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## Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales

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*Print version* ISSN 0370-3908

### Rev. acad. colomb. cienc. exact. fis. nat. vol.35 no.136 Bogotá July/Sept. 2011

**FISICOQUÍMICA**

**STUDY OF SOME VOLUMETRIC PROPERTIES OF GLYCEROL FORMAL + ETHANOL MIXTURES AND CORRELATION WITH THE JOUYBAN-ACREE MODEL**

^{1},Daniel R. Delgado

^{1}, Fleming Martínez

^{1*}Mehri Khoubnasabjafari

^{2}Abolghasem Jouyban

^{3}

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

^{*} Correspondence: E-mail: fmartinezr@unal.edu.co

^{2} Tuberculosis and Lung Disease Research Center, Tabriz University of Medical Sciences, Tabriz, Iran.

^{3} Drug Applied Research Center and Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz, Iran.

**Abstract**

Molar volumes, excess molar volumes, and partial molar volumes were investigated for glycerol formal + ethanol mixtures by density measurements at several temperatures. Excess molar volumes are fitted by Redlich-Kister equation and compared with other systems. The system exhibits negative excess volumes probably due to increased H-bond interactions. Volume thermal expansion coefficients are also calculated. The Jouyban-Acree model was used for density and molar volume correlations at different temperatures. The mean relative deviations between experimental and calculated data were 0.03 ± 0.03% and 0.17 ± 0.13%, respectively for density and molar volume data. Also, using a minimum number of data points, the Jouyban-Acree model can predict density and molar volume with acceptable accuracies (0.03 ± 0.03% and 0.15 ± 0.12%, respectively).

**Key words:** glycerol formal; ethanol; binary liquid mixtures; excess volumes; partial volumes; Jouyban-Acree model.

**Resumen**

En este trabajo se calculan los volúmenes molares, molares de exceso y molares parciales a partir de valores de densidad para el sistema glicerol formal + etanol en todo el intervalo de composición a temperaturas entre 278,15 y 313,15 K. Los volúmenes molares de exceso se modelaron de acuerdo a la ecuación de Redlich-Kister y se compararon con los reportados para otros sistemas. El sistema estudiado presenta volúmenes de exceso negativos probablemente debido a fuertes interacciones por unión de hidrógeno. También se analizó el efecto de la temperatura sobre las diferentes propiedades volumétricas estudiadas. Así mismo se calcularon los coeficientes térmicos de expansión volumétrica. Finalmente se usó el modelo Jouyban-Acree para correlacionar la densidad y el volumen molar de las diferentes mezclas encontrando desviaciones medias relativas de 0,03 ± 0,03% y 0,17 ± 0,13% para densidades y volúmenes molares respectivamente.

**Palabras clave:** glicerol formal; etanol; mezclas líquidas binarias; volúmenes de exceso; modelo de Jouyban-Acree.

** Introduction **

Non-aqueous solvent mixtures have sometimes been used in human and veterinarian pharmacy in order to increase the solubility of drugs poorly soluble in water during the design of injectable homogeneous dosage forms (**Rubino, J.T.,** 1988). Ethanol and propylene glycol are the cosolvents most used in design nowadays and sometimes have been employed blended (**Yalkowsky, S.H.,** 1999). Glycerol formal is a non-toxic and environmentally-friendly organic solvent (**Budavari, S. et al.** 2001), miscible with water, ethanol and propylene glycol in all possible compositions and has been widely used as cosolvent for veterinarian formulations such as those containing the antinematodal drug, ivermectin (

**Lo, P.K.A.**1985;

*et al.***DiPietro, J.A.**1986;

*et al.***Reinemeyer, C.R. & Courtney, C.H.,**2001). Glycerol formal is available as the mixture of 5- hydroxy-1,3-dioxane and 4-hydroxymethyl-1,3-dioxolane (60:40) and as the individual isomers (

**Budavari, S.**2001;

*et al.***Pivnichny, J.V.,**1984).

The mixtures obtained using these cosolvents are nonideal due to increased interactions between unlike molecules and differences in molar volumes of pure components, which leads to non-additive volumes on mixing (**Battino, R.,** 1971; **Kapadi, U.R. et al.** 2001). For this reason it is necessary to characterize the volumetric behavior of these binary mixtures as a function of composition and temperature in order to extend the physicochemical information available for liquid mixtures used in pharmacy. This information is useful to represent the intermolecular interactions present in liquid pharmaceutical systems and to facilitate the processes of medicines design at industrial level (

**Jiménez, J.**2004).

*et al.* In this report, the excess molar volumes and the partial molar volumes of the binary system of glycerol formal + ethanol at various temperatures as well as other volumetric properties are reported. The physicochemical properties reported here were calculated according to several mathematical procedures widely exposed in the literature (**Wahab, M.A. et al.** 2002;

**Salas, J.A.**2002;

*et al.***Peralta, R.D.**2003;

*et al.***Resa, J.M.**2004). This work is a continuation of those presented previously about some volumetric properties of glycerol formal + water mixtures (

*et al.***Delgado, D.R.**2011) and glycerol formal + propylene glycol mixtures (

*et al.***Rodríguez, G.A.**2011).

*et al.***Experimental **

**Materials**

In this investigation glycerol formal (5-hydroxy-1,3 - dioxane isomer) from Lambiotte & Cie S.A. was employed and is in agreement with the quality requirements indicated for veterinarian medicinal products. Density and refractive index of glycerol formal (ρ = 1.2214 g·cm^{-3} and *n*_{D} = 1.4535 at 298.15 K, respectively) were in good agreement with the values reported for the single 5-hydroxy-1,3 dioxane isomer (*ρ*_{4}^{25}= 1.2200 g·cm^{-3} and *n*_{D}^{25}= 1.4527) (**Budavari, S. et al.** 2001). Figure 1 shows the molecular structure of 5-hydroxy- 1,3-dioxane isomer . In the same way, dehydrated ethanol A.R. (Merck, Germany) was also used and is in agreement with the quality requirements indicated for medicinal products indicated in the American Pharmacopeia USP (

**US Pharmacopeia,**1994). The dehydrated glycerol formal and ethanol employed were maintained over molecular sieve to obtain dry solvents prior to prepare the solvent mixtures.

**Cosolvent mixtures preparation**

All glycerol formal + ethanol mixtures were prepared in quantities of 40.00 g by mass using a Ohaus Pioneer TM PA214 analytical balance with sensitivity ± 0.1 mg, in concentrations from 0.05 to 0.95 in mass fraction (varying in 0.05) of glycerol formal, to study 19 mixtures and the two pure solvents. This procedure implies an uncertainty of ± 2 x 10^{–5} in mole fraction. The mixtures were allowed to stand in Magni Whirl Blue M or Neslab RTE 10 Digital Plus (Thermo Electron Company) water baths at temperatures from 278.15 K to 313.15 K varying in 5.00 ± 0.05 K for at least 30 minutes prior to density determinations.

**Density determination**

This property was determined using a DMA 45 Anton Paar digital density meter connected to a Neslab RTE 10 Digital Plus (Thermo Electron Company) recirculating thermostatic water bath according to a procedure previously described (**Martínez, F. et al.** 2002). The equipment was calibrated according to Instruction Manual using air and water at the different temperatures studied (

**Kratky, O.**1980). From density values, all thermodynamic properties were calculated as will be indicate in the next section.

*et al.* ** Results and discussion **

In order to define the solvents 1 and 2 in the binary mixtures according to polarity the Hildebrand solubility parameter (δ) of glycerol formal was calculated as 24.8 MPa^{1/2} according to procedures described by **Barton, A.F.M.** (1991), which are presented in Table 1. Accordingly, glycerol formal is a solvent less polar compared with ethanol (δ value is 26.5 MPa^{1/2}, **Barton, A.F.M.,** 1991).

In Table 2 the composition of glycerol formal + ethanol, in mass (*µ*_{GF}) and mole (x_{GF}) fraction, in addition to studied density values at several temperatures, is presented. Figure 2 plotted experimental density data against fraction of glycerol formal and temperature.

In the literature no values are available for this binary solvent system and therefore no direct comparison is possible. Nevertheless, it is important to remember that **Pineda, L.M. et al.** (2003) and

**Arias, L.J.**(2004) reported density values at 298.15 K for binary mixtures obtained employing material raw without any dehydration process, just as they are used in the pharmaceutical industries. Accordingly, the cosolvents studied by these authors had some low quantities of water, i.e. 0.31 % m/m and 6.52% m/m for glycerol formal and ethanol, respectively. Table 2 shows that in all cases the density increases as the glycerol formal proportion increases in the mixtures and it decreases linearly as the temperature increases. In the other hand, density values decrease as the ethanol proportion increases in the mixtures following concave parabolic trends

*et al.*

Molar volumes and excess molar volumes

In Table 3 the molar volumes (*V ^{0}*) for binary mixtures at all studied temperatures are presented which were calculated from Equation (1).

where M_{1} and M_{2} are the molar masses, for both components respectively (104.10 g·mol^{-1} for glycerol formal and 46.07 g·mol^{-1} for ethanol, **Budavari, S. et al.** 2001), x

_{1}and x

_{2}are the respective mole fraction of components, and ρ is the mixture density. Figure 3 shows the molar volume as a function of mixtures composition and temperature.

On the other hand, the excess molar volumes (V^{0-E}) calculated from Equation (2) (where, ρ1 and ρ2 are the densities of pure components) at all studied temperatures, are also presented in Table 3. This behavior is shown graphically in Figure 4 at all studied temperatures.

In similar way to the behavior obtained in other similar investigations developed in our reseach group with other solvent systems (**Jiménez, J. et al.** 2004;

**Jiménez, J. & Martínez, F.**2005, 2006;

**Ruidiaz, M.A. & Martínez, F.,**2009;

**Rodríguez, S.J.**2010), in almost all cases the excess volumes are negative (especially around 0.60-0.70 in mole fraction of glycerol formal, where it is approximately equal to –0.60 cm

*et al.*^{3}·mol

^{-1}at 313.15 K) indicating contraction in volume, except at 278.15 and 283.15 K in the mixture with composition 0.05 in mass fraction of glycerol formal where positive values near to 0.03 cm

^{3}·mol

^{-1}were obtained. It is interesting to note that glycerol formal + water mixtures exhibited negative excess volumes (

**Delgado, D.R.**2011) whereas glycerol formal + propylene glycol exhibited positive excess volumes (

*et al.***Rodríguez, G.A.**2011).

*et al.*As was already said (

**Jiménez, J & Martínez, F.,**2005, 2006;

**Delgado, D.R.**2011), according to

*et al.***Fort, R.T. & Moore, W.R.**(1966), a negative excess volume is an indication of strong heteromolecular interactions in the liquid mixtures and is attributed to charge transfer, dipoledipole, dipole-induced dipole interactions, and hydrogen bonding between the unlike components, while a positive sign indicates a weak interaction and is attributed to dispersion forces (London interactions) which are likely to be operative in every cases.

In the evaluated system, where the hydrogen bonding predominates, the contraction in volume has been interpreted basically in qualitative terms considering the following events: first: expansion due to depolymerization of glycerol formal and ethanol by one another, second: contraction due to free volume difference of unlike molecules, and third: contraction due to hydrogen bond formation between glycerol formal and ethanol through –OH---O< or –OH---OH bonding.

Thus, the large negative values of *V ^{0}*–E over the free volume contribution indicate the presence of strong specific interactions with predominance of formation of hydrogen bonds between glycerol formal and ethanol over the rupture of hydrogen bonding in ethanol-ethanol and water-water.

The excess molar volumes become more positive as the temperature although this result is not clear at molecular level.

**Partial molar volumes**

The partial specific volumes of glycerol formal ^{0}_{GF} and ethanol ^{0}_{EtOH} were calculated using the classical Bakhuis-Roozeboom method by means of equations (3) and (4) applied to the variation of the respective specific volumes as a function of glycerol formal mass fraction (Reciprocal of densities reported in Table 3 and presented in Figure 5 at four temperatures) and adjusting them to second degree polynomials by least squares regression analyses (**Kestin, J.,** 1979; **Perrot, P., **1998). The first derivatives were taken out on the polynomials obtained and solved at each composition point.

The partial molar volumes were calculated from the respective partial specific volumes multiplied by the molar masses. The ^{0}_{GF} and ^{0}_{EtOH} values are also presented in Table 3 in addition to the slopes obtained (*dV/d µ*

_{GF}) at each composition and temperature. In all cases the partial molar volumes of glycerol formal are lower than those obtained for the pure solvent at all temperatures. In the other hand, the partial molar volumes of ethanol are greater than those for the pure solvent in the mixtures where this cosolvent is in great proportion (0.00 <

*µ*_{GF}< 0.30) but they are lower in the other mixtures (0.30 <

*µ*

_{GF}< 1.00). In cosolvent mixtures, the partial volumes for glycerol formal varied from 81.77 cm3·mol

^{-1}(for

*µ*

_{GF}= 0.05 at 278.15 K) to 86.10 cm3·mol

^{-1}(for

*µ*

_{GF}= 0.95 at 313.15 K), and for ethanol varied from 56.45 cm

^{3}·mol

^{-1}(for

*µ*

_{GF}= 0.95 at 278.15 K) to 59.68 cm3·mol

^{-1}(for

*µ*

_{GF}= 0.10 at 313.15 K). The results obtained for

^{0}

_{GF}and

^{0}

_{EtOH}are in agreement with the negative excess volumes obtained. The variation of this property is presented in Figure 6 as a function of glycerol formal mole fraction at 298.15 K for glycerol formal and ethanol, respectively. These values were calculated as the difference between partial molar volumes and molar volumes presented in Table 3. For both solvents the partial molar volume diminishes as their respective proportion in the mixtures diminishes, except for ethanol in those mixtures where it is in great proportion.

**Redlich-Kister equation**

The Redlich-Kister equation has been used in recent decades for manipulating several kinds of physicochemical values of mixtures such as: excess volumes, excess viscosities, solubilities in cosolvent mixtures, among others (**Redlich, O. & Kister, A.T.**, 1948). When applied to excess molar volumes is presented as Equation (5),

where x_{1} and x_{2} are the respective mole fractions.

In the analysis of our data about excess volumes, the Equation (5) was used in the form of third degree polynomial equations using least square analyses, obtaining four coefficients as presented in Equation (6).

The Redlich-Kister parameters for glycerol formal + ethanol mixtures at all temperatures studied are presented in Table 4 beside related determination coefficients and standard deviations calculated according to Equation (7) (where D is the number of compositions studied and N is the number of terms used in the regression, that is 19 and 4 respectively). Figura 7 shows the Redlich-Kister equation applied to glycerol formal + ethanol data at several temperatures.

The variation coefficients greater than 0.94 (except at 288.15 and 293.15 K) indicate that the obtained regular polynomials regressions describe adequately the excess volumes. In similar way, standard deviations are similar to those presented in the literature for other kind of mixtures (**Kapadi, U.R. et al.** 2001;

**Salas, J.A.**2002;

*et al.***Wahab, M.A.**2002;

*et al.***Peralta, R.D.**2003;

*et al.***Resa, J.M.**2004;

*et al.***Ruidiaz, M.A. & Martínez, F.**2009;

**Cristancho, D.M.**2011). On the other hand, σ values obtained for glycerol formal + ethanol mixtures were in general similarity to those obtained for glycerol formal + propylene glycol (near to 0.030 cm

*et al.*^{3}·mol

^{-1},

**Rodríguez, G.A.**2011), ethanol + propylene glycol (varying from 0.003 to 0.021 cm

*et al.*^{3}·mol

^{-1},

**Jiménez, J. & Martínez, F.,**2006), and glycerol formal + water (near to 0.008 cm

^{3}·mol

^{-1},

**Delgado, D.R.**2011).

*et al.* **Volume thermal expansion**

In pharmaceutical pre-formulation studies, it is too important to know the variation of physicochemical properties related to pharmaceutical dosage forms, with respect to temperature changes; especially the properties that affect the concentration of active ingredients. Thus, the volume thermal expansion coefficients (α) were calculated by means of Equation (8) (**Ott, J.B. & Boerio- Goates, J., **2000) by using the variation of molar volumes with temperature (Table 2).

Table 5 summarizes the (∂*V ^{0}*/∂T) and α values for all mixtures and pure solvents. In all cases linear models were obtained with determination coefficients greater than 0.999. The α values varied from 7.28 x 10

^{–4}K

^{–1}in pure glycerol formal to 1.135 x 10

^{–3}K

^{–1}in pure ethanol at 298.15 K although the α variation is not linear with the mixtures

**Data correlation using the Jouyban-Acree model**

The Jouyban-Acree model was introduced to correlate the physicochemical properties of the solution in mixed solvents including the dielectric constants (**Jouyban, A. et al.** 2004), viscosity (

**Jouyban, A.**2005a), solvatochromic parameter (

*et al.***Jouyban, A.**2006), density (

*et al.***Jouyban, A.**2005b), speed of sound (

*et al.***Hasan, M.**2006;

*et al.***Kadam, U.B.**2006) and more recently molar volumes (

*et al.***Cristancho, D.M.**2011;

*et al.***Delgado, D.R.**2011;

*et al.***Rodríguez, G.A.**2011). The model uses the physicochemical properties of the mono-solvents as input data and a number of curve-fitting parameters representing the effects of solvent-solvent interactions in the solution. It is basically derived for representing the solvent effects on the solubility of non-polar solutes in nearly ideal binary solvent mixtures at isothermal conditions by

*et al.***Acree Jr., W.E.**(1992); and then its applications were extended to the solubility of polar solutes in water + cosolvent mixtures at isothermal conditions (

**Jouyban-Gharamaleki, A.**1998). Further extensions were made to represent the solvent composition and temperature effects on the solubility of drugs (

*et al.***Jouyban, A.**1998); and also some other parameters such as acid dissociation constants (

*et al.***Jouyban, A.**2005c), electrophoretic mobility in capillary electrophoresis (

*et al.***Jouyban-Gharamaleki, A.**2000) and retention factors in high performance liquid chromatography (

*et al.***Jouyban, A.**2005d) have been calculated perfectly.

*et al.*The model for representing the solvent composition and temperature effects on the density of solvent mixtures is:

where ρ_{m,T}, ρ_{1,T}, ρ_{2,T} are densities of mixed solvent, solvents 1 (glycerol formal) and 2 (ethanol) at different temperatures (*T*), respectively. The x_{1}, x_{2} are mole fractions of glycerol formal and ethanol, respectively. The *J _{i}* terms are coefficients of the model computed by using a no intercept regression analysis of:

The following equation was obtained for density correlation of mixtures of glycerol formal and ethanol at different temperatures after excluding non-significant model constants:

The calculated density values using Equation (11) are presented in Table 1. The mean relative deviation (MRD) between experimental and calculated data was calculated as an accuracy criterion using:

and was 0.03 ± 0.03 % for Equation (11). The *N* in Equation (12) is the number of data points in the data set.

An adapted version of Equation (11) was used to represent the effects of solvent composition and temperature on the molar volume of mixed solvents in recent works (**Cristancho, D.M. et al.** 2011;

**Delgado, D.R.**2011;

*et al.***Rodríguez, G.A.**2011). A similar model could be trained to represent the molar volume data of glycerol formal + ethanol data at various temperatures as:

*et al.*

The calculated molar volume values are presented in Table 2. The model fits very well to the experimental data and the MRD was 0.17 ± 0.13 %. In addition to the fitness capability of the model, it could be used to predict the molar volume data using the trained version of the model employing the minimum number of experimental data points. For this purpose, a minimum number of experimental data (11 odd data points of set 278.15 K and 11 odd data points of set 313.15 K) have been used for density and molar volume data and the following equations obtained:

The MRD values of Equation (14) and (15) for predicted densities and molar volumes were 0.03 ± 0.03 % and 0.15 ± 0.12 % (N = 150). Figures 8 and 9 show the predicted values versus experimental values of density and molar volume, respectively. High regression coefficients (R^{2} = 1.0000 (i.e. > 0.9999) for density and R^{2} = 0.9997 for molar volume) suggest the predictability and applicability of the Jouyban- Acree model to predict the density and molar volume data using a minimum number of experimental data.

** Conclusions **

This work reports experimental information about the volumetric behavior of the glycerol formal + ethanol at eight temperatures commonly found in technological conditions. Thus, this work complements the information reported in the literature about volumetric properties of the possible binary mixtures conformed by glycerol formal, ethanol, propylene glycol, and water (**Jiménez, J. et al.** 2004;

**Jiménez, J. & Martínez, F.**, 2005, 2006;

**Delgado, D.R.**2011;

*et al.***Rodríguez, G.A.**2011). It can be concluded that this binary system shows non ideal behavior exhibiting negative deviations. These observations demonstrate that it is necessary to characterize systematically representative binary systems in order to have complete experimental information about the physical and chemical properties useful in the understanding of liquid pharmaceutical systems. Also, the Jouyban-Acree model can predict density and molar volume of solution in mixtures of solvents at different temperatures using minimum number of experimental data points with acceptable accuracy in comparison with experimental data. Furthermore, the reported experimental values could be used to challenge other theoretical methods developed for estimation of thermophysical properties in mixtures (

*et al.***Prausnitz, J.M.**1986).

*et al.* **Acknowledgments**

We thank the DIB of the Universidad Nacional de Colombia (UNC) by the financial support in addition to the Department of Pharmacy of UNC for facilitating the equipment and laboratories used in this investigation.

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Recibido: junio 22 de 2011. Aceptado para su publicación: agosto 30 de 2011.