interface Sci. 1999, 220, 288. (8) Varela, L. M.; Rega, C.; Sua´rez-Filloy, M. J.; Ruso, J. M.; Prieto, G.; Attwood, D.; Sarmiento, F.; Mosquera, V. Langmuir 1999, 15, 6285. (9) Taboada, P.; Attwood, D.; Garcı´a, M.; Jones, M. N.; Ruso, J. M.; Mosquera, V.; Sarmiento, F. J. Colloid Interface Sci. 2000, 221, 242. (10) Taboada, P.; Attwood, D.; Ruso, J. M.; Garcı´a, M.; Sarmiento, F.; Mosquera, V. Langmuir 2000, 16, 3175. (11) Taboada, P.; Attwood, D.; Ruso, J. M.; Mosquera, V. J. Chem. Eng. Data 2000, 45, 512. (12) Funasaki, N.; Hada, S.; Neya, S. Chem. Pharm. Bull. 1994, 42, 779.
10.1021/la011619x CCC: $22.00 © 2002 American Chemical Society Published on Web 04/03/2002
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Chart 1
ring of the hydrophobe (see Chart 1). We have previously shown5,10 that all three drugs form small aggregates with aggregation numbers ranging from only 4-5 in water to 11 in 0.4 mol dm-3 electrolyte. In the present study particular attention has been paid to the possible existence of any second critical concentration which is a characteristic feature of some drugs, notably those based on a phenothiazine ring system. Critical concentrations for aggregation were detected from densities and ultrasound measurements. Experimental Section Materials. Sodium cloxacillin monohydrate ([5-methyl-3(o-chlorophenyl)-4-isoxazolyl]penicillin), sodium dicloxacillin monohydrate ([3-(2,6-dichlorophenyl)-5-methyl-4-isoxazolyl]penicillin), and sodium nafcillin monohydrate ([6,2-ethoxy-1-naphthamido]penicillin) were obtained from Sigma Chemical Co and used as received. Water was double-distilled and degassed before use. Density Measurements. Density was measured at 298.15 K using an Anton Paar DMA 60/602 densimeter with a resolution of (10-6 g cm-3. The temperature control was maintained within (0.005 K, giving rise to uncertainties in density of ca. (1.5 × 10-6 g cm-3. The temperature was maintained constant by a HETO proportional temperature controller and checked with an Anton Paar DT100-30 digital precision thermometer. The densimeter was calibrated with air at known pressure and water, where the density of water was assumed to be 0.997 043 g cm-3. To ensure the complete absence of microbubbles in the solutions, samples were kept for 30 min in a Branson 5200 ultrasound equipment at 298.15 K. Ultrasound Velocity Measurements. Ultrasound velocity was measured at 298.15 K at a frequency of 2 MHz using a Nusonic model 6380 concentration analyzer (Nusonic Inc.) with a temperature transducer connected to a Hewlett-Packard 3455A digital microvoltimeter. Errors in ultrasound velocity measurements arise mainly from variations of temperature; in this study temperature was controlled to within (0.005 K with a HETO temperature controller. The sound velocity transducer was connected to a Hewlett-Packard 3437A multimeter, whose output was assessed continuously by a computer, averaging 100 measurements and giving an accuracy in the velocity of ca. (0.01 m s-1. The uncertainties in the ultrasound velocity measurements were ca. (0.15 m s-1 at molalities above the critical concentration. Measurements on more dilute solutions were subject to increased error associated with the adsorption of penicillin from solution onto the walls of the cell.
Results and Discussion Densities and Molal Apparent Volumes. Figure 1 shows the density, F, of aqueous solutions of nafcillin at 298.15 K as a function of molality, m. Similar plots were obtained for cloxacillin and dicloxacillin. The results obtained for each drug were analyzed to detect the presence of any critical concentration, cc, using the Phillips defini-
Figure 1. Density, F, vs molal concentration, m, of nafcillin at 298.15 K. The Gaussian fit (dotted line) corresponds to the second derivative of the density (see text). The arrow shows the critical concentration.
tion13 of the critical micelle concentration, CMC, as the concentration corresponding to the maximum change in gradient in plots of the density versus concentration:
( ) d3F dm3
)0
(1)
m)cc
The numerical analysis of the data was made by means of a recently developed algorithm based on the RungeKutta numerical integration method and the LevenbergMarquardt least-squares fitting algorithm, which allows the determination of precise values of the critical concentration of drugs and surfactants with weak aggregation characteristics.14 The dotted line of Figure 1 is a Gaussian fit of the second derivative of the curve, the minimum value corresponding to the critical concentration. The critical concentrations for the penicillins cloxacillin, dicloxacillin, and nafcillin derived in this manner were 0.121, 0.104, and 0.126 mol kg-1, respectively. It was not possible to detect any second inflection points (see below) in the density data by this method. The apparent molal volume was calculated from the experimental density data by means of the equation
Vφ )
3 M 10 (F - F0) F mFF0
(2)
where M is the molecular weight of the solute and F0 the density of pure water. Three regions are observed in the plot of Vφ against m for aqueous solutions of dicloxacillin. (Figure 2): in very dilute solution, Vφ increases until the first critical concentration, cc1 (0.07 mol kg-1); in the middle region there is an initial steep rise of Vφ after which Vφ becomes essentially independent of concentration between 0.15 and 0.20 mol kg-1 where there is a clear inflection at a second critical concentration cc2; at higher concentrations Vφ increases with m up to the upper limit of measurement. The presence of a second critical concentration has been reported from static light scattering and NMR measurements on aqueous solutions of this drug,5 and there is reasonable agreement between cc1 and cc2 values of the present study and the previously reported (13) Phillips, J. N. Trans. Faraday Soc. 1955, 51, 561. (14) Pe´rez-Rodriguez, M.; Prieto, G.; Rega, C.; Varela, L. M.; Sarmiento, F.; Mosquera, V. Langmuir 1998, 14, 4442.
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Gutie´ rrez-Pichel et al.
Table 1. Critical Concentrations, cc1 and cc2, Apparent Molal Volumes at Infinite Dilution, VO0 (Values in Parentheses Are from Debye-Hu 1 ckel Limiting Law), Apparent Molal Volumes of Aggregates, VOmic, Changes in Apparent Molal Volumes upon Aggregation, ∆Vm, and Bv Parameter of Nafcillin, Cloxacillin, and Dicloxacillin in Aqueous Solution at 298.15 K nafcillin cloxacillin dicloxacillin
cc1/cc2, mol kg-1
Vφ0, cm3 mol-1
Vφmic, cm3 mol-1
Bv, cm3 kg mol-2
∆Vm, cm3 mol-1
0.11/0.09/0.21 0.07/0.20
311.9 (312.1) 310.6 (310.2) 328.9 (328.8)
315.9 316.5 333.9
-8.3 0.02 0.015
4.0 5.9 5.0
Figure 2. Apparent molal volume, Vφ, as a function of molal concentration, m, for aqueous solutions of dicloxacillin at 298.15 K. Dotted lines are values from the Debye-Hu¨ckel limiting law fit.
values [cc1 ) 0.05 mol kg-1 (light scattering and NMR), cc2 ) 0.20 mol kg-1 (light scattering), 0.24 mol kg-1 (NMR)]. The plots of Vφ against m for aqueous solutions of nafcillin showed only one critical concentration at a cc1 value of 0.11 mol kg-1. The corresponding values from the literature are 0.11 mol kg-1 (light scattering at 303.15 K) and 0.06 mol kg-1 (NMR).10 Vφ against m plots for solutions of cloxacillin indicated a first critical concentration of 0.09 mol kg-1 and evidence of a weak inflection at a possible second critical concentration at approximately 0.2 mol kg-1. In contrast, light scattering and NMR measurements5 showed only a single inflection at concentrations of 0.20 and 0.06 mol kg-1 respectively. The discrepancy between the findings of these experimental techniques and those of the current study may arise from their lack of sensitivity in detecting such a weak inflection. Assuming the pseudophase model of micellization,15 the apparent molar volume may be written in the form
cc m - cc mic Vφ ) Vφ0 + Vφ m m
(3)
where all the water interaction below and above the critical concentration is included in the apparent molal property of the surfactant in monomeric form, Vφ0, and the micellar state, Vφmic, respectively. Equation 3 can be rewritten as
Vφ ) Vφmic +
cc 0 [V - Vφmic] m φ
(4)
The plot of Vφ as a function of 1/m for solutions of nafcillin (Figure 3) shows two linear regions. The intercept of the line corresponding to m > cc gives the value of Vφmic, and that of the line of zero slope obtained at concentrations below cc gives a value for Vφ0 (see Table 1). The two lines intersect at the critical concentration. The corresponding plot for cloxacillin (Figure 3) shows a clear inflection at (15) Rosenholm, J. B. Colloid Polym. Sci. 1981, 259, 1116.
Figure 3. Apparent molal volume, Vφ, vs 1/m for aqueous solutions of (b) cloxacillin and (9) nafcillin at 298.15 K.
Figure 4. Apparent molal volume, Vφ, vs 1/m for aqueous solutions of dicloxacillin at 298.15 K. The arrows denotes the critical concentrations.
the first critical concentration. The variation of Vφ0 with 1/m in the region m > cc of this plot may be represented by two lines intersecting at a possible cc2 of 0.21 mol kg-1. Figure 4 shows clear evidence for a second critical concentration at 0.20 mol kg-1 in the Vφ against 1/m plot for solutions of dicloxacillin. The change in volume associated with the formation of the stable aggregate from monomeric drug was taken to be ∆Vm ) Vφmic - Vφ0. The ∆Vm values are positive and lower than those obtained for typical surfactants (for example, for sodium dodecyl sulfate, the value is 10.8 cm3 mol-1 at 298.15 K).16 Values of the critical concentrations, Vφ0 and Vφmic are shown in Table 1. It is interesting to compare the ∆Vm values with those of the nucleosides studied by Høiland et al.17 These amphiphilic nucleosides are thought to associate by a stacking model and as a (16) Musbally, G. M.; Perron, G.; Desnoyers, J. E. J. Colloid Interface Sci. 1974, 48, 494. (17) Høiland H.; Skauge, A.; Stokkeland, I. J. Phys. Chem. 1984, 88, 6350.
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consequence generally have low ∆Vm values (at 298.15 K: for cytidine, 5.3 cm3 mol-1; for thymidine, 0.0 cm3 mol-1). The low values obtained in the present study may be a consequence of a loose stacking model as proposed for these nucleosides. An alternative method of calculating Vφ0 is to assume that solutions of amphiphilic compounds behave as solutions of 1:1 electrolytes up to the critical concentration; the apparent molal volumes may then be described in the premicellar region by the equation:18
Vφ ) Vφ0 + Avm1/2 + Bvm
(5)
Vφ0 is the apparent molal volume at infinite dilution, Av is the Debye-Hu¨ckel limiting law coefficient, and Bv is an adjustable parameter related to a pair interaction19 and equivalent to the second virial coefficient, which measures the deviation from the limiting law due to the nonelectrostatic solute-solute interactions.16-21 For 1:1 electrolytes in water at 298.15 K, Av ) 1.868 cm3 kg1/2 mol-3/2 and Bv is generally negative except for hydrogen-bonding interactions.16 Values of Vφ0 and Bv obtained are shown in Table 1. Vφ0 values are in close agreement with those derived from the application of the pseudophase model. Since the three penicillins have identical counterions, differences in the Vφ0 values arise from structural differences of the drug monomers. Comparison of values for cloxacillin and dicloxacillin shows a contribution to the volume at infinite dilution of +18.6 cm3 mol-1, arising from the Cl substituent atom. From Table 1, it can be seen that cloxacillin and dicloxacillin have a positive Bv, possibly as a consequence of nonelectrostatic solute-solute interactions such as hydrogen bonding, which lead to weak association of monomers in the premicellar region.16 Positive Bv values have also been obtained for other amphiphilic drugs including the phenothiazine drugs:22 promazine, chlorpromazine, promethazine, and imipramine. With such drugs, calorimetric23,24 and osmotic techniques25 have demonstrated the existence of a preaggregation process at concentrations well below the critical concentration. Other amphiphilic compounds, such as the bile salts potassium cholate and sodium deoxycholate,26 and the anionic surfactant sodium octyl sulfate16 also show positive deviations from the limiting law. In the case of the bile salts, this was attributed to continuous association in a manner similar to a stacking process. On the other hand, nafcillin shows negative Bv values, typical of more conventional surfactants such as the alkyl sulfates or tetraalkylammonium salts.16,27,28 Premicellar association has important implications for the transport of the drug molecules through biological membranes since this (18) Desnoyers, J. E.; De Lisi, R.; Ostiguy, C.; Perron, G. Solution Chemistry of Surfactants; Plenum Press: New York, 1979; Vol. 1. (19) Brun, T. S.; Hoiland, H.; Vikingstad, E. J. Colloid Interface Sci. 1978, 63, 89. (20) Harned, H. S.; Owen, B. B. Physical Chemistry of Electrolyte Solutions; Chapman and Hall: London, 1957. (21) Desnoyers, J. E.; Perron, G.; Roux, A. H. Surfactant Solutions: New Methods of Investigation; Dekker: New York, 1987. (22) Attwood, D.; Blundell, R.; Mosquera, V.; Garcı´a, M.; Rodrı´guez, J. Colloid Polym. Sci. 1994, 272, 108. (23) Attwood, D.; Boitard, E.; Dube`s, J. P.; Tachoire, H. Colloid Surf. 1990, 48, 35. (24) Attwood, D.; Fletcher, P.; Boitard, E.; Dube`s, J. P.; Tachoire, H. J. Phys. Chem. 1990, 94, 6034. (25) Attwood, D. Adv. Colloid Interface Sci. 1995, 55, 271. (26) Djavanbakth, A.; Kale, K. M.; Zana, R. J. Colloid Interface Sci. 1977, 59, 139. (27) De Lisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J. Colloid Interface Sci. 1979, 71, 147. (28) Franks, F.; Quickenden, M. J.; Ravenhill, J. R.; Smith, H. T. J. Phys. Chem. 1968, 72, 2668.
Figure 5. Ultrasound velocity, u, of dicloxacillin in aqueous solution as a function of molality, m, at 298.15 K. The arrows denote the critical concentrations. Table 2. Critical Concentrations, cc1 and cc2, from Ultrasound Velocity Measurements Isentropic Apparent Molal Adiabatic Compressibilities at Infinite Dilution, KO(S)0, Isentropic Apparent Molal Adiabatic Compressibilities of Aggregates, KO(S)m, and Changes in Isentropic Apparent Molal Adiabatic Compressibilities, ∆KO(S), of Nafcillin, Cloxacillin, and Dicloxacillin in Aqueous Solution at 298.15 K cc1/cc2, 103Kφ(S)0, cm3 103Kφ(S)m, cm3 103∆Kφ(S), cm3 mol kg-1 bar-1 mol-1 bar-1 mol-1 bar-1 mol-1 nafcillin 0.13/cloxacillin 0.09/0.20 dicloxacillin 0.06/0.17
-8.1 -4.7 -4.5
-2.3 0.1 4.4
5.8 4.8 0.1
may occur at the low concentrations prevalent in vivo. The differences in the association characteristics indicated for the penicillins of this study may therefore be of importance from a pharmacological viewpoint. Ultrasound Velocity and Compressibilities. The concentration dependence of the sound velocity, u, of solutions of dicloxacillin at 298.15 K (Figure 5) shows two inflection points, which were located by regression analysis of the linear segments of the plots. Similar plots showing only a single inflection point were obtained for nafcillin, and both a clear cc1 and a weaker inflection at cc2 were obtained for cloxacillin. The values so obtained (see Table 2) show a close agreement with those from density methods and also those calculated from the application of the pseudophase model to the apparent molal volume data. For each drug the variation of sound velocity with molality was linear over each of the concentration regions, with a decrease of gradient at both cc1 and cc2, as noted for other surfactant systems.29 Changes of gradient of such plots are a consequence of changes in both the apparent specific volumes and the adiabatic compressibility of the aggregates with an increase of concentration.29 Other drugs, including the amphiphilic phenothiazine tranquillizer drugs chlorpromazine, promethazine, and promazine, show a decrease of gradient when m> cc2,30 although the significance of this is not clear. Density and ultrasound velocity measurements were combined to calculate adiabatic compressibilities using the Laplace equation.19 (29) Zielinski, R.; Ikeda, S.; Nomura, H.; Kato, S. J. Colloid Interface Sci. 1987, 119, 398. (30) Attwood, D.; Doughty, D.; Mosquera, V.; Pe´rez-Villar, V. J. Colloid Interface Sci. 1991, 141, 316.
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ks ) -
1 ∂V V ∂p
( )
) S
106 Fu2
Gutie´ rrez-Pichel et al.
(6)
where V, p, and S refer to volume, pressure, and entropy, respectively. ks is the adiabatic compressibility coefficient, expressed in bar-1 when the ultrasound velocity u is expressed in cm s-1 and the density in g cm-3. The isentropic apparent molal compressibility, Kφ(S), can be calculated from ultrasound measurements:8
Kφ(S) )
103(ks - ks0) + ks V φ mF0
(7)
where ks and ks0 are the isentropic coefficients of compressibility of the solution and solvent, respectively. Previous studies of Kφ(S) have shown (a) that this quantity is large and negative for ionic compounds in water, (b) positive for mainly hydrophobic solutes, and (c) intermediate, small, and negative, for uncharged hydrophilic solutes such as sugars.31,32 Within a homologous series of tetra-n-alkylammonium salts,33 alkyltrimethylammonium bromides34,35 and n-alkyl sulfates,19,36 the isentropic apparent molal compressibilities of the surfactant monomers decreased with increasing chain length due to an increase in the amount of structured water in the vicinity of the hydrocarbon chains, which is less compressible than bulk water. Therefore, it might be expected that the drug monomers would have lower compressibilities than these surfactants because of their larger hydrophobic groups. The isentropic apparent molal compressibilities at infinite dilution, Kφ(S)0, are, however, of similar magnitude to those of the alkyltrimethylammonium bromides (C12 ) -4.2 × 10-3 cm3 mol-1 bar-1, C14 ) -8.1 × 10-3 cm3 mol-1 bar-1 at 298.15 K).34 The reason for these higher than expected Kφ(S)0 values may be that there is a more significant contribution arising from the intrinsic compressibility of the very much bulkier hydrophobic groups of the penicillin drugs. The Kφ(S)m values of Table 2, which reflect the compressibility of the aggregates, are lower than those obtained for penicillin V (65 × 10-4 cm3 mol-1 bar-1)37 or typical surfactants such as sodium dodecyl sulfate (146 × 10-4 cm3 mol-1 bar-1).19 The high compressibilities of the latter are explained in terms of van der Waals interactions between solute and solvent and imply that the micellar interior resembles a bulk liquid (31) Høiland, H.; Vikingstand, E. J. Chem. Soc., Faraday Trans. 1 1976, 72, 1441. (32) Franks, F.; Ravenhill, J. R.; Reid, D. S. J. Solution Chem. 1972, 1, 3. (33) Conway, B. E.; Verall, R. E. J. Phys. Chem. 1966, 70, 3952. (34) Zielinski, R.; Ikeda, S.; Nomura, H.; Kato, S. J. Chem. Soc., Faraday Trans. 1 1988, 84, 151. (35) Mosquera, V.; del Rı´o, J. M.; Attwood, D.; Garcı´a, M.; Jones, M. N.; Prieto, G.; Sua´rez, M. J.; Sarmiento, F. J. Colloid Interface Sci. 1998, 206, 66. (36) Sua´rez, M. J.; Lo´pez-Fonta´n, J. L.; Sarmiento, F.; Mosquera, V. Langmuir 1999, 15, 5265. (37) Varela, L. M.; Rega, C.; Sua´rez, M. J.; Ruso, J. M.; Prieto, G.; Attwood, D.; Sarmiento, F.; Mosquera, V. Langmuir 1999, 15, 6285.
phase.38 Therefore, although the structure of the aggregates of the penicillin drugs was not explored here, the low compressibility of the drug aggregates suggests a stacked aggregate which does not possess the looseness of structure associated with the micelles of typical surfactants. It is interesting to note the similarity of the Kφ(S)m values of dicloxacillin and those of the amphiphilic tricyclic drugs that also have two critical concentrations; chlorpromazine, promazine, promethazine, and imipramine, for example, have Kφ(S)m values21 of 3.9 × 10-3, 2.9 × 10-3, 2.1 × 10-3, and 2.1 × 10-3 cm3 mol-1 bar-1, respectively, and are known to self-associate by a stacking process.39 Moreover, a high-resolution 1H NMR spectroscopic study of dicloxacillin suggested a decrease of packing density in the larger aggregates at the second critical concentration similar to that observed for nonylammonium bromide40 on the transition from globular to cylindrical micelles. The low compressibility of the drug aggregates is responsible for the relatively small changes in partial molal isentropic compressibility on aggregation, ∆Kφ(S), (∆Kφ(S) ) Kφ(S)m - Kφ(S)0) (see Table 2), compared with those for typical surfactants (∆Kφ(S) for dodecyltrimethylammonium bromide ) 16.2 × 10-3 cm3 mol-1 bar-1 at 298.15 K). Summary The concentration dependence of the apparent molal volume, Vφ, calculated from density data shows evidence of a second critical concentration in solutions of dicloxacillin, which is more pronounced when the data are plotted in the form Vφ against reciprocal molality. Inflections at two similar critical concentrations are also observed in plots of ultrasound velocity, u, against molality, m, for this drug. The evidence for a second critical concentration in solutions of cloxacillin is more tenuous; any second inflection in Vφ against m, or u against m plots, is very weak, and our evidence derives mainly from an apparent inflection in the plot of Vφ against 1/m. It is clear from our results that nafcillin exhibits only a single critical concentration. Positive deviations of the concentration dependence of the apparent molal volumes of cloxacillin and dicloxacillin from that predicted by the Debye-Hu¨ckel limiting law in dilute solution provide evidence for limited association at concentrations below the first critical concentration. The low apparent molal compressibilities of the drug aggregates, as calculated from ultrasound measurements, are indicative of the formation of a stacked aggregate, which does not possess the looseness of structure associated with the micelles of typical surfactants. Acknowledgment. The authors thank the Xunta de Galicia for financial support. LA011619X (38) Tanford, C. The Hydrophobic Effect; Wiley: New York, 1973. (39) Attwood, D.; Waigh, R.; Blundell, R.; Bloor, D.; The´vand, A.; Boitard, E.; Dube`s, J. P.; Tachoire, H. Magn. Reson. Chem. 1994, 32, 468. (40) Persson, B. O.; Drakenberg, T.; Lindman, B. J. Phys. Chem. 1976, 80, 2124.
