Determination and Correlation of Solubility of Quetiapine Fumarate in

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX-XXX

pubs.acs.org/jced

Determination and Correlation of Solubility of Quetiapine Fumarate in Nine Pure Solvents and Two Aqueous Binary Solvents Shasha Jin,†,‡ Shichao Du,†,‡ Yumin Liu,†,‡ Dandan Han,†,‡ Zhenfang Li,†,‡ Kangli Li,†,‡ and Junbo Gong*,†,‡ †

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, and ‡The Co-Innovation Center of Chemistry and Chemical Engineering of Tianjin, Tianjin University, Tianjin 300072, People’s Republic of China S Supporting Information *

ABSTRACT: A gravimetric method was used to determine the solubility of quetiapine fumarate (QF) in nine pure solvents and two aqueous binary solvents (water + methanol/ ethanol) at different temperatures from 283.15 to 323.15 K. The solubility of QF increases with the increase of temperature in nine pure solvents, and it is in the order DMF > methanol > ethanol >1-butanol > isopropyl alcohol > (acetone > ethyl acetate > isobutyl alcohol) > water at low temperature, and in the order DMF > methanol > ethanol >1-butanol > isopropyl alcohol > (acetone > isobutyl alcohol > ethyl acetate) > water at relatively high temperature at a given temperature. The solubility of QF in the binary solvents also shows temperature dependence, while at a given temperature the solubility is mainly influenced by the solvent composition with the presence of maximum, reflecting cosolvency. Also the solubility of QF increases with the increase of temperature in binary solvents in a given composition. The Hansen solubility parameters were used to explain the cosolvency and maxima shift, confirming that for large values (>25 MPa1/2) of solute, the solubility shows a peak in the range of 35 to 31 MPa1/2 of solubility parameters of alcohol mixtures. The experimental solubility of QF in pure and binary solvents is well correlated by modified Apelblat equation, the nonrandom two-liquid model, and the CNIBS/R-K equation, respectively.

1. INTRODUCTION Quetiapine fumarate (QF, CASRN 111974-72-2), 2-[2-(4dibenzo[b,f ][1,4]thiazepin-11-yl-1-piperazinyl)ethoxy]ethanol, (E)-2-butenedioate (2:1) salt (C46H54N6O8S2, Figure 1), corresponding to a molecular weight of 883.11, is a psychotropic medicine, belonging to the class of drugs known as dibenzothiazepines.1 QF, marketed as Serouel and developed by AstraZeneca UK limited, was first published in the UK in July 1997,2 then was approved by the U.S. Food and Drugs Administration in September 1997. Now it is also currently

approved in over 70 countries worldwide for the treatment of psychosis associated with schizophrenia.2 QF is now considered to be the first line treatment for schizophrenia with, theoretically, a low propensity for movement disorder adverse effects,2 such as acute dystonia, acute dyskinesia, pseudoParkinsonism, and tardive dyskinesiaused. Previous studies showed that QF possesses potent remyelinating and neuroprotective properties in animal models of demyelination. Therefore, it can also be used to treat multiple sclerosis (MS), a central nervous system disorder that is associated with progressive oligodendrocyte and neuronal loss, axonal degeneration, and demyelination.3 In addition to the above-described efficacy, QF has a very good therapeutic effect on glioma, one of the most common malignancies in clinic.4 On the whole, QF is widely used in psychiatric and nonpsychiatric diseases, MS, and glioma. Up to now, there existed five solid-state forms of QF reported in the literature: three polymorphs and two amorphs.5 Crystal form II and form III both can form as solvates, especially the chloroform or methylene chloride solvates, but Lifshitz-Liron, R., etc. have not designated it by any trivial name.6 Another patent also reported that there existed only Received: June 8, 2017 Accepted: October 20, 2017

Figure 1. Sketch of the molecular structure of QF: red ball, O; purple ball, N; yellow ball, S; gray ball, C. © XXXX American Chemical Society

A

DOI: 10.1021/acs.jced.7b00518 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Properties of Materials Used in This Work

a

chemical name

molecular weight

mass fraction purity

quetiapine fumarate methanol ethanol isopropyl alcohol 1-butanol isobutyl alcohol acetone ethyl acetate DMF

883.10 32.04 46.07 60.07 74.12 74.12 58.08 88.11 74.08

≥0.990 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995

source Meilunbio Co.,Ltd., China Jiangtian Chemical Technology Jiangtian Chemical Technology Jiangtian Chemical Technology Jiangtian Chemical Technology Jiangtian Chemical Technology Jiangtian Chemical Technology Jiangtian Chemical Technology Jiangtian Chemical Technology

Co., Co., Co., Co., Co., Co., Co., Co.,

Ltd., Ltd., Ltd., Ltd., Ltd., Ltd., Ltd., Ltd.,

China China China China China China China China

purification

analysis method

none none none none none none none none none

HPLCa GCb GCb GCb GCb GCb GCb GCb GCb

High performance liquid chromatography. bGas liquid chromatography.

2. EXPERIMENTAL SECTION 2.1. Materials. Quetiapine fumarate (QF) with mass fraction purity higher than 0.99 was supplied by Meilunbio Co., Ltd. (Dalian, China). All solvents used in this work, including methanol, ethanol, isopropyl alcohol, 1-butanol, isobutyl alcohol, acetone, ethyl acetate, and N,N-dimethylformamide (DMF), are of analytical grade (mass fraction purity > 0.995). All of them were purchased from Jiangtian Chemical Co., Ltd., China, and used without purification. The deionized water used was of HPLC grade. The materials used in this paper are listed in Table 1. 2.2. X-ray Powder Diffraction. X-ray powder diffraction (XRPD) was used to identify the crystal form of QF. The XRPD patterns were obtained by using a Rigaku D/max-2500 (Rigaku, Japan) using Cu Kα radiation (1.54046 Å) in the 2theta range of 2° to 50° and scanning rate of 1 step·s−1. Raw materials, excess solid in the conical flasks, and dried solid were characterized by XRPD, respectively. 2.3. Melting Properties Measurements. Differential scanning calorimetry (DSC) (Mettler-Toledo, model DSC 1/ 500, Switzerland), calibrated by standard indium and zinc, was used to determine the melting properties including temperature (Tm) and the enthalpy of fusion (ΔfusH) of QF. About (5−10) mg of QF was used, and the thermal analyses were performed at a heating rate of 10 K/min under 200 mL/min nitrogen purge. 2.4. Solubility Measurement. The solubility of QF in the solvents was measured by a gravimetric method. The experimental solvents included nine different pure solvents and two binary solvents (methanol + water and ethanol + water) with different mole fraction of water (from 0.1 to 0.9). Excess solid QF was added in the stoppered conical flask fitting with 30 g of each given solvent, and the temperature was kept by a thermostatic bath (type 501 A, Shanghai Laboratory Instrument Works Co., Ltd., China) with an uncertainty of ±0.05 K. These flasks were continuously stirred for 12 h at different constant temperatures. It was proven by preliminary experiments that 12 h was enough to ensure the (solid + liquid) equilibrium of QF in the experimental solvents. To obtain the clear saturated supernatant, the solution was allowed to sit for another 2 h without stirring. Then a preheated/cooled disposable syringe equipped with a 0.22 μm filter was used to pipet out approximately (5−10) mL of saturated supernatant from each flask. The samples were placed into preweighed glass vessels and the glass vessels were immediately reweighed. Then the beakers were placed in a vacuum drying oven at 50 °C for about 20 h until the weight remained constant. All of the masses in this work were measured by a balance (type AB204, Mettler Toledo, Switzerland) with a precision of ±0.0001 g.

three crystal forms, i.e. Crystalline form I, Crystalline form II, and the amorphous form. The patent emphasized the stability of form II under different stress conditions, indicating that form II did not undergo polymorphic transition.7 At present, there are various processes disclosed for the preparation of QF.8,9 But the obtained QF contains many impurities, affecting pharmacological effects and side effects.10 Solution recrystallization from organic solvents, such as ethanol, DMF, and acetone has attracted considerable attention to improve the purity of products.9,11 The solubility of QF in these solvents dominates the development of crystals and the crystallization process, and is also closely related to the maximum achievable yield of solid.12 Thus, it would be more informative to represent the solubility distribution curve as a function of the solvents. However, the existing solubility data is limited, most of which were determined at room temperature, and the temperature dependence was not studied. Ogawa et al. reported the solubility of quetiapine hemifumarate in water at constant temperature by HPLC.13 Patel et al. studied the solubility in isopropyl alcohol and isobutyl alcohol at 25 °C by UV.14 Hamed studied the effect of pH, buffer capacity, and ionic strength on QF release, and the author investigated the solubility in DDH2O of zero ionic strength at 37 °C by UV.15 Little attention has been paid to the solubility in other solvents. Here we report the temperature dependence of the solubility of QF in different pure and mixed solvents that differ in polarity and hydrogen-bonding ability. These solvents are often used to purify QF in the preparation and crystallization process owing to their availability and mild toxicity, and to investigate the effects of solvent nature on solubility. Also, often the mixed solvents produce some delightful effects on the results because of the various activities as compared to that of the pure component, so that this work can provide some guidance for industrial processes. The aim of the present work is to determine the solubility of QF in nine pure solvents (methanol, ethanol, isopropyl alcohol, 1-butanol, isobutyl alcohol, acetone, ethyl acetate, and N,Ndimethylformamide) and two binary solvents (methanol + water and ethanol + water) over the temperature range from 283.15 to 323.15 K at atmospheric pressure (p = 0.1 MPa) by a gravimetric method. The solubility of QF in pure solvents was correlated by the modified Apelblat equation and nonrandom two-liquid (NRTL) model while the combined nearly ideal binary solvent/Redlich−Kister (CNIBS/R-K) equation and the NRTL were applied to correlate the solubility of QF in binary solvents. The impacts of temperature and solvent composition on the solubility were investigated. In addition, the dielectric constants of the solvents were discussed for further understanding of the solubility phenomenon. B



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ln x1 = A 0 + A1x 20 + A 2 (x 20)2 + A3(x 20)3 + A4 (x 20)4

Each experiment was run in triplicate, and the average value was used as the final result. The mole fraction solubility (x1) of QF in pure solvents was calculated by the following equation. x1 =

m1/M1 m1/M1 + m2 /M 2

3.3. NRTL Model. For an organic electrolyte, the NRTL model often provides a good regression of experimental data,21 but since the modified NRTL model needs a large body of thermodynamic data and the calculation is heavy and cumbersome, it eventually may not be suitable to the substance of interest.22 On the basis of practical consideration we select the NRTL model in this work. For a (solid + liquid) phase equilibrium system with fixed temperature T and pressure p, the fugacity of the solute in liquid must be coincident with that in solid phases.

(1)

where m1 and m2 are the mass of the solute and solvent, respectively. M1 is the molecular mass of solute and M2 is the molecular mass of solvent. For the binary solvents, the initial mole fraction (x02) of methanol/ethanol in the solvent mixtures and the mole fraction solubility (x1) of QF in the mixed solvent was calculated by the following equations. x 20 =

m2 /M 2 m2 /M 2 + m3 /M3

(2)

x1 =

m1/M1 m1/M1 + m2 /M 2 + m3 /M3

(3)

f il (T , p , xi) = f is (T , p)

ln xi =

ΔfusH ⎛ 1 1⎞ − ⎟ − ln γi ⎜ R ⎝ Tm T⎠

(9)

where ΔfusH, R, and Tm refer to the enthalpy of fusion, gas constant, and melting point of QF, respectively. γi, the activity coefficient of solute in the saturated solution, was obtained by the NRTL model. The NRTL model, one of the local composition models, was derived by Renon and Prausnitz.24 For the binary system (in pure solvents), the activity coefficient γi can be calculated as follows.

3. THERMODYNAMIC AND CORRELATING MODELS 3.1. The Modified Apelblat Equation. The modified Apelblat equation was used to show the relationship between the solubility and temperature.16−18

⎤ ⎡ τjiGji2 τijGij2 ⎥ ln γi = xj2⎢ + ⎢⎣ (xi + Gjixj)2 (xj + Gijxi)2 ⎥⎦

(4)

(10)

where Gij, Gji, τij, and τji are parameters of this model. The definition of these terms can be expressed as eq 11 and eq 12.

where A, B, and C are empirical constants. The value of C denotes the effect of temperature on the fusion enthalpy. The values of A and B refer to the variations in the solution activity coefficient. 3.2. CNIBS/R-K Model. The CNIBS/R-K model19 builds a connection between the isothermal mole fraction solubility and solvent composition of binary solvent mixtures, and the function can be defined as eq 5.

Gij = exp( −αijτij)

(11)

τij = (gij − gjj)/RT

(12)

where Δgij represents the parameters of this model and the cross interaction energy; αij is a criterion of the nonrandomness of the system. For a ternary system (in binary solvent system), the activity coefficient γi can be calculated as follows.24

N

ln x1 = x 20 ln(x1)2 + x30 ln(x1)3 + x 20x30 ∑ Si(x 20 − x30)i i=0

(5)

ln γi = (Gjixj + Gkjxk)(τjiGjixj + τkiGkixk)/(xi + xjGj + xkGki)2

where x1 and (x1)i stand for the mole fraction solubility of QF in the binary solvent mixtures and the mole fraction solubility of QF in the pure solvent of i, respectively; x02 and x03 are the mole fraction of water and methanol or ethanol in the solution without the solute, respectively; N is the number of “curve-fit” parameters, and Si is the model constant. In this work, due to two components contained in each solvent we used, N can be set as 2, and x03 can be represented as (1-x02). By substitution of the data, we changed the above into eq 5, and the function can be expressed as eq 6.

+ [τijGijxj2 + GijGkjxjxk(τij − τkj)]/(xj + xiGij + xkGkj)2 + [τikGijxj2 + GijGkjxjxk(τik − τjk)]/(xk + xiGik + xjGjk)2 (13)

where Gij, Gik, Gji, Gjk, Gki, Gkj, τij, τik, τjk,, τki are parameters of this model. The definition is the same as mentioned before.

4. RESULT AND DISCUSSION 4.1. Identification and Characterization of QF. The raw materials, excess solid in the conical flasks, and dried solid in different mixtures from 283.15 to 323.15 K after 12 h stirring turned out to be unchanged, suggesting that there is no phase transition during the solubility measurement. The XRPD patterns of QF in different solvents are shown in Figure 2. The onset temperature of the endothermic peak in the DSC result was considered as the melting temperature of QF, Tm is 446.62 K (the uncertainty is U = 0.5 K, 0.95 level of

ln x1 = (ln(x1)2 − ln(x1)3 + S0 − S1 + S2)x 20 + ( −S0 + 3S1 − 5S2)(x 20)2 + ( −2S1 + 8S2)(x 20)3 + ( −4S2)(x 20)4 + ln(x1)3

(8)

On the basis of some further assumptions and simplification, a simplified local composition model can be expressed as follows.23

where m1, m2, and m3 represent the mass of the solute, the mass of methanol or ethanol, and the mass of water, respectively; M1, M2, and M3 are the corresponding molecular mass of them.

B ln x1 = A + + C ln(T /K) T /K

(7)

(6)

By replacing the constants in eq 6 with a constant term A (containing A0, A1, A2, A3, A4), the CNIBS/R-K model can be calculated by a final equation.20 C



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addition, at a certain temperature, the order of solubility in pure solvents at low temperature is DMF > methanol > ethanol >1butanol > isopropyl alcohol > (acetone > ethyl acetate > isobutyl alcohol) > water, and the order at relatively high temperature is DMF > methanol > ethanol >1-butanol > isopropyl alcohol > (acetone > isobutyl alcohol > ethyl acetate) > water. The solubility of material is associated with the polarity of solvents. To our knowledge, there is no well-established accurate quantification standard for molecular polarity, and generally the magnitude of the dielectric constant (ε) is used to represent the value of polarity.25 The dielectric constants of pure solvents reported in the literature26,27 of interest in this work has been accumulated in Table S1. As shown in Table S1, the order of dielectric constants of the nine pure solvents is not strictly consistent with the order of solubility data in pure solvents at the same temperature.28 Thus, there may exist other factors that have effects on solubility. In addition, for a certain solvent, the dielectric constant increases as temperature rises. This is in accordance with the temperature dependence of solubility for a pure solvent. It can be concluded that the solubility phenomenon follows a simple rule, “like dissolves like”. Solvent polarity mainly influences the strength of solute− solvent van der Waals interactions, hence influencing the solubility of QF. To expand the application range of solubility values, the modified Apelblat model and the NRTL model were used to correlate the solubility of QF in nine solvents. The accuracy of correlation was evaluated by the average relative deviation (ARD) and the root-mean-square deviation (RMSD). They are defined as follows.

Figure 2. X-ray powder diffraction pattern of QF: (a) raw material; (b) excess solid in solvents; (c) dried solid.

confidence), which is very similar to that in the previous literature.6 The existing deviation between the melting parameters might be due to the operating conditions and the purity of the sample. The enthalpy of fusion ΔfusH is measured as 74.39 KJ·mol−1 (The uncertainty is U = 1.53 KJ·mol−1, 0.95 level of confidence). The entropy of fusion of QF (ΔfusS) can be calculated by the following eq 14, and the value of ΔfusS is determined as 166.56 J·K−1·mol−1 (The uncertainty is U = 3.03 J·K−1·mol−1, 0.95 level of confidence). The DSC plot of QF is shown in Figure 3.

ΔfusS = ΔfusH /Tm

(14)

ARD% =

100 N

⎡ 1 RMSD = ⎢⎢ N ⎣

N

∑ i=1

cal x1,exp i − x1, i

x1,exp i

(15)

⎛ x exp − x cal ⎞2 ⎤ ∑ ⎜⎜ 1,i exp 1,i ⎟⎟ ⎥⎥ x1, i ⎠⎦ i=1 ⎝ N

1/2

(16)

where N refers to the number of experimental points in each cal solvents; xexp 1,i and x1,i stand for the experimental and calculated solubility, respectively. The correlated parameters and ARD, RMSD of each model are given in Tables S2 and S3. It is seen that the experimental and correlated results are in good agreement within the temperature range. Furthermore, the Apelblat equation fits better by comparing the values of ARD and RMSD. 4.3. Solubility Results and Data Correlation in Binary Solvents. The experimental solubility of QF in two different binary mixed solvents at all temperatures is reported in Tables 3 and 4, and the graphic plots are presented in Figures 5 and 6. An analysis of the data shows that for all solvent mixtures under investigation the solubility of QF increases with increasing temperature in a given composition. Second, the solubility in binary solvents of QF is greater than that of both pure solvents, and the solubility curve shows a maximum in the range of mixed solvents composition. This phenomenon is also called cosolvency and is reported in previous studies.29 The solubility in (methanol + water) mixtures reaches maximum values at a methanol mole fraction of 0.6, while the solubility in (ethanol + water) mixtures reaches maximum values at ethanol mole fractions of 0.4 in the range of (283.15 to 303.15) K and 0.3 in

Figure 3. DSC plot of QF.

4.2. Solubility Results and Data Correlation in Pure Solvents. The experimentally measured mole fraction solubility of QF in nine pure solvents from 283.15 to 323.15 K is shown in Table 2, and the graphical plots are presented in Figure 4. Figure 3 illustrates that at a constant temperature, the solubility of QF increases with increasing temperature. The process of dissolution of a solid might be considered as solid melting and liquids mixing. Because the heat the fusion of a solid is accompanied by an intake of heat, the increase of temperature leads to a larger amount of solid dissolving. In D



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Table 2. Experiment and Correlated Solubility of QF in Pure Solvent from 283.15 K to 323,15 K (p = 0.1 MPa) T/K

104xexp 1

104xcal 1 eq 4

104xcal 1 eq 9

T/K

104xexp 1

318.15 323.15

9.88 11.8

Water 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.498 0.557 0.673 0.739 0.799 0.931 1.08 1.31 1.62 3.88 4.53 5.45 6.96 8.79 12.1 16.3 20.2 24.5

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.91 2.44 3.25 4.08 5.02 6.36 8.38 11.0 13.5

0.461 0.536 0.624 0.725 0.844 0.981 1.14 1.33 1.54

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

3.26 4.31 5.65 7.36 9.52 12.2 15.6 19.8 24.9

3.90 4.71 5.76 7.16 9.00 11.6 15.2 19.7 25.6

1.91 2.45 3.14 4.01 5.13 6.56 8.38 10.7 13.6 Isopropyl Alcohol 1.07 1.22 1.26 1.35 1.68 1.56 2.03 1.85 2.51 2.28 2.89 2.90 3.60 3.79 4.94 5.10 7.16 7.03 1-Butanol 1.54 1.57 2.16 2.16 2.92 2.92 3.93 3.85 5.02 4.99 6.19 6.34 7.92 7.93

1.93 2.46 3.14 4.01 5.12 6.55 8.37 10.7 13.7

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

Ethanol

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

104xcal 1 eq 9

1-Butanol 0.525 0.569 0.628 0.706 0.807 0.938 1.10 1.32 1.60

Methanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

104xcal 1 eq 4

a

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.05 1.23 1.52 1.85 2.32 2.87 3.68 5.01 7.25

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.93 2.41 3.03 3.81 4.81 6.06 7.65

9.75 11.8 Isobutyl Alcohol 0.685 0.685 0.853 0.912 1.19 1.20 1.62 1.55 2.04 1.99 2.51 2.52 3.07 3.15 3.95 3.91 4.81 4.80 Acetone 1.06 1.16 1.46 1.43 1.78 1.74 2.17 2.09 2.51 2.50 2.94 2.96 3.45 3.47 3.95 4.05 4.75 4.68 Ethyl Acetate 0.813 0.796 0.987 1.06 1.42 1.37 1.76 1.74 2.18 2.15 2.55 2.61 3.06 3.09 3.65 3.60 4.11 4.12 DMF 30.9 31.4 36.9 36.2 41.9 42.1 49.1 49.4 59.8 58.5 68.4 69.9 84.0 84.0 102 102 123 124

9.64 12.1 0.802 0.989 1.23 1.54 1.93 2.43 3.06 3.88 4.91 1.27 1.47 1.71 2.01 2.38 2.83 3.38 4.05 4.87 1.03 1.20 1.41 1.68 2.01 2.42 2.93 3.57 4.35 31.1 36.0 42.1 49.5 58.8 70.1 84.2 102 123

a

The standard uncertainty of T is u(T) = 0.05 K. The relative standard uncertainty of the solubility measurement is ur (x) = 0.04. The relative uncertainty of pressure is ur (p) = 0.05.

concluded that the solvent composition and temperature influence solvent−solute interactions, thus causing the phenomenon of cosolvency.18 The dielectric constants of (methanol + water) and (ethanol + water) at different temperatures and different mass fractions are collected in the literature.26 It can be found that the trend of dielectric constant with temperature and that of the solubility in solvents mixtures under fixed composition are consistent. The solubility of QF in binary solvents was correlated by the CNIBS/R-K model and the NRTL model. The correlated parameters and ARD and RMSD of each model are listed in

the range of (308.15 to 323.15) K. The statement indicates that the initial mole fraction of ethanol in the binary solvents to which the maximum of solubility corresponds varies with temperature. Previous literature30 has researched that when the solvents are mixed in a certain ratio, the solubility of pharmaceutical drugs might reach a maximum. It is a multifaceted effect of hydrogen-bonding, van der Waals interactions, ionic solute− solvent interactions, etc. In addition, the interaction among water and methanol or ethanol causes a contraction of volume, that may have an effect on the attraction force. It can be E



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4.4. Solubility Parameter. Solubility parameters, originally introduced by Hildebrand,31 are sometimes called cohesion energy parameters. However, the earlier research of the solubility parameter was limited to regular solutions, and did not account for association between molecules.32 The solubility parameter was divided into two components, “nonpolar” and “polar”.33 And further improved, the solubility parameter called HSPs, was divided into three partial components by Hansen, δD, δP, and δH, for the dispersion, the polar, and the hydrogen bonding contributions, respectively. The total solubility parameter is the sum of the individual parameters.34 δ 2 = δ D2 + δ P 2 + δ H 2

(17)

The solubility changes can mainly be attributed to different intermolecular interactions. Therefore, it is noteworthy that the solubility parameter is important in determining the solubility of the system. The group contribution method to calculate the solubility parameters of interest has been confirmed reliable. The group contributions have been summarized by many workers, widely used to estimate the HSPs.35 Table S6 presents the total solubility parameters of different groups employed to calculate that of QF by using the group contribution method. On the basis of these values, the solubility parameter δ of QF is as follows. δ = 530769 (KJ/m 3)1/2 = 25.94 (MPa)1/2

For binary mixture δM can be calculated from the solubility parameters of the pure solvents and the volume fraction ϕi of each component in the mixture; the regular mixing rule is as follows:36 δM = φ1δ1 + φ2δ2

(18)

where δ1 and δ2 represent the solubility parameters of pure solvents. Table 5 lists the mole fraction, volume fraction, and solubility parameter of the solvent mixtures. From the experimental solubility data, we can discover that the mole fraction solubility of QF displays a single maximum. When the solubility reaches the maximum, the initial mole fractions of alcohol in the binary solvent mixtures are different in (methanol + water, x20 = 0.6) and (ethanol + water, x20 = 0.4 at T = (283.15 to 303.15) K and x20 = 0.3 at T= (308.15 to 323.15) K). However, the solubility parameters of the solvents corresponding to the maximum solubility are quite similar in the two (alcohol + water) binary solvent mixtures: in (methanol + water) system, δM = 33.79 MPa1/2 with x20 = 0.6; in (ethanol + water) system, δM = 33.27 MPa1/2 with x20 = 0.4 and δM = 35.45 MPa1/2 with x20 = 0.3). It is consistent with the previous literature:37 for large δ values (δ > 25 MPa1/2) of solute, the solubility shows a peak in the range of 35 to 31 MPa1/2 of solubility parameters of alcohol mixtures. This phenomenon presents a connection between the maximum solubility of QF and the solubility parameters of the solvent mixtures. It indicates that the solubility of QF might have maximum solubility in the binary solvents with the solubility parameters in the range of 33 to 35.5 MPa1/2 which contribute to the strongest solute−solvent interactions. For the (ethanol + water) system, the increase of the temperature has different impacts on the solvent−solvent interactions and solvent−solute interactions, thus the initial mole fraction of ethanol at maximum solubility shift to be lower with temperature rise.37

Figure 4. Mole fraction solubility of QF in nine pure solvents at atmospheric pressure (p = 0.1 MPa) at various temperatures. The solid lines are the calculated values based on the modified Apelblat equation.

Tables S4 and S5. It is seen that the experimental and correlated results are in good agreement within the temperature range. Furthermore, the CNIBS/R-K model fits better by comparing the values of the ARD and RMSD. F



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4 cal Table 3. Experiment (xexp 1 ) and Correlated (10 x1 ) Solubility of QF (Methanol + Water) Binary Solvents at Atmospheric Pressure (p = 0.1 MPa) at Various Temperaturesa

x02

104xexp 1

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

0.881 1.34 2.85 4.64 5.50 6.00 5.71 4.81 3.83

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

1.06 2.02 4.08 5.38 7.04 7.41 7.13 6.49 5.63

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

1.27 2.43 4.79 6.65 8.15 8.74 8.52 7.79 6.74

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

1.84 3.14 5.94 8.98 10.2 11.1 10.7 9.72 8.58

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000

1.62 3.42 6.36 9.64 11.7 12.2 11.8

104xcal 1 eq 7 T = 283.15 K 1.02 2.27 3.98 5.60 6.39 6.45 5.88 5.01 4.12 T = 288.15 K 1.14 2.56 4.54 6.19 7.33 7.42 6.84 5.96 5.00 T = 293.15 K 1.30 2.89 5.12 7.11 8.37 8.61 8.06 7.10 6.01 T = 298.15 K 1.55 3.36 5.97 8.60 9.99 10.4 9.77 8.65 7.41 T = 303.15 K 1.77 3.87 6.82 9.86 11.8 12.2 11.6

104xcal 1 eq 13

x02

104xexp 1

0.681 1.55 2.89 4.42 5.62 6.04 5.66 4.80 3.85

0.8000 0.9000

11.1 9.67

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

2.08 4.24 7.95 11.9 14.5 15.2 14.1 13.3 11.8

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

2.50 5.58 10.4 15.8 18.7 19.6 17.9 16.5 14.4

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

3.07 7.34 13.7 20.4 24.4 25.8 24.5 21.9 18.3

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

3.90 10.2 20.1 29.4 34.4 36.2 33.2 27.1 22.3

1.00 2.18 3.85 5.61 6.91 7.43 7.18 6.46 5.64 1.15 2.63 4.65 6.69 8.15 8.74 8.53 7.77 6.75 1.57 3.44 6.01 8.62 10.5 11.1 10.7 9.68 8.61 1.44 3.52 6.50 9.51 11.6 12.3 11.9

104xcal 1 eq 7 T = 303.15 K 10.5 9.05 T = 308.15 K 2.13 4.63 8.25 12.0 14.5 15.2 14.3 13.0 11.3 T = 313.15 K 2.59 5.71 10.3 15.5 18.6 19.5 18.2 16.5 14.4 T = 318.15 K 3.19 7.17 13.3 20.1 24.5 25.8 24.3 21.6 18.6 T = 323.15 K 3.99 9.39 18.7 28.9 34.9 36.4 33.2 28.2 24.0

104xcal 1 eq 13 10.9 9.74 1.89 4.39 8.03 11.8 14.4 15.2 14.4 13.0 11.9 2.31 5.67 10.6 15.6 18.8 19.5 18.2 16.2 14.5 2.93 7.42 13.8 20.2 24.5 25.8 24.6 21.8 18.3 3.93 10.4 19.9 29.2 35.0 35.9 32.8 27.7 22.1

a

The standard uncertainty of T is u(T) = 0.05 K. The relative standard uncertainty of the solubility measurement is ur (x) = 0.10. The relative uncertainty of pressure is ur (p) = 0.05. The relative standard uncertainty in mole fraction of methanol in the solvent mixtures is ur (x02) = 0.005.

And the phenomenon of cosolvency may allow a nonsolvent mixtures, with a solubility parameter that is initially too high, to pass through a soluble condition to once more become a nonsolvent mixtures as mole fraction of alcohol increases. These could be called “boundary” solvent mixtures, imitating the “boundary” solvents33 related to temperature. The effects are most obvious with systems having a high hydrogen-bonding character. As the mole fraction of alcohol in binary solvents increases, the hydrogen-bonding and intermolecular interactions between solute and solvent become stronger, which favor

the dissolution of QF. Then when the content of alcohol is large enough, hydrogen-bonding between ethanol molecules becomes much stronger, which caused the decrease of the solute−solvent interactions, which hinders the dissolution of QF.

5. CONCLUSION The solubility of QF was measured in nine pure solvents (methanol, ethanol, isopropyl alcohol, 1-butanol, isobutyl alcohol, acetone, ethyl acetate, and N,N-dimethylformamide) G



Article

4 cal Table 4. Experimental (xexp 1 ) and Correlated (10 x1 ) Solubility of QF (Ethanol + Water) Binary Solvents at Atmospheric Pressure (p = 0.1 MPa) at Various Temperaturesa

x02

104xexp 1

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

1.41 4.73 8.11 9.19 7.97 6.31 4.35 3.05 1.68

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

1.98 6.72 10.8 13.5 11.6 7.76 5.66 3.65 2.52

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

2.57 8.48 12.9 15.0 13.5 10.4 7.75 5.01 3.59

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

3.30 11.2 16.7 18.6 17.0 13.3 9.42 6.36 4.14

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000

3.45 12.4 19.4 21.3 19.5 14.7 10.4

104xcal 1 eq 7 T = 283.15 K 1.76 6.61 9.40 9.25 7.53 5.59 3.90 2.67 1.77 T = 288.15 K 2.20 7.89 11.2 11.4 9.34 6.72 4.73 3.21 2.17 T = 293.15 K 2.79 9.51 13.4 13.5 11.3 8.37 5.92 3.99 2.72 T = 298.15 K 3.81 10.6 17.0 18.8 16.7 13.2 9.60 6.53 3.96 T = 303.15 K 4.58 14.3 20.1 20.4 17.3 12.9 9.03

104xcal 1 eq 13

x02

104xexp 1

1.57 5.57 9.65 10.7 9.15 6.83 4.73 3.17 2.09

0.8000 0.9000

6.78 4.76

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

4.68 16.3 26.1 26.0 23.3 17.9 12.4 8.34 5.37

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

6.41 22.6 32.4 31.5 27.5 20.9 14.1 9.26 5.91

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

8.88 30.6 43.5 42.1 35.2 25.6 17.7 11.5 7.38

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

12.4 43.3 56.4 52.8 45.3 33.5 24.1 14.8 10.1

2.00 6.75 11.3 12.7 10.8 7.89 5.52 3.72 2.49 2.57 8.21 13.4 14.7 12.6 9.38 6.60 4.47 3.03 3.33 10.3 16.4 17.7 15.1 11.3 7.94 5.43 3.69 4.28 12.5 19.8 21.2 18.1 13.5 9.57

104xcal 1 eq 7 T = 303.15 K 6.12 4.18 T = 308.15 K 5.09 16.1 25.7 27.0 22.8 17.5 12.8 8.70 4.99 T = 313.15 K 7.78 22.8 32.3 32.5 27.6 20.7 14.3 9.73 6.57 T = 318.15 K 10.24 29.5 42.1 43.0 36.4 26.9 18.7 12.6 8.47 T = 323.15 K 13.6 38.8 55.0 56.3 48.7 36.3 25.4 16.6 11.2

104xcal 1 eq 13 6.60 4.55 5.64 16.1 25.4 26.2 22.2 16.6 11.8 8.17 5.65 7.53 21.4 32.3 32.7 27.4 20.5 14.5 10.1 7.05 10.2 28.9 43.1 42.8 35.1 25.8 18.2 12.7 8.90 13.9 40.7 57.8 55.7 45.6 33.3 23.5 16.2 11.4

a

The standard uncertainty of T is u(T) = 0.05 K. The relative standard uncertainty of the solubility measurement is ur (x) = 0.10. The relative uncertainty of pressure is ur (p) = 0.05. The relative standard uncertainty in mole fraction of methanol in the solvent mixtures is ur (x02) = 0.005.

and two binary solvents (methanol + water) and (ethanol + water) from T = 283.15−323.15 K. The solubility of QF increases with the increase of temperature in nine pure solvents, and it is in the order DMF > methanol > ethanol >1-butanol > isopropyl alcohol > (acetone > ethyl acetate > isobutyl alcohol) > water at low temperature, and at relatively high temperature the order is DMF > methanol > ethanol >1-butanol > isopropyl alcohol > (acetone > isobutyl alcohol > ethyl acetate) > water, not consistent with the polarity (dielectric constant) order of these solvents. The solubility of QF in the binary solvents also

shows temperature dependence, while at a given temperature the solubility is mainly influenced by the solvent composition with the presence of maximum, reflecting cosolvency. And also the solubility of QF increases with temperature increasing in binary solvents in a given composition. The Hansen solubility parameters were used to explain the cosolvency and maxima shift, confirming that for large values (>25 MPa1/2) of solute, the solubility shows a peak in the range of 35 to 31 MPa1/2 of solubility parameters of alcohol mixtures. The experimental solubility of QF in the pure and binary solvents is well H



Article

correlated by the modified Apelblat equation, the NRTL model, and the CNIBS/R-K equation, respectively.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00518. Calculated parameters, ARD, and RMSD for different models; dielectric constant of pure and binary solvents; group contributions to total solubility parameter (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*Tel: +86-22-27405754. Fax: +86-22-27374971. E-mail: [email protected].

Figure 5. Experimental mole fraction solubility (x1) of QF in (methanol + water) binary solvent mixtures at atmospheric pressure (p = 0.1 MPa) at various temperatures.

ORCID

Shichao Du: 0000-0002-8369-2983 Junbo Gong: 0000-0002-3376-3296 Funding

The authors are grateful for the financial support of the National Natural Science Foundation of China (NNSFC 21676179, NNSFC 91634117 and NNSFC 21376164), National 863 Program (2015AA021002), Tianjin Science and Technology Project (15JCZDJC33200 and KJXH2015-01), and the Major Science and Technology Program for Water Pollution Control and Treatment (NO.2015ZX07202-013). Notes

The authors declare no competing financial interest.

■

Figure 6. Experimental mole fraction solubility (x1) of QF in (ethanol + water) binary solvent mixtures at atmospheric pressure (p = 0.1 MPa) at various temperatures.

Table 5. Solubility Parameter of (Methanol + Water) and (Ethanol + Water) Mixtures mole fraction x02 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

volume fraction

solubility parameter δM (MPa1/2)

Methanol + Water 0.00 0.20 0.36 0.49 0.60 0.69 0.77 0.84 0.90 0.95 1.00 Eethanol + Water 0.00 0.26 0.45 0.58 0.68 0.76 0.83 0.88 0.93 0.97 1.00

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Determination and Correlation of Solubility of Quetiapine Fumarate in

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