Determination and Correlation of Solubility of Metformin Hydrochloride in Aqueous Binary Solvents from 283.15 to 323.15 K.

Metformin hydrochloride (MET·HCl) is one of the most widely used oral hypoglycemic drugs in the world. In addition to hypoglycemic effects, MET·HCl also has anti-inflammatory, anti-tumor, anti-aging, and other effects, showing good efficacy and safety of single and combined treatment. The solubility of MET·HCl in water, water + N,N-dimethylformamide, water + acetonitrile, and water + n-propanol was measured by the gravimetric method under atmospheric pressure at temperatures ranging from 283.15 to 323.15 K. The solubility of MET·HCl has a positive correlation with temperature and water content. The experimental solubility data in binary solvents was correlated by the modified Apelblat model, CNIBS/R-K model, Apelblat-Jouyban-Acree model, and λh model. By comparing the average ARD % values of the four models, it is found that the modified Apelblat model (ARD % = 1.26) provides better correlation. Hansen solubility parameters and apparent thermodynamic parameters were calculated to analyze the solubility behavior, indicating that the dissolution process is endothermic and entropically favorable.

Introduction

Metformin hydrochloride (MET·HCl, C4H11N5) is a first-line drug for the treatment of type 2 diabetes (non-insulin-dependent diabetes), and it is also one of the most widely used oral hypoglycemic drugs in the world.[1−3] The chemical structure is shown in Figure . Compared with metformin, MET·HCl is more stable and easier to be absorbed by the body. It can reduce the absorption of glucose in the intestine and increase the uptake of glucose from the blood to the tissues. Meanwhile, it can reduce the production of glucose in the liver and increase insulin sensitivity.

Figure 1

Molecular structure of MET·HCl.

Crystallization refers to the process of precipitation of solids from solution and is a commonly used separation method. In industrial production, the crystallization process is the key operation to purify MET·HCl. Solubility data is the basis for designing the crystallization process. At present, there are some reports on the solubility of MET·HCl. Benmessaoud et al.[4] roughly measured the solubility of MET·HCl in 13 pure solvents (water, dichloromethane, 1-pentanol, 1-propanol, acetone, dimethyl sulfoxide, ethanol, ethylene glycol, formamide, methanol, tetrahydrofuran, toluene, and 1-octanol). Our previous work measured the solubility of MET·HCl (form A)[5] in four binary solvents (water + acetone, water + methanol, water + ethanol, and water + isopropanol) by the gravimetric method.[6] To extend the solubility database, we explored the solid–liquid equilibrium of MET·HCl in other mixed solvents.

In this work, we determined the solubility of MET·HCl in water, water + N,N-dimethylformamide (DMF), water + acetonitrile, and water + propanol at the temperature ranging from 283.15 to 323.15 K by the gravimetric method. In order to verify the reliability of the data and expand the application, the data were correlated by the modified Apelblat model,[7,8] CNIBS/R-K model,[8,9] Apelblat–Jouyban–Acree model,[10−12] and λh model.[13−15]

Thermodynamic Models

Modified Apelblat Model

The modified Apelblat model[16] is an accurate semiempirical equation which expresses the relationship between solubility and temperature. It is expressed by eq where x1 is the mole fraction solubility of MET·HCl, T is the absolute temperature, and A, B, and C are the empirical constants.

CNIBS/R-K Model

The CNIBS/R-K model was proposed by Acree et al.[17] which expressed the relationship between isothermal mole fraction solubility of binary solvent mixture and solvent composition. It is calculated by eq where x1 is the mole fraction solubility of the solute; x20 and x30 are the initial mole fraction of the solvent mixture; X and X refer to the saturated mole solubility of the solute in the corresponding pure solvent. Si and n are the model parameters.

For binary solvents with n = 2, eq can be simplified to eq

The b1–b5 were used to replace the constant parameters, and eq can be simplified to eq (18)

Apelblat–Jouyban–Acree Model

The relationship between the solubility of solute, temperature, and initial component in binary mixed solvents was represented by the Apelblat–Jouyban–Acree model which was proposed by Jouyban Gharamaleki and his co-workers in 1988. The model is calculated by eq (19)where x20 and x30 represent the initial molecular fraction composition of the binary solvent mixture without the solute. X and X are the mole fraction solubility of solute in the pure solvent, and J is the model constant.

For binary solvents with n = 2, eq can be simplified to eq

The A0–A8 were used to replace the constant parameters, and eq can be simplified to eq (20)

λh Model

The λh model was proposed to describe the solubility behavior of solute in solution. It can be calculated as follows[21]where λ and h are two equation parameters and Tm is the melting temperature of the solute. The x1 is the mole fraction solubility of solute, and T is the test temperature.

Hansen Solubility Parameter

The Hansen solubility parameter (HSP)[22−25] is made up of three parts: dispersion solubility parameter (δd), polar solubility parameter (δp), and hydrogen bond solubility parameter (δh). The total HSP can be calculated by eq

In binary solvent, the δmix was obtained from eq

Apparent Thermodynamics

Dissolution behavior of MET·HCl in the three binary solvents is determined by thermodynamic parameters. The parameters can be calculated by the Gibbs and van’t Hoff equations, and the modified van’t Hoff equation is shown as follows[26]where x1 is the mole fraction solubility of MET·HCl; R is the ideal gas constant; and T is the absolute temperature (K). Thm is the mean harmonic temperature which can calculated by eq (27)where n is the number of temperatures studied. By plotting lnx1 against 1/T – 1/Thm, the ΔG and ΔS values are calculated as follows[28]

For binary solvents, the enthalpy (%ζH) and entropy (%ζTS) can compare the relative contributions and they are given as follows[28]

Data Correlation

The average relative deviation (ARD %) and root-mean-square deviation (rmsd) can evaluate the accuracy of thermodynamic model. They are shown as follows

Results and Discussion

Characterization of MET·HCl

The residual solids in different solvent mixtures and raw material of MET·HCl were determined by X-ray powder diffraction (XRPD) and are shown in Figure . The main peaks are mainly at 12.13, 17.42, 24.51, and 37.05° which are consistent with the crystal form A previously reported in the literature.[29,30] The positions of main peaks have no change, demonstrating that no polymorphic transformation or solvate formation occurred during the whole experiment.[31,32] The same XRPD patterns of all solid samples also indicate that HCl did not lost during the entire experiments. The properties of liquid such as pH values were also analyzed, and the results verified that the excess solid could not release HCl into the solution.[6]

Figure 2

XRPD patterns of raw MET·HCl and excess MET·HCl in different solvents.

The thermogravimetry (TGA) and differential scanning calorimetry (DSC) curves of MET·HCl obtained in this study are presented in Figure . It can be seen from Figure that the values of the onset melting temperature are 498.15 K, and the fusion happened before the weightless decomposition. Hence, the material could remain stable during the whole experiment.

Figure 3

Results of TGA and DSC analysis of MET·HCl.

Solubility Results of MET·HCl

In order to verify the accuracy of our experiment, we compared the solubility in pure water at 293.15 and 313.15 K with the data of published articles.[4,6] The result is shown in Table S5. As shown in Table S5, our solubility data is credible. The solubility data of MET·HCl in three binary (water + DMF, water + acetonitrile, and water + n-propanol) solvents and water are listed in Tables –3. The solubility of MET·HCl in three pure solvents, including DMF, acetonitrile, and n-propanol, is very small. When the content of these three organic solvents in the binary mixed solvent is high, the solubility data is still very small, which is easy to cause errors. In order to maintian the accuracy, we only determined the data that the mole fraction of water is higher than 0.3. Figures –6 can display intuitively the relationship between the solubility and temperature as well as water content.

Table 1

Experimental and Fitted Solubility Data of MET·HCl in Water + DMF (P = 0.1 MPa)a,b

	103 x1exp	103x1apelblat	103x1CNIBS	103x1AJA	103x1λh
283.15 K
0.30	5.572	5.932	5.556	5.674	5.540
0.40	8.019	8.100	8.076	8.158	7.938
0.50	10.79	10.83	10.77	11.03	10.45
0.60	13.91	13.82	13.85	14.31	13.61
0.70	17.92	17.84	17.61	18.02	17.70
0.80	21.32	21.07	22.18	22.09	20.96
0.90	27.87	27.71	27.08	26.25	27.75
1.00	30.45	30.27	30.66	29.83	30.92
288.15 K
0.30	6.557	6.208	6.532	6.059	6.070
0.40	8.860	8.795	8.949	8.774	8.719
0.50	11.81	11.78	11.79	11.96	11.63
0.60	15.36	15.33	15.23	15.66	15.25
0.70	19.71	19.88	19.42	19.91	19.82
0.80	23.32	23.51	24.37	24.65	23.48
0.90	30.68	30.94	29.67	29.59	30.97
1.00	33.85	34.32	34.14	34.02	34.62
293.15 K
0.30	7.052	6.571	7.015	6.518	6.637
0.40	9.470	9.560	9.634	9.488	9.557
0.50	13.05	12.87	12.83	13.02	12.90
0.60	16.57	17.01	16.73	17.16	17.04
0.70	22.07	22.13	21.46	21.98	22.14
0.80	25.70	26.19	27.02	27.43	26.22
0.90	34.35	34.43	33.15	33.20	34.44
1.00	38.75	38.66	39.09	38.52	38.63
298.15 K
0.30	7.284	7.030	7.302	7.061	7.245
0.40	10.59	10.40	10.44	10.31	10.46
0.50	13.83	14.11	14.23	14.21	14.28
0.60	19.11	18.87	18.80	18.83	18.98
0.70	24.79	24.59	24.26	24.25	24.65
0.80	29.41	29.11	30.61	30.44	29.19
0.90	38.36	38.21	37.46	37.09	38.20
1.00	43.60	43.25	43.82	43.34	42.97
303.15 K
0.30	7.469	7.5957	7.480	7.698	7.896
0.40	11.62	11.331	11.51	11.26	11.42
0.50	15.70	15.52	16.03	15.56	15.77
0.60	21.33	20.93	21.08	20.68	21.09
0.70	27.49	27.28	26.93	26.73	27.37
0.80	32.52	32.30	33.79	33.70	32.40
0.90	42.40	42.27	41.42	41.26	42.25
1.00	48.33	48.09	48.58	48.46	47.66
308.15 K
0.30	7.790	8.283	7.752	8.443	8.593
0.40	11.71	12.35	11.90	12.35	12.45
0.50	17.17	17.12	16.95	17.08	17.37
0.60	22.87	23.21	22.85	22.75	23.37
0.70	29.89	30.22	29.58	29.46	30.31
0.80	35.87	35.78	37.10	37.22	35.87
0.90	46.52	46.64	45.27	45.71	46.60
1.00	53.25	53.17	53.63	53.88	52.71
313.15 K
0.30	8.600	9.111	8.619	9.311	9.339
0.40	13.74	13.47	13.56	13.60	13.56
0.50	18.71	18.93	19.21	18.80	19.11
0.60	25.95	25.74	25.57	25.03	25.84
0.70	33.57	33.43	32.87	32.44	33.49
0.80	39.70	39.57	41.25	41.03	39.62
0.90	51.38	51.32	50.23	50.44	51.29
1.00	57.72	58.46	58.00	59.58	58.15
318.15 K
0.30	10.61	10.10	10.53	10.32	10.14
0.40	14.44	14.71	14.79	15.03	14.74
0.50	21.13	20.99	20.74	20.74	20.97
0.60	28.40	28.53	28.18	27.58	28.51
0.70	36.77	36.93	36.59	35.69	36.92
0.80	43.50	43.68	45.34	45.12	43.66
0.90	56.38	56.33	54.33	55.46	56.32
1.00	63.98	63.94	64.63	65.55	63.98
323.15 K
0.30	11.56	11.28	11.52	11.50	10.99
0.40	16.41	16.07	16.58	16.67	16.01
0.50	23.31	23.32	23.25	22.93	22.98
0.60	31.61	31.61	31.34	30.40	31.40
0.70	40.85	40.74	40.41	39.25	40.62
0.80	48.08	48.15	49.95	49.52	48.01
0.90	61.57	61.67	59.76	60.77	61.71
1.00	69.87	69.59	70.41	71.76	70.25

x1 is the experimental solubility; the x1apelblat, x1CNIBSx1λh, and x1AJA are the calculated mole solubilities according to the modified Apelblat model, CNIBS/R-K model, λh model, and Apelblat–Jouyban–Acree model, respectively. represents the initial mole fraction of water in the binary aqueous solvent.

The standard uncertainty is u(T) = 0.1 K; the relative standard uncertainties ur are ur(P) = 0.01, ur(x1) = 0.05, and ur() = 0.001.

Table 3

Experimental and Fitted Solubility Data of MET·HCl in Water + n-propanol (P = 0.1 MPa)a,b

	103x1exp	103x1apelblat	103x1CNIBS	103x1AJA	103x1λh
283.15 K
0.30	3.039	2.923	3.042	2.945	3.137
0.40	5.573	5.504	5.543	5.428	5.558
0.50	8.772	8.747	8.839	8.732	8.673
0.60	12.65	12.54	12.75	12.71	12.90
0.70	17.69	17.58	17.08	17.18	17.81
0.80	20.74	20.69	21.63	21.88	20.92
0.90	26.82	26.82	26.23	26.36	27.60
1.00	30.45	30.27	30.59	29.83	30.92
288.15 K
0.30	3.337	3.589	3.339	3.571	3.721
0.40	6.406	6.513	6.372	6.491	6.547
0.50	10.07	10.25	10.18	10.32	10.21
0.60	14.52	14.79	14.53	14.89	14.98
0.70	19.96	20.36	19.37	19.96	20.48
0.80	23.61	23.87	24.63	25.23	23.98
0.90	30.66	30.97	29.93	30.19	31.34
1.00	33.85	34.32	34.03	33.99	34.62
293.15 K
0.30	4.546	4.345	4.524	4.290	4.391
0.40	7.647	7.659	7.759	7.696	7.672
0.50	12.25	11.96	12.14	12.11	11.95
0.60	17.52	17.29	17.49	17.30	17.32
0.70	23.89	23.43	23.35	23.00	23.44
0.80	27.70	27.37	29.21	28.88	27.37
0.90	35.95	35.46	34.57	34.35	35.45
1.00	38.75	38.66	39.13	38.48	38.63
298.15 K
0.30	5.192	5.189	5.177	5.108	5.154
0.40	8.884	8.953	8.936	9.050	8.946
0.50	13.77	13.91	13.83	14.09	13.92
0.60	19.84	20.04	19.65	19.96	19.93
0.70	26.63	26.79	26.07	26.33	26.71
0.80	31.04	31.20	32.69	32.84	31.11
0.90	40.39	40.27	38.93	38.84	39.94
1.00	43.60	43.25	43.99	43.31	42.97
303.15 K
0.30	6.205	6.121	6.185	6.033	6.021
0.40	10.58	10.41	10.66	10.56	10.38
0.50	16.32	16.11	16.37	16.28	16.14
0.60	23.30	23.05	23.01	22.86	22.83
0.70	30.63	30.47	30.17	29.95	30.33
0.80	35.62	35.37	37.34	37.11	35.22
0.90	45.43	45.37	43.85	43.66	44.83
1.00	48.33	48.09	48.76	48.46	47.66
308.15 K
0.30	6.961	7.133	6.946	7.069	7.003
0.40	12.15	12.03	12.19	12.23	12.00
0.50	18.57	18.58	18.70	18.67	18.63
0.60	26.36	26.31	26.07	26.01	26.06
0.70	34.59	34.47	33.94	33.85	34.30
0.80	39.92	39.90	41.84	41.69	39.73
0.90	50.60	50.73	48.93	48.79	50.16
1.00	53.25	53.17	53.69	53.92	52.71
313.15 K
0.30	8.420	8.221	8.372	8.222	8.109
0.40	13.71	13.84	13.93	14.07	13.81
0.50	21.16	21.37	21.03	21.28	21.41
0.60	29.66	29.82	29.25	29.42	29.62
0.70	38.30	38.78	38.00	38.02	38.66
0.80	44.40	44.78	46.44	46.57	44.66
0.90	55.64	56.34	53.58	54.23	55.94
1.00	57.72	58.46	58.30	59.70	58.15
318.15 K
0.30	9.323	9.375	9.286	9.496	9.354
0.40	15.81	15.84	15.98	16.07	15.83
0.50	24.20	24.49	24.13	24.10	24.52
0.60	33.53	33.57	33.26	33.08	33.56
0.70	43.57	43.43	42.88	42.48	43.44
0.80	49.98	50.02	52.32	51.74	50.03
0.90	62.41	62.16	60.28	59.98	62.20
1.00	63.98	63.94	64.54	65.77	63.98
323.15 K
0.30	10.54	10.59	10.48	10.89	10.75
0.40	18.07	18.05	18.45	18.25	18.09
0.50	28.34	27.98	27.77	27.14	27.97
0.60	37.62	37.56	37.72	36.98	37.89
0.70	48.52	48.41	47.94	47.21	48.64
0.80	55.85	55.63	57.94	57.20	55.89
0.90	68.41	68.15	66.37	66.01	68.96
1.00	69.87	69.59	70.44	72.13	70.25

x1 is the experimental solubility; the x1apelblat, x1CNIBSx1λ, and x1AJA are the calculated mole solubilities according to the modified Apelblat model, CNIBS/R-K model, λh model, and Apelblat–Jouyban–Acree model, respectively. represents the initial mole fraction of water in the binary aqueous solvent.

The standard uncertainty is u(T) = 0.1 K; the relative standard uncertainties ur are ur(P) = 0.01, ur(x) = 0.05, and ur() = 0.001.

Figure 4

Experimental and correlated solubility of MET·HCl in water + DMF at 283.15 to 323.15 K: the points are experimental data, and the solid lines are correlative with the CNIBS/R-K model.

Figure 6

Experimental and correlated solubility of MET·HCl in water + n-propanol at 283.15 to 323.15 K: the points are experimental data, and the solid lines are correlative with the CNIBS/R-K model.

Experimental and correlated solubility of MET·HCl in water + acetonitrile at 283.15 to 323.15 K: the points are experimental data, and the solid lines are correlative with the CNIBS/R-K model.

As shown in Figures –6, it is obvious that the solubility of MET·HCl has a positive correlation with temperature and water content at the fixed solvent composition. Figures S1–S4 listing the parameters of the four models are demonstrated in Supporting Information. The order of the solubility is water + DMF > water + acetonitrile > water + n-propanol. When the water content is low, the difference of solubility between the water + acetonitrile and water + n-propanol is very small, but as the water content increases, the solubility differs significantly. Furthermore, the solubility is mainly determined by the interaction between solvent and solute molecules.[33,34] The main physicochemical properties of the solvents are listed in Table . It can be seen that the polarity order of the solvent is water > DMF > acetonitrile > n-propanol, which is consistent with the order of solubility in these solvents, following the “like dissolve like” rule. However, the summation of the hydrogen bond donor propensities of the solvent (∑αb) and the summation of the hydrogen bond accept propensities of the solvent (∑βc) have no obvious correlation with solubility. Moreover, the HSP which can explain the solubility capability is listed in Table . It shows that in water + DMF and water + n-propanol system, the δp, δh, and δmix have a positive correlation with the water content and the δd has a negative correlation. However, in water + acetonitrile, the δd, δh, and δmix have a positive correlation with the water content and the δp has a negative correlation.

Table 4

Main Physicochemical Properties of the Four Pure Solventsa

solvent	πa	∑αb	∑βc
water	1.09	1.17	0.47
DMF	0.88	0.00	0.74
acetonitrile	0.75	0.07	0.32
n-propanol	0.52	0.37	0.48

πa Polarity of the solvent. ∑αb is the summation of the hydrogen bond donor propensities of the solvent. ∑βc is the summation of the hydrogen bond accept propensities of the solvent.

Table 5

Values of HSPs of MET·HCl and the Selected Solventsa

	δd (Mpa)0.5	δp (Mpa)0.5	δh (Mpa)0.5	δmix (Mpa)0.5
Water + DMF
0.30	17.24	13.91	14.11	26.26
0.40	17.16	14.01	15.46	27.01
0.50	17.06	14.13	17.15	28.02
0.60	16.93	14.30	19.32	29.40
0.70	16.77	14.51	22.21	31.38
0.80	16.53	14.81	26.25	34.37
0.90	16.18	15.26	32.28	39.20
1.00	15.60	16.00	42.30	47.84
Water + Acetonitrile
0.30	15.34	17.74	10.76	25.80
0.40	15.36	17.63	12.86	26.68
0.50	15.38	17.49	15.37	27.90
0.60	15.40	17.32	18.43	29.61
0.70	15.43	17.11	22.23	32.02
0.80	15.47	16.84	27.08	35.44
0.90	15.53	16.49	33.47	40.41
1.00	15.60	16.00	42.30	47.84
Water + n-Propanol
0.30	15.96	7.660	19.73	26.51
0.40	15.94	8.070	20.84	27.46
0.50	15.92	8.590	22.23	28.66
0.60	15.89	9.240	24.01	30.24
0.70	15.86	10.11	26.36	32.38
0.80	15.80	11.31	29.62	35.42
0.90	15.73	13.10	34.44	40.06
1.00	15.60	16.00	42.30	47.84
Solute and Pure Solvents
water	15.60	16.00	42.30	47.84
acetonitrile	15.30	18.00	6.100	24.40
n-propanol	16.00	6.800	17.40	24.60
DMF	17.40	13.70	11.30	24.86

δd: dispersion solubility parameter. δp: polar solubility parameter. δh: hydrogen bond solubility parameter. δmix: the total Hansen solubility parameter.

In this work, we used the 1stopt for the modeling. The solubility of MET·HCl in three binary solvents was correlated by the modified Apelblat model, CNIBS/R-K model, Apelblat–Jouyban–Acree model, and λh model. The acquired results are listed in Tables –3, and the model parameters, ARD %, and rmsd are listed in Tables S1–S4. As shown in the tables, all the ARD % values are less than 6%, indicating that these models can fit the solubility data well. The maximum ARD % values for the correlation models are 5.75% in the water + acetonitrile system correlated by the CNIBS/R-K model. The maximum rmsd values for the correlation models is 1.1673 × 10–2 in the water + n-propanol system correlated by the CNIBS/R-K model. In water + DMF, the order of the ARD % is the Apelblat–Jouyban–Acree model (ARD = 0.0270)>CNIBS/R-K model (ARD = 0.0168)>λh model (ARD = 0.0163)>Apelblat model (ARD = 0.0146). In water + acetonitrile and water + n-propanol, the order of the ARD % values are same as that in the water + DMF system. All in all, the modified Apelblat model provided better correlation results than the others.

Thermodynamic Properties of Solution

The apparent thermodynamic parameters including Gibbs energy (ΔG), enthalpy (ΔH), and entropy (ΔS) are calculated and shown in Table . The values of ΔG, ΔH, and ΔS are all positive in the three binary solvents indicating that the dissolution process is endothermic and entropically favorable. Comparing the relative contributions of enthalpy and entropy, the % ζH is more than 60% in all binary solvents while the % ζTS is more than 7%. The main contributor to standard free energy of the solution process of MET·HCl is the enthalpy.

Table 6

Apparent Thermodynamic Parameters for Dissolution Behavior of MET·HCl in Three Binary Solvents at Thm

	ΔG (kJ·mol–1)	ΔH (kJ·mol–1)	ΔS (J·K–1·mol–1)	TΔS (kJ·mol–1)	% ζH	% ζTS
Water + DMF
0.30	12.19	13.56	4.508	1.364	90.86	9.143
0.40	11.27	13.71	8.065	2.440	84.89	15.11
0.50	10.46	15.05	15.19	4.598	76.60	23.40
0.60	9.730	16.09	21.02	6.361	71.67	28.33
0.70	9.075	15.90	22.57	6.830	69.96	30.04
0.80	8.652	15.94	24.09	7.289	68.62	31.38
0.90	7.984	15.31	24.21	7.327	67.63	32.37
1.00	7.685	16.06	27.68	8.375	65.73	34.27
Water + Acetonitrile
0.30	13.19	14.33	3.739	1.131	92.68	7.319
0.40	11.34	16.09	15.71	4.753	77.20	22.80
0.50	10.17	19.74	31.64	9.575	67.34	32.66
0.60	9.182	15.47	20.78	6.288	71.10	28.90
0.70	8.499	14.71	20.53	6.212	70.31	29.69
0.80	8.195	15.27	23.38	7.076	68.34	31.66
0.90	7.732	15.59	25.96	7.856	66.49	33.51
1.00	7.685	16.06	27.68	8.375	65.73	34.27
Water + n-Propanol
0.30	12.92	25.24	40.71	12.32	67.20	32.80
0.40	11.53	22.82	37.29	11.28	66.91	33.09
0.50	10.42	22.42	39.65	12.00	65.14	34.86
0.60	9.550	21.14	38.32	11.59	64.58	35.42
0.70	8.829	19.51	35.30	10.68	64.62	35.38
0.80	8.453	18.98	34.79	10.53	64.32	35.68
0.90	7.845	18.02	33.63	10.18	63.91	36.09
1.00	7.685	16.06	27.68	8.375	65.73	34.27

Conclusions

The mole fraction solubility of MET·HCl (form A) in water, water + DMF, water + acetonitrile, and water + n-propanol in the temperature ranging from 283.15 to 323.15 K was determined by the gravimetric method. The crystal form is stable in the whole experiment which was verified by the XRPD and thermal analysis. The solubility of MET·HCl has a positive correlation with temperature and water content in the three binary solvents. The order of the solubility is water > water + DMF > water + acetonitrile > water + n-propanol, and it is consistent with the polar order. All the selected models give low ARD % values less than 6%. The modified Apelblat model provides better correlation results. Comparing the values of apparent thermodynamic properties, we find the dissolution process is endothermic and entropically favorable. The solubility data would be helpful for separation and purification process of MET·HCl.

Experimental Section

Materials

MET·HCl was obtained from Shandong Fukang Pharmaceutical Co., Ltd., China. The organic solvents (DMF, acetonitrile, and n-propanol) used in this experiment were purchased from Tianjin Fuyu Fine Chemical Co., Ltd. The deionized water was made in the laboratory (arium mini plus, Germany). These solvents have not been further purified, and the detailed sources are listed in Table .

Table 7

Detailed Sources and Information of Materials

chemcials	CAS	molar mass (g·mol–1)	source	mass fraction purity (%)	analysis method
MET·HCl	1115-70-4	165.62	Fukang Pharmaceutical Co., Ltd., China	≥98.0	HPLCa
DMF	68-12-2	73.09	Tianjin Fuyu Fine Chemical Co., Ltd.	≥99.7	GCb
acetonitrile	75-05-8	41.05	Tianjin Fuyu Fine Chemical Co., Ltd.	≥99.7	GCb
n-propanol	71-23-8	60.10	Tianjin Fuyu Fine Chemical Co., Ltd.	≥99.7	GCb

High performance liquid chromatography.

Gas chromatography.

X-ray Powder Diffraction

The XRPD[33,34] was used to detect the crystal form of MET·HCl during the whole experiment. An X’pert3 Powder (PANalytical B.V., Netherlands) instrument was used with the 40 kV tube voltage and 30 mA current during the measurement. The patterns were collected by the EMPYREAN (PANalytical, the Netherlands) with the Cu Kα radiation (0.15405 nm) in the 2θ range (5–45°) at room temperature. The step size was 0.02°, and the scanning speed was 8°/min.

Thermal Analysis

In order to verify the stability of MET·HCl during the entire experiment, we performed the DSC and TGA.[35−38] The melting temperature Tm of MET·HCl was determined by the TGA and DSC (DSC-STA449 F3, NETZSH, Germany). Approximately, 3–5 mg of MET·HCl was added in an aluminum crucible. The sample was heated from 298.15 to 573.15 K at a heating rate of 10 K•min–1 under the protection of nitrogen atmosphere.

Solubility Measurements

The solubility of MET·HCl in water, water + DMF, water + acetonitrile, and water + n-propanol from 283.15 to 323.15 K was measured by the gravimetric method. Approximately, 25–30 mL of the solvent was added in the 100 mL custom test tube; after that, we added the excess solute to the test tubes. The test tubes were added in the constant temperature water bath which was controlled by the thermostat (CF41, Julabo, Germany) with an accuracy of ±0.01 K. The solution was stirred at a speed of 500 rpm for at least 12 h to reach the solid–liquid equilibrium. Then, we stopped the stirring and the solution system was kept still for more than 2 h to precipitate undissolved particles. Finally, we used the preheated/cooled 5 mL needle injector to extract the supernatant through the preheated/cooled 0.45 μm filter membrane and injected it into the Petri dish weighted in advance with the analytical balances (Mettler-toledo, Switzerland, the precision is ±0.0001 g). The total weight of the liquid sample and the Petri dish was measured immediately. The Petri dish containing the liquid sample was placed into the vacuum drying oven (type DZF-6000, Shanghai Yiheng Scientific Instrument Co., Ltd., China) at 318.15 K for 12 h. The experiment was repeated three times, and the mole fraction solubility (x1) of MET·HCl in pure solvents was calculated by eq where m1 is the mass of solute and m2 is the mass of pure solvent, and M1, and M2 are the corresponding molar mass, respectively.

The content ratio of water (x20) in the initial binary solvent and the mole fraction solubility (x1) of MET·HCl in binary solvents were calculated by eqs and 21where m1 is the mass of the solvent and m2 and m3 are the mass of water and organic solvent, respectively. M1, M2, and M3 are molecular mass of the solvent, water, and organic solvent, respectively.

Table 2

Experimental and Fitted Solubility Data of MET·HCl in Water + Acetonitrile (P = 0.1 MPa)a,b

	103x1exp	103x1apelblat	103x1CNIBS	103x1AJA	103x1λh
283.15 K
0.30	3.730	3.656	3.825	3.394	3.648
0.40	7.404	7.356	6.648	7.137	7.154
0.50	9.214	9.898	10.84	11.94	11.07
0.60	17.61	17.43	16.26	17.09	17.16
0.70	22.86	22.85	22.14	21.99	23.05
0.80	26.14	25.62	27.20	26.20	25.76
0.90	30.29	29.75	30.16	29.15	30.92
1.00	30.45	30.27	30.36	29.89	31.26
288.15 K
0.30	3.861	4.016	3.872	3.823	4.019
0.40	8.137	8.103	8.035	7.995	8.019
0.50	13.15	11.94	13.38	13.36	12.54
0.60	18.93	19.27	19.06	19.14	19.16
0.70	25.49	25.49	24.40	24.70	25.58
0.80	27.56	28.58	28.96	29.56	28.67
0.90	33.17	34.04	32.37	33.07	34.72
1.00	33.85	34.32	34.01	34.15	34.62
293.15 K
0.30	4.530	4.407	4.504	4.292	4.418
0.40	8.710	8.945	8.875	8.922	8.963
0.50	14.95	14.11	14.73	14.88	14.15
0.60	21.39	21.30	21.35	21.32	21.33
0.70	28.21	28.31	27.85	27.58	28.30
0.80	32.03	31.78	33.39	33.13	31.81
0.90	38.59	38.50	37.31	37.24	38.45
1.00	38.75	38.66	39.09	38.69	38.63
298.15 K
0.30	4.688	4.831	4.687	4.802	4.847
0.40	9.941	9.894	9.920	9.919	9.989
0.50	16.43	16.34	16.55	16.50	15.91
0.60	23.62	23.54	23.65	23.64	23.67
0.70	31.50	31.33	30.64	30.63	31.24
0.80	35.61	35.21	37.09	36.89	35.19
0.90	43.16	43.10	42.12	41.63	42.46
1.00	43.60	43.25	43.83	43.49	42.97
303.15 K
0.30	5.517	5.290	5.510	5.355	5.308
0.40	11.11	10.96	11.11	10.99	11.10
0.50	18.07	18.57	18.18	18.22	17.84
0.60	25.98	26.02	25.88	26.09	26.21
0.70	34.43	34.53	33.60	33.84	34.40
0.80	39.06	38.89	40.81	40.85	38.84
0.90	47.83	47.76	46.48	46.25	46.77
1.00	48.33	48.09	48.65	48.53	47.66
308.15 K
0.30	5.834	5.787	5.833	5.956	5.804
0.40	12.28	12.17	12.24	12.13	12.31
0.50	19.97	20.73	20.23	20.05	19.95
0.60	28.88	28.76	28.66	28.67	28.95
0.70	37.81	37.94	36.93	37.20	37.79
0.80	42.75	42.83	44.66	44.97	42.76
0.90	52.37	52.43	50.93	51.04	51.39
1.00	53.25	53.17	53.59	53.77	52.71
313.15 K
0.30	6.261	6.324	6.257	6.604	6.336
0.40	13.43	13.53	13.42	13.36	13.62
0.50	22.10	22.77	22.30	21.97	22.24
0.60	31.74	31.78	31.60	31.38	31.90
0.70	41.75	41.54	40.73	40.70	41.44
0.80	47.20	47.03	49.31	49.25	46.97
0.90	57.67	57.05	56.09	56.01	56.35
1.00	57.72	58.46	58.09	59.18	58.15
318.15 K
0.30	6.739	6.90	6.742	7.303	6.908
0.40	15.03	15.06	14.96	14.66	15.05
0.50	24.68	24.62	24.99	24.01	24.73
0.60	35.20	35.11	35.00	34.20	35.09
0.70	45.31	45.33	44.31	44.33	45.34
0.80	51.00	51.50	52.94	53.66	51.49
0.90	61.76	61.56	60.36	61.11	61.65
1.00	63.98	63.94	64.31	64.73	63.98
323.15 K
0.30	7.65	7.531	7.669	8.056	7.522
0.40	16.77	16.78	16.60	16.04	16.58
0.50	27.20	26.23	27.60	26.14	27.44
0.60	38.67	38.78	38.59	37.14	38.51
0.70	49.28	49.33	48.55	48.08	49.53
0.80	56.44	56.24	57.37	58.19	56.34
0.90	65.34	65.90	64.90	66.32	67.32
1.00	69.87	69.59	69.95	70.39	70.25

x1 is the experimental solubility; the x1apelblat, x1CNIBSx1λ, and x1AJA are the calculated mole solubilities according to the modified Apelblat model, CNIBS/R-K model, λh model, and Apelblat–Jouyban–Acree model, respectively. represents the initial mole fraction of water in the binary aqueous solvent.

The standard uncertainty is u(T) = 0.1 K; the relative standard uncertainties ur are ur(P) = 0.01, ur(x1) = 0.05, and ur() = 0.001.