Thermodynamic analysis and correlation of solubility of candesartan cilexetil in aqueous solvent mixtures

Fluid Phase Equilibria 337 (2013) 354–362

Contents lists available at SciVerse ScienceDirect

Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid

Thermodynamic analysis and correlation of solubility of candesartan cilexetil in aqueous solvent mixtures Penglei Cui a , Qiuxiang Yin a,b , Junbo Gong a,b,∗ , Yongli Wang a,b , Hongxun Hao a,b , Chuang Xie a,b , Ying Bao a,b , Meijing Zhang a,b , Baohong Hou a,b , Jingkang Wang a,b a b

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, People’s Republic of China Tianjin Key Laboratory of Modern Drug Delivery and High-Efficiency, TianjinUniversity, Tianjin 300072, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 20 July 2012 Received in revised form 20 September 2012 Accepted 20 September 2012 Available online 2 October 2012 Keywords: Solubility Candesartan cilexetil (NIBS)/Redlich–Kister equation Enthalpy Entropy

a b s t r a c t The solubility of candesartan cilexetil (Form I) was measured by a gravimetric method in aqueous solvent mixtures (ethanol–water, acetonitrile–water and acetone–water), and the calculated values by (NIBS)/Redlich–Kister equation agreed well with the experimental data. The relationship between solubility of candesartan cilexetil (Form I) and molar fraction of organic solvents (ethanol, acetonitrile and acetone) shown unimodal curves, and this phenomenon can be explained by Hsol –Gsol compensation theory. For ethanol–water and acetonitrile–water mixture, the plot of Hsol –Gsol compensation was nonlinear with positive and negative slopes, indicating that the increases of solubility were controlled by two different mechanisms (entropy and enthalpy). However, for acetone–water mixture, the plot of Hsol –Gsol compensation was a linear curve, indicating that enthalpy is the dominant mechanism to control the solubility enhancement. These results can also be used to explain that acetone molecule played an important role in increasing the solute–solvent interactions of the candesartan cilexetil (Form I). © 2012 Elsevier B.V. All rights reserved.

1. Introduction In the pharmaceutical industry, solubility is an important property and given essential information for selection of appropriate solvent, optimization of the operative conditions of crystallization processes, and investigation of the physical stability of liquid dosage forms [1]. In the case of some hydrophobic drugs, the poor water-solubility can cause difficulty in design liquid dosage forms, and lower the bioavailability. Therefore, the water–cosolvent has been widely used to enhance the aqueous solubility of these drugs, and the driving force for the solubility enhancement in water–cosolvent can be investigated by mean of the thermodynamic magnitudes [2]. For example, the solubility of indomethacin in ethanol–ethylacetate was favored by enthalpy changes [3], the solubility of phenacetin in dioxane–water was enthalpy driven at higher dioxane concentrations whereas entropy controlled at lower dioxane concentrations [4], and the solvation of diflunisal and flurbiprofen in aliphatic alcohols were enthalpy-driven phenomenon [5]. Candesartan cilexetil, known as a potent Angiotensin II receptor antagonist, is useful in the treatment of cardiovascular complaints

such as hypertension and heart failure [6]. It has been found that candesartan cilexetil has polymorphs, such as Form I, Form II, amorphous and so on. Among them, Form I is the stable form which is commonly used in pharmacy. Due to the sparing water solubility of Form I, ethanol, acetone and acetonitrile were used as cosolvents to improve the solubility in water. Our group found that the tendency of solubility for candesartan cilexetil (Form I) increase to a maximum at first and then descend as the concentration of water increase in the solvent mixture. This phenomenon has been reported in literature [7,8], and can be explained by considering the polarity of the solvent, solute–solvent, ion–dipole, dipole–dipole, or hydrogen bonding–hydrophobic moiety interaction and so on [9]. In this article, the thermodynamic functions (Gibbs energy, enthalpy and entropy) of solution and mixing were obtained from solubility data in aqueous solvent mixtures (ethanol–water, acetonitrile–water and acetone–water), and the driving force of the solubility enhancement was identified by the enthalpy–entropy compensation analysis [10]. 2. Experimental 2.1. Materials

∗ Corresponding author at: School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, People’s Republic of China. Tel.: +86 22 27405754; fax: +86 22 27314971. E-mail address: junbo [email protected] (J. Gong). 0378-3812/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2012.09.027

Candesartan cilexetil (1-[[(cyclohexyloxy)carbonyl]oxy]ethyl 2-ethoxy-1-[[2-(1H-tetrazol-5-yl)[1,1 -biphenyl]-4-yl]methyl]1H-benzimidazole-7-carboxylate) (Fig. 1, Form I, purity more than 99.5% in mass fraction) was supplied by Huahai Pharmaceutical

P. Cui et al. / Fluid Phase Equilibria 337 (2013) 354–362

355

Fig. 1. Molecular structure of candesartan cilexetil.

Table 1 The substance used in the experiment. Substance

Source

Purity

Candesartan cilexetil (Form I) Ethanol

Huahai Pharmaceutical of China Tianjin Kewei Chemical Reagent Tianjin Kewei Chemical Reagent Tianjin Kewei Chemical Reagent

0.995(HPLC)

Acetonitrile Acetone

Analytical grade Analytical grade

where w2 is the mass of fraction of cosolvent in aqueous mixtures, M1 , M2 , M3 are the molar mass of water, cosolvent and candesartan cilexetil, respectively. Each of the experiment was repeated three times. The mass of the solute and petri dish were measured using an analytical balance (Mettler-Toledo AL104. Shanghai, China, ±0.0001 g). 3. Results

Analytical grade

3.1. Ideal and experimental solubility data of candesartan cilexetil

of China. Ethanol, acetone, acetonitrile and distill deionizer water were purchased from Tianjin Kewei Chemical Reagent of China (Table 1).

The measured mole fraction solubility data of candesartan cilexetil (Form I) in the above-mentioned solvents, which is determined by both temperature and the cosolvent ratios, are reported in the Table 2, which also include the ideal solubility mole fraction of the solute (x3id ) calculated from Eq. (2):

2.2. Melting properties measurements The melting temperature Tfus and enthalpy of fusion Hfus of candesartan cilexetil (Form I) were determined by differential scanning calorimetry (DSC 1/500, Mettler-Toledo, Switzerland). Thermal analyses were performed at a heating rate of 10 K min−1 in a dynamic nitrogen atmosphere (70 mL min−1 ). Nearly 5 mg of candesartan cilexetil (Form I) was used. The measured molar heat and the temperature of fusion are Hfus = 27.74 kJ mol−1 and Tfus = 442 K. 2.3. Solubility measurement The solubility of candesartan cilexetil (Form I) was measured by a gravimetric method that was described in a previous work [11]. Firstly, the excess amount of the drugs and aqueous mixtures with suitable composition were added in the jacketed glass vessel, agitating with a magnetic stirrer for about 4 h to reach the equilibrium. The temperature was maintained by circulating water through the outer jacket from a thermostatic water-circulator bath at the required value. After that, the solution was allowed to settle, and then the upper portion solution was taken, filtered, and poured into a petri dish reweighed (m0 ) by using an analytical balance. The petri dish with upper portion solution was quickly weighted (m1 ) and placed in a blast drying oven at 50 ◦ C for 12 h to evaporate the solvent fully. When the solvent has completely evaporated, the petri dish was reweighed (m2 ) to determine the mass of the residue solid. The mole fraction solubility x3 of candesartan cilexetil (Form I), could be determined from Eq. (1) x3 =

(m2 − m0 )/M3 (m2 − m0 )/M3 + (m2 − m1 )w2 /M1 + (m2 − m1 )(1 − w2 )/M2

(1)

ln x3id = −

Hfus (Tfus − T ) + RTfus



Cp R



Tfus − T + ln T

 T  Tfus

(2)

where Hfus is the molar enthalpy of fusion of candesartan cilexetil (at the melting point), Tfus and T are the melting point and experimental temperature, respectively, R is the gas constant and Cp is the difference between the molar heat capacity of the crystalline form and the molar heat capacity of the hypothetical subcooled liquid form, both at the solution temperature. In this study, it is assumed that Cp may be set equal to the entropy of fusion [12], calculated as Sfus = Hfus /Tfus . Fig. 2 shows the solubility profiles obtained against the cosolvent ratios of the mixtures. At a given cosolvent ratio, the solubilities of candesartan cilexetil increased with temperature in all cases, indicating that the dissolution process is endothermic. During the increase of molar fraction of water in three mixtures, the solubility reached a maximum first, and then decreased. The curve of solubility showed a maximum point at 92.5% ethanol, 80% acetonitrile and 85% acetone. Meantime, these maximum points did not change with temperature. The solubility profiles also showed that at the same condition, the solubility in acetone–water is higher than in ethanol–water and acetonitrile–water, which may be in accordance with the empirical rule “like dissolves like” as two carbonyl groups are contained in the candesartan cilexetil molecule. The activity coefficients of candesartan cilexetil in ethanol–water, acetonitrile–water and acetone–water were calculated as the ratio x3id /x3 (Table 3). A rough estimate of solute–solvent intermolecular interactions can be made from the  3 values by the following expression [13]: ln 3 =

(e11 + e33 − 2e13 )V3 ϕ12 RT

(3)

356

Table 2 Ideal and experimental solubility of candesartan cilexetil (3) in the three mixtures, expressed in molar fraction at different temperatures(values in parentheses are the standard uncertainty). x1

293.15 K

acetonitrile (1) + water(2) mixture 0.100 3.670(0.007) × 10−6 0.200 2.334(0.053) × 10−5 0.300 8.135(0.004) × 10−5 0.400 2.103(0.055) × 10−4 3.852(0.009) × 10−4 0.500 7.253(0.103) × 10−4 0.600 0.700 1.092(0.005) × 10−3 0.800 1.365(0.050) × 10−3 0.900 1.121(0.059) × 10−3 1.000 5.816(0.021) × 10−4 Ideal 4.487 × 10−2 acetone(1) + water(2) mixture 0.100 6.324(0.010) × 10−6 0.200 2.171(0.052) × 10−5 2.318(0.032) × 10−4 0.300 0.400 9.505(0.045) × 10−4 0.500 2.435(0.008) × 10−3 0.600 4.547(0.057) × 10−3 0.700 7.102(0.015) × 10−3 9.050(0.001) × 10−3 0.800 0.850 9.173(0.028) × 10−3 0.900 8.767(0.093) × 10−3 1.000 6.727(0.046) × 10−3 Ideal 4.487 × 10−2

298.15 K

9.330(0.080) × 10−6 2.262(0.031) × 10−5 2.772(0.053) × 10−4 1.119(0.032) × 10−3 2.858(0.032) × 10−3 5.536(0.053) × 10−3 8.475(0.045) × 10−3 1.033(0.027) × 10−2 1.079(0.019) × 10−2 1.022(0.108) × 10−2 7.833(0.014) × 10−3 5.099 × 10−2

303.15 K

313.15 K

323.15 K

333.15 K

343.15 K

2.000(0.009) × 10−6 1.319(0.040) × 10−5 4.874(0.017) × 10−5 1.656(0.030) × 10−4 3.871(0.100) × 10−4 6.813(0.081) × 10−4 1.040(0.024) × 10−3 1.364(0.028) × 10−3 1.485(0.032) × 10−3 1.534(0.050) × 10−3 1.439(0.072) × 10−3 5.781 × 10−2

2.990(0.010) × 10−6 2.369(0.020) × 10−5 9.456(0.050) × 10−5 2.631(0.040) × 10−4 6.336(0.032) × 10−4 1.154(0.040) × 10−3 1.703(0.032) × 10−3 2.180(0.040) × 10−3 2.410(0.054) × 10−3 2.453(0.015) × 10−3 2.350(0.046) × 10−3 7.384 × 10−2

5.740(0.003) × 10−6 4.600(0.016) × 10−5 1.759(0.060) × 10−4 5.332(0.017) × 10−4 1.260(0.045) × 10−3 2.259(0.060) × 10−3 3.358(0.025) × 10−3 4.236(0.060) × 10−3 4.595(0.081) × 10−3 4.775(0.082) × 10−3 4.654(0.057) × 10−3 9.359 × 10−2

1.138(0.019) × 10−5 7.57(0.009) × 10−5 3.163(0.022) × 10−4 9.973(0.025) × 10−4 2.293(0.017) × 10−3 4.180(0.038) × 10−3 6.276(0.017) × 10−3 7.766(0.050) × 10−3 8.325(0.022) × 10−3 8.419(0.096) × 10−3 8.236(0.024) × 10−3 1.178 × 10−1

1.586(0.012) × 10−5 1.200(0.029) × 10−4 4.564(0.015) × 10−4 1.679(0.029) × 10−3 3.050(0.034) × 10−3 5.537(0.090) × 10−3 8.549(0.033) × 10−3 1.090(0.029) × 10−2 1.184(0.012) × 10−2 1.195(0.073) × 10−2 1.178(0.071) × 10−2 1.472 × 10−1

4.480(0.017) × 10−6 2.912(0.032) × 10−5 1.133(0.024) × 10−4 2.644(0.062) × 10−4 5.587(0.005) × 10−4 1.013(0.097) × 10−3 1.503(0.022) × 10−3 1.781(0.040) × 10−3 1.595(0.063) × 10−3 9.122(0.012) × 10−4 5.781 × 10−2

6.420(0.039) × 10−6 4.128(0.059) × 10−5 1.735(0.038) × 10−4 4.521(0.065) × 10−4 1.012(0.040) × 10−3 1.699(0.063) × 10−3 2.465(0.040) × 10−3 2.979(0.033) × 10−3 2.687(0.073) × 10−3 1.598(0.002) × 10−3 7.384 × 10−2

7.17(0.049) × 10−6 5.39(0.022) × 10−5 2.152(0.044) × 10−4 6.508(0.057) × 10−4 1.287(0.068) × 10−3 2.801(0.010) × 10−3 3.891(0.053) × 10−3 4.570(0.005) × 10−3 4.128(0.009) × 10−3 2.627(0.052) × 10−3 9.359 × 10−2

9.16(0.025) × 10−6 6.93(0.012) × 10−5 3.301(0.042) × 10−4 9.587(0.027) × 10−4 2.648(0.112) × 10−3 5.022(0.032) × 10−3 7.255(0.058) × 10−3 8.650(0.013) × 10−3 7.499(0.071) × 10−3 4.414(0.011) × 10−3 1.178 × 10−1

1.37(0.062) × 10−5 3.940(0.023) × 10−5 1.963(0.057) × 10−4 1.419(0.069) × 10−3 3.092(0.054) × 10−3 5.953(0.017) × 10−3 1.005(0.062) × 10−2 1.213(0.022) × 10−2 1.242(0.098) × 10−2 1.179(0.054) × 10−2 9.461(0.073) × 10−3 5.781 × 10−2

308.15 K

1.800(0.017) × 10−5 5.479(0.011) × 10−5 4.560(0.032) × 10−4 1.790(0.044) × 10−3 4.345(0.082) × 10−3 8.149(0.008) × 10−3 1.242(0.081) × 10−2 1.445(0.105) × 10−2 1.506(0.065) × 10−2 1.420(0.055) × 10−2 1.110(0.118) × 10−2 6.540 × 10−2

2.492(0.021) × 10−5 6.499(0.047) × 10−5 5.908(0.073) × 10−4 2.221(0.061) × 10−3 5.335(0.063) × 10−3 9.626(0.016) × 10−3 1.462(0.046) × 10−2 1.737(0.038) × 10−2 1.750(0.033) × 10−2 1.699(0.066) × 10−2 1.329(0.003) × 10−2 7.384 × 10−2

P. Cui et al. / Fluid Phase Equilibria 337 (2013) 354–362

ethanol(1) + water(2) mixture 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.875 0.925 1.000 Ideal

P. Cui et al. / Fluid Phase Equilibria 337 (2013) 354–362

357

Table 3 Activity coefficients of candesartan cilexetil (␥3 ) in the three mixtures at different temperatures. 293.15 K ethanol(1) + water(2) mixture 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.875 0.925 1.000 acetonitrile (1) + water(2) mixture 0.100 12127.0 0.200 1925.8 0.300 551.2 0.400 213.4 0.500 116.5 0.600 61.9 0.700 41.1 0.800 32.9 0.900 40.0 1.000 77.1 acetone(1) + water(2) mixture 7478.3 0.100 2067.7 0.200 0.300 193.6 47.2 0.400 18.4 0.500 0.600 9.9 6.3 0.700 5.0 0.800 4.9 0.850 0.900 5.1 6.7 1.000

298.15 K

303.15 K

5099 2256.2 183.9 45.6 17.8 9.2 6.0 4.9 4.7 5.0 6.5

308.15 K

313.15 K

323.15 K

333.15 K

343.15 K

28905 4379.5 1187.1 349.1 149.3 84.9 55.6 42.4 38.9 37.7 40.2

24613.3 3115.6 778.9 280.7 116.5 64.0 43.4 33.9 30.6 30.1 31.4

16419.3 2034.6 532.1 175.5 74.3 41.4 27.9 22.1 20.4 19.6 20.1

10333.3 1556.1 372.4 118.1 51.4 28.2 18.8 15.2 14.2 14.0 14.3

9257.9 1226.7 322.5 87.7 48.3 26.6 17.2 13.5 12.4 12.3 12.5

12846.7 1986.6 510.2 218.6 103.5 57.1 38.5 32.5 36.2 63.4

11537.5 1787.9 425.6 163.3 73.0 43.5 30.0 24.8 27.5 46.2

13053.0 1736.4 435.0 143.8 72.7 35.6 33.4 24.1 22.7 20.5

12804.3 1699.9 356.9 122.9 44.5 23.5 16.2 13.6 15.7 26.7

4129.3 1467.3 294.5 40.7 18.7 9.7 5.8 4.8 4.7 4.9 6.1

3633.3 1193.4 143.4 36.5 15.1 8.0 5.3 4.5 4.3 4.6 5.9

where e11 , e33 and e13 represent the solvent–solvent, solute–solute and solvent–solute interaction energies, respectively; V3 is the molar volume of solute, and ϕ1 is the volume fraction of the solvent. The term e13 favors solubility, whereas e11 and e33 tend to decrease solubility. The contribution of the e33 term could be considered as constant in all the mixtures [14]. The following analysis could be made based on the energetic quantities and magnitudes: In three aqueous mixtures, waterrich mixtures have higher  3 values which would imply high

2307.5 1136 125.0 33.2 13.8 7.7 5.0 4.3 4.2 4.3 5.6

e11 and low e13 values, meaning that solvent–solvent interaction played a leading role. On the other hand, in cosolvent-rich mixtures (with lower  3 values), the e11 values are relatively low but the e13 values could not to be so great. For a given cosolvent ratio and temperature, the  3 in acetone–water is much lower than in ethanol–water and acetonitrile–water nearly by a magnitude, indicating acetone–water had the relative stronger solute–solvent interactions and lower solvent-solvent interactions than in ethanol–water and acetonitrile–water.

Table 4 Parameters of the (NIBS)/Redlich–Kister equation for candesartan cilexetil (3) in the three mixtures. T (K)

B0

B4

102 rmsd

B1

B2

B3

ethanol(1) + water(2) mixture −4.00291 343.15 −5.96349 333.15 323.15 −8.18265 −8.24334 313.15 −8.56171 303.15

12.19534 20.02821 31.29936 27.62326 26.89043

0.4539 −12.31588 −40.10313 −32.62228 −32.30791

−11.00405 −2.66923 26.07936 19.84488 21.06019

4.82148 3.02909 −7.55552 −5.74643 −6.71513

5.7971 1.1620 1.1025 0.7199 0.600

acetonitrile(1) + water(2) mixture −8.42345 333.15 −7.13289 323.15 −7.76277 313.15 −7.69581 303.15 −6.04361 293.15

36.59521 25.36859 32.17022 28.46041 16.48248

−53.38775 −28.22091 −53.56729 −45.19289 −21.41752

44.24908 18.90689 51.35398 43.5721 25.31371

−17.54578 −7.94888 −21.72338 −19.23073 −14.89168

5.3988 4.9354 1.3612 0.6380 1.1380

acetone(1) + water(2) mixture −7.00241 313.15 −7.50997 308.15 −4.7733 303.15 −8.91383 298.15 −6.72455 293.15

31.1601 32.68236 12.02845 38.79158 24.39087

−37.56419 −40.36768 7.86813 −54.62177 −23.90961

23.63005 26.11955 −20.61109 41.04483 13.34692

−7.63661 −8.51787 7.73256 −14.24407 −5.20199

6.2115 7.7960 7.8728 5.4869 7.4132

358

P. Cui et al. / Fluid Phase Equilibria 337 (2013) 354–362

In this study, the experimental solubility data were correlated by the binary solvent (NIBS)/Redlich–Kister model, which is proposed by Acree and his co-workers [15]: ln x3 = x2 ln (x3 )2 + x1 ln (x3 )1 + x2 x1

n 

si (x2 − x1 )i

(4)

i=0

The model provides very accurate mathematical descriptions for how the solute solubility varies with solvent composition. In Eq. (4), x1 and x2 refer to the initial mole fraction of the binary solvent as if solute (A) was not present, n is the number of curve-fit parameters used, and (x3 )i is the saturated solubility of the solute in pure solvent i. For binary solvent system, substitution of (1 − x1 ) for x2 in Eq. (4) with n = 2 and subsequent rearrangements result in Eq. (5) ln x3 = B0 + B1 x1 + B2 x12 + B3 x13 + B4 x14

(5)

where B0 , B1 , B2 , B3 , B4 are the parameters of the (NIBS)/Redlich–Kister equation that can be obtained by fitting the experimental solubility data. The parameters and root-meansquare deviations (RMSD) calculated by Eq. (6) are given in the Table 4, which show the (NIBS)/Redlich–Kister solubility model provides excellent solubility correlation for candesartan cilexetil (Form I) in aqueous mixtures.

RMSD =

1 (x − xcal )2 n n

1/2 (6)

i=1

3.2. Apparent heat of solution changes as related to solvent composition The enhancement of solubility at given solvent can be attributed to the change of enthalpy and entropy of mixing with a constant contribution from the solid phase at equilibrium [16]. This analysis is performed for each cosolvent ratio of the three mixtures. In this study, the relationship between lnx3 and (1/T–1/Thm ) is linear for three mixtures at all cosolvent ratios, the enthalpy Hsol and free Gibbs energy Gsol are calculated from the slope and intercept of a regression of ln x3 against (1/T–1/Thm ) [4], which is expressed in Eqs. (7) and (8). Thm is the harmonic mean of the experimental  temperatures, namely, Thm = n/ (1/Ti ). Hsol = −R × slope

(7)

Gsol = −RThm × intercept

(8)

The apparent entropy of solution Ssol for the solution process can be obtained from the apparent free energy and enthalpy of solution: Ssoln =

Hsoln − Gsoln Thm

(9)

The relative contributions from enthalpy %  H and entropy %  TS to the standard free energy of solution are obtained from Eqs. (10) and (11).

Fig. 2. Experimental and modeling solubility of candesartan cilexetil (Form I) in three binary mixtures: (a) ethanol–water; (b) acetonitrile–water; (c) acetone–water. The corresponding lines are calculated values based on the (NIBS)/Redlich–Kister model.

%H = 100 ×

|Hsol | |Hsol | + |T Ssol |

(10)

%TS = 100 ×

|TSsol | |Hsol | + |T Ssol |

(11)

The Hsol , Gsol , Ssol , %  H , %  TS are given in Tables 5–7. Dissolution was an endothermic process, Gsol and Hsol are positive in all cases. The plot of apparent molar enthalpy of solution with cosolvent ratios are nonlinear curves (Fig. 3), and the curves of ethanol–water and acetonitrile–water are very similar. In the water-rich region, the enthalpy increases, and then

P. Cui et al. / Fluid Phase Equilibria 337 (2013) 354–362

359

Table 5 Thermodynamic functions of solution for candesartan cilexetil (3) in ethanol (1) + water (2) mixtures including ideal process at 323.15 K. Ethanol (mole fraction)

Gsol (kJ mol−1 )

Hsol (kJ mol−1 )

Ssol (J mol−1 K−1 )

T Ssol (kJ mol−1 )

% H

% TS

0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.875 0.925 1.000 Ideal

32.36 27.03 23.38 20.27 17.81 16.20 15.10 14.46 14.27 14.21 14.32 6.37

47.34 48.31 49.25 51.55 52.98 54.48 54.67 53.77 52.48 52.10 52.68 20.20

46.43 66.00 80.21 96.99 109.04 118.69 122.69 121.89 118.49 117.48 118.95 42.88

14.97 21.28 25.87 31.28 35.16 38.28 39.57 39.31 38.21 37.89 38.36 13.83

76.0 69.4 65.6 62.2 60.1 58.7 58.0 57.8 57.9 57.9 57.9 59.4

24.0 30.6 34.4 37.8 39.9 41.3 42.0 42.2 42.1 42.1 42.1 40.6

Table 6 Thermodynamic functions of solution for candesartan cilexetil (3) in acetonitrile (1) + water (2) mixtures including ideal process at 313.15 K. Acetonitrile (mole fraction)

Gsol (kJ mol−1 )

Hsol (kJ mol−1 )

Ssol (J mol−1 K−1 )

T Ssol (kJ mol−1 )

% H

% TS

0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 Ideal

31.33 26.31 22.66 20.08 18.06 16.41 15.44 14.96 15.30 16.71 6.76

18.68 22.66 27.93 31.88 37.96 39.53 38.30 37.43 38.45 41.45 19.57

−40.37 −11.64 16.85 37.68 63.55 73.81 72.99 71.76 73.93 79.00 40.91

−12.64 −3.64 5.28 11.80 19.90 23.11 22.86 22.47 23.15 24.74 12.81

59.6 86.1 84.1 73.0 65.6 63.1 62.6 62.5 62.4 62.6 60.4

40.4 13.9 15.9 27.0 34.4 36.9 37.4 37.5 37.6 37.4 39.6

Table 7 Thermodynamic functions of solution for candesartan cilexetil (3) in acetone (1) + water (2) mixtures including ideal process at 303.15 K. Acetone (mole fraction)

Gsol (kJ mol−1 )

Hsol (kJ mol−1 )

Ssol (J mol−1 K−1 )

T Ssol (kJ mol−1 )

% H

% TS

0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.850 0.900 1.000 Ideal

28.34 25.70 19.92 16.49 14.21 12.67 11.54 11.07 11.00 11.12 11.75 7.18

51.87 46.96 36.15 33.05 30.29 28.74 27.88 24.99 24.79 25.19 26.09 18.992

77.62 70.13 53.52 54.64 53.05 53.02 53.87 45.92 45.49 46.40 47.31 38.96

23.53 21.26 16.23 16.56 16.08 16.07 16.33 13.92 13.79 14.07 14.34 11.81

68.8 68.8 69.0 66.6 65.3 64.1 63.1 64.2 64.3 64.2 64.5 61.7

31.2 31.2 31.0 33.4 34.7 35.9 36.9 35.8 35.7 35.8 35.5 38.3

reaches maximum (at 70% ethanol and 60% acetonitrile). Since enthalpy is unfavorable, the breaking of the icelike structure of water (hydrogen bonds) around the candesartan cilexetil which increases both the enthalpy and the entropy of the system [4,17]. Above 70% ethanol and 60% acetonitrile, the trend of the enthalpy curve reaches to minimum at 92.5% ethanol and 80% acetonitrile which coincides to the solubility maximum. The solubility of the candesartan cilexetil increases as the apparent enthalpy of the solution decreases, therefore, the dominant mechanism changes and enthalpy controlled the enhancement of solubility at the cosolventrich region. On the other hand, the curve of the apparent molar enthalpies vs. cosolvent ratio in acetone–water is very different for ethanol–water and acetonitrile–water solution. With the molar fraction of water increasing, the enthalpy first decrease, gonging to a minimum at 85% in accordance to the solubility maximum, indicating that the dominant mechanism for solubility in acetone–water was the enthalpy [18]. Fig. 3. Apparent heats of candesartan cilexetil changes in three mixtures.  ethanol;  acetonitrile;  acetone.

3.3. Thermodynamic functions of mixing The thermodynamic properties of mixing are obtained from T Eqs. (11) and (12), using the enthalpy Hfus and entropy

360

P. Cui et al. / Fluid Phase Equilibria 337 (2013) 354–362

Table 8 Thermodynamic functions relative to mixing process of candesartan cilexetil (3) in ethanol (1) + water (2) cosolvent mixtures at 323.15 K. Ethanol (mole fraction)

Gmix (kJ mol−1 )

Hmix (kJ mol−1 )

Smix (J mol−1 K−1 )

T Smix (kJ mol−1 )

% H

% TS

0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.875 0.925 1.000

25.99 20.66 17.01 13.90 11.44 9.83 8.73 8.09 7.89 7.84 7.95

27.14 28.11 29.05 31.35 32.78 34.28 34.47 33.57 32.28 31.90 32.48

3.55 23.12 37.33 54.11 66.16 75.81 79.81 79.01 75.61 74.60 76.07

1.14 7.46 12.04 17.45 21.34 24.45 25.74 25.48 24.38 24.06 24.53

96.0 79.0 70.7 64.2 60.6 58.4 57.3 56.9 57.0 57.0 57.0

4.0 21.0 29.3 35.8 39.4 41.6 42.7 43.1 43.0 43.0 43.0

T Smix (kJ mol−1 )

% H

% TS

−25.45 −16.46 −7.53 −1.01 7.09 10.30 10.05 9.66 10.34 11.93

3.4 15.8 52.6 92.4 72.2 65.9 65.1 64.9 64.6 64.7

96.6 84.2 47.4 7.6 27.8 34.1 34.9 35.1 35.4 35.3

Table 9 Thermodynamic functions relative to mixing process of candesartan cilexetil (3) in acetonitrile (1) + water (2) cosolvent mixtures at 313.15 K. Acetonitrile (mole fraction)

Gmix (kJ mol−1 )

Hmix (kJ mol−1 )

0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

24.57 19.55 15.90 13.32 11.30 9.65 8.68 8.20 8.54 9.95

−0.89 3.09 8.36 12.31 18.39 19.96 18.73 17.86 18.88 21.88

Smix (J mol−1 K−1 ) −81.28 −52.55 −24.06 −3.23 22.64 32.90 32.08 30.85 33.02 38.09

Table 10 Thermodynamic functions relative to mixing process of candesartan cilexetil (3) in acetone (1) + water (2) cosolvent mixtures at 303.15 K. Acetonitrile (mole fraction)

Gmix (kJ mol−1 )

Hmix (kJ mol−1 )

Smix (J mol−1 K−1 )

T Smix (kJ mol−1 )

% H

% TS

0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.850 0.900 1.000

21.16 18.52 12.74 9.31 7.03 5.49 4.36 3.89 3.82 3.94 4.57

32.88 27.97 17.16 14.06 11.30 9.75 8.89 6.00 5.80 6.20 7.10

38.66 31.17 14.56 15.68 14.09 14.06 14.91 6.96 6.53 7.44 8.35

11.72 9.45 4.41 4.75 4.27 4.26 4.52 2.11 1.98 2.26 2.53

73.7 74.7 79.5 74.7 72.6 69.6 66.3 74.0 74.6 73.3 73.7

31.2 31.2 31.0 33.4 34.7 35.9 36.9 35.8 35.7 35.8 35.5

T Sfus of fusion estimated at the harmonic mean experimental temperature (Thm = 323.15 K in ethanol–water, Thm = 313.15 K in acetonitrile–water, Thm = 323.15 K in acetone–water). The relative contribution from enthalpy %  H and entropy %  TS to the standard free energy of mixing can also be calculated by Eqs. (10) and (11), respectively. These results are displayed in Tables 8–10. T Hmix = Hsol − Hfus

(12)

T Smix = Ssol − Sfus

(13)

In aqueous mixture, the free energy of mixing is positive for all cosolvent ratios. This unfavorable contribution decreases as the cosolvent concentration becomes larger (less positive values). The net variation in Hmix values result from the contribution of several kinds of interactions. The enthalpy of cavity formation (required for solute accommodation) is endothermic because work must be done against the cohesive forces of the solvent. On the other hand, the enthalpy of solute–solvent interactions is exothermic and mainly due to van der Waals and Lewis acid–base interactions [19]. The exothermic heat of mixing values suggests that solute–solvent interactions overcome the energetically unfavorable cavity term. In ethanol–water and acetonitrile–water mixture, the structure of water molecules around the non-polar groups of

Fig. 4. Hsol vs. Gsol enthalpy–entropy compensation plot for candesartan cilexetil in three mixtures.  ethanol;  acetonitrile;  acetone.

P. Cui et al. / Fluid Phase Equilibria 337 (2013) 354–362

361

Fig. 5. Simplified packing diagram of candesartan cilexetil (Form I) [22].

solutes (hydrophobic hydration) contributes to lower the net heat of mixing to small or even negative values in aqueous solutions as it is the case of water-rich mixtures. However, in acetone–water mixture, the net heat of mixing is lower as the proportion of acetone increases (with 0.10 ≤ x1 ≤ 0.85), due to favoring solute–solvent interactions in water-rich mixtures [7]. 3.4. Enthalpy–entropy compensation The analysis of enthalpy–entropy compensation is used to identify the mechanism of the cosolvent action. The plots of enthalpy–entropy compensation for three aqueous mixtures are showed in Fig. 4. The results indicate that the variation of the slopes for ethanol–water and acetonitrile–water reveal the change of the dominant mechanism from enthalpy (positive slope at lower Gsol ) to entropy (negative slope at higher Gsol ) [20]. But for acetone–water mixtures, linear compensation with positive slope is obtained at cosolvent compositions, which means that the dominant mechanism is enthalpy [21]. It is an indication that acetone molecules could increase solute–solvent interactions. 4. Discussion In order to propose the possible intermolecular interactions present in the saturated solutions of candesartan cilexetil, the crystal structure of Form I is shown in Fig. 5, which contains intermolecular hydrogen bonds N4 H· · ·N6 and intramolecular hydrogen bonds C14 H· · ·O2 [21]. Therefore, Form I acts in solution as a Lewis acid (due to its CH and NH groups) to establish hydrogen bonds with proton–acceptor functional groups in the solvents (oxygen atoms of OH groups in ethanol, nitrogen atoms of CN groups in acetonitrile and oxygen atoms of C O groups in acetone). On the other hand, candesartan cilexetil can also act as a proton–acceptor compound by means of O2 and N6 to

establish hydrogen bonds with hydrogen atoms of OH groups in ethanol. However, as Lewis base, candesartan cilexetil cannot form hydrogen bonds with acetonitrile and acetone. Therefore, Hmix is negative values at 10% acetonitrile. Molecular structure of candesartan cilexetil also contains two C O groups, according to “like dissolves like”, solubility in acetone–water is higher than in ethanol–water and acetonitrile–water, meaning stronger solute–solvent interactions. Hmix is always positive values in acetone–water as same as in ethanol–water. Moreover, in ethanol–water and acetonitrile–water mixtures, entropy at low cosolvent ratio and enthalpy at high ratio controlled the enhancement of solubility, while enthalpy is the driving force throughout the whole solvent composition in acetone–water. It is well known that the variation of Hmix results from the contribution of several kinds of interactions, endothermic cavity formation and exothermic solute–solvent interactions [23]. The endothermic cavity formation process decreases solubility (compare the discussion of e11 ). On the other hand, the enthalpy of solute–solvent interaction (corresponding to the energy e13 ) is exothermic and results mainly from van der Waals and Lewis acid–base interactions [8]. In the ethanol–water and acetonitrile–water mixtures, the structure of water molecules around the non-polar groups of solutes (hydrophobic hydration) contributes to lower Hmix to small or even negative values in aqueous solutions as it is the case of water-rich mixtures. Nevertheless, this fact is not observed for candesartan cilexetil in acetone–water mixture, where Hmix increases always as the proportion of acetone increasing (0.10 ≤ x1 ≤ 0.85), due to favoring solute–solvent interactions in water-rich mixtures. 5. Conclusions The cosolvency and dominant mechanisms of the cosolvent action for candesartan cilexetil (Form I) in aqueous solvent

362

P. Cui et al. / Fluid Phase Equilibria 337 (2013) 354–362

mixtures (ethanol–water, acetonitrile–water, and acetone–water) were analyzed and explained by enthalpy–entropy compensation. For ethanol–water and acetonitrile–water mixture, nonlinear enthalpy–entropy compensation was obtained. This result indicated that the enhancement of solubility was driven by entropy at the water-rich region, while enthalpy controlled at the ethanol (or acetonitrile) rich region. Nevertheless, for acetone–water mixture, linear compensation with positive slope was obtained, indicating that enthalpy change was the dominant mechanism throughout the whole solvent composition. Analyzing thermodynamic functions (Gibbs energy, enthalpy and entropy) of solution and mixing, the activity coefficient  3 in acetone–water was much lower than those in ethanol–water and acetonitrile–water, and Hmix increased in accordance with the molar fraction of acetone (0.10 ≤ x1 ≤ 0.85) in the mixtures. This result illustrated that there is stronger solute–solvent interactions in acetone–water mixture than in ethanol–water and acetonitrile–water mixtures. List of symbols R gas constant T absolute temperature melting point Tfus Thm medium harmonic temperature V3 molar volume of solute x3 solute mole fraction x3id ideal solubility of solute solvent–solvent interactions term e11 e33 solute–solute interactions term e13 solvent–solute interactions term Greek letters Cp liquid–solid calorific capacities difference Gsol Gibbs free energy of solution enthalpy of fusion Hfus Hmix enthalpy of mixing enthalpy of solution Hsol Smix entropy of mixing entropy of solution Ssol 3 solute activity coefficient solvent volume fraction ϕ1

% %

 H partial enthalpy contribution  TS partial entropy contribution

Acknowledgements This work is supported by National Natural Science Foundation of China (Nos. 20836005 and 21176173) and Tianjin Municipal Natural Science Foundation (Nos. 10JCYBJC14200 and 11JCZDJC20700). The analysis tools used in this study were supported by State Key Laboratory of Chemical Engineering (No. SKL-ChE-11B02). References [1] D.E. Alonzo, G.G.Z. Zhang, D. Zhou, Y. Gao, L.S. Taylor, Pharm. Res. 27 (2010) 608–618. [2] A. Jouyban-Gharamaleki, L. Valaee, M. Barzegar-Jalali, B. Clark, W. Acree, Int. J. Pharm. 177 (1999) 93–101. ˜ P. Bustamante, Fluid Phase Equilib. 308 (2011) 98–106. [3] F. Martínez, M. Pena, [4] C. Bustamante, P. Bustamante, J. Pharm. Sci. 85 (1996) 1109–1111. [5] G.L. Perlovich, S.V. Kurkov, A. Bauer-Brandl, Eur. J. Pharm. Sci. 19 (2003) 423–432. [6] A. Gaitonde, B. Manojkumar, R. Bhalerao, S. Tank, V. Padalkar, WO Patent 754 (2009). [7] M. Gantiva, F. Martínez, Fluid Phase Equilib. 293 (2010) 242–250. [8] E. Tomlinson, Int. J. Pharm. 13 (1983) 115–144. [9] P. Chaudhari, P. Sharma, N. Barhate, P. Kulkarni, C. Mistry, Curr. Sci. 92 (2007) 1586–1591. [10] D.R. Delgado, E.F. Vargas, F. Martinez, J. Chem. Eng. Data 55 (2010) 2900–2904. [11] G.B. Ren, J.K. Wang, Q.X. Yin, M.J. Zhang, J. Chem. Eng. Data 49 (2004) 1376–1378. [12] S.H. Neau, G.L. Flynn, Pharm. Res. 7 (1990) 1157–1162. [13] D. Wei, L. Chen, Fluid Phase Equilib. 277 (2009) 9–14. [14] D.R. Delgado, A.R. Holguín, O.A. Almanza, F. Martínez, Y. Marcus, Fluid Phase Equilib. 305 (2011) 88–95. [15] W.E. Acree, Thermochimi. Acta 198 (1992) 71–79. ˜ B. Escalera, A. Reillo, Int. J. Pharm. 87 (1998) [16] P. Bustamante, S. Romero, A. Pena, 1590–1596. [17] P. Bustamante, J. Navarro, S. Romero, B. Escalera, J. Pharm. Sci. 91 (2002) 874–883. [18] G. Buckton, M. Efentakis, Int. J. Pharm. 62 (1990) 157–163. [19] R. Wolfenden, Biophys. Chem. 105 (2003) 559–572. [20] J.D. Dunitz, Chem. Biol. 2 (1995) 709–712. [21] R. Schmid, Monatshefte für Chemie (Chemical Monthly) 132 (2001) 1295–1326. [22] D. Fernandez, D. Vega, J.A. Ellena, Acta Crystallogr. Sect. E: Struct. Rep. Online 61 (2005) 309–312. [23] M.A. Ruidiaz, D.R. Delgado, F. Martínez, Y. Marcus, Fluid Phase Equilib. 299 (2010) 259–265.