Experimental Solubility and Density Functional Theory Studies of

Apr 8, 2019 - Department of Food and Drug, Alborz University of Medical Sciences, Karaj, PO Box 3198764653, Iran. ∥. Food and Drug Safety Research ...
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Experimental Solubility and Density Functional Theory Studies of Deferasirox in Binary Solvent Mixtures: Performance of Polarizable Continuum Model and Jouyban−Acree Model Anahita Fathi Azarbayjani,*,†,‡ Nasrin Aliasgharlou,‡ Saba Khoshbakht,‡ Peyvand Ghanbarpour,§ Elaheh Rahimpour,∥ Mohammad Barzegar-Jalali,⊥ and Abolghasem Jouyban#,∇

J. Chem. Eng. Data Downloaded from pubs.acs.org by OCCIDENTAL COLG on 04/29/19. For personal use only.

†

Solid Tumor Research Center and ‡Department of Pharmaceutics, School of Pharmacy Urmia University of Medical Sciences, Urmia, PO Box 5715799313, Iran § Department of Food and Drug, Alborz University of Medical Sciences, Karaj, PO Box 3198764653, Iran ∥ Food and Drug Safety Research Center, ⊥Research Center for Pharmaceutical Nanotechnology and Faculty of Pharmacy, # Pharmaceutical Analysis Research Center and Faculty of Pharmacy and ∇Kimia Idea Pardaz Azarbayjan (KIPA) Science Based Company Tabriz University of Medical Sciences, 5166/15731 Tabriz, PO Box 6581151656, Iran ABSTRACT: The molecular structure of deferasirox (DFX) was fully optimized using a hybrid functional B3LYP and 6-311++G** basis set algorithm in Gaussian 09 software. A polarizable continuum model (PCM) was employed as a density functional theory (DFT) method to investigate the solvent effect on DFX solubility in seven different binary solvent mixtures. The polarizable continuum model (PCM) and United Atom for Hartee−Fock (UAHF) radii were used to investigate drug solubility in various mass fractions of binary solvent mixtures. The free energies of solvation (ΔGsol) in kJ/mol, total electrostatic energy (kJ/mol), dipole moment (μ) in Debye, total Gibbs free energy of solvation (kJ/mol), and dielectric constant (ε) of DFX in binary solvent mixtures were computed. The results were used to explain the experimental drug solubility behavior in the studied systems at 298.2 K. It was noted that the DFT/PCM provides good approximation for solubility in pure solvents; however, due to solvent−solvent interaction, it might be more complex to predict drug solubility as a function of solvent ratios in binary systems. Yet, the experimental solubility data were in great agreement with the solubility values predicted using the Jouyban−Acree model. The mean relative deviation (MRD) of the calculated data and experimental data were compared. ε, expressed as solvent polarity, is subjective to the interatomic and intermolecular forces of solvent mixtures.6,7 Computational methods such as density functional theory (DFT) calculations are widely used to study the molecular geometry and calculate energy levels. The polarizable continuum model (PCM) is a DFT calculation method used to investigate the solvent effects on solvation. In brief, the solute molecule is placed within the solvent cavity, and the interaction between the molecular cavity and continuum dielectric solvent is exploited in PCM.8−10 Up to now, the solubility of DFX in some monosolvents including methanol, ethanol, 1-propanol, 2-propanol, 1butanol, acetonitrile, 1,4-dioxane and DMSO, and a binary system of methanol + water has been reported.11 In order to extend the database on its solubility profile, the aim of this

1. INTRODUCTION Deferasirox (DFX), a newly developed drug, belongs to the orally acting iron-chelating agents, and it is widely used for the treatment of iron overload. This drug is weakly acidic and liphophilic in nature. DFX is a Biopharmaceutics Classification System II-type drug, which has the high intestinal permeability and is practically insoluble in water. It is commercially available since its FDA approval in 2005.1,2 Drug solubility is one of the important physicochemical properties with great application in the pharmaceutical industry. One of the most widely used strategies to improve drug solubility is the co-solvency concept. This method has great application in the estimation of preferential solvent composition and design of a drug delivery system.3,4 Molecular descriptors such as intermolecular forces, polarizability, and dielectric constants (ε) have great influence on solubility. These parameters can be used as a predictive rule in drug solubility studies.5,6 Thermodynamic properties of solutions depend directly on the intermolecular forces. The © XXXX American Chemical Society

Received: October 31, 2018 Accepted: April 8, 2019

A

DOI: 10.1021/acs.jced.8b01001 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Details on Sample Information chemical name

source

deferasirox 1,2-propanediol acetonitrile methanol ethanol sodium hydroxide double-distilled water

Osveh Pharmaceutical Merck Merck Merck Merck Merck Milli-Q

CAS no.

grade

mole fraction purity

57-55-6 75-05-8 67-56-1 64-17-5 1310-73-2

working grade analysis HPLC HPLC analysis analysis 99.3% >99.5% ≥99.9% ≥99.8% ≥99.9% 98−100.5%

between 200 and 400 nm. Sodium hydroxide (0.1 M) was used as blank, and λmax was found at 307 nm.14,15 A standard stock solution of DFX was prepared in 0.1 M sodium hydroxide solution. Aliquots of the stock solution were prepared (7.5 to 50 μg/mL) and diluted with 0.1 M sodium hydroxide, and the calibration curve for DFX is illustrated in Figure 1.

work is to investigate the experimental solubility of this drug in various binary solvent mixtures at 298.2 K. DFT was applied in an attempt to elucidate the experimental solubility profile and to explore solubility thermodynamic and solute−solvent interactions. A PCM model by the B3LYP method and 6-311++G** basis set was employed. The molecular structure of DFX was fully optimized, and the free energies of solvation (ΔGsolv), total electrostatic energy (kJ/ mol), total Gibbs free energy of solvation (kJ/mol), dipole moment (μ), and ε of DFX in binary solvents were computed in various mass fractions of the binary solvent system. Finally, the solubility of DFX in the investigated solvent mixture was analyzed using the Jouyban−Acree model.

2. MATERIALS AND METHOD 2.1. Materials. DFX with the mass fraction purity of 0.997 was a gift from Osveh Pharmaceutical (Tehran, Iran). 1,2Propanediol (mass fraction purity of 0.995), acetonitrile (mass fraction purity of 0.999), methanol (mass fraction purity of 0.998), and ethanol (mass fraction purity of 0.999) were purchased from Merck (Darmstadt, Germany). Deionized water was supplied from a Milli-Q system (Direct-Q3, Millipore, France). Sodium hydroxide (Merck, Darmstadt, Germany) was used for the preparation of the standard solution for a spectroscopic analysis. The details on sample information is tabulated in Table 1. 2.2. Experimental Solubility. The experimental solubility of DFX in seven solvent mixtures of {1,2-propanediol (1) + methanol (2)}, {ethanol (1) + methanol (2)}, {1,2-propanediol (1) + ethanol (2)}, {methanol (1) + acetonitrile (2)}, {1,2-propanediol (1) + acetonitrile (2)}, {ethanol (1) + acetonitrile (2)}, and {acetonitrile (1) + water (2)} was measured by the shake-flask method of Higuchi and Connors.12 In brief, an excess amount of drug was added in each investigated mixture (10 g) in triplicate. The weighing of solvents, water, and solutes was performed by an analytical balance (model: Practum 2102-15 Sartorius; standard uncertainty: 0.0001 g). Flasks were placed on a shakerincubator (GFL 3031, Germany) equipped with a temperature controlling system at 298.2 ± 0.05 K for 72 h to equilibrate. All measurements were carried out under local atmosphere pressure 101.32 kPa. The time to reach equilibrium was validated through a previously published paper by our group.13 Dissolution studies were performed, and samples were taken at time intervals. Three consecutive results with same values were related to the equilibrium time. All samples were centrifuged at 13,000 rpm (Eppendorf 5452 Minispin, Germany), filtered (0.45 μm, BioFil, China) and diluted before quantification. Preliminary studies confirm that drug adsorption onto filter paper was not significant. DFX was measured spectrophotometrically (Cecil CE 7200, 7000 series, U.K.). The analytical wavelength was selected by scanning a 20 μg/mL solution

Figure 1. Calibration curve of DFX in 0.1 M NaOH.

2.3. Density Functional Theory Method. Computational modeling allows an alternative method to study the solvation thermodynamics of a drug at a DFT level. A full geometry optimization of the DFX structure was carried out with the hybrid functional B3LYP and 6-311++G** using Gaussian 09 software.16 The optimized geometry of DFX was solvated in the solvent media using the PCM by the B3LYP and 6-311++G** basis set. Computations were performed in the gas phase and in the solvent cavity. The interaction energy between the solute and solvent molecules may be expressed as the solvation free energy. The ΔGsol represents the change in the Gibbs energy of solvation when a solute is relocated from a gas phase into a solution at a constant temperature. ΔGsol is defined as ΔGsol = Ges + Gdr + Gcav

(1)

These components represent the contribution of electrostatic (es), dispersion−repulsion (dr) and the cavitation energy (cav) to the ΔGsol.17 The solubility of DFX was investigated in various binary solvent mixtures by the polarizable continuum model (PCM) and United Atom for Hartee−Fock (UAHF) radii to build the molecular cavity. The Gibbs energy of solvation (ΔGsol), total electrostatic energy (kJ/mol), μ, total Gibbs free energy of solvation (kJ/mol), and ε of DFX in the seven binary solvent systems were directly obtained from the thermochemistry part of the Gaussian software at a B3LYP/6-311++G** level of B

DOI: 10.1021/acs.jced.8b01001 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Experimental Mass Fraction Solubility of DFX in Different Solvent Mixtures at 298.2 ± 0.05 Ka under Local Atmosphere Pressure 101.32 kPa w1a 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1,2-propanediol (1) + ethanol 1.4266 1.6499 1.8292 2.0224 2.2162 2.3794 2.4354 2.3485 2.2227 2.1061 1.9535

× × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

1,2-propanediol (1) + methanol 1.1908 1.4047 1.5792 1.7181 1.8690 1.9681 2.0465 2.0910 2.0972 2.0431 1.9535

× × × × × × × × × × ×

1,2-propanediol (1) + acetonitrile

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

1.0570 2.8600 5.5850 8.9620 1.2331 1.5294 1.7965 2.0298 2.1996 2.2691 1.9535

× × × × × × × × × × ×

ethanol (1) + methanol

10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2

1.1908 1.2689 1.3376 1.3740 1.3966 1.4238 1.4326 1.4506 1.4502 1.4453 1.4266

× × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

ethanol (1) + acetonitrile 1.0570 4.7140 9.2940 1.4788 2.0941 2.6158 3.0693 3.1428 2.8031 2.2547 1.4266

× × × × × × × × × × ×

10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

methanol (1) + acetonitrile 1.0570 4.8140 8.6470 1.2633 1.6034 1.8588 1.9674 1.9803 1.8340 1.5591 1.1908

× × × × × × × × × × ×

10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

acetonitrile (1)+ water 4.0694 6.4621 8.7736 1.8423 4.6098 1.2687 2.4084 3.8551 5.4606 5.1924 1.0568

× × × × × × × × × × ×

10−5 10−5 10−5 10−4 10−4 10−3 10−3 10−3 10−3 10−3 10−3

a

Standard uncertainties u for pressure p and temperature T are u(T) = 0.05 K and ur(p) = 0.05, respectively. The relative standard uncertainty of the mass fraction of co-solvent in the binary solvent mixture is ur(w) = 0.0001. The relative standard uncertainty of the solubilities is ur(w) = 0.001.

Figure 2. Correlation between experimental and calculated solubility of DFX in various binary solvent mixtures: experimental DFX solubility in a binary solvent system (presented in solid lines), PCM calculations of −ΔGsol as a function of solvent mass fraction (presented in dashed lines).

theory. The results were used to elucidate the experimental drug solubility behavior in the studied systems at 298.2 K. 2.4. Computational Validation Using the Jouyban− Acree Model. The general Jouyban−Acree model used to predict solute solubility in binary solvent mixtures is expressed as

To evaluate the accuracy of the data prediction, the mean relative deviation (MRD) between the calculated and observed solubility were computed using the following equation %MRD =

2

ln Cm , T = w1 ln C1, T + w2 ln C2, T +

3. RESULTS AND DISCUSSION 3.1. Experimental Solubility. Mass fraction solubility of DFX in different binary solvents was investigated at 298.2 K, and the results are shown in Table 2. It is seen that the drug solubility varies with the co-solvent ratio. The DFX solubility profile shows a similar trend in all the seven solvent systems, where solubility increases by co-solvent addition and reaches a maximum value at w1 = 0.6−0.9 after which the solubility

where Cm,T is the solute molar solubility in the solvent mixture at temperature T (K), and w1 and w2 denote mass fractions of the solvents 1 and 2 in the absence of a solute. C1,T and C2,T are the solubility of the solute in the monosolvents 1 and 2, and Ji is the model constant obtained by regressing (ln Cm,T − w1 ln w1w2 w1w2(w1 − w2) , , T T

and

(3)

where N is the number of data points in each set. Numerical analyses were carried out using SPSS version 16.0.

w1w2 ∑ J (w1 − w2)i T i=0 i (2)

C1,T − w2 ln C2,T) against

Calculated − C Observed| zy ji |C 100 ∑ jjjjj m,T Observedm,T zzzzz N Cm , T { k

w1w2(w1 − w2)2 18 . T

C

DOI: 10.1021/acs.jced.8b01001 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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systems. Electrostatic energy (Eelec) is a measure of the solute− solvent dipole−dipole interaction and depends on the ε of the system. A negative value indicates attractive electrostatic forces. It is noted that electrostatic energy is large and negative (−183.510 kcal/mol) in the {acetonitrile (1) + water (2)} system at w1 = 0.4 with low drug solubility (4.6098 × 10−4) and −175.142 kcal/mol at the {ethanol (1) + methanol (2)} system at w1 = 0.9 with a mass fraction solubility of 1.4453 × 10−2. The total electrostatic forces in the system with maximum drug solubility 3.1428 × 10−2 is observed in the {ethanol (1) + acetonitrile} system at w1 = 0.7, where the total electrostatic force is −176.397 kJ/mol−1 (Table 3). The correlation of ΔGsol with respect to the solvent mass fraction is shown through dashed lines in Figure 2. The experimental DFX solubility in monosolvents obeys the ΔGsol trend. From Table 1, it is seen that the highest and lowest mass fraction solubility in pure solvent is seen in 1,2-propanediol and water with a DFX solubility of 1.9535 × 10−2 and 4.0694 × 10−5, which corresponds to a ΔGsol of −243.425 kcal/mol and −151.419 kcal/mol, respectively (Table 3). Experimentally obtained solubility data (shown in solid lines) and the calculated ΔGsol of binary solvent systems (shown in dashed lines) at various mass fractions of solvent are illustrated in Figure 2. It is seen that although the overall pattern is quite similar, the theoretical parameters obtained by PCM modeling are not completely in line with the experimental solubility data. These results may suggest the influence of other factors that have not been considered in the PCM modeling. The variation obtained between the PCM parameters and experimental solubility data might be related to the calculation of εm by the general method used by Gaussian

decreases again. The plot of DFX solubility at various mass fractions of co-solvents is given in Figure 2. The lowest mass fraction solubility was observed in neat water at 4.0694 × 10−5, and the maximum solubility was seen in the acetonitrile + ethanol solvent mixture (w1 = 0.7 of ethanol) at 3.1428 × 10−2. The enhanced solubility may be due to the formation of ethanol multimers and role of intermolecular hydrogen bonding, which may have resulted in enhanced drug solubility.19 DFX solubility in pure solvents has been reported previously with slight difference. An important reason for such results may be the difference in the wavelength used for spectrophotometric drug quantification as the exact wavelength, and the solvent type used for the calibration curve is not mentioned in the manuscript. The water solubility reported in this work is 0.00373 mg/mL at 25 °C.11 In our work, the water solubility of this drug is measured to be 0.04 mg/mL at room temperature, which is close to the previously reported DFX aqueous solubility of 0.038 mg/mL at 37 °C.2 3.2. Density Functional Theory Calculation. The optimized structure of DFX by B3LYP/6-311++G** and Gibbs free energy of DFX (Ggas) at its most stable form was computed to be −3345291.31 kJ/mol in the gas state. The optimized structure of DFX at a B3LYP/6-311++G** level of theory is shown in Figure 3a.

εm = w1ε1 + w2ε2

(4)

where w1 and w2 are mass fractions of solvent 1 and 2, which may not be in line with the actual εm of the solvent mixture. The accuracy of the general εm model shown in eq 4 has been previously compared with three other models including the Amirjahed and Blake, King and Queen, and Jouyban−Acree model for their ability to calculate the εm of the solvent mixture. The overall average percent deviation (OAPD) of the above models were calculated for 56 sets of binary solvent mixtures. The results indicate a statistically significant difference in the accuracy of the Jouyban−Acree model in terms of OAPD values. This indicates the superiority of the Jouyban−Acree model in calculating εm of binary solvent mixtures.5 This outcome may either propose the contribution of other parameters in solubility prediction via PCM or suggest the use of an accurate method to calculate εm. The contribution of surface kinetics as a constituent in drug solubility is significant. The solute behavior and its concentration at the solvent interface are different from the bulk phase.19 A shortcoming of PCM might be that the free energy of solvation is calculated assuming the solute is placed within the molecular cavity in the bulk of the solvent surrounded by a homogeneous dielectric medium.20 An illustration of the continuum dielectric charge of the Gaussian model and atom charge is shown in Figure 3. The PCM approach describes the bulk solvent effect, and it has been proven useful in solvation of molecules in monosolvents.21−23 It may be noted that DFT/PCM provides good approximation for solubility in pure solvents; however, due to the intermolecular solvent−solvent interaction force, contribution

Figure 3. Illustration of the (a) optimized structure of DFX at B3LYP/6-311++G** level of theory and its atom charge and (b) continuum dielectric charge density on a single molecule of DFX.

The electrostatic potential contribution of DFX to solvation energy is shown with a surface color map in Figure 3b. The red region corresponds to more electron-rich zones, while the blue zone of the map represents the electron-poor region. The green and yellow regions are the intermediate zones, and the energy increases from the green to the blue zone, while it decreases from the yellow to the red zone. The DFX molecule represents small electronegativity. This is due to the presence of large regions of intermediary potential illustrated in yellow and green, while only small regions of extreme potential shown in red and blue are visible. The dielectric constant (ε), Gibbs free energy of solvation (ΔGsol), total Gibbs free energy in solution (G) (kJ/mol), dipole moment (μ) (Debye), and total electrostatic energy (kJ/mol) for DFX in different binary solvents, which were directly calculated at a B3LYP/6−311++G** level of theory, are from the thermochemistry part of the Gaussian output file as depicted in Table 3. DFX solubility is proportional to the ΔGsol and ε of the solvent system. A negative ΔGsol value indicates thermodynamic feasibility of drug dissolution in the investigated solvent D

DOI: 10.1021/acs.jced.8b01001 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. B3LYP/6-311++G** Calculated Dielectric Constant (ε), Gibbs Free Energy of Solvation (ΔGsol) (kJ/mol), Total Gibbs Free Energy in Solution (G) (kJ/mol), Dipole Moment (μ) (Debye), and Total Electrostatic Energy (kJ/mol) for DFX in Different Binary Solvents

solvent mixture

ε

ΔGsol (kJ/mol)

0/1 0.4/0.6 0.5/0.5 0.7/0.3 0.8/0.2 0.9/0.1 1/0

32.61 30.57 30.81 29.03 28.52 28.01 29.02

−168.950 −241.249 −241.835 −242.044 −242.295 −242.505 −243.425

0/1 0.4/0.6 0.5/0.5 0.7/0.3 0.8/0.2 0.9/0.1 1/0

32.61 29.51 27.76 27.18 26.4 25.63 24.85

−168.950 −239.492 −238.865 −238.906 −238.655 −238.404 −173.343

0/1 0.4/0.6 0.5/0.5 0.7/0.3 0.8/0.2 0.9/0.1 1/0

24.85 25.91 26.93 26.71 26.97 27.23 29.02

−173.343 −240.036 −240.873 −241.417 −241.877 −242.295 −243.425

0/1 0.4/0.6 0.5/0.5 0.7/0.3 0.8/0.2 0.9/0.1 1/0

35.69 34.46 34.98 33.53 33.23 32.92 32.61

−204.388 −241.082 −241.166 −240.580 −240.413 −240.203 −168.950

0/1 0.4/0.6 0.5/0.5 0.7/0.3 0.8/0.2 0.9/0.1 1/0

35.69 32.41 32.35 29.96 29.14 28.32 29.02

−204.388 −242.337 −242.714 −242.630 −242.714 −242.756 −243.425

0/1 0.4/0.6 0.5/0.5 0.7/0.3 0.8/0.2 0.9/0.1 1/0

35.69 31.35 30.07 28.1 27.02 25.94 24.85

−204.388 −240.622 −240.245 −239.534 −239.116 −238.655 −173.343

0/1 0.4/0.6 0.5/0.5 0.7/0.3 0.8/0.2 0.9/0.1 1/0

78.35 61.29 47.07 48.49 44.22 39.95 35.69

−151.419 −243.634 −243.969 −244.346 −245.768 −242.798 −204.388

G (kJ/mol)

1,2-propanediol (1) + methanol −3347105.530 −3347177.994 −3347178.519 −3347178.782 −3347179.044 −3347179.307 −3347179.307 ethanol (1) + methanol −3347105.530 −3347176.156 −3347175.631 −3347175.631 −3347175.369 −3347175.106 −3347109.994 1,2-propanediol (1) + ethanol −3347109.994 −3347176.681 −3347177.732 −3347178.257 −3347178.519 −3347179.044 −3347180.095 methanol (1) + acetonitrile −3347140.975 −3347177.732 −3347177.994 −3347177.206 −3347177.206 −3347176.944 −3347105.530 1,2-propanediol (1) + acetonitrile −3347140.975 −3347179.044 −3347179.569 −3347179.307 −3347179.569 −3347179.569 −3347180.095 ethanol (1) + acetonitrile −3347140.975 −3347177.469 −3347176.944 −3347176.419 −3347175.894 −3347175.369 −3347109.994 acetonitrile (1) + water −3347087.939 −3347182.457 −3347180.620 −3347181.145 −3347180.357 −3347179.569 −3347140.975

E

μ (Debye)

total electrostatic energy(kJ/mol)

2.4012 2.3975 2.3979 2.3943 2.3932 2.3920 2.3943

−178.197 −177.443 −177.527 −176.816 −176.565 −176.356 −176.816

2.4012 2.3953 2.3915 2.3901 2.3881 2.3861 2.3839

−178.197 −177.025 −176.230 −175.979 −175.561 −175.142 −174.724

2.3839 2.3868 2.3895 2.3889 2.3896 2.3902 2.3943

−174.724 −175.310 −175.854 −175.728 −175.854 −175.979 −176.816

2.4060 2.4042 2.405 2.4027 2.4022 2.4017 2.4012

−179.159 −178.782 −178.950 −178.489 −178.406 −178.280 −178.197

2.4060 2.4008 2.4007 2.3962 2.3945 2.3928 2.3943

−179.159 −178.113 −178.071 −177.192 −176.858 −176.481 −176.816

2.4060 2.3989 2.3965 2.3923 2.3897 2.3869 2.3839

−179.159 −177.736 −177.234 −176.397 −175.895 −175.310 −174.724

2.4346 2.4279 2.4185 2.4196 2.4159 2.4115 2.4060

−184.849 −183.510 −181.669 −181.878 −181.125 −180.247 −179.159

DOI: 10.1021/acs.jced.8b01001 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Parameters of the Jouyban−Acree Model for DFX Solubility in the Mixed Solvents (298.2 K) and MRD% Values of Back-Calculated Solubility Data N

solvents

J0

J1

J2

R2

MRD%

1 2 3 4 5 6 7

ethanol + methanol 1,2-propanediol + methanol 1,2-propanediol + ethanol acetonitrile + water methanol + acetonitrile 1,2-propanediol + acetonitrile ethanol + acetonitrile

103.935 302.975 407.092 1852.723 1934.715 1404.481 2288.620

−35.471 9.781 0a 3134.235 −1130.976 −545.659 −670.606

44.685 21.439 0a 1392.445 1316.767 510.731 1311.683

0.999 >0.999 0.994 0.991 0.998 >0.999 0.999

0.1 0.1 1.4 10.1 4.7 0.9 4.1

a

Not statistically significant (p-value > 0.05).

of the surface kinetics or role of nonelectrostatic forces, it might be more complex to predict drug solubility based on PCM parameters as a function of solvent ratios in binary solvent systems. 3.3. Mathematical Representation of Experimental Data. Finally, the Jouyban−Acree model as an accurate method from both correlative and predictive capabilities viewpoints was applied to correlate and calculate the experimental DFX solubility in binary solvent mixtures. The model constants and their predictive performance are depicted in Table 4. Experimental DFX solubility data in various binary solvent mixtures were correlated with the Jouyban−Acree model with good predictive performance. The model constants are depicted in Table 4. The highest MRD was observed for acetonitrile + water mixtures at 10.1% when compared to the nonaqueous solvent systems with MRD values below 4.7%. MRD variation in the correlation of experimental values may be due to the type of solvent system.

Abolghasem Jouyban: 0000-0002-4670-2783 Funding

E.R. would like to thank for a post doctorate grant (no. 241036) of Tabriz University of Medical Sciences for supporting this work. This work is partially supported by the Urmia University of Medical Sciences (grant no. 1395-2104). Notes

The authors declare no competing financial interest.

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4. CONCLUSIONS Here, we represent the application of DFT to estimate the solubility limit of DFX in various binary solvent mixtures and to evaluate the solute−solvent interaction. The solvent effect on drug solubility is proportional to the dipole moment or ε. The results of the calculated ε, μ, electrostatic force, and ΔGsol show moderate correlation with the experimental solubility data in various mass fractions of solvents. DFT/PCM calculations account well for DFX solubility in monosolvents, which may suggest a reliable prediction by this methodology; however, moderate predictability in binary solvent mixtures may suggest the significance of solvent−solvent interactions and other parameters. Consequently, DFT may be used for rapid selection of drug solubility in monosolvents and thus may require further adjustments for solvent mixtures. Furthermore, the Jouyban−Acree model in the investigated binary mixture shows good reliability to predict DFX solubility with MRD% values of 0.1−10.1%. The main drawback of experimental solubility studies is the time-consuming and laborious process involved. A suitable computational model should provide rapid and accurate data. The Jouyban−Acree model proves to be an accurate method, which can provide drug solubility in binary solvent mixtures with the use of their solubility data in pure solvents.

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REFERENCES

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*E-mail: [email protected]. ORCID

Anahita Fathi Azarbayjani: 0000-0002-3502-9802 F

DOI: 10.1021/acs.jced.8b01001 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jced.8b01001 J. Chem. Eng. Data XXXX, XXX, XXX−XXX