Preferential solvation of indomethacin in 1,4 dioxane + water mixtures according to the inverse Kirkwood–Buff integrals method

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(1)Physics and Chemistry of Liquids An International Journal. ISSN: 0031-9104 (Print) 1029-0451 (Online) Journal homepage: http://www.tandfonline.com/loi/gpch20. Preferential solvation of indomethacin in 1,4dioxane + water mixtures according to the inverse Kirkwood–Buff integrals method María Á. Peña, Daniel R. Delgado & Fleming Martínez To cite this article: María Á. Peña, Daniel R. Delgado & Fleming Martínez (2016) Preferential solvation of indomethacin in 1,4-dioxane + water mixtures according to the inverse Kirkwood–Buff integrals method, Physics and Chemistry of Liquids, 54:4, 462-474, DOI: 10.1080/00319104.2015.1115329 To link to this article: http://dx.doi.org/10.1080/00319104.2015.1115329. Published online: 23 Nov 2015.. Submit your article to this journal. Article views: 5. View related articles. View Crossmark data. Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=gpch20 Download by: [Universidad Nacional Colombia]. Date: 15 April 2016, At: 13:56.

(2) PHYSICS AND CHEMISTRY OF LIQUIDS, 2016 VOL. 54, NO. 4, 462–474 http://dx.doi.org/10.1080/00319104.2015.1115329. Preferential solvation of indomethacin in 1,4-dioxane + water mixtures according to the inverse Kirkwood–Buff integrals method. Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. María Á. Peñaa, Daniel R. Delgadob, and Fleming Martínez. c. a Departamento de Ciencias Biomédicas, Facultad de Farmacia, Universidad de Alcalá, Alcalá de Henares, Madrid, Spain; bPrograma de Ingeniería Industrial, Facultad de Ingeniería, Universidad Cooperativa de Colombia, Neiva, Colombia; cGrupo de Investigaciones Farmacéutico Fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de Colombia – Sede Bogotá, Bogotá, Colombia. ABSTRACT. ARTICLE HISTORY. The preferential solvation parameters (δx1,3) of indomethacin (IMC) in 1,4-dioxane + water binary mixtures were derived from their thermodynamic properties by means of the inverse Kirkwood–Buff integrals method. δx1,3 is negative in water-rich and 1,4-dioxane-rich mixtures but positive in cosolvent compositions from 0.17 to 0.69 in mole fraction of 1,4-dioxane at 298.15 K. It is conjecturable that in water-rich mixtures, the hydrophobic hydration around the aromatic and methyl groups of the drug plays a relevant role in the solvation. The higher solvation by 1,4-dioxane in mixtures of similar cosolvent compositions could be mainly due to polarity effects. Finally, the preference of this drug for water in 1,4-dioxane-rich mixtures could be explained in terms of the higher acidic behavior of water molecules interacting with the hydrogenacceptor groups present in IMC.. Received 21 September 2015 Accepted 7 October 2015 KEYWORDS. Indomethacin; 1-dioxane; solubility; inverse Kirkwood– Buff integrals; IKBI; preferential solvation. Introduction Solubility of drugs in cosolvent mixtures is very important for pharmaceutical scientists involved in several development stages such as drug purification and/or design of liquid medicines.[1,2] Although cosolvency has been employed in pharmacy long time ago, it is just recently that the main mechanisms involved in increasing or decreasing drug solubility have been approached from a deep physicochemical point of view, including preferential solvation.[3,4] The inverse Kirkwood–Buff integrals (IKBI) are widely used to evaluate the preferential solvation of non-dissociate electrolyte drugs in solvent mixtures, describing the local compositions around the solute with respect to the different components present in the solvent mixture.[3–5] This treatment depends on the values of the standard molar Gibbs energies of transfer of the solute (compound 3) from neat water (compound 2) to the cosolvent (compound 1) + water (compound 2) solvent mixtures and the excess molar Gibbs energy of mixing for the binary mixtures free of solute. Thus, this treatment is very important in pharmaceutical sciences to understand the molecular interactions of solute–solvent, because most of the solubility studies developed have been focused toward correlating or modeling the solubilities and the possible prediction in mixtures from the solubilities in the neat solvents.[1,6] Nevertheless, just a few of them have been intended to analyze the local environment around the drug molecules describing the local fraction of the solvent components (1 or 2) in the surrounding of solute.[3–5] CONTACT Fleming Martínez © 2015 Taylor & Francis. fmartinezr@unal.edu.co.

(3) PHYSICS AND CHEMISTRY OF LIQUIDS. 463. O Cl N CH3 H3C-O. COOH. Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. Figure 1. Molecular structure of IMC.. Indomethacin (IMC, 2-{1-[(4-Chlorophenyl)carbonyl]-5-methoxy-2-methyl-1 H-indol-3-yl} acetic acid, CAS: 53-86-1, Figure 1) is an analgesic sometimes used in therapeutics considered as insoluble in water.[7,8] In this way, several thermodynamic researches have been published based on the enthalpic and entropic contributions to the Gibbs energy of solution in aqueous and nonaqueous cosolvent mixtures.[9–12] On the other hand, from the solubility data for this drug in all these cosolvent mixtures, some cosolvency models, such as extended Hildebrand solubility approach, Yalkowsky– Roseman and Jouyban–Acree models, have been challenged for correlating or predicting the solubility values in mixtures.[13–17] Moreover, the preferential solvation of IMC studied by means of the IKBI method has been reported in ethyl acetate (1) + ethanol (2), ethanol (1) + water (2) and propylene glycol (1) + water (2) mixtures.[18,19] In this way, the main goal of this paper is to evaluate the preferential solvation of IMC in 1,4-dioxane (1) + water (2) cosolvent mixtures based on IKBI calculations from the solubility values reported previously in the literature.[9] It is noteworthy that 1,4-dioxane is not used to develop liquid medicines due to its high toxicity, but it is widely used as a model cosolvent because it is miscible with water in all the range of compositions although it exhibits a low polarity as described by its dielectric constant, i.e. 2.21 at 298.15 K.[20] Even more, the Jouyban–Acree model has been used to correlate the solubility of a lot of drugs in 1,4-dioxane (1) + water (2) mixtures.[21]. Theoretical The preferential solvation parameter of the solute by 1,4-dioxane (δx1,3) is defined as [22–24]: L δx1;3 ¼ x1;3  x1 ¼ δx2;3. (1). L is the local mole Here x1 is the mole fraction of 1,4-dioxane in the bulk solvent mixture and x1;3 fraction of 1,4-dioxane in the environment near to the drug. If δx1,3 > 0, the solute is preferentially solvated by 1,4-dioxane; on the contrary, if this parameter is <0, the solute is preferentially solvated by water. Values of δx1,3 are obtainable from those of G1,3, and these in turn, from thermodynamic data of the cosolvent mixtures with the solute dissolved on it, as shown below.[5,25] Algebraic manipulation of the basic expressions presented by Newman [26] 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 (2) and (3) [3,4]:. G1;3 ¼ RTκT  V3 þ x2 V2 D=Q. (2). G2;3 ¼ RTκT  V3 þ x1 V1 D=Q:. (3). Here κT is the isothermal compressibility of the 1,4-dioxane + water solvent mixtures (in GPa–1); V1 and V2 are the partial molar volumes of the solvents in the mixtures (in cm3 mol–1); similarly, V3 is the partial molar volume of solute in these mixtures (in cm3 mol–1). The function D is the derivative of the standard molar Gibbs energies of transfer of the drug (from neat water to 1,4-.

(4) 464. M.Á. PEÑA ET AL.. dioxane + 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 −1 two solvents (GExc 1þ2 ) with respect to the water proportion in the mixtures (also in kJ mol ) [27–30]:   @Δtr Go3;2!1þ2 D¼ (4) @x1 T;p . Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. Q ¼ RT þ x1 x1. @ 2 GExc 1þ2 @x22.  :. (5). T;p. Because the dependence of κT on composition is not known for a lot of the systems investigated and because of the small contribution of RT κT to the IKBI, the dependence of κT on composition could be approximated by considering additive behavior, according to Eq. (6) [31]: κT;mix ¼. n X. xi κoT;i. (6). i¼1. where xi is the mole fraction of component i in the mixture and κoT;i is the isothermal compressibility of the pure component i. It is noteworthy that the κT;mix calculation by assuming volume fractions instead of mole fractions does not affect significantly the overall IKBI calculations. In this way, either mole or volume fractions could be used without real differences in the final δx1,3 results.[20,31] Ben-Naim [22] showed that the preferential solvation parameter can be calculated from the Kirkwood–Buff integrals as follows:   x1 x2 G1;3  G2;3 δx1;3 ¼ (7) x1 G1;3 þ x2 G2;3 þ Vcor The correlation volume, Vcor, is obtained by means of the following expression proposed by Marcus [3,4]:  3  1=3 L L  0:085 (8) Vcor ¼ 2522:5 r3 þ 0:1363 x1;3 V1 þ x2;3 V2 Here r3 is the radius of the solute (in nm), and it is calculated as:  1=3 3  1021 V3 rA ¼ 4πNAv. (9). where NAv 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 δx1,3 in Eq. (1) L to calculate x1;3 until a non-variant value of Vcor is obtained.. Results and discussion The solubility of IMC (3) in 1,4-dioxane (1) + water (2) mixtures was taken from Ruidiaz et al. [9] Standard molar Gibbs energy of transfer of this drug from neat water (2) to 1,4-dioxane (1) + water (2) mixtures was calculated and correlated to regular quartic polynomials from the drug solubility data by using Eq. (10). Figure 2 shows the Gibbs energy of transfer behavior at three of five temperatures, whereas Table 1 shows the behavior at all the temperatures studied. Obtained polynomial coefficients are shown in Table 2..

(5) Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. PHYSICS AND CHEMISTRY OF LIQUIDS. 465. Figure 2. Gibbs energy of transfer of IMC (3) from neat water (2) to 1,4-dioxane (1) + water (2) mixtures at several temperatures. ○: 293.15 K; □: 303.15 K; Δ: 313.15 K. Table 1. Gibbs energy of transfer (kJ mol–1) of IMC (3) from neat water (2) to 1,4-dioxane (1) + water (2) mixtures at several temperaturesa. x1 b 0.0000 0.0222 0.0486 0.0806 0.1200 0.1698 0.2348 0.3230 0.3802 0.4500 0.5368 0.6480 0.7953 1.0000. 293.15 K 34.28 32.07 30.44 28.61 25.14 21.30 17.22 13.44 12.28 10.57 9.57 8.72 8.11 9.00. 298.15 K 34.42 32.16 30.47 28.56 24.85 20.99 16.97 13.17 11.78 10.27 9.35 8.56 7.99 8.77. 303.15 K 34.57 32.24 30.39 28.34 24.58 20.61 16.26 12.71 11.40 9.88 9.09 8.30 7.83 8.50. 308.15 K 34.77 32.26 30.41 28.34 24.48 20.17 15.94 12.27 11.01 9.54 8.76 8.10 7.65 8.14. 313.15 K 34.88 32.30 30.34 28.18 24.05 19.87 15.54 11.72 10.66 9.26 8.51 7.87 7.48 7.92. a. Calculated from solubility data reported by Ruidiaz et al. [9]. x1 is the mole fraction of 1,4-dioxane (1) in the 1,4-dioxane (1) + water (2) mixtures free of IMC (3).. b. Table 2. Coefficients of Equation (10) (kJ mol–1) applied to Gibbs energy of transfer of IMC (3) from neat water (2) to 1,4dioxane (1) + water (2) mixtures at several temperatures. Coefficient a b c d e. 293.15 K 0.31 –94.24 104.06 –26.21 –9.30. 298.15 K 0.33 –98.17 113.29 –33.12 –8.08.  Δtr Go3;2!1þ2 ¼ RT ln. x3;2 x3;1þ2. 303.15 K 0.37 –104.67 132.91 –54.22 –0.54. 308.15 K 0.36 –108.77 141.45 –59.05 –0.72. 313.15 K 0.38 –114.10 157.80 –77.11 5.98.  ¼ a þ bx1 þ cx12 þ dx13 þ ex14. (10). Thus, D values were calculated from the first derivative of polynomial models (Eq. 11) solved according to the cosolvent mixture composition varying by 0.05 in mole fraction of 1,4-dioxane (1). D values are reported in Table 3. D ¼ b þ 2cx1 þ 3dx12 þ 4ex13. (11).

(6) 466. M.Á. PEÑA ET AL.. Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. Table 3. D values (kJ mol–1) of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. x1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00. 293.15 K –94.24 –84.03 –74.25 –64.91 –56.05 –47.70 –39.88 –32.62 –25.95 –19.89 –14.48 –9.74 –5.70 –2.39 0.16 1.94 2.90 3.02 2.27 0.63 –1.94. 298.15 K –98.17 –87.09 –76.54 –66.53 –57.09 –48.24 –40.01 –32.42 –25.50 –19.27 –13.75 –8.98 –4.96 –1.74 0.67 2.25 2.97 2.80 1.72 –0.28 –3.25. 303.15 K –104.67 –91.79 –79.72 –68.47 –58.04 –48.42 –39.63 –31.66 –24.51 –18.20 –12.71 –8.05 –4.22 –1.22 0.94 2.27 2.76 2.41 1.21 –0.82 –3.70. 308.15 K –108.77 –95.07 –82.25 –70.33 –59.30 –49.16 –39.92 –31.58 –24.14 –17.60 –11.96 –7.24 –3.42 –0.52 1.47 2.55 2.70 1.94 0.25 –2.36 –5.89. 313.15 K –114.10 –98.90 –84.83 –71.89 –60.04 –49.29 –39.60 –30.96 –23.35 –16.75 –11.15 –6.52 –2.86 –0.14 1.66 2.56 2.57 1.70 –0.01 –2.56 –5.92. In order to calculate the Q values, the excess molar Gibbs energies of mixing GExc 1þ2 at all the temperatures considered are required. Nevertheless, these values are reported only at one temperature, i.e. normally at 298.15 K. For this reason, it is necessary to calculate these values at the other temperatures required. In this way, GExc 1þ2 values were calculated at 298.15 K using Eq. (12), as reported by Marcus.[5] On the other hand, the GExc 1þ2 values at the other Exc temperatures were calculated using Eq. (13), where H1þ2 is the excess molar enthalpy of the cosolvent mixtures, T1 is 298.15 K and T2 is one of the other temperatures under consideraExc values were calculated using Eq. (14) at 298.15 K, as also reported by tion.[5] In turn, H1þ2 Marcus.[5]  2 GExc 1þ2 ¼ x1 ð1  x1 Þ 3835  973ð1  2x1 Þ  421ð1  2x1 Þ. Exc GExc 1þ2 ðT2 Þ ¼ G1þ2 ðT1 Þ  T. ð T2 T1. Exc H1þ2 d.     1 T2 T2 Exc ð Þ  GExc T 1  þ H 1 1þ2 T T1 1þ2 T1.   Exc ¼ x1 ð1  x1 Þ 611 þ 6006ð1  2x1 Þ  1712ð1  2x1 Þ2 H1þ2. (12). (13). (14). It is noteworthy that quartic regular polynomials of GExc 1þ2 , as a function of the mole fraction of water, were obtained. Q values at all temperatures are shown in Table 4. On the other hand, Table 5 shows the RT κT values calculated by assuming additive behavior of κT (Eq. 6) with the values 0.738 and 0.457 GPa–1, for 1,4-dioxane and water, respectively.[31] The partial molar volumes of 1,4-dioxane (Table 6) and water (Table 7) were calculated by means of equations (15) and (16) from the density (ρ) values of 1,4-dioxane (1) + water (2) mixtures reported at all the temperatures under study by Ruidiaz and Martínez.[32] V is the molar volume of the mixtures and it is calculated as V = (x1·M1 + x2·M2)/ρ. The values of M1 and M2 are 88.11 and 18.02 g mol–1, respectively.[7] V 1 ¼ V þ x2. dV dx1. (15).

(7) PHYSICS AND CHEMISTRY OF LIQUIDS. 467. Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. Table 4. Q values (kJ mol–1) of 1,4-dioxane (1) + water (2) mixtures at several temperatures. x1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00. 293.15 K 2.437 2.460 2.353 2.150 1.885 1.584 1.273 0.975 0.707 0.487 0.325 0.233 0.214 0.274 0.410 0.621 0.899 1.234 1.613 2.021 2.437. 298.15 K 2.479 2.518 2.424 2.230 1.968 1.667 1.351 1.044 0.765 0.529 0.351 0.240 0.204 0.247 0.371 0.572 0.847 1.188 1.583 2.019 2.479. 303.15 K 2.520 2.577 2.495 2.310 2.052 1.750 1.430 1.114 0.822 0.571 0.376 0.248 0.194 0.221 0.331 0.524 0.796 1.143 1.554 2.018 2.520. 308.15 K 2.562 2.635 2.567 2.390 2.136 1.833 1.508 1.183 0.879 0.614 0.402 0.255 0.184 0.194 0.291 0.475 0.745 1.097 1.524 2.016 2.562. 313.15 K 2.604 2.694 2.638 2.469 2.219 1.916 1.586 1.253 0.936 0.656 0.427 0.263 0.174 0.168 0.251 0.427 0.694 1.051 1.494 2.015 2.604. Table 5. RT κT values (cm3 mol–1) of 1,4-dioxane (1) + water (2) mixtures at several temperatures. x1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00. 293.15 K 1.114 1.148 1.182 1.217 1.251 1.285 1.319 1.354 1.388 1.422 1.456 1.490 1.525 1.559 1.593 1.627 1.662 1.696 1.730 1.764 1.799. 298.15 K 1.133 1.168 1.202 1.237 1.272 1.307 1.342 1.377 1.411 1.446 1.481 1.516 1.551 1.586 1.620 1.655 1.690 1.725 1.760 1.795 1.829. V 2 ¼ V  x1. 303.15 K 1.152 1.187 1.223 1.258 1.293 1.329 1.364 1.400 1.435 1.471 1.506 1.541 1.577 1.612 1.648 1.683 1.718 1.754 1.789 1.825 1.860. dV dx1. 308.15 K 1.171 1.207 1.243 1.279 1.315 1.351 1.387 1.423 1.459 1.495 1.531 1.567 1.603 1.639 1.675 1.711 1.747 1.783 1.819 1.855 1.891. 313.15 K 1.190 1.226 1.263 1.300 1.336 1.373 1.409 1.446 1.482 1.519 1.556 1.592 1.629 1.665 1.702 1.739 1.775 1.812 1.848 1.885 1.921. (16). Partial molar volumes of non-dissociate weak electrolyte drugs are not frequently reported in the literature. This is because of the high uncertainty in its determination due to the low drug solubilities in aqueous media. For this reason, the molar volume of IMC is considered as independent of the cosolvent composition and temperature, as it is calculated according to the Fedors method.[33,34] Thus, this value was taken as reported by Rodríguez et al. as V3 = 220.3 cm3 mol–1.[18] Additionally, from this volume value, the radius of the drug molecule (required for Eq. 8) was calculated using Eq. (9) as r3 = 0.444 nm..

(8) 468. M.Á. PEÑA ET AL.. Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. Table 6. Partial molar volume (cm3 mol–1) of 1,4-dioxane (1) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. x1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00. 293.15 K 80.49 81.38 82.16 82.83 83.41 83.90 84.30 84.63 84.90 85.10 85.25 85.35 85.41 85.44 85.44 85.42 85.39 85.36 85.33 85.30 85.29. 298.15 K 81.01 81.89 82.66 83.33 83.90 84.39 84.79 85.12 85.39 85.59 85.74 85.84 85.90 85.93 85.93 85.91 85.88 85.85 85.82 85.79 85.78. 303.15 K 81.46 82.34 83.10 83.76 84.33 84.81 85.21 85.54 85.80 86.00 86.15 86.25 86.31 86.34 86.35 86.33 86.30 86.27 86.23 86.21 86.20. 308.15 K 81.97 82.83 83.60 84.26 84.82 85.30 85.70 86.03 86.29 86.49 86.63 86.74 86.80 86.83 86.83 86.81 86.78 86.75 86.72 86.69 86.68. 313.15 K 82.51 83.37 84.13 84.78 85.34 85.82 86.22 86.54 86.80 87.00 87.14 87.24 87.31 87.34 87.34 87.32 87.30 87.26 87.23 87.21 87.20. Table 7. Partial molar volume (cm3 mol–1) of water (2) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. x1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00. 293.15 K 18.03 18.01 17.95 17.85 17.73 17.59 17.43 17.27 17.12 16.97 16.83 16.72 16.64 16.59 16.59 16.64 16.74 16.91 17.15 17.47 17.87. 298.15 K 18.06 18.03 17.97 17.88 17.75 17.61 17.46 17.30 17.15 17.00 16.86 16.75 16.67 16.62 16.62 16.66 16.77 16.93 17.17 17.48 17.88. 303.15 K 18.08 18.06 18.00 17.90 17.78 17.64 17.49 17.33 17.18 17.03 16.90 16.79 16.70 16.66 16.65 16.69 16.79 16.95 17.19 17.49 17.88. 308.15 K 18.11 18.09 18.03 17.94 17.82 17.68 17.53 17.37 17.21 17.07 16.93 16.82 16.74 16.69 16.69 16.73 16.83 16.99 17.22 17.53 17.92. 313.15 K 18.15 18.13 18.07 17.98 17.86 17.72 17.57 17.41 17.26 17.11 16.98 16.87 16.79 16.74 16.73 16.77 16.87 17.03 17.25 17.55 17.93. Tables 8 and 9 show that the G1,3 and G2,3 values are negative with the exception of G2,3 in some mixtures with composition 0.70 ≤ x1 ≤ 0.80 at several temperatures. This indicates that this drug exhibits affinity for both solvents in the mixtures. In order to use the IKBI method, the correlation volume was iterated five times using equations (1), (7), and (8) to obtain the values reported in Table 10. It is interesting to note that these values are almost independent of temperature in water-rich mixtures, but they increase to some extent in 1,4-dioxane-rich mixtures with increasing temperature. According to Table 11 and Figure 3, the values of δx1,3 vary nonlinearly with the 1,4-dioxane proportion in the mixtures at all temperatures. Addition of 1,4-dioxane to water tends to make negative the δx1,3 values of IMC from the pure water up to the mixture 0.17 in mole fraction of 1,4-dioxane reaching a minimum near to −0.045 in the mixture of x1 = 0.10. Probably the.

(9) PHYSICS AND CHEMISTRY OF LIQUIDS. 469. Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. Table 8. G1,3 values (cm3 mol–1) for IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. x1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00. 293.15 K –916.4 –803.6 –728.9 –677.1 –640.9 –616.3 –601.2 –594.7 –595.6 –600.2 –593.3 –533.9 –395.8 –269.5 –216.7 –205.7 –207.8 –212.4 –216.2 –218.3 –218.5. 298.15 K –934.2 –811.6 –729.8 –672.3 –631.0 –601.3 –580.8 –568.1 –561.9 –559.3 –549.4 –500.6 –380.8 –259.6 –209.6 –202.3 –206.9 –212.6 –216.7 –218.6 –218.5. 303.15 K –970.1 –830.2 –736.6 –670.1 –621.4 –585.1 –558.3 –539.2 –526.3 –517.1 –504.2 –464.2 –363.9 –250.9 –204.4 –200.5 –207.0 –213.2 –217.2 –218.8 –218.4. 308.15 K –988.2 –839.1 –739.1 –667.7 –614.7 –574.5 –543.7 –520.2 –502.4 –488.0 –471.1 –433.6 –343.4 –234.2 –193.3 –196.2 –206.3 –214.0 –218.2 –219.5 –218.4. 313.15 K –1014.6 –851.3 –742.0 –663.8 –605.5 –560.8 –525.9 –498.6 –477.0 –459.1 –440.5 –407.3 –329.2 –223.4 –185.4 –193.4 –206.1 –214.4 –218.5 –219.5 –218.4. Table 9. G2,3 values (cm3 mol–1) for IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. x1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00. 293.15 K –219.2 –358.1 –478.4 –594.1 –715.2 –850.7 –1011.1 –1210.2 –1464.5 –1783.6 –2115.3 –2184.7 –1581.7 –703.8 –194.7 –18.9 1.5 –41.2 –110.5 –193.4 –286.3. 298.15 K –219.2 –360.7 –480.1 –591.9 –705.7 –829.5 –972.0 –1143.9 –1357.9 –1621.5 –1899.5 –1983.9 –1471.7 –611.4 –109.2 34.9 22.1 –46.5 –134.4 –230.0 –331.0. 303.15 K –219.1 –365.7 –484.6 –591.5 –696.0 –805.6 –927.6 –1070.0 –1242.6 –1451.4 –1673.7 –1760.1 –1344.1 –528.5 –46.5 61.9 20.5 –64.1 –157.9 –251.8 –345.0. 308.15 K –219.1 –368.5 –486.9 –591.0 –690.0 –790.9 –899.6 –1022.5 –1166.5 –1335.0 –1509.5 –1572.4 –1188.3 –369.0 88.8 130.5 33.4 –88.1 –205.5 –314.7 –417.9. 313.15 K –219.1 –372.1 –489.6 –589.2 –680.8 –770.8 –864.6 –967.5 –1084.5 –1218.6 –1356.6 –1410.8 –1081.3 –264.6 186.1 174.3 39.7 –98.3 –219.1 –323.7 –416.8. structuring of water molecules around the nonpolar groups of this drug (i.e. hydrophobic hydration of aromatic rings and methyl group) contributes to lowering of the net δx1,3 to negative values in these water-rich mixtures. In the mixtures with composition 0.17 < x1 < 0.65 (0.69), the local mole fractions of 1,4-dioxane are higher than those of the mixtures and therefore the δx1,3 values are positive and they decrease with increasing temperature. The cosolvent action may be related to the breaking of the ordered structure of water around the nonpolar moieties of the drug, which increases the solvation having maximum values near to x1 = 0.55. Finally, from this 1,4-dioxane proportion to neat 1,4-dioxane, the δx1,3 values are negative, as they also are in water-rich mixtures. Mixture compositions of maximum magnitudes of negative δx1,3 values vary from 0.70 to 0.75 in mole fraction of 1,4-dioxane. Figure 4 shows the linear temperature-dependence of δx1,3 in the mixtures with maximum variations of these.

(10) 470. M.Á. PEÑA ET AL.. Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. Table 10. Correlation volume (cm3 mol–1) of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures after five iterations. x1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00. 293.15 K 926 946 1013 1124 1256 1395 1540 1693 1864 2068 2276 2243 2045 1897 1873 1913 1974 2040 2105 2166 2222. 298.15 K 927 946 1015 1127 1258 1394 1530 1670 1818 1976 2124 2157 2022 1887 1867 1913 1978 2047 2113 2175 2230. 303.15 K 928 944 1015 1130 1260 1391 1519 1647 1776 1907 2027 2081 1996 1877 1864 1915 1984 2055 2121 2182 2237. 308.15 K 928 943 1016 1133 1263 1391 1515 1635 1752 1868 1972 2027 1964 1856 1852 1913 1990 2063 2131 2191 2245. 313.15 K 929 943 1017 1136 1265 1390 1508 1621 1729 1833 1927 1986 1946 1846 1846 1915 1996 2072 2139 2200 2253. Table 11. δx1,3 values of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. x1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00. 293.15 K 0.0000 –0.0374 –0.0442 –0.0204 0.0214 0.0729 0.1321 0.2006 0.2793 0.3584 0.4130 0.4229 0.2423 0.0670 –0.0028 –0.0200 –0.0185 –0.0118 –0.0050 –0.0006 0.0000. 298.15 K 0.0000 –0.0381 –0.0441 –0.0196 0.0211 0.0689 0.1216 0.1799 0.2453 0.3158 0.3753 0.3712 0.2172 0.0532 –0.0125 –0.0251 –0.0202 –0.0114 –0.0039 0.0003 0.0000. 303.15 K 0.0000 –0.0398 –0.0449 –0.0190 0.0206 0.0646 0.1104 0.1584 0.2097 0.2641 0.3117 0.3102 0.1898 0.0413 –0.0194 –0.0276 –0.0200 –0.0102 –0.0028 0.0008 0.0000. 308.15 K 0.0000 –0.0405 –0.0451 –0.0184 0.0205 0.0620 0.1035 0.1450 0.1871 0.2293 0.2643 0.2606 0.1581 0.0195 –0.0340 –0.0340 –0.0209 –0.0086 –0.0006 0.0023 0.0000. 313.15 K 0.0000 –0.0416 –0.0452 –0.0177 0.0201 0.0586 0.0954 0.1305 0.1643 0.1965 0.2226 0.2204 0.1372 0.0058 –0.0440 –0.0380 –0.0214 –0.0079 0.0000 0.0025 0.0000. values, i.e. x1 = 0.50 and x1 = 0.70 for preferential solvation by 1,4-dioxane and water, respectively. It is noteworthy that in the first case the preferential solvation by 1,4-dioxane decreases with increasing temperature, but in the second case, the preferential solvation by water increases with increasing temperature (it is important to keep in mind that δx2,3 = –δx1,3). IMC could act as a Lewis acid in solution due to the ability of the acidic hydrogen atom in its – COOH group (Figure 1) to establish hydrogen bonds with proton-acceptor functional groups of the solvents (oxygen atoms in –O– and –OH groups). In addition, this drug could act as a Lewis base because of the free electron pairs in oxygen atoms of ether and carboxylic groups (Figure 1), which interact with acidic hydrogen atoms of water. In this context, IMC has one hydrogenbonding donor and two hydrogen-bonding acceptor groups..

(11) Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. PHYSICS AND CHEMISTRY OF LIQUIDS. 471. Figure 3. δx1,3 values of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. ○: 293.15 K; □: 298.15 K; Δ: 303.15 K; ◊: 308.15 K; ×: 313.15 K.. Figure 4. δx1,3 values of IMC (3) in the mixture 1,4-dioxane (1) + water (2) with composition (A): x1 = 0.50 and (B): x1 = 0.70 as a function of the temperature.. According to the preferential solvation results, it is conjecturable that in intermediate composition mixtures, IMC could be acting as a Lewis acid with 1,4-dioxane molecules, although this cosolvent is less basic than water, as described by the Kamlet–Taft hydrogen bond acceptor parameters, i.e. β = 0.37 for 1,4-dioxane and 0.47 for water.[31,35] On the other hand, in 1,4-.

(12) Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. 472. M.Á. PEÑA ET AL.. dioxane-rich mixtures, where IMC is preferentially solvated by water, the drug could be acting mainly as a Lewis base in front to water because this solvent is more acidic than 1,4-dioxane as described by the Kamlet–Taft hydrogen bond donor parameters, i.e. α = 1.17 for water and 0.00 for 1,4-dioxane, respectively.[31,36] Figure 5 compares the preferential solvation of IMC in 1,4-dioxane (1) + water (2), ethanol (1) + water (2), and propylene glycol (1) + water (2), at 303.15 K.[19] Maximum δx1,3 values are highest in 1,4-dioxane mixtures followed by ethanol mixtures and propylene glycol mixtures in those equimolar mixtures, i.e. x1 = 0.50; whereas, in cosolvent-rich mixtures where IMC is preferentially solvated by water, i.e. 1,4-dioxane (1) + water (2) and ethanol (1) + water (2) mixtures, the magnitude is also higher with 1,4-dioxane mixtures. Regarding the behavior in the mixtures with x1 = 0.50 it is interesting to evaluate the effect of drug and solvents polarities on these δx1,3 values. In this way, the Hildebrand solubility parameters (δ) for these equimolar mixtures calculated as ideal volumetric mixing are as follows: 25.3, 31.5, and 33.7 MPa1/2 for 1,4-dioxane, ethanol and propylene glycol aqueous mixtures, respectively.[20,34] On the other hand, the Fedors δ value for IMC is 26.9 MPa1/2,[18] being this value closer to that calculated for 1,4-dioxane (1) + water (2) mixtures, i.e. 25.3 MPa1/2, which demonstrates some proportional relationship of the δx1,3 magnitude and the proximity in δ values between solute and cosolvent mixtures. On the other hand, Figure 6 compares the preferential solvation behavior of several drugs in 1,4dioxane (1) + water (2) mixtures at 298.15 K.[27,28,30] These drugs include meloxicam and some sulfonamides. It is noteworthy that the magnitude of preferential solvation by 1,4-dioxane of IMC and meloxicam are really higher compared with those for the three sulfonamides, because the last ones are not higher than 0.10. Moreover, the highest δx1,3 values observed for meloxicam could be a result of some degree of divergence in the G1,3 and G2,3 values, as reported previously.[28] A similar but no so high behavior has been reported for the preferential solvation of some structurally related sulfonamides by water in 1-propanol-rich binary mixtures.[37] It is conjecturable that these apparently anomalous behaviors are a consequence of the high excess Gibbs energy of mixing of the cosolvent mixtures which could be affecting to some significant extent the Q term, which in turn is affecting both G1,3 and G2,3 values. These high excess Gibbs energies of mixing are a consequence of the significant structural differences between 1,4-dioxane or 1-propanol and water.. Conclusions Classical expressions describing the local mole fraction of 1,4-dioxane (1) and water (2) around of IMC (3) were derived on the basis of the IKBI method applied to reported equilibrium solubility values of this drug in 1,4-dioxane (1) + water (2) mixtures. Thus, this compound is preferentially. Figure 5. δx1,3 values of IMC (3) in different cosolvent (1) + water (2) mixtures at 303.15 K. ○: 1,4-dioxane (1) + water (2); □: ethanol (1) + water (2); Δ: propylene glycol (1) + water (2)..

(13) Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. PHYSICS AND CHEMISTRY OF LIQUIDS. 473. Figure 6. δx1,3 values of different drugs (3) in 1,4-dioxane (1) + water (2) mixtures at 298.15 K. ○: IMC; □: meloxicam; Δ: sulfamethoxazole; ◊: sulfamethizole; ×: sulfadiazine.. solvated by water in water-rich and in 1,4-dioxane-rich mixtures but preferentially solvated by 1,4-dioxane in mixtures with intermediate composition at all the temperatures considered. These results are in good agreement with that described previously for this ternary system and that was based in more classical thermodynamic treatments.[9]. Disclosure statement No potential conflict of interest was reported by the authors.. ORCID Fleming Martínez. http://orcid.org/0000-0002-4008-7273. References [1] Jouyban A. Handbook of solubility data for pharmaceuticals. Boca Raton, FL: CRC Press; 2010. [2] Rubino JT. Cosolvents and cosolvency. In: Swarbrick J, Boylan JC, editors. Encyclopedia of pharmaceutical technology. New York (NY): Marcel Dekker, Inc.; 1988. Vol. 3. p. 375–398. [3] Marcus Y. On the preferential solvation of drugs and PAHs in binary solvent mixtures. J Mol Liq. 2008;140:61–67. DOI:10.1016/j.molliq.2008.01.005. [4] Marcus Y. Preferential solvation of ibuprofen and naproxen in aqueous 1,2-propanediol. Acta Chim Slov. 2009;56:40–44. [5] Marcus Y. Solvent mixtures: properties and selective solvation. New York (NY): Marcel Dekker, Inc.; 2002. [6] Jouyban A. Review of the cosolvency models for predicting solubility of drugs in water-cosolvent mixtures. J Pharm Pharmaceut Sci. 2008;11:32–58. [7] Budavari S, O’Neil MJ, Smith A, et al. The Merck index: an encyclopedia of chemicals, drugs, and biologicals [Monographs]. 13th ed. Whitehouse Station (NJ): Merck & Co., Inc.; 2001. [8] Raffa RB. Analgesic, antipyretic, and anti-inflammatory drugs. In: Gennaro A, editor. Remington: the science and practice of pharmacy. 21st ed. Philadelphia (PA): Lippincott Williams & Wilkins. 2005. p. 1524–1542. [9] Ruidiaz MA, Delgado DR, Martínez F, et al. Solubility and preferential solvation of indomethacin in 1,4dioxane + water solvent mixtures. Fluid Phase Equilib. 2010;299:259–265. DOI:10.1016/j.fluid.2010.09.027. [10] Martínez F, Peña MÁ, Bustamante P. Thermodynamic analysis and enthalpy-entropy compensation for the solubility of indomethacin in aqueous and non-aqueous mixtures. Fluid Phase Equilib. 2011;308:98–106. DOI:10.1016/j.fluid.2011.06.016. [11] Holguín AR, Rodríguez GA, Cristancho DM, et al. Solution thermodynamics of indomethacin in propylene glycol + water mixtures. Fluid Phase Equilib. 2012;314:134–139. DOI:10.1016/j.fluid.2011.11.001. [12] Cantillo EA, Delgado DR, Martinez F. Solution thermodynamics of indomethacin in ethanol + propylene glycol mixtures. J Mol Liq. 2013;181:62–67. DOI:10.1016/j.molliq.2013.02.008..

(14) Downloaded by [Universidad Nacional Colombia] at 13:56 15 April 2016. 474. M.Á. PEÑA ET AL.. [13] Ruidiaz MA, Delgado DR, Mora CP, et al. Estimation of the indomethacin solubility in ethanol + water mixtures by the extended Hildebrand solubility approach. Rev Colomb Cienc Quím Farm. 2010;39:79–95. [14] Ruidiaz MA, Delgado DR, Martínez F. Correlating the solubility of indomethacin in 1,4-dioxane + water mixtures by means of the Jouyban-Acree model. Rev Colomb Cienc Quím Farm. 2010;39:211–226. [15] Ruidiaz MA, Delgado DR, Martínez F. Indomethacin solubility estimation in 1,4-dioxane + water mixtures by the extended Hildebrand solubility approach. Quím Nova. 2011;34:1569–1574. DOI:10.1590/S010040422011000900016. [16] Ruidiaz MA, Delgado DR, Martínez F. Performance of the Jouyban-Acree and Yalkowsky-Roseman models for estimating the solubility of indomethacin in ethanol + water mixtures. Rev Acad Colomb Cienc. 2011;35:329–336. [17] Holguín AR, Delgado DR, Martínez F. Indomethacin solubility in propylene glycol + water mixtures according to the extended Hildebrand solubility approach. Lat Am J Pharm. 2012;31:720–726. [18] Rodríguez GA, Delgado DR, Martínez F. Preferential solvation of indomethacin and naproxen in ethyl acetate + ethanol mixtures according to the IKBI method. Phys Chem Liq. 2014;52:533–545. DOI:10.1080/ 00319104.2013.842474. [19] Peña MÁ, Delgado DR, Martínez F. Preferential solvation of indomethacin in some aqueous co-solvent mixtures. Chem Eng Commun. 2015. DOI:10.1080/00986445.2015.1074898. [20] Martin A, Bustamante P, Chun AHC. Physical chemical principles in the pharmaceutical sciences. 4th ed. Philadelphia (PA): Lea & Febiger; 1993. [21] Jouyban A. In silico prediction of drug solubility in water-dioxane mixtures using the Jouyban-Acree model. Pharmazie. 2007;62:46–50. DOI:10.1691/ph2007.1.6057. [22] Ben-Naim A. Theory of preferential solvation of nonelectrolytes. Cell Biophys. 1988;12:255–269. DOI:10.1007/BF02918361. [23] Ben-Naim A. Preferential solvation in two- and in three-component systems. Pure Appl Chem. 1990;62:25– 34. DOI:10.1351/pac199062010025. [24] Marcus Y. Solubility and solvation in mixed solvent systems. Pure Appl Chem. 1990;62:2069–2076. DOI:10.1351/pac199062112069. [25] Delgado DR, Martínez F. Preferential solvation of sulfadiazine, sulfamerazine and sulfamethazine in ethanol + water solvent mixtures according to the IKBI method. J Mol Liq. 2014;193:152–159. DOI:10.1016/j. molliq.2013.12.021. [26] Newman KE. Kirkwood-Buff solution theory: derivation and applications. Chem Soc Rev. 1994;23:31–40. DOI:10.1039/CS9942300031. [27] Delgado DR, Peña MÁ, Martínez F. Preferential solvation of some sulfonamides in 1,4-dioxane + water cosolvent mixtures at 298.15 K according to the inverse Kirkwood-Buff integrals method. Rev Acad Colomb Cienc. 2014;38:104–114. DOI:10.18257/raccefyn.44. [28] Jiménez DM, Cárdenas ZJ, Delgado DR, et al. Solubility and solution thermodynamics of meloxicam in 1,4dioxane and water mixtures. Ind Eng Chem Res. 2014;53:16550–16558. DOI:10.1021/ie503101h. [29] Jiménez DM, Cárdenas ZJ, Delgado DR, et al. Preferential solvation of methocarbamol in aqueous binary cosolvent mixtures at 298.15 K. Phys Chem Liq. 2014;52:726–737. DOI:10.1080/00319104.2014.915755. [30] Jiménez DM, Cárdenas ZJ, Delgado DR, et al. Solubility temperature dependence and preferential solvation of sulfadiazine in 1,4-dioxane + water co-solvent mixtures. Fluid Phase Equilib. 2015;397:26–36. DOI:10.1016/j. fluid.2015.03.046. [31] Marcus Y. The properties of solvents. Chichester (UK): John Wiley & Sons; 1998. [32] Ruidiaz MA, Martínez F. Volumetric properties of the pharmaceutical model cosolvent system 1,4-dioxane + water at several temperatures. Vitae Rev Fac Quím Farm. 2009;16:327–337. [33] Fedors RF. A method for estimating both the solubility parameters and molar volumes of liquids. Polym Eng Sci. 1974;14:147–154. DOI:10.1002/pen.760140211. [34] Barton AFM. Handbook of solubility parameters and other cohesion parameters. 2nd ed. New York (NY): CRC Press; 1991. [35] Kamlet MJ, Taft RW. The solvatochromic comparison method. I. The beta-scale of solvent hydrogen-bond acceptor (HBA) basicities. J Am Chem Soc. 1976;98:377–383. DOI:10.1021/ja00418a009. [36] Taft RW, Kamlet MJ. The solvatochromic comparison method. II. The alpha-scale of solvent hydrogen-bond donor (HBD) acidities. J Am Chem Soc. 1976;98:2886–2894. DOI:10.1021/ja00426a036. [37] Delgado DR, Martínez F. Preferential solvation of some structurally related sulfonamides in 1-propanol + water cosolvent mixtures. Phys Chem Liq. 2015;53:293–306. DOI:10.1080/00319104.2014.961191..

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Figure

Table 1. Gibbs energy of transfer (kJ mol –1 ) of IMC (3) from neat water (2) to 1,4-dioxane (1) + water (2) mixtures at several temperatures a

Table 1.

Gibbs energy of transfer (kJ mol –1 ) of IMC (3) from neat water (2) to 1,4-dioxane (1) + water (2) mixtures at several temperatures a p.5
Figure 2. Gibbs energy of transfer of IMC (3) from neat water (2) to 1,4-dioxane (1) + water (2) mixtures at several temperatures

Figure 2.

Gibbs energy of transfer of IMC (3) from neat water (2) to 1,4-dioxane (1) + water (2) mixtures at several temperatures p.5
Table 2. Coefficients of Equation (10) (kJ mol –1 ) applied to Gibbs energy of transfer of IMC (3) from neat water (2) to 1,4- 1,4-dioxane (1) + water (2) mixtures at several temperatures.

Table 2.

Coefficients of Equation (10) (kJ mol –1 ) applied to Gibbs energy of transfer of IMC (3) from neat water (2) to 1,4- 1,4-dioxane (1) + water (2) mixtures at several temperatures. p.5
Table 3. D values (kJ mol –1 ) of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures.

Table 3.

D values (kJ mol –1 ) of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. p.6
Table 4. Q values (kJ mol –1 ) of 1,4-dioxane (1) + water (2) mixtures at several temperatures.

Table 4.

Q values (kJ mol –1 ) of 1,4-dioxane (1) + water (2) mixtures at several temperatures. p.7
Table 5. RT κ T values (cm 3 mol –1 ) of 1,4-dioxane (1) + water (2) mixtures at several temperatures.

Table 5.

RT κ T values (cm 3 mol –1 ) of 1,4-dioxane (1) + water (2) mixtures at several temperatures. p.7
Table 7. Partial molar volume (cm 3 mol –1 ) of water (2) in 1,4-dioxane (1) + water (2) mixtures at several temperatures.

Table 7.

Partial molar volume (cm 3 mol –1 ) of water (2) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. p.8
Table 6. Partial molar volume (cm 3 mol –1 ) of 1,4-dioxane (1) in 1,4-dioxane (1) + water (2) mixtures at several temperatures.

Table 6.

Partial molar volume (cm 3 mol –1 ) of 1,4-dioxane (1) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. p.8
Table 9. G 2,3 values (cm 3 mol –1 ) for IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures.

Table 9.

G 2,3 values (cm 3 mol –1 ) for IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. p.9
Table 8. G 1,3 values (cm 3 mol –1 ) for IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures.

Table 8.

G 1,3 values (cm 3 mol –1 ) for IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. p.9
Table 10. Correlation volume (cm 3 mol –1 ) of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures after five iterations

Table 10.

Correlation volume (cm 3 mol –1 ) of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures after five iterations p.10
Table 11. δx 1,3 values of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures.

Table 11.

δx 1,3 values of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures. p.10
Figure 4. δx 1,3 values of IMC (3) in the mixture 1,4-dioxane (1) + water (2) with composition (A): x 1 = 0.50 and (B): x 1 = 0.70 as a function of the temperature.

Figure 4.

δx 1,3 values of IMC (3) in the mixture 1,4-dioxane (1) + water (2) with composition (A): x 1 = 0.50 and (B): x 1 = 0.70 as a function of the temperature. p.11
Figure 3. δx 1,3 values of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures

Figure 3.

δx 1,3 values of IMC (3) in 1,4-dioxane (1) + water (2) mixtures at several temperatures p.11
Figure 5 compares the preferential solvation of IMC in 1,4-dioxane (1) + water (2), ethanol (1) + water (2), and propylene glycol (1) + water (2), at 303.15 K.[19] Maximum δx 1,3 values are highest in 1,4-dioxane mixtures followed by ethanol mixtures and p

Figure 5

compares the preferential solvation of IMC in 1,4-dioxane (1) + water (2), ethanol (1) + water (2), and propylene glycol (1) + water (2), at 303.15 K.[19] Maximum δx 1,3 values are highest in 1,4-dioxane mixtures followed by ethanol mixtures and p p.12
Figure 6. δx 1,3 values of different drugs (3) in 1,4-dioxane (1) + water (2) mixtures at 298.15 K

Figure 6.

δx 1,3 values of different drugs (3) in 1,4-dioxane (1) + water (2) mixtures at 298.15 K p.13

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