562
Langmuir 2002, 18, 562-565
Determination of the Association Characteristics of a Weakly Associating Amphiphile by Conductivity and Dielectric Constant Measurements: The Self-Association of Penicillin V in Aqueous Solution Martı´n Pe´rez-Rodrı´guez,† Luis M. Varela,† Pablo Taboada,† David Attwood,‡ and Vı´ctor Mosquera*,† Grupo de Fı´sica de Coloides y Polı´meros Departamento de Fı´sica de la Materia Condensada 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, United Kingdom Received July 3, 2001. In Final Form: October 21, 2001
Introduction The critical micelle concentration (cmc) is usually determined on the basis of an abrupt change in the physicochemical properties of the surfactant solution due to cooperative formation of aggregates in the bulk solution. However, such changes in properties do not occur at a single concentration but rather over a range of concentration, and it is common practice to determine the cmc as the intersection point of two lines representing the measured properties below and above the region of slope change. The width of the transition region is directly related to the existence of partial aggregation at concentrations lower than the cmc and the subsequent polydispersity of the system; the precise location of an inflection becomes particularly problematic for systems such as the amphiphilic drugs that form small aggregates. In an earlier study,1 we demonstrated the potential of dielectric constant measurement as a means of detecting critical concentrations of such systems, and we now report the use of this technique in the determination of the thermodynamics of the self-association of the amphiphilic drug penicillin V (see Chart 1) from measurements over a temperature range of 15-40 °C. Interest in the colloidal properties of penicillins dates from the late 1940s and early 1950s and includes studies by McBain and co-workers,2 Hauser et al.,3 and Few and Schulman.4 These investigations were strongly affected by surface-active impurities that complicated the characterization of the self-association process. Recently, we have studied in detail the self-assembly of amphiphilic anionic penicillins5-8 and have shown that in common * To whom correspondence should be addressed. E-mail:
[email protected]. Tel: +34 981 563 100. Fax: +34 981 520 676. † Universidad de Santiago de Compostela. ‡ University of Manchester. (1) Pe´rez-Rodrı´guez, M.; Prieto, G.; Rega, C.; Varela, L. M.; Sarmiento, F.; Mosquera, V. Langmuir 1998, 14, 4422. (2) McBain, J. W.; Huff, H.; Brady, A. 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. (5) Taboada, P.; Attwood, D.; Ruso, J. M.; Sarmiento, F.; Mosquera, V. Langmuir 1999, 15, 2022. (6) Varela, L. M.; Rega, C.; Suarez-Filloy, M. J.; Ruso, J. M.; Prieto, G.; Attwood, D.; Sarmiento, F.; Mosquera, V. Langmuir 1999, 15, 6285. (7) Taboada, P.; Attwood, D.; Garcı´a, M.; Jones, M. N.; Ruso, J. M.; Mosquera, V.; Sarmiento, F. J. Colloid Interface Sci. 2000, 221, 242. (8) Taboada, P.; Attwood, D.; Ruso, J. M.; Garcı´a, M.; Sarmiento, F.; Mosquera, V. Langmuir 2000, 16, 3175.
Chart 1
with some of the phenothiazine drugs,9 the penicillins may exhibit a multiple association pattern5,6 with more than one inflection in the concentration dependence of their solution properties. Our studies on the self-association of penicillin V at 25 °C using conductivity and light scattering techniques6 have shown an inflection at a critical concentration of 0.23 mol kg-1 in agreement with the previously reported value of the cmc but also an additional inflection at 0.045 mol kg-1 representing a previously unreported lower critical concentration. Light scattering measurements indicated the formation of trimers at this first critical concentration and subsequent formation of aggregates of aggregation number 12 at the second critical concentration. Our determinations of association characteristics for this drug from conductivity data have involved the numerical analysis of data using an algorithm based on the Runge-Kutta numerical integration method and the Levenberg-Marquardt least-squares fitting algorithm to identify inflections in the conductivity/ concentration plots, which are not apparent from visual inspection of the raw data. In contrast, the dielectric constant shows a greater sensitivity to both frequency and concentration changes1 and should therefore provide a more sensitive technique of examining structural changes of polydisperse media. Precise determination of the cmc allows the calculation of the thermodynamic functions of aggregation using either the mass action or the phase separation model of micelle formation.10 An important contribution to the free energy of formation of aggregates is the enthalpy change involved in the process. This is linked directly to intermolecular interactions and is most directly influenced by changes in the nature of the amphiphile. In the present study, we have derived the enthalpy change on association for penicillin V from the variation of first critical concentration with temperature and compared this value with an experimental value from microcalorimetry. Experimental Section Materials. Penicillin V (potassium salt) of at least 98.5% purity was obtained from Sigma Chemical Co. and was used as received. Solutions were made in double-distilled, deionized, and degassed water. Apparatus and Procedure. Conductivities and dielectric constants of the drug solutions were measured with a HP 4285A Precision LCR meter ((0.1% accuracy) equipped with a HP E5050A colloid dielectric probe operating in a frequency range between 200 kHz and 20 MHz. The probe is especially designed to measure inductances and to avoid the polarization that occurs in the plain condenser probe. The measurement cell design was conceived to obtain the highest degree of accuracy. It consists of a cylinder of 8 cm diameter and 5 cm height with the probe entrance at a side. This geometry ensures the probe head to be always surrounded by at least 2 cm of solution during the measurement process, which avoids possible interferences of the cell walls. The cell was immersed in a Techne model RB-12A thermostated bath equipped with a Tempunit TU-16A thermo(9) Attwood, D. Adv. Colloid Interface Sci. 1995, 55, 271. (10) Attwood, D.; Florence, A. T. Surfactant Systems; Chapman and Hall: London, 1983.
10.1021/la011009x CCC: $22.00 © 2002 American Chemical Society Published on Web 12/22/2001
Notes
Langmuir, Vol. 18, No. 2, 2002 563
Figure 1. Plot of the real part of the electrical conductivity (κ′) of an aqueous solution of penicillin V against frequency (f) and concentration at 25 °C. stat. Temperature control was achieved using an Anton Paar DT 100-30 thermometer, maintaining the temperature constant to within (0.01 °C. A Variomag 20P shaker was used to homogenize the solution.
Results and Discussion Conductometric Measurements. Figure 1 shows a representative plot of the concentration and frequency dependence of the measured real part of the electrical conductivity, κ, of aqueous solutions of penicillin V at 25 °C for frequencies ranging from 200 kHz to 20 MHz and concentrations up to 0.35 mol kg-1. The curve shows a gradual change over the concentration range examined, and no clear inflection points can be detected by visible inspection. The electrical conductivity is seen to be almost independent of frequency; the relative variations of κ from 200 kHz to 20 MHz are less than 1% at 1 mmol kg-1 and less than 0.2% at 35 mmol kg-1. Similar plots were obtained at selected temperatures over the range 15-40 °C. Dielectric Constant Measurements. Measured dielectric constants of aqueous solutions of penicillin V at 25 °C are plotted in Figure 2 as a function of concentration and frequency. The figure shows that this property is frequency dependent suggesting a relaxation mechanism. Figure 3 shows the concentration dependence of the real part of the dielectric constant, ′, of aqueous solutions of penicillin V over a wide concentration range at 25 °C. The dielectric property of the amphiphile exhibits an abrupt transition in the neighborhood of the first critical concentration and a smoother change at the second one. Similar plots showing two critical concentrations were obtained at 15, 20, 30, and 35 °C; only the first critical concentration was discernible at 40 °C. The concentration dependence of ′ at concentrations below the first critical concentration is similar to that observed for solutions of the cationic surfactant n-dodecyl trimethylammonium
bromide and also the phenothiazine drug chlorpromazine1 and may be a consequence of premicellar association, which has influence on the characteristic frequency and dielectric relaxation of the medium.11-14 The values of the critical concentrations at different temperatures (see Table 1) were obtained as the intersections of polynomials above and below each transition as shown in Figure 3. Good agreement was noted between critical concentrations measured in this way and those derived previously at 25 °C by the numerical analysis of conductivity data (0.045 and 0.23 mol kg-1) and by light scattering techniques (0.040 and 0.246 mol kg-1).6 Thermodynamics of Micellization. Assuming that the mass action equation is applicable to this system, the equilibrium between the anionic monomers and aggregates may be represented by
nS- + (n - p)G+ T Mp-
(1)
where S- represents the drug ion, G+ represents the counterion, and Mp- represents the aggregate formed by n monomers with net charge p. The equilibrium constant Km for the formation of the micelles is
Km )
[Mp-] [S-]n[G+]n-p
(2)
where [Mp-], [S-], and [G+] are the molar concentration of micelles, monomers, and counterions, respectively. The (11) Schwarz, G. A. J. Phys. Chem. 1962, 66, 2636. (12) Kijlstra, J. R.; Wegh, R. A. J.; van Leeuwen, H. P. J. Electroanal. Chem. 1994, 366, 37. (13) Hidalgo-Alvarez, R.; Martı´n, A.; Ferna´ndez, A.; Bastos, D.; Martı´nez, F.; de las Nieves, F. J. Adv. Colloid Interface Sci. 1996, 67, 1. (14) Minor, M.; van Leeuwen, H. P.; Lyklema, J. J. Colloid Interface Sci. 1998, 206, 397.
564
Langmuir, Vol. 18, No. 2, 2002
Notes
Figure 2. Plot of the permittivity (′) of an aqueous solution of penicillin V against frequency (f) and concentration at 25 °C.
expression used for the calculation of Km was15
(2n - p)(4n - 2p - 1) 1 )n Km 2n - p - 2 (2n - p)(4n - 2p - 1) x (2n - p - 1)(4n - 2p + 2) cmc
[
]
2n-p-1
(3)
where xcmc is the cmc (the first critical concentration) expressed as a mole fraction. Values of n and p were derived from light scattering measurements.6 The standard free energy of micelle formation per monomer unit was calculated using Km values from eq 3 and the expression
∆G°m ) -
RT ln Km n
(4)
The enthalpy of formation of the aggregate was calculated from the temperature dependence of the cmc using the Gibbs-Helmholtz relation:
∆H°m )
[
]
∂ (∆G°m/T) ∂(1/T)
P
)
(
)
RT2 ∂ ln Km n ∂T
P
(5)
Table 1 shows the values obtained for ∆G°m and ∆H°m. The ∆H°m value at 25 °C was in good agreement with the value determined experimentally by calorimetric measurements.6 The low and positive values of the enthalpy of aggregation formation show that the process is endothermic and mainly entropic. The enthalpy values remain almost constant over the studied range of temperature, revealing the small influence of the temperature on the energy of formation of the aggregate. Positive values of ∆H°m are generally attributed to the release of structured water from the hydration layers around the hydrophobic (15) Phillips, J. N. Trans. Faraday Soc. 1955, 51, 561.
Figure 3. Dielectric constant (′) of penicillin V as a function of concentration at 25 °C for frequencies of 200 kHz (9), 2.1 MHz (b), and 20 MHz (2). Solid lines represent the quadratic fitting curves.
parts of the molecule16 during the formation of the aggregates. Summary A method of determining critical concentrations for aggregation in self-associating systems of low aggregation number by dielectric constant measurement has been applied in a study of the self-association of penicillin V as a function of temperature. Dielectric properties of penicillin V are more sensitive to structural modifications in bulk amphiphilic solutions than the electrical conductivity (16) Kresheck, G. C. Water, a Comprehensive Treatise; Franks, F., Ed.; Plenum Press: New York, 1975; Vol. 4, Chapter 2.
Notes
Langmuir, Vol. 18, No. 2, 2002 565
Table 1. Values of the First Critical Concentration, cmc, Second Critical Concentration, cc, and Thermodynamic Parameters of Micellization of Penicillin V at Different Temperatures from Dielectric Constant Measurements T (°C)
cmc/cc mmol kg-1
∆G°m (kJ mol-1)
∆H°m (kJ mol-1)
∆S°m (kJ mol-1)
15 20 25 30 35 40
39/202 38/225 40/220 38/195 36/167 36/s
-34.1 -34.7 -35.1 -35.8 -36.5 -37.1
0.64 0.66 0.69 (0.76)a 0.71 0.73 0.76
34.8 35.4 35.8 36.5 37.2 37.8
a The value shown in parentheses corresponds to an experimental enthalpy value (ref 6).
and exhibit a stronger dependence on the external field frequency. They provide a simpler method for the determination of critical concentrations of such systems without the necessity of the complex numerical data analysis
required in the determination of inflection points in electrical conductivity data, which show a more gradual change throughout the measured concentration range and relative insensitiveness to frequency variation. The two critical concentrations derived by each of these methods at 25 °C were in good agreement. Thermodynamic parameters of micelle formation were derived from the variation of the first critical concentration using a modified form of the mass action model applicable to systems of low aggregation number. The good agreement between the experimental and theoretical ∆H°m values supports the validity of the proposed model to predict thermodynamic parameters of aggregation. Acknowledgment. The authors thank the Xunta de Galicia for financial support. LA011009X
