Preferential solvation of xylitol in ethanol + water co-solvent mixtures according to the IKBI and QLQC methods

Solvatación preferencial del xilitol en mezclas cosolventes etanol + agua según los métodos IKBI y QLQC

Solvatação preferencial do xilitol no misturas cosolventes etanol + água acordo o métodos IKBI e QLQC

Daniel R. Delgado¹, Edgar F. Vargas², Fleming Martínez¹*

¹ Grupo de Investigaciones Farmacéutico Fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de Colombia, A.A. 14490, Bogotá D.C., Colombia.
² Grupo de Termodinámica de Soluciones, Departamento de Química, Facultad de Ciencias, Universidad de los Andes, Bogotá D.C., Colombia.
* Autor para correspondencia: fmartinezr@unal.edu.co

Abstract

The preferential solvation parameters, i.e., the differences between the local around the solute and bulk mole fractions of the solvents in solutions of xylitol in ethanol + water binary mixtures are derived from their thermodynamic properties by means of the inverse Kirkwood-Buff integrals (IKBI) and quasi-lattice quasi-chemical (QLQC) methods. According to IKBI method it is found that xylitol is sensitive to solvation effects, so the preferential solvation parameter δx_E,S, is slightly positive in water-rich and negative in mixtures beyond 0.25 in mole fraction of ethanol. In different way, according to QLQC method, negative values of δx_E,S are found in all the compositions evaluated. The more solvation by ethanol observed in water-rich mixtures could be due mainly to polarity effects. Otherwise, the preference of this compound for water in ethanol-rich mixtures could be explained in terms of the bigger acidic behavior of water interacting with hydrogen-acceptor hydroxyl groups in xylitol.

Keywords: Xylitol, ethanol, solubility, IKBI, QLQC, preferential solvation.

Resumen

Partiendo de algunas propiedades termodinámicas clásicas se calcularon los parámetros de solvatación preferencial del xilitol (δx_E,S) en mezclas etanol + agua mediante el método de las integrales inversas de Kirkwood-Buff (IKBI) y el método cuasi-enrejado-cuasi-químico (QLQC). Los parámetros δx_E,S corresponden a las diferencias entre las fracciones molares locales alrededor del soluto y en el grueso de la solución. Con base en estos valores, se encuentra que este compuesto es altamente sensible a los efectos específicos de solvatación según la composición cosolvente. Así, según el método IKBI, los valores de δx_E,S son positivos en mezclas ricas en agua pero negativos en composiciones desde 0.25 en fracción molar de etanol hasta el etanol puro. Sin embargo, según el método QLQC, los valores de δx_E,S son negativos en todas las composiciones co-solventes analizadas. En mezclas ricas en agua la mayor solvatación por las moléculas de etanol podría deberse principalmente a efectos de polaridad. De otro lado, la preferencia que manifiesta este compuesto por el agua en mezclas ricas en etanol podría explicarse en términos del mayor comportamiento ácido del agua que estaría interactuando con los grupos aceptores de hidrógeno presentes en el soluto.

Palabras clave: xilitol, etanol, solubilidad, IKBI, QLQC, solvatación preferencial.

Resumo

Começando a partir de algumas propriedades termodinâmicas clássicos neste trabalho, foram calculados os parâmetros de solvatação preferenciais de xilitol (δx_E,S) em misturas etanol + água pelo método de integrais inversas de Kirkwood-Buff (IKBI) e o método quase-reticulado quase-químicas (QLQC). Parâmetros δx_E,S correspondem às diferenças entre as fracções molares locais ao redor do soluto na solução e a granel. Com base nestes valores se verifique que este composto é extremamente sensível aos efeitos específicos de solvatação por composição de cosolvente. Assim, de acordo com o método IKBI, valores δx _E,S são positivas em misturas ricas em água, mas negativas em composições 0,25 de fracção mole de etanol a etanol puro. No entanto, de acordo com o método QLQC, os valores de δx_E,S são negativas em todas as composições testadas. Solvatação de xilitol por moléculas de etanol em misturas ricas em água pode ser devido por polaridade. Por outro lado, a preferência de este composto por água em misturas em etanol pode ser explicada em termos de comportamento ácido de água com os grupos aceitadores de hidrogénio presentes no soluto.

Palavras-chave: xilitol, etanol, a solubilidade, IKBI, QLQC, solvatação preferencial.

Introducción

Xylitol (2R,4S)-Pentane-1,2,3,4,5-pentol, CAS RN 87-99-0) is an alditol commonly used as additive in several cosmetic and nutraceutical formulations and products (Figure 1). As nutrient agent it is given as oral and intravenous way (1). This compound has been used as a sweetener for diabetic patients and it is actively beneficial for dental health by reducing caries to a third when used regularly. Thus, this sweetening agent is finding increasing application in chewing gum, mouth-rinses, and toothpastes. Unlike sucrose, xylitol is not fermented into cariogenic acid end products (2). According to the US Pharmacopeia it is classified as an official pharmaceutical aid (3).

Normally xylitol is obtained from xylose by following several biotechnological procedures (4-6). In its industrial manufacture, xylitol is purified through crystallization from solution as the final step and dilution crystallization generally is preferable. Aqueous alcoholic mixtures are widely used for this purpose. Because the knowledge about solubility is crucial for crystallization processes, Wang et al. (7) studied the xylitol solubility in several ethanol + water mixtures at several temperatures.

Solubility of drugs and other pharmaceutical ingredients, as well as cosmetically and food ingredients, in co-solvent mixtures knowledge is very important for scientists involved in several development stages such as drug and excipients purification and design of liquid medicines (8). Although co-solvency has been employed in pharmacy for several decades it is recently that the mechanisms involved to increase or decrease organic compounds solubility have been approached from a physicochemical point of view (9). In this way, a recent thermodynamic work has been published based on the enthalpic and entropic contributions to the Gibbs energy of solution of this sweetener agent (7). Nevertheless, the preferential solvation, i.e., the co-solvent specific composition around the xylitol molecules has not been studied. Therefore, the main goal of this paper is to evaluate the preferential solvation of xylitol in ethanol + water co-solvent mixtures, based on some classical thermodynamic definitions. Thus, this work is similar to the ones presented previously in the literature for some analgesic drugs in similar co-solvent mixtures (10-13).

The inverse Kirkwood-Buff integral (IKBI) is a powerful tool for evaluating the preferential solvation of nonelectrolytes in solvent mixtures, describing the local compositions around a solute with respect to the different components present in the solvent mixture (14-16). In similar way, quasi-lattice quasi-chemical (QLQC) approach is also useful to do this although is not too much exact as IKBI is (17).

The first treatment depends on the values of the standard molar Gibbs energies of transfer of the solute xylitol from neat water to the ethanol + water co-solvent mixtures and the excess molar Gibbs energy of mixing for the co-solvent binary mixtures. As has been indicated previously, this treatment is very important in pharmaceutical sciences to understand the molecular interactions solute-solvent because most of the solubility studies developed have been directed towards correlating or modeling the solubilities, and possibly predicting them, from the solubilities in the neat solvents, but not to analyze the local environment around the solute molecules describing the local fraction of the solvent components (E or W) in the surrounding of solute (S) (18, 19).

In the second case, the QLQC method, proposed by Marcus (17), supposes that the number of nearest neighbors a molecule has (the lattice parameter Z) is the weighted mean of the lattice parameter of the pure components. It also presumes that the interaction energy of a molecule of any component with others is independent of the nature of the other neighbors. The model also assumes that ideal volumes and entropies of mixing take place (V^Exc = 0; S^Exc = 0). The main advantage of this method is that non-derivative functions are required as in the case of IKBI method (17).

In this work the IKBI and QLQC approaches are applied to evaluate the preferential solvation of xylitol in the binary mixtures conformed by ethanol (E or EtOH) and water (W). The results are expressed in terms of the preferential solvation parameter δx _E,S of the solute by the two solvent components.

Theoretical

The KBIs (Kirkwood-Buff integrals, G_i,S) are given by the following expression:

Here g _i,S is the pair correlation function for the molecules of the solvent i in the ethanol + water mixtures around the solute xylitol, r the distance between the centers of the molecules of xylitol and ethanol or water, and r_cor is a correlation distance for which g_i,S (r > r_cor) ≈ 1. Thus, for all distances r > r_cor up to infinite, the value of the integral is essentially zero. Therefore, the results are expressed in terms of the preferential solvation parameter δx_i,S for the solute in solution by the component solvents ethanol and water (20). For ethanol (E) this parameter is defined as:

Where x_E is the mole fraction of ethanol in the bulk solvent mixture and x ^L_E,S is the local mole fraction of ethanol in the environment near to the solute. If δx_E,S > 0 then the solute xylitol is preferentially solvated by ethanol; on the contrary, if it is < 0 the solute is preferentially solvated by water, within the correlation volume, V_cor =(4π/3)r³_cor, and the bulk mole fraction of ethanol, x_E. Values of δx_E,S are obtainable from those of G_E,S, and these in turn, from thermodynamic data of the co-solvent mixtures with the solute dissolved on it, as shown below (18).

Algebraic manipulation of the basic expressions presented by Newman (20) leads to expressions for the Kirkwood-Buff integrals (in cm³ mol^-1) for the individual solvent components in terms of some thermodynamic quantities as shown in equations [3] and [4] (15, 18, 19):

Where κ_T is the isothermal compressibility of the ethanol + water solvent mixtures (in GPa^-1), V_E and V_W are the partial molar volumes of the solvents in the mixtures (in cm3 mol-1), similarly, V_S is the partial molar volume of xylitol in these mixtures (in cm³ mol^-1). The function D is the derivative of the standard molar Gibbs energies of transfer of the solute (from neat water to ethanol + water mixtures) with respect to the solvent composition (in kJ mol^-1, as also is RT) and the function Q involves the second derivative of the excess molar Gibbs energy of mixing of the two solvents (G^Exc _E+W) with respect to the water proportion in the mixtures (also in kJ mol^-1) (18-21):

Because the dependence of k_T on composition is not known for a lot of the systems investigated and because of the small contribution of RT k_T to the IKBI the dependence of k_T on composition could be approximated by considering additive behavior according to the equation [7] (22):

Where x_i is the mole fraction of component i in the mixture and k⁰_T,i is the isothermal compressibility of the pure component i.

Ben-Naim (15) showed that the preferential solvation parameter could be calculated from the Kirkwood-Buff integrals as follows:

Here, N_Av is the Avogadro number. However, the definitive correlation volume requires iteration, because it depends on the local mole fractions. This iteration is done by replacing δx_E,S in the equation [2] to calculate X ^L E,S until a non-variant value of V_cor is obtained.

For the QLQC method, the local mole fraction of solvent component ethanol around the xylitol molecules is defined as (17, 19):

In these equations, the lattice parameter Z is usually assumed as 10. N_E and N_W are the number of molecules of both components in the bulk, whereas, N_EE, N_WW, and N_EW are the number of neighboring pairs of these molecules in the quasi lattice. Equation [14] expresses the difference in the molar neighbor interaction energies of xylitol with the solvents ethanol and water, ΔE_EW,S, by the molar Gibbs energy of transfer from water to ethanol per neighboring lattice. ΔE_EW denotes the molar energy of interaction of solvent on neighboring quasi-lattice sites. It is important to note that only the Gibbs energy of the xylitol transfer between the neat solvents and the excess Gibbs energy of mixing at equimolar composition of both solvents are required for this method.

Results and discussion

The solubility of xylitol in ethanol + water mixtures (Table 1) was taken from Wang et al. (7). Xylitol solubility diminishes with the increasing the proportion of ethanol in the mixtures at all the temperatures studied. It is fo r this reason that this compound is purified by precipitation after adding ethanol to its aqueous solutions.

Standard molar Gibbs energy of transfer of this sweetening agent from neat water to ethanol + water mixtures is calculated and correlated to regular quartic polynomials from the drug solubility data by using equation [16]. Figure 2 shows the Gibbs energy of transfer behavior at several temperatures whereas Table 2 shows the behavior at all the temperatures studied. Otherwise, polynomials coefficients are shown in Table 3.

Thus D values are calculated from the first derivative of the polynomial models (equation [17]) solved according to the co-solvent mixtures composition. This procedure was done varying by 0.05 in mole fraction of ethanol but in the following tables the respective values are reported varying only by 0.10 in mole fraction. D values are reported in Table 4.

In order to calculate the Q values the excess molar Gibbs energies of mixing G^Exc _E,W at all the temperatures considered are required. Nevertheless, normally these values are reported only at one temperature, i.e. 298.15 K. For this reason, it is necessary to calculate it at other temperatures. In this way, GExc E,W values were calculated at 298.15 K by using the equation [18] as reported by Marcus (18). On the other hand, the G^Exc _E,W values at the other temperatures were calculated by using the equation [19], where, H^Exc_E,W is the excess molar enthalpy of the co-solvent mixtures, T₁ is 298.15 K and T₂ is one of the other temperatures under consideration (18). In turn, H^Exc_E,W values were calculated by using the equation [20] at 298.15 K as also reported by Marcus (18).

It is important to note that quartic regular polynomials of G^Exc_E,W as a function of the mole fraction of water were obtained. Q values at all temperatures are shown in Table 5. On the other hand, Table 6 shows the RT k_T values calculated by assuming additive behavior of k_T (equation [7]) with the values 1.153 and 0.457 GPa^-1, for ethanol and water, respectively (22).

The partial molar volumes of ethanol (Table 7) and water (Table 8) were calculated by means of equations [21] and [22] from the density (ρ) values of ethanol + water mixtures reported by Jiménez et al. at all the temperatures under study (23). In these equations V is the molar volume of the mixtures and it is calculated as V = (x_E M_E + x_W·M_W)/ρ. M_E and M_W are 46.06 and 18.02 g mol^-1, respectively (1).

Partial molar volumes of non-electrolyte drugs are not frequently reported in the literature. This is because this property is dependent on temperature and composition and therefore it requires a lot of experiments. For this reason, in a first approach the molar volume of xylitol is considered here as independent of co-solvent composition and temperature, and equal to that presented in solid state, just as it is calculated by considering the density value reported in the literature (1.52 g cm^-3) (2) obtaining the value 100.10 cm³ mol^-1. Additionally, from this volume value the radius of the drug molecule (required for equation [9]) was calculated by using the equation [10] as r_S = 0.341 nm.

Table 9 shows that all the G_E,S values are negative with the maximum in x_EtOH = 0.60. In different way, Table 10 shows that G_W,S values are negative in water-rich mixtures but positive beyond the mixture with x_EtOH = 0.40 reaching maximum value in the mixture with x_EtOH = 0.80. This could be interpreted as the preference of xylitol by water in ethanol-rich mixtures.

In order to use the IKBI method, the correlation volume was iterated three times by using the equations [2], [8] and [9] to obtain the values reported in Table 11. It is interesting to note that this value is almost independent on temperature in water-rich mixtures but increases in some extent in ethanol-rich mixtures. This could be a consequence of the greater molar expansibility of ethanol in comparison with water (23).

The values of δx_E,S vary non-linearly with the ethanol concentration in the aqueous mixtures at all the temperatures studied (Table 12 and Figure 3). In the beginning, the addition of ethanol to water tends to make positive the δx_E,S values of xylitol from the pure water up to the mixture 0.25 in mole fraction of ethanol reaching a maximum of 4.8 x 10 ^-3. This maximum diminishes with the temperature increasing.

From this ethanol proportion up to neat ethanol, the local mole fraction of the ethanol around the solute decreases, being the δx_E,S values negative, and therefore, xylitol is preferentially solvated by water.

Xylitol acts in solution as a Lewis acid due to the hydrogen atoms in its -OH groups (see Figure 1) in order to establish hydrogen bonds with proton-acceptor functional groups in the solvents (oxygen atoms in -OH). In addition, this drug could act as a Lewis base due to free electron pairs in oxygen atoms of hydroxyl groups to interact with acidic hydrogen atoms in both solvents.

According to the preferential solvation results, it is conjecturable that in water-rich mixtures, the xylitol is acting as Lewis acid with ethanol molecules because this co-solvent is more basic than water, i.e. the Kamlet-Taft hydrogen bond acceptor parameters are β = 0.75 for ethanol and 0.47 for water (24). On the other hand, in ethanol-rich mixtures, where the solute is preferentially solvated by water, this compound is acting mainly as a Lewis base in front to water because the Kamlet- Taft hydrogen bond donor parameters are, α = 1.17 for water and 0.86 for ethanol, respectively (25). Thus, water is more acidic than ethanol. In this way, the specific and nonspecific interactions between xylitol and the co-solvent decrease in these mixtures (12, 26).

On the other hand, in order to use the QLQC method, the excess Gibbs energy of mixing of equimolar mixture of both solvents was used as follows: 0.709, 0.727, 0.744, 0.762, and 0.780 kJ mol^-1, at temperatures from 293.15 to 313.15 K, respectively (12). According to QLQC method (Table 13 and Figure 3) xylitol is preferentially solvated by water in all the mixtures and the δx_E,S values are bigger (as negative magnitude) than the ones obtained by using the IKBI method in mixtures with composition 0.25 < x_EtOH < 0.50 but they are lower in the other mixtures (0.50 < x_EtOH < 1.00). Therefore, as has been indicated in the literature the IKBI method is more indicate than QLQC to discriminate the effect of co-solvent composition on the local mole fraction around the drugs molecules (12, 13). Nevertheless, it is important to keep in mind that QLQC requires only two specific values, i.e. Gibbs energy of transfer of xylitol from water to ethanol and the excess Gibbs energy of mixing at x_EtOH = 0.50, so it is more easy to use.

Conclusions

Explicit expressions for local mole faction mof ethanol and water around of xylitol were derived on the basis of the IKBI and QLQC methods applied to equilibrium solubility values of this sweetening agent in ethanol + water mixtures. Thus, this compound is preferentially solvated by ethanol in water-rich mixtures but preferentially solvated by water in mixtures beyond 0.25 in mole fraction of ethanol at all temperatures considered. These results are in agreement with that described previously and base in more classical thermodynamic treatments (7).

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