Scientific paper
Preferential Solvation of Ibuprofen and Naproxen in Aqueous 1,2-Propanediol
Yizhak Marcus
Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel * Corresponding author: E-mail: ymarcus@vms.huji.ac.il
Received: 26-08-2008 Dedicated to Professor Josef Barthel on the occasion of his 80'' birthday
Abstract
The recently published study of the solubility of Ibuprofen (IBP) and naproxen (NAP) in aqueous 1,2-propanediol (PG) at several temperatures had as its purpose the modeling of the solubilities in terms of the solvent composition. It did not show how these drugs are preferentially solvated by water and by PG. The inverse Kirkwood-Buff integral (IKBI) and the quasi-lattice quasi-chemical (QLQC) approaches are here applied to this problem of the preferential solvation. The interactions involved are deduced from the results.
Keywords: Ibuprofen, naproxen, 1,2-propanediol, preferential solvation, inverse Kirkwood Buff integrals, quasi-lattice quasi chemical method.
1. Introduction
Most studies of the solubility of drugs in solvent mixtures have as their purpose the modeling of the solubilities in terms of the solvent composition, possibly also the prediction of the solubilities in the mixtures from those in the pure components. A very recent example is the study by Manrique et al.1 of the solubility of ibuprofen (IBP, 2-[4-(2-methylpropyl)phenyl]propanoic acid, CAS reg. No. 15687-27-1) and naproxen (NAP, (+)-(S)-2-(6-methoxynaphthalen-2-yl)propanoic acid, CAS reg. No. 22204-53-1) in mixtures of water (W) and 1,2-propanediol (PG) at several temperatures. Thermodynamic functions of the solvation of the drugs were obtained, but not how they are preferentially solvated by water and by PG in the aqueous solvent mixtures. Such modeling of drug solubilities has been carried out over the years by means of various approaches, such as the 'nearly ideal binary solvent' (NIBS) approach of Acree and co-workers2 or the model of Jouyban-Acree,3 mobile order theory,4 or Kirk-wood-Buff integrals,5 among others. More insight into the interactions of the drug molecules with those of the components of the mixed solvent would help in the choice of better co-solvents for the enhancement of drug solubilities in aqueous media, because these after all constitute the body fluids. Such insights should be obtainable from de-
tailed information on how these drug molecules are preferentially solvated, since not only the direct drug-solvent interactions but also interactions between the components of the mixed solvent are involved.
The recent publication by Marcus6 addressed this problem by means of two approaches: the inverse Kirk-wood-Buff integral (IKBI) method and the quasi-lattice quasi-chemical (QLQC) one, each having its merits and drawbacks. The preferential solvation parameter 5xA S for the solute S by the component solvents A and B is defined as:
§xA,S= xLA,S- xA = - §xB,S
(1)
where xLA,S is the local mole fraction of A in the surroundings of the solute S and xA is its mole fraction in the bulk solvent mixture. S is preferentially solvated by A when 5xAS > 0, otherwise by B. Negligible preferential solvation is indicated when |5xA,S| < 0.01, but values 5xA,S « xB signify xLAS « 1 or complete selective solvation of S by A. The magnitude and shape of the 5xA S = f(xA) curve provide the desired information on the relative strength of the interactions of S with A and with B in their mixture.
In order to apply the IKBI and QLQC methods, the solubility data need to be transformed into standard molar Gibbs energies of transfer from one of the components,
say A, into the mixture A + B. If s(xA) is the solubility as a function of the solvent composition, then:
= xaxb(Ga,s - G + XbGb,s + ^cor]
A,S = xAxB(GA,S gB,S) ^ [XAGA,S
(7)
AtG^(S, A ^ A + B) = -RT ln[s(S in A + B)/s(S in A)] (2)
provided that the solid that is at equilibrium with the saturated solutions is the same at all the solvent compositions and no solvates are formed. Another requirement is that the solute S is only sparingly soluble, so that an essentially infinite dilution quantity, AtG", results. Otherwise, activity coefficients of S at each solvent composition need to be employed. 5^G" implies that solute-solute interactions may be disregarded and the solute molecules are surrounded by solvent molecules only.
2. Methods and Data
The IKBI approach depends on obtaining the Kirk-wood-Buff integrals6 as follows.
Ga,s= rtkt- vs + xbvbd/q
Gb,s = rtkt- Vs+ xavad/q
(3)
(3a)
Here GA S and GB S are the Kirkwood-Buff integrals (in cm3 mol-1) as obtained from the thermodynamic data: the isothermal compressibility of the mixtures, kt (in GPa-1), and the partial molar volume of the solute, VS, and
those of the solvents, VA and VB (in cm3 mol
-1). The functions D and Q (in kJ mol1, as is RT) are given in eqs. (4) and (5), and depend on the first derivative of standard molar Gibbs energies of transfer, AtG", and the second derivative of the excess Gibbs energy of mixing of the two solvents, Ge,b, with respect to the composition.
D = dAtG^(S, A ^ A + B)/dxB Q = RT + xAxBd2GEA,B/dxB2
(4)
(5)
A final quantity that is required is the correlation volume around S, Vcor, within which preferential solvation takes place and the local mole fraction, xLA S, is defined.
Vcor = 2522.5[rs + 0.1363 {Xal Va + + (1-Xal)Vb}1/3 - 0.085]3
(6)
This volume involves one solvation shell and depends on the size of the solute molecule (its radius, rs in nm) plus a distance of one mean solvent diameter from the surface of the solute. The resulting correlation volume, in cm3 mol-1, the numerical coefficients of which relate sizes to volumes,6 requires iteration, since it involves the local mole fractions of the two solvents.
The resulting preferential solvation parameter is
then:6
The QLQC approach counts the pairs of adjacent molecules on the quasi lattice of the solution, that has a lattice parameter Z (coordination number), the neighboring pairs being so arranged because of the interactions involved in the quasi-chemical model. At infinite dilution of the solute, the fraction of A-A contacts in a mixture of NA + Nb solvent molecules is NAA/Z(NA + NB) = xA -Nab/Z(Na + Nb) and similarly for B-B contacts. The fraction of A-B contacts depends on the interaction energy between these molecules, AEAB according to the quasi-chemical aspect:
Nab/Z(Na + Nb) = [1-{1-4XaXb
(1-exp(-A£AB/RT))}1/2]/[2(1-exp(-A£AB/RT))]
(8)
The interaction energy AEAB is obtained from the excess Gibbs energy at the equimolar composition:
exp(A£AB/RT) = [{2exp(-GAB (x = 0.5)/ZRT)} - 1]2 (9)
When the solute S is introduced at infinite dilution it interacts with the two solvents, with the difference in the interaction energy given by its standard molar Gibbs energy of transfer:
AEab,s = AtG^(S, A ^ B)/Z
(10)
Finally, the local mole fraction of solvent component A in the surroundings of S is given by the quasi-chemical expression:
xaL = 1/[1 + (NBB/NAA)1/2exp(AEAB,s/2RT]	(11)
The derivation of the expressions employed here is described in the references given in the previous publication6 as are also the relative merits of the two methods (the IKBI has fewer unverifiable assumptions) and their drawbacks (the need for derivative functions for IKBI implying highly accurate data).
The data required for the application of the IKBI and QLQC methods in the present instance are first of all the solubilities s of the IBP and NAP in the solvent mixtures, water (W) + PG. These were provided by Manrique et al.1 at 5 temperatures between 20 and 40 °C at 6 solvent compositions. The latter were at 20 mass % steps from neat W to neat PG, and when transformed to xPG: 0, 0.0588, 0.1363, 0.2621, 0.4864, 1, they show a gap beyond the equimolar composition. The solubility of NAP in neat PG is still sufficiently low permitting the disregard of solute-solute interactions, but that of IBP, at the higher temperatures, is considerable. For the lack of activity coefficient data (not the quantities so designated by Manrique et al.1 but those relating to solute-solute interac-
Fig. 1. The standard molar Gibbs energies of transfer, AjrG"/kJ mol-1, of IBP (circles) and NAP (triangles) from W to W + It'G as a function of the PG content, xPG, at 25 °C (filled symbols) and 40 °C (empty symbols). The curves are 3rd degree polynomials fitted to the data.
tions), eq. (2) must still be applied. The resulting values at 25 and 40 °C are shown in Fig. 1, third degree polynomials being fitted to them.
No excess Gibbs energies of mixing have been reported for the W + PG system, but such values can be derived from published data. Water activities at 80 °F (26.67 °C) were reported by Curme and Johnston,7 from which the excess chemical potential of water, ^WE, is readily obtained. Its derivative with respect to xPG can be used in lieu of d2GEA,B/dxB2 in eq. (5), and when expressed as a Redlich-Kister expression ^WE is readily transformed into Gew,pG for use in eq. (9). Subsequently, Sloan and Labuza8 reported water activity data at 23 °C that can be treated si-
o E
5
LU
eoo
500
400
300
200
100
-100
-200 0.00
X	'k \
/ p' / / ■	\ ■
/ jr^	V \ \ \ \\
	—à-* /
, 1	1 1
0.20
0.40
0.00
0.80
1.00
Fig. 2. The excess Gibbs energy of mixing, GEWpG/J mol 1, of W and PG as a function of the PG content, XpG, at several temperatures: • 23 °C,8 ▲ 26.67 °C,7 T 80 °C,10 and ■ 98 °C.11
milarly, although the resulting curve appears to be rather wave-like. It is deduced from these two sources that Gewpg < 0 at these two temperatures, although Verlinde et al. 9 considered that GEWpG « 0 at 15 to 50 °C from vapor pressure data. Application of the UNIQUAC method by Jonsdottir and Klein10 to W + PG at 80 °C, however, yielded positive values of GEWPG, and larger positive values were provided from UNIQUAC calculations (albeit with different group contributions) by Lancia et al.11 at 98 °C. These results are summarized in Fig. 2. The vapor pressures and compositions reported by Chu et al.12 at 80 and 110 °C lead to still positive but smaller GEW_PG values than obtained from the UNIQUAC calculations, but the nonavailability of the 2nd virial coefficients at the high temperatures and considerable vapor pressures does not permit the accurate calculation of GEWPG.
The isothermal compressibility, kt, and partial molar volumes, VW and VPG of the W + PG mixtures, required in eq. (3), were calculated from the densities and excess molar volumes at ambient and at elevated pressures at several temperatures reported by Geyer et al.13 The partial molar volumes VjBP and VNAP, also needed for eqs. (3), are assumed equal to the molar volumes of the liquid drugs, but neither these nor the densities of the solid drugs were found. However, the molecular volumes vm were reported as 0.2816 nm3 for IBP14 and 144.50 (without units!) for NAP.15 Since phenobarbital appeared in both lists1415, the NAP value was converted by the same ratio as for this drug to 0.3226 nm3, some 15% larger than that for IBP, in view also of the larger molar mass,1 230.26 (NAP) and 206.28 (IBP) g mol-1. The molar volume of the (assumed liquid solute) is obtained from the molecular volume and the assumed packing fraction of molecules in liquids of 58%.6 The radius required in eq. (6) is calculated as rS = (3 vm/4n)1/3. The approximations so incurred in the values of VS and rS have only slight (±5%) effects on the results of the IKBI calculation.
3. Results and Discussion
For the application of the IKBI method, the derivatives of the fitted 3rd degree polynomial of AtG^(lBP or NAP, W^ W + PG) = f(xPG) were obtained. In view of the scarcity of the experimental points (Fig. 1) and their absence at xPG > 0.5 except for xPG = 1, the accuracy of these derivatives leave much to be wanted. No GEW,PG data for 40 °C are available nor could be estimated, but for 25 °C the ^EW at 26.67 °C7 could serve. In fact, the first derivative d^EW/dxPG can with advantage replace the second derivative d2GEW,PG/dxPG2. The results of the application of the IKBl method with the solubility data at 25 °C are shown in Fig. 3.
For the application of the QLQC method, the solubility data at both 25 and 40 °C could be used. The AtG^(lBP or NAP, W^W + PG) = f(xPG) values were fitted with values of Z between 8 and 12 and were found not
Fig. 3. The preferential solvation parameter, 5xpG = f(XpG) obtained by the IKBI method: for IBP (—) and NAP (----) at 25 °C.
to be very sensitive to them, so that Z = 10 was employed. The excess Gibbs energies of mixing W + PG at the equi-molar composition and at various temperatures were interpolated from Fig. 2. The results of the application of the QLQC method are shown in Fig. 4. They are seen to be in general agreement with those from the IKBI method (Fig. 3), though not with regard to the detailed shapes of the curves: the IKBI values of 5xA S = f(xPG) peak at a somewhat lower PG content than the QLQC ones. This is to be expected in view of the lack of solubility data at 0.5 < xPG < 1 on the one hand (with regard to the IKBI method) and
Fig. 4. The preferential solvation parameter, 5xPG = f(xPG) obtained by the QLQC method: for IBP (upper curves) and NAP (lower curves), — for 25 °C and----for 40 °C. The dots at the top denote the
solvent mole fractions of the experimental data.
the use of only AtG"(IBP or NAP, W^ PG) rather than the full curve (for the QLQC method).
Both methods indicate that PG is preferred over W in the surroundings of both drug molecules, of IBP more than of NAP, although the preference is not large, the maximal 5xA,S being <0.12 and <0.09 respectively. The temperature dependence for both drugs (Fig. 4) is a small increase of the preferences with increasing temperatures. Ibuprofen (2-[4-(2-methylpropyl)phenyl]propanoic acid) has a hydrophilic head, the carboxylic group, and a hydrophobic tail. Naproxen ((+)-(S)-2-(6-methoxynapht-halen-2-yl)propanoic acid) has in addition to the hydrop-hilic head also a methoxy group in the, albeit more bulky, hydrophobic tail. Neat PG solvated both drugs many times better than W (at 30 °C, AsojvG°/kJ mol1 are -38.03 in PG vs. -15.27 in W for IBP and -45.38 in PG vs 26.95 in W for NAP).1 The neat solvents have a network of hydrogen bonds, more pronounced and stiff for water than for PG, so that the formation of a cavity in the solvents to accommodate the bulky solutes is an endoergic process, more in W than in PG. This is compensated by the exoer-gic solvation of the polar groups of the drug molecules. It stands to reason that the water component of the mixed solvent clusters around the carboxylic group, but not exclusively, because PG has two hydroxyl groups that can donate hydrogen bonds to and accept them from the car-boxylic group. However, such hydrogen bond donation by PG can, in the case of NAP, also take place with the oxygen atom of the methoxy group, so that the preferential solvation by W should be smaller than for IBP. The hydrocarbon part of PG can interact by means of dispersion forces with the aromatic hydrophobic part of the drug molecules that W can do much less effectively (by dipole-pola-rizable aromatic ring interaction, mainly).
In the mixtures, the interactions between PG and W moderate the difference in the solvation abilities of the neat solvents. The negative Gew_pg values at room temperature shows that the molecules of the solvent components interact more strongly with each other than with their own kind. This interaction loosens the tight hydrogen bond network of the water and facilitates the inclusion of the drug molecules, in addition to the direct solvation of the polar groups. The result is a preferential solvation of both drug molecules by PG at all compositions, but not as much as would have been suggested by the differences in the solvation abilities of the neat solvent components. The results are compatible with the thermodynamic analysis of the solubilities by Ma-nrique et al.,1 but provide additional information.
4. References
1.	Y. J. Manrique, D. P. Pacheco, F. Martinez, J. Solution Chem. 2008, i7, 165-181.
2.	W. E. Jr. Acree, J. H. Rytting J. Pharm. Sci. 1982, 71, 201205.
3.	A. Jouyban, M. Khoubnasabiafari, W. E. Jr. Acree, Chem. Pharm. Bull. 2006, 54, 1124-1130.
4.	W. E. Jr. Acree, S. A. Tucker, Fluid Phase Equil. 1994,102, 17-29.
5.	E. Ruckenstein, I. L. Shulgin, Int. J. Pharm. 2003, 258, 193201.
6.	Y. Marcus, J. Mol. Liq. 2008 140, 61-67.
7.	G. O. Curme, Jr., F. Johnston, eds.: Glycols, Reinhold, New York, 1953, p. 161.
8.	A. E. Sloan, T. P. Labuza, Food Proc. Dev. 1975, 9, 68.
9.	J. R. Verlinde, R. M. H. Verbeck, H. P. Thun, Bull. Soc. Chim. Belges. 1975, 84, 1119-1130.
10.	S. O. Jonsdottir, R. A. Klein, Fluid Phase Equil. 1997, 132, 117.
11.	A. Lancia, D. Musmarra, F. Pepe, J. Chem. Eng. Jpn, 1996, 29, 449.
12.	L. T. Chu, W. Hirsch, V. Fried, AIChE Symp. Series, 1989, 85, 1-5.
13.	H. Geyer, P. Ulbig, M. Görnert, J. Chem. Thermodyn. 2000, 32, 1585-1596; H. Geyer, P. Ulbig, M. Görnert, A. Susanto, J. Chem. Thermodyn., 2001, 33, 987-997.
14.	X. Fu, Zh. Song, W. Liang, Internet Electron. J. Mol. Des., 2005, 4, 737-750.
15.	J. Ghasemi, S. Saaidpour, Anal. Chim. Acta, 2007, 604, 99106.
Povzetek
Delo obravnava preferencno solvatacijo na osnovi podatkov o temperaturni odvisnosti topnosti ibuprofena (IBP) in na-proksena (NAP) v mešanicah vode in 1,2-propandiola (PG) z uporabo inverznega Kirkwood-Buffovega integrala (IKBI) ter "quasi-lattice quasi-chemical" (QLQC) metode.