Thermodynamic analysis and applications of the Abraham solvation parameter model in the study of the solubility of some sulfonamides

1Universidad Surcolombiana, Environmental Management and Engineering, Neiva, Huila, Colombia. 2Research Group of Science, Engineering and Innovation, Crimarpez S.A.S, Calle 12 Sur # 6-45, Neiva, Colombia. 3Universidad Antonio Nariño, Programa de Odontología, Sede Buganviles Calle 19 # 42-98, Neiva, Huila, Colombia. 4Universidad Surcolombiana, Faculty of Engineering, Agroindustrial engineering Program, Hydro Engineering and Agricultural Development Research Group (GHIDA), Avenida Pastrana Borrero Carrera 1, Neiva, Huila, Colombia 5Corporación Universitaria Minuto de Dios, Programa de Administración en Seguridad y Salud en el Trabajo, Grupo de Investigación en Seguridad y Salud en el Trabajo, Neiva, Huila, Colombia 6Universidad Surcolombiana, Faculty of Engineering, Agricultural Engineering Program, Hydro Engineering and Agricultural Development Research Group (GHIDA), Avenida Pastrana Borrero Carrera 1, Neiva, Huila, Colombia. 7Universidad Cooperativa de Colombia, Department of Engineering, Industrial Engineering Program, GRIAUCC Research Group, Calle 11 # 1-51, Neiva, Huila, Colombia *Address for correspondence: E-mail: danielr.delgado@ucc.edu.co


Introduction
Sulfonamides, first synthetic antimicrobial drugs [1], have been extensively used for human health treatment, in animal husbandry and management [2,3]. Sulfonamides are effective against Grampositive bacteria, and their spectrum of actions includes many Gram-negative bacteria, as well as some protozoa and fungi [4]. Sulfonamides also experience other pharmacological activities, namely antitumor [5], diuretic [6], anti-neuropathic pain [7] and anti-carbonic anhydrase [8] actions.
Owing to its extensive use, sulfonamides have become a relatively serious environmental problem, and it is one of the emerging pollutants with a greater presence in wastewater, aquifers, and bodies of water such as lakes. This could eventually put aquatic ecosystems at high risk [9]. This makes these antimicrobial agents one of the most dangerous emerging contaminants for beneficial aquatic microorganisms due to its toxicity, with the corresponding risk for human health as well [10].
Although the solubility studies are of great importance for the activities of the design and development of medicines, due to the environmental problems that have been generated by their release into the environment. A clear example is the significant fraction of the pharmaceutically active compounds sold each year find their way into the environment as the result of human/animal urine and feces excretion (excreted unchanged drugs or as drug metabolites). Or by direct disposal of unused household drugs by flushing into sewage systems, accidental spills and releases from manufacturing production sites, and underground leakage from municipal sewage systems and infrastructures. Currently, several thousand tons of medicinal compounds find their way into aquatic environments on an annual basis. The occurrence of pharmaceutical residues and metabolites in the environment is of significant public concern. Therefore, reports from the NORMAN network, promote that solubility studies have regained importance in environmental studies and/or development of more efficient methodologies for remediation processes. In this context, another area where the solubility has incurred is cleaner production [11]. Therefore, the primary objectives of this investigation were to determine the solubility of SD, SMR and SMT (figure 1) in {octanol (1) + methanol (2)} {OcOH (1) + MeOH (2)] cosolvent mixtures at nine different temperatures from 278.5 K to 313.15 K and to evaluate its thermodynamic behavior using the van't Hoff and Gibbs equations.

Reagents
The following reagents were used in this investigation: Sulfadiazine, sulfamerazine and sulfamethazine (Sigma-Aldrich, USA, approximate purity 0.990 in mass fraction); methanol, ethanol, and octanol (Merck AR, Germany, approximate purity 0.998 in mass fraction).

Preparation of the solvent mixture
The {OcOH (1) + MeOH (2)} mixtures were prepared in quantities of 10 g, using an analytical balance with sensitivity ±0.0001 g (RADWAG AS 220.R2, Poland). The mass fractions of OcOH varied by 0.10 from 0.10 to 0.90. Each mixture was prepared in triplicate.

Determination of solubility
The method used for determining the solubility of the three sulfonamides (SD, SMR and SMT) was the bottle-shaking method proposed by Higuchi and Connors [12] and previously reported in several investigations by our research groups [13,14]. This method consists of placing approximately 10 g of pure solvent or solvent mixture in an amber glass bottle and then adding excess sulfonamide until a solid phase is reached at the bottom of the bottle. Subsequently, the flasks (solvent + solute) are placed in a thermostatized recirculation bath (Medingen K-22/T100, Germany) for 72 h, stirring periodically until reaching the saturation equilibrium (constant solubility). A sample of the saturated solution is taken after 72 h using a syringe under isothermal conditions and filtered using a membrane with 0.45 μm pore size to ensure the absence of solid particles in the sample, which will be tested. The concentration of the drug in each sample was determined using UV/Vis spectrophotometry (EMC-11-UV UV/VIS spectrophotometer, Germany), making the corresponding dilutions with ethanol to avoid the precipitation of the drug during the dilution. Each solubility experiment was performed three times. all cases, the maximum solubility of the substances studied is reached in the solvent or cosolvent mixtures whose polarity is like that of each of the sulfonamides.

Activity coefficients
The activity coefficient (table 2) is calculated through equation 1, and can be interpreted based on possible molecular interactions solute-solute, solvent-solvent and solute solvent according to equation 2 [19].  Regarding SD, the activity coefficients increase from pure methanol to pure octanol; however, they diminish with and decrease in temperature. For SMR and SMT, the coefficient of activity, decrease from pure methanol to w1 = 0.1 or w1 = 0.

Thermodynamic functions of solution
Thermodynamic functions (tables 3-5) are calculated from experimental solubility data (table 1), using the van't Hoff and Gibbs equations, following the approach proposed by Krug et al. [20][21][22]: where ΔsolnH°, ΔsolnG° and ΔsolnS° denote the enthalpy, Gibbs energy and entropy of the solution, The contribution of the energy factors (solution enthalpy) and organizational aspects (entropy) to the Gibbs energy of the solution can be obtained by using Eqs. (7) and (8)    The Gibbs energy of solution is positive in all the cases. As for the SD, the Gibbs energy increase from pure MeOH to pure OcOH, because the solubility of the SD decreases with the decrease of the polarity of the system, as a consequence of the addition of octanol. SMR and SMT, the Gibbs energy decrease from pure MeOH to mixture with a mass fraction of 0.10-0.20 OcOH, beginning from this mixture, the Gibbs energy of the solution denotes an increase up to pure OcOH because the solubility decreases, possibly due to the effects of the polarity change of the medium, making it less favorable with respect to SMR and SMT.
On the other hand, the enthapy of soluctión is positive in all cases, therefore the process us always endothermic [24,25], so, the entropy solution like enthalpy, is positive in all cases favoring the porcess of solution [26][27][28].
Although, main contributor to the (positive) standard molar Gibbs energy of solution (H > 65%) is the enthalpy, the process presents an important entropic favorice.

Thermodynamic functions of the SD, SMR and SMT mixing
The solute behavior in the dissolution process can generally be divided into two stages, the solute fusion and its subsequent mixing with the solvent, so this hypothetical process can be represented according to the following scheme [29,30]:

Enthalpy-Entropy Compensation
Changes in the free energy landscape upon tethering can be attributed to changes in entropy or enthalpy [33][34][35]. Very often, the changes in entropy and enthalpy are coupled. In many cases, a perturbation produced by a change in the solvent composition, leads to a change in the enthalpy of solution processes is correlated with a similar change in entropy in what is commonly referred to as "entropy-enthalpy compensation" [36]. Entropy-enthalpy compensation is reported for many chemical processes and is often accounted for as a general thermodynamic principle. In this case, analysis has been used to identify the mechanism of the co-solvent action [37][38][39].

Estimation of solubility and lethal median molar concentration of SD, SMR and SMT towards aquatic organisms from Abraham model solute descriptors
The solubility of each of the sulfonamides (SD, SMR and SMT) can be calculated from Abraham model (equation 14), the solute descriptors can be from were calculated using the page of the Helmholtz Environmental Research Center-UFZ, or from solubility data of each sulfonamide in pure solvents [41]. 3    %Dev 100 The model results show a good approximation to the experimental data. Although deviation percentages of 38% are presented, which could be considered high, any theoretical approach to solubility data is of great importance.
The main advantage that the Abraham model is that can be used to predict other solute properties such as the toxicity of organic compounds towards different aquatic organisms. Yue et al. [35], has compiled Abraham model equation coefficients for predicting the median lethal molar concentration of organic compounds towards five species of fish (fathead minnow, guppy, bluegill, golden orfe and Medaka high-eyes) [43][44] and three species of water fleas (Daphnia magna, Ceriodaphnia dubia and Daphnia pulex) [45].
In table 9 show tabulated the predicted median lethal molar concentration of SD, SMR and SMT calculated using equation 15 towards various species of fish and water fleas based the solute descriptors.
the results reflect that species like Golden Orfe and Medaka high-eyes, they are extremely sensitive to sulfonamides, which shows the great danger to which some aquatic organisms are exposed, due to the dumping of these substances into the aquatic environment.

Conclusions
The solubility of the three sulfonamides is thermodependent, increasing with increasing temperature, indicating an endothermic process, and the peak of maximum solubility is reached where the cosolvent mixture has a polarity like that of the sulfonamide. Regarding the thermodynamics of solution, both enthalpy and entropy are positive, indicating an entropic conduction of the solution process. The Abraham model, allows the calculation of the solubility of sulfonamides in an acceptable way, the calculation of the LC50, indicates that some aquatic species are extremely sensitive to these drugs and evidences the environmental problem that is being generated by the dumping of drugs to water bodies.