Artículo de Investigación científica

Estimation of the indomethacin solubility in ethanol + water mixtures by the extended Hildebrand solubility approach

Método extendido de Hildebrand en la estimación de la solubilidad de la indometacina en mezclas etanol + agua

Miller A. Ruidiaz ¹ , Daniel R. Delgado ¹ , Carolina P. Mora ² , Alicia Yurquina ³ , Fleming Martínez ¹ *

¹ Grupo de Investigaciones Farmacéutico-Fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de Colombia, A. A. 14490, Bogotá D. C., Colombia. *Corresponding author e-mail: fmartinezr@unal.edu.co
² Departamento de Química Farmacéutica, Facultad de Ciencias Naturales, Universidad ICESI, Santiago de Cali, Colombia.
³ Instituto de Química Inorgánica, Facultad de Bioquímica, Química y Farmacia, Universidad Nacional de Tucumán, San Miguel de Tucumán, Argentina.

Recibido para evaluación: March 31, 2010 Aceptado para publicación: May 17, 2010

RESUMEN

Key words: Binary mixtures, Extended Hildebrand Solubility Approach, Indomethacin, Solubility parameter.

RESUMEN

La indometacina (IMC) es un analgésico cuyas propiedades fisicoquímicas aún no han sido totalmente estudiadas. En la presente investigación, se aplicó el Método Extendido de Solubilidad de Hildebrand (MESH) al estudio de la solubilidad de la IMC en mezclas binarias etanol + agua a 298,15 K. Se obtuvo una capacidad predictiva aceptable del MESH (desviación general inferior al 4,1%) al utilizar un modelo polinómico regular de cuarto orden relacionando el parámetro de interacción W con el parámetro de solubilidad de las mezclas solventes. De esta forma, las desviaciones obtenidas en la solubilidad estimada, fueron de magnitud inferior a las obtenidas al calcular esta propiedad directamente, utilizando una regresión empírica regular del mismo orden, de la solubilidad experimental del fármaco en función del parámetro de solubilidad de las mezclas disolventes.

Palabras clave: Indometacina, Método Extendido de Solubilidad de Hildebrand, Mezclas binarias, Parámetro de solubilidad.

INTRODUCTION

Indomethacin (IMC, Fig. 1) is a non-steroidal anti-inflammatory drug used as analgesic and antipyretic, among other indications (1, 2). In the Colombian market this drug is available as capsules, oil ophthalmic drops, and injectable powder for reconstitution intended to intramuscular administration, but it is not available as any homogeneous liquid dosage form (3). Although IMC is used in therapeutics, the physicochemical information about its solubility is not abundant. On this way, it is well known that several physicochemical properties such as, the solubility of active ingredients and excipients close to the respective occupied volumes in useful solutions, are very important for the pharmaceutical scientist, because they facilitate the processes associate to design and development of new products in the pharmaceutical industries (4). In view of the facts, there is considerable scope for the study the behavior of IMC in hydroalcoholic solutions. Taking into account that IMC is practically insoluble in water by the low polarity in comparison with that, the hydroalcoholic solution reduces the polarity of the medium and is expected then an increase of IMC solubility.

THEORETICAL

The ideal solubility ( X^id₂ ) of a solid solute in a liquid solution is calculated adequately by means of the expression,

where, ΔH ^fus is the fusion enthalpy of the solute, R is the universal gas constant (8.314 J mol ^-1 K ^-1 ), T ^fus is the melting point of the solute, and T is the absolute temperature of the solution. On the other hand, the real solubility (X ₂ ) is calculated by adding the non-ideality term, (log γ ₂ ), to equation 1 (16, 17), in order to obtain the following expression,

where, V ₂ is the partial molar volume of the solute (cm ³ mol ^-1 ),Φ ₁ is the volume fraction of the solvent in the saturated solution, and δ ₁ and δ₂ are the solubility parameters of solvent and solute, respectively. The solubility parameter,δ , is calculated as ((ΔH_v-RT)/V₁)^1/2 , where, ΔH _v is the vaporization enthalpy and V _l is the molar volume of the liquid.

The vast majority of pharmaceutical dissolutions deviate notoriously of that predicted by the regular solutions theory (because of the strong interactions present, such as hydrogen bonding, in addition to the differences in molar volumes among solutes and solvents). On this way, at the beginning of the 80s of the past century, Martin et al. developed the EHSA method, which has been useful to estimate the solubility of several drugs in binary and ternary cosolvent systems (5-7). Accordingly, if the A term (defined as V₂Φ²₁/(2.303 RT)) is introduced in the equation 3, the real solubility of drugs and other compounds in any solvent can be calculated from the expression,

where, the W term is equal to 2Kδ ₁δ ₂ (where, K is the Walker parameter, Ref. 16). The W factor compensates the deviations observed with respect to the behavior of regular solutions, and it can be calculated from experimental data by means of the following expression,

where, γ ₂ is the activity coefficient of the solute in the saturated solution, and it is calculated as the quotient, X^id₂/X₂

The experimental values obtained for the W parameter can be correlated by means of regression analysis by using regular polynomials in superior order as a function of the solubility parameter of the solvent mixtures, as follows,

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These empiric models can be used to estimate the drug solubility by means of back calculation resolving this property from the specific W value obtained in the respective polynomial regression.

EXPERIMENTAL

Reagents

Indomethacin [1-(4-Chlorobenzoyl)-5-methoxy-2-methyl-1H-indole-3-acetic acid, CAS: 53-86-1] used was in agreement with the quality requirements indicated in the British Pharmacopoeia, BP (19). In similar way, absolute ethanol A.R. Merck (EtOH), distilled water with conductivity < 2 mS cm ^-1 , and Millipore Corp. Swinnex®-13 filter units, were also used.

Solvent mixtures preparation

The dehydrated ethanol employed was maintained over molecular sieve (Merck Number 3, 0.3 nm in pore diameter) to obtain a dry solvent previously to prepare the solvent mixtures. The ethanol dryness was demonstrated by the respective density value obtained (0.7854 g cm ^-3 at 298.15 K), which was thus coincident with those reported in the literature (20, 21). All EtOH + water solvent mixtures were prepared in quantities of 50.00 g by mass using an Ohaus Pioneer TM PA214 analytical balance with sensitivity ± 0.1 mg, in mass fractions from 0.10 to 0.90 varying by 0.10, in order to study nine mixtures and both pure solvents.

Solubility determination

An excess of IMC was added to each cosolvent mixture evaluated in stoppered dark glass flasks. Solid-liquid mixtures were placed on a thermostatic bath (Neslab RTE 10 Digital One Thermo Electron Company) kept at 298.15 ± 0.05 K with sporadic stirring for at least seven days to reach the saturation equilibrium (this equilibrium time was established by quantifying the IMC concentration up to obtain a constant value). In the case of neat water or water-rich mixtures the equilibration time was 14 days. Once at equilibrium, supernatant solutions were filtered (at isothermal conditions) to remove insoluble particles before composition analysis. IMC concentrations in neat EtOH and the EtOH + W mixtures up to 0.40 in mass fraction of water were determined by mass balance by weighing a specified quantity of the respective saturated solutions and allowing the solvent evaporation up to constant masses. In the other hand, IMC concentrations in all the other systems studied (from 0.50 in mass fraction of water to pure water) were determined by measuring UV-absorbance after appropriate gravimetric dilutions with ethanol and interpolation from a previously constructed UV spectrophotometric calibration curve (UV/VIS BioMate 3 Thermo Electron Company spectrophotometer). In order to make the equivalence between volumetric and gravimetric concentration scales, the density of the saturated solutions was determined with a digital density meter (DMA 45 Anton Paar) connected to the same recirculating thermostatic bath.

Estimation of the volumetric contributions

where, m ₂ and m ₁ are the masses of solute and solvent in the saturated solution, respec- tively, VE ₁ is the specific volume of the solvent, and Ρ _soln is the solution density. The IMC apparent molar volume is calculated by multiplying the Φ_V ^spc value and the molar mass of the solute (357.8 g mol ^-1 , Ref. 1). Otherwise, the calculated molar volume value obtained by means of the Fedors method was used in the later calculations and it was taken from the literature (230.0 cm ³ mol ^-1 , Ref. 15).

RESULTS AND DISCUSSION

The information about polarity and volumetric behavior of EtOH + water mixtures as a function of the composition is shown in Table 1 and it was taken from the literature (13, 14, 23). It is important to note that the solubility parameter values of the solvent medium are in good agreement with those obtained from experimental permittivity data (24), which were thus calculated by using the Paruta equation (25). On the other hand, the calorimetric values reported in the literature for IMC were as follows, T _fus = 432.6 K and ΔH _fus = 39.46 kJ mol ^-1 . (26). From these values the calculated ideal solubility for this drug was 7.123 x 10 ^-3 in mole fraction (15).

Table 1 also summarizes the IMC solubility expressed in molarity and mole fraction, the density of the saturated mixtures, the apparent molar volume of IMC, and the sol- vent volume fraction in the saturated solutions at 298.15 K. Figure 2 shows the experimental solubility and the calculated solubility by using the regular solution model (Equation 3) as a function of the solubility parameter of solvent mixtures.

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The IMC solubility is greater in EtOH but this value is lower than the obtained in the mixture of 0.6720 in volume fraction of ethyl acetate in mixtures conformed by ethyl acetate + EtOH (whose mixture has δ ₁ = 20.86 MPa ^1/2 )(15).

From density values of cosolvent mixtures (23) and saturated solutions (Table 1), in addition to IMC solubility (Table 1), the solvent volume fraction (Φ ₁ ) and apparent molar volume of the solute (Φ_V ^mol) in the saturated mixtures, were calculated. These values are also presented in Table 1.

In the literature (16, 17), the solute molar volume in the saturated solution has been considered as a constant value when EHSA method is used. On this way, for solid compounds this property is generally calculated by means of groups´ contribution methods such as developed by Fedors (27). Nevertheless, this property is not independent on the solvent composition as can be see in Table 1 for apparent molar volume of IMC. This fact would be due to the different intermolecular interactions, depending on the respective solvent proportions. Nevertheless, the experimental values are variable and unclear, in particular for water-rich mixtures, where negative values were obtained. For this reason, in this investigation the calculated molar volume (230.0 cm ³ mol ^-1 , Ref. 15) was employed in the following calculations.

On the other hand, according to the literature (16, 17), the volume fraction of the solvent mixture in the saturated solution has been calculated by means of the expression, where, V 1 is the molar volume of the solvent (calculated for solvent mixtures as V _{V mix} = ΣV_1iφ_i, assuming additive volumes). Nevertheless, it is well known that the mixing volumes are not additives in those mixtures with strong presence of hydrogen bonding and great differences in molar volumes among their components. For this reason, the experimental volume fractions were used in this investigation for all the calculations involved (Table 1).

Ultimately, the activity coefficients of IMC as decimal logarithms are also presented in Table 1. These values were calculated from experimental solubility values (Table 1) and ideal solubility at 298.15 K (X ₂ = 7.123 x 10 ^-3 ). In all cases, γ ₂ values were greater than unit because the experimental solubilities are lower than the ideal one. On the other hand, the parameters A, K, and W are presented in Table 2. In order to calculate the W parameter the experimental solubility parameter of IMC obtained in ethyl acetate + ethanol mixtures (20.86 MPa ^1/2 ) was used. This δ ₂ value is the same of the solvent mixture where the greatest drug solubility was found (15).

According to Table 5 it follows that, as more complex the polynomial used is, better the agreement found between experimental and calculated solubility is. This fact is confirmed based on the mean deviation percentages (4.1 % and 4.2 %, for orders 4 and 5, respectively). In similar way to that found in other similar investigations (4-11), in this case, the most important increment in concordance is obtained passing from order 1 to order 2 (from 67871 to 35.2 % as mean value), although significant increment is also obtained form order 2 to order 3 (from 35.2 to 6.1% as mean value). Thereby, in the following calculations the model with lowest general deviation was used (order 4, Table 3).

Based on mean deviation percentages presented in Table 6 (4.1% and 4.1% for direct calculation and EHSA method, respectively) it follows that non-significant differences are found between the values obtained by using both methods. In similar way with that found for naproxen and ketoprofen (other analgesic drugs) in the same cosolvent system (13, 14), and for IMC in ethyl acetate + ethanol mixtures (15), the present results would be showing non-significant usefulness of EHSA method for practical purposes. The last point exposed would be a big controversial subject considering that EHSA method implies additional experimentation including density determinations and thermal characterization of the solid-liquid equilibrium for the solid compound. Nevertheless, it is necessary keep in mind that EHSA method considers the drug solubility from a systematic physicochemical point of view. Moreover, it is just necessary to found an effective method to calculate the Walker K parameter in order to calculate the W term according to the expression 2Kδ₁δ₂ , because the δ₁ and δ₂ terms would be known, and thus, the drug experimental solubility could be calculated in any mixture in particular.Table 5 summarizes the solubility values obtained by using the W values obtained by back-calculation from the polynomial models presented in Table 4. Because we are searching the best adjust, the first criterion used to define the polynomial order of W as function of δ ₁ was the fitting standard uncertainties obtained, whose values were as follows, 22.0, 1.23, 0.247, 0.208, and 0.208 (Table 3), for orders one to five, respectively. As another comparison criterion, Table 5 also summarizes the percentages of difference between IMC experimental solubility and those calculated by using EHSA.

CONCLUSION

In this investigation the EHSA method has been adequately used to study the solubility of IMC in EtOH + water mixtures by using experimental values of molar volume and Hildebrand solubility parameter of this analgesic drug. In particular, a good predictive character has been found by using a regular polynomial in order four of the interaction parameter W as a function of the solubility parameter of solvent mixtures free of solute. Form a practical viewpoint EtOH + water binary mixtures were thus constituted in good cosolvent systems for IMC, especially at higher fractions of alcohol, by generate a decrease on polarity of the medium.

ACKNOWLEDGEMENTS

The authors thank to the Department of Pharmacy of the Universidad Nacional de Colombia for facilitating the equipments and installations used in this investigation.

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