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Thermodynamics of Solutions IV: Solvation of Ketoprofenin Comparison with other NSAIDs GERMAN L. PERLOVICH,1,2 SERGEY V. KURKOV,2 ANDREY N. KINCHIN,2 ANNETTE BAUER-BRANDL1 1University of Tromsø, Institute of Pharmacy, Breivika, N-9037 Tromsø, Norway 2Institute of Solution Chemistry, Russian Academy of Sciences, 153045 Ivanovo, Russia Received 28 May 2003; revised 26 June 2003; accepted 2 July 2003 ABSTRACT: The present work discusses the characteristics of solvation (Gibbs energy,enthalpic and entropic terms of Gibbs energy) for ketoprofen together with othernonsteroidal antiinflammatory drugs (NSAIDs) in aliphatic alcohols. Ketoprofen wasstudied by classical thermoanalytical methods of sublimation calorimetry, solutioncalorimetry, and solubility. Temperature dependence of the saturated vapor pressurewas determined, and the sublimation enthalpy, DH0 , and sublimation entropy, DS0 , as well as their respective relative fractions in the total process were calculated.
The parameters yielded for ketoprofen were compared with the respective literaturedata of other benzophenone derivatives. The Gibbs energy of solvation as well asenthalpic and entropic terms thereof in aliphatic alcohols were also studied for keto-profen and compared with the properties of model substances and other NSAIDs (benzoicacid, diflunisal, flurbiprofen, and naproxen). In all cases, the major driving force of thesolvation process is enthalpy. Correlations were derived between Gibbs energy of solva-tion in octanol, DGoct , and the transfer Gibbs energy from water to octanol, DG0 .
ß 2003 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 92:2511–2520, 2003Keywords: ketoprofen; solubility; solvation; calorimetry (ITC); thermodynamics partition coefficient, P. P is a relative measure ofthe lipophylic–hydrophylic balance of a compound Although receptor affinity is a key issue in devel- and characterizes the driving force of the partiti- oping a potent drug preparation, other factors oning process in a water–octanol system. From such as solubility, partitioning, passive transport the point of view of equilibria thermodynamics, properties, absorption, and biodegradation are the difference in chemical potentials for the drug equally important. In many cases, unfortunately, molecule within the two different phases is the these important aspects are studied late in the driving force of transfer for a molecule from one drug discovery/development process. Therefore, phase to the other. However, most of the transport studying biopharmaceutically relevant physico- and delivery processes in a biological environment chemical and biophysical properties of compounds take place under essentially nonequilibrium con- affecting the optimization process is an important ditions and in nonhomogeneous media, just to name the difference between trans- and paracel- lular pathways from the point of view of their meters to describe various physicochemical and lipophylic–hydrophylic composition. Moreover, pharmokinetic properties of drug candidates is the questions connected with the mechanism of diffu-sion into biological membranes (e.g., What controlsthe size of activation volume for passive trans- port?; What is the nature and dimension of the 47 77646160; Fax: 47 77646151; E-mail: [email protected]) units that are transferred by the diffusion process: Journal of Pharmaceutical Sciences, Vol. 92, 2511–2520 (2003)ß 2003 Wiley-Liss, Inc. and the American Pharmacists Association is it the drug molecule or the drug molecule þ its JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 12, DECEMBER 2003 solvation shell?) have widely been out of focus for discussion. The purpose of the present work is Solubilities of KETO were obtained at 25 Æ 0.18C to look at this problem from the point of view of by a spectrophotometrical method with an accu- energetic aspects of the interaction of drugs with racy of $2.5% using the protocol described previously.4 The wavelengths of the ketoprofen The present work is a continuation of our earlier absorption band were 255.0 nm in methanol, studies,1–3in which experimental data were ob- 255.5 nm in ethanol; 254.1 nm in 1-propanol, tained by using the classical thermoanalytical 256.6 nm in 1-butanol, 277.0 nm in 1-pentanol, methods of sublimation, solution calorimetry, 265.8 nm in 1-hexanol, 254.2 nm in 1-heptanol, and solubility. In contrast to our previous work, where phenyl derivatives (acetylsalicylic andbenzoic acids),1 biphenyl derivatives (diflunisaland flurbiprofen),2 and naphthalene derivatives [(þ)-Naproxen]3 were considered, in the presentstudy, the benzophenone derivative ketoprofen Enthalpies of solution at a concentration m (KETO) was chosen as a representative of the (DHmsol) were measured with an isothermal same class of drugs [nonsteroidal antiinflamma- Precision Solution Calorimeter that has been pre- tory drugs (NSAIDs), see Figure 1]. This choice viously described in detail.5 The sum of uncer- enables one to compare solvation characteristics tainties of the heat effect of each experiment did for a wide spectrum of compounds using quanti- not exceed 1%. The measuring temperature was tative thermodynamic parameters derived from 25 Æ 10À4 8C, the volume of the vessel was 100 mL, experimental data. The objective may as well be to the stirrer speed was 500 rpm, and the mass of correlate these with pharmokinetic properties of the each sample was $18 mg. The accuracy of the weight measurements corresponded to Æ 0.0005 mg.
The calorimeter was calibrated with KCl (analy-tical grade >99.5%, from Merck) in water over a wide concentration interval, with >10 measure-ments. The standard value for the solution entha- lpy obtained was DH0 ¼ 17225 Æ 50 J molÀ1. This value is in good agreement with that of DH0 ¼ The ketoprofen studies were carried out using a 17217 Æ 33 J molÀ1 recommended by IUPAC.6 commercially available substance (KETO; 2-[3-benzoylphenyl]-propionic acid, C16H14O3, MW 254.3)from Sigma Chemical Company, St. Louis, MO Sublimation experiments were carried out by the The following alcohols were used: methanol HPLC transpiration method as described previously.7 grade from (lot K27636907; Merck, Germany); In brief, a stream of an inert gas passes above the ethanol extra pure grade (99.6% v/v, maximum sample at a constant temperature and at a known water content 0.4%; Aldrich, Germany); 1-propa- slow constant flow rate to (practically) achieve nol (HPLC grade; lot U00874; Aldrich); 1-butanol saturation of the carrier gas with the vapor of the analytical reagent grade (ARG) (lot K22047090; substance under investigation. The vapor is con- Merck); 1-pentanol ARG (lot 35757-101; Aldrich); densed at some point downstream, and the mass 1-hexanol ARG (lot 31562-011; Aldrich); 1-hepta- of sublimate and its purity are determined. The nol ARG (lot 60K3706; Sigma Chemical Company); vapor pressure over the sample at this tempera- 1-octanol ARG (lot 11K3688; Sigma Chemical ture can be calculated from the amount of sub- limated sample and the volume of the inert gasused.
The equipment was calibrated with benzoic acid (standard substance obtained from Polish Com-mittee of Quality and Standards). The standardvalue for the sublimation enthalpy obtained wasDH0 ¼ 90.5 Æ 0.3 J molÀ1. This value is in good agreement with that of DH0 ¼ 89.7 Æ 0,5 J molÀ1 Structure of the ketoprofen molecule.
recommended by IUPAC.6 The saturated vapor JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 12, DECEMBER 2003 pressures were measured at each temperature fusion processes of ketoprofen are summarized in at least five times, and the statistical error was Table 1. It is a prerequisite of the method that within 3–5%. The experimentally determined within the temperature interval used and during vapor pressure data were described in (ln P;1/T) the whole experiment that neither any chemical decomposition of the compound both in the mea-suring cell and in the sublimated products nor a temperature dependence of the stripping gas The value for the enthalpy of sublimation was vapor pressure occurs. Then, the relation between calculated by the Clausius–Clapeyron equation: the saturation vapor pressure of the compoundsand the temperature may be described using eqs.
1–3, yielding a linearity that can be extrapolated The entropy of sublimation at a given temperature to standard conditions. The results of the linear T was calculated from the following relationship: regression as well as the calculated standard Gibbs energy, entropy as well as enthalpy of sub- To derive regularities between thermodynamic where DHTsub ¼ ÀRT Á ln(P/P0) and P0 ¼ 1.013 Á parameters of sublimation and compound struc- ture, a selection of substances with similarstructures to ketoprofen were studied with respect to published data. The thermodynamic parame- Regression analysis of the data was performed ters of the sublimation process and structures of all substances are shown in Table 2. It is evident that introducing a substituent in 3- position(ketoprofen, compound 1) into the unsubstitutedbenzophenone (compound 2) essentially incre- ases the crystal lattice energy (by 21 kJ molÀ1).
Probably, this increase is a consequence of hydro- gen bonding, which occurs when two ketopro- Temperature dependencies of vapor pressure, fen molecules form a dimeric structure between thermodynamic parameters of sublimation, and their carboxyl-groups in the crystal lattice.8 An Temperature Dependence of Vapor Pressure, Thermodynamic Parameters of Sublimation, and Fusion aln(P[Pa]) ¼ (33.0 Æ 0.2) À (13250 Æ 60)/T, where r ¼ 0.999; s ¼ 1.35 Á 10À2; F ¼ 47818; n ¼ 16.
d&TS ¼ T Á ÁS0 = ÁH0 þ T Á ÁS0 JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 12, DECEMBER 2003 Thermodynamic Parameters of Sublimation of Some Ketoprofene Derivativesa aÁG0 ¼ (55 Æ 7) þ (1.00 Æ 0.07) Á ÁH0 , where r ¼ 0.990; s ¼ 1.71; F2:5% ¼ 9.365; F ¼ 199; n ¼ 6.
b&H ¼ [ÁH0 /(ÁH0 þ T Á ÁS0 )] Á 100%.
c&TS ¼ [(T Á ÁS0 /ÁH0 þ T Á ÁS0 )] Á 100%.
analogous regularity is obvious when compounds lattice energy. Increasing the distance between 3 and 5 are compared, where the introduction of the phenyl rings by adding another—CH2 group an—OH group increases the enthalpy of sublima- (compounds 7 and 8) does not change the crystal tion by 9 kJ molÀ1. Furthermore, it is interesting to lattice energy. This result is also observed when study the effect of the distance between the two the C–O bridge is lengthened by adding two phenyl fragments within one molecule on crystal additional —CH2 groups (compounds 2 and 6).
lattice energy. Exchanging the keto group in However, when increasing the length by introdu- ketoprofen in between the phenyl rings by methy- cing additional —O (3) or —C–O (4) groups, the lene (compounds 2 and 7) decreases the crystal crystal lattice energy rises by a large and similar JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 12, DECEMBER 2003 shown by Li et al. for ephedrine and its deriva-tives,10 there are correlations between the entha-lpy of fusion and the van der Waals term for crystallattice energy. If it is supposed that during themelting of a crystalline substance only the numberof degrees of freedom of the molecules, but notthe nature of molecular interactions (the ratiobetween energetic terms of the crystal lattice),essentially changes, then a correlation betweenenthalpies of sublimation and evaporation shouldconsequently be observed. This correlation isdepicted in Figure 3, where DH0 DH0 . It is evident that there is a common correla- tion, where diflunisal is an outlier from the trend(an anomalous low DH0 melting diflunisal compared to the other sub- stances). This behavior may be explained as on sublimation enthalpy, DH0 , for the com- follows: the diflunisal molecule has three hydrogen pounds with benzophenone motif (numbering corre- bonding centers (OH— and COOH—), all of which sponds to that in Table 2; that is, 1 is ketoprofen; 2 is actually take part in intermolecular bonding in benzophenone; 4 is benzyl; 7 is diphenyl methane; 8 is the crystal lattice, which in part are carried into dibenzyl; and 9 is triphenyl methane).
the molten state (where there are formed intra-molecular hydrogen bonds as well).
The dependence of the ratio DHfus/ DH0 versus the temperature of fusion (Tf) is shown in Figure 4.
value for both types ($10 kJ molÀ1) with regard to It is not difficult to see that there is a correlation between these variables. Taking into account that Dependence between the Gibbs energy of sub- DSfus ¼ DHfus/Tf, the entropy of fusion DSfus incre- ases proportionally to the crystal lattice energy.
is presented in Figure 2 (numbering corre- This regularity is in accordance with the findings sponds to that in Table 2). A compensation effect of thermodynamic functions between the GibbsDG0 studied is evident in Figure 2 (the result of linearregression is also presented in Table 2). It shouldbe noted that for the benzophenone (ketoprofen)derivates, DG0 than it is for naphthalene derivates3 (which includes naproxen; A1 ¼ 0.65 Æ 0.03 <1.00 Æ 0.07).
It may be supposed that at the same increase ofDH0 derived by derivatization of the respective unsubstituted ring systems (benzophenone andnaphthalene, respectively), the derivates of ben-zophenone yield a higher increase of DG0 less increase in vapor pressure) in comparisonwith derivates of naphthalene. It can be assumedthat this regularity will be useful for synthesis ofmolecules of better solvation because the approachpresented here gives the opportunity to carry outpreliminary estimation of sensitivity of solvationcharacteristics with respect to derivatization.
Based on literature data of the ketoprofen DH0 , on sublimation enthalpy, DH0 . Key: (BA) melting process,9 one can calculate enthalpy and benzoic Acid; (DIF) diflunisal; (FBP) flurbiprofen; entropy of evaporation (Table 1). As has been JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 12, DECEMBER 2003 temperature, Tf. Key: (BA) benzoic Acid; (DIF) difluni- sal; (FBP) flurbiprofen; (KETO) ketoprofen; (NAP) Thermodynamics of Ketoprofen Solvation inAliphatic Alcohols The thermodynamic solubility parameters DG0 ; ; TDS0 Þ and those of the solvation processes (DG0 , DH0 , T DS0 ) for ketoprofen in aliphatic alcohols are presented in Table 3, where DH0 The concentration of ketoprofen in all the al- cohols is $2.5 times lower than the ideal solubility.
The dependence of Gibbs energy of solvation versus the alcohol chain length (n) is shown in Figure 5 together with analogous values for benzoic acid (BA), diflunisal (DIF), flurbiprofen (FBP), and naproxen (NAP) obtained in earlier studies.1–3 It is evident that the noted drugs have much higher (absolute) values than benzoic acid, and may be arranged in the order of increasing values as BA( FBP < NAP < DIF < KETO. Based on literature data for the solubility in water, drugs were estimated (Table 4). At equilibrium conditions for drug molecules in a water–octanol system, the driving force of the partitioning between the phases is the difference between the Gibbs energies in the water and in the octanol phase. This driving force is commonly estimated from the log P value. It is interesting to analyze whether there are correlations between the driv- ing force and the absolute value of Gibbs energy of solvation. A schematic depiction of the transfer energies is shown in Figure 6. The transfer energies from aqueous into octanol medium, JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 12, DECEMBER 2003 , on the alcohol chain length, n. Key: (}) BA (benzoic acid); (&) DIF (diflunisal); (~) FBP (flurbipro-fen); (~) KETO (ketoprofen); (*) NAP (naproxen).
molecules from the water phase to the octanol phase.
solvation energies in octanol, DGoct , for the expenses for the resolvation process (destroying and rebuilding the solvation shell). Therefore, Figure 7. It is evident that there is a linear within a group of compounds with similar proper- correlation between these variables; that is, an ties, the Gibbs energy of solvation (in water or increase of the absolute value of Gibbs energy of octanol) should be a more appropriate measure for solvation (or hydration) for the drug leads to a the selection of drug candidates with optimized decrease of the driving force, which means the transport characteristics than the commonly used better the solvation, the lower the driving force value log P. Drugs with low solvation tendency into the octanol phase. As the solvation energy of the drug increases, probably the activation barrier Dependence of the enthalpy of solvation, DH0 , of phase transition from the water to the octanol in different aliphatic alcohols versus the alcohol phase also rises because of the larger energy chain length (n) for ketoprofen is shown in Figure 8 Values of Partitioning, Solubility, and Gibbs Energy of Hydration c[kJ Á molÀ1] concentrations have been recalculated in mol fraction.
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 12, DECEMBER 2003 octanol, DGoct . Key: (BA) benzoic Acid; (DIF) diflunisal; on the alcohol chain length, n. Key: (}) BA (benzoic acid); (&) DIF (diflunisal); (~) FBP (flurbiprofen); (~) KETO (together with data for BA, NAP, DIF, and FBP1–3 substances for which the enthalpic term of solubi- for comparison). The function is not monoto- lity (solvation) is less sensitive (in comparison with nous and has a maximum at n ¼ 5. The analyzed the entropic term) to a change of the surrounding compounds may be arranged according to increas- medium [i.e., alcohol chain length (A1) is <1]; these are, KETO, NAP, DIF, and ASA. The second class KETO < FBP < NAP < DIF. It is not difficult to see includes the drugs with the opposite behavior (i.e., that, on the one hand, ketoprofen has the largest A1 is >1); these are, FBP and BA.
value (within the studied drug compounds, Dependence of the entropy term of the Gibbs see Figure 5) and, on the other hand, an anom- energy of solvation, T Á DS0 , versus the alcohol chain length (n) is shown in Figure 9 for ketoprofen (together with data for BA, DIF, FBP, and NAP1–3 In accordance with results for compounds in- for comparison). This term is a measure of the vestigated previously, 1–3 a correlation between degree of order of the octanol molecules within the the enthalpic and the entropic terms of Gibbs solvation shell of the drug molecule. This func- energy are observed for the solution process (solubility) for the alcohols (so called compensation values): KETO < FBP < BA < NAP < DIF. There- effect11). The result of the correlation analysis is fore, as follows from Figure 8, ketoprofen has the presented in Table 5. As follows from the values most disordered solvation shell: the entropic term presented, the studied compounds can be divided for it is approximately half of the analogous values into two classes. The first class includes the for NAP and DIF, which have maximum order.
Results of Regression Analysis for DH0sol ¼ A0 þ A1(T Á DS0sol) in Aliphatic Alcohols JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 92, NO. 12, DECEMBER 2003 ratio of these terms, the following parameters wereintroduced: &H¼ðjDH0 j=ðjDH0 j þ jTDS0 jÞÞ100% &S¼ðjTDS0 j=ðjDH0 j þ jTDS0 jÞÞ100% Dependence of &H ¼ f(n), the chain length of thealcohols, for ketoprofen and the other NSAIDs1–3is shown in Figure 10. The investigated sub-stances, in the order of decreasing fraction ofenthalpy &H, are KETO > FBP > DIF & NAP >BA. For all the compounds considered, the majordriving force for the solvation process is enthalpy,and ketoprofen has the maximum &H value.
Gibbs energy, T Á DS0 , on the alcohol chain length, n.
Key: (}) BA (benzoic acid); (&) DIF (diflunisal); (~) FBP(flurbiprofen); (~) KETO (ketoprofen); (*) NAP This work was generously supported by NorgesForskningsra˚d, project number HS 58101, and the A low degree of order in the solvation shell will personal grant for German Perlovich of Russian probably favor conditions for the first elementary steps of chemical reactions and also for the dif-fusion process, particularly passive transportthrough membrane (easier change of the solvation shell during diffusion and membrane transition).
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