Solution thermodynamics of simvastatin in pure solvents and binary solvent mixtures

Accepted Manuscript Title: Solution thermodynamics of simvastatin in pure solvents and binary solvent mixtures Author: Jiaqi Yan Qiuxiang Yin Chen Jiang Junbo Gong Meijing Zhang Yongli Wang Baohong Hou Hongxun Hao PII: DOI: Reference:

S0378-3812(15)30070-4 http://dx.doi.org/doi:10.1016/j.fluid.2015.07.055 FLUID 10707

To appear in:

Fluid Phase Equilibria

Received date: Revised date: Accepted date:

26-5-2015 31-7-2015 31-7-2015

Please cite this article as: Jiaqi Yan, Qiuxiang Yin, Chen Jiang, Junbo Gong, Meijing Zhang, Yongli Wang, Baohong Hou, Hongxun Hao, Solution thermodynamics of simvastatin in pure solvents and binary solvent mixtures, Fluid Phase Equilibria http://dx.doi.org/10.1016/j.fluid.2015.07.055 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Solution thermodynamics of simvastatin in pure solvents and binary solvent mixtures Jiaqi Yana, Qiuxiang Yina,b, Chen Jianga, Junbo Gonga,b, Meijing Zhanga,b, Yongli Wanga,b, Baohong Houa,b, Hongxun Haoa,b*

a

State Key Laboratory of Chemical Engineering, School of Chemical Engineering and

Technology, Tianjin University

b

Collaborative Innovation Center of Chemical Science and Chemical Engineering (Tianjin),

Tianjin 300072, People's Republic of China

*

Corresponding author. Tel.:86-22-27405754; Fax: 86-22-27314971.

E-mail address: [email protected].

Highlights ► The experimental solubility data of simvastatin in pure solvents and binary solvent mixtures were determined by a gravimetrical method.

► The experimental

solubility data were correlated by several empirical models.

► The

Solubility-Polarity model was modified and used to interpret the dissolution behaviors of simvastatin.

► The dissolution thermodynamic properties of simvastatin were

calculated both in pure solvents and binary solvent mixtures.

Abstract

►

The solubility data of simvastatin in five pure solvents and binary solvent mixtures of isobutyl acetate and n-heptane were experimentally determined by a gravimetrical method under atmospheric pressure. It was found that the solubility of simvastatin increases with temperature rising in all investigated solvents. In binary solvent mixtures, the solubility of simvastatin increases with the decreasing of the mole fraction of n-heptane. The Solubility-Polarity model was modified and used to interpret the dissolution behaviors of simvastatin in binary solvent mixtures. The experimental solubility data in all investigated solvents were correlated by empirical models with the relative average deviation percentage between experimental and calculated solubility less than 5%. The thermodynamic properties of simvastatin, including the Gibbs energy change, the entropy and the enthalpy of dissolution process, were also calculated. The results indicate that the dissolution process of simvastatin is a spontaneous, endothermic and entropy-driving process in all solvent systems.

Keywords: Simvastatin; Solubility; Pure solvents; Binary solvent mixtures; Solubility-Polarity model; Thermodynamic properties

1. Introduction Simvastatin (Figure 1, CAS Registry No.79902-63-9, hereinafter referred as SMV), is a member of the statin family, which occurs as a white to off-white crystalline

powder. SMV is widely used to treat hypercholesterolemia as a cholesterol-lowering agent due to its well proven efficacy and safety behavior [1-4]. It has been reported that SMV is practically insoluble in water (7.25·10-5 g·L-1 in water at 298.15 K) [5]. The poor aqueous solubility of pharmaceuticals is a main barrier for their formulation development [6,7]. Solubility of pharmaceuticals is an extremely useful physicochemical property, and indispensable for designing and optimization of crystallization process. As an important unit operation for production of pharmaceuticals, the crystallization process which is used to purify SMV during its manufacturing will directly determine the quality of the products and the yield of the process. Although solubility data of SMV in a family of alcohols at various temperatures have been reported [8], it has been found that alcohols might not be the ideal solvents for the purification and refinement processes [9] of SMV since some problems such as wide size distribution and poor flowability of products exist. Furthermore, based on the dissolution characters of SMV, anti-solvent crystallization is generally used in the purification of SMV. Therefore, it is crucial to know the solubility data of SMV in good solvents, anti-solvents and the mixtures of these two kinds of solvents. From literature review, it was found that the solubility of SMV in various mixed solvents and pure esters have not been reported. In this work, the solubility data of SMV in five pure esters (methyl acetate, ethyl acetate, n-propyl acetate, n-butyl acetate and isobutyl acetate) from 278.15 K to 318.15 K and binary solvent mixtures of isobutyl acetate with n-heptane from 278.15 K to 308.15 K were

experimentally determined with a gravimetrical method under atmospheric pressure. The experimental solubility data were correlated by empirical models, including the non-random, two-liquid model (NRTL model) and the combined nearly ideal binary solvent (NIBS)/Redlich-Kister model (CNIBS/R-K model). Meanwhile, the Solubility-Polarity model was modified and applied for quantitative interpretation of the dissolution behaviors of SMV in binary solvent mixtures. Furthermore, the thermodynamic properties (the Gibbs energy, the enthalpy and the entropy) of dissolution process of SMV were also calculated and analyzed. 2. Experimental section 2.1. Materials and Reagents Simvastatin (≥ 99 %, mass) was provided by PKU Health Care Co., Ltd. of China. The identification of SMV samples was confirmed by X-ray power diffraction (XPRD) pattern. The organic solvents (methyl acetate, ethyl acetate, n-propyl acetate, n-butyl acetate, isobutyl acetate and n-heptane) selected in this work are analytical reagents. More details about these materials are listed in Table 1. All the materials were directly used without any further purification in the experiments. 2.2. Thermal analysis Differential scanning calorimetry (DSC 1/500, Mettler Toledo, Co., Switzerland) experiments were performed to obtained thermal properties of SMV. The amount of samples was 5-10 mg and the measurements were carried out form 298.15 K to 523.15 K with a heating rate of 10 K/min under the protection of nitrogen. The

enthalpy of fusion and melting temperature were determined by using the DSC data. The uncertainties of the measurements were ±0.5 K for the temperature and around 2 % for the enthalpy of fusion. 2.3. Solubility Measurements The solubility of SMV in pure solvents and binary solvent mixtures were determined by the gravimetrical method [10,11]. Excess of solid SMV was added to strictly sealed conical flasks, containing the corresponding solvents. The conical flasks were shaken continuously in a bath oscillator for 10 h to equilibrate then kept still for 4 h. The temperature was controlled by a thermostat (Julabo CF41, Germany) with temperature uncertainty of ± 0.01 K. Afterwards, the supernatant clear solution was withdrawn and filtered through a cellulose membrane filter (0.2 µm) into a vessel which has been weighed beforehand. The total weight was measured immediately. The vessel was dried until the mass did not change any more. All the masses were weighed by an analytical balance (Mettler ToledoML204, Switzerland) with an accuracy of ± 0.0001 g. Experiments were performed in triplicate and the average value was used to calculate the solubility. The experimental mole fraction solubility (x1) of SMV can be obtained from the following equation: x1 =

m1 M 1 m1 M 1 +

n

∑ (m i= 2

i

Mi)

(1)

where m1 and M1 represent the mass and the molar mass of SMV respectively. mi and Mi (i = 2,3...n) represent the mass and the molar mass of the solvents respectively. When n = 2, it indicates pure solvent while n = 3 means binary solvent mixtures. The initial mole fraction (x02 ) of n-heptane in isobutyl acetate and n-heptane mixtures in absence of SMV was calculated as follow:

x20 =

m2 M 2 m2 M 2 + m3 M 3

(2)

where m2 and m3 represent the mass of n-heptane and isobutyl acetate respectively. M2 and M3 represent the molar mass of n-heptane and isobutyl acetate respectively. 3. Thermodynamic models 3.1. The Solubility-Polarity Model Effects of solvent on solubility of solute are pervasive but not fully understood. The empirical rule, namely “like dissolves like”, is widely used as the qualitative description for the effects. Due to the absence of clear definition and direct measuring method of polarity of solvents, the empirical polarities (ENT ), the relative dielectric constants (εr) and the dipole moments (µ) are usually used as the criterions of solvent polarity. However, the visual correlation of either the empirical polarities (ENT ) or the dipole moments (µ) with the solubility of solute is not very obvious [12]. As a result, by using the relative dielectric constant (εr) as the measurement of solvent polarity, which is proportional to the relative dielectric constant, the Solubility-Polarity model has been proposed [13].

  Ex x1cal = k exp  −   RTε rmix (T ) 

(3)

where xcal is the calculated mole fraction solubility of SMV. k is a pre-exponential 1 factor, and Ex stands for the dissolution energy barrier. R is the gas constant. T is the absolute temperature. εrmix(T), the relative dielectric constant of binary solvent mixtures at various temperatures, is relevant to temperature and composition of solvents. The dependence of relative dielectric constant on temperature can be reflected by equation (4) [14]. Additionally, the sum law of cube roots, equation (5) [15], was chosen to calculate the relative dielectric constants of solvent mixtures at fixed temperatures. Taking both temperature and composition of solvents into consideration, εrmix(T) can be calculated by equation (6).

εr (T) = a+bT +cT2 +dT3

(4)

where a, b, c and d are empirical coefficients whose values are available from the literature [14].

ε rmix1/3 = ∑ yiε ri1/3

(5)

i

where yi is the volume fraction of component i in the solvent mixtures in absence of solute, and εri is the relative dielectric constant of pure component i. 



ε rmix (T ) =  ∑ yiε ri (T )  

1/3

i

3



(6)

Since the original equation (3) was found to be inaccurate for the investigated binary solvent mixtures in this work, the model was modified as follow.

  Ex x1cal = k exp  − 2  RT ε (T )    rmix  1/3  ε rmix (T ) =  ∑ x i0ε ri ( T )   i 

(7)

3

(8)

where x0i is the mole fraction of component i in the solvent mixtures in absence of solute. 3.2. The Interactional Mixing Model: CNIBS/R-K Model The dependence of solubility of solute on binary solvent composition can be expressed by CNIBS/R-K model [16].

ln x1 = x ln ( x1 )2 + x ln ( x1 )3 + x x cal

0 2

0 3

∑S ( x N

0 0 2 3

i =1

i

0 2

− x30 )

i

(9)

where Si is the model constant, N can be 0, 1, 2 or 3, xcal is the calculated solubility 1 of SMV in binary solvent mixtures of isobutyl acetate and n-heptane, (x1)2 and (x1)3 are the solubility of SMV in pure n-heptane and isobutyl acetate respectively, x02 and x03 represent the initial mole fraction of n-heptane and isobutyl acetate in binary solvent mixtures in absence of SMV. When x03 was substituted for (1 − x02 ), and N = 2, equation (9) can be simplified into the General Single model [17]. ln x1cal = B0 + B1 x20 +B2 ( x20 ) + B3 ( x20 ) + B4 ( x20 ) 2

3

4

where B0, B1, B2, B3 and B4 are empirical parameters of the CNIBS/R-K model. 3.3. The Local Composition Model: NRTL Model

(10)

According to the solid-liquid phase equilibrium theory and the solute-solvent interactions, the local composition equation [18] could be simplified and expressed by equation (11):

ln x1cal =

∆fus H  Tm  1 −  − ln γ1 RTm  T 

(11)

where ∆fusH and Tm stand for the enthalpy of fusion and melting temperature of pure solute. γ1 is the activity coefficient of solute in the saturated solution, which can be calculated by NRTL model [19] with three parameters.

 τ G2 τ12G12  21 21 ln γ 1 = x  + 2 2  ( x1 + G21 x2 ) ( x2 + G12 x1 )  2 2

(12)

where

G12 = exp ( −α12τ12 ) G21 = exp ( −α12τ 21 )

τ 12 =

g 12 − g 11 ∆ g 12 = RT RT

τ 21 =

g 21 − g 22 ∆ g 21 = RT RT

(13)

with g12 = g21 where ∆g21 and ∆g21 stand for the cross interaction energy which are independent of the composition and temperature. The parameter α12 which is an empirical constant between 0 and 1 is a criterion of the non-randomness of the solution. 4. Results and discussion 4.1. Identification and Characterization

The X-ray power diffraction (XPRD) patterns of SMV are shown in Figure 2. The DSC data of SMV are shown in Figure 3. The XPRD pattern verifies that only one crystalline form of SMV was used in all experiments. No new polymorph was observed. The melting temperature Tm and fusion enthalpy ∆fusH of SMV which can be obtained from DSC data are 415.1 K and 30.13 kJ·mol-1, respectively. 4.2. Experimental solubility data Experimental mole fraction solubility data of SMV in all solvent systems at investigated temperatures are listed in Table 2 and Table 3. The solubility of SMV in pure solvents increases with the increasing of temperature. At the same temperature, the order of the solubility of SMV in pure solvents is methyl acetate > ethyl acetate > n-propyl acetate > n-butyl acetate > isobutyl acetate. The order of the relative dielectric constants of pure solvents is methyl acetate > ethyl acetate > n-propyl acetate > n-butyl acetate > isobutyl acetate (Table 4). It can be said that the solubility of SMV in pure solvents almost completely follow the principal of “like dissolves like”. This means that the solubility of SMV in solvents with higher polarity will be higher. In the binary solvent mixtures of isobutyl acetate and n-heptane, the solubility of SMV increases with the temperature rising while decreases with the increasing of mole fraction of n-heptane. The decreasing of mole fraction solubility of SMV with the increasing of mole fraction of n-heptane is probably due to lower polarity of n-heptane compared to isobutyl acetate.

4.3. Modeling of solubility data In this work, the original Solubility-Polarity model was modified and used to correlate the experimental solubility data of SMV in binary solvent mixtures of isobutyl acetate and n-heptane. To prove the reliability and applicability of the modified Solubility-Polarity model, solubility data of some pharmaceuticals in binary solvent mixtures which have been published in literature were used to evaluate the modified model. The calculated results by both the modified model and the original model are listed in Table 5. It can be seen that the coefficient of determination (R2) values for all tested pharmaceuticals obtained by the modified model are larger than those obtained by the original model, which indicate that the modified Solubility-Polarity model is applicable and accurate for correlating solubility data of pharmaceuticals in binary solvent mixtures. Then this modified model was used to correlate the experimental solubility data of SMV in binary solvent mixtures. The calculated results are given in Table 3 and graphically shown in Figure 4. It can be found that the experimental data are very close to the correlated results, indicating the applicability and reliability of the modified model for SMV. The R2 values of the modified Solubility-Polarity model for SMV in isobutyl acetate and n-heptane mixtures are listed in Table 6. All of R2 values are larger than 0.9918, which again confirm the accuracy of this modified model. Additionally, this modified model can be used to explain the effects of solvents on the dissolution behaviors of SMV. The relative dielectric constants together with the dissolution

energy barriers of isobutyl acetate and n-heptane mixtures at various temperatures are also shown in Table 6. It can be found that the polarity of the binary solvent mixtures of isobutyl acetate and n-heptane decreases with the increasing of n-heptane content. This can explain why the solubility of SMV decreases with the increasing of n-heptane content. This indicates again that the solubility of SMV is higher when the polarity of the binary solvent mixtures is larger. In addition, it can be seen that the dissolution energy barriers increase with the temperature rising although the polarity of the binary solvent mixtures decreases with the increasing of temperature. That is to say, the dissolution process is harder when the polarity of the binary solvent mixtures is lower. This can be explained by the fact that the polarity of binary solvent mixtures might affect the dissolving rate of SMV. According to literature [20], the dissolution process of SMV can be described as SMV molecules filling in vacancies of the binary solvent molecular clusters. With the polarity decreasing, the solute-solvent interactions weaken. The resistance for SMV molecules to fill in the vacancies of mixed solvent molecular clusters becomes stronger, which will cause the increasing of dissolution energy barriers of SMV. In addition, to extend the application range and help the easy usage of the solubility data, the empirical models were adopted to correlate the solubility data of SMV. The NRTL model was used for correlating experimental solubility data in pure solvents while the CNIBS/R-K model was applied for correlating experimental solubility data

in the binary solvent mixtures. And the relative average deviation percentage (RADP) was used to evaluate these models and it can be calculated by the following equation: 1 RADP = N

N

x1,i − x1,cali

i =1

x1,i

∑

(14)

where N is the number of experimental data points in each solvent. The calculated data of solubility of SMV in pure solvents by the NRTL model are presented in Figure 5. The RADP along with the NRTL model parameters are shown in Table 7. It can be seen that the calculated solubility data are consistent with the experimental data and all of the RADP values were less than 5%. This confirms the accuracy and reliability of NRTL model for correlating the solubility data in pure solvents. The RADP along with the CNIBS/R-K model parameters are shown in Table 8. The calculated results of solubility data in binary solvent mixtures are shown in Figure 6. It can be seen that the RADP values are less than 2% and the experimental solubility data are consistent with the calculated results, indicating the accuracy and reliability of CNIS/R-K model for binary solvent mixtures.

4.4. Thermodynamic Properties The dissolution process could be represented by the following hypothetic stages [21,22]: fusion cooling mixing Solute(solid)  →Solute(liquid)atTm  →Solute(liquid)atT   →Solute(solution)

Solute melts at Tm, then cools to T, finally mixes with the solvent at T. This approximation permits us to calculate the partial thermodynamic properties of the overall dissolution process as following.

∆disG = ∆fusG + ∆cG + ∆mixG ∆dis H = ∆fus H + ∆c H + ∆mix H ∆dis S = ∆fus S + ∆c S + ∆mix S

(15)

where ∆disG, ∆fusG, ∆cG and ∆mixG, ∆disH, ∆fusH, ∆cH and ∆mixH, ∆disS, ∆fusS, ∆cS and ∆mixS refer to the dissolution thermodynamic properties, the fusion thermodynamic properties, the thermodynamic properties of cooling process, and the mixing thermodynamic properties, respectively. The thermodynamic properties of cooling process can be estimated with the assumption that the heat capacity of SMV (Cp) is equal to the fusion entropy [23], calculated as ∆fusS = ∆fusH/Tm.

∆ cG = ∆ c H − T ∆ c S

∆c H = Cp (T − Tm ) ∆c S = Cp ln

T Tm

(16)

For ideal solution systems conforming to the Lewis-Randall rule, the mixing thermodynamic properties of real solution systems can be calculated as follow [24].

∆mixG = RT ∑ xi ln xiγ i i

∆ mixG = ∆ mix H − T ∆mix S

(17)

where xi and γi are the mole fraction and activity coefficient of

component i in real

solution, respectively. i = 2 means binary solution and i = 3 means ternary solution. Based on the NRTL equation, the mixing Gibbs energy of real binary solution can be deduced as the following equation [25].  τ G τ G ∆ mix G = RTx1 x2  21 21 + 12 12  x1 + x2 G21 x2 + x1G12

  + RT ( x1 ln x1 + x2 ln x2 ) 

∆mixH = 0

(18)

According to the Wilson equation [25], the mixing Gibbs energy of real ternary solution can be obtained as the following description.

∆mixG = RT(x1 ln x1γ1 + x2 ln x2γ2 + x3 ln x3γ3) ∆mixH = 0

(19)

  Α12 Α21 ln γ 1 = − ln( x1 + Α12 x2 + x3 A13 ) + x2  −   x1 + Α12 x2 + x3 A13 x1 A21 + x2 + Α23 x3    A13 A31 + x3  −   x1 + x2 A12 + x3 A13 x1 A31 + x2 A32 + x3    A21 A12 ln γ 2 = − ln( x1 A21 + x2 + x3 A23 ) + x1  −   x1 A21 + x2 + x3 A23 x1 + x2 A12 + A13 x3    A23 A32 + x3  −   x1 A21 + x2 + x3 A23 x1 A31 + x2 A32 + x3    A31 A13 ln γ 3 = − ln( x1 A31 + x2 A32 + x3 ) + x1  −   x1 A31 + x2 A32 + x3 x1 + x2 A12 + A13 x3    A32 A23 + x2  −   x1 A31 + x2 A32 + x3 x1 A21 + x2 + x3 A23 

where A12 =

V2  Λ  exp  − 12  V1  RT 

A21 =

V1  Λ  exp  − 21  V2  RT 

(20)

A13 =

V3  Λ  exp  − 13  V1  RT 

A31 =

V1  Λ  exp  − 31  V3  RT 

A23 =

V3  Λ  exp  − 23  V2  RT 

A32 =

V2  Λ  exp  − 32  V3  RT 

where Λ12, Λ21, Λ13, Λ31, Λ23 and Λ32 stand for parameters of Wilson equation which are independent of temperature. V1, V2 and V3 refer to the molar volume of SMV, n-heptane and isobutyl acetate, respectively. The values are shown in Table 9. The calculated results of the thermodynamic properties of cooling process for SMV are shown in Table 10. The calculated mixing thermodynamic properties of SMV in pure solvents and binary solvent mixtures of isobutyl acetate and n-heptane are given in Table 11 and 12, respectively. The calculated results of dissolution thermodynamic properties are given in Table 13 and 14. From these two tables, it can be found that the values of ∆disG are all negative, which indicate that the dissolution of SMV in all investigated solvents is a spontaneous and favorable process. The positive ∆disH and ∆disS reveal that the dissolution of SMV in all investigated solvents is endothermic and entropy-driven. The weaker interaction forces between SMV and solvent than those corresponding to pure substances may account for this phenomenon. 5. Conclusions The solubility of SMV in five pure solvents and one kind of binary solvent mixtures were determined and correlated. The solubility of SMV increases with the temperature rising in all tested solvent systems. In pure solvents, the dissolution behaviors of SMV follow the “like dissolves like” rule. In the binary solvent mixtures

of isobutyl acetate and n-heptane, the solubility of SMV decreases with the increasing of n-heptane content. The Solubility-Polarity model was modified and applied to explain the dissolution behaviors of SMV in binary solvent mixtures. The calculated results of SMV solubility by all models are consistent with the experimental results. According to the dissolution thermodynamic data of SMV, the dissolution process of SMV was found to be a spontaneous, endothermic and entropy-driving process in all investigated solvents. Acknowledgements This research is financially supported by National Natural Science Foundation of China (No. 21376165) and Key Project of Tianjin Science and Technology Supporting Program (No. 13ZCZDNC02000).

Nomenclature Symbol x1 x2 x3 m1 m2 m3 M1 M2 M3 ENT εr

µ k Ex R T

Name the molar fraction solubility of simvastatin the molar fraction of the solvents the mass of simvastatin (g) the mass of the solvents (g) the molar mass of simvastatin (g·mol-1) the molar mass of the solvents (g·mol-1) the empirical polarity the relative dielectric constant the dipole moment a pre-exponential factor for Solubility-Polarity model the dissolution energy barrier (kJ·mol-1) the gas constant (J·mol-1·K-1) the absolute temperature (K)

Tm p a b c y2 y3 B0 to B4 γ1 γ2 γ3 ∆fusH ∆fusG ∆fusS ∆g21 ∆g21 α12 Λ12 to Λ32 V1 V2 V3 RADP ∆disH ∆disG ∆disS ∆mixH ∆mixG ∆mixS ∆cH ∆cG ∆cS

melting temperature of simvastatin (K) pressure (Pa) empirical coefficients for the relative dielectric constant volume fraction of solvents parameters of the CNIBS/R-K model the activity coefficient of simvastatin the activity coefficients of n-heptane and isobutyl acetate the enthalpy of fusion (kJ·mol-1) the Gibbs energy of fusion (kJ·mol-1) the entropy of fusion (J·mol-1·K-1) parameters for the NRTL model (J·mol-1) empirical constant of the non-randomness of the solution parameters for the Wilson model (J·mol-1) molar volume of simvastatin (m3·mol-1) molar volume of n-heptane and isobutyl acetate (m3·mol-1) the relative average deviation percentage the dissolution enthalpy (J·mol-1) the dissolution Gibbs energy (J·mol-1) the dissolution entropy (J·mol-1·K-1) the mixing enthalpy of solution (J·mol-1) the mixing Gibbs energy of solution (J·mol-1) the mixing entropy of solution (J·mol-1·K-1) the cooling enthalpy (J·mol-1) the cooling Gibbs energy (J·mol-1) the cooling entropy (J·mol-1·K-1)

References [1] R. G. Simões, C. E. S. Bernardes, H. P. Diogo, F. Agapito, M. E. Minas da Piedade, Energetics and structure of simvastatin, Mol. Pharm. 10 (2013) 2713-2722. [2] J. Čejka, B. Kratochvíl, I. Císařova, A. Jegorov, Simvastatin, Acta Cryst. C59 (2003) 428-430. [3] M. Hušák, B. Kratochvíl, A. Jegorov, J. Brus, J. Maixner, J. Rohlíček, Simvastatin: structure solution of two new low-temperature phases from synchrotron powder diffraction and ss-NMR, Struct. Chem. 21 (2010) 511-518.

[4] G. Murtaza, Solubility enhancement of simvastatin: a review, Acta Poloniae Pharmaceutica-Drug Res. 69 (2012) 581-590. [5] K. Matsuyama, K. Nakagawa, A. Nakai, Y. Konishi, M. Nishikata, H. Tanaka, T. Uchida, Evaluation of myopathy risk for HMG-CoA reductase inhibitors by urethane infusion method, Biol. Pharm. Bull. 25 (2002) 346-350. [6] F. Shakeel, N. Haq, N. A. Siddiqui, F. K. Alanazi, I. A. Alsarra, Thermodynamics of the solubility of reserpine in {{2-(2-ethoxyethoxy)ethanol + water}} mixed solvent systems at different temperatures, J. Chem. Thermodyn. 85 (2015) 57-60. [7] M. El-Badry, N. Haq, G. Fetih, F. Shakeel, Measurement and correlation of tadalafil solubility in five pure solvents at (298.15 to 333.15) K, J. Chem. Eng. Data. 59 (2014) 839-843. [8] J. M. Aceves-Hernández, J. Hinojosa-Torres, I. Nicolás-Vázquez, R. M. Ruvalcaba, R. M. L. García, Solubility of simvastatin: a theoretical and experimental study, J. Mol. Struct. 995 (2011) 41-50. [9] Y. Qin, A research of new synthetic methods of simvastatin. Shandong. 2006. [10] P. Cui, Q. Yin, J. Gong, Y. Wang, H. Hao, C. Xie, Y. Bao, M. Zhang, B. Hou, J. Wang, Thermodynamic analysis and correlation of solubility of candesartan cilexetil in aqueous solvent mixtures, Fluid Phase Equilib. 337 (2013) 354-362. [11] C. Du, L. Wang, G. Yu, C. Qi, Solubilities of phosphonic acid, P,P'-(1,4-Piperazinediyl)bis-,P,P,P',P'-tetraphenyl ester in selected solvents, J. Chem. Eng. Data. 58 (2013) 2768-2774. [12] Z. Ma, F. Zaera, Role of the solvent in the adsorption-desorption equilibrium of cinchona alkaloids between solution and a platinum surface: correlations among solvent polarity, cinchona solubility, and catalytic performance, J. Phys. Chem. 109 (2005) 406-414. [13] X. Zhang, Q. Yin, P. Cui, Z. Liu, J. Gong, Correlation of solubilities of hydrophilic pharmaceuticals versus dielectric constants of binary solvents, Ind. Eng. Chem. Res. 51 (2012) 6933-6938.

[14] D. R. Lide, CRC handbook of chemistry and physics. CRC press, Florida, 2002. [15] H. Looyenga, Dielectric constants of heterogeneous mixtures, Physica 31 (1965) 401-406. [16] W. E. Acree Jr., Mathematical representation of thermodynamic properties part 2. derivation of the combined nearly ideal binary solvent (NIBS)/Redlich-Kister mathematical representation from a two-body and three-body interactional mixing model, Thermochimica Acta. 198 (1992) 71-79. [17] J. Zhou, H. Fu, H. Cao, C. Lu, C. Jin, T. Zhou, M. Liu, Y. Zhang, Measurement and correlation of the solubility of florfenicol in binary 1,2-propanediol + water mixtures from 293.15 K to 316.25 K, Fluid Phase Equilib. 360 (2013) 118-123. [18] Y. Zhao, Y. Wang, Measurement and correlation of solubility of tetracycline hydrochloride in six organic solvents, J. Chem. Thermodyn. 57 (2013) 9-13. [19] H. Renon, J. M. Prausnitz, Local compositions in thermodynamic excess functions for liquid mixtures, AlChE J. 14 (1968) 135-144. [20] J. Knoblauch, I. Zimmermann, Thermochemical analysis of the dissolution process of griseofulvin, Eur. J. Pharm. Biopharm. 67 (2007) 743-751. [21] A. R. Holguín, D. R. Delgado, F. Martínez, Y. Marcus, Solution thermodynamics and preferential solvation of meloxicam in propylene glycol + water mixtures, J. Solution Chem. 40 (2011) 1987-1999. [22] D. R. Delgado, F. Martínez, Solubility and solution thermodynamics of sulfamerazine and sulfamethazine in some ethanol + water mixtures, Fluid Phase Equilib. 360 (2013) 88-96. [23] S. L. Neau, G. L. Flynn, Solid and liquid heat capacities of n-alkyl para-aminobenzoates near the melting point, Pharm. Res. 7 (1990) 1157-1162. [24] J. M. Smith, H. C. V. Ness, M. M. Abbott, Introduction to chemical engineering thermodynamics, McGraw-Hill, New York, 2001. [25] D. Kondepudi, Introduction to modern thermodynamics, John Wiley & Sons, Ltd., Chichester, 2008.

[26] S. Wang, L. Qin, Z. Zhou, J. Wang, Solubility and solution thermodynamics of betaine in different pure solvents and binary mixtures, J. Chem. Eng. Data. 57 (2012) 2128-2135. [27] V. Jouyban-Gharamaleki, K. Jouyban-Gharamaleki, J. Soleymani, W. E. Acree Jr., A. Jouyban, Solubility of tris(hydroxymethyl)aminomethane in water + 1-propanol mixtures at various temperatures, J. Chem. Eng. Data. 59 (2014) 3723-3727. [28] T. Li, Y. Li, Y. Li, B. Ren, Solubilities of {a-D-glucose in water + (acetic acid or propionic acid)} mixtures at atmospheric pressure and different temperatures, J. Chem. Thermodyn. 65 (2013) 7-10. [29] F. Lei, Q. Wang, X. Gong, B. Shen, W. Zhang, Q. Han, Solubilities of succinic acid in acetic acid + water mixtures and acetic acid + cyclohexane mixtures, J. Chem. Eng. Data. 59 (2014) 1714-1718. [30] Q. Zhang, Y. Yang, L. Cheng, C. Cao, Z. Ding, C. Wang, W. Yang, Y. Hu, Y. Li, Thermodynamic models for determination of the solubility of DL-malic acid in methanol plus (acetonitrile, N,N-dimethylformamide, isopropyl alcohol) binary solvent mixtures, J. Chem. Thermodyn. 85 (2015) 148-154. [31] Y. Shen, Z. Liu, J. Zhi, T. Li, B. Ren, Solubility correlation and thermodynamic analysis of solution of tylosin tartrate in (methanol + tetrahydrofuran or acetone) mixtures, J. Mol. Liq. 203 (2015) 131-136.

Table headings: TABLE 1 Sources, mass fraction purities and general properties of chemicals.

TABLE 2 Experimental mole fraction solubility (x1) and calculated mole fraction solubility (xcal) of simvastatin in pure solvents at various temperatures (p = 0.1 MPa). abcd

TABLE 3 Experimental mole fraction solubility (x1) and calculated mole fraction solubility (xcal) of simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane at various initial mole fractions of n-heptane ( x20 ) and various temperatures (p = 0.1 MPa). abcdef TABLE 4 Relative dielectric constant (εr) of pure solvents (p = 0.1 MPa). ab TABLE 5 The comparison results of the original Solubility-Polarity model and the modified Solubility-Polarity model by using data of pharmaceuticals from literatures. TABLE 6 Relative dielectric constant (εrmix) of binary solvent mixtures of isobutyl acetate and n-heptane at various initial mole fractions of n-heptane ( x20 ) (p = 0.1 MPa) and the parameters of the modified Solubility-Polarity model. abcd TABLE 7 Parameters of the NRTL model for the solubility of simvastatin in pure solvents. TABLE 8 Parameters of the CNIBS/R-K model for the solubility of simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane at various temperatures. TABLE 9 The parameters of Wilson equation for simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane and the molar volume of pure component. TABLE 10 The thermodynamic properties of cooling process for simvastatin. a TABLE 11 The mixing thermodynamic properties of simvastatin in pure solvents. a

TABLE 12 The mixing thermodynamic properties of simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane at various initial mole fractions of n-heptane (x02 ) ab. TABLE 13 The dissolution thermodynamic properties of simvastatin in pure solvents. a

TABLE 14 The dissolution thermodynamic properties of simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane at various initial mole fractions of n-heptane (x02 ) ab.

Figure captions: Fig. 1. Chemical structure of simvastatin. Fig. 2. X-ray power diffraction patterns of simvastatin. Fig. 3. DSC data of simvastatin. Fig. 4. Mole fraction solubility (x1) of simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane at various temperatures: ■, 278.15 K; ○, 283.15 K; ▲, 288.15 K; △, 293.15 K; ★, 298.15 K; ※, 303.15 K; □, 308.15 K; solid lines are correlated data by the modified Solubility-Polarity model. Fig. 5. Mole fraction solubility (x1) of simvastatin in pure solvents at various temperatures: ■, methyl acetate; ▲, ethyl acetate; ☆, n-propyl acetate; △, n-butyl acetate; ※, isobutyl acetate; solid lines are correlated data by the NRTL model.

Fig. 6. Mole fraction solubility (x1) of simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane at various initial mole fractions of n-heptane (x02 ): ■, 278.15 K; ○, 283.15 K; ▲, 288.15 K; △, 293.15 K; ☆, 298.15 K; ※, 303.15 K; ★, 308.15 K; solid lines are correlated data by the CNIBS/R-K model.

TABLE 1 Sources, mass fraction purities and general properties of chemicals. Chemicals

Mass purity

Simvastatin

≥0.990

none

HPLCa

Methyl acetate

≥0.980

none

GCb

Ethyl acetate

≥0.995

none

GCb

n-Propyl acetate

≥0.980

none

GCb

n-Butyl acetate

≥0.990

none

GCb

Isobutyl acetate

≥0.985

none

GCb

n-Heptane

≥0.985

none

GCb

a b

Method of purification

Analysis method

Source PKU Health Care Co., Ltd. Tianjin Damao Chemical Co., Ltd. Tianjin Guangfu Chemical Co., Ltd. Tianjin Guangfu Chemical Co., Ltd. Tianjin Yuxiang Science and Technology Co., Ltd. Tianjin Guangfu Chemical Co., Ltd. Tianjin Jiangtian Chemical Co., Ltd

High-performance liquid chromatography. Gas chromatography.

TABLE 2 Experimental mole fraction solubility (x1) and calculated mole fraction solubility (xcal) of simvastatin in pure solvents at various temperatures (p = 0.1 MPa). abcd

T/K 278.15 283.15 288.15 293.15 298.15

102x1 Methyl acetate 2.41 2.90 3.39 4.14 5.03

102xcal,NRTL

T/K

2.36 2.93 3.61 4.42 5.36

278.15 283.15 288.15 293.15 298.15

102x1 Ethyl acetate 2.19 2.61 3.18 3.79 4.28

102xcal,NRTL 1.99 2.47 3.05 3.74 4.55

303.15 308.15 313.15 318.15

6.08 6.46 303.15 5.19 5.50 7.65 7.72 308.15 6.31 6.59 9.49 9.16 313.15 8.07 7.82 11.22 10.82 318.15 9.43 9.26 n-Propyl acetate n-Butyl acetate 278.15 1.97 1.92 278.15 1.93 1.68 283.15 2.33 2.29 283.15 2.27 2.03 288.15 2.90 2.76 288.15 2.51 2.43 293.15 3.48 3.32 293.15 3.08 2.93 298.15 3.82 3.91 298.15 3.45 3.50 303.15 4.57 4.69 303.15 4.19 4.21 308.15 5.53 5.64 308.15 5.03 5.05 313.15 6.97 6.87 313.15 5.97 6.04 318.15 8.16 8.21 318.15 7.03 7.22 Isobutyl acetate Isobutyl acetate 278.15 1.64 1.61 303.15 3.93 4.02 283.15 1.97 1.96 308.15 5.01 4.73 288.15 2.39 2.36 313.15 5.46 5.58 293.15 2.82 2.84 318.15 6.51 6.52 298.15 3.28 3.39 a x1 represents the experimental solubility of simvastatin and xcal,NRTL represents the calculated solubility data of simvastatin by the NRTL model. b The standard uncertainty of temperature is u(T) = 0.05 K. c The standard uncertainty of pressure is u(p) = 3 kPa. d The relative standard uncertainty of the solubility measurement u is ur (x1)= 0.05. TABLE 3 Experimental mole fraction solubility (x1) and calculated mole fraction solubility of simvastatin (xcal) in binary solvent mixtures of isobutyl acetate and n-heptane at various initial mole fractions of n-heptane (x02 ) and various temperatures (p = 0.1 MPa). abcdef T/K 278.15 283.15 288.15 293.15 298.15 303.15

103x1

103xcal,CNIBS x02 = 0.000 16.42 16.68 19.69 19.71 23.93 23.96 28.23 28.03 32.79 32.87 39.27 39.34

103xcal,SP

T/K

15.90 18.93 22.41 26.16 31.20 36.96

278.15 283.15 288.15 293.15 298.15 303.15

103x1

103xcal,CNIBS x02 = 0.092 13.70 13.44 16.10 16.04 18.31 18.26 21.06 21.00 24.69 24.43 29.09 28.95

103xcal,SP 13.57 16.12 19.06 22.22 26.41 31.27

308.15

50.11 0 2

x 278.15 283.15 288.15 293.15 298.15 303.15 308.15

13.04 14.89 17.09 19.59 22.72 27.06 33.03 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

9.07 11.03 12.93 15.83 17.48 20.50 24.98 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

4.56 5.29 6.44 8.08 9.29 10.85 13.35 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

1.07 1.31 1.49 1.77 2.13 2.44 2.62 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

0.26 0.30 0.36 0.45 0.50 0.62 0.71

50.57 = 0.115 12.70 15.13 17.16 19.80 22.95 27.18 32.64 = 0.233 9.42 11.07 12.85 15.39 17.52 20.72 25.18 = 0.476 4.61 5.31 6.51 8.19 9.40 10.96 13.43 = 0.714 1.09 1.30 1.49 1.77 2.12 2.44 2.68 = 0.864 0.25 0.31 0.36 0.44 0.51 0.61 0.69

45.34

308.15

35.54 0 2

x 12.97 15.40 18.20 21.22 25.20 29.83 36.36

278.15 283.15 288.15 293.15 298.15 303.15 308.15

11.48 13.98 15.60 17.64 20.95 24.85 29.24 x02

9.96 11.79 13.90 16.19 19.14 22.66 27.41

278.15 283.15 288.15 293.15 298.15 303.15 308.15

6.85 7.82 9.46 12.05 13.48 15.99 19.54 x02

4.39 5.17 6.09 7.10 8.30 9.87 11.71

278.15 283.15 288.15 293.15 298.15 303.15 308.15

2.76 3.12 3.74 4.46 5.39 6.18 7.34 x02

0.94 1.11 1.32 1.57 1.81 2.19 2.54

278.15 283.15 288.15 293.15 298.15 303.15 308.15

0.44 0.53 0.61 0.75 0.87 1.00 1.12 x02

0.26 0.31 0.38 0.46 0.53 0.65 0.75

278.15 283.15 288.15 293.15 298.15 303.15 308.15

0.17 0.21 0.25 0.31 0.36 0.43 0.50

34.92 = 0.154 11.52 13.68 15.54 18.11 20.85 24.67 29.60 = 0.353 6.82 7.88 9.54 11.88 13.45 15.85 19.67 = 0.603 2.65 3.09 3.67 4.51 5.32 6.12 7.11 = 0.820 0.45 0.54 0.62 0.74 0.87 1.02 1.13 = 0.891 0.17 0.21 0.25 0.31 0.35 0.43 0.51

38.17 11.97 14.20 16.77 19.54 23.17 27.43 33.35 7.02 8.29 9.76 11.37 13.36 15.84 18.99 2.31 2.72 3.21 3.76 4.37 5.23 6.14 0.42 0.50 0.60 0.72 0.84 1.02 1.18 0.19 0.23 0.28 0.34 0.39 0.48 0.55

a

x1 represents the experimental solubility of simvastatin, xcal,CNIBS and xcal,SP represent the calculated solubility data of simvastatin by the CNIBS/R-K model and the modified Solubility-Polarity model, respectively. b 0 x2 represents the initial mole fraction of n-heptane in binary solvent mixtures of isobutyl acetate and n-heptane in absence of simvastatin. c The standard uncertainty of temperature is u(T) = 0.05 K. d The standard uncertainty of pressure is u(p) = 3 kPa. e The relative standard uncertainty of the solubility measurement u is ur (x1)= 0.05. f The relative standard uncertainty of mole fraction of n-heptane u is ur (x02 ) = 0.001. TABLE 4 Relative dielectric constant (εr) of pure solvents (p = 0.1 MPa). ab Pure Solvents εr Methyl Ethyl n-Propyl n-Butyl Isobutyl acetate acetate acetate acetate acetate 278.15 7.2860 6.4170 5.9510 5.3183 5.3279 283.15 7.1799 6.3065 5.8382 5.2336 5.2360 288.15 7.0737 6.1979 5.7288 5.1514 5.1465 293.15 6.9676 6.0914 5.6229 5.0715 5.0595 T/K 298.15 6.8615 5.9867 5.5205 4.9941 4.9750 303.15 6.7553 5.8841 5.4215 4.9191 4.8929 308.15 6.6492 5.7834 5.3260 4.8465 4.8133 313.15 6.5431 5.6846 5.2339 4.7763 4.7362 318.15 6.4369 5.5878 5.1453 4.7085 4.6615 a Relative dielectric constants of pure solvents were calculated by equation (4). b The standard uncertainty of temperature is u(T) = 0.05 K.

TABLE 5 The comparison results of the original Solubility-Polarity model and the modified Solubility-Polarity model by using data of pharmaceuticals from literatures. Materials

Mixed solvents

T/K

R2o a

R2m

a

References b

Betaine

Ethanol + Water

282.85~318.75

<0.9522

>0.9703

26

Tris(hydroxymethyl) aminomethane

Water + 1-Propanol

293.20~313.55

<0.9255

>0.9625

27

D-glucose

Propionic acid + Water

297.65~331.40

<0.9038

>0.9170

28

Succinic acid

Acetic acid + Cyclohexane

303.20~333.20

<0.9686

>0.9876

29

DL-malic acid

N,N-Dimethylformamide + Methanol

278.15~328.15

<0.9519

>0.9827

30

Tylosin tartrate

Methanol + Acetone

298.15~323.15

<0.8216

>0.9275

a

R2o and R2m represent the coefficients of determination for the original and the modified Solubility-Polarity model respectively. b The number in references represents the provenance of the tested pharmaceuticals. TABLE 6 Relative dielectric constant (εrmix) of binary solvent mixtures of isobutyl acetate and n-heptane at various initial mole fractions of n-heptane (x02 ) (p = 0.1 MPa) and the parameters of the modified Solubility-Polarity model. abcd εrmix

a

278.15 283.15 0.092 4.920 4.840 0.115 4.821 4.743 0.154 4.657 4.583 0.233 4.336 4.271 0.353 3.875 3.821 0 x2 0.476 3.437 3.395 0.603 3.025 2.993 0.714 2.637 2.615 0.820 2.394 2.377 0.864 2.277 2.262 0.891 2.208 2.194 2 R 0.9980 0.9980 -1 Ex /(kJ·mol ) 60.2 60.8 Relative dielectric constants of

T/K 288.15 293.15 298.15 4.761 4.684 4.610 4.667 4.592 4.521 4.511 4.441 4.374 4.207 4.145 4.086 3.769 3.719 3.670 3.354 3.314 3.275 2.961 2.931 2.901 2.592 2.570 2.549 2.359 2.342 2.326 2.247 2.233 2.219 2.181 2.168 2.155 0.9966 0.9939 0.9929 61.0 61.1 62.2 binary solvent mixtures of

303.15 308.15 4.539 4.468 4.452 4.384 4.309 4.244 4.029 3.971 3.625 3.577 3.239 3.201 2.874 2.845 2.529 2.508 2.311 2.295 2.206 2.192 2.144 2.131 0.9918 0.9924 62.2 63.7 isobutyl acetate and

n-heptane were calculated by equation (8). b 0 x2 represents the initial mole fraction of n-heptane in binary solvent mixtures of isobutyl acetate and n-heptane in absence of simvastatin. c The dissolution energy barrier Ex was calculated by equation (7), and the uncertainty of Ex is u(Ex) = 0.5. d The standard uncertainty of temperature is u(T) = 0.05 K.

TABLE 7 Parameters of the NRTL model for the solubility of simvastatin in pure solvents.

Parameters ∆g12 a /(J·mol-1)

Methyl acetate 730.2

Pure Solvents Ethyl n-Propyl n-Butyl acetate acetate acetate 2582.1 -1132.9 -1018.8

Isobutyl acetate 1250.7

31

∆g21 a /(J·mol-1) -1840.1 -3220.3 1802.1 1554.6 a a12 0.95 0.10 0.10 0.10 2 b 10 RADP 4.15 4.61 2.56 4.20 a ∆g12, ∆g21 and a12 are the parameters of the NRTL model. b RADP is the relative average deviation percentage.

-772 0.10 1.94

TABLE 8 Parameters of the CNIBS/R-K model for the solubility of simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane at various temperatures. T/K b0 a b1 a b2 a b3 a b4 a 278.15 -4.094 -2.210 -2.050 6.183 -8.493 283.15 -3.927 -1.964 -3.924 9.708 -10.405 288.15 -3.731 -3.235 3.320 -3.261 -3.176 293.15 -3.575 -3.760 7.816 -12.171 1.996 298.15 -3.415 -3.762 6.524 -8.359 -0.716 303.15 -3.236 -3.953 7.608 -10.891 1.055 308.15 -2.984 -5.155 14.314 -23.647 8.495 a b0, b1, b2, b3 and b4 are the parameters of the CNIBS/R-K model. b RADP is the relative average deviation percentage.

102RADP b 1.93 0.94 0.76 1.31 0.77 0.88 1.33

TABLE 9 The parameters of Wilson equation for simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane and the molar volume of pure component. Λ12 a Λ21 a Λ13 a Λ31 a Λ23 a Λ32 a /(J·mol-1) /(J·mol-1) /(J·mol-1) /(J·mol-1) /(J·mol-1) /(J·mol-1) 21766 5854 -1641 1894 -21682 151 V Simvastatin n-Heptane Isobutyl acetate 3 -1 /(cm ·mol ) 358.7 146.5 133.3 a Λ12, Λ21, Λ13, Λ31, Λ23 and Λ32 stand for parameters of Wilson equation. Parameters

TABLE 10 The thermodynamic properties of cooling process for simvastatin. a T/K

∆cG/(J·mol-1)

∆cH/(J·mol-1)

∆cS/(J·mol-1·K-1)

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

-1858 -1716 -1581 -1451 -1328 -1210 -1099 -994.1

-9941 -9579 -9216 -8853 -8490 -8127 -7764 -7401

-29.06 -27.77 -26.50 -25.25 -24.02 -22.82 -21.63 -20.46

318.15 a

-894.7

-7038

-19.31

The combined expanded uncertainties are Uc(∆cH) = 0.050∆cH, Uc(∆cS) = 0.065∆cS,

Uc(∆cG) = 0.044∆cG (0.95 level of confidence). TABLE 11 The mixing thermodynamic properties of simvastatin in pure solvents. a T/K

∆mixG /(J·mol-1)

∆mixS /(J·mol-1·K-1)

Methyl acetate

T/K

∆mixG ∆mixS -1 /(J·mol ) /(J·mol-1·K-1) Ethyl acetate

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

a

-294.0 1.057 278.15 -263.0 0.946 -346.1 1.222 283.15 -308.1 1.088 -398.4 1.383 288.15 -365.7 1.269 -472.9 1.613 293.15 -425.8 1.452 -557.9 1.871 298.15 -475.3 1.594 -653.5 2.156 303.15 -558.5 1.842 -786.9 2.554 308.15 -656.4 2.130 -933.7 2.982 313.15 -796.9 2.545 -1065 3.348 318.15 -902.7 2.837 n-Propyl acetate n-Butyl acetate 278.15 -236.7 0.851 278.15 -228.0 0.820 283.15 -271.9 0.960 283.15 -261.1 0.922 288.15 -326.2 1.132 288.15 -285.5 0.991 293.15 -378.4 1.291 293.15 -338.4 1.154 298.15 -408.7 1.371 298.15 -372.3 1.249 303.15 -472.6 1.559 303.15 -436.1 1.439 308.15 -550.0 1.785 308.15 -505.2 1.639 313.15 -659.4 2.106 313.15 -579.0 1.849 318.15 -745.2 2.342 318.15 -658.3 2.069 Isobutyl acetate Isobutyl acetate 278.15 -200.6 0.721 303.15 -420.0 1.385 283.15 -234.7 0.829 308.15 -486.5 1.579 288.15 -277.1 0.962 313.15 -547.8 1.749 293.15 -310.1 1.058 318.15 -628.6 1.976 298.15 -362.1 1.215 The combined expanded uncertainties are Uc(∆mixH) = 0.050∆mixH, Uc(∆mixS) =

0.065∆mixS, Uc(∆mixG) = 0.044∆mixG (0.95 level of confidence).

TABLE 12 The mixing thermodynamic properties of simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane at various initial mole fractions of n-heptane (x02 ) ab. T/K

∆mixG /(kJ·mol-1)

∆mixS /(J·mol-1·K-1)

T/K

x02 = 0.092 278.15 283.15 288.15 293.15 298.15 303.15 308.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 278.15

-2.782 -2.815 -2.846 -2.880 -2.917 -2.954 -3.009 x02 = 0.154 -4.325 -4.359 -4.389 -4.420 -4.453 -4.483 -4.525 x02 = 0.353 -8.751 -8.777 -8.803 -8.829 -8.848 -8.859 -8.885 x02 = 0.603 -13.208 -13.214 -13.218 -13.222 -13.221 -13.215 -13.219 x02 = 0.820 -15.448

10.001 9.940 9.877 9.826 9.785 9.745 9.765

278.15 283.15 288.15 293.15 298.15 303.15 308.15

15.548 15.394 15.231 15.078 14.936 14.787 14.684

278.15 283.15 288.15 293.15 298.15 303.15 308.15

31.461 30.997 30.551 30.116 29.677 29.223 28.834

278.15 283.15 288.15 293.15 298.15 303.15 308.15

47.484 46.666 45.874 45.105 44.344 43.591 42.896

278.15 283.15 288.15 293.15 298.15 303.15 308.15

55.537

278.15

∆mixG /(kJ·mol-1) x02 = 0.115 -3.371 -3.401 -3.433 -3.466 -3.500 -3.535 -3.586 0 x2 = 0.233 -6.161 -6.192 -6.223 -6.256 -6.281 -6.302 -6.339 0 x2 = 0.476 -11.123 -11.142 -11.160 -11.176 -11.187 -11.189 -11.205 x02 = 0.714 -14.834 -14.816 -14.800 -14.782 -14.762 -14.740 -14.724 x02 = 0.864 -15.488

∆mixS /(J·mol-1·K-1) 12.118 12.011 11.913 11.825 11.738 11.659 11.636 22.149 21.869 21.598 21.342 21.066 20.787 20.572 39.990 39.349 38.729 38.123 37.521 36.911 36.362 53.329 52.327 51.362 50.426 49.513 48.622 47.782 55.681

283.15 288.15 293.15 298.15 303.15 308.15

a

-15.407 54.412 283.15 -15.429 54.491 -15.366 53.325 288.15 -15.371 53.344 -15.324 52.275 293.15 -15.313 52.235 -15.283 51.258 298.15 -15.255 51.165 -15.241 50.274 303.15 -15.198 50.133 -15.200 49.325 308.15 -15.139 49.129 0 0 x2 = 0.891 x2 = 0.891 278.15 -15.363 55.233 298.15 -15.079 50.575 283.15 -15.292 54.006 303.15 -15.010 49.514 288.15 -15.220 52.821 308.15 -14.938 48.477 293.15 -15.149 51.677 The combined expanded uncertainties are Uc(∆mixH) = 0.050∆mixH, Uc(∆mixS) =

0.065∆mixS, Uc(∆mixG) = 0.044∆mixG (0.95 level of confidence). b 0 x2 represents the initial mole fraction of n-heptane in binary solvent mixtures of isobutyl acetate and n-heptane in absence of simvastatin.

TABLE 13 The dissolution thermodynamic properties of simvastatin in pure solvents. a

T/K

∆disG/(kJ·mol-1)

∆disH/(kJ·mol-1)

∆disS/(J·mol-1·K-1)

Methyl acetate 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

-2.152 -2.062 -1.978 -1.924 -1.885 -1.864 -1.886 -1.928 -1.960

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

-2.121 -2.024 -1.946 -1.876 -1.803 -1.769 -1.756 -1.791

20.189 20.552 20.915 21.278 21.641 22.004 22.367 22.730 23.093 Ethyl acetate 20.189 20.552 20.915 21.278 21.641 22.004 22.367 22.730

44.580 46.038 47.469 48.948 50.434 51.925 53.511 55.107 56.623 44.468 45.904 47.355 48.788 50.157 51.612 53.087 54.670

a

318.15

-1.797

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

-2.094 -1.988 -1.906 -1.829 -1.736 -1.683 -1.649 -1.654 -1.640

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

-2.086 -1.977 -1.866 -1.789 -1.700 -1.647 -1.604 -1.573 -1.553

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

-2.058 -1.950 -1.857 -1.761 -1.690 -1.630 -1.586 -1.542 -1.523

23.093 n-Propyl acetate 20.189 20.552 20.915 21.278 21.641 22.004 22.367 22.730 23.093 n-Butyl acetate 20.189 20.552 20.915 21.278 21.641 22.004 22.367 22.730 23.093 Isobutyl acetate 20.189 20.552 20.915 21.278 21.641 22.004 22.367 22.730 23.093

56.112 44.374 45.776 47.218 48.626 49.933 51.329 52.742 54.231 55.617 44.342 45.738 47.077 48.489 49.811 51.208 52.596 53.974 55.344 44.244 45.645 47.048 48.393 49.777 51.155 52.536 53.875 55.251

The combined expanded uncertainties are Uc(∆disH) = 0.050∆disH, Uc(∆disS) =

0.065∆disS, Uc(∆disG) = 0.044∆disG (0.95 level of confidence). TABLE 14 The dissolution thermodynamic properties of simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane at various initial mole fractions of n-heptane (x02 ) ab. T/K

∆disG/(kJ·mol-1)

∆disH/(kJ·mol-1) x02 = 0.092

∆disS/(J·mol-1·K-1)

278.15 283.15 288.15 293.15 298.15 303.15 308.15

-4.640 -4.530 -4.426 -4.331 -4.245 -4.165 -4.108 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

-5.228 -5.116 -5.013 -4.917 -4.827 -4.745 -4.685 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

-6.182 -6.075 -5.969 -5.871 -5.781 -5.693 -5.624 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

-8.019 -7.908 -7.803 -7.707 -7.608 -7.512 -7.438 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

-10.609 -10.493 -10.383 -10.279 -10.176 -10.069 -9.985 x02

278.15 283.15

-12.981 -12.858

20.189 20.552 20.915 21.278 21.641 22.004 22.367 = 0.115 20.189 20.552 20.915 21.278 21.641 22.004 22.367 = 0.154 20.189 20.552 20.915 21.278 21.641 22.004 22.367 = 0.233 20.189 20.552 20.915 21.278 21.641 22.004 22.367 = 0.353 20.189 20.552 20.915 21.278 21.641 22.004 22.367 = 0.476 20.189 20.552

53.524 54.756 55.963 57.161 58.347 59.515 60.722 55.641 56.826 57.999 59.160 60.301 61.429 62.593 59.071 60.210 61.317 62.413 63.499 64.557 65.641 65.672 66.685 67.684 68.677 69.629 70.557 71.529 74.983 75.813 76.637 77.451 78.240 78.993 79.792 83.512 84.165

288.15 293.15 298.15 303.15 308.15

-12.740 -12.626 -12.514 -12.400 -12.304 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

-15.065 -14.929 -14.799 -14.673 -14.549 -14.425 -14.318 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

-16.691 -16.532 -16.380 -16.233 -16.090 -15.950 -15.823 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

-17.305 -17.122 -16.946 -16.775 -16.610 -16.451 -16.299 x02

278.15 283.15 288.15 293.15 298.15 303.15 308.15

-17.345 -17.145 -16.951 -16.763 -16.582 -16.408 -16.238 x02

278.15 283.15 288.15 293.15

-17.221 -17.007 -16.800 -16.600

20.915 21.278 21.641 22.004 22.367 = 0.603 20.189 20.552 20.915 21.278 21.641 22.004 22.367 = 0.714 20.189 20.552 20.915 21.278 21.641 22.004 22.367 = 0.820 20.189 20.552 20.915 21.278 21.641 22.004 22.367 = 0.864 20.189 20.552 20.915 21.278 21.641 22.004 22.367 = 0.891 20.189 20.552 20.915 21.278

84.815 85.458 86.084 86.680 87.319 91.007 91.482 91.960 92.440 92.907 93.361 93.854 96.852 97.143 97.448 97.761 98.076 98.392 98.739 99.060 99.228 99.412 99.610 99.821 100.044 100.282 99.203 99.307 99.430 99.570 99.727 99.903 100.086 98.756 98.822 98.908 99.012

a

298.15 -16.406 303.15 -16.221 308.15 -16.038 The combined expanded uncertainties

21.641 99.137 22.004 99.284 22.367 99.434 are Uc(∆disH) = 0.050∆disH, Uc(∆disS) =

0.065∆disS, Uc(∆disG) = 0.044∆disG (0.95 level of confidence). b 0 x2 represents the initial mole fraction of n-heptane in binary solvent mixtures of isobutyl acetate and n-heptane in absence of simvastatin.

Fig. 1. Chemical structure of simvastatin.

Fig. 2. X-ray power diffraction patterns of simvastatin.

Fig. 3. DSC data of simvastatin.

Fig. 4. Mole fraction solubility (x1) of simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane at various temperatures: ■, 278.15 K; ○, 283.15 K; ▲, 288.15 K; △, 293.15 K; ★, 298.15 K; ※, 303.15 K; □, 308.15 K; solid lines are correlated data by the modified Solubility-Polarity model.

Fig. 5. Mole fraction solubility (x1) of simvastatin in pure solvents at various temperatures: ■, methyl acetate; ▲, ethyl acetate; ☆, n-propyl acetate; △, n-butyl acetate; ※, isobutyl acetate; solid lines are correlated data by the NRTL model.

Fig. 6. Mole fraction solubility (x1) of simvastatin in binary solvent mixtures of isobutyl acetate and n-heptane at various initial mole fractions of n-heptane (x02 ): ■, 278.15 K; ○, 283.15 K; ▲, 288.15 K; △, 293.15 K; ☆, 298.15 K; ※, 303.15 K; ★, 308.15 K; solid lines are correlated data by the CNIBS/R-K model.