Edgar A. Ahumada¹, Daniel R. Delgado¹, Fleming Martínez^1*

¹Group of pharmaceutical-physicochemical research, Department of Pharmacy, Universidad Nacional de Colombia,PO Box 14490, Bogotá, D. C., Colombia.

^*Correspondence concerning this paper should be addressed to Fleming Martínez, Department of Pharmacy, Universidad Nacional de Colombia. fmartinezr@unal.edu.co

Recibido: 20/08/12 – Aceptado: 27/11/12

Abstract

The Extended Hildebrand Solubility Approach(EHSA) was applied in the present work to evaluate the solubility of the analgesic drug acetaminophen (paracetamol) in polyethylene glycol 400 + water mixtures at 298.15 K. An acceptable correlative capacity of EHSA was found using a regular polynomial model in order four (overall deviation below 0.7%), when the W interaction parameter is related to the solubility parameter of the mixtures. Thus, the deviations obtained in the estimated solubility with respect to experimental solubility were lower than those obtained directly by means of an empiric regression of the experimental solubility as a function of the mixtures´ solubility parameters (close to 1.5%).

Key words: acetaminophen, binary mixtures, extended Hildebrand solubility approach, solubility parameter.

Resumen

En el presente trabajo se aplicó el Método Extendido de Solubilidad de Hildebrand (MESH) al estudio de la solubilidad del acetaminofeno en mezclas binarias polietilenglicol 400 + agua a 298,15 K. Se obtuvo una capacidad predictiva aceptable del MESH (desviación general inferior al 0,7%) al utilizar un modelo polinómico regular de cuarto orden que relaciona el parámetro de interacción W con el parámetro de solubilidad de las mezclas solventes. Las desviaciones obtenidas en la solubilidad estimada fueron de menor magnitud que 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 (cerca del 1.5%).

Palabras clave: acetaminofeno, Método Extendido de Solubilidad de Hildebrand, mezclas binarias, parámetro de solubilidad.

Resumo

O método estendido de solubilidade de Hildebrand (MESH) foi aplicado nesta pesquisa para avaliar a solubilidade do paracetamol em água de misturas binárias + polietileno glicol 400 em 298,15 K. Obteve-se boa capacidade preditiva com o MESH (desvio inferior a 0,7%) quando se utiliza um polinômio regular de quarta ordem do parâmetro de interação W com o parâmetro de solubilidade das misturas de solventes. Os desvios obtidos na solubilidade estimada foram inferiores do que os obtidos através do cálculo desta propriedade diretamente, utilizando uma regressão normal empírica da mesma ordem da solubilidade experimental da droga em função do parâmetro de solubilidade das misturas solventes (cerca de 1,5 %).

Palavras-chave: acetaminofeno, Método estendido de solubilidade de Hildebrand, misturas binárias, parâmetro de solubilidade.

INTRODUCTION

Acetaminophen (ACP, Figure 1) is a drug widely used as analgesic and antipyretic which physicochemical properties have not yet been studied throroughly (1). In particular, its solubility in aqueous media is very important in several processes associated to research and development during the design of homogeneous liquid dosage forms intended mainly for pediatric patients (2). It is important to note that cosolvency is the best technique used in pharmacy to increase drug solubility (3). On the other hand, it is clear that predictive methods of physicochemical properties of drugs, in particular its solubility, are very important for industrial pharmacists because they allow the optimization of design processes (4).

For this reason, the present work presents a physicochemical study about the solubility prediction of ACP in binary mixtures conformed by polyethylene glycol 400 (PEG) and water. The study was made based on the Extended Hildebrand Solubility Approach (EHSA) (5). Thus, this work is a continuation of previous research on acetaminophen in ethanol + water (6), propylene glycol + water (7), and ethanol + propylene glycol (8) mixtures. It is important to take into consideration that the EHSA method has been widely used to study the solubility of a lot of pharmaceutical compounds (9-27). On the other hand, PEG is after ethanol and propylene glycol the most used cosolvent to develop liquid pharmaceutical dosage forms (28). Moreover, PEG is also employed to regulate product evaporation (29).

THEORETICAL

The real solubility (X2) of a solid solute in a liquid solution is calculated adequately by means of the expression:

[1]

where, ΔH_fus is the fusion enthalpy of the solute, R is the gas constant, T_fus is the melting point of the solute, T is the absolute temperature of the solution, log Υ₂ is the non-ideality term. The Υ₂ term is the activity coefficient of the solute and it is determined experimentally. One method of calculating γ2 is the referent to regular solutions obtained from

[2]

where V₂ is the partial molar volume of the solute, ø₁ is the volume fraction of the solvent in the saturated solution, and δ1 and δ2 are the solubility parameters of solvent and solute, respectively. Pharmaceutical dissolutions deviate from predicted by the regular solutions theory. In this respect, Martin et al. developed the EHSA method (9-15). If the A term (defined as V₂ø/²₁(2.303RT ) is introduced in the Eq. [2], the real solubility of drugs can be calculated from the expression

[3]

where the W term is equal to 2Kδ1δ2 (where, 2Kδ₁δ₂ is the Walker parameter). The W factor can be calculated from experimental data by means of

[4]

where Υ₂ is the activity coefficient of the solute in the saturated solution, and it is calculated as X^id₂/ X₂ . The experimental values of the W parameter can be correlated by means of regression analysis by using regular polynomials as a function of δ1, as follows

[5]

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 and materials

Acetaminophen (Paracetamol, N-Acetyl- p-aminophenol, CAS RN: 103-90-2) was in agreement with the quality requirements of the American Pharmacopeia, USP (30). Polyethylene glycol 400 from DOW Chemicals (PEG), distilled water with conductivity < 2 mS cm^–1, and filter units from Millipore Corp. Swinnex®-13 were also used.

Solvent mixtures preparation

The PEG employed was maintained over molecular sieve (Merck Number 3, 0.3 nm in pore diameter) to obtain a dry solvent prior to preparing the solvent mixtures. All PEG + water solvent mixtures were prepared in quantities of 50.00 g by mass using an Ohaus Pioneer TM PA214 analytical balance, in mass fractions from 0.10 to 0.90 varying by 0.10.

Solubility determination

An excess of ACP was added to each mixed solvent 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 K for at least 7 days to reach the saturation equilibrium. Once at equilibrium, supernatant solutions were filtered before analysis. ACP concentrations were determined by measuring UV-absorbance after appropriate gravimetric dilutions with water and interpolation from a previously constructed UV spectrophotometric calibration curve (UV/VIS BioMate 3 Thermo Electron Company spectrophotometer). Density of the saturated solutions was determined with a digital density meter (DMA 45 Anton Paar) according to the procedure described in the literature (31).

Estimation of the volumetric contributions

Apparent specific volumes ( φ_V^spc ) of the drug were calculated according to Eq. [6], where, m₂ and m₁ are the masses of solute and solvent in the saturated solution, respectively, VE₁ is the specific volume of the solvent, and ρ_soln is the solution density (2).

[6]

The ACP apparent molar volume is calculated by multiplying the ø_V φ^spc value and the molar mass of the solute.

RESULTS AND DISCUSSION

The information about polarity and volumetric behavior of PEG + water mixtures, as a function of the composition, is shown in Table 1. On the other hand, the reported ideal solubility for this drug is 2.602 ×10^–2 in mole fraction (32). Table 1 also summarizes the ACP solubility expressed in molarity and mole fraction, the density of the solvent and saturated mixtures, the apparent molar volume of ACP, and the solvent 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 as a function of the solubility parameter of solvent mixtures.

From density values of cosolvent mixtures and saturated solutions, in addition to ACP solubility, the solvent volume fraction (ø₁) and apparent molar volume of the solute (ø_V^mol) of the drug in the saturated mixtures, were calculated. These values are also presented in Table 1.

Ultimately, the activity coefficients of ACP as decimal logarithms are also presented in Table 1. These values were calculated from experimental solubility val ues and ideal solubility at 298.15 K (X₂ = 2.602 × 10^–2). In water rich mixtures, Υ₂ values were greater than unit because the experimental solubilities are lower than the ideal value but in PEG rich mixtures these values were below one.

In order to calculate the W parameter, the solubility parameter of ACP (δ₂) is required and for this reason it was calculated by using Fedors and Van Krevelen methods as showed in Table 2 (34) obtaining the value 27.3 MPa^1/2 which is similar to that obtained experimentally in ethanol + water and ethanol (6) + propylene glycol mixtures (8), i.e. 28.0 MPa^1/2. In the next calculations the experimental value was used. It is interesting that PEG, where the maximum drug solubility is obtained, has a lower δ value (23.1 MPa^1/2) compared to ACP. This result demonstrates that the maximum solubility is not always obtained in mixtures where the solubility parameters of drug and solvent are coincident.

Table3 summarizes the parameters A, K, and W for ACP in PEG + water mixtures. Figure 3 shows that the variation of the W parameter with respect to the solubility parameter of solvent mixtures, presents deviation from linear behavior.

W values were adjusted to regular polynomials in orders from 1 to 5 (Eq.5). Table 4 summarizes the coefficients obtained in all the regular polynomials from degrees one to five, whereas the W values back-calculated by using the respective polynomials are presented in Table 5. It is clear that these values depend on the model used in the W back-calculation. Similar behaviors have been reported in the literature for this drug and for several other compounds in different solvent mixtures (6-27).

Table 6 summarizes the solubility values obtained by using the W values obtained by back-calculation from the polynomial models (Table 4) which are presented in Table 5. In the same way it was made previously (6-27) and because the best adjustment is being searched, the first criterion used to define the polynomial order of W term as function of δ1 was the fitting standard uncertainties obtained, which values were as follows, 30.4, 0.420, 0.282, 0.074, and 0.066 (Table 4), for orders one to five, respectively. As another comparison criterion, Table 6 also summarizes the percentages of difference between ACP experimental solubility and those calculated by using EHSA.

It was found that the more complex the polynomial used, the better the agreement found between experimental and calculated solubility. The most important increment in concordance is obtained when going from order 1 to order 2 (From 2925 to 4.13%). It is important to note that for pharmaceutical purposes an uncertainty below 5% is useful for practical purposes but for academic purposes a better agreement is required. In this way, the best improvement is obtained going from 3rd to 4th degree, i.e. from 3.27 to 0.69%. Thereby, in the following calculations the model in order 4 was used, just as has been made earlier on (26, 27). Nevertheless, it is interesting that the mean deviation using a polynomial of order 5 (0.49%, Table 6) is almost the same obtained as mean in the experimental uncertainties obtained (0.50%, Table 1)

As it has been described previously,an important consideration about the usefulness of the EHSA method is that which refers to justifying the complex calculations involving any other variables, instead of the simple empiric regression of the experimental solubility as a function of the solvent mixtures´ solubility parameters (Table 1, Figure 4). For this reason, in the Table 7 the experimental solubilities are confronted to those calculated directly by using a regular polynomial in order 4 of log X₂ as a function of δ1 values (Equation [7],with adjusted determination coefficient r² = 0.9998 and fitting standard uncertainty = 0.0111) and also to those calculated involving the W parameters obtained from Eq. [5] adjusted to order 4 (Tables 4 and 5). The respective difference percentages are also presented in Table 7.

[7]

Based on mean deviation percentages presented in Table 6(1.54% and 0.69% for direct calculation and EHSA method, respectively) it follows that a slight difference is found between the values obtained by using both methods. As it has happened for several drugs, the present the EHSA method for practical and academic purposes, in particular, if differences below 1% are required.

On the other hand, it is very interesting that this drug mainly exhibits posi tive deviations with respect to the ideal log-linear additive model proposed by Yalkowsky and Roseman (dotted line in Figure 4) (3). This behavior is different compared to those observed by Rubino and Obeng (35) who found negative deviations in water-rich mixtures and positive deviations in propylene glycol-rich mixtures by studying the solubility of homologous series of some alkyl p-hydroxybenzoates and p-aminobenzoates. It is also different compared to those reported for ibuprofen, naproxen, ketoprofen, and indomethacin in the similar cosolvent mixtures (36-40) where negative and positive deviations were also found in water-rich and cosolvent-rich mixtures, respectively. The results for ACP in PEG mixtures could be attributed to a better solvation of the drug by the cosolvent molecules by means of hydrogen bonding where the phenolic hydroxyl group of ACP would be interacting with the ether groups of PEG.

CONCLUSION

The EHSA method has been adequately used in the present work to study the solubility of acetaminophen in PEG + 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. In this way, the predictive character of EHSA is better than that obtained by direct correlation between solubility and mixtures composition.

ACKNOWLEDGEMENTS

The authors wish to thank the Department of Pharmacy of the Universidad Nacional de Colombia for facilitating the use of equipment and facilities used in this research work.

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