Solubility of sulfacetamide in aqueous propylene glycol mixtures: Measurement, correlation, dissolution thermodynamics, preferential solvation and solute volumetric contribution at saturation

MOLLIQ-111889; No of Pages 10 Journal of Molecular Liquids xxx (xxxx) xxx

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Solubility of sulfacetamide in aqueous propylene glycol mixtures: Measurement, correlation, dissolution thermodynamics, preferential solvation and solute volumetric contribution at saturation Irmis P. Osorio a, Fleming Martínez a,⁎, Daniel R. Delgado b, Abolghasem Jouyban c,d, William E. Acree Jr

e

a Grupo de Investigaciones Farmacéutico-Fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de Colombia, Sede Bogotá, Carrera 30 No. 45-03, Bogotá D.C., Colombia b Programa de Ingeniería Industrial, Facultad de Ingeniería, Universidad Cooperativa de Colombia, Neiva, Colombia c Pharmaceutical Analysis Research Center and Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz 51664, Iran d Kimia Idea Pardaz Azarbayjan (KIPA) Science Based Company, Tabriz University of Medical Sciences, Tabriz 51664, Iran e Department of Chemistry, University of North Texas, Denton, TX 76203-5070, USA

a r t i c l e

i n f o

Article history: Received 12 August 2019 Received in revised form 18 September 2019 Accepted 8 October 2019 Available online xxxx Keywords: Sulfacetamide Propylene glycol + water mixtures Solubility Jouyban-Acree model Solution thermodynamics Preferential solvation Apparent specific volume

a b s t r a c t The equilibrium solubility at temperatures from (278.15 to 318.15) K, dissolution thermodynamics, preferential solvation, and apparent specific volume at saturation of sulfacetamide (SCM) in {propylene glycol (PG) (1) + water (2)} mixtures is reported. Mole fraction solubility of SCM (x3) increases when temperature arises and also increases with the PG proportion arising. Solubility behavior was adequately correlated and/or predicted by the Jouyban-Acree and Jouyban-Acree-van't Hoff models and the obtained mean percentage deviations (MPD) are varied between 6.5 and 11.5%. Apparent thermodynamic analysis of dissolution and mixing was performed in all the mixtures and neat solvents. Based on the inverse Kirkwood-Buff integrals (IKBI) is observed that SCM is preferentially solvated by water molecules in water-rich mixtures but preferentially solvated by PG in the other mixtures. Further, the apparent specific volumes of SCM at saturation were also calculated. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Sulfacetamide (SCM, N-Acetyl-4-aminobenzenesulfonamide, molar mass 214.24 g mol−1, CAS number 144-80-9) is a sulfonamide drug widely used to treat ophthalmic and skin infections. In this way, SCM is commonly available as eye-drop solutions alone or in combination with other drugs [1–3]. This sulfonamide is a white crystalline powder exhibiting two pKa values in neat water with ionic strength 0.15 mol dm−3: 1.94 and 5.26 [4]. From an empirical point of view, this drug is considered as slightly soluble in water [4,5]. Its solubility in neat water has been reported varying from (11.0 to 14.8) g dm −3 at human body temperature (37.0 °C) [6]. Nevertheless, despite its continuous use in therapeutics, its equilibrium solubility in aqueous-cosolvent mixtures has only been reported in {ethanol (1) + water (2)} mixtures from (278.15 to 313.15) K [7]. Cosolvency has widely been used in pharmaceutical sciences as a powerful drug solubilizing technique long time ago. Moreover, the mechanisms involved in the increasing of the drug solubility have ⁎ Corresponding author. E-mail address: [email protected] (F. Martínez).

been approached from deep classical thermodynamic studies, including the analysis of the preferential solvation of the solute by the components of the mixtures [8–12]. As widely described in the literature, the experimental drug behavior in aqueous-cosolvent mixtures is commonly evaluated as a function of both, the mixtures-composition and temperature. These studies are intended to improve the purification of raw materials by re-crystallization, drug preformulation studies, and also the understanding of the molecular mechanisms involved in the physical and chemical stabilization of liquid medicines [13]. Therefore, the equilibrium solubility of active pharmaceutical ingredients is a crucial property to be considered in all the duties associated to pharmaceutical dosage forms design because it could affect several biopharmaceutical and pharmacokinetic properties [14]. Moreover, the preferential solvation of the drug by the solvent components of the mixtures provides a powerful tool in the understanding of the molecular interactions involved thorough the dissolution processes [11,12]. On the other hand, although several theoretical and semiempirical models have been reported to predict drug solubilities in aqueous cosolvent mixtures, the availability of experimental solubility data is still crucial for the pharmaceutical and chemical scientists [10].

https://doi.org/10.1016/j.molliq.2019.111889 0167-7322/© 2019 Elsevier B.V. All rights reserved.

Please cite this article as: I.P. Osorio, F. Martínez, D.R. Delgado, et al., Solubility of sulfacetamide in aqueous propylene glycol mixtures: Measurement, correlation, dissolut..., Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111889

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Because the solubility of sulfonamides in neat water is very low [15], several {cosolvent (1) + water (2)} mixtures have been evaluated in order to increase the solubility of these drugs as has been recently exemplified in the literature [7]. Several of these reported investigations have also been performed to approach the understanding the role of the cosolvents on the molecular mechanisms involved in the sulfonamides dissolution processes. Regarding SCM, only aqueous-ethanolic mixtures have been studied as already indicated [7]. For the reasons set out above, the main objectives of this work are as follows: i) to expand the database on experimental solubility of sulfonamides by determining the solubility of SCM in {propylene glycol (PG) (1) + water (2)} mixtures at five temperatures from 278.15 to 318.15 K, ii) to correlate the solubility data by using several wellknown correlation models, iii) to evaluate the effect of the cosolvent composition on the solubility, dissolution and mixing thermodynamics, and preferential solvation of this drug in these binary mixtures, and iv) to calculate the apparent specific volumes of SCM at saturation in all the systems under study. It is noteworthy that PG, after ethanol, is the most important cosolvent as has been described in the literature [8–11,16]. Moreover, aqueous PG mixtures have been investigated as solubilizing tool for several other sulfonamides [17–20]. In this way, this research is a continuation of our previous one about the solubility study of SCM in {ethanol (1) + water (2)} mixtures [7]. 2. Experimental 2.1. Reagents In this research, SCM (Fagron Iberica, Spain; the component 3; purity at least 0.990 in mass fraction), PG (Dow Chemical Co., USA; the solvent component 1; purity at least 0.995 in mass fraction) and distilled water with conductivity lower than 2.0 μS cm−1 (the solvent component 2) were used. SCM and PG were used without further purification. 2.2. Preparation of solvent mixtures All {PG (1) + water (2)} solvent mixtures were prepared by mass in quantities of 40.00 g, using an analytical balance with sensitivity ± 0.1 mg (Ohaus Pioneer TM PA214, USA). The mass fractions of PG (1), w1, of the nine mixtures prepared varied by 0.10 from 0.10 to 0.90. 2.3. Solubility determinations An excess amount of SCM was added to approximately 40.00 g of each binary {PG (1) + water (2)} solvent mixture or the neat solvents, i.e. PG or water, in stoppered dark glass flasks. The flasks containing the solid-liquid mixtures were placed in an ultrasonic bath (Elma® E 60 H Elmasonic, Germany) during 15 min and later were transferred to a thermostatic bath (Neslab RTE 10 Digital One Thermo Electron Company, USA) maintained at 318.15 (±0.05) K for at least three days with sporadic vortex agitation at 2500 rpm (Heidolph REAX, Germany) to reach the saturation equilibrium. After this time, the supernatant solutions were filtered at isothermal conditions (Millipore Corp. Swinnex®-13, USA) to ensure that they were free of particulate matter before sampling for composition analysis. SCM concentrations were determined after appropriate gravimetric dilution with pure water by measuring the UV light absorbance at the wavelength of maximum absorbance, 262 nm (UV/ VIS BioMate 3 Thermo Electron Company spectrophotometer, USA), followed by interpolation from a previously constructed UV spectrophotometric gravimetric calibration curve. Later, the thermostat temperature was adjusted at 308.15 K during two days allowing the respective SCM precipitation. Composition analysis was performed as indicated above. After this, the temperature was sequentially diminished varying by 10.0 K following the same procedures to reach 278.15 K.

Density of the saturated solutions was determined by using a digital density meter (DMA 45 Anton Paar, Austria) connected to the same re-circulating thermostatic bath (Neslab RTE 10 Digital One Thermo Electron Company, USA) at every temperature. Densities were determined for transforming mole fractions into molarity concentrations (mol dm−3) and also used to calculate the volumetric contribution of SCM to the saturated solutions. 2.4. Calculations and statistical analyses All the calculations associated with solubility correlation, thermodynamic analysis and preferential solvation estimation, were performed with different utilities of MS Excel®. 3. Results and discussion 3.1. Equilibrium solubility of SCM in aqueous-cosolvent mixtures Tables 1 and 2 report the experimental solubility of SCM expressed in mole fraction and molarity at (278.15 to 318.15) K. Mean relative uncertainty in solubility determinations was 2.3%. As observed x 3 increases when temperature arises and also increases with the PG proportion increasing reaching maximum values in neat PG at almost all temperatures, except in molarity scale at 313.15 K, where the maximum solubility was obtained in the mixture w1 = 0.90 (Table 2). At 298.15 K the mole fraction solubility of this drug increased almost 50 times when passing from neat water (2) to neat PG (1), where the maximum solubility is observed (Table 1). Our solubility values in neat water are in very good agreement with those reported earlier in buffer of pH 3.60 (isoelectric point of SCM), at temperatures (298.15 and 308.15) K [2], as well as with those reported previously in neat water at (278.15, 288.15, 298.15 and 308.15) K [7]. Because no solubility values of SCM has been reported in {PG (1) + water (2)} water mixtures no more comparisons are possible. To analyze the effect of the mixtures polarity on the SCM mole fraction solubility, Fig. 1 shows the solubility profile in {PG (1) + water (2)} mixtures, as a function of the Hildebrand solubility parameters of the mixtures free of drug (δ1+2) at all temperatures. As described earlier, the δ1+2 values were calculated as: δ1+2 = f1δ1 + (1 – f1)δ2 [21,22], from the Hildebrand solubility parameter of the neat solvents (δ1 = 30.2 MPa1/2 for PG (1) and δ2 = 47.8 MPa1/2 for water (2) [23]) as reported at 298.15 K and the volume fraction (f) of each component in the mixture. Normally, f is calculated assuming additive volumes [21,22]. As indicated above, the maximal solubilities are observed in neat PG.

Table 1 Experimental mole fraction solubility (1000 x3) values of sulfacetamide (3) in {propylene glycol (1) + water (2)} mixtures at different temperatures. w1a

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Ideal

T/Kb 278.15

288.15

298.15

308.15

318.15

0.393 0.620 0.832 1.18 1.95 3.24 5.32 8.15 11.80 17.15 27.57 20.80

0.514 0.795 1.15 1.63 2.60 4.23 6.76 10.28 14.53 20.37 31.16 27.46

0.717 1.17 1.72 2.46 3.76 5.95 9.25 13.51 18.47 25.20 35.82 35.91

1.001 1.68 2.37 3.56 5.59 8.66 12.95 18.07 23.73 30.88 40.77 46.55

1.47 2.55 3.82 5.51 8.37 12.64 18.22 24.79 33.11 41.18 49.06 59.83

a w1 is mass fraction of propylene glycol (1) in the {propylene glycol (1) + water (2)} mixtures in the absence of sulfacetamide (3). Mean uncertainty in w1, u(w1) = 0.0005. b Mean relative uncertainty in x3, ur(x3) = 0.023.

Please cite this article as: I.P. Osorio, F. Martínez, D.R. Delgado, et al., Solubility of sulfacetamide in aqueous propylene glycol mixtures: Measurement, correlation, dissolut..., Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111889

I.P. Osorio et al. / Journal of Molecular Liquids xxx (xxxx) xxx Table 2 Experimental molar solubility (100C, mol dm−3) values of sulfacetamide (3) in {propylene glycol (1) + water (2)} mixtures at different temperatures. w1a

T/Kb 278.15

288.15

298.15

308.15

318.15

2.17

2.84

3.95

5.48

7.99

3.19

4.08

5.98

8.52

12.81

3.96

5.43

8.10

11.05

17.60

5.15

7.08

10.58

15.15

23.10

7.74

10.23

14.65

21.43

31.44

11.48

14.81

20.57

29.39

41.88

16.48

20.70

27.89

38.26

52.46

21.64

26.95

34.85

45.62

60.99

26.12

31.75

39.71

50.04

67.82

30.46

35.71

43.52

52.39

68.26

36.92

41.26

46.85

52.68

62.46

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 a w1 is mass fraction of propylene glycol (1) in the {propylene glycol (1) + water (2)} mixtures in the absence of sulfacetamide (3). Mean uncertainty in w1, u(w1) = 0.0005. b Mean relative uncertainty in C, ur(C) = 0.023.

Regarding {ethanol (1) + water (2)} mixtures, the maximum solubility was found in the mixture of δ1+2 = 30.0 MPa1/2 instead of neat ethanol. According to the literature [1–3], solutes reach their maximum solubility in solvents with the same solubility parameter, which allows supposing a δ3 value of SCM of 30.0 MPa1/2, which is slightly different of the one estimated from the Fedors method, i.e. δ3 = 28.4 MPa1/2 [7,24]. On the other hand, Table 1 also shows the ideal solubility values of SCM from (278.15 to 318.15) K, which were calculated as described in our previous research [7]. Ideal solubility of SCM is higher than the experimental solubility in neat water and all the mixtures at all the temperatures studied. In neat PG the behavior is more interesting because ideal solubility is lower than real solubility at (278.15 and 288.15) K, they are almost the same at 298.15 K, and ideal solubility is higher than real solubility at (308.15 and 318.15) K.

3

3.2. Activity coefficients of SCM Table 3 shows the SCM (3) activity coefficients γ3, which were calculated as the quotient x3-id/x3 from the respective solubility values presented in Table 1. It is remarkable that these activity coefficients are defined on asymmetrical basis. At 298.15 K γ3 values vary from 50.1 in neat water to 1.00 in neat PG. In neat water and mixtures of 0.00 ≤ w1 ≤ 0.70, γ3 values diminish with the temperature increasing, whereas, in mixtures of 0.80–0.90 and neat PG γ3 values diminish with the temperature increasing. It is interesting to note that γ3 values in neat PG at (278.15 and 288.15) K is lower than unit because real solubilities are higher than ideal solubilities (Table 1). As described earlier, from γ3 values a rough estimate of solutesolvent intermolecular interactions can be made by considering that ln γ3 = (e11 + e33 – 2e13)V3φ21/RT, where the subscript 1 stands for the solvent, which in the present case it corresponds to the neat solvents or the {PG (1) + water (2)} mixtures, e11, e33 and e13 represent the solvent-solvent, solute-solute and solvent-solute interaction energies, respectively; V3 is the molar volume of the supercooled liquid solute, whereas, φ1 is the volume fraction of the solvent mixture [25]. As has been made earlier, for relatively low x3 values, V3φ21/RT may be considered as constant regardless the saturated system. Thus, γ3 would depend mainly on e11, e33 and e13 [25]. As well known, the e11 and e33 terms are unfavorable for solubility and dissolution, whereas the e13 term favors the dissolution process. The contribution of the e33 term could be considered as constant in all the mixtures as indicated earlier. Thus, in a qualitative way the following analysis could be made based on the energetic quantities described: The term e 11 is highest in neat water (2) (δ = 47.8 MPa 1/2 ) and lowest in PG (1) (δ = 30.2 MPa1/2) [23]. Pure water (2) and water-rich mixtures having high γ3 values (near 50) would imply high e11 and low e13 values, whereas, in PG-rich mixtures (exhibiting γ 3 values near 2), the e11 values are relatively low and the e13 values would relatively be high. Accordingly, the SCM (3) solvation would be higher in PG-rich mixtures implying higher solubilities regarding neat water.

Table 3 Activity coefficients (γ3) of sulfacetamide (3) in {propylene glycol (1) + water (2)} mixtures at different temperatures. w1a

T/Kb 278.15

288.15

298.15

308.15

318.15

52.93

53.39

50.06

46.52

40.72

33.54

34.55

30.69

27.71

23.43

25.01

23.97

20.87

19.67

15.65

17.65

16.86

14.61

13.09

10.85

10.66

10.56

9.54

8.32

7.15

6.41

6.50

6.03

5.38

4.73

3.91

4.06

3.88

3.59

3.28

2.55

2.67

2.66

2.58

2.41

1.76

1.89

1.94

1.96

1.81

1.21

1.35

1.42

1.51

1.45

0.75

0.88

1.00

1.14

1.22

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Fig. 1. Experimental solubility of sulfacetamide expressed in mole fraction (x3) against the solubility parameter of the {propylene glycol (1) + water (2)} mixtures (δ1+2) at different temperatures. ○: 278.15 K, ●: 288.15 K, ■: 298.15 K, ▲: 308.15 K, and ♦: 318.15 K. Lines correspond the best regular polynomials correlating mole fraction solubility with solubility parameter.

1.00 a w1 is mass fraction of propylene glycol (1) in the {propylene glycol (1) + water (2)} mixtures in the absence of sulfacetamide (3). Mean uncertainty in w1, u(w1) = 0.0005. b Mean relative uncertainty in γ3, ur(γ3) = 0.028.

Please cite this article as: I.P. Osorio, F. Martínez, D.R. Delgado, et al., Solubility of sulfacetamide in aqueous propylene glycol mixtures: Measurement, correlation, dissolut..., Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111889

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3.3. The cosolvency models applied to SCM solubility Solubility measurement is a time consuming and costly process and any strategy to estimate the solubility of drugs in mixed solvent systems is highly in demand in the pharmaceutical and chemical industries [10]. To provide an estimation tool, a number of mathematical models have been presented so far; including the log-linear model of Yalkowsky [26], the combined nearly ideal binary solvent/Redlich-Kister (CNIBS/R-K) [27], modified CNIBS/RK (MCNIBS/R-K) [28], general single model (GSM) [29], modified Wilson [30] and Machatha et al. [31] models. Some of these models have been reviewed in previous papers [32,33] and challenged to correlate the solubility of several drugs [32]. All above mentioned models correlate the drug solubility with respect to solvent composition, however, in practical applications solvent composition and temperature changes are employed. To cover this industrial requirement, the Jouyban-Acree model was derived from the CNIBS/ R-K model [34,35]. The model is expressed as: ln x3ð1þ2Þ;T ¼ w1 ln x3ð1Þ;T þ w2 ln x3ð2Þ;T þ

2
w w  X 1 2 J i ðw1 −w2 Þi ð1Þ T i¼0

where x3(1+2), T , x3(1), T and x 3(2), T are solute solubility in the mixed and mono-solvents 1 and 2 at temperature T, w1 and w2 denote the mass fractions of PG (solvent 1) and water (solvent 2) in the absence of the solute and Ji terms are the model constants computed using a no intercept least square analysis [36]. The generated solubility of SCM in {PG (1) + water (2)} mixtures was fitted to Eq. (1) and the obtained trained model is:
w w  1 2 T  ½191:733 þ 139:791ðw1 −w2 Þ

ln x3ð1þ2Þ;T ¼ w1 ln x3ð1Þ;T þ w2 ln x3ð2Þ;T þ

ð2Þ

The correlation coefficient of Eq. (2) was 0.683, F value was 23, and the correlation and the model constants were significant with p b .001. Eq. (2) is valid for calculating the solubility of SCM in {PG (1) + water (2)} mixtures at various temperatures by employing the solubility data of SCM in neat PG and neat water at each temperature of interest. The obtained mean percentage deviation (MPD) for the back-calculated solubility data of SCM using Eq. (2) was 6.8% (N = 55). The MPD values are calculated using:    cal  100 X x3−ð1þ2Þ −x3−ð1þ2Þ  MPD ¼ N x3−ð1þ2Þ

ð3Þ

this could restrict its practical applications in the pharmaceutical industry. To cover this point, the model was combined with the van't Hoff model as [36]:     D2 D4 ln x3ð1þ2Þ;T ¼ w1 D1 þ þ w2 D3 þ T T 2
w w  X 1 2 J i ðw1 −w2 Þi þ T i¼0

ð5Þ

where D 1 -D 4 are the model constants for van't Hoff equation for solubility of SCM in the mono-solvents. The trained model for SCM data in {PG (1) + water (2)} mixtures at various temperatures is:     1882:472 3575:592 þ w2 4:837− lnx3ð1þ2Þ;T ¼ w1 2:989− T T
w w  1 2 þ ½187:281 þ 191:750ðw1 −w2 Þ T

ð6Þ

which correlates the experimental data with the MPD of 6.5% (N = 55). The corresponding MPD for predicted data after training the model using 7 experimental data points (solubility data in neat water and neat PG at 278.15 and 318.15 K, and the solubility data in w 1 = 0.30, w 1 = 0.50 and w 1 = 0.70 at 298.15 K) is 11.5% (N = 48 (number of predicted data points) = 55 (total solubility data points) –7 (training data points)). Using an accurate cosolvency model after training employing the minimum number of experimental data points is the best practical strategy for industrial applications of the variations of the solubility of a drug in solvent mixtures at various temperatures as has been shown in a recent work [33]. As shown in this work, using just seven experimental data points collected using the proposed pattern enables one to predict the solubility of the drug with the expected prediction error of ~12% which is quite reasonable when compared with ~10% of experimental differences between some solubility data reported for a given drug in similar conditions by different research groups [10]. 3.4. Apparent thermodynamic quantities of dissolution of SCM Apparent standard enthalpy change of dissolution is obtained from the Eq. (7) by using the mean harmonic temperature (Thm) [calculated P as: T hm ¼ n= ni¼1 ð1=TÞ], where n is the number of temperatures studied [37]. In this case, at five temperatures from (278.15 to 318.15) K, the Thm value is 297.5 K. As example, van't Hoff plot shown as Fig. 2 depicts the behavior of SCM solubility in the mixtures w1 = 0.20, 0.40 and

where N is the number of experimental data points. To evaluate the capability of the Jouyban-Acree model for prediction of SCM solubility in the other mass fractions of PG and temperatures, the training by using the minimum number of experimental data was performed. In this respect, the minimum number of experimental solubility data of w1 = 0.30, w1 = 0.50 and w1 = 0.70 at 298.15 K and the solubility data in the mono-solvents at each temperature were selected. Employing the mentioned data points, the following equation was generated:
w w  1 2 T  ½185:766 þ 248:781ðw1 −w2 Þ

ln x3ð1þ2Þ;T ¼ w1 lnx3ð1Þ;T þ w2 lnx3ð2Þ;T þ

ð4Þ

The above equation was applied to predict the remaining data and the obtained MPD was 11.2% (N = 42) which means that the Eq. (4) can predict the solubility data of SCM at other mass fractions of PG and temperatures with acceptable accuracy. The Jouyban-Acree model (Eq. (1)) requires the solubility of the drug in the neat mono-solvents at each temperature of interest and

Fig. 2. Van't Hoff plot of the solubility of sulfacetamide in some {propylene glycol (1) + water (2)} mixtures. ●: w1 = 0.20, ■: w1 = 0.40, and ▲: w1 = 0.60. Lines correspond the best regular polynomials correlating logarithmic mole fraction solubility with normalized reciprocal absolute temperature.

Please cite this article as: I.P. Osorio, F. Martínez, D.R. Delgado, et al., Solubility of sulfacetamide in aqueous propylene glycol mixtures: Measurement, correlation, dissolut..., Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111889

I.P. Osorio et al. / Journal of Molecular Liquids xxx (xxxx) xxx

jTΔsoln S °j jΔsoln H °j þ jTΔsoln S °j

5

0.60. It is noteworthy that parabolic regressions were used obtaining determination coefficients (r2) higher than 0.997 in all studied mixtures compositions.

ζ TS ¼



As shown in Table 4, in all cases the main contributor to the positive standard molar Gibbs energy of dissolution of SCM (3) in {PG (1) + water (2)} mixtures is the positive enthalpy (ζH N 0.66), which demonstrates the energetic predominance on the dissolution processes of SCM in {PG (1) + water (2)}.

 ∂ ln x3 Δ H° ¼ − soln R ∂ð1=T−1=T hm Þ P

ð7Þ

The apparent standard Gibbs energy change for the dissolution process (ΔsolnG°), considering the approach proposed by Krug et al. [37], is calculated at Thm = 297.5 K by means of: Δsoln G ° ¼ −R  T hm  intercept

ð8Þ

in which, the intercept used is the one obtained by treatment of ln x3 as a function of (1/T – 1/Thm), as shown in Fig. 2. Finally, the standard apparent entropic change for the dissolution process (ΔsolnS°) is obtained from the respective ΔsolnH° and ΔsolnG° values at Thm = 297.5 K by using [38]: Δsoln S0 ¼

ðΔsoln H °−Δsoln G °Þ T hm

ð9Þ

Table 4 presents the standard apparent molar thermodynamic functions for SCM (3) dissolution in all the {PG (1) + water (2)} mixtures at Thm = 297.5 K, including those for the neat solvents and the ideal dissolution process. It is noteworthy that the thermodynamic quantities reported are just apparent because no calorimetric dissolution enthalpies were measured directly, and moreover, mole fraction solubilities instead of activities were used in all these calculations. Moreover, the SCM mole fraction concentrations at saturation were considered equivalent to the respective activities. The standard Gibbs energies of dissolution are positive in every case as also are the apparent enthalpy and entropy of dissolution. Therefore the process is always endothermic and entropy-driven as usually observed in similar systems. The ΔsolnG° values decrease continuously from neat water to neat PG. The Δ solnH° and Δ soln S° values increase from neat water to the mixture of w 1 = 0.30 and later they decrease continuously to reach the minimum value in neat PG. The relative contributions by enthalpy (ζ H ) and entropy (ζ TS ) toward the solution process are given by Eqs. (10) and (11) [39]. ζH ¼

jΔsoln H °j jΔsoln H °j þ jTΔsoln S °j

ð10Þ

Table 4 Apparent thermodynamic parameters for dissolution behavior of sulfacetamide (3) in {propylene glycol (1) + water (2)} mixtures at Thm = 297.5 K. w1a

ΔsolnG°/ kJ mol–1b

ΔsolnH°/ kJ mol–1b

ΔsolnS°/ J mol−1 K–1b

TΔsolnS°/ kJ mol–1b

ζH

ζTS

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Ideal

17.99 16.81 15.89 14.98 13.88 12.74 11.64 10.70 9.93 9.17 8.28 8.25

24.51 26.59 28.00 28.66 27.30 25.52 23.11 20.70 19.00 16.12 10.55 19.43

21.94 32.89 40.69 45.98 45.11 42.97 38.55 33.62 30.46 23.36 7.65 37.58

6.53 9.78 12.11 13.68 13.42 12.78 11.47 10.00 9.06 6.95 2.28 11.18

0.790 0.731 0.698 0.677 0.670 0.666 0.668 0.674 0.677 0.699 0.823 0.635

0.210 0.269 0.302 0.323 0.330 0.334 0.332 0.326 0.323 0.301 0.177 0.365

a w1 is mass fraction of propylene glycol (1) in the {propylene glycol (1) + water (2)} mixtures in the absence of sulfacetamide (3). Mean uncertainty in w1, u(w1) = 0.0005. b Mean relative uncertainties in thermodynamic quantities were as follows: ur (ΔsolnG°) = 0.025; ur(ΔsolnH°) = 0.046; ur(ΔsolnS°) = 0.051; ur(TΔsolnS°) = 0.051.

ð11Þ

3.5. Apparent thermodynamic quantities of mixing of SCM The overall dissolution process may be represented by the following hypothetic stages: SoluteðSolidÞ at T→SoluteðSolidÞ at T fus →SoluteðLiquidÞ at T fus →SoluteðLiquidÞ at T→SoluteðSolutionÞ at T

where the hypothetical dissolution stages are the heating and fusion of SCM, the cooling of the liquid drug to the considered temperature (Thm = 297.5 K), and the subsequent mixing of both the hypothetical super-cooled liquid SCM and the solvent mixture at this temperature [40]. This treatment allows the calculation of the individual thermodynamic contributions to the overall dissolution process by means of Eqs. (12) and (13), respectively. Δsoln H ° ¼ Δfus H 297:5 þ Δmix H °

ð12Þ

Δsoln S ° ¼ Δfus S297:5 þ Δmix S °

ð13Þ

where ΔfusH297.5 and ΔfusS297.5 represent the thermodynamic functions of fusion of SCM (3) and its cooling at Thm = 297.5 K. However, the ΔsolnH°-id and ΔsolnS°-id values for the ideal dissolution process, reported in Table 4, were used instead of those calculated by Eqs. (12) and (13) because some reasons earlier described [41]. The same procedure was followed with SCM in {ethanol (1) + water (2)} mixtures [7]. Fig. 3 summarizes the thermodynamic quantities of mixing of super-cooled liquid SCM (3) with all the cosolvent mixtures and neat solvents at Thm = 297.5 K. Gibbs energy of mixing is positive in all cases because the experimental solubilities are lower than ideal solubility, except in neat PG where both real and ideal solubilities are almost equal, and thus ΔmixG° = 0.0 kJ mol−1. The contributions by ideal dissolution (ΔsolnH°-id and ΔsolnS°-id) to enthalpies and entropies of real dissolution of SCM (3) are positive as shown in Table 4, but the contributions of the mixing process quantities toward the overall dissolution are variable. Thus, ΔmixH° are positive in compositions with 0.00 ≤ w1 ≤ 0.70 but negative in mixtures of w1 = 0.80–0.90 and in neat PG; whereas, the entropy of mixing (ΔmixS°) is positive in compositions 0.20 ≤ w1 ≤ 0.60 but negative in both neat solvents and the mixtures of w1 = 0.10, 0.70–0.90.

Fig. 3. Apparent thermodynamic quantities of mixing of sulfacetamide (3) in {propylene glycol (1) + water (2)} mixtures at Thm = 297.5 K as function of cosolvent mixtures composition. ●: ΔmixG°, ■: ΔmixH°, and ▲: TΔmixS°. Lines are just visual guides.

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The net variation in ΔmixH° values depends on the contribution of several kinds of intermolecular interactions. The enthalpy of cavity formation, required to accommodate the solute molecules, is endothermic because energy in some extent must be supplied against the cohesive forces of the solvent, which decreases the drug solubility. Oppositely, the enthalpy of solvent-solute interaction is exothermic and results mainly from van der Waals and Lewis acid-base interactions [42]. As a special case, the structuring of water molecules around the non-polar groups, like the aromatic ring and methyl group of SCM, contributes to lowering of the net ΔmixH° to small or even negative values in waterrich mixtures [42]. Nevertheless, this fact is not observed in the case of SCM in water nor in water-rich mixtures (Fig. 3). The same behavior was observed for SCM in {ethanol (1) + water (2)} mixtures [7]. The energy of cavity formation should be lower as the proportion of PG (1) increases. This effect is well observed for SCM (3) in all the {PG (1) + water (2)} mixtures, where ΔmixH° diminish continuously as the proportion of cosolvent increases beyond w1 = 0.30. According to the literature [42], in the initial part of the SCM solubility curve the hydrogen bonding of the drug will increase with the PG proportion in water-rich cosolvent mixtures. However, at high PG proportions this kind of interaction may be saturated, becoming a constant contribution. Nevertheless, nonspecific and cavity effects are not saturated and vary with the PG proportion in PG-rich mixtures. Moreover, solute-solvent interactions should be strong in PG-rich mixtures as well as in neat PG because the negative values of ΔmixH° and ΔmixS° observed in this mixtures composition region. 3.6. Enthalpy-entropy compensation of SCM A lot of studies demonstrated the presence of non-enthalpy-entropy compensation effects during the drug dissolution in several aqueous cosolvent systems. These studies have been performed to identify the main mechanisms of the cosolvent action on the solubility increasing or decreasing. Thus, weighted graphs of ΔsolnH° vs. ΔsolnG°, at the harmonic mean temperature, allows this kind of analysis [43,44]. This because of the enthalpy-entropic compensation pattern is a thermodynamic consequence of “bonds formation and/or rupture”, being the hydrogen bridge the most important factor in the aqueous dissolutions processes [45]. Thus, the changes in the standard enthalpy of solution, correlate with the changes in the intermolecular forces between the drug and the solvents through hydrogen bonds and van der Waals interactions, so it becomes a quantitative indicator of changes in energy of intermolecular bonds that are generated during the solute-solvent interaction. Regarding the dissolution entropy, it can be interpreted in terms of the rearrangements of the solute and solvent molecules in the dissolution process [46]. In this context, Fig. 4 shows that SCM (3) in {PG (1) + water (2)}

mixtures exhibits a non-linear ΔsolnH° vs. ΔsolnG° trend with two different regions defined by the slope signs. Negative slope is observed in the composition region 0.00 ≤ w1 ≤ 0.30 and positive slope in the 0.30 ≤ w1 ≤ 1.00 interval. Accordingly, in the first case, the driving mechanism for the SCM transfer is the entropy, whereas in the last case, the driving mechanism is the enthalpy. 3.7. Preferential solvation of SCM The preferential solvation parameter of SCM (compound 3) by PG (compound 1) in the {PG (1) + water (2)} mixtures is defined as [47]: δx1;3 ¼ xL1;3 −x1 ¼ −δx2;3

where xL1, 3 is the local mole fraction of PG (1) in the environment near to SCM (3) and x1 is the bulk mole fraction composition of PG (1) in the initial binary solvent in the absence of SCM. If δx1,3 is positive, SCM (3) is preferentially solvated by PG (1), but if this parameter is negative, SCM (3) is preferentially solvated by water (2). Values of δx1,3 are obtainable from the inverse Kirkwood-Buff integrals based on the following equations [11,12]:   x1 x2 G1;3 −G2;3 x1 G1;3 þ x2 G2;3 þ V cor

ð15Þ

G1;3 ¼ RTκ T −V 3 þ x2 V 2 D=Q

ð16Þ

G2;3 ¼ RTκ T −V 3 þ x1 V 1 D=Q

ð17Þ

δx1;3 ¼ With,

V cor




1=3 ¼ 2522:5  r 3 þ 0:1363  xL1;3 V 1 þ xL2;3 V 2 −0:085

ð18Þ

As has been previously described [47,48], in these equations κT is the isothermal compressibility of the {PG (1) + water (2)} mixtures, V 1 and V 2 are the partial molar volumes of the solvents in the mixtures, whereas V 3 is the partial molar volume of SCM in these mixtures. The function D, defined by Eq. (19), is the derivative of the standard molar Gibbs energies of transfer of SCM from neat water (2) to {PG (1) + water (2)} mixtures with respect to the PG proportion in the mixtures. The function Q, defined by Eq. (20), involves the second derivative of the excess molar Gibbs energy of mixing of the two solvents (GExc 1+2) with respect to the water proportion in the mixtures [47,48]. Vcor is the correlation volume and r3 is the molecular radius of SCM calculated by means of Eq. (21) where NAv is the Avogadro's number. D¼

∂Δtr Gο3;2→1þ2 ∂x1

! ð19Þ T;p

2

Q ¼ RT þ x1 x2

r3 ¼

Fig. 4. Enthalpy-entropy compensation plot for the solubility of sulfacetamide (3) in {propylene glycol (1) + water (2)} mixtures at Thm = 297.5 K. The points represent the mass fraction of propylene glycol (1) in the {propylene glycol (1) + water (2)} mixtures in the absence of sulfacetamide (3). Lines are just visual guides.

ð14Þ

∂ GExc 1þ2 ∂x22

3  1021 V 3 4πNAv

! ð20Þ T;p

!1=3 ð21Þ

Definitive correlation volume requires iteration because it depends on the local mole fractions of solvents around the solute. This iteration is performed by replacing δx1,3 and Vcor in the Eqs. (14), (15) and (18) to recalculate xL1, 3 until a non-variant value of Vcor is obtained. Fig. 5 shows the Gibbs energy of transfer behavior of SCM (3) from neat water (2) to {PG (1) + water (2)} mixtures at 298.15 K, as function of the mixtures composition, which is expressed in mole fraction of cosolvent in the absence of solute, as required in Eq. (19). These values

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Table 5 Some properties associated to preferential solvation of sulfacetamide (3) in {propylene glycol (1) + water (2)} mixtures at 298.15 K. x1 a

Vcor/ cm3 mol−1

100 δx1,3

D/ kJ mol−1

G1,3/ cm3 mol−1

G2,3/ cm3 mol−1

−38.52

−414.1

−133.0

689

0.00

−31.68

−353.3

−178.0

726

−1.54

−25.81

−302.8

−207.1

778

−1.53

−20.82

−261.7

−223.3

837

−0.81

−16.64

−229.1

−229.6

895

0.01

−13.21

−203.7

−229.0

951

0.65

−10.44

−184.4

−223.9

1003

1.05

−8.27

−170.2

−216.6

1053

1.24

−6.62

−160.0

−209.1

1101

1.29

−5.41

−152.9

−202.5

1147

1.27

−4.58

−148.0

−197.8

1193

1.22

−4.04

−144.7

−195.5

1238

1.17

−3.74

−142.5

−195.6

1283

1.14

−3.58

−140.8

−197.6

1327

1.11

−3.50

−139.5

−200.8

1371

1.06

−3.43

−138.3

−204.0

1414

0.98

−3.28

−137.0

−205.8

1456

0.84

−3.00

−135.7

−204.1

1498

0.64

−2.49

−134.5

−196.4

1538

0.40

−1.70

−133.5

−179.6

1578

0.15

−0.54

−132.9

−149.1

1618

0.00

0.00 0.05 0.10 0.15 0.20 Fig. 5. Gibbs energy of transfer of sulfacetamide (3) from neat water (2) to {propylene glycol (1) + water (2)} mixtures at 298.15 K. Line corresponds to non-linear trend as calculated with Eq. (23).

were calculated from the mole fraction drug solubility data shown in Table 1, by using the following expression: Δtr Gο3;2→1þ2



x2;3 ¼ RT ln x3;1þ2



0.25 0.30 0.35 0.40 0.45

ð22Þ 0.50

ΔtrGο3, 2→1+2 values were correlated according to the fourth degree regular polynomial presented as Eq. (23). The obtained coefficients are as follows: a = −0.13, b = −38.52, c = 73.46, d = −69.05 and e = 24.56, with adjusted r2 = 0.999.

0.55

Δtr Gο3;2→1þ2

0.70

¼ a þ bx1 þ

cx21

þ

3 dx1

þ

ex41

ð23Þ

0.60 0.65

0.75

Thus, D values reported in Table 5 were calculated from the first derivative of the respective polynomial model and solved according to the cosolvent mixtures composition. For these {PG (1) + water (2)} mixtures the Q, RTκT, V 1 and V 2 values were taken from the literature [48]. The V 3 value was assumed here as the one calculated by the Fedors' method reported as 134.1 cm3 mol−1 [7,24]. Based on the negative G1,3 and G2,3 values shown in Table 6, it follows that SCM exhibits good affinity for both solvents, PG (1) and water (2). On the other hand, the SCM radius value (r3) was taken as 0.376 nm [7]. Table 5 and Fig. 6 show that the values of δx1,3 vary non-linearly with the PG (1) proportion in the mixtures. It is important to remark that the mole fraction of cosolvent in absence of solute is used to express the mixtures composition, which is required in IKBI calculations as shown in Eqs. (14) to (20). Addition of PG (1) makes negative the δx1,3 values of SCM (3) from the pure water to the mixture x1 = 0.19. Maximum negative δx1,3 value is obtained in the mixture x1 = 0.05 (−1.54 × 10−2). Possibly the structuring of water molecules around the non-polar groups of this drug (aromatic ring and methyl group), following hydrophobic hydration, contributes to lowering of the net δx1,3 to negative values in these water-rich mixtures. In mixtures with composition 0.19 b x1 b 1.00, the δx1,3 values are positive indicating preferential solvation of SCM (3) by PG (1). The cosolvent action to increase the SCM solubility could be associated to the breaking of the ordered structure of water around the non-polar moieties of SCM, which increases the solvation of this drug. Maximum positive δx1,3 value is observed in x1 = 0.40 (1.29 × 10−2). It is noteworthy that absolute maximum δx1,3 values are higher than 1.00 × 10−2, indicating that they are consequence of real preferential solvation effects rather than merely propagation of uncertainties in the IKBI calculations [49,50]. It is conjecturable that in mixtures 0.19 b x1 b 0.54, SCM is acting as Lewis acid with PG molecules because this cosolvent is more basic than water, as shown by the respective Kamlet-Taft hydrogen bond acceptor parameters, which are β = 0.78 for PG and 0.47 for water [51,52]. Similar behaviors have been observed with other drugs in {PG

0.80 0.85 0.90 0.95 1.00 a x1 is the mole fraction of propylene glycol (1) in the {propylene glycol (1) + water (2)} mixtures free of sulfacetamide (3).

(1) + water (2)} mixtures, like sulfanilamide, sulfapyridine and sulfamethizole [53], ketoprofen [54], acetaminophen [55], daidzein [56], indomethacin [57], some n-alkyl p-substituted-benzoates [58], vanillin [59], nifedipine [60], etoricoxib [61], phenobarbital [62], and lamotrigine, diazepam and clonazepam [63]. On the other hand, it is noteworthy that SCM in {ethanol (1) + water (2)} mixtures exhibits two regions of preferential solvation by water, i.e. in water-rich mixtures (0.00 b x 1 b 0.24) and also in ethanol-rich mixtures (0.54 ≤ x 1 ≤ 1.00) (Fig. 6) [7]. Regarding the last case, it has been proposed that SCM is acting mainly as a Lewis base in front to water, as also described by the Kamlet-Taft hydrogen bond donor parameters of the solvents, which are, α = 1.17 for water and 0.86 for ethanol, respectively [51,64], being water more acidic than ethanol.

3.8. Apparent specific volumes of SCM at saturation The volumetric contribution of drugs and excipients in aqueous cosolvent mixtures is very important from both practical and theoretical viewpoints during design of liquid dosage forms. Thus, a well-considered property of solid pharmaceutical compounds in their saturated solutions

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Table 6 Density of cosolvent mixtures free of drug (ρ1+2), density of saturated solutions (ρ1+2+3) and apparent specific volume of sulfacetamide (3) at saturation (ϕsp V ) in {propylene glycol (1) + water (2)} mixtures at different temperatures. w1a

T/Kb 278.15

288.15

298.15

308.15

318.15

ρ1+2/g cm−1 1.0000 0.9992

0.9970

0.9940

0.9902

1.0082

1.0065

1.0043

1.0007

0.9964

1.0180

1.0154

1.0128

1.0083

1.0033

1.0283

1.0245

1.0213

1.0160

1.0099

1.0379

1.0328

1.0290

1.0227

1.0160

1.0453

1.0391

1.0348

1.0282

1.0207

1.0500

1.0432

1.0388

1.0314

1.0243

1.0519

1.0448

1.0404

1.0335

1.0248

1.0513

1.0441

1.0401

1.0323

1.0244

1.0490

1.0412

1.0375

1.0297

1.0218

1.0445

1.0389

1.0328

1.0251

1.0175

ϕsp V ¼

ρ1+2+3/g cm−1 1.0014 1.0009

0.9995

0.9973

0.9952

1.0103

1.0094

1.0077

1.0057

1.0036

1.0208

1.0191

1.0170

1.0147

1.0128

1.0320

1.0294

1.0264

1.0243

1.0229

1.0430

1.0398

1.0365

1.0342

1.0333

1.0524

1.0484

1.0452

1.0432

1.0430

1.0600

1.0558

1.0529

1.0511

1.0521

1.0655

1.0616

1.0587

1.0570

1.0585

1.0684

1.0645

1.0615

1.0597

1.0616

1.0695

1.0648

1.0620

1.0585

1.0609

1.0700

1.0646

1.0601

1.0560

1.0550

3 −1 ϕsp V /cm g 0.700

0.721

0.707

0.723

0.715

0.687

0.664

0.731

0.726

0.740

0.658

0.672

0.748

0.724

0.746

0.647

0.661

0.759

0.733

0.730

0.667

0.659

0.740

0.733

0.731

0.681

0.680

0.738

0.741

0.736

0.683

0.686

0.736

0.737

0.735

Here, w3 and w1+2 are the mass fractions of SCM and {PG (1) + water (2)} mixture in the saturated solution, respectively. ρ1+2+3 and ρ1+2 are the densities of the saturated solution and the cosolvent mixture free of SCM, respectively. The density values of the {PG (1) + water (2)} mixtures at temperatures from (278.15 to 308.15) K were taken from the literature [67,68], whereas the values at 318.15 K were determined in this research. The density of the cosolvent mixtures free of drug, density of saturated solutions, as well as the apparent specific volumes of SCM, at all temperatures and compositions, are presented in Table 6. Moreover, Fig. 7 allows the visual comparison of densities of the saturated solutions and the respective {PG (1) + water (2)} cosolvent mixtures free of SCM at 298.15 K. As expected, all the saturated solutions exhibit density values higher than those of the cosolvent mixtures free of SCM, indicating that this solute is denser than PG, water and all the respective solvent mixtures. As observed, the density of both the saturated mixtures and the cosolvent mixtures free of SCM initially increase with the PG proportion because the higher density of PG regarding water and the increase in solubility of SCM. Maximal density of {PG (1) + water (2)} mixtures free of SCM is observed in the mixture w1 = 0.70 at all temperatures. This is a consequence of the volume contraction after mixing PG and water as has been discussed earlier [67,68]. On the other hand, maximal density of saturated solutions is observed in the mixture w1 = 0.90 at T = (278.15, 288.15 and 298.15) K but in the mixture w1 = 0.80 at T = (308.15 and 318.15) K. This could be attributed to the increase of the SCM solubility with the PG proportion in the mixtures, as well, as the volume contraction after the mixing of the solvents free of drug. Table 6 shows that ϕsp V values of SCM diminish in several cases as the PG proportion increases in the mixtures. This behavior could be a consequence of the specific solvation effects. On the other hand, with several

0.672

0.679

0.726

0.735

0.724

0.661

0.671

0.720

0.721

0.726

0.654

0.664

0.711

0.722

0.717

0.649

0.683

0.705

0.708

0.707

0.00 0.10 0.20 0.30 0.40 0.50

Fig. 6. δx1,3 values of sulfacetamide (3) in {propylene glycol (1) + water (2)} (●) and {ethanol (1) + water (2)} (○) mixtures at 298.15 K. Lines correspond to non-linear trends as calculated with Eq. (15).

0.60 0.70 0.80

is the apparent specific volume (ϕsp V ), which is calculated by means of Eq. (24) [65,66]:

0.90 1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60

  w3 þ w1þ2 1−ρ1þ2þ3 =ρ1þ2 w3 ρ1þ2þ3

ð24Þ

0.70 0.80 0.90 1.00

Notes to Table 6: a w1 is mass fraction of propylene glycol (1) in the {propylene glycol (1) + water (2)} mixtures in the absence of sulfacetamide (3). Mean uncertainty in w1, u(w1) = 0.0005. b Mean uncertainty in density of cosolvent mixtures free of drug, u(ρ1 −3 [65,66]; mean uncertainty in density of saturated solutions, u(ρ1+2 +2) = 0.0002 g cm −3 ) = 0.0012 g cm ; mean uncertainty in apparent specific volume of sulfacetamide, u +3 3 −1 (ϕsp . V ) = 0.006 cm g

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References

Fig. 7. Density of the saturated solutions of sulfacetamide (3) in {propylene glycol (1) + water (2)} mixtures (●) and density of the {propylene glycol (1) + water (2)} mixtures free of sulfacetamide (3) (■) at 298.15 K. Lines correspond the best regular polynomials correlating densities with the mixtures composition free of drug expressed in mass fraction of cosolvent.

exceptions, the ϕsp V values of SCM increase with the temperature arising as expected because the thermal volume expansion. If all the ϕsp V values of SCM are considered the obtained average value is: 0.706 (±0.031) cm3 g−1 (with RSD = 4.41%), which is slightly higher than the one obtained in {ethanol (1) + water (2)} mixtures, i.e. 0.694 (±0.032) cm3 g−1 (with RSD = 4.55%). It is noteworthy that considering the respective variations, a mean value of 0.70 cm3 g−1 could be used as representative of ϕsp V for SCM in aqueous mixtures of PG and/or ethanol despite the temperature and mixtures composition. As observed, the RDS values are lower than 5.0%, which is normally accepted during the different stages of design and development of liquid pharmaceutical dosage forms. As indicated earlier, similar variations have been reported for several other pharmaceutical compounds including non-electrolytes and some organic salts [65,66,69–74]. As mentioned earlier, these ϕsp V values could help during design and development of liquid medicines because allow estimate approximately the volumetric contribution of every solute to the total volume formulation. 4. Conclusions Equilibrium solubility values and correlating expressions of SCM (3) in {PG (1) + water (2)} mixtures were provided. SCM solubility increases with temperature arising and also with the PG proportion in the mixtures. Measured solubility data were correlated by various cosolvency models. Also, the accuracy of the Jouyban-Acree model was examined by its trained version using a minimum number of seven data points in which the MPD for predicted data points was ~11% (N = 48). Enthalpy-entropy compensation analysis shows that in the composition region 0.00 ≤ w1 ≤ 0.30 the transfer mechanism is the entropy but in the composition region 0.30 ≤ w1 ≤ 0.80 the mechanism is the enthalpy. IKBI calculations demonstrated that SCM is preferentially solvated by water in water-rich mixtures but preferentially solvated by PG in mixtures with composition, 3 −1 0.19 ≤ x 1 ≤ 1.00. Furthermore, a mean ϕ sp V value of 0.706 cm g for SCM was obtained by considering all the {PG (1) + water (2)} mixtures and all the temperatures. Acknowledgements We thank the Department of Pharmacy of the National University of Colombia for supplying reagents and facilitating the equipment and laboratories used. Declaration of competing interest The authors claim that there is no conflict of interest.

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Please cite this article as: I.P. Osorio, F. Martínez, D.R. Delgado, et al., Solubility of sulfacetamide in aqueous propylene glycol mixtures: Measurement, correlation, dissolut..., Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111889