Measurement and Correlation of Solubility of Amorphous Cefmetazole

Article pubs.acs.org/jced

Measurement and Correlation of Solubility of Amorphous Cefmetazole Sodium in Pure Solvents and Binary Solvent Mixtures Xiaolong Tao,† Baohong Hou,†,‡ Xiaoxue Hu,† Fuli Zhou,† Haijiao Lu,† Ting Wang,† Jiangfeng Zhao,† and Hongxun Hao*,†,‡ †

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, People’s Republic of China ‡ The Co-Innovation Center of Chemistry and Chemical Engineering of Tianjin, Tianjin University, Tianjin 300072, People’s Republic of China ABSTRACT: The development and design of the crystallization process strongly depend on accurate solid−liquid equilibrium data. In this paper, the solubility data of amorphous cefmetazole sodium in pure solvents (ethanol, n-propanol, i-propanol, n-butanol, n-amyl alcohol, ethyl acetate, n-butyl acetate, n-hexane, and cyclohexane) and binary solvent mixtures (methanol and ethanol) were measured by using the UV spectroscopic method and gravimetrical method, respectively, at temperatures from 278.15 to 313.15 K. The results show that the solubility data of cefmetazole sodium increase with the increasing temperature in all investigated solvents and decrease with the rise of the mole fraction of ethanol in the binary solvent mixtures. The Apelblat equation was successfully used to correlate the experimental solubility data in pure solvents, and the Apelblat equation, the CNIBS/R-K model, and the Jouyban−Acree model were successfully applied to correlate the solubility data in methanol + ethanol systems. It was found that the correlated data are in good agreement with the experimental data. Additionally, the molecular surface electrostatic potential (MSEP) correlated with the solubility data was also calculated and used to explain the difference of the solubility data of amorphous cefmetazole sodium in various solvents.

1. INTRODUCTION Cefmetazole sodium (C15H16N7O5S3Na, CAS Registry No.: 56796-39-5, Figure 1), the structural formula of which is sodium

no publication about the solubility data of cefmetazole sodium was found. In this paper, the solubility of cefmetazole sodium in nine common organic solvents (ethanol, n-propanol, i-propanol, n-butanol, n-amyl alcohol, ethyl acetate, n-butyl acetate, n-hexane and cyclohexane) and binary solvent mixtures (methanol and ethanol) were measured by using the UV spectroscopic method and gravimetrical method, respectively, at temperatures from 278.15 to 313.15 K. To extend the applicability of the solubility data, the Apelblat equation was used to correlate the experimental solubility data in pure solvents. At the same time, the Apelblat equation, the CNIBS/R-K model, and the Jouyban− Acree model were applied to correlate the solubility data in mixed mixtures. Additionally, the molecular surface electrostatic potential (MSEP) correlated with the solubility was also calculated and used to explain the difference of the solubility data of amorphous cefmetazole sodium in various solvents.

Figure 1. Chemical structure of cefmetazole sodium.

(6R,7S)-7-[2-[(cyanomethyl)thio] acetamidol]-7-methoxy-3[[(1-methyl-1H-tetrazol-5-yl)thio]methyl]-8-oxo-5-thia-l-azabicyclo [4.2.0] oct-2-ene-2-carboxylate, has a broad spectrum of activity comparable to other second-generation cephalosporins.1,2 Compared with other cephalosporins, it is chemically unique because the cephem nucleus is substituted with a 7α-methoxy to increase the steric hindrance of the parent nucleus and its resistance to destruction by bacterial β-lactamase. It is also active against β-lactamase-producing organisms which are resistant to cephalosporins or penicillins.2 The commercial cefmetazole sodium is basically amorphous powder.3 In industry, cefmetazole sodium is mainly produced by crystallization. Solubility data of cefmetazole sodium are essential for the successful development of its crystallization processes.4 However, through extensive literature screening, © XXXX American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials. Cefmetazole sodium was supplied by Hainan Full Fangyuan Pharmaceutical Co., Ltd. (Hainan China). Methanol, ethanol, n-propanol, isopropanol, n-butyl alcohol, Received: August 19, 2016 Accepted: December 2, 2016

A

DOI: 10.1021/acs.jced.6b00741 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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acetate, n-hexane, and cyclohexane) were determined by the UV spectroscopic method,7,8 which has been verified in our previously published ref 8. The detailed description of the apparatus and procedures could be found in the literature,8 which could be briefly explained as follows: (1) Determination of the calibration curve: water was used as dilution solvent, and the maximum absorption wavelength in water was determined to be 272 nm from 200 and 290 nm. The obtained calibration curve, as shown in Figure 2, is linear, which complies with the

n-amyl alcohol, ethyl acetate, butyl acetate, hexane, and cyclohexane (mass fraction purity >0.995) used in the experimental process were purchased from Tianjin Jiangtian Chemical Co., Ltd. (Tianjin, China). More detailed information about chemicals used in this study is shown in Table 1. All chemicals were used in experiments without any further purification. Table 1. Description of Materials Used in This Papera,b chemical name

source

cefmetazole sodium methanol ethanol n-propanol i-propanol n-butyl acetate n-butanol ethyl acetate n-amyl alcohol n-hexane cyclohexane

Hainan Full Fangyuan Pharmaceutical Tianjin Jiangtian Chemical Tianjin Jiangtian Chemical Tianjin Jiangtian Chemical Tianjin Jiangtian Chemical Tianjin Jiangtian Chemical Tianjin Jiangtian Chemical Tianjin Jiangtian Chemical Tianjin Jiangtian Chemical Tianjin Jiangtian Chemical Tianjin Jiangtian Chemical

a

mass fraction purification analysis purity method method >0.985

none

HPLCa

>0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995

none none none none none none none none none none

GCb GCb GCb GCb GCb GCb GCb GCb GCb GCb

High-performance liquid chromatography. bGas chromatography.

2.2. Characterization of the Solid Crystal Form. Since chemical material instabilities for most amorphous drugs normally arise on a time scale that is much longer than the time required for solubility data measurement, such instabilities can be neglected.3,5 Crystal transformation might be a serious problem if crystal transformation does take place during solubility data determination.5 In order to ensure that the amorphous cefmetazole sodium did not transform into other forms, X-ray powder diffraction (XRPD) patterns of the samples, both before and after all experiments, were measured by the Cu Kα radiation (1.5405 Å) in the 2-theta range from 2 to 50°. 2.3. Determination of Solubility. In this study, the solubility data of amorphous cefmetazole sodium were measured by the shake flask method which is based on the phase equilibrium technique developed by Higuchi and Connors.6 The method can be mainly divided into five steps: (1) sample preparation, (2) determination of equilibration, (3) separation of phases, (4) measurement of the saturated solution, and (5) characterization of the residual solid and dried samples. Since the choice of method for measuring the concentration of saturated solution will directly determine the accuracy of the final solubility data, in order to select the appropriate measurement method, first, the solubility data of amorphous cefmetazole sodium in pure solvents (methanol, ethanol, n-propanol, isopropanol, n-butyl alcohol, ethyl acetate, and butyl acetate) were roughly measured by a gravimetrical method at 298.15 K. The results showed that cefmetazole sodium is soluble in methanol and ethanol while less soluble in the several other tested solvents. As a result, the solubility data of amorphous cefmetazole sodium in pure solvents (ethanol, n-propanol, isopropanol, n-butyl alcohol, ethyl acetate, and butyl acetate) and binary solvent mixtures (methanol and ethanol) were measured by using a UV spectroscopic method and gravimetrical method, respectively, according to their ability to dissolve amorphous cefmetazole sodium. 2.3.1. Determination of Solubility in Pure Solvents by the UV Spectroscopic Method. The solubility data of amorphous cefmetazole sodium in pure solvents (ethanol, n-propanol, i-propanol, n-butanol, n-amyl alcohol, ethyl acetate, n-butyl

Figure 2. Absorbance A versus concentration (mg/mL) calibration curve of cefmetazole sodium.

Lambert−Beer law. The slope αi of the linear fitting line is 2.7629 with R2 = 0.99989. (2) Preparation of the saturated solution: At first, an excess amount of amorphous cefmetazole sodium was added into the pure solvent. Several sealed Erlenmeyer flasks with a volume of 50 mL were kept at a specific temperature in a shaker (Tianjin Ounuo Instrument Co., Ltd., China, with a temperature-controlling system with accuracy of ±0.05 K) for about 18 h to reach (solid + liquid) equilibrium. The shaker was then stopped, and the solutions were kept still for 7 h to allow the undissolved solid to settle down. (3) Measurement of the concentration of saturated solution: The upper clear saturated solutions were filtered by an organic membrane filter (0.22 μm, Tianjin Legg Technology Co., Ltd, Tianjin, China) and diluted by water to a certain concentration suitable for UV assay which was carried out on UV-3010 spectrophotometer (Hitachi, Japan with a 1 cm path length cell). In order to minimize measurement error, each measurement process illustrated above was repeated until at least three subsequent absorbance measurements were very close (within 0.02). The mole fraction solubility x1 can be calculated by the following equations: A ×V m1 = αi (1) x1 =

m1/M1 m1/M1 + m2 /M 2

(2)

where A represents absorbance obtained from UV spectrophotometer, αi refers to the slope of calibration curve with value of 2.7629, V is the diluted volume, m1 and m2 are the masses of cefmetazole sodium and solvent, respectively, and M1 and M2 refer to the corresponding mole masses of cefmetazole sodium and solvent, respectively. B



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2.3.2. Determination of Solubility in the Binary Solvent Mixtures by Gravimetrical Method. The solubility data of amorphous cefmetazole sodium in the binary solvent mixtures (methanol and ethanol) were measured by a gravimetrical method,9−11 which has been verified in our previously published ref 18 and could be briefly described as follows: (1) Preparation of the saturated solution: This step is the same as step 2 of the UV spectroscopic method. (2) Measurement of the concentration of saturated solution: The upper clear saturated solution were filtered by an organic membrane filter (0.22 μm, Tianjin Legg Technology Co., Ltd, Tianjin, China) and quickly moved into preweighted small beakers. The small beakers containing saturated solution were immediately weighted by electronic analytical balance. The samples were dried in vacuum oven at T = 303.15 K for 24 h. In order to minimize measurement error, each experiment was repeated three times, and the average value was used as the final experimental solubility data. The mole fraction solubility x1 and the composition of solvent mixtures xA can be calculated by the following equations: x1 =

m1/M1 m1/M1 + mA /MA + mB /MB

(3)

xA =

mA /MA mA /MA + mB /MB

(4)

Figure 3. XRD pattern of cefmetazole sodium in ethanol at T = 298.15 K: blue , the initial sample; red , excess solid sample; , dried sample after solubility measuring experiments.

where σ2tot refers to the tendency for noncovalent interactions which may reflect polarity force, and the polarity force increases with the increasing of σ2tot, V+(ri) and V−(ri) are positive, and negative electrostatic value, Vs+ and Vs− are their average value:

where xA refers to the mole fraction of ethanol in the binary solvent mixtures (methanol and ethanol), m1, mA, and mB represent the mass of the solute, ethanol, and methanol respectively, and M1, MA, and MB are the corresponding mole mass of them. 2.4. Molecular Surface Electrostatic Potential (MSEP). From the theoretical analysis, the solubility of the same compound in different solvents mainly depends on the interaction of the solute molecule and solvent molecule. Therefore, the solvency of the same compound in different solvents can be predicted by the relationship between solvent molecular structure parameters and solute solubility. In this paper, theoretical parameters of dimensional electrostatic potential, which was proposed by Murray12,13 and successfully applied to the solute− solvent interaction studies related to QSAR’s, was used to establish the relationship between the solubility of amorphous cefmetazole sodium and solvent molecular structure. The purpose is to find the key factors affecting the dissolution and propose a useful method to predict the solvency of different compounds. The related parameters were defined as the following equations: V (r ) =

∑ A

ZA − |RA − r |

∫

ρ(r′) dr′ |r ′ − r |

V s+ =

V s− =

∏=

1 + n

1 m

1 n

∑ V −(ri)

1 n

i=1

(7)

n j=1

(8)

n

∑ |V (ri) − Vs| i=1

(9)

3. THERMODYNAMIC MODELS In this paper, to extend the applicability of the solubility data, the Apelblat equation was used to correlate the experimental solubility data in pure solvents, and the Apelblat equation, the CNIBS/R-K model, and the Jouyban−Acree model were applied to correlate the solubility data in mixed mixtures. Matlab7.0 was mainly used to carry out the regression of the parameters and all calculations. 3.1. The Apelblat Equation. The Apelblat equation, which is a widely used semiempirical model and deduced from Clausius−Clapeyron equation, was applied to correlate the mole fraction solubility against temperature:14 B ln x1 = A + + C ln(T /K) (10) T /K

(5)

where x1 is the mole fraction solubility of solute, T is the absolute temperature, and A, B, and C refer to model parameters. The values of A and B are pertinent to the variation in solution activity coefficients, and C is the effect of temperature on fusion enthalpy.8 3.2. CNIBS/R-K Model. The CNIBS/R-K model, which is considered to be one of the most appropriate models for binary solvent systems, was used to express the relationship between

m

∑ [V +(ri) − V s+]2 i=1

n

∑ [V −(rj) − V s−]2 j=1

∑ V +(ri)

where Π is the average deviation of V(r) on the molecular surface. To a certain extent, it can also reflect polarity force.

where V(r) refers to electrostatic potential, situated at r, Vmin refers to the most negative electrostatic potential and the ability to receive proton increases with the decreasing of Vmin, Vmax refers to the most positive electrostatic potential and the ability to provide proton increases with the increasing of Vmax, ZA is the charge on nucleus A, located at RA, and p(r) is the electronic density function of the molecule. 2 σtot = σ+2 + σ −2 =

m

1 m

(6) C



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Table 2. Experimental (xexp) and Correlated (xAp) Mole Fraction Solubility of Cefmetazole Sodium in Different Pure Solvents (P = 0.1 MPa)a,b solvent ethanol

i-propanol

n-propanol

ethyl acetate

n-butanol

T/K

104 xexp

104 xAp

solvent

T/K

105 xexp

105 xAp

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

4.71 5.08 5.42 5.99 6.85 8.18 10.5 12.8 0.674 0.758 0.893 1.17 1.40 1.70 2.10 2.86 0.612 0.702 0.812 1.05 1.25 1.53 1.91 2.44 0.531 0.603 0.694 0.861 1.05 1.37 1.68 2.21 0.493 0.569 0.642 0.826 0.989 1.24 1.52 1.96

4.78 4.97 5.37 6.01 6.95 8.31 10.2 12.9 0.660 0.770 0.920 1.11 1.37 1.71 2.17 2.79 0.600 0.710 0.840 1.01 1.24 1.54 1.92 2.43 0.530 0.600 0.710 0.860 1.05 1.33 1.70 2.22 0.490 0.570 0.670 0.800 0.980 1.22 1.54 1.96

n-butyl acetate

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

3.86 4.39 5.19 6.35 7.49 8.96 10.9 12.4 3.10 3.94 4.82 5.84 6.75 8.00 9.75 11.3 0.160 0.210 0.259 0.298 0.350 0.410 0.492 0.600 0.131 0.175 0.210 0.250 0.310 0.360 0.462 0.569

3.80 4.50 5.30 6.30 7.50 8.90 10.6 12.7 3.10 3.90 4.80 5.70 6.90 8.20 9.60 11.2 0.166 0.203 0.248 0.298 0.357 0.423 0.498 0.582 0.136 0.167 0.206 0.252 0.309 0.377 0.459 0.558

n-amyl alcohol

n-hexane

cyclohexane

a exp x is the experimental solubility; xAp is the solubility calculated by the Apelblat equation. bThe standard uncertainty of T is u(T) = 0.05 K. The relative standard uncertainty of the solubility is ur(x) = 0.05. The relative standard uncertainty of pressure is ur(P) = 0.05.

solubility and the composition of binary solvent mixtures at a certain temperature.15

The simplified CNIBS/R-K model was derived by ref 16: ln x1 = B1 + B2 xA + B3xA 2 + B4 xA 3 + B5xA 4

N

(13)

i

ln x1 = xA ln XA + x B ln XB + xAx B ∑ Si(xA − x B) i=0

where x1 is the mole fraction solubility of solute, xA refers to the initial mole fraction of ethanol in the binary solvent mixtures in the absence of solute, and B1, B2, B3, B4, and B5 are model parameters. 3.3. Jouyban-Acree Model. Jouyban-Gharamaleki and his co-workers proposed the Jouyban−Acree model in 1988. This model can express the solubility of a solute in the binary solvent mixtures at various temperatures and solvent compositions in the following equation:17

(11)

where x1 is the mole fraction solubility of solute, xA and xB refer to the initial mole fraction composition of ethanol and methanol in the binary solvent mixtures in the absence of solute, respectively. XA and XB refer to the saturated mole solubility of solute in pure ethanol and methanol, respectively. Si is the model constant, and N is the number of the experimental points. Because xA plus xB is equal to 1 in the binary solvent mixtures, the equation above can be deduced into the following equation:

N

ln x1 = xA ln XA + (1 − xA ) ln XB + (1 − xA )xA × [S0 + S1(2xA − 1) + S2(2xA − 1)2 ]

ln x1 = xA ln XA + XB ln x B + xAx B ∑

(12)

i=0

D

Ji (xA − x B)i T

(14)



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Table 3. Experimental (xexp) and Correlated (xAp, xRK, xJA) Mole Fraction Solubility of Cefmetazole Sodium in the Binary Solvent Mixtures of Methanol and Ethanol (P = 0.1 MPa)a,b xA

103 xexp

0.099 0.201 0.301 0.395 0.500 0.599 0.698 0.799 0.8997

16.9 13.3 7.72 4.37 3.23 1.84 1.18 0.982 0.612

0.099 0.201 0.301 0.395 0.500 0.599 0.698 0.799 0.900

17.5 13.7 8.14 4.58 3.42 1.92 1.48 1.04 0.691

0.099 0.201 0.301 0.395 0.500 0.599 0.698 0.799 0.900

18.0 14.1 8.64 4.80 3.62 2.12 1.73 1.12 0.843

0.099 0.201 0.301 0.395 0.500 0.599 0.698 0.799 0.900

19.0 14.7 9.32 5.60 4.11 2.46 1.95 1.21 0.96

103 xAp 278.15 K 17.0 13.3 7.81 4.37 3.22 1.81 1.22 0.994 0.624 283.15 K 17.31 13.6 8.05 4.55 3.39 1.93 1.43 1.02 0.696 288.15 K 18.07 14.0 8.55 4.93 3.70 2.15 1.67 1.10 0.799 293.15 K 19.3 14.7 9.34 5.55 4.17 2.48 1.96 1.23 0.94

103 xRK

103 xJA

xA

103 xexp

17.1 12.7 7.82 4.75 2.80 1.83 1.28 0.918 0.620

16.9 13.3 7.72 4.37 3.23 1.84 1.18 0.982 0.612

0.099 0.201 0.301 0.395 0.500 0.599 0.698 0.799 0.900

21.0 15.7 10.4 6.62 4.99 2.90 2.25 1.36 1.12

17.71 13.2 8.12 4.96 2.99 2.01 1.46 1.06 0.688

17.5 13.7 8.14 4.58 3.42 1.92 1.48 1.04 0.691

0.099 0.201 0.301 0.395 0.500 0.599 0.698 0.799 0.900

23.5 17.0 12.1 7.88 5.79 3.80 2.70 1.73 1.30

18.31 13.5 8.47 5.30 3.25 2.21 1.61 1.19 0.825

18.0 14.1 8.64 4.80 3.62 2.12 1.73 1.12 0.843

0.099 0.201 0.301 0.395 0.500 0.599 0.698 0.799 0.900

26.0 18.7 14.1 9.29 7.37 4.86 3.14 2.17 1.80

19.3 14.0 9.24 6.06 3.81 2.55 1.79 1.30 0.94

19.0 14.7 9.32 5.60 4.11 2.46 1.95 1.21 0.96

0.099 0.201 0.301 0.395 0.500 0.599 0.698 0.799 0.900

29.8 20.6 17.3 12.6 8.95 5.93 3.85 2.60 2.30

103 xAp 298.15 20.9 15.7 10.5 6.47 4.86 2.97 2.31 1.42 1.13 303.15 23.2 17.0 12.1 7.79 5.83 3.67 2.71 1.70 1.40 308.15 26.1 18.6 14.2 9.68 7.19 4.67 3.19 2.09 1.76 313.15 29.8 20.6 17.1 12.4 9.10 6.13 3.76 2.65 2.25

103 xRK

103 xJA

21.3 15.1 10.3 7.11 4.59 3.04 2.06 1.45 1.10

21.0 15.7 10.4 6.62 4.99 2.90 2.25 1.36 1.12

23.7 16.8 11.8 8.35 5.61 3.81 2.61 1.79 1.28

23.5 17.0 12.1 7.88 5.79 3.80 2.70 1.73 1.30

26.2 18.3 13.5 10.1 7.00 4.73 3.17 2.21 1.78

26.0 18.7 14.1 9.29 7.37 4.86 3.14 2.17 1.80

29.6 21.2 16.5 12.9 9.00 5.92 3.81 2.62 2.30

29.8 20.6 17.3 12.6 8.95 5.93 3.85 2.60 2.30

K

K

K

K

a xA is the initial mole fraction of ethanol in the binary solvent mixture; xexp is the experimental solubility; xAp, xRK, and xJA are the solubility calculated by the Apelblat equation, the CNIBS/R-K, and the Jouyban−Acree models, respectively. bThe relative standard uncertainty of xA is ur(x) = 0.045.

b1 + c1 ln T + (a1 − a 2)xA T x x 2 + (b1 − b2 + J0 − J1 + J2 ) A + (3J1 − J0 − 5J2 ) A T T xA 3 xA 4 + (8J2 − 2J1) + ( −4J2 ) + (c1 − c 2)xA ln T T T

where Ji is a model constant and other symbols represent the same meanings as in eq 11. XA and XB can be determined by the Apelblat equation and are described by the following equations: ln XA = a1 +

b1 + c1 ln T /K T /K

b ln XB = a 2 + 2 + c 2 ln T /K T /K

ln x1 = a1 +

(15)

(17)

It can be transformed into eq 18 by introducing a constant term: (16)

A2 x x 2 + A3 ln T + A4 xA + A5 A + A 6 A T T T 3 4 x x + A 7 A + A8 A + A 9xA ln T (18) T T

ln x1 = A1 +

For the binary solvent mixtures, N = 2 and xA = (1 − xB) and then the derivation of eq 14 can give the following equation: E



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where A1 to A9 are model parameters and other symbols mean the same as in eq 11. The Jouyban−Acree model can well describe how the solubility of a solute varies with temperature and initial mole fraction of binary solvent mixtures.10,18

4. RESULTS AND DISCUSSION 4.1. Identification of Solid Stability. In this paper, in order to ensure that the measured solubility data belongs to amorphous cefmetazole sodium, the X-ray powder diffraction (XRPD) patterns of the experimental samples, including samples before and after solubility measuring experiments, were measured. The representative results are shown in Figure 3. The results confirm that the XRPD patterns of all of the samples tested in this work remain the same. 4.2. Solubility Data and MSEP Simulation. The solubility data of amorphous cefmetazole sodium in pure solvents (ethanol, n-propanol, i-propanol, n-butanol, n-amyl alcohol, ethyl acetate, n-butyl acetate, n-hexane, and cyclohexane) and binary solvent mixtures (methanol and ethanol) are listed in Tables 2 and 3 and graphically shown in Figures 4 and 5,

Figure 5. Mole fraction solubility of cefmetazole sodium depending on temperature T and the mole fraction of ethanol (xA) in methanol and ethanol solvent mixtures.

Table 4. Calculated Electrostatic Potential for Ten Pure Solventsa,b solvent

Vmin

Vmax

Π

σtot2

methanol ethanol i-propanol n-propanol ethyl acetate n-butanol n-butyl acetate n-amyl alcohol n-hexane cyclohexane

−2.5366 −2.5163 −2.5308 −2.5192 −2.3996 −2.5279 −2.4469 −2.5298 −0.138 −0.1659

1.9982 1.9548 1.9229 1.9635 0.74 1.9683 0.7314 1.9596 0.2499 0.2412

0.5683 0.3966 0.3782 0.3589 0.3908 0.3126 0.329 0.2846 0.0926 0.083

0.5683 0.3835 0.3938 0.3966 0.3147 0.3938 0.337 0.3426 0.0056 0.0056

The units of Vmin, Vmax, and Π are 102 kJ/mol; the unit of σ is 104 (kJ/mol)2. bThe values of Vmin, Vmax, Π, and σ were obtained from the literature.19 a

Figure 4. Logarithm of experimental and correlated mole fraction solubility (x1) of cefmetazole sodium in nine solvents: ■, ethanol; pink ★, i-propanol; blue ▲, n-propanol; pink ▼, ethyl acetate; green ■, n-butanol; blue ◀, n-butyl acetate; purple ▶, n-amyl alcohol; brown ⬢, n-hexane; brown ★, cyclohexane, the solid lines are the values fitted by the Apelblat equation.

respectively.The results show that the solubility of cefmetazole sodium increases with the increasing of temperature at constant solvent composition. At fixed temperature, the order of cefmetazole sodium solubility in pure solvent is ethanol > i-propanol > n-propanol > ethyl acetate > n-butanol > n-butyl acetate > n-amyl alcohol > n-hexane > cyclohexane. The solubility of cefmetazole sodium in the binary solvent mixtures decreases with the increasing mole fraction of ethanol. To explain the difference of solubility and to better understand the thermodynamic behavior of cefmetazole sodium in different solvents from intermolecular forces, the molecular surface electrostatic potential (MSEP) simulation was used to investigate the interactions between solvent molecules and solute molecules and their effect on solubility, which was also carried out previously by Zhou et al.19 to examine and explain the solubility of other drugs. The computed electrostatic potential for several pure solvents used in this paper are listed in Table 4. The electrostatic potential was fitted with the logarithm of the solubility in pure solvents

Figure 6. Logarithm of the experimental mole fraction solubility (x1) of cefmetazole sodium depending on molecular polarity force v in nine solvents: ■, ethanol; pink ●, i-propanol; blue ▲, n-propanol; pink ▼, ethyl acetate; green ■, n-butanol; blue ◀, n-butyl acetate; purple ▶, n-amyl alcohol; brown ⬢, n-hexane; brown ★, cyclohexane. F



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Table 5. Parameters of the Apelblat Equation for the Solubility in Pure Solvents A

B/104

C

102 ARD

P value

−869 ± 12.3 −536 ± 42.1 −459 ± 23.1 −664 ± 25.3 −523 ± 42.5 −1693 ± 60.6 777 ± 36.9 492 ± 54.2 −1056 ± 75.8

3.59 ± 0.21 2.02 ± 0.12 1.69 ± 0.30 2.58 ± 0.56 1.97 ± 0.45 4.49 ± 0.11 −6.55 ± 0.21 −5.39 ± 0.45 1.10 ± 0.15

130 ± 12.1 810 ± 11.2 690 ± 35.2 100 ± 20.1 790 ± 35.1 254 ± 30.0 −115 ± 25.4 −770 ± 25.8 157 ± 14.9

1.38 2.59 1.31 1.08 1.42 1.57 1.48 2.57 2.33 1.75

2.1 × 10−10 3.4 × 10−11 3.6 × 10−10 3.8 × 10−9 1.5 × 10−11 2.1 × 10−10 3.4 × 10−9 4.5 × 10−10 32.5 × 10−10

solvent methanol ethanol i-propanol n-propanol ethyl acetate n-butanol n-butyl acetate n-amyl alcohol n-hexane mean value of 102 ARD

Table 6. Parameters of the Apelblat Equation for the Solubility in the Binary Solvent Systems of Methanol and Ethanol xA

A

0.099 −504 ± 23.4 0.201 −384 ± 29.8 0.301 −687 ± 14.3 0.395 −910 ± 29.8 0.500 −828 ± 51.2 0.599 −932 ± 35.8 0.698 −1438 0.799 −921 ± 34.2 0.900 −680 ± 20.5 mean value of 102 ARD

B/104

C

102 ARD

P value

2.09 ± 0.15 1.58 ± 0.28 2.85 ± 0.27 3.77 ± 0.14 3.41 ± 0.29 3.83 ± 0.24 3.69 ± 0.21 3.82 ± 0.61 2.70 ± 0.42

750 ± 20.1 570 ± 18.9 103 ± 25.5 137 ± 12.3 124 ± 16.7 140 ± 12.3 220 ± 25.1 138 ± 15.4 102 ± 10.2

0.69 0.39 0.84 1.76 1.52 2.11 2.25 2.22 2.89 1.63

1.2 × 10−10 2.3 × 10−11 3.7 × 10−10 1.3 × 10−10 4.1 × 10−10 2.3 × 10−11 1.4 × 10−10 2.3 × 10−10 3.9 × 10−11

Table 7. Parameters of the CNIBS/R-K Model for the Solubility in the Binary Solvent Systems of Methanol and Ethanol T/K

B1

278.15 −4.13 ± 0.11 283.15 −4.12 ± 0.21 288.15 −4.01 ± 0.04 293.15 −3.82 ± 0.14 298.15 −3.54 ± 0.07 303.15 −3.41 ± 0.05 308.15 −3.14 ± 0.08 313.15 −2.94 ± 0.05 mean value of 102 ARD

B2

B3

B4

B5

102 ARD

P value

3.01 ± 0.12 3.52 ± 0.11 2.34 ± 0.21 −0.07 ± 0.31 −2.99 ± 0.14 −3.43 ± 0.24 −6.14 ± 0.27 −7.72 ± 0.25

−28.1 ± 0.14 −30.9 ± 0.24 −25.6 ± 0.34 −14.2 ± 0.45 −1.20 ± 0.05 0.600 ± 0.07 13.5 ± 0.12 23.0 ± 0.22

39.2 ± 0.32 44.7 ± 0.54 36.6 ± 1.31 18.5 ± 0.24 −1.50 ± 0.26 −2.80 ± 0.32 −23.5 ± 0.12 −40.4 ± 2.23

−17.9 ± 0.15 −21.2 ± 0.21 −17.0 ± 0.32 −7.80 ± 0.12 2.30 ± 0.12 2.00 ± 0.24 13.0 ± 0.35 22.3 ± 0.42

5.08 3.78 5.35 4.76 4.77 2.54 2.98 1.35 3.83

3.8 × 10−9 3.1 × 10−8 3.4 × 10−8 2.7 × 10−9 3.6 × 10−8 1.1 × 10−9 3.1 × 10−8 2.4 × 10−8

of ν which is equal to Π plus square root of σtot2 was used to represent molecular polarity force, and the relationship between the logarithm of the solubility ln x1 in pure solvents at 298.15 K and ν is shown in Figure 6. The results indicate that ln x1 increases with the increasing of ν, which further confirms that the solubility of cefmetazole sodium in pure solvents increases with the increasing molecular polarity. Based on above analysis, it can be concluded that the molecular polarity force has a significant effect on the solubility of cefmetazole sodium and the solubility of cefmetazole sodium in pure solvents increase with the increasing of molecular polarity. The above conclusions can also explain the difference of the solubility of amorphous cefmetazole sodium in the binary solvent mixtures (methanol and ethanol). Because the total molecular polarity of mixed solvents decreases with the rising of the mole fraction of ethanol in the binary solvent mixtures, the solubility of amorphous cefmetazole sodium in the binary solvent mixtures (methanol and ethanol) will decrease with the rising of the mole fraction of ethanol in the binary solvent mixtures. 4.3. Correlation of Experimental Solubility Data. The experimental solubility data of amorphous cefmetazole sodium in pure solvents (ethanol, n-propanol, i-propanol, n-butanol, n-amyl alcohol, ethyl acetate, n-butyl acetate, n-hexane, and cyclohexane)

(ethanol, n-propanol, i-propanol, n-butanol, n-amyl alcohol, ethyl acetate, n-butyl acetate, n-hexane, and cyclohexane) at 298.15 K by using multiple linear regression. The results are given as the following: ln(x1) = ( −13.1189 ± 2.1) − (0.1237 ± 0.041)Vmin + (0.0407 ± 0.0031)Vmax + (5.0102 ± 0.12)Π + (4.9777 ± 0.452)σtot 2

(19)

where the statistical values of correlation coefficient R2, residuals SD, distribution value F are 0.9984, 0.0095, and 463.76 respectively. These data can verify that eq 19 can give satisfactory fitting results. It should be noted that eq 19 was obtained by removing outlier (the solubility in ethanol because the residual of point is large). It can be found that the ability to receive proton, the ability to provide proton, and polarity force help to improve the solubility of cefmetazole sodium in pure solvents and the effect of polarity force is more apparent than the other two forces. According to the definition of electrostatic potential, both Π and σtot2 can reflect molecular polarity force and the polarity force increases with the increasing of Π or σtot2 in general. In this study, the value G



Article

the solubility was calculated and used to explain the difference of the solubility data of amorphous cefmetazole sodium in various solvents. The results show that the molecular polarity force has a significant effect on the solubility of cefmetazole sodium and the solubility of cefmetazole sodium in all tested solvents increase with the increasing of molecular polarity.

were correlated by the Apelblat equation, while the solubility of amorphous cefmetazole sodium in the binary solvent mixtures (methanol and ethanol) were correlated by the Apelblat equation, the CNIBS/R-K model, and the Jouyban−Acree model. The calculated solubility data of amorphous cefmetazole sodium in pure solvents are listed in Table 2, and the calculated solubility data in the binary solvent mixtures are listed in Table 3. The parameters of the Apelblat equation, the CNIBS/R-K model, and the Jouyban−Acree model are given in Tables 5−8, respectively.

■

Corresponding Author

*Tel.: 86-22-27405754. Fax: 86-22-27314971. E-mail: [email protected].

Table 8. Parameters of the Jouyban−Acree Model for the Solubility in the Binary Solvent Systems of Methanol and Ethanol parameter

value

A1 A2/103 A3 A4 A5/10 A6/102 A7/102 A8 10 A9 102 ARD P value

−563 ± 40.6 23.6 ± 1.2 840 ± 36.5 −203 ± 34.9 760 ± 40.7 −23.8 ± 3.8 27.0 ± 6.1 −938 ± 45.9 310 ± 32.5 5.64 ± 2.9 2.8 × 10−11

ORCID

Hongxun Hao: 0000-0001-6445-7737 Funding

This research is financially supported by National Natural Science Foundation of China (No. 21376165) and Major National Scientific Instrument Development Project (No. 21527812). Notes

The authors declare no competing financial interest.

■

1 N

N

∑ i−1

xi exp − xi cal xi cal

REFERENCES

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The accuracy of the model correlation was evaluated by using the average relative deviation (ARD), which was defined as follows: ARD =

AUTHOR INFORMATION

(20)

where xical is the calculated solubility data, xiexp is the experimental solubility data, and N is the number of the experimental points. The value of ARD of the Apelblat equation for the solubility in pure solvents is 1.75%, and the values of ARD of the Apelblat equation, the CNIBS/R-K model, and the Jouyban−Acree model for the solubility in the binary solvent systems are 1.63%, 3.83%, and 5.64%, respectively. These results indicate that the selected models can give correlation results with satisfactory accuracy. The Apelblat equation could give better correlation results than the other models since it have lower ARD.

5. CONCLUSIONS The UV spectroscopic method and gravimetrical method were used to determine the experimental solubility data of amorphous cefmetazole sodium in pure solvents and binary solvent mixtures at temperatures from 278.15 to 313.15 K. The results show that the solubility data of cefmetazole sodium increases with the increasing of temperature in all investigated solvents. At fixed temperature, the order of cefmetazole sodium solubility in pure solvent is ethanol > i-propanol > n-propanol > ethyl acetate > n-butanol > n-butyl acetate > n-amyl alcohol > n-hexane > cyclohexane. The solubility data of cefmetazole sodium in the binary solvent mixtures decrease with the increasing of mole fraction of ethanol. The Apelblat equation was used to correlate the experimental solubility data in pure solvents, while the Apelblat equation, the CNIBS/R-K model, and the Jouyban− Acree model were applied to correlate the solubility data in the binary solvent mixtures. It was found that the selected models can give satisfactory correlation results. Additionally, the molecular surface electrostatic potential (MSEP) correlated with H



Article

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Measurement and Correlation of Solubility of Amorphous Cefmetazole

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