Solubility measurements and thermodynamic modeling of pyrazinamide in five different solvent-antisolvent mixtures

Fluid Phase Equilibria 497 (2019) 33e54

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Solubility measurements and thermodynamic modeling of pyrazinamide in five different solvent-antisolvent mixtures Abhishek Maharana, Debasis Sarkar* Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 March 2019 Received in revised form 1 June 2019 Accepted 3 June 2019 Available online 8 June 2019

Pyrazinamide, an important first line drug for the treatment of Mycobacterium tuberculosis, has different polymorphic forms among which the plate like metastable d-polymorphic form is desirable for ease of downstream processing. Pyrazinamide has reasonably good solubility in acetone, 1,4-dioxane and methanol; but very low solubility in toluene and cyclohexane. Also, the d-polymorphic form of pyrazinamide can be obtained by antisolvent crystallization using any of these five solvent-antisolvent pairs. In this work, the solubility of pyrazinamide in acetone-toluene, acetone-cyclohexane, 1,4-dioxanetoluene, 1,4-dioxane-cyclohexane and methanol-toluene mixtures is measured by gravimetric method within the temperature range of 283.15 K to 333.15 K over antisolvent composition upto 70 wt%. The solubility of pyrazinamide increases with increase in temperature for all systems at constant antisolvent (toluene and cyclohexane) composition and decreases with increase in antisolvent composition for the given temperature range for all systems except methanol-toluene system. The solubility of pyrazinamide in methanol-toluene system increases with increase in toluene composition upto 40 wt% and then decreases with increase in toluene composition. Three thermodynamic models namely UNIQUAC, NRTL, and Wilson are used to correlate the solubility of pyrazinamide in above solvent-antisolvent mixtures. A nonlinear optimization technique was used to determine the adjustable parameters of various models. The accuracy of the model correlation has been evaluated on the basis of relative average deviation, root mean square deviation and Akaike Information Criterion. All the models represented the experimental solubility data with good accuracy, the maximum root mean square deviation being 5.21. The dissolution enthalpy and dissolution entropy of pyrazinamide in above solution mixtures were calculated from the slope and intercept of van't Hoff equation which shows that solvation of pyrazinamide in these mixed solvents is endothermic and enthalpy-driven. © 2019 Elsevier B.V. All rights reserved.

Keywords: Phase equilibrium Pyrazinamide Solubility Mixed solvent Thermodynamic model

1. Introduction The knowledge of solubilities of an active pharmaceutical ingredient in various solvents is extremely important in successful design and development of separation and purification process using crystallization. Experimental determination of solubility is generally expensive and time consuming and, therefore, the computation of solubility using different thermodynamic models has emerged as an attractive option [1,2]. Various thermodynamic models such as UNIFAC [3], UNIQUAC [2], Wilson [4], NRTL [2] and NRTL-SAC [5] have received much attention in recent literature for successfully correlating solubility data. The UNIFAC model uses

* Corresponding author. E-mail address: [email protected] (D. Sarkar). https://doi.org/10.1016/j.fluid.2019.06.004 0378-3812/© 2019 Elsevier B.V. All rights reserved.

group-contribution method and information about chemical structure of molecules whereas UNIQUAC, NRTL, NRTL-SAC and Wilson models are semi-empirical in nature. They require experimental data for identifying certain adjustable model parameters. Pyrazinamide (C5H5N3O, Fig. 1) is an important first line drug for treatment of Mycobacterium tuberculosis [6]. Tuberculosis (TB) is a very serious health disorder and despite use of vaccine more than 8 million people get infected with TB each year, among which 1.8 million die [4]. World Health Organization (WHO) guidelines recommend the administration of pyrazinamide in association with two other drugs such as rifampicin and isoniazid in order to reduce bacterial growth during the initial phase of tuberculosis treatment [7]. Pyrazinamide shortens the anti-tuberculosis treatment process from 9-12 months to 6 months [4]. Pyrazinamide is known to have four different polymorphic forms: a, b, g and d. However, pyrazinamide is generally found in three polymorphic forms in nature

34

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

toluene. The maximum temperature for determination of solubility for acetone and methanol is taken as 323.15 K as acetone and methanol have boiling points of 329.15 K and 337.85 K, respectively. For 1,4-dioxane, the temperature range selected is 293.15 K to 333.15 K as 1,4-dioxane has a boiling point of 374.15 K and freezing point of 284.95 K. All the experiments are performed at 101.3 kPa. Three thermodynamic models such as UNIQUAC, NRTL, and Wilson have been used to correlate the measured solubility data with good accuracy. The adjustable parameters of the models are estimated from experimental data using a nonlinear optimization method. Dissolution enthalpy and dissolution entropy are computed by van't Hoff equation. To the best of our knowledge, the solubilities of pyrazinamide in such solvent-antisolvent pairs of acetone-toluene, acetone-cyclohexane, 1,4-dioxane-cyclohexane, 1,4-dioxane-cyclohexane and methanol-toluene mixtures have not been reported yet in open literature. The rest of the paper is organized as follows. Section 2 describes the experimental setup, solubility measurements and different analysis carried out for pyrazinamide. Section 3 represents different thermodynamic models used in this work to correlate the experimental data. The experimental results on solubility and thermodynamic modeling are discussed in Section 4. Finally, some concluding remarks are made in Section 5.

Fig. 1. Pyrazinamide.

as the fourth b-form is very unstable and readily undergoes phase transition to stable a-form. The a-form has a crystalline structure of needle shape, g-form is prismatic and d-from has plate like crystalline structure [8]. Commercially available pyrazinamide is of aform with needle shaped structure. Such needle shaped crystals form mesh-like structure during cyrstallization and this makes downstream processing very difficult and inefficient [8,9]. The next stable polymorph of pyrazinamide is the metastable d-form and it has a plate like structure which is more desirable for efficient downstream processing and improved flowability. Hermanto et al. [2015] [8] selected five different solvents (water, methanol, 1,4dioxane, ethanol, and nitromethane) from ICH (International Conference on Harmonisation) class 2/3 table based on Hansen Solubility Parameters to obtain d-form by cooling crystallization. The authors reported that a mixture of 20% 1,4-dioxane/80% methanol is appropriate solvent for obtaining d-form of pyrazinamide based on yield, toxicity, solubility and cost. Zhang et al. [2017] [4] studied the solubility of pyrazinamide in ten different pure solvents (water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile, and ethylacetate) in the temperature range of 278.15 K to 323.15 K. The authors used Wilson and NRTL models to correlate the solubility of pyrazinamide in these solvents. Antisolvent crystallization is an attractive option for producing crystals with high yield and desired polymorphic form. Pyrazinamide has reasonably good solubility in acetone, 1,4-dioxane and methanol, but it has very low solubility in cyclohexane and toluene. Through a series of screening experiments, we established that all these solvent-antisolvent systems yield the d-form of pyrazinamide. Therefore, the solubility data on such mixed solvents will be useful for design and analysis of antisolvent cyrstallization of pyrazinamide. In this work, we measure the solubility of pyrazinamide in various solvent-antisolvent mixtures of acetonetoluene, acetone-cyclohexane, 1,4-dioxane-toluene, 1,4-dioxanecyclohexane and methanol-toluene (10e70 wt% toluene or cyclohexane) in the temperature range of 283.15 K to 333.15 K. Acetone belongs to ICH class 3/3 [10], so it is safe to be used as a solvent. 1,4Dioxane and methanol belong to ICH class 2/3 table and have limitation of 3.8 mg/day and 30 mg/day, respectively. The antisolvents toluene and cyclohexane are classified as ICH class 2/3 table solvent having a limitation of 8.9 mg/day and 38.8 mg/day, respectively. Both toluene and cyclohexane are miscible with acetone and 1,4-dioxane, but methanol is miscible with only

2. Experimental section 2.1. Materials Pyrazinamide (>98 mass purity) was obtained from Tokyo Chemical Industry Co. Ltd. (Japan). Acetone and 1,4-dioxane were purchased from Loba Chemie Pvt. Ltd. (India), methanol was purchased from Spectrochem (India), toluene and cyclohexane were purchased from Merck (India). The detailed information is provided in Table 1. 2.2. Solubility measurements The experiments for determination of solubility of pyrazinamide were carried out in a 100 ml conical flask with glass stopper to avoid any loss of solvent. The solubility of pyrazinamide in various acetone-toluene, acetone-cyclohexane, 1,4-dioxane-toluene, 1,4dioxane-cyclohexane and methanol-toluene mixtures (10e70 wt% of toluene or cyclohexane) was measured gravimetrically in the temperature range of 283.15 K to 323.15 K for acetone-toluene (or cyclohexane) and methanol-toluene, and in temperature range of 293.15 K to 333.15 K for 1,4-dioxane-toluene (or cyclohexane). All the measurements were performed using an analytic balance (Sartorius, Germany) having an accuracy of ±0.0005. For measurement of solubility at a particular temperature, an excess amount of pyrazinamide was added to 50 ml of mixed solvent (solvent-antisolvent mixture of given composition) taken in a sealed conical flask. The slurry was then agitated at 170 rpm in a temperature controlled incubator shaker with a temperature

Table 1 Details of the materials used. Name of chemical

Chemical formula

Molecular weight

Purity(mass%)

Analysis method

Pyrazinamide Acetone 1,4-Dioxane Methanol Cyclohexane Toluene

C5H5N3O ðCH3 Þ2 CO C4H8O2 CH3OH C6H12 C6H5CH3

123.12 58.08 88.11 32.04 84.16 92.14

>98 99 99 99.5 99.7 99.5

GCa GCa GCa GCa GCa

Analysis method, molecular weight and mass% purity were provided by the supplier

a

Gas chromatography.

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

precision of ±0.5 K for 18 h to reach solid-liquid equilibrium. Saturated solution was then kept for another 2 h at the same temperature without any agitation for undissolved particles to settle. A small amount of clear saturated solution was transferred quickly to a pre-heated/cooled petridish by a syringe filter and was weighed accurately. The petridish was then kept in vacuum oven at 55+C for complete evaporation of solvent and the weight was taken repeatedly until constant weight was obtained. All the experiments were repeated thrice and the mean value is reported as solubility.

35

3. Thermodynamic models In this work, we have used three different thermodynamic models namely UNIQUAC, NRTL, and Wilson models to correlate the experimental solubility data of pyrazinamide in various solvent-antisolvent mixtures. 3.1. Solid-liquid phase equilibrium According to phase equilibrium theory, a solid-liquid equilibrium phase can be expressed as [11]:

2.3. Thermal analysis Differential scanning calorimetry (DSC Q-20, TA instruments Ltd., USA) was used to determine thermal properties of pyrazinamide and was calibrated using pure indium as reference material. For a particular measurement, 4.2 mg of pyrazinamide was placed in a sealed aluminum pan under nitrogen purging at 50 ml/min. The sample was then heated from 20+C to 400+C at 10+C/min to establish the melting point and enthalpy of fusion of the sample. The latent heat of fusion of pyrazinamide was computed from the area under the peak. 2.4. FTIR analysis Pyrazinamide was characterized by FTIR analysis (PerkinElmer, USA). The number of scans and the resolution were set at 8 and 4 cm1, respectively to record the FTIR spectra using potassium bromide (KBr) pellet method within the wave number range of 4000 to 400. The spectra were analyzed by Spectra 100 software.

 X 



n DCp Tm 1 DHfus Tm DHtr Ttr 1 þ 1  ¼ ln x i gi RTm T RTtr T R T tr¼1  DCp Tm ln 1 þ R T (1) Here xi, gi and DHfus represent the mole fraction of solute at equilibrium, solute activity coefficient in real solution, and enthalpy of fusion, respectively. R is the universal gas constant whereas T and Tm are the experimental temperature and melting point of the solute, respectively. Ttr and DHtr are thermal transition temperature and enthalpy for solid-solid transition (polymorphic form) of solute, respectively, and DCp represents the difference of heat capacities between liquid and solid at temperature T. The activity coefficient gi is considered unity for ideal solutions and Eq. (1) can then be written as

ln

2.5. PXRD(Powder X-ray diffraction) The X-ray diffraction spectrum for pyrazinamide was obtained by PXRD equipment (PANalytical, USA) using Cu Ka radiation. The diffraction angle (2q) range was set from 7+ to 50+ with a step angle of 0.05+. 2.6. FESEM Field emission scanning electron microscope (JEOL, JSM-7610F, Japan) was used to capture images with 150x magnification.

1

!




¼

 X 

n DCp Tm DHtr Ttr 1 þ 1  T RTtr T R T tr¼1

DHfus Tm

RTm xideal i  DCp Tm ln 1 þ R T

(2) In general, DCp has a minor effect for simple uses as small change in pressure doesn't affect the equilibrium appreciably. Thus, the last two terms on the right hand side can be neglected. The second term on the right hand side of Eq. (2) takes into account the solid-solid (polymorphic) transition of pure compounds. Although this is often neglected, a relatively large value of DHtr can

Fig. 2. DSC thermogram of pyarzinamide

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A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

significantly influence the modeling results [11]. Thus Eq. (1) can now be written as

lnðxi Þ ¼

DHfus R




1 1  Tm T




n X DHtr 1 1 þ  lnðgi Þ  Ttr T R tr¼1

fi ¼ (3)

The saturation mole fractions for an ideal solution ðxideal Þ and i real solution (xi) are related by

xi ¼

which is assumed to be 10 for a cyclic compound.

ri xi m P rj xj

(6)

j¼1

qi ¼

q i xi m P qj xj

(7)

j¼1

xideal i

(4)

gi

The activity coefficient gi is generally estimated from experimental data or various thermodynamic models for solutions.

q0 i ¼

q0i xi

m P

j¼1

z li ¼ ðri  qi Þ  ðri  1Þ 2

3.2. UNIQUAC model theory

(8)

q0j xj

(9)

Abrams and Prausnitz were the first to develop the UNIQUAC (Universal Quasi Chemical theory) model in 1975, which is an extension of Guggenheim's quasi chemical theory [1,12]. The activity coefficient for a multi-component system is given by Ref. [13]:

tij ¼ exp

k m X f z q f X lngi ¼ ln i þ qi ln i þ li  i xj lj  q0i ln q0j tji þ q0i xi 2 fi xi

aij and aji are two adjustable interaction parameters and can be estimated from experimental solubility data. Structural parameters ri, qi and q'i for pure components can be obtained from literature [14].

j¼1

 q0i

m X j¼1

j¼1

q0j tji Pm 0 k¼1 qk tkj




 
aij aji ; tji ¼ exp T T

(10)

(5) 3.3. Non-random two-liquid (NRTL) model theory

where qi and q0i are area fractions i.e. the fraction of area around a species filled by molecules of the same species and, fi is the total volume fraction of a species. qi and qi' are pure component structural parameters. z is the coordination number for a molecule,

NRTL excess Gibbs free energy model was proposed by Renon and Prausnitz by combining the concept of local composition by Wilson and two-liquid solution theory by Scott [13,15]. For a multicomponent mixture, the NRTL model is expressed as:

Table 2 DSC thermogram data of pyrazinamide. Peak 1 Ttr, K (onset of transition temperature from a-form to g-form) 420.65 (reported, [7]) 420.05 (reported, [18]) 421.11 (this work)

Peak 2

DHtr, J/g (enthalpy of transition) 11.35 (reported, [7]) 13.24 (reported, [18]) 12.34 (this work)

Tm, K (onset of melting point temperature) DHfus, J/g (heat of fusion) 461.55 (reported, [7]) 200.70 (reported, [7]) 461.45 (reported, [18]) 228.23 (reported, [18]) 462.11 (this work) 206.90 (this work)

The standard uncertainty u in temperature (T) is u(T) ¼ ±0.5 K, and in enthalpy (DH) is u(DH) ¼ ±4%.

Fig. 3. FTIR spectrum of pyrazinamide.

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

37

Fig. 4. X-ray diffraction pattern of two polymorphic forms of pyrazinamide.

Fig. 5. FESEM images of two polymorphic forms of pyrazinamide.

Table 3 Experimental solubility data of pyrazinamide in various acetone-toluene mixtures over the temperature range of 283.15e323.15 K Toluene, wt%

Temperature, K

Mole fraction, (1000 xexp)

Toluene, wt%

Temperature, K

Mole fraction, (1000 xexp)

0

283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15

2.436 3.863 5.830 7.683 11.569 2.300 3.388 5.120 7.252 10.591 2.194 3.241 4.377 6.657 9.601 2.033 2.786 4.161 6.357 8.893

40

283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15

1.490 2.428 3.688 5.336 8.239 1.317 1.972 2.866 4.385 6.842 0.997 1.458 2.337 3.854 5.661 0.604 0.947 1.462 2.875 3.848

10

20

30

50

60

70

The standard uncertainty u in temperature (T) is u(T) ¼ ±0.5 K, in pressure (p) is u(p) ¼ ±0.05 kPa and in solubility (S) measurement is u(S) ¼ ±3%.

38

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

Table 4 Experimental solubility data of pyrazinamide in various acetone-cyclohexane mixtures over the temperature range of 283.15e323.15 K Cyclohexane, wt%

Temperature, K

Mole fraction, (1000 xexp)

Cyclohexane, wt%

Temperature, K

Mole fraction, (1000 xexp)

0

283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15

2.436 3.863 5.830 7.683 11.569 2.222 3.432 4.673 7.008 9.556 1.969 3.155 4.014 5.968 8.482 1.574 2.527 3.274 5.233 7.237

40

283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15

1.260 1.843 2.737 3.947 5.521 0.814 1.408 2.134 2.816 3.746 0.566 0.896 1.109 1.662 2.290 0.164 0.349 0.531 0.890 1.437

10

20

30

50

60

70

The standard uncertainty u in temperature (T) is u(T) ¼ ±0.5 K, in pressure (p) is u(p) ¼ ±0.05 kPa and in solubility (S) measurement is u(S) ¼ ±3%.

Table 5 Experimental solubility data of pyrazinamide in various 1,4-dioxane-toluene mixtures over the temperature range of 293.15e333.15 K Toluene, wt%

Temperature, K

Mole fraction, (1000 xexp)

Toluene, wt%

Temperature, K

Mole fraction, (1000 xexp)

0

293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15

7.195 10.743 13.820 20.229 28.531 5.092 7.692 9.812 14.274 20.016 3.634 5.323 6.759 10.596 13.997 2.520 3.572 5.204 7.052 11.012

40

293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15

1.955 2.779 4.091 5.456 7.816 1.424 2.090 3.107 4.005 5.951 0.912 1.461 2.249 2.987 4.126 0.518 0.803 1.505 1.762 3.057

10

20

30

50

60

70

The standard uncertainty u in temperature (T) is u(T) ¼ ±0.5 K, in pressure (p) is u(p) ¼ ±0.05 kPa and in solubility (S) measurement is u(S) ¼ ±3%.

N P

lngi ¼

experimental solubility data.

tji Gji xj

j¼1 N P

þ Gij xi

i¼1

N X j¼1

xj Gij N P i¼1

Gij xi

"

N P

xi tij Gij #

tij i¼1N

P

(11)

3.4. Wilson model theory

Gij xi

i¼1

gji  gii Dgij ¼ RT RT

(12)

  Gji ¼ exp  aji tji

(13)

The Wilson equation for activity coefficient was first proposed by Wilson in 1964 based on Flory-Huggin's (1942) theory. Since then, it has undergone a number of modifications by Prausnitz et al. [1966], Schreiber et al. [1971] and Hankinson et al. [1972] [16]. For a multicomponent mixture, the Wilson model is represented by the following expression [13,17].

aij ¼ aji

(14)

lngk ¼  ln

tji ¼

where Dgij is interaction energy parameter and aij is nonrandomness factor in the mixture. This model requires only binary parameters (Dgij and aij ) which are estimated from

m  X xL xj Lkj þ 1  Pmi ik j¼1 xj Lij j¼1 i¼1

m X

(15)

where Lkj,Likand Lij are model parameters and can be evaluated as follows.

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

39

Table 6 Experimental solubility data of pyrazinamide in various 1,4-dioxane-cyclohexane mixtures over the temperature range of 293.15e333.15 K Cyclohexane, wt%

Temperature, K

Mole fraction, (1000 xexp)

Cyclohexane, wt%

Temperature, K

Mole fraction, (1000 xexp)

0

293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15

7.195 10.743 13.820 20.229 28.531 5.047 7.202 9.721 13.038 19.839 3.569 4.645 6.638 9.017 13.039 2.453 3.323 4.366 5.749 9.337

40

293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15

1.321 2.019 2.829 3.871 6.570 0.752 1.289 1.926 2.734 4.305 0.516 0.689 1.258 1.444 2.525 0.243 0.477 0.571 0.963 1.489

10

20

30

50

60

70

The standard uncertainty u in temperature (T) is u(T) ¼ ±0.5 K, in pressure (p) is u(p) ¼ ±0.05 kPa and in solubility (S) measurement is u(S) ¼ ±3%.

Table 7 Experimental solubility data of pyrazinamide in various methanol-toluene mixtures over the temperature range of 283.15e323.15 K Toluene, wt%

Temperature, K

Mole fraction, (1000 xexp)

Toluene, wt%

Temperature, K

Mole fraction, (1000 xexp)

0

283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15

2.677 3.981 5.864 8.600 12.248 3.078 4.515 6.428 9.722 13.573 3.530 4.794 7.176 10.127 14.889 3.709 5.083 7.707 11.064 15.546

40

283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15 283.15 293.15 303.15 313.15 323.15

3.789 5.484 8.040 11.317 16.422 3.806 5.497 8.082 11.270 16.079 4.131 5.309 7.653 10.946 15.652 3.365 5.158 7.090 10.552 15.054

10

20

30

50

60

70

The standard uncertainty u in temperature (T) is u(T) ¼ ±0.5 K, in pressure (p) is u(p) ¼ ±0.05 kPa and in solubility (S) measurement is u(S) ¼ ±3%.

Table 8 Comparison of experimental solubility data of pyrazinamide in pure acetone, methanol and 1,4-dioxane with literature data.

Temperature, K 283.15 293.15 303.15 313.15 323.15 333.15

Acetone mole fraction, 1000 xexp

Methanol mole fraction, 1000 xexp

1,4-Dioxane mole fraction, 1000 xexp

This study 2.436 3.863 5.830 7.683 11.569 -

This study 2.677 3.981 5.864 8.600 12.248 -

This study 7.195 10.743 13.820 20.229 28.531

Literature [4] 3.006 4.250 5.810 7.709 9.955 -

Literature [4] 2.604 3.898 5.743 8.338 -

Literature [8] 7.447 10.447 13.634 -

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A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

4.2. Experimental solubility

Lij ¼

 

vj lij  lii vj Dlij ¼ exp  exp  vi RT vi RT

(16)

Lji ¼

 

lji  ljj Dlji vi v ¼ i exp  exp  vj RT vj RT

(17)

Here vi and vj are molar volume of component i and j, respectively. Dlij and Dlji are model parameters indicating interaction energy between component i and j, respectively.

The gravimetrically determined experimental solubility data for pyrazinamide in different acetone-toluene, acetone-cyclohexane, 1,4dioxane-toluene, 1,4-dioxane-cyclohexane and methanol-toluene mixtures over the temperature range of 283.15 K to 333.15 K are presented in Tables 3e7, respectively. The mole fraction solubility of pyrazinamide can be converted to g of solute (pyrazinamide) per 100 g of solvent (solvent-antisolvent mixtures) as follows

S¼ 4. Results and discussion 4.1. Characterization of pyrazinamide crystals The DSC result of commercially available pyrazinamide is presented in Fig. 2. The figure represents three endothermic peaks upon heating a sample of pyrazinamide (4.2 mg) from 293.15 K to 673.15 K. The first peak shows the solid-solid phase transition of a to g form as reported by Castro et al., [2010] [18]. The onset of this transition takes place at a temperature (Ttr) of 421.11 K which matches well with reported literature values (420.65 K and 420.05 K) [7,18]. The phase transition is complete at a temperature of 426.92 K. The area under this peak gives the enthalpy of transition (DHtr) and it is computed as 12.34 J/g. The second sharp peak represents the melting point of pyrazinamide. The onset of melting point temperature (Tm) is 462.11 K which also matches well with literature values (461.45 K and 461.55 K) as reported by Castro et al. [2010] [18] and Baaklini et al. [2015] [7], respectively. The completion of melting takes place at 463.41 K. The area under the peak gives the enthalpy of fusion (DHfus) and it is computed as 206.9 J/g. Third peak represents the complete decomposition of gform pyrazinamide at 556.94 K. The DSC thermogram data along with standard uncertainties are summarized in Table 2. Fig. 3 represents the FTIR spectrum of commercially available pyrazinamide. The PXRD pattern of a-form (commercially available) and d-form (synthesized) of pyrazinamide are shown in Fig. 4 whose 2q values of the peaks match well with the reported literature data for both a and d polymorphic forms of pyrazinamide [18]. The FESEM images of two polymorphic forms of pyrazinamide are shown in Fig. 5.

Table 9 Structural parameters of solvents/antisolvents [14]. Solvent

ri

qi

q'i

Acetone 1,4-Dioxane Methnaol Toluene Cyclohexane Pyrazinamide

2.574 3.185 1.431 3.923 4.046 2.670

2.336 2.640 1.432 2.968 3.240 2.138

2.336 2.640 0.960 2.968 3.249 2.138

xsol MWsol  100 ð1  xsol ÞMWsolvavg

(18)

Here xsol is the mole fraction of the solute, MWsol is the molecular weight of solute, and MWsolvavg is the average molecular weight of solvent mixtures. The average molecular weight of solvent mixture is calculated as:

MWsolvavg ¼ xantisolvent  MWantisolvent þ xsolvent  MWsolvent (19) Here xantisolvent and MWantisolvent are mole fraction and molecular weight of antisolvents (toluene or cyclohexane), respectively. xsolvent and MWsolvent are mole fraction and molecular weight of the solvent considered, respectively. The solubility data exhibit an increasing trend with increasing temperature at constant solventantisolvent ratio for four solvent-antisolvent pairs (acetonetoluene, acetone-cyclohexane, 1,4-dioxane-toluene, and 1,4dioxane-cyclohexane) and decreases at constant temperature with increase in amount of antisolvent in the mixed solvent. This is due to the formation of hydrogen bonds between solvent and antisolvent (toluene or cyclohexane) molecules, thus reducing the free solvent molecules for solvation of pyrazinamide [19]. In case of methanol-toluene system, however, the solubility shows a different trend. The solubility increases initially with increase in toluene weight percent and then gradually decreases. This may be due to the reason that toluene is an aromatic compound with dense electron cloud at the center of the ring which facilitates the polarity of solvent (methanol), thus increasing the solubility. But later with increase in toluene concentration the solubility decreases due to large bulkier group of toluene which decreases the interaction between methanol and pyrazinamide molecules. Although the solubility of pyrazinamide in mixed solvents are not reported yet, the solubility of pyrazinamide in pure acetone, 1,4dioxane and methanol has been reported recently [4,8]. In order to assess the reliability of our experimental data, we compare the reported solubilities for these three pure solvents (acetone, 1,4dioxane and methanol) with our experimental data corresponding to 0 wt% antisolvent composition for these three solvents (Table 3 to Table 7). Such a comparison is summarized in Table 8 and it can be seen that our experimental observations match well with corresponding literature data.

Table 10 Estimated UNIQUAC model parameters for acetone-toluene (or cyclohexane), 1,4-dioxane-toluene (or cyclohexane) and methanol-toluene mixed solvents. Interaction parameters

Pyrazinamide-acetonetoluene

Pyrazinamide-acetonecyclohexane

Pyrazinamide-1,4-dioxanetoluene

Pyrazinamide-1,4-dioxanecyclohexane

Pyrazinamide-methanoltoluene

a12 a21 a13 a31 a23 a32

330.93 8.25 159.39 750.54 118.13 4306.50

495.65 36.99 351.21 48834 108.69 342.10

296.77 53.32 475.31 465.32 331.98 292.99

247.17 31.48 431.15 831.21 221.99 116.99

395.71 13.26 109.75 413.06 36.25 84.74

subscript 1,2,3 represents pyrazinamide, solvent (acetone, 1,4-dioxane or methanol) and toluene (or cyclohexane), respectively.

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54 exp

adjustable parameters, xi and xcal are the experimental and the i model calculated solubility, respectively.

4.3. Correlation of experimental solubility data As mentioned before, three different thermodynamic models (UNIQUAC, NRTL, and Wilson) were used to correlate experimental solubility data. The adjustable parameters of these models were obtained by regression of the experimental solubility data using a nonlinear optimization technique on MATLAB environment. The following objective function (F) that represents the difference between experimental solubility and model predicted solubility was minimized using functions available in MATLAB optimization toolbox.

minF ¼ w

N  X

xexp  xcal i i

2

41

(20)

i¼1

Here N is the number of experimental data, w is the set of

4.3.1. Algorithm The following algorithm was used for estimating the adjustable parameters for the thermodynamic models: 1. For a given temperature and solvent-antisolvent mixture, the initial guess for mole fraction was made by Eq. (3) considering it to be an ideal solution (gi equal to 1). 2. The average molecular weight of solvent was then calculated based on the composition of solvent-antisolvent mixtures (Eq. (19)) and the mole fraction of each component was computed. 3. The activity coefficient was then computed from different model equations (Eqs. (5), (11) and (15)) using initially guessed mole fraction of solute.

Fig. 6. Comparison of UNIQUAC model predictions and experimental solubility data of pyrazinamide in various (a) acetone-toluene and (b) acetone-cyclohexane mixtures at different temperatures: 283.15 K(circle,+), 293.15 K(cross,), 303.15 K(square,,), 313.15 K(plus,þ), 323.15 K(diamond, ).

⋄

42

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

4. Using the calculated activity coefficient, a new mole fraction of solute was computed using Eq. (4). 5. If the difference between initially guessed mole fraction and computed new mole fraction was less than a predefined tolerance value (104) then the new mole fraction was the desired mole fraction for calculating solubility. Otherwise, the estimated mole fraction was considered as new initial guess for mole fraction and the previous steps were followed. 6. Once we obtained the desired mole fraction solubility by repeated iteration, it can also be used to calculate solubility in g of solute per 100 g solvent by Eq. (18).

4.3.2. UNIQUAC model The adjustable binary interaction parameters for UNIQUAC model are aij and aji. The structural parameters for acetone, methanol, 1,4-dioxane, toluene and cyclohexane for UNIQUAC model

were obtained from literature [14] and are presented in Table 9. The parameter q' is usually the same as q for all solvents except water and alcohols. There is no information available about the structural parameters for pyrazinamide. For such cases, Catarina et al. [20] suggested an alternate way to estimate the structural parameters.

r ¼ 0:028281Vm

q¼

(21)

ðz  2Þr 2ð1  lÞ þ z z

(22)

Here Vm is the molar volume of pyrazinamide at 289.15 K which was calculated by group contribution method as 94.5 cm3/mol [20]. The coordination number Z and bulk factor l for cyclic molecules are assumed to be 10 and 1, respectively. The regressed adjustable parameters for UNIQUAC model are presented in Table 10. The model computed solubility along with experimental solubility for

Fig. 7. Comparison of UNIQUAC model predictions and experimental solubility data of pyrazinamide in various (a) 1,4-dioxane-toluene and (b) 1,4-dioxane-cyclohexane mixtures at different temperatures: 293.15 K(circle,+), 303.15 K(cross,), 313.15 K(square,,), 323.15 K(plus,þ), 333.15 K(diamond, ).

⋄

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

43

Fig. 8. Comparison of UNIQUAC model predictions and experimental solubility data of pyrazinamide in various methanol-toluene mixtures at different temperatures: 283.15 K(circle,+), 293.15 K(cross,), 303.15 K(square,,), 313.15 K(plus,þ), 323.15 K(diamond, ).

⋄

acetone-toluene (or cyclohexane), 1,4-dioxane-toluene (or cyclohexane) and methanol-toluene systems are shown in Figs. 6 to 8. It can be seen that the model represents the experimental data very well. 4.3.3. NRTL model NRTL model has two adjustable binary interaction parameters, aij and gji. The value of aij generally lies within 0.2e0.47 and this range was set during regression of solubility data. The optimized adjustable parameters for NRTL model for all five solventantisolvent systems are presented in Table 11. The model computed solubility matches very well with experimental data for all the systems as shown in Figs. 9 to 11. The mutual interaction energy (Dg12 and Dg21) of pyrazinamide-acetone is higher than pyrazinamide-1,4-dioxane which shows that pyrazinamide can easily interact with acetone than 1,4-dioxane. However, the mutual interaction of pyrazinamide-methanol is more than pyrazinamideacetone. The negative interaction energy of pyrazinamidemethanol (Dg12) shows that the interaction energy between pyrazinamide-methanol is less than the interaction energy between methanol-methanol. Dg13 and Dg31 is positive for all the systems investigated here. Thus, both toluene and cyclohexane can be considered good antisolvents as more energy is required for interactions between pyrazinamide and antisolvents. Again the mutual interaction energy between pyrazinamide and cyclohexane is more or nearly same compared to interaction energy between

pyrazinamide and toluene. This justifies that cyclohexane is better antisolvent than toluene for pyrazinamide. The mutual interaction energy between solvents and antisolvents (Dg23 and Dg32) are very low which signify that the solvents used are easily miscible in the antisolvents. 4.3.4. Wilson model The binary interaction parameters lij and lji for Wilson model depend on the molar volume of the components involved. The obtained regressed parameters for all five solvent-antisolvent mixtures are presented in Table 12. The molar volumes of acetone, 1,4-dioxane, methanol, toluene and cyclohexane are obtained from literature [13] and shown in Table 13. The model predicted solubility along with the experimental observations for all five systems are shown in Figs. 12 to 14, respectively, and it can be seen that the Wilson model also correlates the experimental observations very well. It may be noted that the mutual energy interaction parameters (l12 and l21 ) between pyrazinamide-acetone for acetone-toluene (or cyclohexane) system and pyrazinamide-1,4-dioxane for 1,4-dioxane-toluene (or cyclohexane) system are nearly same as presented in Table 12. The values of the mutual energy interaction parameters between pyrazinamide and cyclohexane (l13 and l31 ) for all systems studied are higher than mutual energy interaction parameters between pyrazinamide and toluene. This signifies that interaction between pyrazinamide and cyclohexane requires higher

Table 11 Estimated NRTL model parameters for acetone-toluene (or cyclohexane), 1,4-dioxane-toluene (or cyclohexane) and methanol-toluene mixed solvents. Interaction parameters

Pyrazinamide-acetonetoluene

Pyrazinamide-acetonecyclohexane

Pyrazinamide-1,4-dioxanetoluene

Pyrazinamide-1,4-dioxanecyclohexane

Pyrazinamide-methanoltoluene

Dg12 Dg21 Dg13 Dg31 Dg23 Dg32 a12 ¼ a21 a13 ¼ a31 a23 ¼ a32

5340 1519.50 2063 13980 935.06 18246 0.37 0.23 0.20

8728.40 2197.30 11646 15389 7950.10 10931 0.47 0.21 0.47

4810.40 432.34 7001.30 8210.30 3668 6311.70 0.28 0.20 0.20

3781.80 548.43 6183.90 12609 1999.90 4724.40 0.47 0.20 0.20

6511.70 15411 81.09 4520.90 2797.80 2248.40 0.21 0.20 0.47

subscript 1,2,3 represents pyrazinamide, solvent (acetone, 1,4-dioxane or methanol) and toluene (or cyclohexane), respectively.

44

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

Fig. 9. Comparison of NRTL model predictions and experimental solubility data of pyrazinamide in various (a) acetone-toluene and (b) acetone-cyclohexane mixtures at different temperatures: 283.15 K(circle,+), 293.15 K(cross,), 303.15 K(square,,), 313.15 K(plus,þ), 323.15 K(diamond, ).

⋄

energy which is also indicated by NRTL interaction parameters. Again the mutual energy interaction parameters of solventscyclohexane (l23 and l32 ) are less than such interaction parameters for solvents-toluene system. Thus, the energy required to form a bond between solvents and cyclohexane is less compared to bond formation between solvents and toluene. Also, the bond formation energy between pyrazinamide and cyclohexane is more compared to pyrazinamide and toluene which represents that it is difficult for pyrazinamide to form bond with cyclohexane rather than with toluene. Thus we can conclude that cyclohexane is a better antisolvent than toluene which is also evident from our experimental solubility data. 4.3.5. Evaluation of thermodynamic models The relative average deviation (RAD) and root mean square deviation (RMSD) of thermodynamic models indicate the goodness of correlation with experimental solubility and can be

computed as follows. N  2P

6 RMSD ¼ 4i¼1

exp

xi

 xcal i

N

  N xexp  xcal  1 X  i i  RAD ¼    xexp  N i¼1

2 31=2 7 5

(23)

(24)

i

Here xiexp and xical are experimental and model calculated solubility values, respectively. N refers to the number of experimental solubility data. The RAD and RMSD values for all the thermodynamic models used for five ternary systems are presented in Table 14. Comparing RAD% and RMSD values, it may be noted that all the thermodynamic models correlate the data reasonably well.

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

45

Fig. 10. Comparison of NRTL model predictions and experimental solubility data of pyrazinamide in various (a) 1,4-dioxane-toluene and (b) 1,4-dioxane-cyclohexane mixtures at different temperatures: 293.15 K(circle,+), 303.15 K(cross,), 313.15 K(square,,), 323.15 K(plus,þ), 333.15 K(diamond, ).

⋄

Inspecting Table 14, we find that the RAD values are minimum for methanol-toluene system and maximum for acetone-cyclohexane system. The maximum and minimum RAD values are 12% (Wilson model for 1,4-dioxane-cyclohexane system) and 0.2% (NRTL model for methanol-toluene system), respectively. Similarly, the maximum and minimum values of RMSD are 5.21 (Wilson model for 1,4-dioxane-cyclohexane system) and 2.71 (NRTL model for acetone-cyclohexane), respectively. Thus all the thermodynamic models studied are able to successfully correlate the experimental data of all five systems studied. For evaluating the best fit thermodynamic model, one can also use Akaike Information Criterion (AIC) which in its simplified form, is obtained as follows [21].

RSS ¼

(25)

xexp  xcal

2

(26)

i¼1

Here N is the number of experimental data, RSS is residual sum of squares, xexp and xcal are experimental and model computed solubility data of pyrazinamide, and k is the number of estimable parameters of the model. The model with the lowest value of AIC can, in general, be considered as the best fit model. We also calculate Akaike weight to evaluate the best model among the three models studied. The model with highest Akaike weights (wi) is considered the best fit model and can be computed as follows:

wi ¼ AIC ¼ N lnðRSS=NÞ þ 2k

N  X

expðAICmin  AICi Þ=2 M P expðAICmin  AICi Þ=2 i¼1

(27)

46

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

Fig. 11. Comparison of NRTL model predictions and experimental solubility data of pyrazinamide in various methanol-toluene mixtures at different temperatures: 283.15 K(circle,+), 293.15 K(cross,), 303.15 K(square,,), 313.15 K(plus,þ), 323.15 K(diamond, ).

⋄

Table 12 Estimated Wilson model parameters for acetone-toluene (or cyclohexane), 1,4-dioxane-toluene (or cyclohexane) and methanol-toluene mixed solvents. Interaction parameters

Pyrazinamide-acetonetoluene

Pyrazinamide-acetonecyclohexane

Pyrazinamide-1,4-dioxanetoluene

Pyrazinamide-1,4-dioxanecyclohexane

Pyrazinamide-methanoltoluene

l12 l21 l13 l31 l23 l32

0.073 0.014 1.045 0.395 0.499 0.192

0.069 0.014 2.503 2.069 0.037 2.497

0.048 0.014 0.527 0.003 0.007 0.016

0.051 0.015 0.576 0.274 0.000 0.263

0.061 0.001 0.032 0.285 0.031 0.282

subscript 1,2,3 represents pyrazinamide, solvent (acetone, 1,4-dioxane or methanol) and toluene (or cyclohexane), respectively.

Table 13 Molar volume of different components. Solvents/solute

molar volume (cm3.mol1)

Pyrazinamide Acetone Methanol 1,4-Dioxane Cyclohexane Toluene

94.50 74.17 40.46 94.50 108.10 106.30

(Ref (Ref (Ref (Ref (Ref (Ref

[20]) [13]) [13]) [13]) [13]) [13])

where M is number of model used to correlate the experimental data, AICmin is the minimum value of AIC obtained from the selected models, and AICi is the AIC value of the ith model. The AIC values and Akaike weights for all thermodynamic models are presented in Table 15. Considering the lowest of AIC values and the highest of Akaike weights as given in Table 15, we find that UNIQUAC model performs best in correlating the solubility data for all systems except methanol-toluene and acetone-cyclohexane systems where the NRTL model gives a better fit. 4.3.6. van't Hoff equation The van't Hoff equation can also be used to compute solubility in real solutions. According to the van't Hoff equation, the logarithm of mole fraction solubility shows a linear relationship with the reciprocal of the absolute temperature as follows:

lnx ¼ 

DHd RT

þ

DSd R

(28)

where R is the gas constant, and DHd and DSd are the enthalpy of dissolution and entropy of dissolution, respectively. The van't Hoff plot of lnx versus T1 for acetone-toluene (or cyclohexane), 1,4dioxane-toluene (or cyclohexane) and methanol-toluene systems are plotted in Figs. 15 to 17. The DHd and DSd values are calculated from slopes and intercepts, respectively for different solventantisolvent ratios at different temperatures. These values are presented in Tables 16e18. The Gibb's free energy DGd can be calculated as

DGd ¼ DHd  Thm  DSd

(29)

where Thm is the harmonic mean temperature and can be calculated as

Thm ¼

N N P 1 i¼1

(30)

Ti

Here N is the number of temperature (T) data. The harmonic mean temperature was calculated as 302.48 K for acetone-toluene (or cyclohexane) and methanol-toluene systems. For 1,4-dioxanetoluene (or cyclohexane) system the harmonic mean was calculated as 312.51 K. The relative enthalpy contribution (%zH ) and relative entropy contribution (%zTS ) can be computed as follows and are presented in Tables 16e18.

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47

Fig. 12. Comparison of Wilson model predictions and experimental solubility data of pyrazinamide in various (a) acetone-toluene and (b) acetone-cyclohexane mixtures at different temperatures: 283.15 K(circle,+), 293.15 K(cross,), 303.15 K(square,,), 313.15 K(plus,þ), 323.15 K(diamond, ).

⋄

48

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

Fig. 13. Comparison of Wilson model predictions and experimental solubility data of pyrazinamide in various (a) 1,4-dioxane-toluene and (b) 1,4-dioxane-cyclohexane mixtures at different temperatures: 293.15 K(circle,+), 303.15 K(cross,), 313.15 K(square,,), 323.15 K(plus,þ), 333.15 K(diamond, ).

⋄

jDHd j %zH ¼ 100  jDHd j þ jThm DSd j

(31)

toluene (or cyclohexane). But DGd decreases with increase in toluene wt% for methanol-toluene system. Further investigation shows that DHd is the main contributor towards DGd and solute dissolution, because %zH values are always greater than 62%.

jThm DSd j jDHd j þ jThm DSd j

(32)

5. Conclusions

%zTS ¼ 100 

The correlation coefficient values show that good correlation of minimum R20.971 and maximum RMSE0.124 are obtained for all five systems. It can be seen that DHd has positive values in between 25.972 and 40.198 kJ mol1 for all wt% of toluene and cyclohexane in all five systems, indicating that all processes undergo endothermic dissolution. DGd values (between 11.020 and 19.172 kJ mol1) for all systems are positive which indicate pyrazinamide can be easily recrystallized from all the five solventantisolvent systems. The DGd increases with increase in antisolvent wt% for acetone-toluene (or cyclohexane) and 1,4-dioxane-

In this work, we have reported the solubility of pyrazinamide in five different solvent-antisolvent systems (acetone-toluene, acetone-cyclohexane, 1,4-dioxane-toluene, 1,4-dioxane-cyclohexane and methanol-toluene) over a temperature range of 283.15 K to 333.15 K and antisolvent (toluene and cyclohexane) weight percentage of 0e70 wt%. The temperature range for acetone and methanol systems is chosen from 283.15 K to 323.15 K due to boling point limitation. Similarly, for 1,4-dioxane the temperature range is chosen from 293.15 K to 333.15 K due to freezing point limitation of solvent. The solubility of pyrazinamide shows an

A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

49

Fig. 14. Comparison of Wilson model predictions and experimental solubility data of pyrazinamide in various methanol-toluene mixtures at different temperatures: 283.15 K(circle,+), 293.15 K(cross,), 303.15 K(square,,), 313.15 K(plus,þ), 323.15 K(diamond, ).

⋄

Table 14 Estimated error values for solubility models. model

NRTL UNIQUAC Wilson

Pyrazinamide-acetonetoluene

Pyrazinamide-acetonecyclohexane

Pyrazinamide-1,4dioxane-toluene

Pyrazinamide-1,4dioxane-cyclohexane

Pyrazinamidemethanol-toluene

RAD%

104RMSD

RAD%

104RMSD

RAD%

104RMSD

RAD%

104RMSD

RAD%

104RMSD

1.41 1.70 8.10

3.28 3.37 4.93

2.34 4.55 11.73

2.71 3.44 4.28

0.37 0.56 5.77

4.00 4.03 4.50

1.96 2.98 11.88

4.76 4.85 5.21

0.19 0.70 0.59

4.23 4.68 5.07

Table 15 AIC values and Akaike weights for the thermodynamic models studied. Solution mixtures/Models Acetone-toluene NRTL UNIQUAC Wilson Acetone-cyclohexane NRTL UNIQUAC Wilson 1,4-Dioxane-toluene NRTL UNIQUAC Wilson 1,4-Dioxane-cyclohexane NRTL UNIQUAC Wilson Methanol-toluene NRTL UNIQUAC Wilson

104RSS

N

Parameters(k)

AIC

eðAICmin AICi Þ=2

Akaike weight wi

0.0121 0.0129 0.0320

40 40 40

9 6 6

674.59 677.96 641.67

0.1860 1.0000 0.0000

0.1568 0.8432 0.0000

0.0074 0.0121 0.0211

40 40 40

9 6 6

694.43 680.67 658.34

1.0000 0.0010 0.0000

0.9990 0.0010 0.0000

0.0320 0.0325 0.0413

40 40 40

9 6 6

635.66 641.03 631.47

0.0680 1.0000 0.0084

0.0632 0.9290 0.0078

0.0439 0.0456 0.0525

40 40 40

9 6 6

623.01 627.48 621..88

0.1069 1.0000 0.0608

0.0915 0.8564 0.0521

0.0089 0.0113 0.0131

40 40 40

9 6 6

687.01 683.17 677.41

1.0000 0.1467 0.0082

0.8659 0.1270 0.0071

50

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Fig. 15. The van't Hoff plots of pyrazinamide in (a) acetone-toluene and (b) acetone-cyclohexane mixtures of various compositions: 0 wt%(circle,+), 10 wt%(square, ,), 20 wt %(diamond, ), 30 wt%(asterik,*), 40 wt%(cross,), 50 wt%(plus, þ), 60 wt%(triangle, △), 70 wt%(star, ☆).

⋄

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51

Fig. 16. The van't Hoff plots of pyrazinamide in (a) 1,4-dioxane-toluene and (b)1,4-dioxane-cyclohexane mixtures of various compositions: 0 wt%(circle,+), 10 wt%(square, ,), 20 wt %(diamond, ), 30 wt%(asterik,*), 40 wt%(cross,), 50 wt%(plus, þ), 60 wt%(triangle, △), 70 wt%(star, ☆).

⋄

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A. Maharana, D. Sarkar / Fluid Phase Equilibria 497 (2019) 33e54

Fig. 17. The van't Hoff plots of pyrazinamide in (a) methanol-toluene mixtures of various compositions: 0 wt%(circle,+), 10 wt%(square, ,), 20 wt%(diamond, 40 wt%(cross,), 50 wt%(plus, þ), 60 wt%(triangle, △), 70 wt%(star, ☆).

⋄), 30 wt%(asterik,*),

Table 16 Thermodynamic parameters of pyrazinamide dissolution in acetone-toluene and acetone-cyclohexane (0e70 wt% of toluene or cyclohexane) mixtures at harmonic mean temperature of 302.48 K and correlation coefficients (R2 and RMSE). Toluene wt%

DHd1 kJ.mol

1 DSd 1 JK mol

DGd1 kJ.mol

%zH

%zTS

R2

RMSE

0 10 20 30 40 50 60 70 Cyclohexane wt% 0 10 20 30 40 50 60 70

28.974 29.024 27.893 28.733 32.025 31.086 33.779 36.606

52.469 51.863 47.423 49.368 59.046 54.340 61.399 67.285

13.103 12.337 13.549 13.800 14.165 14.649 15.207 16.254

64.61 64.91 66.04 65.80 64.19 65.41 64.52 64.27

35.39 35.09 33.96 34.19 35.79 34.59 35.47 35.73

0.996 0.999 0.995 0.995 0.999 0.995 0.996 0.989

0.043 0.021 0.046 0.049 0.026 0.052 0.055 0.093

28.974 27.644 27.078 28.749 28.275 28.650 25.972 40.198

52.469 46.899 43.956 47.930 44.264 42.692 29.697 70.698

13.103 13.457 13.782 14.251 14.887 15.736 16.990 19.005

64.61 66.08 67.07 66.48 67.86 68.93 74.30 65.48

35.39 33.91 32.93 33.52 32.13 31.07 25.69 35.52

0.996 0.998 0.993 0.991 0.999 0.982 0.989 0.993

0.043 0.028 0.053 0.056 0.013 0.079 0.058 0.071

Table 17 Thermodynamic parameters of pyrazinamide dissolution in 1,4-dioxane-toluene and 1,4-dioxane-cyclohexane (0e70 wt% of toluene or cyclohexane) mixtures at harmonic mean temperature of 312.51 K and correlation coefficients (R2 and RMSE). Toluene wt%

DHd1 kJ.mol

1 DSd 1 JK mol

DGd1 kJ.mol

%zH

%zTS

R2

RMSE

0 10 20 30 40 50 60 70 Cyclohexane wt% 0 10 20 30 40 50 60 70

27.481 26.526 26.355 26.044 31.234 34.173 31.736 35.117

52.672 46.530 42.646 38.473 51.256 57.002 44.933 51.021

11.020 11.984 13.028 14.021 15.216 16.359 17.694 19.172

62.54 64.59 66.42 68.42 66.10 65.73 69.33 68.77

37.46 35.41 33.59 31.58 33.89 34.27 30.67 31.23

0.995 0.989 0.993 0.977 0.987 0.994 0.971 0.979

0.045 0.064 0.051 0.090 0.079 0.058 0.124 0.115

27.484 27.232 27.464 29.418 27.983 28.514 30.410 35.241

52.684 49.008 46.871 50.339 43.512 42.786 45.884 57.362

11.020 11.916 12.817 13.686 14.385 15.143 16.071 17.315

62.54 64.00 65.22 65.16 67.29 68.08 67.96 66.28

37.46 35.99 34.78 34.84 32.70 31.92 32.04 33.72

0.995 0.995 0.991 0.994 0.999 0.996 0.995 0.981

0.446 0.045 0.056 0.053 0.024 0.039 0.049 0.111

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Table 18 Thermodynamic parameters of pyrazinamide dissolution in methanol-toluene (0e70 wt% of toluene) mixtures at harmonic mean temperature of 302.48 K and correlation coefficients (R2 and RMSE). Toluene wt%

DHd1 kJ.mol

1 DSd 1 JK mol

DGd1 kJ.mol

%zH

%zTS

R2

RMSE

0 10 20 30 40 50 60 70

28.997 28.456 27.497 27.640 27.742 27.308 25.634 28.318

53.051 53.119 51.264 52.665 53.598 52.221 46.504 54.530

12.950 12.388 11.990 11.710 11.529 11.512 11.567 11.824

64.38 63.91 63.94 63.44 63.12 63.35 64.57 63.19

35.63 36.09 36.06 36.56 36.89 36.65 35.43 36.81

0.999 0.998 0.995 0.997 0.999 0.999 0.991 0.998

0.014 0.027 0.046 0.036 0.022 0.017 0.060 0.030

increasing trend with increase in temperature at constant solvent composition and decreasing trend with increase in antisolvent ratio for all systems except for methanol-toluene system. The methanoltoluene system shows an increasing trend with increase in antisolvent weight percent upto 40 wt% and then decreases with increase in antisolvent weight per cent. Three different thermodynamic models namely UNIQUAC, Wilson, and NRTL are successfully used to correlate the experimental solubility data. The energy interaction parameters of NRTL and Wilson models indicate that cyclohexane is better antisolvent than toluene which is also evident from the experimental data presented. According to Akaike Information Criterion (AIC), the UNIQUAC model best fits the experimental data for all systems except acetone-cyclohexane and methanol-toluene systems for which NRTL represents experimental data better. The minimum Relative Average Deviation (RAD) of 0.2% is obtained for NRTL model correlation on methanoltoluene system and the maximum RAD (12%) is obtained for Wilson model correlation on acetone-cyclohexane system. Similarly, the maximum and minimum values of RMSD are 5.21 (Wilson model for 1,4-dioxane-cyclohexane system) and 2.71 (NRTL model for acetone-cyclohexane), respectively. Further, the van't Hoff equation is used to predict the enthalpy of dissolution, entropy of dissolution and Gibb's free energy of dissolution which indicate that all five systems are endothermic and enthalpy driven.

Greek letters polymorphic form of solute polymorphic form of solute activity coefficient of solute, polymorphic form of solute polymorphic form of solute non-randomness factor area fraction of the component i fi solute segment fraction tij parameter for binary interaction

a b g d aij qi and q0i

Superscript and Subscript C combinatorial part R residual part e experimental data c calculated data i, j component i or j d dissolution Abbreviations MW Molecular weight RAD Relative Average Deviation RMSD Root Mean Square Deviation AIC Akaike Information Criterion References

Acknowledgment The financial assistance received from the Science and Engineering Research Board (SERB), Government of India, New Delhi (Project File Number: EMR/2015/002266) is gratefully acknowledged. Nomenclature R T Ttr DHtr Tm DHfus z xi xideal i xexp i xcal i S N DCp DHd DSd gij

Gas constant, R ¼ 8.3145 J/(mol K) experimental temperature(K) onset of transition temperature enthalpy of transition onset of melting point temperature heat of fusion coordination number mole fraction of solute saturation mole fration in an ideal solution experimental mole fraction solubility data model computed mole fraction solubility data solubility of solute number of experimental data points difference in heat capacities difference in dissolution enthalpy(KJ/mol) difference in dissolution entropy(JK1mol1) parameter for energy interaction

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