THERMODYNAMICS OF THE MIXING PROCESS OF SEVERAL SODIUM SULFONAMIDES IN ETHANOL + WATER COSOLVENT MIXTURES

ESTUDIO TERMODINÁMICO DEL PROCESO DE MEZCLA DE ALGUNAS SULFONAMIDAS SÓDICAS EN MEZCLAS COSOLVENTES ETANOL + AGUA

Daniel R. DELGADO¹; Edgar F. VARGAS²; Fleming MARTÍNEZ³

1 Grupo de Investigaciones Farmacéutico-Fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de Colombia, A.A. 14490, Bogotá D.C., Colombia.

2 Laboratorio de Termodinámica de Soluciones, Departamento de Química, Facultad de Ciencias, Universidad de los Andes, Bogotá D.C., Colombia.

Received: 25 January 2011; Accepted: 29 April 2011

ABSTRACT

Sodium sulfonamides have been extensively used for the treatment of certain infections caused by several types of microorganisms. Although sulfonamides are still widely used in therapeutics, the physicochemical information about their aqueous solutions has not been completed. In this context, the thermodynamic functions of mixing three structurally related sodium sulfonamides were evaluated: Gibbs energy, enthalpy, and entropy. The quantities of mixing were calculated based on the fusion calorimetric values obtained from differential scanning calorimetry measurements and equilibrium solubility values reported in the literature for all the drugs with ethanol + water mixtures. By means of an enthalpy-entropy compensation analysis, non-linear ΔH⁰_mix vs. ΔG⁰_mix plots with negative slopes from neat ethanol to a 0.60 ethanol mass fraction, and positive slopes from the latter composition to neat water were obtained. From these results, it was concluded that the dissolution process of these drugs in ethanol-rich mixtures was entropy-driven; whereas, in water-rich mixtures the process was enthalpy-driven. Nevertheless, the molecular and ionic events involved in the dissolution of these drugs in this cosolvent system remain unclear.

Keywords: Sodium sulfonamides, mixing process, cosolvency, ethanol, solution thermodynamics.

RESUMEN

Las sulfonamidas sódicas han sido ampliamente utilizadas en el tratamiento de ciertas infecciones causadas por diferentes microorganismos. Si bien las sulfonamidas siguen siendo ampliamente usadas en la terapéutica actual, la información fisicoquímica de sus soluciones acuosas aún no es completa. En este contexto, estudiamos aquí las funciones termodinámicas de mezcla de tres sulfonamidas sódicas relacionadas estructuralmente y que fueron calculadas a partir de las propiedades calorimétricas de fusión y de los valores de solubilidad en equilibrio en mezclas etanol + agua publicados en la literatura. Mediante análisis de compensación entálpica-entrópica se obtuvieron gráficos no lineales de ΔH⁰_mix vs. ΔG⁰_mix exhibiendo pendientes negativas desde el etanol puro hasta la mezcla cosolvente de 0,60 en fracción másica de etanol y pendientes positivas desde esta mezcla hasta el agua pura; de acuerdo a este resultado se tiene que el proceso de disolución de estos fármacos en mezclas ricas en etanol es conducido entrópicamente, mientras que en mezclas ricas en agua el proceso es conducido entálpicamente. Sin embargo, los eventos moleculares e iónicos involucrados en el proceso de disolución de este fármaco en este sistema cosolventes aún no son claros.

Palabras clave: sulfonamidas sódicas, proceso de mezcla, cosolvencia, etanol, termodinámica de soluciones.

INTRODUCTION

Sodium sulfonamides (Sulfadiazine: Na-SD, Sulfamerazine: Na-SMR, and Sulfamethazine: Na-SMT, which molecular structures are presented in figure 1) are drugs extensively used for the treatment of certain infections caused by several types of microorganisms (1). Although these drugs are widely used nowadays in therapeutics, the physicochemical information about their aqueous solutions is not complete at present, even though several physicochemical studies have been done. Thus, the solution thermodynamics in aqueous media for these drugs (as dissociate and non-dissociate compounds) has been presented in the literature (2, 3). Moreover, the transfer physicochemical aspects of these drugs (as non-dissociate compound) from aqueous media up to octanol and some phospholipidic vesicles have also been reported (4). In addition, the apparent molar volumes in water and ethanol have also been studied as a function of drug concentration at 298.15 K (2, 5). Finally, the solubility in ethanol + water cosolvent mixtures has been studied as a function of cosolvent composition and temperature, and the results have been correlated by means of the Jouyban-Acree solubility model (6). Similarly, the thermodynamic quantities of the Na-SD solution were reported in the literature (7).

As it has been already described, the solubility behavior of drugs in cosolvent mixtures is very important because cosolvent blends are frequently used in purification methods, preformulation studies, and pharmaceutical dosage forms designs, among other applications (8). For these reasons, it is important to systematically determine and collect data about the equilibrium solubility of pharmaceutical compounds. It is also particularly important because it is not possible yet to predict the solubility of drugs in water, organic solvents and/or mixed solvent systems with an acceptable margin of error in the prediction (9). Moreover, temperature-solubility dependence allows us to carry out the respective thermodynamic analysis, which, on the other hand, also permits inside the molecular mechanisms, involved toward the solution processes (10).

In this context, the main objective of this research is to evaluate the effect of the cosolvent composition on the thermodynamics of mixing of Na-SD, Na-SMR and Na-SMT in some ethanol (EtOH) + water cosolvent mixtures. This study is based on both the calorimetric properties of fusion obtained by differential scanning calorimetry (DSC), and the van't Hoff treatment of equilibrium solubility values reported in the literature (6, 7).

MATERIALS AND METHODS

All the sodium sulfonamides (Na-SD: 4-Amino- N-2-pyrimidinylbenzenesulfonamide sodium salt, CAS: [547-32-0]; Na-SMR: 4-Amino-N-(4- methyl-2-pyrimidinyl)benzenesulfonamide sodium salt, CAS: [127-58-2]; and Na-SMT: 4-Amino-N- (4,6-dimethyl-2-pyrimidinyl)benzenesulfonamide sodium salt, CAS: [1981-58-4] (11)) used were in agreement with the quality requirements indicated in the American Pharmacopeia, USP (12), as well as in the British Pharmacopoeia, BP (13).

Calorimetric study

Melting point and enthalpy of fusion of three sodium sulfonamides were determined through entrópicamente, mientras que en mezclas ricas en agua el proceso es conducido entálpicamente. Sin embargo, los eventos moleculares e iónicos involucrados en el proceso de disolución de este fármaco en este sistema cosolventes aún no son claros. Palabras clave: sulfonamidas sódicas, proceso de mezcla, cosolvencia, etanol, termodinámica de soluciones. DSC studies (DSC 823E Mettler Toledo). Thermal analyses were performed at a heating rate of 10 K min^–1 in a dynamic nitrogen atmosphere (60 mL min^–1). Approximately 1.5 mg of drugs were used. The equipment was calibrated using Indium as a standard (14).

RESULTS AND DISCUSSION

Before presenting the results, it is important to consider that these drugs (in similar way to procaine hydrochloride and sodium naproxen) have an electrolyte behavior (15, 16). Therefore, such drugs dissociate in aqueous solution, interacting with the cosolvent mixture by strong ion-dipole interactions, as well as by other weak non covalent interactions due to their nonpolar groups. Thus, they also could act as a Lewis acid (–NH₂ group) or as a Lewis base (–NH₂ and –SO₂– groups), in order to establish hydrogen bonds with proton-acceptor or donor functional groups in the solvents (–OH groups) (17, 18).

Ideal solubility of sodium sulfonamides

The ideal solubility of non-electrolyte crystalline solutes in a liquid solvent can be calculated by means of equation 1:

In this context, tables 1 and 2 summarize the thermodynamic properties of fusion and the ideal solubilities of the three sodium sulfonamides, respectively. At the same temperature, x^id₂ diminishes in the following order: Na–SMR > Na–SD > Na–SMR; whereas for the respective molecular drugs it diminishes in the following order: SMT > SMR > SD (3). In the case of sulfamethazine, the ideal solubilities are similar for the sodium salt and the molecular form (1.068 x 10^–2 and 1.051 x 10^–2 for Na–SMT, and molecular SMT at 298.15 K, respectively). Now, in the case of sulfadiazine, the ideal solubilities are also similar but slightly greater for sodium salt (4.03 x 10^–3 and 3.03 x 10^–3 for Na–SD and molecular SD at 298.15 K, respectively). Finally, in the case of sulfamerazine, the ideal solubilities are greater for the molecular form in comparison to sodium salt (2.458 x 10^–3 and 5.46 x 10^–3 for Na–SMR and SMR at 298.15 K, respectively).

Moreover, the experimental equilibrium solubility values for these drugs have been reported in the literature (6).

Thermodynamic quantities of sodium sulfonamide solution

Due to the fact that the drugs considered in this study are electrolyte compounds, it is important to keep in mind that in general terms, it could be stated that a strong electrolyte dissociates according to the following expression: C_v+A_v- --> v₊C^z+ + v_-A^z-, where v₊ is the number of cations (C^z+) of valence 195 z⁺, and v_– is the number of anions (A^z–) of valence z^–., The concept of mean ionic activity (a^v_±) is used because is not possible to determine experimentally the activity of ions separately. Thus, the thermodynamic activity for an electrolyte can be defined as follows: a₂ = a₊^v+ a_-^v- = a_±^v (23-25).

Therefore, according to van't Hoff's analysis, the apparent standard enthalpy change of solution (ΔH⁰_soln) for electrolytes type one-one (such as the sodium sulfonamides studied here), is obtained using the mean harmonic temperature (T_hm is 292.8 K in our case) according to equation 2 (7, 15, 16), that is if the inter-ionic interactions are not considered.

where, R is the universal gas constant (8.314 J mol^–1 K^–1). In all the studied cases, linear models with good determination coefficients were obtained.

The apparent standard Gibbs energy change for the solution process (ΔG⁰_soln) of electrolytes type one-one was calculated at the mean harmonic temperature by means of equation 3, considering the approach proposed by Krug et al., 1976 (26).

in which, the intercept used was the one obtained in the analysis taking ln x_Na-Sulf as a function of 1 /T – 1/T_hm. Finally, the apparent standard entropic change for the solution process (ΔS⁰_soln) was obtained from the respective ΔH⁰_soln and ΔG⁰_soln values by means of the following equation:

Table 3 summarizes the apparent standard thermodynamic functions for the experimental solution process of sodium sulfonamides in all EtOH + water cosolvent mixtures. In order to calculate the thermodynamic quantities for the experimental solution processes, some uncertainty propagation methods were used (27). As it was expected, it was found that the standard Gibbs energy of the solution is positive in all cases because the mole fraction is always lower than the unit; thus its logarithmic term is negative, therefore, the standard Gibbs energy will be a positive quantity.

The apparent enthalpy of solution is positive in all cases, therefore, the process is always endothermic. Similarly, the entropy of solution is also positive for Na-SMT in all solvent systems and Na- SMR in compositions from neat water to 0.80 in a mass fraction of EtOH. Oppositely, this quantity is negative for Na-SD in all solvent systems and Na-SMR in the mixture of 0.90 in mass fraction of EtOH and neat EtOH. These results do not show enthalpy or entropy-driving overall in the solution process for the last indicated systems. For all sodium sulfonamides, ΔH⁰_soln values increase from neat water to 0.60 in mass fraction of EtOH, and decrease from this EtOH proportion to neat EtOH. In contrast with enthalpy, ΔS⁰_soln values increase from neat water to the mixtures of 0.30, 0.40 and 0.50 in mass fraction of EtOH for Na-SD, Na-SMR and Na-SMT respectively, despite the sign obtained and diminishing beyond this composition to neat EtOH. The apparent enthalpic and entropic values obtained for the dissolution process of Na-SD in neat water are in good agreement regarding those reported in the literature (11.0 ± 0.6 kJ mol^–1 and ^–13.5 ± 0.7 J mol^–1 K^–1, respectively) (2). However, the same quantities for Na-SMT are not in agreement with those reported in the same research (10.9 ± 0.6 kJ mol^–1 and ^–19.7 ± 1.0 J mol^–1 K^–1, respectively) (2). That is why, it is important to note that the studied temperature intervals and the used analytical techniques were significantly different in both investigations.

From the ζ_H and ζ_TS values shown in table 3, it was concluded that the main contributor of the standard Gibbs energy of the solution process of SD-Na is enthalpy, except for Na-SD in the following cosolvent composition interval: 0.80 ≤ μ_EtOH ≤ 1.00. This result evidences the relevance of the energetic factor on the dissolution processes of these drugs.

Thermodynamic quantities of the sodium sulfonamide mixture

The solution process can be represented by the following hypothetical stages (10):

where, the respective partial processes regarding the solution are solute fusion and mixing at the same temperature (292.8 K), which allows calculating the partial thermodynamic contributions to the overall solution process by means of equations 7 and 8, respectively.

where, ΔH^292.8_fus and ΔS^292.8_fus represent the thermodynamic functions of the fusion process at the harmonic temperature (292.8 K). ΔH^292.8_fuswas calculated by means of the following equation:ΔH^T_fus = ΔH^MP_fus - ΔC_p(T_fus - T), using ΔS^MP_fus instead of ΔC_p, for obtaining the values of 17.16, 18.98 and 16.49 kJ mol^–1 for Na-SD, Na-SMR, and Na- SMT, respectively. These values coincide with the enthalpic changes for the ideal solution processes, as it is shown in table 3. In contrast, the entropies of fusion at 292.8 K (58.6, 64.8, and 56.3 J mol^–1 K^–1 for Na-SD, Na-SMR, and Na-SMT, respectively) do not coincide with the entropic changes of the ideal solution processes at this temperature, as it is also shown in table 3. For this reason and for practical purposes, ΔS^0id_soln values were used instead of ΔS^292.8_fus, as it was previously done with several non electrolyte drugs in EtOH + water cosolvent mixtures (10, 29 - 31). Table 4 summarizes the thermodynamic quantities of the sodium sulfonamide mixing processes. The Gibbs energy of mixing was positive in all the systems studied. It is interesting to note that the Gibbs energies of transfer from water to EtOH (calculated as the difference between Gibbs energies of mixing in EtOH and water) diminish in the following order: Na-SD (30.7 kJ mol^–1) > Na- SMR (22.9 kJ mol^–1) > Na-SMT (14.3 kJ mol^–1).

When the partial contributions of the ideal solution (related to the solute fusion process) and mixing processes to the enthalpy and entropy of solution were analyzed, it was found that ΔH^0id_soln and ΔS^0id_soln are positive (as it is shown in table 4), while the contribution of the thermodynamic quantities related to the mixing process toward the solution processes is variable. Thus, ΔH⁰_mix is positive for all sodium sulfonamides except for Na-SD in the following cosolvent composition interval: 0.30 ≤ µ_EtOH ≤ 0.70. However, the entropy of mixing (ΔS⁰_mix) is negative for Na-SD in all mixtures, whereas for Na-SMR and Na-SMT, this quantity is positive from neat water to 0.80 or 0.90 in mass fraction of EtOH, respectively. If the contribution of the mixing processes to the dissolution processes is considered, it can be concluded that, i) the mixing process is driven by enthalpy (ΔH⁰_mix < 0 and ΔS⁰_mix < 0) for Na-SD in the intervals 0.00 ≤ μ_EtOH ≤ 0.20 and 0.80 ≤ μ_EtOH ≤ 1.00, ii) the mixing process is driven by entropy (ΔH⁰_mix > 0 and ΔS⁰_mix > 0) for Na-SMR in the interval 0.00 ≤ μ_EtOH ≤ 0.80; and iii) the mixing process is also driven by entropy (ΔH⁰_mix > 0 and ΔS⁰_mix > 0) for Na-SMT in the interval 0.00 ≤ μ_EtOH ≤ 0.90. It was found that all other cases were not enthalpy or entropy-driven (ΔH⁰_mix > 0 and ΔS⁰_mix < 0).

As it was already stated, the energy of the cavity formation process should be lower as the proportion of EtOH increases because the polarity of the medium decreases, which is a fact that favors solutesolvent interactions, except for ion-dipole. This fact is shown in table 4, where ΔH⁰_mix decreases as the proportion of cosolvent increases in EtOH-rich mixtures. According to Romero et al., 1996 (32), for non-electrolytes in the initial portion of the solubility curve, the hydrogen bonding of the drug will increase according to the EtOH concentration. For large cosolvent proportions (from 0.60 in mass fraction of EtOH to neat EtOH), this interaction may be saturated, becoming a constant contribution. However, nonspecif ic and cavity effects are not saturated, and vary according to the EtOH concentration. Nevertheless, these considerations do not explain the behavior observed in waterrich mixtures, where the ion-dipole interactions predominate for all sodium sulfonamides.

Enthalpy-Entropy Compensation of sodium sulfonamide mixing process

According to the literature, weight graphs of ΔH^0-app_soln as a function of ΔG^0-app_soln at the mean harmonic temperature allows us to observe similar mechanisms for the solution process according to the tendencies that can be seen in the results (33, 34).

In this context, figure 2 comprehensively shows that sodium sulfonamides, in the EtOH + water cosolvent system, present non-linear ΔH^0-app_soln vs. ΔG^0-app_soln compensation with negative slopes if the composition interval 0.60 ≤ μ_EtOH ≤ 1.00 is considered for all sodium sulfonamides; whereas from this EtOH proportion to neat water, positive slopes are obtained. According to this graph, it can be concluded that the driving function for the drug mixing processes is the entropy in the former case, while in the latter the driving function is the enthalpy. Nevertheless, the molecular and ionic events, which are involved in the dissolution of these drugs in this cosolvent, system are unclear.

CONCLUSIONS

From all the previously discussed topics, it can be concluded that the mixing processes of these sodium sulfonamides in EtOH + water mixtures is variable according to the cosolvent composition. Also, non linear enthalpy-entropy compensation was found for the drugs evaluated in this cosolvent system. In this context, the solution processes in compositions from pure EtOH to the mixture having 0.60 in mass fraction of ethanol were found to be enthalpy-driven; whereas, the systems from this ethanol proportion to neat water were found to be enthalpy-driven. Finally, it can be stated that the thermodynamic quantities presented in this report broaden the physicochemical information about electrolyte drugs in aqueous and alcoholic solutions.

ACKNOWLEDGMENTS

We would like to thank the DIB of Universidad Nacional de Colombia (UNC) for the financial support. Additionally, we would like to thank the UNC Department of Pharmacy for providing us access to the equipment and laboratories. Finally, we would like to thank Mr. R. Sotomayor (Procaps Labs., Colombia) for collaborating in the DSC determinations.

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