Solid-liquid phase equilibrium and thermodynamic analysis of griseofulvin in twelve mono-solvents

Journal Pre-proof Solid-liquid phase equilibrium and thermodynamic analysis of griseofulvin in twelve mono-solvents Shaolei Zhao, Yiming Ma, Junbo Gong, Baohong Hou, Weiwei Tang PII:

S0167-7322(19)34929-3

DOI:

https://doi.org/10.1016/j.molliq.2019.111861

Reference:

MOLLIQ 111861

To appear in:

Journal of Molecular Liquids

Received Date: 3 September 2019 Revised Date:

21 September 2019

Accepted Date: 29 September 2019

Please cite this article as: S. Zhao, Y. Ma, J. Gong, B. Hou, W. Tang, Solid-liquid phase equilibrium and thermodynamic analysis of griseofulvin in twelve mono-solvents, Journal of Molecular Liquids (2019), doi: https://doi.org/10.1016/j.molliq.2019.111861. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Graphical abstract The crystal structure analysis reveals that the H⋯H and O⋯H contacts apparently dominate in the solid-state structure and the solubility of griseofulvin is monotonously rising with increasing temperature in all the twelve mono-solvents. The solubility spectra reveal that the solvent polarity plays a key role in the solid-liquid phase equilibrium behavior of griseofulvin in the studied solvent systems.

Solid-liquid phase equilibrium and thermodynamic analysis of griseofulvin in twelve mono-solvents

1 2

3 Shaolei Zhaoa,b, Yiming Maa,b, Junbo Gonga,b, Baohong Houa,b, Weiwei Tanga,b,*

4 5

a

6

Tianjin University, Tianjin 300072, People’s Republic of China

7

b

8

People’s Republic of China

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering,

The Co-Innovation Center of Chemistry and Chemical Engineering of Tianjin, Tianjin 300072,

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

AUTHOR INFORMATION

Corresponding Author *

E-mail: [email protected] (W. Tang). Tel: 86-22-27405754, Fax: 86-22-27374971.

25 26 27 28

1

1

Abstract

2

The structure and properties of griseofulvin (GSF) were investigated in both solution and solid

3

phases. The intermolecular interactions within griseofulvin crystal structure probed by Hirshfeld

4

surface analysis reveal that the H⋯H and O⋯H contacts apparently dominate in the solid-state

5

structure. The solution thermodynamic properties including solid-liquid phase equilibrium solubility

6

and thermodynamic functions of mixing were determined in twelve solvents (methanol, ethanol,

7

n-propanol, n-butanol, isobutanol, methyl acetate, ethyl acetate, n-propyl acetate, n-butyl acetate,

8

isopropyl acetate, isobutyl acetate and acetonitrile). The equilibrium solubility data was measured by

9

gravimetric method at temperature ranging from 283.15 to 323.15 K, and the measurement results

10

show the solubility is monotonously rising with increasing temperature as expected in all solvents.

11

Besides, the investigations over the effect of solvent properties in terms of solvent polarity, hydrogen

12

bonding donor and acceptor propensity, as well as cohesive energy density on solid-liquid phase

13

equilibrium behaviors reveal that the solvent polarity determines the solubility of griseofulvin in the

14

studied solvent systems. Further, the statistical correlations were well performed by the modified

15

Apelblat equation, λh equation, and NRTL model, in which the modified Apelblat equation receives

16

the best fitting performance. Finally, thermodynamic functions of mixing (enthalpy, entropy, and

17

Gibbs energy) were derived, and the results suggest a spontaneous, exothermic and entropy-driven

18

mixing process. All the thermodynamic data and models presented here will certainly provide

19

fundamental basis for separation and purification of griseofulvin in industrial production.

20 21 22 23 24

Keywords: Solid-liquid phase equilibrium; Thermodynamic analysis; Intermolecular interactions;

25

Solvent properties; Griseofulvin

26 27 28 2

1

1. Introduction

2

Griseofulvin (C17H17ClO6, GSF, Fig.1) is a classic antifungal drug initially isolated from

3

penicillium griseofulvum in 1939 by Oxford et al, and mainly used for the treatment of tinea disease

4

[1]. More recently, griseofulvin has attracted renewed attention due to reports on the biological

5

activity toward a range of mammalian cancer cell lines [2]. The first crystal structure of GSF was

6

reported in 1977 [3], which has a P41 space group, and subsequent intensive works of solution

7

crystallization consistently produced the same crystal form (form I) despite variations of

8

crystallization protocols [4-6], thus it has long been believed to exist in only one crystalline phase.

9

But recent studies found two new polymorphic phases of griseofulvin (named form II and form III)

10

during the melt crystallization process [7]. While metastable compared to form I, these two new

11

forms have a long lifetime at room temperature.

12 13

Fig. 1. Molecular structure of griseofulvin.

14

As an effective antibiotic, griseofulvin can be obtained by fermentation from various

15

penicillium and then refined by extraction, concentration, and crystallization in sequence [8].

16

Solution crystallization is an important purification technology and commonly applied to produce

17

active pharmaceutical ingredients (APIs) with high quality in pharmaceutical industry, and it is the

18

key step that influences the quality of final products, especially in crystal habit, purity, and crystal

19

size. In order to achieve better design and control of crystallization process, the fundamental

20

understandings of solid-liquid phase equilibrium and basic thermodynamic data such as solubility,

21

thermodynamic models, and mixing peripeties are the first and foremost [9]. Moreover, the solubility

22

of solid compounds in solvents is also of scientific interest for the development of the solution theory

23

[10]. 3

1

Since 1939 when griseofulvin was found at the first time, research topics mainly focused on

2

micronization methods and dissolution properties of this hydrophobic compound [11-13], but few

3

attentions were paid on crystallization and thermodynamic studies. In our previous work, the

4

solid-liquid phase equilibrium of griseofulvin in binary solvent mixtures of ketones (good solvent)

5

with isopropanol (anti-solvents) was investigated in order to precisely design and control the

6

antisolvent crystallization which is considered as a potentially scalable technique of micronization

7

for the production of ultrafine particles of poorly water-soluble griseofulvin [14]. However, to our

8

best of knowledge, there is no literature making a systematical study on the solubility of griseofulvin

9

in different mono-solvents such as alcohols, esters, and nitriles, which is essential for the selection of

10

solvents for crystallization and other operation process [15]. Therefore, a thorough investigation of

11

equilibrium solubility and thermodynamic properties of griseofulvin in different mono-solvent

12

systems is critical and desirable.

13

In this work, the structure and properties of griseofulvin were investigated in both solution and

14

solid phases. The intermolecular interactions within crystal structure were probed by Hirshfeld

15

surface analysis. The solid-liquid phase equilibrium solubility of griseofulvin was firstly determined

16

in twelve solvents (methanol, ethanol, n-propanol, n-butanol, isobutanol, methyl acetate, ethyl

17

acetate, n-propyl acetate, n-butyl acetate, isopropyl acetate, isobutyl acetate and acetonitrile) by

18

gravimetric method at temperature ranging from 283.15 K to 323.15 K under atmospheric pressure

19

(0.1 MPa). The effect of solvent properties on griseofulvin solubility behaviors was then investigated

20

in terms of solvent polarity, hydrogen bonding donor and acceptor propensity, and cohesive energy

21

density. Experimental solubility data was further correlated by three thermodynamic models

22

including the modified Apelblat equation, λh equation, and NRTL model. Finally, thermodynamic

23

functions (enthalpy, entropy, and Gibbs free energy) of mixing were derived and their indications on

24

equilibrium thermodynamic behaviors were discussed.

25 26 27 28 29

2. Materials and methods 2.1. Materials Griseofulvin was obtained from Bide Pharmaceutical Co., Ltd. (Shanghai, China) with mass 4

1

percentage purity > 98.0%. The detailed description of the organic solvents used in this work is given

2

in Table 1. All chemicals were used as received.

3 4 5

Table 1 Detail information of materials used in this study.

Chemicals

CAS registry no.

Griseofulvin

126-07-8

Methanol

67-56-1

Ethanol

64-17-5

n-Propanol

71-23-8

n-Butanol

71-36-3

Isobutanol

78-83-1

Methyl acetate

79-20-9

Ethyl acetate

141-78-6

n-Propyl acetate

109-60-4

n-Butyl acetate

123-86-4

Isopropyl acetate

108-21-4

Isobutyl acetate

110-19-0

Acetonitrile

75-05-8

6

a

High performance liquid chromatography.

7

b

Gas chromatography.

Mass percentage Analysis purity method

Source Bide Pharmaceutical Co., Ltd., China Tianjin Damao Chemical Reagent Factory, China Tianjin Li Anlong Bohua Pharmaceutical Chemical Co., Ltd., China Tianjin Li Anlong Bohua Pharmaceutical Chemical Co., Ltd., China Tianjin Li Anlong Bohua Pharmaceutical Chemical Co., Ltd., China Tianjin Fuchen Chemical Reagent Factory, China Tianjin Li Anlong Bohua Pharmaceutical Chemical Co., Ltd., China Tianjin Yuanli Chemical Co., Ltd., China Shanghai Aladdin Industrial Corporation, China

98.37%

HPLCa

≥99.5%

GCb

≥99.7%

GCb

≥99.0%

GCb

≥99.5%

GCb

≥99.0%

GCb

≥99.0%

GCb

≥99.5%

GCb

≥99.0%

GCb

Tianjin Kermel Chemical ≥99.5% Reagent Co., Ltd., China

GCb

Tianjin Yuanli Chemical ≥99.0% Co., Ltd., China Chengdu Kelon Chemical ≥98.5% Reagent Factory, China Tianjin Yuxiang Technology ≥99.5% Co., Ltd., China

5

GCb GCb GCb

1

2.2. Powder X-ray diffraction analysis

2

Powder X-ray diffractometer was used to identify any polymorphic behaviors such as phase

3

transformation, new polymorphs and solvates throughout the experiments. The X-ray diffraction

4

measurement was performed on Rigaku D/max-2500 (Rigaku, Japan) with Cu Kα radiation (1.5405

5

Å). The powder X-ray diffraction (PXRD) pattern was collected over the diffraction angle range

6

from 2 to 40° at a scanning rate of 8°/min.

7

2.3. Thermal Analysis

8

Differential scanning calorimeter and thermogravimetric analyzer (TGA/DSC1, Mettler-Toledo,

9

Switzerland) were employed to determine melting properties and thermal stability of solid samples.

10

A total of 5–10 mg griseofulvin sample was added to thermal analyzer and the experiments were

11

conducted at a heating rate of 10 K/min under a nitrogen atmosphere. The melting point and enthalpy

12

were then determined by Mettler-Toledo Stare software v10.00.

13

2.4. Hirshfeld surface analysis

14

Molcular Hirshfeld surface and fingerprint analysis were constructed to identify the

15

intermolecular interactions within griseofulvin crystal structure. The plotting was based on electron

16

distribution computed at the level of B3LYP/6-31G(d) using the CrystalExplorer 3.1 software

17

program.

18

2.5. Solubility Measurements

19

The solubility of griseofulvin in twelve mono-solvents (methanol, ethanol, n-propanol,

20

n-butanol, isobutanol, methyl acetate, ethyl acetate, n-propyl acetate, n-butyl acetate, isopropyl

21

acetate, isobutyl acetate and acetonitrile) was determined under atmosphere pressure at the

22

temperature ranging from 283.15 K to 323.15 K by a gravimetric method [16,17]. Excess amounts of

23

griseofulvin solid samples were added in a 50 mL stoppered conical flask containing 30 mL solvent.

24

Then the conical flasks with the mixtures (solid+liquid) were shaken in an air bath shaker (type HNY,

25

Tianjin Honour Instrument Co., Ltd., China) at a certain temperature with an uncertainty of 0.1 K for

26

over 24 h to reach the solid-liquid equilibrium. It has been proved in the preliminary experiment that

27

24 h is sufficient to reach a stable solid-liquid system. Thereafter, the shaker was stopped and the 6

1

solution was kept static at corresponding experimental temperature for another 2 h to obtain the clear

2

saturated supernatant. Approximately 4 mL of the supernatant was transferred to a 10 mL

3

pre-weighed beaker by a preheated/cooled 5 mL syringe with a 0.22 µm filter membrane. And the

4

small beaker with the solution was immediately weighed by an analytical balance (AB204-N,

5

Mettler-Toledo, Switzerland) with an accuracy of ±0.0001 g. Finally, the beakers were dried in a

6

vacuum oven (DZ-2BC,Tianjin Taisite Instrument Co. Ltd., China) at 323.15 K and the samples were

7

periodically measured until the data was unchanged. Each measurement was conducted for three times

8

to get an average value. The residual solids of griseofulvin not dissolved were analyzed by PXRD.

9 10

The experimental solubility of griseofulvin in different solvents was calculated by the following equation:  =

11

 /  / +  /

(1)

where  represents the mole fraction solubility of griseofulvin;  and  refer to the mass of

12

solute in saturated solution and the mass of certain solvent, respectively;  and  are the molar

13

mass of griseofulvin and the corresponding solvent, respectively.

14 15

3. Results and discussion

16 17

3.1. Physical properties of pure materials

18

The powder X-ray diffraction (PXRD) measurement was utilized to determine the equilibrium

19

solid phase structure in different solvents. Fig. 2 displays the PXRD patterns of both raw materials

20

and excess samples suspended in twelve organic solvents. It is evident that the slurry griseofulvin

21

crystals bear the same crystal form as that of raw material (Form I), indicating the absence of

22

polymorphic transformation or formation of solvates throughout solid-liquid phase equilibrium

23

experiments. The thermal analysis by TGA/DSC further confirms this conclusion and typical

24

TGA/DSC curve is given in Fig. 3. Note that the melting of griseofulvin crystals occurs before its

25

chemical degradation. The melting point Tm of griseofulvin was thus determined to be 491.61 ± 0.5 K,

26

and the enthalpy of fusion ∆   was 36.36 ± 0.5 kJ/mol (calculated by Mettler Stare software

27

v10.00), which is consistent with the values (36 to 45 kJ/mol) reported in the previous literature 7

1

[18,19]. Further, the fusion entropy of griseofulvin ∆   can be calculated by: ∆   =

2

3 4 5 6

7 8 9 10

∆   

(2)

and ∆   was determined to be 73.97 J·mol-1·K-1.

Fig. 2. Typical PXRD patterns of griseofulvin solid samples. A represents the raw material; B to M represent the excess slurry solids after shaken for 24 h in methanol, ethanol, n-propanol, n-butanol, isobutanol, methyl acetate, ethyl acetate, n-propyl acetate, n-butyl acetate, isopropyl acetate, isobutyl acetate and acetonitrile, respectively.

Fig. 3. Typical TGA/DSC curve of griseofulvin solid samples.

3.2. Hirshfeld surface analysis Hirshfeld surface analysis is a valuable method for identifying intermolecular interactions 8

1

within crystal structure [20,21]. The Hershfield surface is defined as the spatial division in the crystal

2

of the electron distribution of the sum of the spherical atoms for a molecule [22]. By virtue of the

3

extraction of 3D Hirshfeld surface, the important 2D fingerprint can be deduced and decomposed

4

into different molecular indirect contacts. These fingerprints are plotted as functions of the values of

5

both de and di which are respectively the separation distance from a point on the isosurface to the

6

nearest atom outside and inside [23].

7

The 2D fingerprint plots of griseofulvin is presented in Fig. 4 and percent relative contribution

8

of various intermolecular contacts to the Hirshfeld surface area is shown in Fig. 5. Among all the

9

contacts, the H⋯H contacts compose 34.6% of the Hirshfeld surface, whereas the O⋯H contacts

10

comprise 34.0%, these two contact interactions apparently dominate in crystal structure of

11

griseofulvin. Besides, the C⋯H contacts and Cl⋯H contacts account for 12.6% and 12.1%,

12

respectively. Additionally, other weak contacts including the C⋯O contacts, Cl⋯O contacts and

13

O⋯O contacts compose the rest of the Hirshfeld surface.

14 15

Fig. 4. Hirshfeld analysis and 2D fingerprint plots of griseofulvin.

9

1 2 3

Fig. 5. Percent relative contribution of various intermolecular contacts to the Hirshfeld surface area.

3.3. Equilibrium solubility and effect of solvent properties

4

One nitrile solvent, five alcohol solvents and six ester solvents were chosen in this research. The

5

mole fraction solubility data of griseofulvin in these mono-solvents at temperature ranging from

6

283.15 K to 323.15 K are presented in the Table 2 and shown graphically in Fig. 6. Obviously, the

7

solubility of griseofulvin increases as the temperature increase for all cases.

8

Among the twelve solvents, griseofulvin has the highest solubility in acetonitrile and followed

9

by the ester solvents and alcohol solvents in sequence. In alcohol solvents, the solubility of

10

griseofulvin can be ranked as: methanol > n-propanol > ethanol > n-butanol > isobutanol; and the

11

solubility sequence in ester solvents is easy to be ranked as: methyl acetate > ethyl acetate > n-propyl

12

acetate > n-butyl acetate > isopropyl acetate > isobutyl acetate.

13 14 15

Table 2 Experimental and correlated mole fraction solubility ( ) of griseofulvin in twelve mono-solvents (p =0.1 MPa).a

T/K

103x1exp

103x1cal,Apelbat

103x1cal,λh

103x1cal,NRTL

Methanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.308 0.327 0.427 0.522 0.627 0.756 0.943 1.101 1.339

0.291 0.352 0.425 0.514 0.623 0.756 0.917 1.113 1.352

0.282 0.349 0.429 0.525 0.637 0.769 0.923 1.103 1.311

0.282 0.349 0.429 0.524 0.636 0.769 0.924 1.105 1.315

10

Ethanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 n-Propanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 n-Butanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 Isobutanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 Methyl acetate 283.15

0.263 0.304 0.358 0.433 0.501 0.605 0.774 0.899 1.113

0.262 0.305 0.359 0.426 0.510 0.614 0.745 0.909 1.116

0.246 0.301 0.366 0.442 0.531 0.634 0.754 0.891 1.049

0.243 0.299 0.364 0.441 0.531 0.636 0.758 0.898 1.059

0.266 0.315 0.385 0.465 0.525 0.646 0.816 0.986 1.165

0.267 0.317 0.378 0.453 0.545 0.658 0.797 0.969 1.180

0.255 0.314 0.384 0.466 0.562 0.674 0.804 0.955 1.129

0.255 0.313 0.383 0.465 0.562 0.674 0.805 0.957 1.133

0.261 0.288 0.349 0.413 0.479 0.541 0.742 0.886 1.099

0.260 0.296 0.341 0.401 0.478 0.579 0.709 0.881 1.105

0.236 0.289 0.351 0.424 0.508 0.607 0.720 0.852 1.002

0.239 0.290 0.350 0.422 0.506 0.605 0.720 0.854 1.009

0.178 0.268 0.322 0.355 0.419 0.494 0.675 0.797 0.999

0.194 0.238 0.292 0.357 0.438 0.535 0.654 0.798 0.973

0.189 0.237 0.294 0.363 0.445 0.542 0.656 0.790 0.946

0.191 0.237 0.293 0.361 0.442 0.540 0.655 0.793 0.955

3.358

3.337

3.347

3.466

11

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 Ethyl acetate 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 n-Propyl acetate 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 n-Butyl acetate 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 Isopropyl acetate 283.15 288.15 293.15

3.706 4.189 4.867 5.287 5.776 6.465 7.148 7.972

3.760 4.222 4.724 5.268 5.857 6.493 7.178 7.914

3.763 4.218 4.714 5.256 5.845 6.487 7.185 7.943

3.746 4.131 4.663 5.127 5.689 6.436 7.272 8.304

2.087 2.462 2.749 3.008 3.216 3.537 4.022 4.410 4.923

2.149 2.398 2.670 2.965 3.286 3.634 4.011 4.418 4.858

2.149 2.399 2.670 2.966 3.286 3.633 4.010 4.418 4.860

2.043 2.318 2.620 2.948 3.306 3.691 4.105 4.552 5.031

1.572 1.884 2.036 2.190 2.375 2.571 2.948 3.214 3.662

1.634 1.797 1.979 2.181 2.406 2.657 2.935 3.245 3.589

1.614 1.794 1.989 2.200 2.428 2.675 2.941 3.230 3.542

1.539 1.737 1.953 2.188 2.442 2.715 3.007 3.322 3.657

1.371 1.501 1.623 1.895 2.006 2.160 2.527 2.841 3.117

1.372 1.500 1.648 1.819 2.014 2.240 2.498 2.796 3.138

1.335 1.492 1.664 1.850 2.053 2.273 2.512 2.771 3.052

1.251 1.428 1.621 1.832 2.064 2.316 2.587 2.881 3.199

1.330 1.420 1.519

1.324 1.418 1.533

1.263 1.403 1.556

1.150 1.315 1.496

12

298.15 303.15 308.15 313.15 318.15 323.15 Isobutyl acetate 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 Acetonitrile 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1 2 3 4

a

1.667 1.839 2.052 2.316 2.556 2.892

1.674 1.842 2.043 2.283 2.568 2.906

1.721 1.900 2.094 2.303 2.530 2.775

1.694 1.910 2.145 2.400 2.676 2.974

1.178 1.246 1.368 1.547 1.661 1.929 2.097 2.372 2.689

1.164 1.264 1.383 1.523 1.688 1.882 2.110 2.378 2.692

1.119 1.253 1.400 1.559 1.733 1.921 2.126 2.349 2.590

1.025 1.179 1.349 1.536 1.741 1.965 2.211 2.478 2.767

3.845 4.182 4.761 5.511 6.144 7.093 8.007 9.080 10.302

3.782 4.262 4.814 5.448 6.177 7.015 7.978 9.085 10.358

3.694 4.241 4.851 5.527 6.276 7.104 8.016 9.021 10.126

3.829 4.176 4.688 5.350 6.036 6.989 8.045 9.341 10.916

x1exp is the experimental solubility of griseofulvin in mono-solvents; x1cal, Apelbat , x1cal, λh and x1cal, NRTL are the

calculated solubility by Eqs. (4), (5) and (6), respectively. The standard uncertainty of temperature is u(T) = 0.05 K. The relative uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of the solubility measurement is ur(x) = 0.026.

13

1 2 3

Fig. 6. Experimental solubility of griseofulvin ( ) in twelve mono-solvents at the temperature ranging from

4

In order to further understand solid-liquid phase equilibrium solubility behaviors of griseofulvin

5

in different solvents, we looked into the effect of solvent properties. The studied solvents are

6

classified into two categories: (1) alcohols of different length and structure of carbon chains and (2)

7

non-alcohols solvents that are acetonitrile and esters.



283.15 K to 323.15 K at atmospheric pressure (0.1 MPa).

8

According to Gu and his co-workers [24], the accessible physicochemical properties of the

9

selected solvents are listed in Table 3. The solvent properties are thus divided into four categories,

10

namely solvent polarity, hydrogen bond donor propensity, hydrogen bond acceptor propensity, and

11

cohesive energy density. The cohesive energy density (ε) characterizing the strength of

12

solvent-solvent interactions is expressed by [25]:  = (∆  − )/

13

(3)

in which ∆  and  represent the evaporation enthalpy and the molar volume, respectively.

14

To visualize the effect of solvent properties, the solubility of griseofulvin was plotted as a

15

function of solvent polarity, hydrogen bond donor propensity, hydrogen bond acceptor propensity,

16

and cohesive energy density for alcohols and non-alcohols solvents, which were called as “solubility 14

1

spectra” and shown in Figs. 7 and 8, respectively. As can be seen, neither hydrogen bond donor

2

propensity nor hydrogen bond acceptor propensity can be correlated with the solubility rank of

3

griseofulvin in the studied solvents. But the solubility correlates well and increases with increasing

4

polarity of solvents and cohesive energy density. The values of cohesive energy density of alcohols

5

and non-alcohols solvents are directly proportional to their polarity, but have better extent of

6

differentiation. The reason for the good solubility correlation with solvent polarity thus can be

7

attributed to the rule of “like dissolves like”. Besides, the branched alcohols (e.g. isobutanol) affect

8

the polarity and bring extra steric hindrances to interact with solute molecules, which may lead to the

9

decrease of solubility in comparison with the straight chain alcohols.

10

Actually, the solubility greatly depends on the mutual competition of the interaction between the

11

solute-solvent and solvent-solvent [26]. The interaction between solvent and solvent could be

12

represented by the cohesive energy density [25]. The higher value of cohesive energy density usually

13

shows the stronger interaction of solvent and solvent molecule. But in this case, as shown in Figs. 7

14

and 8, the solubility of griseofulvin in alcohols and non-alcohols solvents increases with increasing

15

cohesive energy density, indicating the strength of solute-solvent interaction may play a dominant

16

role in determining solubility.

17 18

Table 3

19 20 21 22

The main physicochemical properties of some of the selected solvents [24].

Solvent name

Πa

∑αb

∑βc

Cohesive energy densityd

Methanol Ethanol n-Propanol n-Butanol Isobutanol Methyl acetate Ethyl acetate n-Propyl acetate n-Butyl acetate Acetonitrile

0.60 0.54 0.52 0.47 0.40 0.60 0.55 0.50 0.46 0.75

0.43 0.37 0.37 0.37 0.37 0.00 0.00 0.00 0.00 0.07

0.47 0.48 0.48 0.48 0.48 0.45 0.45 0.45 0.45 0.32

808.26 618.87 520.37 446.01 425.37 350.86 300.64 273.15 256.96 522.95

a

Polarity of solvents.

b

Summation of the hydrogen bond donor propensities of the solvent..

c

Summation of the hydrogen bond acceptor propensities of the solvent..

d

Cohesive energy density in the unit of J/mol/mL.

15

1 2 3

Fig. 7. Solubility spectra of griseofulvin in alcohols at 298.15 K as a function of solvent polarity (a), hydrogen bond donor propensity (b), hydrogen bond acceptor propensity (c), and cohesive energy density (d).

4 16

1 2

Fig. 8. Solubility spectra of griseofulvin in non-alcohols at 298.15 K as a function of solvent polarity (a), hydrogen

3

3.4. Data correlation of solubility

bond donor propensity (b), hydrogen bond acceptor propensity (c), and cohesive energy density (d).

4

In order to extend the application of the measured solubility data, three thermodynamic models

5

including the modified Apelblat equlation, λh equation, and NRTL model were employed to describe

6

and correlate solid-liquid equilibrium behaviors of griseofulvin in different solvents.

7

3.4.1. Modified Apelblat equation

8 9

The modified Apelblat equation is a semi-empirical equation and widely applied to describe the solubility behavior as a function of temperature. The equation can be expressed by [27]: ln  =  +

/!

+ "#$(/!)

(4)

10

in which  is the mole fraction solubility of the solute; T refers to the temperature of the system; A,

11

B, C are parameters of the equation. The value of A and B reflects the nonidealities of the real

12

solution in terms of variation of activity coefficient in the solution, and C represents the effect of

13

temperature on the fusion enthalpy [28].

14 15 16

3.4.2. λh equation λh equation correlates the solubility with temperature by the following expression [29]: ln %1 + λ

1 −  1 1 ( = λh( − )   *

(5)

17

in which * is the melting temperature of griseofulvin; λ and h are the two model parameters. λ is

18

pertinent to the non-ideality of the real solution, and h is a enthalpy factor.

19

3.4.3. NRTL model

20 21

According to the solid-liquid phase equilibrium principle, the equilibrium solubility can be expressed by the following simplified equation [30,31]: ln + =

22

∆   1 1 % − ( − ln ,  

(6)

where + stands for the mole fraction solubility of the solute; ∆   refers to the fusion enthalpy.

23

,+ is the activity coefficient of solute in the saturated solution, which can be calculated based on

24

activity coefficient models for example NRTL model. 17

1

NRTL model (Non-Random Two-Liquid model) is widely used to correlate solubility and

2

predict solid-liquid equilibrium properties for many non-ideal solutions. The NRTL model is derived

3

based on the molecular local composition concept and can be expressed by: 0 /  0  ln,+ =  [/ % ( + ] ( +  0  )  +  0

(7)

/+2 = (7+2 − 722 )/ = ∆7+2 /

(9)

0+2 = exp (−6/+2 )

(8)

4

where i ≠ j and i, j = 1,2. ∆7+2 stands for the cross interaction energy and α is an adjustable constant,

5

which is generally from 0 to 1 and related to the nonrandomness and nonideality of the solution [32].

6

In this work, the solubility of griseofulvin in the studied solvent systems was correlated with

7

above models using least-square regression method in MATLABTM software. In order to examine the

8

applicability and accuracy of these models [33], the average relative deviation (ARD%) and

9

root-mean square deviation (RMSD) are defined as follows: A



 − +>?@ 100 8% = < = +  = ; + A



+B

1  8 = C ?@ E F ;



(10)

(11)

+B

10

where +

and +>?@ represent the experimental and calculated solubility of griseofulvin,

11

respectively; N stands for the number of experimental points.

12

The optimized results including the corresponding parameters as well as the average relative

13

deviation (ARD %) and root-mean square deviation (RMSD) of the three models mentioned above

14

are summarized in Tables S1-S3. The calculated solubility data of griseofulvin in pure solvents by

15

using the modified Apelblat equation, λh equation, and NRTL model are in well agreement with

16

experimental ones and supplemented in Table 2. The overall fitting ARD % are respectively 1.77%

17

for the modified Apelblat equation, 2.67% for λh equation, and 3.58% for NRTL model. Therefore, the

18

modified Apelblat equation achieves the best fitting results. The experimental data and correlation

19

models obtained in this work can be very useful in the industrial production and purification of

20

griseofulvin.

21 18

1

3.5. Thermodynamic functions of mixing

2

Based on the Lewis-Randall rule, thermodynamic functions of mixing of real solution can be

3

derived from the ideal one. For an ideal binary system, the mixing properties that are mixing enthalpy,

4

mixing entropy and mixing Gibbs free energy could be calculated by [34]: ∆*+G 0

+H

A

=  < + ln+ +

(12)

∆*+G  +H = 0

(13)

∆*+G  +H = − < + ln+

(14)

A +

5

where + is the mole fraction of component i. In this study, the value of i is equal to 2 when the

6

solute is dissolved in mono-solvents.

7 8

In a real binary mixture system, the mixing properties can be calculated from ideal ones given the known excess properties [35].

∆*+G 0 = ∆*+G 0 +H + 0 I

∆*+G  = ∆*+G  +H +  I ∆*+G  = ∆*+G  +H +  I

9 10

(15) (16) (17)

where 0 I ,  I , and  I refer to the excess properties, which can be computed by the following equations [36]: A

0 I =  < + ln,+ A

+

 = − < + ( I



+

J ln,+ ) J K,G

I − 0 I  =  I

(18) (19)

(20)

11

in which ,+ is the activity coefficient of component i in real system and can be calculated from the

12

above NRTL model.

13

The derived thermodynamic functions of mixing including enthalpy, entropy and Gibbs free

14

energy in twelve pure solvents are listed in Table 4. It was found the values of mixing Gibbs free

15

energy in all mono-solvents are negative, indicating a spontaneous and favorable mixing process of 19

1

griseofulvin with each solvent [37]. Additionally, the negative values of mixing enthalpy in all cases

2

suggest that mixing of griseofulvin with various mono-solvents is exothermic process [38]. The values

3

of mixing entropy are all positive, demonstrating the entropy-driven process of mixing [39].

4

Furthermore, the values of |∆mixG| for each solvent were found to increase with the increasing

5

temperature, and thus increasing temperature is favorable for dissolution and hence increasing the

6

solubility. While at a given temperature, the rank of values of |∆mixG| appears to be the same as the

7

order of solubility. In general, these results are expected and consistent with general thermodynamics

8

theory [40].

9 10 11

Table 4 Mixing thermodynamic properties of griseofulvin in twelve mono-solvents (P = 0.1 MPa)a

T/K Methanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 n-Propanol 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 Isobutanol 283.15 288.15 293.15 298.15

∆mixG J·mol-1

∆mixH J·mol-1

∆mixS J·mol-1·K-1

-5.4090 -5.7524 -7.3134 -8.7626 -10.3468 -12.2226 -14.8483 -17.0544 -20.2135

-2.3305 -2.4337 -3.1260 -3.7512 -4.4277 -5.2322 -6.3978 -7.3214 -8.7079

0.0109 0.0115 0.0143 0.0168 0.0195 0.0227 0.0270 0.0306 0.0356

-4.6994 -5.4945 -6.5793 -7.8143 -8.7297 -10.4926 -12.8751 -15.1847 -17.5544

-2.2093 -2.5954 -3.1360 -3.7558 -4.1874 -5.0915 -6.3529 -7.5696 -8.8124

0.0088 0.0101 0.0117 0.0136 0.0150 0.0175 0.0208 0.0239 0.0271

-3.1885 -4.5913 -5.4459 -5.9692

-1.2596 -1.8004 -2.0569 -2.1409

0.0068 0.0097 0.0116 0.0128

T/K

∆mixG J·mol-1

Ethanol 283.15 -4.6264 288.15 -5.2862 293.15 -6.1475 298.15 -7.2901 303.15 -8.3171 308.15 -9.8438 313.15 -12.1857 318.15 -13.9044 323.15 -16.7103 n-Butanol 283.15 -4.5897 288.15 -5.0314 293.15 -5.9743 298.15 -6.9601 303.15 -7.9540 308.15 -8.8890 313.15 -11.6718 318.15 -13.6294 323.15 -16.3966 Methyl acetate 283.15 -58.1381 288.15 -62.6504 293.15 -68.9977 298.15 -77.8808 20

∆mixH J·mol-1

∆mixS J·mol-1·K-1

-2.2472 -2.5872 -3.0406 -3.6574 -4.2061 -5.0536 -6.4126 -7.3895 -9.0745

0.0084 0.0094 0.0106 0.0122 0.0136 0.0155 0.0184 0.0205 0.0236

-2.6516 -2.8290 -3.3111 -3.7915 -4.2453 -4.6293 -6.1176 -7.0371 -8.3980

0.0068 0.0076 0.0091 0.0106 0.0122 0.0138 0.0177 0.0207 0.0248

-57.4219 -61.2841 -67.2590 -75.8100

0.0025 0.0047 0.0059 0.0069

1 2

303.15 -6.9611 -2.3937 0.0151 303.15 -82.8600 -80.5953 0.0075 308.15 -8.0736 -2.6566 0.0176 308.15 -88.6349 -85.9996 0.0086 313.15 -10.6159 -3.4212 0.0230 313.15 -96.8965 -93.3551 0.0113 318.15 -12.3243 -3.7960 0.0268 318.15 -104.8274 -100.5507 0.0134 323.15 -15.0085 -4.4575 0.0327 323.15 -114.3032 -109.3126 0.0154 Ethyl acetate n-Propyl acetate 283.15 -37.0183 -36.6201 0.0014 283.15 -27.8693 -27.3947 0.0017 288.15 -42.6279 -41.8106 0.0028 288.15 -32.5120 -31.9028 0.0021 293.15 -46.7679 -45.7208 0.0036 293.15 -34.6629 -33.6483 0.0035 298.15 -50.3991 -49.0874 0.0044 298.15 -36.7884 -35.3146 0.0049 303.15 -53.2022 -51.2306 0.0065 303.15 -39.2817 -37.6521 0.0054 308.15 -57.5032 -55.3066 0.0071 308.15 -41.8669 -39.7935 0.0067 313.15 -63.8447 -60.4320 0.0109 313.15 -46.7878 -43.9634 0.0090 318.15 -68.7103 -64.6752 0.0127 318.15 -50.0687 -46.2825 0.0119 323.15 -74.9630 -70.1812 0.0148 323.15 -55.5105 -50.9066 0.0142 n-Butyl acetate Isopropyl acetate 283.15 -24.0750 -23.1818 0.0032 283.15 -23.1897 -22.6699 0.0018 288.15 -26.0200 -24.9277 0.0038 288.15 -24.5167 -23.6348 0.0031 293.15 -27.7862 -26.4926 0.0044 293.15 -25.9522 -24.6793 0.0043 298.15 -31.6659 -29.9067 0.0059 298.15 -28.0612 -25.9843 0.0070 303.15 -33.1842 -30.9551 0.0074 303.15 -30.4596 -27.5132 0.0097 308.15 -35.2491 -31.9516 0.0107 308.15 -33.3526 -30.0603 0.0107 313.15 -40.1163 -36.4355 0.0118 313.15 -36.8356 -33.1008 0.0119 318.15 -44.0987 -40.0912 0.0126 318.15 -39.8980 -35.8784 0.0126 323.15 -47.4745 -43.0183 0.0138 323.15 -44.0556 -39.8248 0.0131 Isobutyl acetate Acetonitrile 283.15 -20.5522 -20.4516 0.0004 283.15 -66.2383 -63.8637 0.0084 288.15 -21.5858 -21.2857 0.0010 288.15 -70.5891 -67.3830 0.0111 293.15 -23.3839 -22.8329 0.0019 293.15 -78.4106 -74.1860 0.0144 298.15 -25.9605 -24.9601 0.0034 298.15 -88.3890 -83.6191 0.0160 303.15 -27.5547 -26.3379 0.0040 303.15 -96.4252 -91.0025 0.0179 308.15 -31.2199 -29.5613 0.0054 308.15 -108.5013 -102.1366 0.0207 313.15 -33.4392 -31.0303 0.0077 313.15 -119.7385 -111.2856 0.0270 318.15 -36.9975 -34.1269 0.0090 318.15 -132.6931 -121.0954 0.0365 323.15 -40.9636 -37.5073 0.0107 323.15 -147.1795 -130.1910 0.0526 a The expanded uncertainties are U(∆mixG)=0.05∆mixG, U(∆mixS)=0.05∆mixS, and U(∆mixH)=0.05∆mixH (0.95 level of confidence).

3 4 5 6 21

1

4. Conclusions

2 3

In this work, the solid-state structure and thermodynamic properties in solution of the antifungal

4

drug griseofulvin was studied. The crystal structure analysis by Hirshfeld surface reveals that the

5

H⋯H and O⋯H contacts apparently dominate in crystal structure of griseofulvin. The solution

6

thermodynamic properties including solid-liquid phase equilibrium solubility and thermodynamic

7

functions of mixing were determined in twelve solvents (methanol, ethanol, n-propanol, n-butanol,

8

isobutanol, methyl acetate, ethyl acetate, n-propyl acetate, n-butyl acetate, isopropyl acetate, isobutyl

9

acetate and acetonitrile). The equilibrium solubility data was measured by gravimetric method at

10

temperature ranging from 283.15 to 323.15 K, and the measurement results show the solubility is

11

monotonously rising with increasing temperature as expected in all solvents. Besides, the effect of

12

solvent properties on solid-liquid phase equilibrium of griseofulvin was investigated in terms of

13

solvent polarity, hydrogen bonding donor and acceptor propensity, as well as cohesive energy density.

14

The results reveal that the solvent polarity plays the key role in the solid-liquid phase equilibrium

15

behavior of griseofulvin in the studied solvent systems. Moreover, experimental data can be well

16

correlated by the modified Apelblat equation, λh equation and NRTL model, in which the modified

17

Apelblat equation receives the best regression performance. Finally, thermodynamic functions of

18

mixing (enthalpy, entropy, and Gibbs energy) were derived, and the results suggest a spontaneous,

19

exothermic and entropy-driven mixing process. The solubility data, correlated models, and

20

thermodynamic functions presented in this work could provide crystallization fundamentals for

21

separation and purification of griseofulvin.

22 23 24 25 26 27 28 22

1 2

Notes The authors declare no competing financial interest.

3 4

Acknowledgments

5

The authors are grateful to the financial support of National Natural Science Foundation of

6

China (no. 21808159), China Postdoctoral Science Foundation 2018M640237, Major National

7

Science and Technology Projects 2017ZX09101001, and Innovative Group Project 21621004.

8 9 10 11

Appendix A. Supplementary data Optimized parameters for the modified Apelblat equation, λh equation, and NRTL model are given in Tables S1-S3, respectively.

12 13

23

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

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26

Highlights •

The equilibrium solubility of griseofulvin was determined by the static method in twelve mono-solvents.

•

The intermolecular interactions within crystal structure were probed by Hirshfeld surface analysis.

•

The effect of solvent properties on solid-liquid phase equilibrium of griseofulvin was investigated.

•

Thermodynamic analyses were performed on the basis of thermodynamic functions of mixing.

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: