Self-Association of the Penicillin Sodium Nafcillin in Aqueous Solution

The predicted Δ at 298.15 K was in good agreement with the value determined experimentally by calorimetry. Critical concentrations and the size and e...
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Langmuir 2000, 16, 3175-3181

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Self-Association of the Penicillin Sodium Nafcillin in Aqueous Solution Pablo Taboada,† David Attwood,‡ Juan M. Ruso,† Manuel Garcı´a,† Fe´lix Sarmiento,† and Vı´ctor Mosquera*,† Grupo de Fı´sica de Coloides y Polı´meros, Departamento de Fı´sica de la Materia Condensada y Departamento de 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 September 17, 1999. In Final Form: December 17, 1999 The self-association of the penicillin drug, sodium nafcillin monohydrate, in aqueous solution has been examined as a function of temperature and electrolyte concentration. Critical concentrations determined by conductivity measurements in water over the temperature range 288.15 to 313.15 K indicated a minimum critical concentration at 303 K. Thermodynamic parameters of aggregation were derived from the critical concentration data using a form of mass action model modified for application to systems of low aggregation number. Values for the enthalpy of aggregate formation ∆H0m calculated by this method showed that the aggregation became increasingly exothermic with increase of temperature. The predicted ∆H0m at 298.15 K was in good agreement with the value determined experimentally by calorimetry. Critical concentrations and the size and effective charge of aggregates were determined in the presence of added electrolyte (0.05-0.40 mol kg-1 NaCl) by static light scattering. The interaction between aggregates was interpreted from diffusion data from dynamic light scattering using the DLVO theory. Changes of 1H NMR chemical shift on aggregation suggested stacking of molecules. Application of mass action theory to the concentration dependence of 1H NMR chemical shifts confirmed the aggregation number from light scattering.

Introduction Although the pharmacological effect of amphiphilic drug molecules is usually manifest at low concentrations where self-association is negligible, it is possible that their accumulation at certain sites in the body may cause a localized high concentration, with important consequences for membrane transport and hence for drug activity.1 With some drugs, for example the phenothiazine tranquillizers, correlations have been established between clinical potency and colloidal properties.1 The importance of investigating the aggregation characteristics of penicillin drugs was stressed by Funasaki and co-workers2 in a discussion of the effects of self-association on their bacterial activity and chemical stability. The earliest reports of the colloidal properties of the penicillin drugs were those of McBain et al.3 in 1949, who determined the critical micelle concentration of Penicillin G (benzylpenicillin) from conductivity and surface tension techniques. Other workers around this time also working on this drug included Hauser et al.4 and Hocking5 who reported the presence of small aggregates in aqueous solution. Later studies on Penicillin G by Thakkar and Wilham6 confirmed its limited association in D2O using NMR techniques. Dimerization constants for Penicillin G and Penicillin V (phenoxy* 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; Chapter 4. (2) Funasaki, N.; Hada, S.; Neya, S. Chem. Pharm. Bull. 1994, 42, 779. (3) McBain, J. W.; Huff, H.; Brady, A. P. J. Am. Chem. Soc. 1949, 71, 373. (4) Hauser, E. A.; Marlow, G. J. J. Phys. Coll. Chem. 1950, 54, 1077. (5) Hocking, C. S. Nature 1951, 168, 423. (6) Thakkar, A. L.; Wilham, W. L. J. Chem. Soc., Chem. Commun. 1971, 26, 320.

methylpenicillin) in 0.15 mol dm-3 KCl have been determined from an analysis of data from gel filtration chromatography.2 The micellar properties of several synthetic penicillins in water and 0.15 mol dm-3 NaCl were reported by Attwood and Agarwal.7 NMR studies by Kupka et al.8 established the importance of hydrogen bonding and weak interaction between hydrophobic molecular fragments in the formation of the aggregates of cloxacillin. In recent papers, we have examined the relationship between molecular structure and association characteristics in the structurally related penicillins, cloxacillin, dicloxacillin, and flucloxacillin. We have presented a detailed comparison of their association characteristics,9 the thermodynamics of their association,10 and their surface activity11 in water and electrolyte solution and have analyzed the influence of the molecular structure on the ideality of mixing in micellar solutions of these drugs.12 In the present study we report the association characteristics of the penicillin drug nafcillin (I) in water and electrolyte using conductivity, light scattering, and NMR techniques. Intermicellar interactions have been quantified by analysis of diffusion data from dynamic light scattering using a method proposed by Corti and Degiorgio13 which is based on the Derjaguin-Landau-VerweyOverbeek (DLVO) theory of colloid stability. (7) Attwood, D.; Agarwal, S. P. J. Pharm. Pharmacol. 1984, 36, 563. (8) Kupka, T.; Dziegielewski, J. O.; Pasterna, G. J. Pharm. Biomed. Anal. 1993, 11, 103. (9) Taboada, P.; Attwood, D.; Ruso, J. M.; Sarmiento, F.; Mosquera, V. Langmuir 1999, 15, 2022. (10) Taboada, P.; Attwood, D.; Garcı´a, M.; Jones, M. N.; Ruso, J. M.; Mosquera, V.; Sarmiento, F. Submitted for publication in J. Colloid Interface Sci. (11) Taboada, P.; Attwood, D.; Ruso, J. M.; Garcı´a, M.; Sarmiento, F.; Mosquera, V. Submitted for publication in J. Colloid Interface Sci. (12) Taboada, P.; Attwood, D.; Ruso, J. M.; Garcı´a, M.; Sarmiento, F.; Mosquera, V. J. Colloid Interface Sci. 1999, 216, 270. (13) Corti, M.; Degiorgio, V. J. Phys. Chem. 1981, 85, 711.

10.1021/la991237f CCC: $19.00 © 2000 American Chemical Society Published on Web 02/19/2000

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Experimental Section Materials. Sodium nafcillin monohydrate, [6-2-ethoxy-1naphthamido]penicillin, was obtained from Sigma Chemical Co. and was sufficiently well characterized and purified to be used as received. Sodium chloride was of AnalaR grade. Water was double-distilled and deaerated before use. Conductivity Measurements. The conductivity of aqueous solutions of nafcillin was measured at temperatures between 288.15 and 313.15 K using a specific conductivity meter (Kyoto Electronics, type C-117). The cell constant was determined with aqueous solutions of KCl over the appropriate concentration range using the molar conductivity data of Shedlovsky14 and Chambers et al.15 Water was progressively added to concentrated aqueous solutions of nafcillin of known molality using a peristaltic pump (Dosimat, model 655, Metrohmn AG) under computer control. Calorimetric Measurements. Enthalpy measurements were made at 298.15 K with a LKB 10700 batch microcalorimeter which utilizes the twin-vessel principle, each vessel being divided into two compartments.16 The microcalorimeter was calibrated electrically at frequent intervals during the course of the study. On the most sensitive range used for the measurements (30 µV), the mean sensivity of the detectors in the heat sinks of the two vessels was 14.66 ( 0.32 µW µV-1 (i.e., (2.2%). The two detector sensitivities differed by only 0.37%, which is less than the standard deviation of the sensitivity measurements of the two detectors; i.e., the vessels were matched. The reaction vessel was charged with 2 mL of penicillin solution of concentration two times the critical concentration and 2 mL of water. The reference vessel was charged with 2 mL of water in both compartments. On mixing, the final drug concentration is the critical concentration and the enthalpy of deaggregation is obtained. Static Light Scattering. Static light scattering measurements were made at 303.15 ( 0.1 K using a Malvern 7027 laser light scattering instrument equipped with a 2-W argon ion laser (Coherent Innova 90) operating at 488 nm with vertically polarized light. Solutions were clarified by ultrafiltration through 0.1 µm filters with the ratio of light scattering at angles of 45° and 135° not exceeding 1.10. The refractive index increments of the penicillin aggregates were measured at 303.15 ( 0.1 K using an Abbe´ 60/ED precision refractometer (Bellingham and Stanley, Ltd.) giving a value of 0.086 ( 0.001 kg mol-1 for nafcillin in water. Measurements in the most concentrated electrolyte solutions showed no effect of electrolyte on the value of the refractive index increment within the limits of error of measurement. The refractive index increment of NaCl was taken from literature.17 Dynamic Light Scattering. Measurements were made at 303 ( 0.1 K and at a scattering angle of 90° with the Malvern instrument described above combined with a Brookhaven BI 9000 AT digital correlator with a sampling time range of 25 ns to 40 ms. Solutions were clarified as described above. Diffusion coefficients were determined from a single-exponential fit to the correlation curve. Hydrodynamic radii were calculated from measured diffusion coefficients by means of the Stokes-Einstein equation. Nuclear Magnetic Resonance. 1H NMR was recorded on a JEOL EX270 270 MHz spectrometer at 298.15 ( 1 K. The chemical shifts of selected peaks were accumulated using a “peak pick” facility. All spectra were compared with sodium 3-(trimethylsilyl)propionate (TSP) which acted as an internal standard.

Results and Discussion

Figure 1. Specific conductivity, κ, against molality, m, for nafcillin at 298.15 K. The dotted line represents the Gaussian fit of the second derivative. Table 1. Critical Concentrations, cc¸ Standard Gibbs Energies, ∆G0m, Enthalpies, ∆H0m, and Entropies, ∆S0m of Aggregate Formation of Nafcillin as a Function of Temperature T/K

cc/ mol kg-1

∆G0m/ kJ mol-1

∆H0m/ kJ mol-1

∆S0m/ J mol-1 K-1

288.15 293.15 298.15 303.15 308.15 313.15

0.110 0.107 0.103 0.102 0.103 0.106

-22.0 -22.4 -23.0 -23.4 -23.8 -24.0

7.5 3.7 -0.3 (0.3)a -4.7 -9.3 -14.2

102.2 89.3 75.9 61.8 47.0 31.3

a

Value in parentheses was obtained by microcalorimetry.

with the Phillips18 definition of the critical concentration

d3κ/dc3 ) 0

(1)

The numerical analysis of the data was made by means of a recently developed algorithm based on the RungeKutta numerical integration method and the LevenvergMarquardt least-squares fitting algorithm which allows the determination of precise values of the critical concentrations of drugs and surfactants of low aggregation number.19 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. We have recently demonstrated the applicability of this method for the determination of critical concentrations from conductivity data in other systems of low aggregation number.19,20 The variation of the critical concentration with temperature was fitted to the equation

ln Xcc ) aT2 + bT + c

(2)

Thermodynamics of Micellization. Figure 1 shows a representative plot of specific conductivity, κ, as a function of the molar concentration for nafcillin in aqueous solution at 298.15 K. Similar plots were obtained at temperatures between 288.15 and 313.15 K. Critical concentrations (Table 1) were determined in accordance

where (Xcc) is the critical concentration expressed as mole fraction and the values of the fitting constants were a ) 3.3 × 10-4 ( 5 × 10-5 K-2, b ) -0.20 ( 0.03 K-1, and c ) 24 ( 4. The curve passes through a minimum at 303 K. The thermodynamics properties of aggregation were derived by application of a modified form of the mass action

(14) Shedlovsky, T. J. Am. Chem. Soc. 1932, 54, 1411. (15) Chambers, J. F.; Stokes, J. H.; Stokes, R. H. J. Phys. Chem. 1956, 60, 985. (16) Wadso, I. Acta Chem. Scand. 1968, 22, 927. (17) Kruis, A. Z. Phys Chem. B 1936, 34, 13.

(18) Phillips, J. N. Trans. Faraday Soc. 1955, 51, 561. (19) Pe´rez-Rodrı´guez, M.; Prieto, G.; Rega, C.; Varela, L. M.; Sarmiento, F.; Mosquera, V. Langmuir 1998, 14, 4422. (20) Mosquera, V.; Ruso, J. M.; Attwood, D.; Jones, M. N.; Prieto, G.; Sarmiento, F. J. Colloid Interface Sci. 1999, 210, 97.

Self-Association of Drugs in Aqueous Solution

Langmuir, Vol. 16, No. 7, 2000 3177 Table 2. Critical Concentrations (cc), Aggregation Numbers (N), Degree of Ionization (r), Limiting Diffusion Coeffcients, (D0), and Hydrodynamic Radii, (rh) of Nafcillin in Aqueous Electrolyte Solution at 303.15 K [NaCl]/mol kg-1

cc/mol kg-1

N

R

1010D0/m2 s-1

rh/nm

0.000 0.050 0.075 0.100 0.200 0.400

0.100 0.095 0.093 0.091 0.077 0.059

3 4 6 6 10 11

0.18 0.22 0.25 0.32 0.34

3.32 2.91 2.83 2.64 1.99 1.80

2.63 3.01 3.08 3.31 4.39 4.87

Figure 2. ln of aggregation equilibrium constant, Km, for nafcillin in water as a function of temperature. Continuous line calculated from eq 3.

model18,21 in which the equilibrium constant for the aggregation process is expressed as

(2N - z)(4N - 2z - 1) 1 × )N Km 2N - z - 2 (2N - z)(4N - 2z - 1) X (2N - z - 1)(4N - 2z + 2) cc

[

]

2N-z-1

(3)

Values of the aggregation number N and the effective charge z were determined by light scattering measurements, as described below. The variation of ln Km with temperature (Figure 2) was attributed only to the temperature coefficient of the critical concentration and was fitted to a second-order polynomial of the form

ln Km ) fT2 + gT + h

(4)

with f ) -1.7 × 10-3 ( 2 × 10-4 K-2, g ) 1.01 ( 0.14 K-1, and h ) -126 ( 21. Values (per mole of monomer) of the standard Gibbs energy change, ∆G0m, the standard enthalpy change, ∆H0m, and the standard entropy change, ∆ S0m, on aggregation, were calculated from the following expressions

ln K (RT N)

∆G0m ) ∆H0m )

[

]

∂(∆G0m)/T ∂(1/T)

p

)

(5)

m

(

)

RT2 ∂ ln Km N ∂T

1 ∆S0m ) - (∆G0m - ∆H0m) T

(6)

p

(7)

∆G0m values become increasing negative with temperature increase as the systems become more hydrophobic (see Table 1). The ∆H0m values show that the aggregation of nafcillin becomes progressively exothermic with increase of temperature. Positive ∆H0m values such as those noted for nafcillin at 288.15 and 293.15 K are generally attributed to the release of structured water from the hydration layers around the hydrophobic parts of the molecule.22 Such hydrophobic interactions become in(21) Sarmiento, F.; del Rı´o, J. M.; Prieto, G.; Attwood, D.; Jones, M. N.; Mosquera, V. J. Phys Chem. 1995, 99, 17628. (22) Kresheck, G. C. In Water, A Comprehensive Treatise; Franks, F., Ed.; Plenum Press: New York, 1975; Vol. 4, Chapter 2.

Figure 3. Variation of the scattering ratio, S90, with molality, m, for nafcillin in (b) water and in aqueous NaCl solutions of concentration (9) 0.05, (2) 0.075, (1) 0.1, ([) 0.2, and (+) 0.4 mol kg-1 at 303.15 K. (- - -) Monomer line.

creasingly insignificant with the partial breakdown of the structure of water as the temperature is increased and the aggregation becomes an enthalpic process; the negative ∆H0m values at higher temperatures suggest the importance of the London-dispersion interactions as the major force for aggregation.23 The progressive decrease of ∆S0m with temperature shows that at temperatures below the minimum of the critical concentration the aggregation is driven only solely by the positive ∆S0m. Similar changes from entropic to enthalpic aggregation with temperature increase have been reported for surfactants,24 and for the surface-active drugs thioridazine,25 propranolol,20 imipramine,26 and clomipramine,27 and the penicillin drugs cloxacillin, dicloxacillin, and flucloxacillin.10 Table 2 shows (in parentheses) the experimental value of ∆H0m at 298.15 K obtained by microcalorimetry for nafcillin. The good agreement between the experimental value and that calculated using the modified mass action model supports the validity of this model for the prediction of thermodynamic parameters of aggregation, at least at this temperature. Aggregation Characteristics. The concentration dependence of the static light scattering ratio, S90 (intensity of light scattered by the solution relative to that from benzene), for nafcillin in aqueous solution containing between 0.0 and 0.4 mol kg-1 NaCl is shown in Figure 3. Critical concentrations were determined from the intersection of the scattering curves with theoretical lines (23) Nusselder, J. J. H.; Engberts, J. B. F. N. J. Colloid Interface Sci. 1992, 148, 353. (24) Zielinski, R.; Ikeda, S.; Nomura, H.; Kato, S. J. Colloid Interface Sci. 1989, 129, 175. (25) Czerniawski, M.; Kupczyk-Radecka, H. Pol. J. Chem. 1985, 59, 901. (26) Attwood, D.; Fletcher, P. J. Colloid Interface Sci. 1987, 115, 104. (27) Attwood, D.; Mosquera, V.; Garcı´a, M.; Sua´rez, M. J.; Sarmiento, F. J Colloid Interface Sci. 1995, 175, 201.

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representing the scattering from unassociated molecules (shown as a dashed line in Figure 3). Comparison of the critical concentration (cc) values of nafcillin (Table 2) with those reported for related penicillins at equivalent electrolyte concentrations9 shows hydrophobicity increasing in the sequence cloxacillin < flucloxacillin and nafcillin < dicloxacillin. Thus, the ethoxynaphthamido ring system of nafcillin is of roughly equivalent hydrophobicity to the hydrophobic ring systems of flucloxacillin. The presence of a second Cl atom in a meta position to the first in dicloxacillin produces a higher hydrophobicity than a F substituent in this position (flucloxacillin). It is interesting to note the absence of a second critical concentration in the scattering plots for nafcillin over the concentration range of the study. Such inflections were reported9 for dicloxacillin at a drug concentration of 0.2 mol kg-1 in water decreasing to 0.06 mol kg-1 in 0.2 mol kg-1 electrolyte. Second critical concentrations were at higher drug concentrations for the less hydrophobic drug flucloxacillin (0.39 mol kg-1 in water, decreasing to 0.3 mol kg-1 in 0.2 mol kg-1 NaCl). If, as these studies indicate, the second critical concentration is a function of drug hydrophobicity, then an inflection might be expected at similar concentrations for nafcillin. The absence of second critical concentrations in the light scattering results of the present study may thus be possibly a consequence of an insufficiently wide concentration range. In this respect it is interesting to note the changes in the aggregation characteristics of nafcillin at much higher concentrations indicated by the NMR data below. Aggregation numbers, N, and the degree of ionization, R (R ) z/N), were calculated from light scattering data according to the Anacker and Westwell28 treatment in which the light scattering from the solutions of ionic aggregates is represented by

Figure 4. Logarithm of critical concentration, cc, as a function of logarithm of counterion concentration, [X-]. Concentrations are in mole fractions.

2m3 + N-1(z + z2)m2 K′m2 ) R90 [2N + (2N)-1(z + z2)f2 - 2fz]m3 + zm2

(8)

Figure 5. Diffusion coefficient, D, as a function of the micellar concentration for nafcillin in (b) water and in aqueous NaCl solutions of concentrations (9) 0.05, (2) 0.075, (1) 0.1, ([) 0.2, and (+) 0.4 mol kg-1 at 303.15 K.

∆R90 is the Rayleigh ratio of the solution in excess of that of a solution at the critical concentration, m2 is the molality of the micellar species in terms of monomer, m3 is the molality of supporting electrolyte, and f ) (dn/dm3)m2/(dn/ dm2)m1 with n the refractive index of the solution. K′ for vertically polarized incident light is defined by

and an increase of ionization with increasing electrolyte concentration. Standard free energies of micellization (per mole of monomeric drug ion), ∆G0m, were derived by the application of the mass-action model using the equation29

2 V0/Lλ4 K′ ) 4π2n20(dn/dm2)m 3

(9)

with n0 being the refractive index of the solvent, V0 the volume of solution containing 1 kg of water, L the Avogadro number, and λ the wavelength of the incident light (488 nm). Expansion of eq 8 in powers of m2 leads to

K′m2/∆R90 ) A + Bm2 + ...

(10)

A ) 4N[(2N - fz)2 + z f 2]-1

(11)

B ) zA(2m3)-1[(1 + z)N-1 - A]

(12)

where

and

Table 2 shows low aggregation numbers, of similar magnitude to those reported for the related penicillins,9 (28) Anacker, E. W.; Westwell, A. E. J. Phys. Chem. 1964, 68, 3490.

log cc ) -(1 - R) log[X-] + ∆G0m/2.303RT + (1/N) log F(m+p) (13) where m+p is the mole fraction of aggregates and F is a term involving the activity coefficients of all species in solution. Approximate values of ∆G0m and R of -21.4 kJ mol-1 and 0.6, respectively, were calculated from the intercept and gradient of cc data plotted in accordance with eq 13, ignoring the activity coefficient term (see Figure 4). The ∆G0m value is of the same order as that of Table 1 at 303.15 K, but R is in poor agreement with values derived from light scattering. Figure 5 shows the apparent diffusion coefficients, D, derived from dynamic light scattering measurements, plotted as a function of micellar concentration (m-cc, where m is the molality of the solution) in water and aqueous electrolyte solutions. The contribution of monomers to the effective value of D in the proximity of the critical concentration may cause considerable curvature of the (29) Anacker, E. W. In Cationic Surfactants; Jungermann, E., Ed.; Marcel Dekker: New York, 1970.

Self-Association of Drugs in Aqueous Solution

Langmuir, Vol. 16, No. 7, 2000 3179

data.30 For this reason, measurements of D were restricted to a concentration region in which D was a linear function of molality. Extrapolation of the data to cc yielded the limiting diffusion coefficients, D0, of the aggregates formed at the critical concentration. Hydrodynamic radii, rh, derived assuming spherical aggregates from D0, using the Stokes-Einstein equation

rh ) kBT/6πηD0

(14)

where kB is the Boltzmann constant and η the solvent viscosity, are given in Table 2 and show the expected increase of aggregate size with increase of the electrolyte concentration. To relate the changes of gradient of the diffusionconcentration plots with changes in the interacting forces between aggregates, the data were analyzed according to Corti and Degiorgio’s treatment.13 For interacting particles, the concentration dependence of D may be described as

D ) D0[1 + kD(m-cc)]

D ) D0(1 + kD′φ)

(16)

where kD′ ) kD/νj and νj is the specific volume of the solute particles. kD may be related to the pair-interaction potential, V(x), between spherical particles of radius a (equated to rh) using the expression proposed by Felderhof31

∫0∞[24(1 + x)2 - F(x)][1 exp(V(x)/kBT] dx (17)

where x ) (R - 2a)/2a, R is the distance between the centers of two particles and F(x) is given as

F(x) ) 12(1 + x) -

27 15 (1 + x)-2 + (1 + x)-4 + 8 64 75 (1 + x)-5 (18) 64

The interaction potential V(x), as it is usually written in DLVO theory, is the sum of an attractive London-van der Waals interaction VA(x) and a repulsive interaction due to the electric charge of the spheres, VR(x). The expression for VA(x) derived by Hamaker32 for the case of two spheres is

VA(x) ) -

[

A 2 (x + 2x)-1 + (x2 + 2x + 1)-1 + 12 2 ln(x2 + 2x) (x2 + 2x + 1)

kD [NaCl] (mol kg-1)

experimental

theoretical

ψ0/kBT

0.05 0.075 0.10 0.20 0.40

2.0 1.0 0.5 0.2 0.1

1.7 1.3 1.1 0.5 -0.8

0.35 0.26 0.18 0.06 0.03

κa > 1. We have used the expression,33

aΨ02 ln[1 + exp(-2κax)] VR(x) ) 2

]

(19)

where A is the attractive Hamaker constant. Two approximate expressions have been proposed for the repulsive interaction, VR(x), for the limiting cases of κa < 1 and (30) Degiorgio, V.; Corti, M. J. Colloid Interface Sci. 1984, 101, 289. (31) Felderhof, B. U. J. Phys. 1978, 11, 929. (32) Hamaker, H. C. Physica 1937, 4, 1058.

(20)

which is appropriate for the aggregates investigated here. In eq 20 Ψ0 is the surface potential and κ the DebyeHu¨ckel reciprocal length parameter, expressed by the equation

κ2 )

(15)

Expressed in terms of the volume fraction φ of the particles

kD ) 1.56 +

Table 3. Experimental and Theoretical Slopes, kD, and Reduced Potential at Shear Surface, Eψ0/kBT, of Nafcillin at 303.15 K as a Function of Electrolyte Concentrations

8πcse2z2 kBT

(21)

where  is the relative dielectric constant of the suspending medium, z the valence of the ionic species in solution, cs the concentration of the same species, and e the electronic charge. The computational procedure involved the iteration of values of A and Ψ0 to give the best fit of computed and experimental values of kD over the range of electrolyte concentration. Agreement between computed and experimental values of kD shown in Table 3 is similar to that reported by other workers13 and is reasonable in view of the assumptions inherent in these calculations. The micellar charge, q, is related to the surface potential, Ψ0, by the expression34

Ψ0 )

(

)

2kBT 2πeκ-1qe sinh-1 e 4π2a2kBT

(22)

The value of the q derived from eq 22 was 1.46 uce and the Hamaker constant was 1.1 × 10-22 J. This value of the Hamaker constant is in agreement with the low aggregation numbers obtained from static light scattering measurements and very similar to those values previously reported for other penicillins9 (1.2 × 10-22, 2.2 × 10-22, and 1.4 × 10-22 J for cloxacillin, dicloxacillin, and flucloxacillin, respectively). To obtain an evaluation of the unknown parameters appearing in the expression of the interaction potential V ) VA(x) + VR(x), we have made the simplifying assumption that A and q are both independent of the salt concentration. With regard to A, measurements of forces between two surfaces in aqueous electrolyte solutions35 clearly show that the attractive London-van der Waals forces are largely independent of the type and concentration of the aqueous electrolyte solution. The effect of electrolyte on the reduced potential eΨ0/ kBT and V(x)/kBT is shown in Table 3 and Figure 6, respectively, from which it is clear that the electrostatic potential becomes progressively more screened and the (33) Minero, C.; Pramuro, E.; Pelizzeti, E.; Degiorgio, V.; Corti, M. J. Phys. Chem. 1986, 90, 1620. (34) Anderson, J. L. Rauh, F.; Morales, A. J. Phys. Chem. 1978, 82, 608. (35) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 1 1978, 74, 975.

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Figure 6. Pair interaction potential, V(x), for nafcillin at the electrolyte concentrations indicated. Values of the parameters are given in the text.

Figure 7. Variation of the 1H chemical shift, δ, of the aromatic protons Hf of nafcillin as a function of the reciprocal concentration at 298.15 K.

Table 4. Critical Concentrations, cc, Aggregation Numbers, N, and Chemical Shifts, ∆δ, of Nafcillin in D2O at 298.15 K from Nuclear Magnetic Resonance Measurements Calculated for Protons Shown in Scheme 1 Ha Hb Hd He Hf

cc (mol kg-1)

∆δ

N

0.054

0.094 0.086 0.665 0.263 0.763

3 6 5

0.057 0.055 0.057

Scheme 1

Figure 8. Variation of the 1H chemical shift, δ, of the β-lactam protons Hc1 and Hc2 of nafcillin as a function of the reciprocal concentration at 298.15 K.

London-van der Waals attraction becomes more important as the electrolyte concentration is increased. The aggregation behavior of nafcillin has been investigated by high-resolution NMR spectroscopy. 1H NMR spectra of nafcillin solutions at a range of concentrations well below and above the critical concentration show pronounced upfield shifts of the protons indicated in Table 4 and Scheme 1 on increase of concentration above the critical concentration. Critical concentrations determined from the intersection of the linear portions of plots of the chemical shift of these protons as a function of reciprocal concentration (Figure 7) at concentrations well above and below the inflection region were lower than the equivalent values from conductivity and light scattering. Discrepancies in critical concentrations from different experimental techniques arise from differences in the sensitivity of the experimental probes in detecting the presence of aggregated species. In polydisperse systems of low aggregation number, changes in solution properties may occur over a relatively wide concentration range and the choice of a particular point as the critical concentration often depends on the type of plot and the method of data extrapolation.36 The method of location of cc in this study is widely used to determine critical micelle concentration (cmc) and reportedly gives good agreement with values (36) Mukerjee, P., Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems; National Bureau of Standards NSRDSNBS36, U.S. Government, Printing Office: Washington, DC, 1971.

from other techniques.37 An alternative procedure in which the critical concentration is identified as the first departure of the chemical shift from the monomer value38 clearly gives poorer agreement in the present study. It should also be noted that the critical concentrations determined by the NMR technique were measured in D2O in which the effects of hydrophobic hydration are significantly different compared to water. The direction of the change of chemical shift of nafcillin upon aggregation is similar to that reported earlier for the penicillins cloxacillin, dicloxacillin, and flucloxacillin9 and can be attributed to an intermolecular aromatic ring current effect.39,40 Although the aromatic proton Hf shown in Figure 7 exhibits only an upfield shift on increase of concentration, it is interesting to note that the β-lactam protons (Hc1 and Hc2 in Scheme 1) exhibit an additional initial downfield shift with increasing concentration at very high concentrations (Figure 8). Similar behavior was noted with the penicillins flucloxacillin and dicloxacillin, the downfield shift occurring at the second critical concentration. Table 4 shows the change of the chemical shift, ∆δ (calculated from the difference between the micellar chemical shift, δm, at an infinite drug concentration and (37) Drakenberg, T.; Lindman, B. J. Colloid Interface Sci. 1973, 44, 184. (38) Wang, Z.; Morris, K. R.; Chu, B. J. Pharm. Sci. 1995, 84, 609. (39) Haigh, C. W.; Mallion, R. B. Org. Magn. Reson. 1972, 4, 203. (40) Haigh, C. W.; Mallion, R. B. Prog. Nucl. Magn. Reson. Spectrosc. 1980, 13, 203.

Self-Association of Drugs in Aqueous Solution

Langmuir, Vol. 16, No. 7, 2000 3181

that of the monomer, δmon, measured at high dilution, ∆δ ) δm - δmon), for selected protons of nafcillin (see Scheme 1). Protons of the benzene ring and the adjacent methylene group show the largest shifts on aggregation, with only small shifts being observed for protons on the carbon bearing the ionized carboxyl group and on the methyl group on the thiazidoline ring. The much larger chemical shifts on aggregation of the aromatic protons suggest a greater involvement of the aromatic rings in the association process. An upfield shift of aromatic protons as the concentration is increased above the critical concentration has been noted, for example, for the micellization of ω-phenylalkyltrimethylammonium bromides41,42 and sodium ω-phenyldecanoate.43 Similar shifts are also characteristic of surfactants which exhibit a stacking mode of association including nucleotides,44 dyes,45,46 and phenothiazine drugs.47 The chemical shifts of Table 4 suggest the stacking or overlap of the ethoxynaphthamido ring systems of nafcillin such that the ring system of one molecule is placed directly in the shielding region of that of an adjacent molecule. Similar conclusions were reported from an analysis of chemical shift data for penicillin G by Thakker et al.6 and for cloxacillin by Kupka et al.8 The small chemical shift changes of the protons in the vicinity of the charge indicate no significant change of environment on aggregation as expected for groups on the periphery of the aggregate. The small downfield shift of the β-lactam protons at high solution concentration (Figure 8) suggests interionic hydrogen bonding between the amide groups of adjacent penicillin molecules6 in concentrated solution. Assuming an idealized situation where the amphiphile may exist as either a monomer or in a single type of micelle with an aggregation number N, the chemical shift accompanying aggregation can be written as48

δobs )

mm δ mt m

(23)

where mm and mt are the concentration of aggregated amphiphile and the total amphiphile concentration, respectively. δobs is the observed chemical shift both taken relative to the chemical shift of the monomer as determined from measurements at high dilution. From the mass action equation we may express the concentration of monomer as

[A] ) mt

δm - δobs δm

(24)

(41) Nakagawa, T.; Tokiwa, F. In Surface and Colloid Science; Majitevic, E., Ed.; Wiley: New York, 1976; Vol. 9, p 69. (42) Nakagawa, T.; Inoue, H.; Jizomoto, H.; Horiuchi, K. Kolloid-Z. Z. Polym. 1969, 229, 159. (43) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J. Colloid Interface Sci. 1990, 137, 137. (44) Ts’O, P. O. P. J. Am. N. Y. Acad. Sci. 1969, 153, 785. (45) Blears, D. J.; Danyluk, S. S. J. Am. Chem. Soc. 1966, 88, 104; 1967, 89, 21. (46) Asakura, T.; Ishida, M. J. Colloid Interface Sci. 1989, 130, 184. (47) 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. (48) Persson, B. O.; Drakenberg, T.; Lindman, B. J. Phys. Chem. 1987, 19, 183.

Figure 9. Chemical shift data plotted according to eq 26 for the aromatic protons, Hf for nafcillin in aqueous solution at 298.15 K.

and the aggregate concentration as

N[A] ) mt

δobs δm

(25)

The expression for the equilibrium constant K may be written as

ln(mtδobs) ) N ln[mt(δm - δobs)] + ln K + ln N - (N - 1) ln δm (26) Plots of ln(mtδobs) against ln[mt(δm - δobs)] may in principle give the aggregation number and the equilibrium constant. Figure 9 shows the chemical shift data for the Hf proton plotted according to eq 26 for solutions of nafcillin in D2O. Aggregation numbers ranging from 3 to 6 were derived by this method using chemical shift data for the aromatic protons Hd, He, and Hf.. The determination of aggregation numbers by the application of mass action theory to the concentration dependence of chemical shifts has been criticized45 because of the influence of monomers on the shift observed at concentrations above the critical concentration. There is a shift difference between free and aggregated amphiphile, and since the observed shifts are weighted averages of these two environments, the shifts will change as the fraction of free monomers decreases with increase of total concentration. Aggregation numbers obtained from NMR measurements tend to be lower than those obtained using other techniques;49,50 this study, however, shows a reasonable agreement between NMR aggregation numbers and those from conductivity and light scattering. Acknowledgment. This work received financial support from Xunta de Galicia. P.T. Thanks Fundacio´n Caixa Galicia for his grant. LA991237F (49) Soderman, O.; Guering P. Colloid Polym. Sci. 1987, 265, 76. (50) Chachaty, C. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 183.