Extended Hildebrand solubility approach applied to some structurally related sulfonamides in ethanol + water mixtures

^len^aExtended Hildebrand Solubility Approach (EHSA) was applied to evaluate the solubility of sulfadiazine, sulfamerazine, and sulfamethazine in some ethanol + water mixtures at 298.15 K. Reported experimental equilibrium solubilities and some fusion properties of these drugs were used for the calculations. In particular, a good predictive character of EHSA (with mean deviations lower than 3.0%) were found by using regular polynomials in order four correlating the interaction parameter W with the Hildebrand solubility parameter of solvent mixtures without drug. The predictive character of EHSA was the same as that obtained by direct correlation of drug solubilities with the same descriptor of polarity of the cosolvent mixtures.^les^aSe aplico el Metodo Extendido de Solubilidad de Hildebrand (MESH) al estudio de la solubilidad de sulfadiazina, sulfamerazina y sulfametazina en mezclas binarias etanol + agua a 298,15 K. Se utilizaron valores reportados de solubilidad en equilibrio y algunas propiedades fisicoquimicas de fusion de estos compuestos. Se obtuvo una adecuada capacidad predictiva del MESH (con desviaciones promedio menores del 3,0%) al utilizar modelos polinomicos regulares de cuarto orden relacionando el parametro de interaccion W con el parametro de solubilidad de Hildebrand de las mezclas solventes. El caracter predictivo del MESH fue de magnitud semejante al que se obtuvo calculando esta propiedad directamente, donde se utilizo una regresion empirica regular de cuarto orden de la solubilidad experimental logaritmica de los farmacos en funcion del parametro de solubilidad de las mezclas disolventes.^lpt^aNa presente investigacao, aplicou-se o Metodo Estendido de Solubilidade do Hildebrand (MESH) ao estudo da solubilidade da sulfadiazina, sulfamerazina e sulfametazina em misturas binarias etanol + agua a 298,15 K. Obteve-se uma adequada capacidade preditiva (com menor desvio padrao de 3,0%) do MESH ao utilizar modelos polinomiais regulares de quarta ordem relacionando o parâmetro de interacao W com o parâmetro de solubilidade do Hildebrand das misturas de solventes. O carater preditivo do MESH foi semelhante ao obtido pelo calculo utilizando uma regressao empirica regular da quarta ordem, da solubilidade experimental logaritmica dos farmacos em funcao do parâmetro de solubilidade das misturas dissolventes.

Método extendido de Hildebrand en la estimación de la solubilidad de algunas sulfonamidas estructuralmente relacionadas en mezclas etanol + agua Extended Hildebrand solubility approach applied to some structurally related sulfonamides in ethanol + water mixtures Método ampliado de Hildebrand na estimação da solubilidade da algumas sulfamidas estruturalmente relacionadas em misturas do etanol + agua Se aplicó el Método Txtendido de Solubilidad de Hildebrand 6MTSHv al estudio de la solubilidad de sulfadiazina2 sulfamerazina y sulfametazina en mezclas binarias etanol 7 agua a C-G2UA KP Se utilizaron valores reportados de solubilidad en equilibrio y algunas propiedades fisicoquímicas de fusión de estos compuestosP Se obtuvo una adecuada capacidad predictiva del MTSH 6con desviaciones promedio menores del N2Fgv al utilizar modelos polinómicos regulares de cuarto orden relacionando el parámetro de interacción W con el parámetro de solubilidad de Hildebrand de las mezclas solventesP Tl carácter predictivo del MTSH fue de magnitud semejante al que se obtuvo calculando esta propiedad directamente2 donde se utilizó una regresión empírica regular de cuarto orden de la solubilidad experimental logarítmica de los fármacos en función del parámetro de solubilidad de las mezclas disolventesP Txtended Hildebrand Solubility Kpproach 6THSKv was applied to evaluate the solubility of sulfadiazine2 sulfamerazine2 and sulfamethazine in some ethanol 7 water mixtures at C-GPUA KP Reported experimental equilibrium solubilities and some fusion properties of these drugs were used for the calculationsP In particular2 a good predictive character of THSK 6with mean deviations lower than NPFgv were found by using regular polynomials in order four correlating the interaction parameter W with the Hildebrand solubility parameter of solvent mixtures without drugP The predictive character of THSK was the same as that obtained by direct correlation of drug solubilities with the same descriptor of polarity of the cosolvent mixturesP Na presente investigação2 aplicouyse o Método Tstendido de Solubilidade do Hildebrand 6MTSHv ao estudo da solubilidade da sulfadiazina2 sulfamerazina e sulfametazina em misturas binárias etanol 7 agua a C-G2UA KP Obteveyse uma adequada capacidade preditiva 6com menor desvio padrão de N2Fgv do MTSH ao utilizar modelos polinomiais regulares de quarta ordem relacionando o parâmetro de interação W com o parâmetro de solubilidade do Hildebrand das misturas de solventesP O caráter preditivo do MTSH foi semelhante ao obtido pelo cálculo utilizando uma regressão empírica regular da quarta ordem2 da solubilidade experimental logarítmica dos fármacos em função do parâmetro de solubilidade das misturas dissolventesP Extended Hildebrand solubility approach applied to some structurally related sulfonamides in ethanol + water mixtures

Introduction
Sulfonamides are synthetic drugs used to treat certain infections caused by a wide group of microorganisms in human and veterinary medicine practice :1-3FH NeverthelessE the physicochemical properties of these drugs in aqueous solutions have not yet been studied completely :4FH Regarding their aqueous solubilitiesE it is well known that they are very lowE being considered as very slightly soluble or even practically insoluble :5FH In this wayE it has been reported that the cosolvency is the best technique used in pharmacy for increasing the drugs equilibrium solubility :6-8FH MoreoverE it is clear that predictive methods of physicochemical properties of drugsE in particular those intended to estimate their solubilitiesE are very important for pharmaceutical and chemical industryH This is because these methods allow the optimization of several design and development processes :4FH In this regardE some recent examples of these developments about the solubility prediction of drugs are described in the literature as follows/ in neat water :9FE in simulated gastrointestinal fluids :10FE in organic solvents :11F and in mixed solvents :12-14FH In additionE some attempts to estimate the solubility of sulfonamides in different aqueous or organic media have been reported in the literature :15-17FH For this reasonE this research presents a physicochemical study about the solubility prediction of three structurally related sulfonamidesE namelyE sulfadiazine :SDZE FigH 8FE sulfamerazine :SMRE FigH 8F and sulfamethazine :SMTE FigH 8FE in binary mixtures conformed by ethanol :EtOHF and water at 5J]H8+ KH The study was performed based on the Extended Hildebrand Solubility Approach :EHSAF :8E 18F by using reported experimental equilibrium solubility values and some thermal properties relative to the fusion of these drugs :19-21FH ThusE this communication is similar to those developed previously for other drugs in the same cosolvent mixtures :22-26FE and also to that developed about the behavior of other sulfonamides in propylene glycol Z water mixtures :27FH It is crucial to note that EHSA method has been widely used to study the solubility of many pharmaceutical compounds as has been exposed previously :28FH FurthermoreE it is still employed to analyze the behavior of several drugs in different cosolvent mixtures :29-32FH On the other handE it is remarkable that EtOH and its aqueous mixtures are the most employed solvent systems to develop liquid pharmaceutical dosage forms owing its solubilizing and antimicrobial properties :33E 34FH Theoretical background In a first approachE based on the Henry's lawE the ideal solubility : F of a solid solute could be calculated by means of the following expression/ ) [( whereE is the molar enthalpy of fusion of the pure solute :at the melting pointFE T fus is the absolute melting pointE T is the absolute solution temperatureE R is the constant gas :]HK8A J2mol•KF and ∆C p is the difference between the molar heat capacity of the crystalline form and the molar heat capacity of the hypothetical supercooled liquid formE both at the solution temperatureH Since ∆C p values are not commonly reportedE they may be approximated to the entropy of fusionE calculated as follows/ Ideal solubility depends on the physicochemical properties of the solid compound without considering the properties of the solventH In this wayE the ideal solubility would be higher if the soluteOsolute interactions are lower :35FH AccordinglyE compounds with high values of melting point and enthalpy of fusion have lower ideal solubilitiesH On the other handE the real solubility :X 5 F of a solid solute in a liquid solution is analyzed by means of the following expression :25-27F/ HereE is the nonOideality term with as the solute activity coefficient defined on asymmetric basisH This property is determined experimentally from real and ideal solubilitiesH NeverthelessE a classical method of calculations is based on the regular solutions model as/ whereE V 5 is the partial molar volume of the soluteE is the volume fraction of the solvent in the saturated solution and and are the Hildebrand solubility parameters of solvent and soluteE respectivelyH is calculated as/ where V 8 is the molar volume of the solventH HoweverE all the pharmaceutical aqueous dissolutions deviate significantly from that predicted by the regular solutions theoryH For this reasonE Martin et alH :36-42F developed the EHSA methodH TherebyE if the A term :defined as F is introduced in the equation [A]E the real solubility of drugs can be calculated from the expression/ Here+ the W term is equal to IK gwhere+ K is the Walker parameter g1888z The W factor can be calculated from experimental data by means of= where+ is the activity coefficient of the solute in the saturated solution and it is calculated as= z The experimental values of the W parameter can be correlated by means of regression analysis by using regular polynomials as a function of as follows= These empiric models can be used to estimate the drug solubility by means of backVcalculation+ resolving this property from the specific W value obtained in the respective polynomial regression g25, 268z

Results and discussion
The required properties about the sulfonamides studied such as ideal solubility+ molar volume+ and Hildebrand solubility parameter are presented in Table F g5,21,228z The volumetric behavior and polarity of EtOH O water mixtures+ as a function of the composition+ is shown in Table Iz Volume fractions and Hildebrand solubility parameters were calculated assuming additive behavior g8, 438z Table I also summarizes the experimental solubility of the sulfonamides expressed in molarity and mole fraction reported in the literature g20, 218z

Mixtures composition
x FR -0 SzS% x FR -K KzMF x FR -0 0z%F x FR -% FzKS x FR -I LzFM x FR -% a wF and fF are the mass and volume fraction of ethanol in the cosolvent mixtures free of sulfonamidez b Zata from Refz (20)z c Zata from Refz (21)z In all cases the relative standard deviations in reported solubilities were lower than IzR7 g20, 218z It is important to note that by using the inverse KirkwoodVAuff integrals g44-468 these drugs are preferentially solvated by water in waterVrich and EtOHVrich mixtures but preferentially solvated by EtOH in mixtures with similar proportions of both solvent components g478z These results were interpreted as a consequence of hydrophobic hydration around the nonVpolar moieties of these sulfonamides in aqueousVrich mixtures and by polarity effects in those mixtures of similar proportionsz Similar considerations about the aqueous behavior have been reported from the temperatureVdependence of their octanolVwater partition coefficients g488z Moreover+ these sulfonamides are acting as Lewis acids with ethanol molecules+ because this cosolvent is more basic than water based on their KamletVTaft hydrogen bond acceptor parameters reported gas β 6 RzSK for ethanol and Rz%S for water8 g498z Furthermore+ in EtOHVrich mixtures+ where these drugs are preferentially solvated by water again+ these results were analyzed by considering that the sulfonamides are acting mainly as Lewis bases with water based on the Kamlet-Taft hydrogen bond donor parameters of the solvents+ izez α 6 FzFS for water and RzMB for EtOH+ respectively g50, 518z Figure I shows the ideal and experimental solubility+ as well as those calculated by using the regular solution model gequation [%]8+ as a function of the Hildebrand solubility parameter of the solvent mixtures+ izez from IBzK to %SzM MPa FDI z In order to use equation [%] the molar volume and Hildebrand solubility parameter of the sulfonamides were taken from the literature as shown in Table F g20+ 218z These values were calculated by using the groups' contribution method proposed by Fedors g528z Extended Hildebrand solubility approach applied to some structurally related sulfonamides in ethanol + water mixtures Regarding Fig8 6= it is noteworthy that the regular solutions model predicts that the maximum solubility value corresponds to the ideal solubility and this is obtained when both the Hildebrand solubility parameters of drug and solvent mixture are coincident8 In a similar way= according to the literature the maximum experimental solubility values are found when the Hildebrand solubility parameters of both solute and solvent are also coincident ]8, 180= despite they can be very different regarding the ideal solubility8

The
/ values for all these sulfonamides= calculated according to equation [j]= are almost equal to /8PPP because the solubility of these sulfonamides is very low in all the solvent system considered ]Table O08 The activity coefficients of these sulfonamides expressed as decimal logarithms are also shown in Table O8 Analysis of these activity coefficients has been reported previously in the literature ]20= 2108 Briefly= based on the activity coefficients magnitudes it follows that the solvent7solvent interactions are higher in neat water ]with Hildebrand solubility parameter = 9E8+ MPa /M6 0 and they are smaller in ethanol ]with = 6z8j MPa /M6 0 ]5008 Pure water and water7rich mixtures exhibiting larger log γ 6 values ]even higher than 68+P0 would imply high solvent7solvent interactions and low solvent7solute interactions8 On the other hand= in ethanol7rich mixtures ]exhibiting log γ 6 values between P8-P and /8OP0= the solvent7solvent interactions are comparatively low and the solvent7 solute interactions would relatively be high8 Accordingly= the solvation of these sulfonamides would be just higher in ethanol7rich mixtures8 Table O also summarizes the calculated parameters A, K= and W of the sulfonamides in EtOH B water mixtures8 Figure O shows that the W parameter of all sulfonamides exhibits some deviation from the linear behavior with respect to the Hildebrand solubility parameter of the solvent mixtures8 This behavior is expectable because the W term implies the summation of two quadratic ] 6 and 0 and one non7constant7quotient ]-log γ 6 MA0 terms ]equation [E]08 W values were adjusted to regular polynomials in orders from 6 to j ]equation [+]0 ]5308 As comparison the linear equation was also considered8 Table 9 summarizes the coefficients obtained in all the regular polynomials for these sulfonamides8 Searching for the best adjust= the first criterion used to define the best polynomial order of W term as function of δ / was the fitting standard error ]Table 908 As another comparison criterion= the difference percentages between the experimental solubilities and those calculated by using EHSA were also calculated as shown in  It is observed that as more complex is the polynomial used= there is a better correlation between experimental and calculated solubility8 Accordingly= the most important increment= in concordance= is obtained by passing from linear equation to polynomial in order 68 The concordances also increase significantly from orders 6 to O and O to 98 Delgado, D. R; Peña, M. Á; Martínez, F.
Nevertheless2 from order M to P the concordance increment is not so much relevant2 because in the last case the mean uncertainties obtained are in the same order or lower than those reported experimentally S20, 21F9 It is important to know that uncertainties lower than PA are useful for pharmaceutical purposes2 but better agreements are required for academic and theoretical purposes9 As it has already been described2 regarding the practical usefulness of the EHSA2 a very important consideration is about the complex calculations involving other experimental variables of solute and solvents2 instead of the simple empirical regression of the experimental solubility values as a function of the Hildebrand solubility parameters of solvent mixtures as shown in Fig9 M S18F9 For this reason2 Table B shows the coefficients of regular polynomials in order M of log X / vs9 values Sequation [z]F S18F2 whereas Table ' shows the calculated values of solubility by using equation [z] and also the respective deviation percentages in front of the experimental ones9 Table 3. Volume fraction of solvent, sulfonamide activity coefficients, and A, K, and W experimental parameters of sulfonamides in ethanol + water mixtures at 298.15 K.

Sulfadiazine
It is noteworthy that empirical regular polynomials2 as shown in equation [z]2 are commonly referred as Bustamante's Equation and are widely used in pharmaceutical sciences owing its as has been described in the literature S4F9 By using both calculation methods2 the same mean deviation percentages were obtained as shown in Tables P and '2 i9e9 /9BPA2 /98/A and J9MJA for sulfadiazine2 sulfamerazine2 and sulfamethazine2 respectively9 This behavior is similar to those described earlier for other drugs in different cosolvent mixtures S22-28F9 Thereby2 the results for these sulfonamides could indicate a non[significant usefulness of EHSA method for practical and academic purposes9 Nevertheless2 it is necessary to know that this correlative method considers the drug solubility from a complete thermodynamic viewpoint9

Figure 2 .
Figure 2. Ideal solubility ;---), experimental solubility ;○), and calculated solubility according to the regular solutions model of Hildebrand ;) of sulfonamides as a function of the Hildebrand solubility parameter in ethanol + water mixtures at 298.15 K.

Table 1 .
Some properties of the sulfonamides considered

Table 2 .
Ethanol + water solvent mixtures composition, Hildebrand solubility parameter of mixtures and solubility of sulfonamides expressed in molarity and mole fraction at 298.15 K.

Table 5 .
Calculated solubility of sulfonamides in ethanol + water mixtures by using the W parameters obtained from regression models in orders 1, 2, 3, 4 and 5, and standard deviations with respect to the experimental values, at 298.15 K.

Table 6 .
Coefficients and statistical parameters of regular polynomials in fourth degree of log X 2 as a function of solubility parameters of cosolvent mixtures free of sulfonamide(Eq.[9]) in ethanol + water mixtures.

Table 7 .
Calculated solubility of sulfonamides in ethanol + water mixtures by using the equations of log X 2 vs. δ 1 as regression models in order 4, and standard deviations with respect to the experimental values, at 298.15 K.