Solubility Determination and Correlation of Gatifloxacin, Enrofloxacin

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

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Solubility Determination and Correlation of Gatifloxacin, Enrofloxacin, and Ciprofloxacin in Supercritical CO2 Ke Shi,† Liefeng Feng,‡ Liangnian He,§ and Hongru Li*,† †

State Key Laboratory of Medicinal Chemical Biology, College of Pharmacy and Tianjin Key Laboratory of Molecular Drug Research, Nankai University, Tianjin 300353, PR China ‡ Department of Physics, Faculty of Science, Tianjin University, Tianjin 300354, PR China § State Key Laboratory and Institute of Elemento-Organic Chemistry, Collaborative Innovation Center of Chemical Science and Engineering, Nankai University, Tianjin 300071, China S Supporting Information *

ABSTRACT: The solubilities of gatifloxacin, enrofloxacin, ciprofloxacin in SC−CO2 were determined by the dynamic method under pressures of 12−36 MPa and temperature of 313, 323, and 333 K. The consistency of the resulting solubility data was verified by the MendezSantiago and Teja model, Chrastil model, Bartle model, and K-J model and these models give comparable AARDs (between 6.70% and 13.51%). The compressed gas model and modified expanded liquid model were also used to correlate the resulting solubilities of the three fluoroquinolone drugs. By introducing the reference solubility and calculating the fugacity coefficient of the solute using the Carnahan−Starling-VDW hard sphere equation of state (CS-VDW EoS), the compressed gas model gives the AARDs between 0.86% and 23.65%. The intrinsic proximity of the model parameters in this model is also confirmed for the structurally similar fluoroquinolone drugs. This intrinsic proximity can be used in mutual solubility prediction between the fluoroquinolone drugs once the reference solubilities were known. The modified expanded liquid model gives the AARDs between 10.88% and 16.65% in solubility correlation. However, the predictive capability of the modified expanded liquid model based on the group contribution method needs to be improved further.

1. INTRODUCTION Fluoroquinolones, including gatifloxacin, enrofloxacin, and ciprofloxacin, are widely used as antibacterial drugs. Their low solubilities in aqueous systems may limit their bioavailability.1 Micronizing the drug or impregnating it into hydrophilic polymeric matrices may improve its solubilities.2,3 In the pharmaceutical industry, the micronization and impregnation process realized by SC−CO2 technology is attractive because the process using SC−CO2 can be operated at moderate temperature and avoids the use of organic solvent. Besides, the nontoxic and nonflammable properties of CO2 meet the requirements of green processes. To evaluate the feasibility of SC−CO2 based technologies, the solubilities of concerned compounds in SC−CO2 are always needed. For example, the solubility of related compound in SC−CO2 can determine the throughput of the micronization processes.4,5 The solubilities of related drug in SC−CO2 can also affect the partition coefficient of the drug between the SC−CO2 phase and the polymeric phase in the impregnation process.6 The solubilities of target compounds in SC−CO2 can be determined by the experimental method. The accuracy depends on the device and operation. The consistency of the determined solubilities are often tested by the semiempirical models, such as Mendez-Santiago and Teja model,7 Chrastil model,8 Bartle model,9 and K-J model.10 The semiempirical models have simple expressions and the properties of the solutes are not needed. © XXXX American Chemical Society

The theoretical methods containing the compressed gas model and the expanded liquid model are very attractive in solubility correlation and estimation for compounds in SC−CO2 because of their good theoretical foundation.11 However, the need for the properties of solute, such as critical properties, acentric factor, and sublimation pressure, limits the use of the compressed gas model. The expanded liquid model needs some easily obtained properties, such as the fusion enthalpy, melting point, and liquid molar volume of the solute. But more simplified assumptions are made in the expanded liquid. Moreover, the biggest obstacle in predicting the solubilities could be the empirical parameters in the theoretical models. Gratifyingly, the progress has been seen in solubility prediction using the theoretical methods. By modifying the mixing rules of Peng−Robinson equation of state (PR-EoS) using the UNIFAC group contribution activity coefficient equation, the solubilities of some compounds in SC−CO2 were estimated by the compressed gas model.12−14 Soon afterward, the expanded liquid model showed outstanding role in solubility prediction of some pharmaceutical compounds by correlating the model parameters to the molecular weight of the solutes by C.Y. Huang et al.15 Received: July 4, 2017 Accepted: November 8, 2017

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DOI: 10.1021/acs.jced.7b00601 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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2.2. Equipment and Solubility Determination. The solubilities of gatifloxacin, enrofloxacin, ciprofloxacin in SC−CO2 were measured using the dynamic method. This method has been verified using niflumic acid in our previous report.18 The instrument and operation procedures are same as those used in our method verification. The illustration of the instrument is presented in Figure 1. In each run, about 2 g

In our previous studies, the intrinsic proximity of the compressed gas model parameters for the solubilities of structure similar compounds in SC−CO2 was revealed by introducing reference solubilities.16−18As the calculated solubilities are not sensitive to the model parameter any more, the average model parameter can be used to calculate the solubilities of the related compounds in SC−CO2. This estimation method has been verified for many compounds.16−18 The applicability of this method for fluoroquinolones remains unclear so far. We also modified the expanded liquid model with only two temperature independent parameters to correlate the solubilities of compounds in SC−CO2. By introducing the group contribution method, this modified model can relate the solubilities of compounds in SC−CO2 to their structures directly. In this work, the solubilities of three fluoroquinolone drugs (gatifloxacin, enrofloxacin, and ciprofloxacin) in SC−CO2 at pressures from 12 to 36 MPa and temperatures 313, 323, and 333 K were measured by the dynamic method. The consistency of the resulting solubility data was tested using the semiempirical models namely Mendez-Santiago and Teja model, Chrastil model, Bartle model, and K-J model. The solubilities of the fluoroquinolone drugs were correlated using the compressed gas model containing reference solubility. The intrinsic proximity of the model parameters for the fluoroquinolone drugs was verified. So in solubility prediction, the average of the model parameters can be used to estimate the solubilities of related fluoroquinolone drugs knowing their reference solubilities. The modified expanded liquid model also provides acceptable correlation results for the solubilities of the fluoroquinolone drugs.19 However, the predictive power of the modified model needs to be further improved.

Figure 1. Diagram of the apparatus for solubility determination.

solute was used. The volume of the sample chamber is 32 mL. The extracted gatifloxacin and enrofloxain were trapped by 5 mL ethanol and ciprofloxacin was trapped by 5 mL, 0.1 M HCl in the glass vial. When about 2 L CO2 was used according to the roller flowmeter, the experiment was stopped and the resulting solution was analyzed using UV−Vis spectrophotometer. The detection wavelength was 297, 284, and 278 nm for gatifloxacin, enrofloxacin, ciprofloxacin, respectively. The UV−vis spectra of compounds in ethanol or HCl before and after solubility determination are identical (Figures S2−S4, Supporting Information) and this means the impurities in the drugs do not affect their solubility determination. To get accurate solubility data, the dissolution equilibrium must be ensured in the dynamic method. So the flow rate of

2. EXPERIMENTAL SECTION 2.1. Materials. The properties and structures of the concerned fluoroquinolones and other chemicals are presented in Table 1. They were used without further purification.

Table 1. Description and Properties of Related Compounds at Atmospheric Pressure

a Ref 20. bhttp://www.lookchem.com. cMeasured using the differential scanning calorimetry method (DSC) under atmospheric pressure (101.441 kPa). Standard uncertainties u are u(Tm) = 1.42 K, u(ΔfusH) = 1.83 kJ·mol−1, u(patm) = 0.077 kPa. The DSC curve and details of measurement can be found in Supporting Information (Figure S1). dRef 21. eRef 22. fRef 23. gRef 24.

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pressure of the solute can be eliminated. The expression is as follows:16

CO2, which reflects the contact time of the sample and SC−CO2 in the solubility determination, was studied. The solubilities of these fluoroquinolone drugs were measured under the pressures of 12−36 MPa and temperature of 313, 323, and 333 K. 2.3. Semiempirical Models. The simplicity of the semiempirical models makes them widely used in consistency test of the experimental solubility data. The Mendez-Santiago and Teja model, Bartle model, Chrastil model and K−J model are the most widely used semiempirical models. Derived from the theory of dilute solution, Mendez-Santiago and Teja model is widely used in self-consistency test of the solubility data. The expression of this model is as follows:7 T ln(y2 p) − CT = A + Bρ

⎡ v2s(p − p ) ⎤ p φ 0 ⎥ 0 20 y2 = y20 exp⎢ RT ⎦ pφ2 ⎣

where p (MPa) and T (K) are the pressure and temperature, respectively, y2 (mol·mol−1) is the molar solubility of the solute, y20 (mol·mol−1) is a known solubility datum at the temperature T and pressure p0 (Mpa), p0 is the reference pressure, vs2 (cm3·mol−1) is the solid molar volume of the solute, φ20 and φ2 are the fugacity coefficients of the solute in supercritical phase under the condition (p0, T) and (p, T) and can be calculated according to the CS−VDW EoS.

(1)

ln φ2 =

−1

where T (K) is temperature, p (Pa) is pressure, y2 (mol·mol ) is the mole fraction solubility of the solute, ρ (g·L−1) is the density of the SC−CO2 and can be calculated by Huang’s 27-parameter equation.25 A, B, and C are the fitting parameters. By introducing the reference pressure and reference density, Bartle model gives the following expression to correlate the solubilities:9 ⎛ py ⎞ B* ln⎜⎜ 2 ⎟⎟ = A* + + C*(ρ − ρref ) T ⎝ pref ⎠

(2)

where p is pressure, pref (0.1 MPa) and ρref (700 g·L ) are reference pressure and reference density respectively, ρ is the density of SC−CO2. A*, B*, and C* are the fitting parameters. The parameter B* gives the information on the vaporization enthalpy of the solute: ΔHvap = −B* × R. The Chrastil model derived from the association theory is also a widely used semiempirical model:8 a ln s = k ln ρ + +b (3) T where s (g·L−1) is the solubility of the solute; ρ (g·L−1) is the density of the SC−CO2; k, a, and b are the fitting parameters. The parameter a gives information about the sum of vaporization and solvation enthalpy of the solute: ΔHvap + ΔHsol = −a × R K-J model correlates the solubility of solute with the temperature and density of SC−CO2 using the following expression:10 B** + C**ρ T

2y a12 pv 3ξ 3 − 9ξ 2 + 8ξ − 1 − ln 3 RTv RT (1 − ξ)

(6)

where ξ is the reduced density of the solution and ξ = b1v/v, v (cm3·mol−1) is the molar volume of the mixed gas and can be regarded as that of the SC−CO2; b1v is the van der Waals volume of CO2 (19.7 cm3·mol−1);26 p is the experimental pressure and a12 is the fitting parameter in this model. According to our previous study, introduction of the reference solubility can reduce the applied pressure range of the equations of state and the mixing rules. It can also eliminate the variability of parameters with temperature and the sensitivity of the calculated solubility to the model parameter.16 Besides, for structurally similar compounds, the model parameters are close. This means that the solubilities of a compound in SC−CO2 can be extrapolated to other temperature with one experimental solubility datum at that temperature and the model parameter. The model parameter can be derived from its own solubilities at a certain temperature or from other structurally similar compounds. 2.5. Modified Expended Liquid Model. In our previous study, the expanded liquid model was modified with two temperature independent parameters. The modified liquid model is expressed as follows.19

−1

ln(y2 ) = A** +

(5)

⎞ ⎛ ΔH ⎛ 1 1⎞ 1 l 2 m y2 = exp⎜⎜ − ⎟− v2ϕ1 (δ2 − δ1)2 ⎟⎟ ⎜ T ⎠ RT ⎠ ⎝ R ⎝ Tm

(7)

δ2 = a′δ1/v1 + b′

(8)

ϕ1 = (4)

y1v1 y1v1 + y2 v2l

(9) −1

where ΔHm (J·mol ) is the melting enthalpy, Tm (K) is the melting point. ϕ1 is the volume fraction of SC−CO2. vl2 (cm3·mol−1) is the liquid molar volume of the solute, v1 (cm3·mol−1) is the molar volume of the SC−CO2. y1 is the mole fraction of SC−CO2. δ1 (MPa0.5) is the accurate solubility parameter of SC−CO2 calculated using Huang’s 27-parameter equation according to the following expession.

where A**, B**, and C** are the fitting parameters. The parameter B** in this model also gives information about the sum of the vaporization and solvation enthalpy of the solute: ΔHvap + ΔHsol = −B** × R. 2.4. Compressed Gas Model Combined with Reference Solubility. The compressed gas models have good theoretical basis. However, its demands for critical properties, acentric factor and sublimation pressure of the solute limit its application on the pharmaceutical compounds. By introducing the reference solubility and calculating the fugacity coefficient of the solute using the CS-VDW EoS, we have avoided using these unavailable properties of the pharmaceutical compounds ingeniously in the compressed gas model.16−18 The reference solubility is an experimental solubility datum under investigation temperature. After introducing a known solubility datum (reference solubility), the sublimation

δ1 = [T (∂p /∂T )v − p]0.5

(10)

δ2 (MPa ) is the solubility parameter of solute. a′ and b′ are the empirical model parameters. They can be obtained by correlating the solubilities of the compounds. Without solubility data, they can also be obtained using the group contribution values provided in our previous study.19 2.6. Optimization Objective Function. The solubilities of gatifloxacin, enrofloxacin, ciprofloxacin were measured and the 0.5

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dissolution equilibrium. The contact time τ (s) can be expressed by the following equation:

consistency of the resulting solubilities was tested using the semiempirical models. The solubility correlation and prediction capability of the compressed gas model containing reference solubility and the modified expanded liquid model was also studied. For all the models, the objective function to be minimized in solubility correlation is defined as follows: AARD% =

100 N

N

∑ 1

τ=

(12)

where W (g) is the mass of drug used in solubility determination (2 g in a typical run), F (g·s−1) is the flow rate of CO2. As the mass of drug was kept constant in the experiments, the contact time τ was determined by the flow rate of CO2. In the preliminary experiment, the flow rate of CO2 during sample capture was controlled at 10 mL/min, 20 mL/min, and 30 mL/min (at the room temperature and atmospheric pressure), respectively, by regulating the metering valve when the experiment was carried out at the severe conditions (333 K and 36 MPa). The corresponding value of τ were 2222, 3333, 6666 s, respectively (the density of CO2 is 1.80 g/L at the room temperature and atmospheric pressure). The results in Figure 2 indicate that when τ is larger than 3333 s, the determined solubilities attain plateau. This means that for the three drugs, the flow rate less than or equal to 20 mL/min can guarantee the dissolution equilibrium. Considering the capture time, the flow rate of 20 mL/min was selected in the following experiments. The solubilities of the gatifloxacin, enrofloxacin, and ciprofloxacin were measured at pressure 12−36 MPa and temperature 313, 323, and 333 K. The experimental data are shown in Table 2. The solubility determination experiment was carried out in triplicate in each condition. The listed results are the average values and uncertainties (u) are also shown. By comparing the solubilities of the three fluoroquinolone drugs in SC−CO2, it can be seen that the presence of secondary amine

|y2exp − y2cal | y2exp

W F

(11)

cal where N is the number of solubility data, yexp 2 and y2 are the experimental and calculated solubility, respectively.

3. RESULTS AND DISCUSSION In solubility determination using the dynamic method, the contact time of solute and SC−CO2 is critical to ensure the

Figure 2. Effect of the CO2 flow rate on the solubility determination.

Table 2. Mole Fraction Solubilities of Gatifloxacin, Enrofloxacin, and Ciprofloxacin in SC−CO2 and the Standard Uncertainties in Solubility Determination T/K

pressure/MPa

density of SC−CO2a/g·L−1

313

12 14 17 20 24 28 32 36 12 14 17 20 24 28 32 36 12 14 17 20 24 28 32 36

721 766 810 841 873 899 921 940 588 675 743 786 827 858 883 905 440 565 667 725 777 815 844 869

323

333

gatifloxacin y2 ± u (10−6)b 0.132 0.181 0.256 0.335 0.441 0.514 0.592 0.627 0.125 0.190 0.319 0.382 0.564 0.679 0.857 0.974 0.106 0.193 0.389 0.553 0.888 1.235 1.524 1.605

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.035 0.016 0.067 0.021 0.055 0.070 0.012 0.011 0.013 0.008 0.071 0.034 0.023 0.036 0.060 0.046 0.018 0.064 0.050 0.024 0.062 0.182 0.029 0.087

enrofloxacin y2 ± u (10−6)b,c

ciprofloxacin y2 ± u (10−6)b,c

0.061 0.190 0.435 0.590 1.020 1.570 2.030 2.585 0.022 0.127 0.415 0.830 1.190 2.310 2.980 3.530

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.049 0.030 0.011 0.092 0.059 0.060 0.050 0.010 0.002 0.039 0.030 0.019 0.070 0.021 0.047 0.008

0.0265 0.0389 0.0434 0.0685

± ± ± ±

0.0015 0.0014 0.0008 0.0021

0.0464 0.0635 0.0858 0.1069

± ± ± ±

0.0013 0.0021 0.0032 0.0044

0.414 0.930 1.490 2.700 3.575 5.605

± ± ± ± ± ±

0.026 0.060 0.101 0.050 0.070 0.045

0.0297 0.0555 0.0962 0.1159 0.1449 0.1887

± ± ± ± ± ±

0.0046 0.0012 0.0013 0.0084 0.0010 0.0041

a c

Calculated using Huang’s 27-parameter equation.25 bStandard uncertainties u are u(T) = 1 K, u(p) = 0.1 MPa in solubility determination. Some solubility data are absent from the table because the solubilities are too low to be determined. D



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group is detrimental to the dissolution of fluoroquinolone drugs in SC−CO2. The substituents of 8-methoxyl and 3′-methyl in the fluoroquinolone structure are beneficial to the solubilities of fluoroquinolones. In solubility determination, the crossover pressure of gatifloxacin is about 14 MPa and that of enrofloxacin is about 17 MPa according to Figure 3. The crossover pressure of ciprofloxacin

the higher temperature are higher than those at lower temperature. 3.1. Correlation Results of the Semiempirical Model. The solubilities of gatifloxacin, enrofloxacin, and ciprofloxacin in SC−CO2 were correlated by the semiempirical modes. The results are shown in Figures 4, 5, and 6 and Table 3. Most of the solubility data correlate well with the semiempirical models except for some data under lower pressure. This may be derived from the larger determination errors as a result of the lower solubilities or from the oversimplified assumptions of the semiempirical models. In addition to consistency testing, some semiempirical models can provide the vaporization enthalpy and the sum of solvation and vaporization enthalpy by solubility correlation. The corresponding values are listed in Table 4. The similarity of the sums of solvation and vaporization enthalpy derived from different models confirmed the reliability of the solubility results. Although widely used in experimental solubility polishing, these semiempirical models have great limitation in predicting solubilities of complicated compounds in SC−CO2. The reason is that the model parameters in these models are difficult to obtain without the experimental solubility data. 3.2. Correlation and Estimation Results of the Compressed Gas Model Containing Reference Solubilities. By introducing the reference solubility into the compressed gas model and calculating the fugacity coefficient of the solute using the CS−VDW EoS, the complicated properties of the solute can be avoided in solubility correlation.16−18 This method was used to correlate the solubilities of gatifloxacin, enrofloxacin, ciprofloxacin in SC−CO2 and the results are shown in Figure 7 and Table 5. The solubilities of ofloxacin and norfloxacin reported in ref 20 were also correlated using this modified compressed gas model. The correlation results in Table 5 show that for the same medicine, the model parameters at different temperatures are close. According to our previous

Figure 3. Crossover pressure for gatifloxacin and enrofloxacin.

can not be found because of the absence of solubility data at lower pressure. The presence of crossover pressure in solubility determination is caused by the different effect of temperature on the density of SC−CO2 and the sublimation pressure of solute. Below the crossover pressure, the effect on the density of SC−CO2 prevails. Since lower temperature means higher density of SC−CO2, the solubilities of solute at lower temperature are higher than those at higher temperature. However, above the crossover pressure, the effect of temperature on the sublimation pressure of solute prevails and the solubilities at

Figure 4. Correlation results of the solubilities of gatifloxacin using semiempirical models. E



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Figure 5. Correlation results of the solubilities of enrofloxacin using semiempirical models.

Figure 6. Correlation results of the solubilities of ciprofloxacin using semiempirical models.

the reference solubilities (the experimental solubilities at 36 MPa for each temperature were used as reference solubilities in this work) and the model parameter derived from its own average model parameter at different temperatures. Figure 8 shows the calculated solubilities are correlated well with the experimental results. There is some difference for the average model parameters of different drugs. This may be resulted from the larger structural difference among these fluoroquinolone drugs. To investigate the possibility of estimating the solubilities

study, the calculated solubilities are insensitive to the model parameter.16 So a12 can be considered temperature independent for a specified compound. Once the model parameter is derived at a certain temperature, the solubilities of this compound under other temperature can be extrapolated using only one known solubility datum (which can be regarded as the reference solubility) at this temperature. By using this method, a great deal of experimental work can be reduced. The solubilities of the five fluoroquinolone drugs were calculated using F



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Table 3. Correlation Results with the Semiempirical Models for Gatifloxacin, Enrofloxacin, and Ciprofloxacin models

model parameters

gatifloxacin Mendez-Santiago and Teja model A B −12888.3200 3.6168 Bartle model A* B* 20.9420 −10076.5115 Chrasil model k a 6.3496 −7594.3294 K-J model A** B** 3.0100 −7472.5661 enrofloxacin Mendez-Santiago and Teja model A B −17301.1182 6.4272 Bartle model A* B* 26.6220 −12023.5515 Chrasil model k a 13.0603 −9421.8828 K-J model A** B** 4.3443 −9834.8146 ciprofloxacin Mendez-Santiago and Teja model A B −15333.3704 4.2606 Bartle model A* B* 22.5386 −11426.3013 Chrasil model k a 7.8349 −9250.6474 K-J model A** B** 5.6141 −9670.4239

C 33.3220

AARD% 10.20

C* 0.0112

AARD% 11.50

b −24.5974

AARD% 10.23

C** 0.0070

AARD% 6.70

Figure 7. Solubility correlation results for the fluoroquinolone drugs in SC−CO2 using the compressed gas model combined with the reference solubilities and CS-VDW EoS.

C 40.5322

AARD% 11.29

Table 5. Solubility Correlation Results for the Fluoroquinolone Drugs in the SC−CO2 Using the Compressed Gas Model

C* 0.0200

AARD% 13.02

compound

temperature/K

a12

a12a

a12b

AARD%

gatifloxacin

1.2147

AARD% 12.23

enrofloxacin

C** 0.0152

AARD% 13.51

ciprofloxacin

C 36.8303

AARD% 8.48

norfloxacin

C* 0.0127

AARD% 9.37

ofloxacin

1.0169 1.0395 1.0434 1.5221 1.5349 1.4436 1.4368 1.2751 1.1957 1.0232 1.3973 1.5119 0.8361 0.7292

1.0333

b −63.2675

313 323 333 313 323 333 313 323 333 313.15 318.15 323.15 318.15 323.15

12.67 5.65 9.71 19.05 23.65 4.96 2.76 0.86 5.99 13.72 24.65 24.21 15.37 9.26

a

b −31.9783

AARD% 8.54

C** 0.0092

AARD% 7.23

b

1.5002

1.3025

1.3108

0.7826

Average a12 of the same compound at different temperature. Average a12 of all the compounds.

model was modified and only two temperature independent parameters are needed. Besides, the parameters in this model can be related to the structure of the solute by the group contribution method according to our previous study.19 The solubilities of the fluoroquinolone drugs in SC−CO2 were correlated by our modified model. The correlation results are listed in Table 6 and Figure 10. Considering only two temperature independent parameters were used, the solubility correlation results for gatifloxacin, enrofloxacin, and ciprofloxacin in SC−CO2 are acceptable. The unsatisfying correlation results for ofloxacin and norfloxacin may be caused by their inaccurate solubility data (the self-consistency test of the solubilities are unsatisfying, which can be found in the Figures S5 and S6 in the Supporting Information). We have tried to estimate the solubilities of gatifloxacin, enrofloxacin, and ciprofloxacin in SC−CO2 using the group

of fluoroquinolone drugs according to the solubilities of other structural similar drugs, the solubilities of the five fluoroquinolone drugs were also calculated according to the reference solubilities and the average model parameter of the five fluoroquinolone drugs at different temperatures. The results in Figure 9 show that the solubilities of the five fluoroquinolone drugs can also be predicted in the order of magnitude. 3.3. Correlation Results of the Modified Expanded Liquid Model. With only the melting point and fusion enthalpy of the solute needed, the expanded liquid models are especially suitable for correlating the solubilities of pharmaceutical compounds. In our previous report, the expanded liquid

Table 4. Values of ΔHvap and ΔHvap + ΔHsol Derived from the Semiempirical Models compound

ΔHvap from Bartle model/kJ·mol−1

(ΔHvap + ΔHsol) from Chrastil model/kJ·mol−1

(ΔHvap + ΔHsol) from K-J model/kJ·mol−1

gatifloxacin enrofloxacin ciprofloxacin

83.78 99.97 95.00

63.13 78.34 76.91

62.13 81.77 80.40

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Figure 8. Solubility calculation results for the fluoroquinolone drugs in SC−CO2 using the average model parameter of drug itself in the compressed gas model combined with CS-VDW EoS and reference solubilities (The dotted line area represents the error within the order of magnitude).

Figure 10. Solubility correlation results for the fluoroquinolone drugs in SC−CO2 using the modified expanded liquid model.

The consistency of the resulting solubility data was verified by the semiempirical models and these models give comparable AARDs (between 6.70% and 13.51%). The resulting solubilities of the three fluoroquinolone drugs were also correlated using the compressed gas model containing the reference solubility and the modified expanded liquid model. By calculating the fugacity coefficient of the solute using the CS-VDW EoS, the compressed gas model containing the reference solubility gives the AARDs between 0.86% and 23.65%. The intrinsic proximity of the model parameters in this model is also confirmed for the structurally similar fluoroquinolone drugs. This intrinsic proximity can be used in mutual solubility prediction between the fluoroquinolone drugs once the reference solubilities were known. The modified expanded liquid model gives the AARD between 10.88% and 16.65%. However, it cannot be used to estimate the solubilities of fluoroquinolone drugs. The reason is that the group contribution value of cyclopropyl in these compounds needs to be improved further.

Figure 9. Solubility calculation results for the fluoroquinolone drugs in SC−CO2 using the average model parameter of all the drugs in the compressed gas model combined with CS-VDW EoS and reference solubilities (The dotted line area represents the error within the order of magnitude).

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00601. DSC curve for gatifloxacin; UV−vis spectra of gatifloxacin, enrofloxain, and ciprofloxacin before and after solubility determination; consistency test of the solubilities of norfloxacin and ofloxacin in SC−CO2; and solubility estimation results for the fluoroquinolone drugs in the SC−CO2 using the modified expanded liquid model combined with the group contribution method (PDF)

Table 6. Solubility Correlation Results for the Fluoroquinolone Drugs in the SC−CO2 Using the Modified Expanded Liquid Model solubility correlation results compound

a′

b′

AARD%

gatifloxacin enrofloxacin ciprofloxacin ofloxacin norfloxacin

24.85 17.58 20.68 30.87 33.11

17.50 18.30 17.00 14.31 14.25

16.47 16.65 10.88 26.42 38.78

ASSOCIATED CONTENT

S Supporting Information *

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AUTHOR INFORMATION

Corresponding Author

contribution method. However, the estimation results were unsatisfying (Table S1 and Figure S7). This can be attributed to the inaccurate group contribution value of cyclopropyl. When establishing the group contribution method, only one compound containing ring closure 3 or 4 atoms was included. So the group contribution value for cyclopropyl in fluoroquinolone drugs is inaccurate.

*Tel: (86)22-23507760; Fax: (86)22-23507760; E-mail: [email protected]. ORCID

Liangnian He: 0000-0002-6067-5937 Hongru Li: 0000-0002-4916-2815 Notes

The authors declare no competing financial interest.

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4. CONCLUSION The solubilities of gatifloxacin, enrofloxacin, and ciprofloxacin were determined by the dynamic method under pressures of 12−36 MPa and temperatures of 313, 323, and 333 K.

ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundations of China (Grant Nos. 21206077, 21106107) H



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