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. 2023 Oct 11;8(42):39390–39400. doi: 10.1021/acsomega.3c04987

Solubility Measurement and Correlation of Itraconazole Hydroxy Isobutyltriazolone in Four Kinds of Binary Solvent Mixtures with Temperature from 283.15 to 323.15 K

Qi Dong †,‡, Shuai Yu ‡, Xingzhu Wang ‡, Shangzhi Ding ‡, Enxia Li ‡, Yuanxing Cai †,*, Fumin Xue ‡,*
PMCID: PMC10601064  PMID: 37901582

Abstract

graphic file with name ao3c04987_0005.jpg

The solubility of itraconazole hydroxy isobutyltriazolone (IHI) in four commonly used binary solvent mixtures of N,N-dimethylformamide (DMF) + water, DMF + ethanol, tetrahydrofuran (THF) + water, and THF + ethanol was determined with gravimetric method at temperatures ranging from 283.15 to 323.15 K under atmospheric pressure. The solubility of IHI in all selected solvents increases with the increase of temperature. The maximum solubility of IHI exists in the solvent of DMF + ethanol (0.06523 mol·mol–1, x02 = 0.7, T = 323.15 K), while the minimum solubility exists in DMF + water (0.0003723 mol·mol–1, x02 = 0.3, T = 283.15 K). There is a co-solvency phenomenon in the mixed solvents of DMF+ ethanol, THF + water, and THF + ethanol. Four thermodynamic models, including the modified Apelblat model, the Yaws model, the Sun model, and the modified Jouyban–Acree model, were selected to fit the solubility data of IHI. All the RAD values are less than 0.0484, and RMSD values are not more than 0.001319. The Yaws model and the modified Apelblat model fit the solubility data of IHI better than the other two models. All the selected four models can fit the solubility data of IHI well.

1. Introduction

Itraconazole hydroxy isobutyltriazolone (chemical name: 2,4-Dihydro-4-[4-[4-(4-hydroxyphenyl)-1-piperazinyl] phenyl]-2-(1-methylpropyl)-3H-1,2,4-triazol-3-one, empirical formula: C22H27N5O2, CAS No. 106461-41-0, MW = 393.48 g·mol–1) is a dark white powder in crystalline form. Itraconazole hydroxy isobutyltriazolone (IHI for short) is almost insoluble in water.1 The molecular structure of IHI is shown in Figure 1. IHI is an important medicine intermediate and has mainly been used as a medical intermediate of itraconazole.

Figure 1.

Figure 1

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Chemical structure of IHI.

Currently, there is little research on the crystallization process of IHI. Crystallization is the final step in the preparation of active pharmaceutical ingredients (API) and plays a crucial role in the properties of product particles. It is undeniable that solubility data is required by the optimization of the crystallization process. Solubility data can guide the selection of solvent systems and crystallization methods (cooling crystallization, reaction crystallization, antisolvent crystallization, evaporation crystallization, etc.2,3). Nevertheless, there is currently no detailed reference material on the solubility of IHI in pure or binary solvent systems.

In the field of pharmaceuticals, it can be used as a drug intermediate to produce Itraconazole. The solubility of IHI in four commonly used binary solvent mixtures of N,N-dimethylformamide (DMF) + water, DMF + ethanol, tetrahydrofuran (THF) + water, and THF + ethanol was determined. Previous studies have discussed the selection of binary solvents, such as solvents that are easily soluble in drugs as good solvents and solvents that are slightly soluble or insoluble in drugs as antisolvents.4−6 The static gravimetric method was selected to measure the solubility of IHI. The temperature ranges from 283.15 to 323.15 K (interval 5.0 K). The pressure is approximately 0.1 MPa. The solubility data were fitted by different thermodynamic models. These solubility data contain important practical significance for the optimization of the crystallization process of IHI and its corresponding industrial production.

Measuring the solubility of drugs in different solvents and temperatures not only helps to select appropriate solvents and temperatures for drug purification but also optimizes the crystallization process and improves the product quality of drugs, and the determination of solubility is of great significance.7,8

2. Theoretical Models

With the aim of finding better models to correlate the solubility data of IHI in binary solvents and predicting the solubility data of IHI, different thermodynamic models were selected.9−11 In this investigation, four classical models, including the modified Apelblat model, the Yaws model, the Sun model, and the modified Jouyban–Acree model, were selected.

2.1. Modified Apelblat Model

The Apelblat model is a semiempirical model widely used to correlate the solubility data and temperature, which can be described as follows12−15

2.1. 1

where x1 is the mole fraction of IHI, T is the absolute thermodynamic temperature, and A, B, and C are model parameters.

2.2. Yaws Model

Another semiempirical model, the Yaws model was also used to fit the solubility data. Just as the modified Apelblat model, it can also be used to correlate the solubility at different temperatures in mono solvents. On the right side of the equation, the form and meaning of the first two terms are similar to those of the expression of the modified Apelblat equation, while the third term can be helpful to improve the performance on describing some special varying tendencies of solubility data, which can be described as follows16−19

2.2. 2

2.3. Sun Model

The Sun model is used to correlate the solubility data at different temperatures and different compositions of mixed solvents, which can be described as follows20

2.3. 3

where D1 to D7 are the model parameters.

2.4. Modified Jouyban–Acree Model

The Jouyban–Acree model can be defined as21,22

2.4. 4

where x1, x02, and x03 are the mole fractions of solute, good solvent, and antisolvent, respectively; T is the absolute temperature; N is the number of the solvents, which is equal to two for a binary solvent mixture; and Ji constitutes the model parameters. When combined with the modified Apelblat model, the modified Jouyban–Acree model can be obtained and expressed as follows23

2.4. 5

where A1 to A9 are the final model parameters.

2.5. Data Correlation

Relative average deviation (RAD) and root mean square deviation (RMSD) were selected to evaluate the fitting level of each model24−26

2.5. 6
2.5. 7

where x1exp and x1cal are the experimental and calculated solubility data, respectively, with N denoting the number of experimental points.

3. Experimental Section

3.1. Materials

Itraconazole hydroxy isobutyltriazolone (IHI, mass fraction 98%) was purchased from Aladdin Holdings Group Co., Ltd. Information about all of the solvents used in this investigation is listed in Table 1. The organic solvents (including ethanol, tetrahydrofuran, and N,N-dimethylformamide) were of analytical grade as purchased from Sinopharm Chemical Reagent Co., Ltd. or Fuyu Fine Chemical Co., Ltd. All of the solvents were used without further purification. Ultrapure water was produced in our laboratory (Arium Advance EDI, Sartorius, Germany).

Table 1. Detailed Information of Materials Used.

chemicals CAS no. molar mass (g·mol–1) mass fraction puritya source
itraconazole hydroxy isobutyltriazolone (IHI) 106461-41-0 393.48 ≥ 0.980 Aladdin Holdings Group Co., Ltd.
water 7732-18-5 18.02 ultrapure produced in our laboratory
ethanol 64-17-5 46.07 ≥ 0.997 Sinopharm Chemical Reagent Co., Ltd.
tetrahydrofuran 109-99-9 72.11 ≥ 0.995 Fuyu Fine Chemical Co., Ltd.
N,N-dimethylformamide (DMF) 68-12-2 73.09 ≥ 0.995 Fuyu Fine Chemical Co., Ltd.
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a

Both the analysis method and mass fraction purity were claimed by suppliers.

3.2. X-ray Powder Diffraction

The residual solids of IHI in solubility measurement experiments in different solvent systems and raw materials were characterized using X-ray powder diffraction (XRPD). X’Pert3 Powder (PANalytical B.V., Netherlands) and Cu Kα were used radiation together. The tube voltage is 40 kV, and the current is 30 mA. Under nitrogen environment protection, the testing range is 3–50 ° (2θ), and the scanning speed is 8 °/min. All measured temperatures and pressures were 298.15 K and 0.1 MPa, respectively.

3.3. Solubility Determination

A gravimetric method was selected to measure the solubility of IHI in four binary solvents (DMF + water, DMF + ethanol, THF + water, and THF + ethanol) at temperatures ranging from 283.15 to 323.15 K at 0.1 MPa. The measurement system used here has been widely used in our previous work.5,6,21 First, each pure solvent was accurately weighed into a beaker to prepare binary solvents with different antisolvent compositions. Then, approximately 150 mL of mixed solvents were added to a 200 mL volume glass jacketed container. A rubber stopper was used to minimize the evaporation of solvent. A thermostatic water-circulating bath (CF41, JULABO, Germany) with an uncertainty of ± 0.05 K was selected to control the temperature. To mix the solute and solvent, a magnetic stirrer was used. The solutions were stirred for ten hours. The concentration was confirmed every 0.5 h to determine when solid–liquid equilibrium was reached. After that, the solution was allowed to stand for another four hours without stirring. Approximately 5 mL of the upper clear solution was sampled. A 0.45 μm pore size syringe filter (preheated to the corresponding temperature before use) was utilized to filter the solution.27 All samples were dried in a vacuum drying oven at 328.15 K for 12 hours (to constant weight even if a longer drying time was required). A balance (Model AL204, Mettler Toledo, Switzerland) was used to measure all masses with an accuracy of ± 0.0001 g. All experiments were repeated at least three times, and the mole fraction solubility (x1) of IHI in different solvent systems was calculated based on the following formula28,29

3.3. 8

where m1 represents the mass of the solute (IHI); mi represents the mass of the solvent; M1 and Mi are the corresponding relative molecular weights, respectively; and N is the amount of solvent. In a pure solvent system, n equals 2, and in a binary solvent system, it equals 3. The initial molar fraction (x02) of a good solvent (DMF or THF) in a binary solvent system is defined by the following equation

3.3. 9

4. Results and Discussion

4.1. XRPD

The crystal form of IHI was determined by the XRPD method. The XRPD patterns of IHI in different solvents including the residual solids in DMF + water, DMF + ethanol, THF + water, and THF + ethanol in each good solvent compositions and temperatures. The representative data are shown in Figure 2 (take the residual solid under x02 = 0.6 as representative). It is obvious that there is no change in crystal form during the dissolution equilibrium process. The main peaks of the XRD patterns are 7.11, 14.84, 17.92, 18.98, 21.09, 25.14, and 28.58°. There is no difference in peak position and only a slight difference in peak intensity, which indicates that there is no crystal form transformation during the solid–liquid equilibrium process of IHI.

Figure 2.

Figure 2

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XRPD patterns of IHI raw material and IHI in different solid–liquid equilibrium systems (x02 = 0.6).

4.2. Solubility Data

In the pre-experiments, more than 20 kinds of pure solvents (such as methanol, ethanol, n-propanol, i-propanol, n-butanol, i-butanol, s-butanol, n-pentanol, i-pentanol, 2-butanone, methyl isobutyl ketone, cyclohexanone, ethyl formate, ethyl acetate, propyl acetate, isopropyl acetate, butyl acetate, amyl acetate, N,N-dimethylformamide, tetrahydrofuran, toluene, 1,4-dioxane, etc.) were used for the solubility measurement of IHI. However, in most of the above solvents, solubility data are almost impossible to measure because IHI dissolves slightly. Thus, in this investigation, DMF and THF were selected as good solvents, while water and ethanol were selected as antisolvents.30,31 The mole fraction of good solvent was ranging from 0.3 to 1.0 with an interval of 0.1 in the four binary mixed solvents. The solubilities of IHI in binary solvents are presented in Figure 3.

Figure 3.

Figure 3

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Mole fraction solubility of IHI in different binary mixed solvents: (a) DMF + water, (b) DMF + ethanol, (c) THF + water, and (d) THF + ethanol.

From Tables 2–5, it can be seen that the solubility of IHI in four binary solvents increases with the increase of temperature. The solubilities of IHI in DMF + water solvents increase with a rise in the mole fraction of DMF and investigated temperature, while for the mixtures of DMF+ ethanol, THF + water, and THF + ethanol, the solubility increased at first and then decreased with the increasing mass fraction of DMF or THF at a given temperature. That is to say, there is a co-solvency phenomenon in these three mixed solvents (DMF + ethanol, THF + water, and THF + ethanol). The maximum solubility occurred with the mole fraction of good solvent at x02 = 0.7 (DMF + ethanol), 0.7 (THF + water), and 0.8 (THF + ethanol) at a given temperature, respectively. The co-solvency phenomenon has important guiding significance for the selection of initial concentration in the process of industrial crystallization. At a given temperature and solvent ratio, the solubility sequence of IHI is basically consistent as DMF + ethanol ≥ THF + water ≥ DMF + water ≥ THF + ethanol. The effect of solvent polarity on solubility is not obvious here. Solubility is affected by many factors. The intermolecular interactions such as hydrogen bonds and van der Waals forces between solvent–solvent and solute–solvent will also influence the solubility.

Table 2. Experimental and Fitted Solubility Data of IHI in DMF + Water Binary Solvent Mixtures (P = 0.1 MPa)a.

T/K 103xexp1 103xApelblat1 103xYaws1 103xSun1 103xJA1
x02 = 0.3          
283.15 0.3723 0.4142 0.4145 0.3537 0.3690
288.15 0.5552 0.5943 0.5946 0.5264 0.5560
293.15 0.7951 0.8418 0.8421 0.7728 0.8239
298.15 1.275 1.178 1.178 1.120 1.202
303.15 1.715 1.630 1.630 1.604 1.727
308.15 2.237 2.231 2.231 2.269 2.447
313.15 2.896 3.021 3.021 3.176 3.421
318.15 4.084 4.051 4.051 4.398 4.722
323.15 5.394 5.382 5.383 6.030 6.439
x02 = 0.4          
283.15 1.192 1.055 1.059 1.284 1.241
288.15 1.657 1.582 1.586 1.833 1.796
293.15 2.294 2.328 2.332 2.584 2.560
298.15 3.239 3.369 3.372 3.600 3.595
303.15 4.737 4.797 4.798 4.963 4.980
308.15 6.813 6.727 6.724 6.771 6.809
313.15 9.139 9.297 9.292 9.145 9.194
318.15 12.91 12.67 12.67 12.24 12.27
323.15 16.96 17.05 17.06 16.23 16.19
x02 = 0.5          
283.15 2.693 2.584 2.588 2.885 2.755
288.15 3.586 3.582 3.584 3.981 3.857
293.15 4.653 4.933 4.932 5.433 5.323
298.15 6.633 6.750 6.748 7.337 7.246
303.15 9.268 9.180 9.180 9.811 9.738
308.15 12.85 12.41 12.41 13.00 12.93
313.15 16.74 16.69 16.69 17.06 16.96
318.15 21.83 22.32 22.32 22.21 22.01
323.15 29.89 29.69 29.69 28.67 28.27
x02 = 0.6          
283.15 4.318 4.065 3.997 4.819 4.651
288.15 5.593 5.739 5.690 6.461 6.329
293.15 7.537 7.941 7.916 8.578 8.498
298.15 10.57 10.78 10.78 11.28 11.26
303.15 14.84 14.38 14.40 14.70 14.75
308.15 19.03 18.86 18.90 18.99 19.09
313.15 24.32 24.34 24.37 24.34 24.44
318.15 30.73 30.94 30.95 30.95 30.97
323.15 38.83 38.77 38.73 39.06 38.85
x02 = 0.7          
283.15 6.498 6.582 6.499 6.834 6.652
288.15 8.615 8.856 8.803 8.932 8.825
293.15 11.74 11.71 11.69 11.57 11.56
298.15 15.23 15.22 15.24 14.85 14.96
303.15 19.86 19.49 19.53 18.91 19.13
308.15 24.64 24.58 24.63 23.89 24.21
313.15 30.25 30.57 30.61 29.96 30.31
318.15 37.62 37.52 37.53 37.30 37.58
323.15 45.47 45.48 45.43 46.13 46.17
x02 = 0.8          
283.15 9.244 8.641 8.604 8.941 8.675
288.15 11.25 11.45 11.43 11.41 11.24
293.15 14.53 14.85 14.86 14.43 14.38
298.15 18.51 18.91 18.92 18.11 18.19
303.15 23.76 23.64 23.65 22.56 22.77
308.15 29.21 29.04 29.04 27.90 28.19
313.15 35.13 35.11 35.09 34.28 34.58
318.15 42.06 41.81 41.78 41.84 42.02
323.15 48.85 49.08 49.07 50.75 50.61
x02 = 0.9          
283.15 10.67 10.12 10.07 11.15 10.72
288.15 13.23 13.31 13.30 13.89 13.58
293.15 16.84 17.12 17.13 17.18 16.99
298.15 21.17 21.56 21.58 21.09 21.04
303.15 26.48 26.60 26.63 25.73 25.77
308.15 32.26 32.22 32.22 31.18 31.27
313.15 38.82 38.32 38.31 37.55 37.59
318.15 44.94 44.83 44.81 44.96 44.79
323.15 51.36 51.62 51.62 53.53 52.93
x02 = 1.0          
283.15 11.49 10.98 10.96 13.01 12.63
288.15 14.53 14.30 14.31 15.86 15.64
293.15 17.66 18.23 18.25 19.19 19.16
298.15 22.14 22.76 22.79 23.08 23.23
303.15 28.04 27.89 27.91 27.59 27.88
308.15 33.87 33.57 33.56 32.79 33.16
313.15 40.14 39.72 39.70 38.75 39.10
318.15 46.04 46.25 46.24 45.56 45.73
323.15 52.99 53.05 53.09 53.29 53.05
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a

xexp1 is the experimental solubility of IHI in DMF + water binary solvent system, and x02 denotes the initial mole fraction of DMF in the binary solvent mixture. xApelblat1, xYaws1, xSun1, and xJA1 represent the calculated solubilities using the modified Apelblat model, Yaws model, Sun model, and modified Jouyban–Acree model, respectively. The standard uncertainty of temperature is u(T) = 0.05 K, and the relative standard uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of mole fraction solubility is ur(x1) = 0.03, and the relative standard uncertainty of the solvent composition is ur(x20) = 0.0002.

Table 5. Experimental and Fitted Solubility Data of IHI in THF + ethanol Binary Solvent Mixtures (P = 0.1 MPa)a.

T/K 103xexp1 103xApelblat1 103xYaws1 103xSun1 103xJA1
x02 = 0.3          
283.15 5.132 5.204 4.905 4.860 5.210
288.15 6.023 5.914 5.721 5.696 5.913
293.15 6.711 6.736 6.645 6.641 6.733
298.15 7.795 7.689 7.689 7.703 7.686
303.15 8.686 8.793 8.864 8.890 8.792
308.15 9.931 10.07 10.18 10.21 10.08
313.15 11.69 11.55 11.66 11.68 11.56
318.15 13.32 13.27 13.30 13.30 13.28
323.15 15.23 15.27 15.14 15.09 15.27
x02 = 0.4          
283.15 6.458 6.489 6.433 6.374 6.501
288.15 7.460 7.357 7.468 7.441 7.357
293.15 8.285 8.383 8.637 8.641 8.377
298.15 9.564 9.596 9.953 9.984 9.588
303.15 11.07 11.03 11.43 11.48 11.03
308.15 12.88 12.72 13.08 13.14 12.73
313.15 14.55 14.73 14.93 14.98 14.74
318.15 17.14 17.11 16.99 17.00 17.12
323.15 19.95 19.93 19.27 19.23 19.93
x02 = 0.5          
283.15 8.321 8.294 8.130 8.044 8.294
288.15 9.377 9.409 9.400 9.359 9.398
293.15 10.73 10.70 10.83 10.83 10.69
298.15 12.19 12.21 12.44 12.48 12.19
303.15 13.81 13.96 14.24 14.30 13.95
308.15 16.06 15.99 16.25 16.33 15.99
313.15 18.32 18.36 18.49 18.55 18.36
318.15 21.27 21.11 20.99 21.00 21.12
323.15 24.23 24.31 23.75 23.68 24.31
x02 = 0.6          
283.15 9.886 10.17 9.853 9.735 10.18
288.15 11.62 11.52 11.36 11.30 11.52
293.15 13.44 13.06 13.04 13.04 13.06
298.15 14.97 14.85 14.94 14.98 14.84
303.15 16.64 16.89 17.06 17.13 16.90
308.15 19.24 19.26 19.42 19.51 19.27
313.15 21.87 21.97 22.06 22.12 21.99
318.15 25.15 25.10 24.98 24.99 25.12
323.15 28.76 28.70 28.22 28.12 28.70
x02 = 0.7          
283.15 11.58 11.85 11.23 11.08 11.86
288.15 13.43 13.31 12.91 12.84 13.30
293.15 15.27 14.98 14.80 14.80 14.97
298.15 16.83 16.90 16.92 16.97 16.90
303.15 19.19 19.11 19.29 19.38 19.12
308.15 21.79 21.65 21.94 22.04 21.67
313.15 24.29 24.57 24.88 24.96 24.59
318.15 27.78 27.93 28.15 28.16 27.94
323.15 31.98 31.79 31.77 31.64 31.78
x02 = 0.8          
283.15 12.18 12.50 11.63 11.46 12.51
288.15 14.03 14.00 13.36 13.28 14.00
293.15 16.07 15.72 15.31 15.31 15.71
298.15 17.73 17.67 17.50 17.56 17.67
303.15 20.19 19.91 19.95 20.05 19.91
308.15 22.39 22.46 22.68 22.80 22.47
313.15 24.99 25.37 25.73 25.83 25.39
318.15 28.48 28.69 29.12 29.13 28.71
323.15 32.78 32.49 32.88 32.74 32.48
x02 = 0.9          
283.15 10.79 10.95 10.40 10.25 10.98
288.15 12.33 12.27 11.98 11.90 12.28
293.15 13.92 13.82 13.76 13.76 13.81
298.15 15.69 15.63 15.76 15.82 15.62
303.15 17.96 17.74 18.00 18.11 17.74
308.15 20.21 20.23 20.52 20.64 20.23
313.15 22.87 23.13 23.32 23.42 23.15
318.15 26.41 26.55 26.46 26.48 26.56
323.15 30.74 30.55 29.95 29.82 30.55
x02 = 1.0          
283.15 7.294 7.202 7.550 7.421 7.202
288.15 8.352 8.308 8.740 8.673 8.297
293.15 9.424 9.602 10.09 10.08 9.587
298.15 11.04 11.12 11.62 11.66 11.10
303.15 12.86 12.90 13.35 13.43 12.88
308.15 15.04 14.98 15.30 15.38 14.98
313.15 17.41 17.42 17.48 17.55 17.42
318.15 20.46 20.28 19.94 19.94 20.29
323.15 23.53 23.63 22.69 22.57 23.64
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a

xexp1 is the experimental solubility of IHI in the THF + ethanol binary solvent system, and x02 denotes the initial mole fraction of DMF in the binary solvent mixture. xApelblat1, xYaws1, xSun1, and xJA1 represent the calculated solubilities using the modified Apelblat model, Yaws model, Sun model, and modified Jouyban–Acree model, respectively. The standard uncertainty of temperature is u(T) = 0.05 K, and the relative standard uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of mole fraction solubility is ur(x1) = 0.03, and the relative standard uncertainty of the solvent composition is ur(x20) = 0.0002.

Table 3. Experimental and Fitted Solubility Data of IHI in DMF + Ethanol Binary Solvent Mixtures (P = 0.1 MPa)a.

T/K 103xexp1 103xApelblat1 103xYaws1 103xSun1 103xJA1
x02 = 0.3          
283.15 4.329 4.649 4.640 4.954 5.034
288.15 5.803 5.951 5.944 6.284 6.336
293.15 7.880 7.558 7.553 7.905 7.925
298.15 9.760 9.525 9.524 9.869 9.855
303.15 12.05 11.92 11.92 12.23 12.19
308.15 14.64 14.81 14.81 15.05 14.99
313.15 18.35 18.28 18.28 18.40 18.35
318.15 21.99 22.43 22.42 22.36 22.34
323.15 27.59 27.35 27.33 27.00 27.08
x02 = 0.4          
283.15 7.091 7.382 7.272 7.635 7.755
288.15 9.022 9.008 8.926 9.575 9.654
293.15 11.06 11.05 11.01 11.92 11.95
298.15 13.65 13.63 13.64 14.72 14.70
303.15 17.27 16.90 16.95 18.06 18.00
308.15 20.91 21.03 21.12 22.01 21.93
313.15 26.09 26.27 26.38 26.65 26.58
318.15 33.22 32.93 32.99 32.08 32.07
323.15 41.28 41.42 41.31 38.40 38.52
x02 = 0.5          
283.15 10.64 10.59 10.60 10.91 11.08
288.15 12.96 13.02 13.02 13.55 13.65
293.15 16.28 15.96 15.96 16.70 16.74
298.15 19.21 19.53 19.52 20.44 20.41
303.15 23.52 23.85 23.84 24.85 24.77
308.15 29.43 29.05 29.04 30.02 29.91
313.15 35.28 35.31 35.31 36.05 35.95
318.15 42.85 42.83 42.83 43.04 43.02
323.15 51.79 51.83 51.83 51.11 51.27
x02 = 0.6          
283.15 15.09 15.01 15.02 13.89 14.09
288.15 18.18 18.15 18.15 17.11 17.24
293.15 21.82 21.85 21.85 20.93 20.98
298.15 25.78 26.19 26.19 25.43 25.40
303.15 31.35 31.26 31.26 30.69 30.60
308.15 37.82 37.16 37.17 36.83 36.69
313.15 43.74 43.99 44.01 43.93 43.81
318.15 51.64 51.90 51.91 52.11 52.09
323.15 61.16 61.00 61.01 61.49 61.67
x02 = 0.7          
283.15 18.69 18.41 18.41 15.55 15.77
288.15 21.48 21.31 21.28 19.05 19.18
293.15 24.25 24.76 24.73 23.17 23.22
298.15 28.49 28.89 28.87 28.00 27.96
303.15 33.88 33.83 33.82 33.62 33.52
308.15 39.92 39.73 39.75 40.14 40.00
313.15 47.09 46.81 46.84 47.65 47.53
318.15 55.38 55.29 55.30 56.26 56.24
323.15 65.23 65.48 65.41 66.09 66.29
x02 = 0.8          
283.15 17.14 16.82 16.84 15.52 15.73
288.15 19.81 19.89 19.88 18.94 19.07
293.15 23.29 23.51 23.49 22.96 23.01
298.15 27.49 27.79 27.77 27.65 27.62
303.15 32.93 32.85 32.83 33.10 33.00
308.15 38.82 38.82 38.81 39.38 39.25
313.15 46.01 45.87 45.87 46.61 46.49
318.15 54.36 54.18 54.19 54.86 54.84
323.15 63.79 63.98 63.96 64.25 64.44
x02 = 0.9          
283.15 13.88 13.44 13.44 14.39 14.58
288.15 16.71 16.74 16.74 17.52 17.64
293.15 20.14 20.61 20.63 21.19 21.23
298.15 24.97 25.13 25.14 25.46 25.43
303.15 30.42 30.34 30.35 30.41 30.32
308.15 36.36 36.31 36.31 36.11 35.99
313.15 43.36 43.07 43.07 42.64 42.54
318.15 50.66 50.67 50.67 50.09 50.08
323.15 59.06 59.15 59.18 58.55 58.73
x02 = 1.0          
283.15 11.49 10.98 10.96 13.27 13.43
288.15 14.53 14.30 14.31 16.11 16.21
293.15 17.66 18.23 18.25 19.44 19.47
298.15 22.14 22.76 22.79 23.31 23.28
303.15 28.04 27.89 27.91 27.78 27.69
308.15 33.87 33.57 33.56 32.92 32.81
313.15 40.14 39.72 39.70 38.80 38.70
318.15 46.04 46.25 46.24 45.49 45.48
323.15 52.99 53.05 53.09 53.08 53.23
Open in a new tab
a

xexp1 is the experimental solubility of IHI in DMF + ethanol binary solvent system, and x02 denotes the initial mole fraction of DMF in the binary solvent mixture. xApelblat1, xYaws1, xSun1, and xJA1 represent the calculated solubilities using the modified Apelblat model, Yaws model, Sun model, and modified Jouyban–Acree model, respectively. The standard uncertainty of temperature is u(T) = 0.05 K, and the relative standard uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of mole fraction solubility is ur(x1) = 0.03, and the relative standard uncertainty of the solvent composition is ur(x20) = 0.0002.

Table 4. Experimental and Fitted Solubility Data of IHI in THF + Water Binary Solvent Mixtures (P = 0.1 MPa)a.

T/K 103xexp1 103xApelblat1 103xYaws1 103xSun1 103xJA1
x02 = 0.3          
283.15 8.843 8.920 9.505 9.252 8.942
288.15 10.35 10.45 11.23 11.08 10.46
293.15 12.84 12.33 13.23 13.20 12.32
298.15 14.59 14.61 15.56 15.62 14.60
303.15 16.80 17.41 18.25 18.38 17.40
308.15 20.88 20.83 21.35 21.53 20.84
313.15 25.58 25.03 24.93 25.08 25.06
318.15 29.89 30.20 29.05 29.08 30.22
323.15 36.62 36.56 33.77 33.56 36.56
x02 = 0.4          
283.15 13.32 13.63 14.12 13.69 13.65
288.15 15.81 15.59 16.43 16.20 15.58
293.15 18.17 17.96 19.10 19.05 17.94
298.15 20.86 20.80 22.17 22.29 20.78
303.15 23.97 24.23 25.70 25.94 24.22
308.15 28.59 28.37 29.75 30.05 28.37
313.15 33.24 33.36 34.40 34.64 33.37
318.15 39.21 39.40 39.72 39.75 39.41
323.15 46.84 46.72 45.80 45.42 46.68
x02 = 0.5          
283.15 19.16 18.83 18.54 17.91 19.07
288.15 21.64 21.43 21.3 20.98 21.54
293.15 24.34 24.45 24.47 24.43 24.46
298.15 27.83 27.99 28.11 28.30 27.92
303.15 31.89 32.12 32.27 32.64 32.00
308.15 36.61 36.94 37.02 37.46 36.82
313.15 42.71 42.57 42.46 42.80 42.48
318.15 49.52 49.15 48.67 48.71 49.15
323.15 56.72 56.85 55.76 55.20 56.99
x02 = 0.6          
283.15 24.46 24.23 22.34 21.51 24.26
288.15 27.39 27.12 25.38 24.96 27.12
293.15 29.84 30.39 28.86 28.82 30.38
298.15 33.75 34.11 32.84 33.12 34.10
303.15 38.45 38.32 37.38 37.88 38.32
308.15 43.43 43.10 42.57 43.14 43.11
313.15 48.35 48.52 48.49 48.93 48.54
318.15 55.12 54.66 55.24 55.28 54.68
323.15 61.33 61.62 62.95 62.21 61.63
x02 = 0.7          
283.15 26.39 26.11 24.50 23.50 26.14
288.15 29.33 29.05 27.57 27.08 29.04
293.15 31.93 32.37 31.08 31.05 32.35
298.15 35.54 36.13 35.09 35.44 36.10
303.15 40.30 40.38 39.66 40.27 40.35
308.15 45.46 45.17 44.89 45.58 45.16
313.15 50.61 50.59 50.86 51.38 50.59
318.15 57.44 56.72 57.67 57.70 56.72
323.15 63.09 63.63 65.45 64.56 63.62
x02 = 0.8          
283.15 22.63 22.72 23.2 22.18 22.75
288.15 25.34 25.24 25.93 25.43 25.24
293.15 28.07 28.18 29.05 29.03 28.16
298.15 31.96 31.59 32.62 32.99 31.57
303.15 35.35 35.54 36.7 37.33 35.53
308.15 39.93 40.14 41.38 42.08 40.14
313.15 45.53 45.47 46.72 47.25 45.49
318.15 51.75 51.67 52.84 52.86 51.67
323.15 58.82 58.88 59.85 58.93 58.83
x02 = 0.9          
283.15 16.23 16.69 17.22 16.40 16.70
288.15 19.03 18.74 19.19 18.80 18.74
293.15 21.49 21.17 21.45 21.45 21.16
298.15 23.97 24.02 24.05 24.36 24.02
303.15 27.83 27.38 27.04 27.56 27.40
308.15 30.92 31.35 30.48 31.05 31.37
313.15 35.75 36.02 34.43 34.85 36.05
318.15 41.64 41.53 38.97 38.97 41.55
323.15 48.13 48.04 44.19 43.43 48.01
x02 = 1.0          
283.15 7.294 7.202 8.687 8.240 7.202
288.15 8.352 8.308 9.717 9.510 8.297
293.15 9.424 9.602 10.91 10.91 9.587
298.15 11.04 11.12 12.29 12.47 11.10
303.15 12.86 12.90 13.89 14.18 12.88
308.15 15.04 14.98 15.75 16.07 14.98
313.15 17.41 17.42 17.89 18.13 17.42
318.15 20.46 20.28 20.38 20.38 20.29
323.15 23.53 23.63 23.26 22.82 23.64
Open in a new tab
a

xexp1 is the experimental solubility of IHI in THF + water binary solvent system, and x02 denotes the initial mole fraction of DMF in the binary solvent mixture. xApelblat1, xYaws1, xSun1, and xJA1 represent the calculated solubilities using the modified Apelblat model, Yaws model, Sun model, and modified Jouyban–Acree model, respectively. The standard uncertainty of temperature is u(T) = 0.05 K, and the relative standard uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of mole fraction solubility is ur(x1) = 0.03, and the relative standard uncertainty of the solvent composition is ur(x20) = 0.0002.

The maximum solubility of IHI exists in the solvent of DMF + ethanol (0.06523 mol·mol–1, x02 = 0.7, T = 323.15 K), while the minimum solubility exists in DMF + water (0.0003723 mol·mol–1, x02 = 0.3, T = 283.15 K). The maximum solubility value is approximately 175 times than the minimum solubility value. Except for the solvent DMF + water, the theoretical molar yield of each binary mixed solvent ranges from 58 to 84% with cooling conditions ranging from 323.15 to 283.15 K. The theoretical molar yield of the antisolvent method is 80% in all of the selected solvent systems. The solvent composition is more sensitive to solubility than temperature changes. In addition, when the cooling and antisolvent methods were combined, the theoretical molar yield can reach higher than 88%. What should be especially mentioned is that, in the solvent of DMF + water, when using the cooling method with the antisolvent method, the theoretical molar yield can reach more than 99%.

4.3. Data Correlation

Parameters, RADs, and RMSDs values of the selected model in this article are listed in Tables 6–9. All of the RAD values are less than 0.0484 (Sun model, DMF + water), and RMSD values are no more than 0.001319 (Sun model, THF + water). Considering the RAD values, the fitting order of the selected four thermodynamic models is Yaws ≥ modified Apelblat ≥ Sun ≥ modified Jouyban–Acree. Considering the RMSD values, the fitting order of the selected four thermodynamic models is modified Apelblat ≥ Yaws ≥ modified Jouyban–Acree ≥ Sun. The Yaws model and the modified Apelblat model fit the solubility data of IHI better than the other two models. All in all, all of the selected four models can fit the solubility data of IHI well.

Table 6. Parameters of the Modified Apelblat Model for IHI in Binary Solvent Mixturesa.

x02 A1 B2 C3 100 RAD 104 RMSD
DMF + water        
0.3 22.5674 6300.0844 –1.4358 4.71 0.66
0.4 111.3980 10677.0421 –14.2657 3.13 1.27
0.5 –89.8601 –918.8117 15.4352 2.17 2.62
0.6 202.3326 13696.3584 –28.2443 2.30 2.54
0.7 181.0354 12095.6740 –25.3881 0.87 1.88
0.8 257.4723 15147.7968 –36.9690 1.65 3.03
0.9 311.3921 17362.2711 –45.1060 1.32 3.14
1.0 293.8373 16462.8750 –42.5448 1.68 3.89
average       2.23 2.38
DMF + ethanol        
0.3 –0.1104 –3645.7022 1.3487 2.43 2.54
0.4 –272.2591 8719.3702 41.8982 1.01 2.04
0.5 –98.1654 1159.4091 15.8560 0.83 2.41
0.6 –34.9823 –1312.0190 6.2729 0.64 2.94
0.7 –203.4855 6541.5136 31.2414 0.84 2.82
0.8 –125.2021 2883.5480 19.6482 0.61 1.95
0.9 83.0580 –6783.9999 –11.2307 0.84 0.25
1.0 293.8373 16462.8750 –42.5448 1.68 3.89
average       1.11 2.36
THF + water        
0.3 –250.4788 8351.1064 38.3044 1.46 3.42
0.4 –244.5529 8447.3423 37.2697 0.90 2.04
0.5 –164.3752 5096.3882 25.2222 0.74 2.52
0.6 –116.8804 3299.5604 17.9787 0.84 3.35
0.7 –116.4081 3363.4658 17.8683 0.89 4.22
0.8 –181.0344 6148.4414 27.5480 0.42 1.70
0.9 –205.5813 7037.6446 31.2848 1.14 3.13
1.0 –151.6913 4321.7412 23.2900 0.72 1.03
average       0.89 2.68
THF + ethanol        
0.3 –147.8303 4348.9300 22.5316 1.04 0.96
0.4 –204.8489 6837.1695 31.1132 0.73 0.96
0.5 –158.2689 4841.3186 24.1550 0.44 0.85
0.6 –136.9302 3963.4145 20.9609 1.09 1.91
0.7 –144.5506 4410.9687 22.0577 0.99 1.94
0.8 –131.9881 3908.2125 20.1566 1.13 2.55
0.9 –194.7470 6591.9896 29.5701 0.74 1.55
1.0 –151.6913 4321.7412 23.2900 0.72 1.03
average       0.86 1.47
Open in a new tab

Table 9. Parameters of the Modified Jouyban–Acree Model for IHI in Binary Solvent Mixtures.

parameters DMF + water DMF + ethanol THF + water THF + ethanol average
A1 68.8139 –32.6042 –24.1136 –13.7357  
A2 –12053.4224 –2427.8886 –2644.7130 –2108.8953  
A3 –7.4778 6.1879 4.5754 2.5957  
A4 21.5197 7.6931 –143.8933 –32.2577  
A5 13836.4102 167.8674 12250.2571 3006.3646  
A6 –18758.9719 4951.2611 10116.9373 –2345.4093  
A7 14004.9985 –7581.2933 11247.8913 2940.2240  
A8 –4054.0639 3168.5933 –5281.0276 –1759.4633  
A9 –4.9018 –1.4623 20.9284 4.8521  
100 RAD 4.23 3.78 4.03 2.10 3.54
104 RMSD 6.42 9.47 11.86 3.72 7.87
Open in a new tab

Table 7. Parameters of the Yaws Model for IHI in Binary Solvent Mixturesa.

x02 E F G 100 RAD 104 RMSD
DMF + water        
0.3 12.2847 –5477.0572 –58510.4966 4.72 0.66
0.4 8.7927 –2227.6943 –623436.3669 3.10 1.27
0.5 21.6593 –10374.2692 723389.6447 2.14 2.55
0.6 –3.6129 4770.9081 –1503950.0617 2.33 2.52
0.7 –3.9627 4425.6486 –1339183.8988 0.66 1.78
0.8 –9.7620 7580.5954 –1745056.1789 1.70 3.14
0.9 –14.6948 10389.4395 –2132322.7153 1.40 3.31
1.0 –13.3147 9455.1423 –1971594.9422 1.72 4.02
average       2.22 2.41
DMF + ethanol        
0.3 9.3546 –4299.8374 36725.4325 2.41 2.54
0.4 27.3784 –15050.0483 1671630.1098 0.99 1.91
0.5 16.4720 –8601.2413 750303.6222 0.81 2.26
0.6 10.3187 –5141.7090 291959.5130 0.64 2.93
0.7 21.7350 –12290.4383 1417173.5731 0.81 2.64
0.8 16.7583 –9153.2231 920744.3453 0.58 1.83
0.9 2.0512 12.8836 –513592.2951 0.86 2.52
1.0 –13.3147 9455.1423 –1971594.9422 1.72 4.02
average       1.10 2.58
THF + water        
0.3 26.1017 –15009.0456 1778952.7732 1.48 3.39
0.4 24.4614 –14223.9309 1722057.3704 0.96 2.15
0.5 20.0187 –11680.2372 1384829.3937 0.49 2.00
0.6 12.9774 –7689.6051 838717.4450 0.82 3.28
0.7 12.6826 –7576.9785 836426.9433 0.86 4.12
0.8 17.7787 –10592.3306 1270508.1810 0.42 1.73
0.9 19.9980 –11848.7988 1423551.8673 1.16 3.19
1.0 –13.3147 9455.1423 –1971594.9422 0.68 0.98
average       0.86 2.61
THF + ethanol        
0.3 14.8295 –9371.8146 1043194.4387 1.05 0.97
0.4 19.8265 –12149.8137 1446915.8547 0.72 0.96
0.5 16.1600 –9895.8537 1122192.4710 0.40 0.80
0.6 14.2763 –8731.3099 959908.4919 1.13 1.96
0.7 14.5356 –8928.2408 1007115.0780 1.01 2.01
0.8 13.335 –8249.8836 915551.3089 1.17 2.65
0.9 18.8343 –11483.2133 1379738.0820 0.79 1.64
1.0 –13.3147 9455.1423 –1971594.9422 0.68 0.98
Average       0.87 1.50
Open in a new tab

Table 8. Parameters of the Sun Model for IHI in Binary Solvent Mixtures.

parameters DMF + water DMF + ethanol THF + water THF + ethanol average
A1 18.3570 9.0364 6.7092 3.7187  
A2 –10091.9754 –4329.7198 –4062.1280 –2912.2647  
A3 –11.3094 –2.1572 –3.2787 0.3646  
A4 17709.6379 611.4711 5881.1666 1588.5918  
A5 –24248.9096 4973.8211 –10113.4012 –2507.9924  
A6 19342.9012 –7604.7556 11243.5788 3110.1740  
A7 –5936.5594 3177.4279 –5279.2760 –1823.1146  
100 RAD 4.84 3.73 4.09 2.38 3.76
104 RMSD 7.27 9.62 13.19 4.20 8.57
Open in a new tab

5. Conclusions

The solubility of IHI in four commonly used binary solvent mixtures of N,N-dimethylformamide (DMF) + water, DMF + ethanol, tetrahydrofuran (THF) + water, and THF + ethanol was determined with the gravimetric method at temperatures ranging from 283.15 to 323.15 K under atmospheric pressure. The solubility of IHI in all selected solvents increases with the increase of temperature. There is a co-solvency phenomenon in the mixed solvents of DMF+ ethanol, THF + water, and THF + ethanol. The maximum solubility of IHI exists in the solvent of DMF + ethanol (0.06523 mol·mol–1, x02 = 0.7, T = 323.15 K), while the minimum solubility exists in DMF + water (0.0003723 mol·mol–1, x02 = 0.3, T = 283.15 K). Four thermodynamic models including the modified Apelblat model, the Yaws model, the Sun model, and the modified Jouyban–Acree model were selected to fit the solubility data of IHI. The Yaws model and the modified Apelblat model fit the solubility data of IHI better than the other two models. All in all, all of the selected four models can fit the solubility data of IHI well.

Acknowledgments

This investigation work received support from the Shandong Provincial Natural Science Foundation (grant reference: ZR2023MB036, and ZR2020QB177), Central Guidance on Local Science and Technology Development Fund of Shandong Province (grant references: YDZX2021054, and YDZX2022098), the National Natural Science Foundation of China (grant reference: 82204288), Shandong Keypoint Research & Development Plan (grant references: 2021CXGC010514, and 2021CXGC010811), and Science, Education and Industry Integration Technology Innovation Project (grant references: 2022PX036, and 2022PT117).

Author Contributions

§ Q.D. and S.Y. contributed equally to this work and should be regarded as co-first authors.

The authors declare no competing financial interest.

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