Prediction of Mefenamic Acid Solubility and Molecular Interaction

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Thermodynamics, Transport, and Fluid Mechanics

Prediction of Mefenamic Acid Solubility and Molecular Interaction Energies in Different Classes of Organic Solvents and Water Siti Kholijah Abdul Mudalip, Mohd Rushdi Abu Bakar, Parveen Jamal, and Fatmawati Adam Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b02722 • Publication Date (Web): 04 Oct 2018 Downloaded from http://pubs.acs.org on October 14, 2018

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Industrial & Engineering Chemistry Research

Prediction of Mefenamic Acid Solubility and Molecular Interaction Energies in Different Classes of Organic Solvents and Water Siti K. Abdul Mudalip †*, Mohd R. Abu Bakar §, P. Jamal ‡, F. Adam, † †

Centre of Excellence for Advanced Research in Fluid Flow, Faculty of Chemical & Natural Resources Engineering, University Malaysia Pahang, Gambang, 26300 Kuantan, Pahang, Malaysia. §

Department of Pharmaceutical Technology, Kulliyyah of Pharmacy, International Islamic University Malaysia, Bandar Indera Mahkota, 25200 Kuantan, Pahang, Malaysia.

‡

Department of Biotechnology Engineering, Kulliyyah of Engineering, International Islamic University Malaysia, 50728 Kuala Lumpur, Malaysia

*Corresponding

Author:

Tel.:

(+609)-549

2356;

Fax:

[email protected].

1

ACS Paragon Plus Environment

(+609)-549

2889;

E-mail:

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT: Determination of solubility data either through experimental or model based approaches become a necessity in crystallization of pharmaceutical compound. The current work predicts the mefenamic acid solubility and molecular interaction energy, namely electrostatic (HMF), hydrogen bonding (H-HB) and van der Waals (H-vdW) in different solvents at temperatures from 298 to 323 K using Conductor-like Screening Model for Real Solvents (COSMO-RS). The solvents used were N, N-dimethylacetamide, N,N-dimethylformamide, acetone, ethyl acetate, ethanol, iso-propyl alcohol, n-hexane, n-heptane, cyclohexane and water. The Gibbs free energy of fusion required in COSMO-RS computation was determined using differential scanning calorimetry and reference solubility method. The accuracy of methods employed in prediction of solubility were evaluated using mean squared quadratic error (MSE). The mefenamic acid solubility predicted using COSMO-RS with reference solubility method showed a small MSE value, which was less than 2%. The predicted solubility also follows the same trend as the experimental values and increases with temperature. The predicted H-HB energy and Gibbs free energy changes of mefenamic acid dissolution in the solvents studied highly influence the solubility data. Therefore, COSMO-RS with reference solubility method is promising approach to predict solubility and intermolecular interaction energy of mefenamic acid in different solvents. Keywords: COSMO-RS, mefenamic acid, solubility, intermolecular interactions, Gibbs energy. 1. Introduction Solubility data of a targetted compound as a function of temperatures or solvent compositions is essential and has become the first step in designing crystallization process in the pharmaceutical industries.1, 2 The solubility data can be obtained using experimental approach or predicted using

2


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various thermodynamics equations. Through experimental approach, unknown amount of solute is dissolved in a particular solvent at a constant temperature with agitation for 4 to 24 h.3 The amount of solute dissolved can be determined using either differential scanning calorimetry method,4 gravimetric method,3, 5 UV-spectroscopic, or high-performance liquid chromatography (HPLC).6 In addition to experimental approaches, the solubility data can be predicted using modified van’t Hoff equation:

ln x 

H f  1 1      ln  R T f T 

(1)

where 𝑥 is the mole fraction of the solute in the solution, 𝛾 is the activity coefficient, ∆𝐻 is the molar enthalpy of fusion of the solute (J/mol), 𝑅 is the gas constant (J.mol-1.K-1), 𝑇 is the fusion temperature of the solute (K) and 𝑇 is the solution temperature (K).3 The activity coefficient values can be predicted using various thermodynamic models such as Wilson equation,7 universal functional activity coefficient (UNIFAC),8 non-random two-liquid (NRTL) equation,9 UNIQUAC equation,10 segment activity coefficient (SAC),11,

12

and Van Laar equation.13 Some of these

thermodynamic models, such as Wilson’s model may not be very suitable for solubility prediction and solvent screening purposes because it requires many experimental data under different conditions.14 The thermodynamic models, i.e. UNIFAC and modified UNIFAC have been reported for solubility prediction of various drugs such as ibuprofen and aspirin.15 Accroding to Gracin et al., the UNIFAC model could predict the solubility of drugs, but show some restrictions as the results were accurate for limited compunds.16

3



There has been growing interest in using novel Conductor-like Screening Model for Real solvents (COSMO-RS) developed by Klamt and co-workers for quick prediction of thermodynamics properties of fluids and liquid mixtures.This method only requires data on screening charge density of molecular surface (σ-profile) and surface chemical potential (σpotential) of compounds under investigation that can be obtained by molecular quantum chemical calculation (COSMO).17-20 The data are needed for estimation of solvents' ability either to donate or accept hydrogen bonds with the solute and calculate the pair-wise intermolecular interaction energies such as miss-fit or electrostatic (H-MF), hydrogen bonding (H-HB) and van der Waals interaction (H-vdW).21 The detail description of σ-profile, σ-potential and pair-wise intermolecular interaction energies have been reported previously. 17, 20, 22, 23 The application of COSMO-RS can be found for solubility predictions of ionic liquids, dyes, synthesis gas, salts and other hydrocarbons.24-28 Recent progress made in COSMO-RS also can be found in solubility prediction of organic compounds such as ascorbic acid, ibuprofen, loratadine, paracetamol, and polymers.21, 29, 30

COSMO-RS, however, shows some limitation since the non-equilibrium dynamic properties

for system beyond or close to critical point cannot be determined directly.30 Moreover, since this method was initially design for prediction of thermophysical data of liquids and solution, the Gibbs free energy of fusion ∆𝐺

has to be considered for cases involving solid compound.21, 23

In the present work, the solubility of mefenamic acid (2-[(2,3-dimethylphenyl)amino]benzoic acid, C15H15NO2) in various organic solvents and water were predicted using COSMO-RS. The chemical structure and 3D COSMO surface screening charge densities of mefenamic acid are illustrated in Figure 1. This drug is extensively used for control of pain due to menstrual disorder and as anti-proliferative agents.31, 32 Based on extensive literature review, no work has been done to predict or investigate the solubility of mefenamic acid in organic solvents using COSMO-RS. 4


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(a)

(b)

Figure 1. Chemical structure (a) and 3D COSMO-surface screening charge densities (b) of mefenamic acid. The blue, red and green colour shown in 3D surface of mefenamic acid indicate the presence of hydrogen donor, hydrogen acceptor and non-polar region, respectively. The aim of the present work is to predict and investigate the solubility of mefenamic acid as a function of solvent types and temperatures using COSMO-RS with ∆𝐺

obtained from

differential scanning calorimetry (DSC) analysis and reference solubility method. The solvents used in this work were divided into three groups. Group 1 comprises of dipolar aprotic solvents (N, N-dimethylacetamide (DMA), N, N-dimethylformamide (DMF), acetone and ethyl acetate) which mefenamic acid show higher solubility value. Group 2 consist of polar protic solvents (ethanol, propan-2-ol, and water). Group 3 consist of apolar aprotic solvents (hexane, heptane, and cyclohexane). For validation purposes, the predicted solubility data were compared with the experimental results obtained from the literature. The qualitative screening based on σ-profiles and σ-potentials of the substances involved were discussed. In addition, the molecular interaction energies between mefenamic acid and solvents, i.e. H-MF, H-HB and H-vdW obtained from COSMO-RS calculation were analyzed and correlated with the solubility results. 5



2. Material and Methods 2.1 Material The mefenamic acid powder (98 wt% purity) supplied by Baoji Tianxin Pharmaceutical Co. Ltd., China was used without further purification. 2.2 Determination of melting properties of mefenamic acid The thermodynamic properties of the mefenamic acid were determined using a Mettler Toledo differential scanning calorimetry (DSC) and analyzed using Mettler Toledo Stare SW 9.10. The temperature program was set from 25 to 300°C with a heating rate of 10°C/min under constant purging of nitrogen.33 2.3 COSMO-RS computational method The solubility of mefenamic acid in different solvents for the temperature of 298 K to 323 K were predicted using COSMOthermX software Version C3.0 (COSMOlogic GmbH & Co KG, Leverkusen, Germany) with Becke-Perdew triple valence plus polarization function (BP-TZVP) basis set. The input files for solvents were obtained from COSMO-RS database. The mefenamic acid molecule was sketched and optimised in TmoleX (COSMOlogic GmbH & Co KG, Leverkusen, Germany) with BP-TZVP parametrization. The COSMO calculation of the molecule was performed before imported into COSMOthermX software. The COSMO output of the molecule provides total energy and 3D screening charge density, i in a virtual conductor environment which used to compute σ-profile, chemical potential and pair-wise intermolecular interaction energies as detailed in literature. 17, 22, 23 The solubility of mefenamic acid, i in targeted

6


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solvent at a particular temperature, S was calculated using COSMOthermX solubility tool with iterative algorithm as shown below:



 







( n 1) ( n) log10 x sol   Pure   Sj x sol  max0, G fus  / RT ln(10) j j j

where 𝑥

(2)

is the mole fraction of mefenamic acid dissolved in the targeted solvent, 𝜇

is the

chemical potential of pure compound j, 𝜇 is the chemical potential of pure compound j at infinite dilution in the solvent and ∆𝐺 ∆𝐺

is the Gibbs free energy of fusion.34 For liquid substance, the

is zero and thus, it has to be specified or estimated for solid compound.23, 34 Since mefenamic

acid exist as solid compound at room temperature, COSMO-RS treats mefenamic acid as a subcooled liquid, and therefore, the ∆𝐺

that required in Eq. 2 was estimated using reference

solubility method and melting properties of mefenamic acid. The methods were introduced since the properties of the subcooled liquid beyond the fusion temperature are difficult to be measured. In reference solubility method, the solubility data of mefenamic acid in different solvents and at a particular temperature was used to determine ∆𝐺 used melting properties, the melting temperature, 𝑇 DSC analysis were used to estimate the ∆𝐺

∆𝐺

(T)=- 𝛥𝐻

by solving Eq. 2. Meanwhile for method that and enthalpy of fusion, 𝛥𝐻

obtained from

by solving Eq. 3. 1, 22, 23, 35

1

(3)

3. Results & Discussion 3.1 Melting properties of mefenamic acid The DSC thermogram for mefenamic acid obtained in this work is shown in Figure 2. Two endothermic peaks are observed. The minor peak at an onset temperature of 166.07°C (TT) and an 7



enthalpy value of 2.09 kJmol-1 (ΔHT) corresponds to the transition of Form I to Form II. The major peak at an onset temperature of 232.15°C (Tfus) and enthalpy of 37.64 kJmol-1 (𝛥𝐻

) contribute

to the melting of Form II. Table 1 tabulates the melting properties of mefenamic acid obtained in this work and literature. 36-40 The melting properties obtained in this work shows slight deviation from the literature. This is probably due to a different source of mefenamic acid used during the analysis.

1.00 0.00 -1.00 Heat Flow (Wg-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-2.00 -3.00

TT= 166.07°C HT= 2.09 kJmol-1

-4.00 -5.00

Tfus= 232.15°C 𝐻 = 37.64 kJmol-1

-6.00 -7.00 -8.00 -9.00 25.00

75.00

125.00

175.00

225.00

275.00

Temperature (°C)

Figure 2. DSC thermogram of the mefenamic acid. Table 1. Melting properties of mefenamic acid. Enthalpy of fusion, 𝐻 (kJmol-1)

Melting Temperature, Tfus (C)

37.64±1.40

232.15±0.62

Romero et al.36, 37

36.86 – 40.85

230- 231.5

Panchagnula et al.38

Not available

231

38.7

230.35

Experimental

Surov et al39

8


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SeethaLekshmi and Guru Row40 Deviation, 𝐷a a

𝐷

Not available

229

2.12-7.85

0.28 – 1.36

𝑥100

3.2 Enthalpy of fusion and its influence to solubility prediction Figure 3 illustrates the solubility values predicted using COSMO-RS calculation with ∆𝐺 estimated from the melting properties of mefenamic acid in comparison with literature. This method assumed mefenamic acid exists in subcooled liquid with random particle distribution and formed an ideal solution with the solvents studied.22 This assumption, however, has systematically overestimated the solubility values for all solvents in Group 1 and Group 2 except for solvents in Group 3 which are cyclohexane, heptane, and hexane as compared with experimental solubility data reported in literature.5 This is probably due to the non-ideal behavior of the solution and intermediate phase changes of mefenamic acid from solid to liquid that occur during solubility study. The non-ideal behavior of the solution is probably due to the ability of solute and solvents’ molecules under investigation to interact either through hydrogen bonding formation or van der Waals interaction.5 Recently, Loschen and Klamt showed that the deviation of the drugs solubility i.e. lovastatin, sulfamethoxypyridazine and meloxicam in different solvent predicted using COSMO-RS with ∆𝐺

estimated from the melting properties are quite high from the experimental result.22

Wichmann and Klamt, however, reported the solubility of acetaminophen in various organic solvents and water are in good agreement with experimental data except for carbon tetrachloride, diethylamine, 1,4-dioxane and tetrahydrofuran.23 Based on the studies, it can be suggested that the

9



solubility of drugs predicted using COSMO-RS calculation with ∆𝐺

obtained from the melting

properties only produced good agreement with experimental data for a particular case. Thus, the decision to predict solubility of drugs using COSMO-RS with ∆𝐺

value estimated from the

melting properties has to be carefully considered.35 0.30

0.030

0.25

0.025

xCOSMO-RS (Mole fraction)

xCOSMO-RS (Mole fraction)

0.20 0.15 DMA DMF Propanone Ethyl Acetate

0.10 0.05 0.00 0.00

0.10 0.20 xLiterature (Mole fraction)

0.30

0.020 0.015 0.010

Ethanol Propan-2-ol Water

0.005 0.000 0.000

(a) xCOSMO-RS (Mole fraction)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.020 xLiterature (Mole fraction)

(b)

0.0020 0.0015

Cyclohexane Heptane Hexane

0.0010 0.0005 0.0000 0.0000

0.0010

0.0020

xLiterature (Mole fraction)

(c) Figure 3. Predicted mefenamic acid solubility values using COSMO-RS calculation with ∆𝐺 estimated from the melting properties versus literature5 in different classes of organic solvents: (a) Group 1: DMA, DMF, propanone and ethyl acetate (dipolar aprotic); (b) Group 2: Ethanol and propan-2-ol (polar protic); and (c) Group 3: Cyclohexane, heptane and hexane (Apolar aprotic). 10


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Figure 4 illustrates the mefenamic acid solubility prediction values from COSMO-RS calculation with ∆𝐺

estimated from the reference solubility method in comparison with

literature. In this method, the non-ideal behavior of the solution is assumed. As seen in Figure 4, this approach seems to produce more reasonable results since the predicted solubility shows slight deviations with literature for all solvents studied. For quantitative evaluation of the model accuracy in comparison to the experimental data, the average mean squared quadratic errors (MSE) have been calculated using Eq. 4 and tabulated in Table 2.

𝑀𝑆𝐸

∑

,

,

(4)

,

Based on the MSE values, it can be affirmed that COSMO-RS can be used for prediction of mefenamic acid solubility provided with a suitable assumption made during the calculation. This assumption will help user to select a suitable enthalpy values which require for computation of ∆𝐺

during solubility prediction of solid compound. For the case of mefenamic acid, the melting

properties of mefenamic acid obtained from DSC analysis cannot be used as an input during the COSMO-RS calculation. This is because, the polar and non-polar characteristics of mefanamic acid molecule enable the molecule to either attract or repulse with the solvents in the solution, and thus formed non-ideal solution. Therefore, an assumption on ideal solution behavior is not suitable.

11


0.20

0.008

0.18

0.007 xCOSMO-RS (mole fraction)

0.16 0.14 0.12 0.10 0.08

DMA

0.06

DMF

0.04

Propanone

0.02 0.00 0.00

0.05

0.10 0.15 xExperimental (mole fraction)

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0.006 0.005 0.004 0.003

Ethanol

0.002

Propan-2-ol

0.001

Ethyl acetate 0.20

Water

0.000 0.000

0.002 0.004 0.006 xExperimental (mole fraction)

(a)

0.00

(b)

0.006 xCOSMO-RS (mole fraction)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

xCOSMO-RS (mole fraction)


0.005 0.004 0.003 0.002

Cyclohexane Heptane

0.001 0 0.000

Hexane 0.002

0.004

0.006

xExperimental (mole fraction)

(c) Figure 4. Comparison of mefenamic acid solubility values predicted using COSMO-RS with reference solubility method and literature5 in different classes of organic solvents: (a) Group 1: DMA, DMF, propanone and ethyl acetate (dipolar aprotic); (b) Group 2: Ethanol and propan-2-ol (polar protic); and (c) Group 3: Cyclohexane, heptane and hexane (Apolar aprotic).

12


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Table 2. Mean squared quadratic errors (MSE) of COSMO-RS solubility prediction with enthalpy of fusion obtained from differential scanning calorimetry analysis and literature. Solvents

Average mean squared quadratic errors, MSE Differential scanning calorimetry

Literature5

DMA

0.13

0.0010

DMF

27.42

0.0002

Propanone

107.64

0.0200

Ethyl Acetate

44.85

0.0040

Ethanol

10.54

0.0001

Propan-2-ol

21.47

0.0010

Cyclohexane

0.80

0.0020

Heptane

0.74

0.0010

Hexane

0.93

0.0020

3.3 Van’t Hoff plot of solubility data predicted using COSMO-RS The solubility results calculated using COSMO-RS at different temperatures are shown as Van’t Hoff plot in Figure 5. This figure suggests that the solubility of mefenamic acid depends on types of solvent and the temperature of the solution. The rank of mefenamic acid solubility in the solvents studied is DMA > DMF > propanone > ethyl acetate > propan-2-ol (IPA) > ethanol > hexane > heptane > cyclohexane > water. This behaviour is expected due to different molecular characteristics and interaction energies exist between mefenamic acid in the solvents which discussed in the subsequent section. The solubility trend is also increase with the increase of the solution temperature. This is probably due to the increase of molecules’ kinetic energy at higher temperatures that leads to more effective movement or interactions between solvents with the solute molecules. Moreover, the heat adsorbed at high temperature facilitate the dissolution of 13



solute compound by breaking the bonds in the solute molecules.41, 42 These findings are aligned with the experimental solubility data discussed in the previous work.5 Moreover, the increase of mefenamic acid solubility with temperature indicates the endothermic dissolution process.43

0.04

-1.96

-3.96

ln x

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-5.96

-7.96

-9.96

-11.96 0.00305

0.00310

0.00315

0.00320

0.00325

0.00330

0.00335

0.00340

Temperature (1/K) DMA Ethanol

DMF Hexane

Propanone Heptane

Ethyl acetate Cyclohexane

Propan-2-ol Water

Figure 5. Van’t Hoff plot of mefenamic acid solubility calculated using COSMO-RS in different organic solvents and water.

14


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3.4 σ-Profiles and molecular interaction energies The -profile of mefenamic acid and solvents shown in Figure 6 are useful for estimation of the solvation and intermolecular interactions between solute and solvent.18 A compound that has a peak at region less than – 0.01 e/Å2 or more than +– 0.01 e/Å2 is strongly polar and considered as hydrogen bonding donor and hydrogen bonding acceptor, respectively. As seen in Figure 6 (a), mefenamic acid shows a large peak in the non-polar region and small peak in hydrogen donor and acceptor region, which indicates the non-polar and polar characteristic of the compound. The presence of aromatic and methyl groups caused non-polar characteristic, while the carboxylic acid and amine group are polar. Figure 6 (b) shows that the polar protic solvents which are IPA, ethanol and water have a broad peak in a hydrogen bond donor and hydrogen bond acceptor region due to the presence of hydroxyl group. The presence of peak in those regions indicate that the molecules are able to accept or donor its partial charges to form hydrogen bond during solvation process.17

The -profiles of dipolar aprotic solvents which are DMA, DMF, acetone and ethyl acetate illustrated in Figure 6 (c) shows the highest peaks in the non-polar region followed by a significant peak in hydrogen bond acceptor indicating that the molecule is able to accept its partial charges to form hydrogen bond. As for apolar aprotic solvents studied in this work, namely hexane, heptane and cyclohexane, the -profiles shown in Figure 6 (d) are narrowed in the non-polar region due to the non-polar characteristic of the molecule. The presence of non-polar and polar groups in mefenamic acid and solvents studied caused different H-MF, H-HB and H-vdW interaction energies in the solution. Details on the intermolecular interaction energies at different temperatures between mefenamic acid and solvents studied are provided in supplementary data Figure S1.

15



18.0

25.0

20.0

DMA DMF Propanone EA

Non-polar

16.0 14.0 12.0

15.0

ρ(σ)

ρ(σ)

10.0

10.0

8.0 6.0

5.0

Hydrogen bond donor

4.0

Hydrogen bond acceptor

Non-polar

-3.5

-2.5

-1.5

-0.5

0.5

1.5

σ(e/Å2)

2.5

0.0

3.5

-3.5

-2.5

-1.5

-0.5

x10-2

0.5

1.5

2.5

3.5

x10-2

σ(e/Å2)

(a)

(b)

14.0

35.0 Propan-2-ol Ethanol Water

Non-polar

12.0

20.0

ρ(σ)

8.0

4.0

Cyclohexane

15.0 10.0


Hydrogen bond donor

Heptane

30.0 25.0

6.0

Hexane

Non-polar

10.0

2.0


Hydrogen bond donor

2.0

0.0

ρ(σ)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 26

Hydrogen bond donor

5.0

0.0


0.0

-3.5 -2.5 -1.5 -0.5 0.5 σ(e/Å2)

1.5

2.5

3.5

-3.5

-2.5

-1.5

-0.5

0.5

σ(e/Å2)

x10-2

1.5

2.5

3.5

x10-2

(c) (d) Figure 6. -Profiles for: (a) mefenamic acid; (b) Group 1: DMA, DMF, propanone and ethyl acetate (dipolar aprotic); (c) Group 2: Ethanol and propan-2-ol (polar protic); and (d) Group 3: Cyclohexane, heptane and hexane (Apolar aprotic). To understand the microscopic properties that play the role in different solubility behaviour of mefenamic acid in various solvents studied, the H-vdW, H-HB and H-MF energy at 298 K are plotted in Figure 7. As seen in Figure 7, the changes of H-vdW or dispersion forces of mefenamic

16


Page 17 of 26

acid molecules in the solvents studied are very small, which are between -12.7230 and -12.3293 kcalmol-1 except for water. The H-vdW for mefenamic acid in water is smaller than other solvents, which is -10.1422 kcalmol-1. This is particularly due to the size of water molecule which is smaller than the size of other solvents under investigation. Tang and co-workers also found that the changes of vdW energy are very small for molecules that have similar size or number of atoms.1 10.00

0.1200 5.00 0.1000 0.00

0.0800 0.0600

-5.00

0.0400 -10.00 0.0200 0.0000

Molecular Interaction Energy (kcalmol-1)

0.1400

x (mole fraction)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-15.00

Type of solvents Solubility

H-HB

H-MF

H-vdW

H-Total

Figure 7. Microscopic energies of mefenamic acid in different solvents at 298 K.

As can be observed from Figure 7, the changes of H-HB and H-MF energy are from 5.296 kcalmol-1 to 2.973 kcalmol-1 and -4.821 kcalmol-1 to -0.085 kcalmol-1, respectively. The changes of H-HB energy are more significant than the H-MF energy. This findings may suggest that the hydrogen bonding interactions between mefenamic acid and solution are more responsible for the

17



differences in the mefenamic acid solubility behaviour. The significant changes of H-HB energy are expected due to different hydrogen donor and acceptor propensity of mefenamic acid and solvents under investigation as shown in Figure 6. Several literature reported that the stronger hydrogen bonding energy between solute and solvent molecules, the higher the H-HB energy gained in the solutions, and, thus increase the solubility value.1, 44 The H-HB energy illustrated in Figure 7 increases with the increases of solubility values. An offset from this trend is observed for polar protic solvents under investigation, which are IPA, ethanol, and water. This is because, although the H-HB energy of mefenamic acid in IPA, ethanol, and water are much higher than the H-HB energy in DMA, DMF, propanone and ethyl acetate, the solubility of mefenamic acid in those solvents are much lower. The high H-HB energy of mefenamic acid in ethanol, IPA and water solvents are expected, due to the high polarisation charge density or high propensity of the solvents as hydrogen bonds donor and acceptor (Refer Figure 8).

Although water is highly polar solvent and show higher H-HB with mefenamic acid molecule, the diffusivity of mefenamic acid in water is low, indicating that mefenamic acid is difficult to diffuse through water molecules thus leads to poor solubility.45 The H-HB energy in DMA, DMF, propanone, and ethyl acetate are less due to the solvents characteristics which have less polarisation charge density and less intense hydrogen acceptor propensity. The low solubility of mefenamic acid in hexane, heptane and cyclohexane are due to their low H-HB energy. The low H-HB energy in these solvents are due to the non-existence of hydrogen bonding acceptor or donor in the molecules. Although the van der Waals interactions between mefenamic acid and these solvents are quite high as compared to water, the H-vdW gained is not enough to increase the solubility values.

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Page 18 of 26

0.8

0.6

0.6

0.4

0.4

0.2

0.2

μ(σ) (kcal/mol.Å2)

0.8

0.0 -0.2 -0.4 -0.6

0.0 -0.2 -0.4

-0.8

-1.0

-1.0 -3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5

DMA DMF Propanone Ethyl acetate

-0.6

-0.8 -1.2

-1.2

3.5

-3.5

-2.5

-1.5

-2

x10

σ (e/Å2)

0.6

0.6

0.4

0.4


0.8

0.2 0.0 -0.2 -0.4 -0.6

Propan-2-ol

-0.8

Ethanol

-1.0

Water -1.5

-0.5

σ

1.5

2.5

3.5

x10-2

(e/Å2)

0.5

(e/Å2)

1.5

0.2 0.0 -0.2 -0.4 -0.6

Hexane

-0.8

Heptane

-1.0

Cyclohexane

-1.2

-1.2 -2.5

0.5

(b)

0.8

-3.5

-0.5

σ

(a)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 19 of 26

2.5

-3.5

3.5

-2.5

-1.5

-0.5

0.5

σ (e/Å2)

x10-2

(c)

1.5

2.5

3.5

x10-2

(d)

Figure 8. -Potentials for: (a) mefenamic acid; (b) Group 1: DMA, DMF, propanone and ethyl acetate (dipolar aprotic); (c) Group 2: Ethanol and propan-2-ol (polar protic); and (d) Group 3: Cyclohexane, heptane and hexane (Apolar aprotic).

3.5 Gibbs free energy change in different solvents Besides the microscopic properties, other factors such as Gibbs free energy of dissolution also play a significant role in solubility.27 Literature reported that the higher the energy change during the

19



Page 20 of 26

dissolution process, the higher stability of the solute compound in a solid phase, thus cause low solubility value in a solvent.5 The changes of Gibbs free energy, ΔGdiss during the dissolution process of mefenamic acid in a solvent can be obtained from the enthalpy dissolution, ΔHdiss and entropy of dissolution, ΔSdiss using the following relationship:46, 47

Gdiss  H diss  TS diss

(5)

In this relationship, a linear dependency of solubility values with the temperature between 298 and 323 K is assumed. The values of enthalpy of dissolution, ΔHdiss and entropy of dissolution, ΔSdiss can be determined from the slope and the intercept of the linear van’t Hoff plot in Figure 5, respectively. The plot of Gibbs free energy change, Gdiss that was estimated from the COSMO-RS solubility data for each solvent studied as a function of temperature is illustrated in Figure 9. The Gdiss values are positive in all solvents, which indicates the dissolution processes are endothermic, entropy driven and not a spontaneous process.46 Moreover, the trend of Gibbs free energy change decreases with the increase in temperature. This indicates less energy is required at a higher temperature to initiate the dissolution of mefenamic acid in the respective solvent. Although COSMO-RS predicts a strong H-HB energy between mefenamic acid and water, the highest Gdiss is observed during dissolution of mefenamic acid in water. These findings may suggest that the calculated H-HB energy is not enough to promote the solute-solvent interactions between mefenamic acid and water molecules and thus, cause low solubility value. The low value of Gdiss in DMA indicates high solubility or good solute-solvent interactions.

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Page 21 of 26

40 35 30 ΔGdiss (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25 20 15 10 5 0 295

300 DMA Ethanol

305 DMF Hexane

310 315 Temperature (K) Propanone Heptane

320

325

Ethyl acetate Cyclohexane

330

Propan-2-ol Water

Figure 9. The plot of Gibbs free energy estimated from the COSMO-RS solubility data versus temperature

Conclusion Mefenamic acid solubility in different classes of solvents and water were predicted and investigated using COSMO-RS at temperatures ranging from 298 K to 323 K. The predicted mefenamic solubility using COSMO-RS with reference solubility method concurs with literature and the solubility trend increases with increasing temperature. The mefenamic acid solubility is high in dipolar aprotic solvents (DMA, DMF, propanone and ethyl acetate), moderate in polar protic sovents (IPA and ethanol) and poor in apolar aprotic

solvents (hexane, heptane,

cyclohexane) and water. The prevailing microscopic intermolecular interactions, namely misfit, hydrogen bonding, and van der Waals that determined the solubility behaviour have been identified. Although in some cases, the trend of the microscopic interactions energy predicted 21



using COSMO-RS does not follow the solubility trend, the most dominant interaction energy, which was hydrogen bonding was revealed. The calculated Gibbs free energy change of mefenamic acid dissolution in the solvents studied agreed with the solubility data. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources The work was financially supported by the International Islamic University Malaysia (Endowment Fund B12-363-0841) and the Universiti Malaysia Pahang (RDU150359 and RDU1803107). Acknowledgment One of the authors (Siti K. Abdul Mudalip) is grateful to the Malaysian Ministry of Higher Education and the Universiti Malaysia Pahang. The authors are grateful to F. Eckert and A. Klamt, COSMOtherm, Version C3.0, Release 13.01; COSMOlogic GmbH & Co. KG, Leverkusen, Germany, 2013 for their technical support.

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For Table of Content Graphic Only Solubility COSMO-RS (mole fraction)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.008 0.007 0.006 0.005 Mefenamic acid 0.004 0.003 0.002 0.001 0.000 0.000 0.002

σ-profile 0.004

0.006

0.008

Solubility Experimental (mole fraction)

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Prediction of Mefenamic Acid Solubility and Molecular Interaction

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