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Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K
Journal of Molecular Liquids xxx (xxxx) xxx
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Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K Beiqian Tian a, Yaoguang Feng a, Xin Li a, Jinyue Yang a, Zhiyong Ding a, Xin Huang a, b, **, Qiuxiang Yin a, b, Chuang Xie a, b, Hongxun Hao a, b, * a
National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin, 300072, China Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300072, China
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 July 2019 Received in revised form 10 September 2019 Accepted 13 September 2019 Available online xxx
In this work, solution thermodynamic properties including solubility, mixing thermodynamic properties and dissolution thermodynamic properties are investigated in detail. Gravimetric method was utilized for measuring the solubility data of flurbiprofen in twelve pure solvents including n-propanol, isopropanol, n-butanol, isobutanol, isopentanol, isopropyl acetate, methyl tert-butyl ether, isopropyl ether, acetonitrile, n-octane, n-heptane and n-hexane over the temperatures range from 283.15 to 323.15 K under atmospheric pressure. The results indicated that the solubility of flurbiprofen increased with the increasing temperature. Furthermore, the experimental solubility data were correlated by the modified Apelblat equation, lh equation, Wilson model and NRTL model. And the modified Apelblat equation can give better correlation results with lower values of ARD%. Moreover, mixing and dissolution thermodynamic properties of flurbiprofen in different solvents were calculated according to the experimental data and the NRTL model. © 2019 Elsevier B.V. All rights reserved.
Keywords: Flurbiprofen Solubility Mixing thermodynamic properties Dissolution thermodynamic properties
1. Introduction Flurbiprofen, whose molecular formula is C15H13FO2 and CAS Registry No. is 86-55-5, is a member of the phenylalkanoic acid series. The chemical structure of flurbiprofen is presented in Fig. 1. Flurbiprofen is a weakly acidic drug possessing poor aqueous solubility and gastrointestinal irritation, classified as Biopharmaceutical Classification System Type II drug [1e3]. It is widely used for treating rheumatoid arthritis, and moderating pain of migraine, osteoarthritis, and sore throat with analgesic, antipyretic and anti-inflammatory properties [4e6]. According to previous reports, three polymorphic forms (Forms I, II and III) of flurbiprofen have been reported [7,8]. Form I is the thermodynamically stable form under ambient condition and hence Form I flurbiprofen is used in clinic. During manufacture of Form I
* Corresponding author. National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin, 300072, China. ** Corresponding author. Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300072, China. E-mail addresses: [email protected] (X. Huang), [email protected] (H. Hao).
flurbiprofen, solution crystallization is the final step which will determine the final quality of the product. Thermodynamic solubility represents the saturation concentration of a compound in equilibrium with undissolved solid phase. It is undeniably true that the solid-liquid phase equilibrium is an important part of chemical thermodynamics, which is crucial to design and optimize a crystallization process for the fact that solution crystallization is generally used as the final process to obtain pure objective crystal form products industrially. However, from literature review, reports on solubility data of flurbiprofen in organic solvents is rare. In this study, the solubility data of flurbiprofen in twelve pure organic solvents (n-propanol, isopropanol, n-butanol, isobutanol, isopentanol, isopropyl acetate, methyl tert-butyl ether, isopropyl ether, acetonitrile, n-octane, n-heptane and n-hexane.) were systematically measured from 283.15 to 323.15 K under atmospheric pressure through gravimetric method. Four thermodynamic models including the Apelblat equation, lh equation, Wilson model and NRTL model were implemented to correlate the solubility data of flurbiprofen Form I. Furthermore, the mixing and dissolution thermodynamic properties including the enthalpy, the entropy, and the Gibbs free energy change were derived through the experimental data and the NRTL model.
https://doi.org/10.1016/j.molliq.2019.111744 0167-7322/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
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2.4. Solubility measurements
Fig. 1. Chemical structure of flurbiprofen.
2. Experimental 2.1. Materials Flurbiprofen with mass-based fraction of 0.990 was purchased from Wuhan Yuancheng Co-creation Technology Co., Ltd. Isopropyl acetate was purchased from Shanghai Macklin Biochemical Co., Ltd. N-butanol and isopentanol were purchased from Lianlong Bohua Chemical Co., Ltd. Isopropyl ether was purchased from Tianjin Kangkede Technology Co., Ltd. All other solvents like n-propanol, isopropanol, isobutanol, methyl tert-butyl ether, acetonitrile, noctane, n-heptane and n-hexane were purchased from Tianjin Kemiou Chemical Reagent Co., Ltd. All the materials of which more detailed information are listed in Table 1 were used without further purification. 2.2. Powder X-ray diffraction The powder X-ray diffraction (PXRD) was performed to characterize the crystal form of flurbiprofen before and after each experiment. And the data were collected on Rigaku D/max-2500 (Rigaku, Japan) with voltage of 40 kV, current of 100 mA, step size of 0.02 and scanning rate of 8 /min over diffraction angle (2q) from 2 to 40 .
In this work, the classical shake-flask method [9e11] was implemented to measure the solubility data of flurbiprofen in pure solvents including n-propanol, isopropanol, n-butanol, isobutanol, isopentanol, isopropyl acetate, methyl tert-butyl ether, isopropyl ether, acetonitrile, n-octane, n-heptane and n-hexane over the temperatures range from 283.15 to 323.15 K. In this method, approximately 25 mL of solvent was added to a conical flask (50 mL) which was kept at constant temperature under the control of a shaker with thermostatic bath (Tianjin Ounuo Instrument Co. Ltd., China). Subsequently, excess flurbiprofen was added to the solvent. Undissolved solid and solution were constantly shaken at a speed of 200 rpm for 12 h to ensure that the mixture reached complete equilibrium which has been demonstrated in the preliminary experiments. After the shaker was stopped, the system was remained still for 6 h at the experimental temperature so as to precipitate the undissolved solid. After that, the supernatant liquid was withdrawn by a pre-heated or pre-cooled syringe and then was filtered into a pre-weighed beaker through an organic membrane filter (0.45 mm, f13 mm, Tianjin Jinteng Experimental Equipment Co., Ltd). The beaker with saturated solution was weighted immediately and dried in an electronic oven at 318.15 K for 36 h until the total weight of the sample did not change any more. Finally, the residual solute together with the beaker was weighed again. All samples were measured by an electronic analytical balance (Mettler Toledo ML204, Switzerland) with an accuracy of ±0.0001 g. (The wet solids which did not dissolve were analyzed by XRPD. The XRPD patterns are shown in Fig. 2). The procedure above all was carried out three times in parallel and the average value was used to calculate the mole fraction solubility of flurbiprofen based on the following equations [12]:
x1 ¼
m1 =M1 m1 =M1 þ m2 =M2
(1)
where m1 and m2 represent the mass of flurbiprofen and solvent; M1 and M2 denote the respective molar mass of flurbiprofen and solvent, respectively.
2.3. Differential scanning calorimetry 3. Thermodynamic models The melting temperature (Tm) and fusion enthalpy (DfusH) of flurbiprofen were obtained using DSC instrument (DSC 1/500, Mettler-Toledo, Switzerland). The measurements were carried out at a heating rate of 10 K/min under protection of a nitrogen atmosphere. An empty pan was used as contrast while another 5e10 mg flurbiprofen was put into an aluminum pan scanning from 298.15 K to 403.15 K.
3.1. Modified apelblat equation Deduced from the Clausius-Clapeyron equation, the modified Apelblat equation is a commonly used semi-empirical model to correlate the absolute temperature and the solubility of solute. The formula is given as follows [13].
Table 1 The sources and mass-based fraction of experimental materials. Chemical name
CAS Registry No.
Source
Mass purity
Analysis method
N-propanol Isopropanol N-butanol Isobutanol Isopentanol Isopropyl acetate Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane
71-23-8 67-63-0 71-36-3 78-83-1 123-51-3 108-21-4 1634-04-4 108-20-3 75-05-8 111-65-9 142-82-5 110-54-3
Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Lianlong Bohua Chemical Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Lianlong Bohua Chemical Co., Ltd., Tianjin, China Shanghai Macklin Biochemical Co., Ltd., Shanghai, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Tianjin Kangkede Technology Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China
0.995 0.997 0.995 0.990 0.985 >0.990 0.995 0.950 0.995 0.995 0.995 0.995
GCa GCa GCb GCa GCb GCc GCa GCd GCa GCa GCa GCa
a b c d
Gas Gas Gas Gas
chromatography, chromatography, chromatography, chromatography,
conducted conducted conducted conducted
by by by by
Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China. Lianlong Bohua Chemical Co., Ltd., Tianjin, China. Shanghai Macklin Biochemical Co., Ltd., Shanghai, China. Tianjin Kangkede Technology Co., Ltd., Tianjin, China.
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
B. Tian et al. / Journal of Molecular Liquids xxx (xxxx) xxx
3
thermodynamic model, which is written as follows [17,18].
lnx1 ¼
DfusH
R
ðT ðT 1 1 1 1 DCp lng1 dT DCpdT þ Tm T RT R T Tm
Tm
(4) where x1, DfusH, R, Tm, g1, DCp, and T are the equilibrium mole fraction of the solute, the fusion enthalpy of solute, the gas constant, the melting point of the solute, the activity coefficient, the difference of heat capacities between subcooled liquid and solid, and the absolute temperature, respectively. In addition, the latter two items in Eq. (4) are generally much lower in value than the first two due to the diminutive value of DCp, Eq. (4) can be simplified as follows.
lnx1 ¼ Fig. 2. Powder X-ray diffraction patterns of residual solid in different solvents: (a) simulated from a single crystal structure; (b) raw flurbiprofen; (c) residual solid in npropanol; (d) residual solid in isopropanol; (e) residual solid in n-butanol; (f) residual solid in isobutanol; (g) residual solid in isopentanol; (h) residual solid in isopropyl acetate; (i) residual solid in methyl tert-butyl ether; (j) residual solid in isopropyl ether; (k) residual solid in acetonitrile; (l) residual solid in n-octane; (m) residual solid in n-heptane; (n) residual solid in n-hexane.
lnx1 ¼ A þ
B þ C ln T T
(2)
where x1 is the mole fraction solubility of flurbiprofen. T is the corresponding absolute temperature. A, B, and C are fitted model parameters. The values of A and B reveal the variation in the solution activity coefficient, and C is the indication of the influence of temperature on the enthalpy of fusion [14].
DfusH R
1 1 lng1 Tm T
(5)
The NRTL model can be used to calculate the solute activity coefficient (g1). In pure solvents, the activity coefficient can be calculated by Eqs. (6-10)
" lng1 ¼ x22
t21 G221 ðx1 þ G21 x2 Þ
þ 2
t12 G212
# (6)
ðx2 þ G12 x1 Þ2
G12 ¼ eðat12 Þ
(7)
G21 ¼ eðat21 Þ
(8)
t12 ¼
g12 g22 Dg12 ¼ RT RT
(9)
3.2. lh equation
t21 ¼
g21 g11 Dg21 ¼ RT RT
(10)
Another empirical formula, the lh equation proposed by H. Buchowski et al., can also be implemented to describe the equilibrium data [15]. The equation can be described as Eq. (3) [16].
where R is the gas constant (8.314 J mol1 K1). T refers to thermodynamic temperature. Dg12 and Dg21 are parameters of this model which represent the Gibbs free energy of intermolecular interaction. The parameter a is a regulable constant between 0 and 1 standing for the non-randomness of the system [19]. In this work, a ¼ 0.2 was chosen for the correlation of flurbiprofen solubility data in twelve different pure solvents.
1 x1 1 1 ¼ lh ln 1 þ l T Tm x1
(3)
where l and h are two model parameters in the equation, T is absolute temperature and Tm refers to the melting temperature of solute.
3.4. Wilson model 3.3. NRTL model The solubility of solute can be expressed by a general
The Wilson equation proposed by Wilson [20] can be used to determine the activity coefficients and is described as follows
Table 2 Density and molar volumes of flurbiprofen and all the organic solvents used. Substance
r(g/cm3)
V(cm3/mol)c
Substance
r(g/cm3)
V(cm3/mol)c
Flurbiprofena N-propanolb Isopropanolb N-butanolb Isobutanolb Isopentanolb Isopropyl acetateb
1.279 0.804 0.786 0.810 0.802 0.810 0.888
191 74.8 76.5 91.5 92.4 109 115
Methyl tert-butyl etherb Isopropyl etherb Acetonitrileb N-octaneb N-heptaneb N-hexaneb
0.741 0.725 0.790 0.703 0.680 0.660
119 141 52.0 162 147 131
a b c
The density of flurbiprofen was obtained by the tapping density tester. The density of solvents were obtained from literature [21]. The molar volume of flurbiprofen and solvents were calculated by Eq. (14).
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
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where x1 and x2 stand for the mole fraction of flurbiprofen and solvent respectively. The mixing thermodynamic properties of the real solution system can be calculated by using Eqs. (18-20).
Dmix G ¼ GE þ Dmix Gid
(18)
Dmix H ¼ HE þ Dmix Hid
(19)
Dmix S ¼ SE þ Dmix Sid
(20)
where DmixG, DmixH and DmixS refer to mixing properties of Gibbs energy, enthalpy and entropy respectively, and GE, HE and SE represent the excess mixing properties of Gibbs energy, enthalpy and entropy of the real solution, respectively. They can be deduced from Eqs. (21-23) [22].
GE ¼ RTðx1 lng1 þ x2 lng2 Þ Fig. 3. DSC plot of flurbiprofen. E
lng1 ¼ lnðx1 þ L12 x2 Þ þ x2
L12 L21 x1 þ L12 x2 x2 þ L21 x1
H ¼ T
l l V Dl V2 11 ¼ 2 exp 12 exp 12 V1 RT V1 RT
(12)
L21 ¼
l l V Dl V1 22 ¼ 1 exp 21 exp 21 V2 RT V2 RT
(13)
M
r
" E . # v G T vT
vlng1 vlng2 þ x2 ¼ RT 2 x1 vT vT p;x p;x
(11)
L12 ¼
V¼
2
(21)
(14)
where L12 and L21 represent Wilson parameters. Dl12 and Dl21 are two model parameters which represent the cross interaction energy parameters. V1 and V2 represent the molar volume of the solute and the solvent respectively, which can be determined by the molar mass and density by Eq. (14), where M represents the molar mass and r is the density. In addition, the density of the solvents were obtained from literature and the density of flurbiprofen was measured by the tapping density tester (ZS-201, Liaoning Instrumentation Research Institute Co. Ltd). In detail, pre-weighted flurbiprofen was put into a 25 mL graduated cylinder. Subsequently, the graduated cylinder was put on the tapping density tester shaking for 40 min at a frequency of 150 times/minute until the volume remained constant. The experiment was repeated three times to obtain the density of flurbiprofen. The values of molar volume and density are listed in Table 2. 3.5. Mixing and dissolution thermodynamic properties It is of great importance to investigate the mixing and dissolution properties of flurbiprofen in real solutions. For the ideal solution, its mixing properties including Gibbs energy, enthalpy, and entropy can be described as Eqs. (15-17)
Dmix Gid ¼ RTðx1 lnx1 þ x2 lnx2 Þ
(15)
Dmix Hid ¼ 0
(16)
Dmix Sid ¼ Rðx1 lnx1 þ x2 lnx2 Þ
(17)
(22) SE ¼
H E GE T
(23)
where g1 and g2 denote the activity coefficient of solute and solvent respectively, which can be calculated from the NRTL model. With regard to thermodynamic dissolution properties, they can be calculated on the basis of the mixed thermodynamic properties, since four processes including mixing can be considered to be the constitutive stages of dissolution process, which is expressed as follows [23]. heating fusion Solute(solid) at T!Solute(solid) at Tm ! Solute(liquid) at Tm cooling mixing !Solute(liquid) at T! Solute(solution) at T. Then the entire dissolution thermodynamic can be described as
Ddis M ¼ x1 Dheat M þ Dfus M þ Dcool M þ Dmix M
(24)
where M stands for enthalpy (H), entropy (S) and Gibbs energy (G) respectively. x1 is the mole fraction of solute. DdisM, DheatM, DfusM, DcoolM and DmixM mean the thermodynamic property of dissolution, heating, fusion cooling and mixing process respectively. The thermodynamic properties of the heating process and the cooling process can be calculated from Eqs. (25-30).
Dheat H ¼ CpðsÞ ðTm TÞ
(25)
Dcool H ¼ CpðlÞ ðT Tm Þ
(26)
Tm T
(27)
T Tm
(28)
Dheat S ¼ CpðsÞ ln Dcool S ¼ CpðlÞ ln
The Cp(s) and Cp(l) representing the constant pressure heat capacity of solid and liquid respectively, which are very close in most circumstances. Therefore, the values of (DheatH þ DcoolH) and (DheatS þ DcoolS) can be considered as zero. And the following equations can be used to calculate the dissolution thermodynamics:
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
B. Tian et al. / Journal of Molecular Liquids xxx (xxxx) xxx Table 3 Experimental and calculated mole fraction solubility of flurbiprofen in the twelve pure solvents from 283.15 K to 323.15 K under p ¼ 101.3 kPaa,b T/K
103xexp,a 1
N-propanol 283.15 60.3 288.15 71.7 293.15 84.8 298.15 101 303.15 119 308.15 139 313.15 160 318.15 190 323.15 233 Isopropanol 283.15 64.1 288.15 76.7 293.15 93.5 298.15 109 303.15 127 308.15 151 313.15 177 318.15 205 323.15 239 N-butanol 283.15 66.4 288.15 78.7 293.15 92.4 298.15 108 303.15 125 308.15 150 313.15 175 318.15 201 323.15 240 Isobutanol 283.15 50.3 288.15 58.3 293.15 68.3 298.15 81.5 303.15 100 308.15 119 313.15 140 318.15 165 323.15 200 Isopentanol 283.15 68.7 288.15 77.4 293.15 91.1 298.15 107 303.15 124 308.15 145 313.15 170 318.15 197 323.15 230 Isopropyl acetate 283.15 89.5 288.15 97.6 293.15 113 298.15 135 303.15 152 308.15 176 313.15 203 318.15 230 323.15 277 Methyl tert-butyl ether 283.15 172 288.15 185 293.15 196 298.15 212 303.15 236 308.15 251 313.15 280 318.15 305 323.15 335 Isopropyl ether 283.15 32.1 288.15 40.2
Apelblat
lh
Wilson
NRTL
103xcal 1
103xcal 1
103xcal 1
103xcal 1
60.7 71.6 84.6 100 118 139 164 193 227
57.3 69.6 83.9 100 120 141 166 194 225
56.6 69.2 83.9 101 120 142 167 194 222
60.3 72.6 86.7 103 121 142 166 192 220
64.3 77.1 91.8 109 129 151 176 205 238
63.5 76.6 91.7 109 129 152 177 206 237
61.9 75.8 91.9 110 131 153 178 205 234
66.1 79.2 94.1 111 131 152 176 203 233
66.7 78.3 91.9 108 127 148 174 204 238
63.6 76.6 91.6 109 128 151 176 204 235
65.9 78.9 93.8 111 130 151 175 202 231
65.5 78.5 93.4 111 130 151 175 203 231
49.7 58.7 69.4 82.4 98.0 117 140 167 200
46.2 56.7 69.0 83.5 100 120 142 167 196
46.2 56.6 68.9 83.3 100 120 142 167 196
48.6 58.9 71.1 85.1 101 120 141 166 193
67.8 78.6 91.3 106 124 144 169 197 231
64.3 76.8 91.1 108 126 147 171 197 227
64.2 76.9 91.3 108 126 147 171 197 226
63.9 76.6 91.1 108 126 148 171 197 226
87.8 100 114 131 151 175 203 235 274
82.2 97.2 114 133 155 179 206 235 268
82.5 97.9 115 134 156 180 206 235 265
82.2 97.9 115 134 156 180 206 235 264
172 184 198 214 232 253 277 305 336
166 182 199 217 236 257 280 304 330
160 178 201 221 237 262 280 303 325
161 179 201 221 237 262 280 303 325
32.5 39.7
29.6 37.7
30.7 38.5
31.5 39.0
5
Table 3 (continued ) Apelblat
lh
Wilson
NRTL
103xcal 1
103xcal 1
103xcal 1
103xcal 1
49.3 58.8 72.7 89.0 109 131 167
48.5 59.3 72.6 89.0 109 134 164
47.6 59.5 73.9 90.9 111 135 162
47.9 59.2 73.3 90.1 110 134 164
48.1 59.0 72.7 89.4 110 134 165
11.8 15.2 20.7 26.0 33.3 43.8 56.9 70.5 93.2
11.8 15.4 20.1 26.1 33.8 43.6 56.1 72.1 92.2
10.9 14.7 19.7 26.0 34.1 44.2 56.8 72.5 91.6
12.4 15.8 20.5 26.1 33.5 43.2 55.8 71.3 93.3
13.0 16.3 20.8 26.2 33.3 42.9 55.5 70.8 93.7
0.409 0.531 0.700 0.919 1.21 1.52 1.94 2.41 3.17
0.407 0.537 0.703 0.916 1.18 1.52 1.94 2.47 3.12
0.405 0.535 0.702 0.914 1.18 1.52 1.94 2.47 3.14
0.410 0.539 0.704 0.914 1.18 1.51 1.94 2.46 3.15
0.416 0.550 0.720 0.935 1.21 1.54 1.96 2.47 3.12
0.350 0.455 0.598 0.750 0.959 1.23 1.66 2.10 2.84
0.355 0.453 0.581 0.748 0.968 1.26 1.64 2.14 2.80
0.308 0.417 0.558 0.742 0.978 1.28 1.67 2.16 2.78
0.322 0.428 0.568 0.745 0.973 1.27 1.66 2.14 2.81
0.353 0.468 0.615 0.800 1.03 1.33 1.69 2.14 2.71
0.306 0.394 0.550 0.713 0.921 1.20 1.49 1.91 2.48
0.303 0.406 0.538 0.706 0.920 1.19 1.52 1.93 2.44
0.308 0.409 0.538 0.704 0.914 1.18 1.51 1.93 2.46
0.313 0.413 0.543 0.707 0.915 1.18 1.51 1.93 2.48
0.322 0.426 0.559 0.728 0.940 1.21 1.53 1.94 2.44
103xexp,a 1
T/K
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 N-octane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-heptane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-hexane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
a Standard uncertainties are u(T) ¼ 0.05 K and u(p) ¼ 0.3 kPa. Relative standard uncertainty is ur(x1) ¼ 0.05. b xexp is the experimental mole fraction solubility, xcal 1 1 is the calculated mole fraction solubility of flurbiprofen.
Ddis H ¼ xN Dfus H þ Dmix H
(29)
Ddis S ¼ xN Dfus S þ Dmix S
(30)
Ddis G ¼ Ddis H T Ddis S
(31)
As for the fusion process, the value of DfusG can be considered as zero now that the system is in equilibrium. The value of DfusH can be measured by DSC, and the value of DfusS can be calculated from Eq. (32).
Dfus S ¼
Dfus H Tm
(32)
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
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4. Results and discussion 4.1. Characterization of flurbiprofen The PXRD patterns of the raw material, wet solid recovered from the equilibrium solid phase after the solubility experiments and Form I by simulating from a single crystal structure (CCDC 1157849) [24] are shown in Fig. 2. It can be seen that there was no polymorphic transformation and crystal forms of all the samples remained unchanged during the experiments. The DSC analysis results of flurbiprofen are shown in Fig. 3. It can be seen from the curve that a clear endothermic peak is located at T ¼ 388.8 K, which is in accordance with data reported in the literature (Tm ¼ 389.3 K) [25]. And the molar enthalpy of fusion is 26.335 kJ/mol. These tiny deviations from the reported values might be resulted from the differences of instruments, measurement methods and environment of experiments. The standard uncertainties of the Tm and DfusH are 0.5 K and 0.02 kJ/mol, respectively. Fig. 4. Mole fraction solubility of flurbiprofen in nine pure solvents (n-propanol, isopropanol, n-butanol, isobutanol, isopentanol, isopropyl acetate, methyl tert-butyl ether, isopropyl ether, acetonitrile) at temperatures ranging from 283.15 K to 323.15 K.
Fig. 5. Mole fraction solubility of flurbiprofen in three pure solvents (n-octane, nheptane, n-hexane) at temperatures ranging from 283.15 K to 323.15 K.
Table 4 Physicochemical properties of some solvents used in this work. P b Solvent name pa a N-propanol Isopropanol N-butanol Isobutanol Isopentanol Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane a b c d e f
0.52 0.48 0.47 0.4 0.4 0.27 0.27 0.75 0.01 0.08 0.04
P
bc
4.2. Solubility data of flurbiprofen The mole fraction data of flurbiprofen in twelve pure solvents including n-propanol, isopropanol, n-butanol, isobutanol, isopentanol, isopropyl acetate, methyl tert-butyl ether, isopropyl ether, acetonitrile, n-octane, n-heptane, n-hexane at temperatures ranging from 283.15 K to 323.15 K are presented in Table 3 and graphically shown in Figs. 4e5. The data set can provide a reference for the selection of solvents and antisolvents in crystallization process of flurbiprofen. It can be found that all the solubility data increase apparently with the increasing temperature, and the average solubility values over full temperature range are ranked as methyl tert-butyl ether > isopropyl acetate > isopropanol z nbutanol z isopentanol > n-propanol > isobutanol > isopropyl ether > acetonitrile > n-octane > n-heptane > n-hexane. Futhermore, the solubility values in alkane solvents are approximately 102 times that in alcohol solvents, indicating that alkane solvents including n-octane, n-heptane and n-hexane should be suitable as anti-solvents. Solvent properties were collected to explain solubility data, as summarized in Table 4 [26,27]. The polarity of the chosen solvents is ranked as acetonitrile > n-propanol > isopropanol > nbutanol > isopentanol ¼ isobutanol > methyl tert-butyl ether > isopropyl ether > n-octane > n-heptane > n-hexane. The order of polarity is the same as the solubility order of alkane solvents, which are consistent with “like dissolves like” rules. However, the
Dipole momentd
Dielectric constante
Cohesive energy densityf
0.37 0.33 0.37 0.37
0.48 0.56 0.48 0.48
1.55 1.56 1.66 1.64
20.52 19.26 17.33 16.78
520.37 489.11 446.01 425.37
0 0 0.07 0 0 0
0.4 0.41 0.32 0 0 0
1.2 1.13 3.92 0 0 0
4.5 3.38 35.69 1.94 1.91 1.88
226.7 188.66 522.95 195.23 200.08 200.76
Polarity/dipolarity of the solvent. Summation of the hydrogen bond donor propensities of the solvent. Summation of the hydrogen bond acceptor propensities of the solvent. Dipole moment in the unit of debye. Dielectric constant. Cohesive energy density in the unit of J$cm3.
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
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7
Table 5 Parameters and deviations of the modified Apelblat equation for flurbiprofen in different solvents at p ¼ 101.3 kPaa,b,c Parameters
A
B
C
ARD%
104RMSD
N-propanol Isopropanol N-butanol Isobutanol Isopentanol Isopropyl acetate Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane Average ARD% Average 104RMSD
120.0008 8.723133 111.4824 185.4493 151.2062 185.4241 171.8818 177.4563 121.2018 43.85164 290.5385 1.819414 1.030 11.15
2735.926 2250.103 2447.088 5535.778 4330.283 6049.515 6367.543 4720.636 1300.659 2296.237 8753.383 4460.212
19.04660 2.466449 17.73520 28.85186 23.59599 28.62680 26.14818 27.87108 19.86686 7.820382 44.57698 1.032880
1.074 0.5546 0.7262 1.103 0.5343 1.449 0.6779 1.033 1.319 1.015 1.393 1.480
25.21 8.887 14.26 13.15 6.871 25.37 18.60 13.27 7.424 0.2852 0.2292 0.2106
a b c
The values of A, B, C were obtained by correlating the experimental data with the Apelblat equation. The values of the average relative deviation (ARD%) and the root-mean-square deviations (RMSD) were calculated by Eqs. (33-34). Standard uncertainty is u(p) ¼ 0.3 kPa.
solubility data of flurbiprofen in all selected solvents are not entirely in accordance with the principle, resulted from the fact that solvent effects usually depend on more than a single property of solvents. And the dissolution is a complicated process influenced by not only polarity, but also other factors, such as ability to form hydrogen bond, size of molecules, viscosity and solutesolvent interaction. For instance, there are both hydrogen donor and hydrogen acceptor in the molecular structure of flurbiprofen, which is beneficial to the formation of hydrogen bonds with solvent molecules. Alcohol solvents including isopropanol, nbutanol, isopentanol, n-propanol and isobutanol have smaller polarity and larger solubility values than acetonitrile. It can be interpreted by the larger hydrogen bond donor/acceptor propensities of the alcohol solvents. In order to expand its application, the experimental solubility data of flurbiprofen were correlated with four thermodynamic models, whose accuracy and credibility were evaluated by the average relative deviation (ARD%) and the root-mean-square deviations (RMSD) calculated by Eqs. (33-34) [28,29].
N exp cal 100 X x i x i ARD% ¼ N i¼1 xexp i
(33)
Table 6 Parameters and deviations of the lh equation for flurbiprofen in different solvents at p ¼ 101.3 kPaa,b,c
Table 7 Parameters and deviations of the Wilson model for flurbiprofen in different solvents at p ¼ 101.3 kPaa,b,c Parameters
Dl12
Dl21
ARD%
104RMSD
N-propanol Isopropanol N-butanol Isobutanol Isopentanol Isopropyl acetate Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane Average ARD% Average 104RMSD
1581.831 2870.684 3024.858 721.4851 3140.182 3909.440 1049.001 3213.852 990.5119 8880.201 9885.675 9074.320 2.097 26.29
150.0347 595.2338 2249.938 118.8022 2738.922 3117.037 1887.890 1006.763 2499.568 5129.523 2787.283 5134.956
2.756 1.593 1.686 2.288 1.640 2.647 2.959 2.229 1.754 0.9258 3.040 1.642
48.07 24.07 37.66 24.66 23.73 54.66 77.49 18.55 5.960 0.2166 0.2744 0.1482
a The values of Dl12, Dl21 were obtained by correlating the experimental data with the Wilson model. b The values of the average relative deviation (ARD%) and the root-mean-square deviations (RMSD) were calculated by Eqs. (33-34). c Standard uncertainty is u(p) ¼ 0.3 kPa.
Table 8 Parameters and deviations of the NRTL model for flurbiprofen in different solvents at p ¼ 101.3 kPaa,b,c
Parameters
l
h
ARD%
104RMSD
Parameters
103Dg12
103Dg21
ARD%
104RMSD
N-propanol Isopropanol N-butanol Isobutanol Isopentanol Isopropyl acetate Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane Average ARD% Average 104RMSD
1.262651 1.263332 1.218218 1.164163 1.041613 1.192716 0.4249432 1.347271 1.201529 0.02965729 0.03271015 0.02446566 2.108 20.28
2542.710 2456.439 2515.937 2882.661 2783.458 2325.463 2801.019 2947.024 4075.853 151361.0 148913.9 186958.4
2.290 0.7003 1.796 2.301 1.500 2.384 1.478 3.367 2.568 0.9714 4.380 1.555
38.36 11.29 25.93 24.48 21.29 45.78 38.92 26.33 10.13 0.2611 0.4018 0.1707
N-propanol Isopropanol N-butanol Isobutanol Isopentanol Isopropyl acetate Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane Average ARD% Average 104RMSD
5.476433 2.653021 1.365753 1.247220 1.485232 2.835769 0.08064158 4.700646 4.590171 1.153305 0.5321919 1.953050 2.345 26.90
3.369539 3.557660 2.057813 1.723598 2.127835 2.984171 0.1173505 8.378196 10.17783 10.14455 11.06854 10.13745
2.786 2.757 1.834 1.956 1.688 1.723 2.329 1.341 2.743 1.905 4.190 2.892
73.51 57.91 28.39 49.65 35.95 24.35 31.11 12.57 8.138 0.3262 0.6462 0.2715
a The values of l, h were obtained by correlating the experimental solubility data with the lh equation. b The values of the average relative deviation (ARD%) and the root-mean-square deviations (RMSD) were calculated by Eqs. (33-34). c Standard uncertainty is u(p) ¼ 0.3 kPa.
a The values of Dg12, Dg21 were obtained by correlating the experimental data with the NRTL model. b The values of the average relative deviation (ARD%) and the root-mean-square deviations (RMSD) were calculated by Eqs. (33-34). c Standard uncertainty is u(p) ¼ 0.3 kPa.
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Table 9 The mixing thermodynamic properties of flurbiprofen in pure solvents.a,b T(K)
DmixG (J$mol1)
N-propanol 283.15 570.77 288.15 658.35 293.15 754.68 298.15 866.43 303.15 984.02 308.15 1105.1 313.15 1226.0 318.15 1379.5 323.15 1567.3 Isopropanol 283.15 611.71 288.15 709.05 293.15 829.19 298.15 936.24 303.15 1053.2 308.15 1198.9 313.15 1340.3 318.15 1481.2 323.15 1634.8 N-butanol 283.15 626.71 288.15 720.55 293.15 820.18 298.15 925.63 303.15 1042.7 308.15 1187.7 313.15 1328.3 318.15 1459.6 323.15 1634.7 Isobutanol 283.15 471.39 288.15 534.45 293.15 610.04 298.15 702.85 303.15 820.29 308.15 938.32 313.15 1059.3 318.15 1187.6 323.15 1351.9 Isopentanol 283.15 638.27 288.15 706.52 293.15 806.11 298.15 911.80 303.15 1024.7 308.15 1152.4 313.15 1288.0 318.15 1428.3 323.15 1577.8 Isopropyl acetate 283.15 830.31 288.15 896.21 293.15 1005.0 298.15 1151.9 303.15 1265.7 308.15 1406.0 313.15 1555.7 318.15 1692.6 323.15 1887.4 Methyl tert-butyl ether 283.15 1753.1 288.15 1846.6 293.15 1920.6 298.15 2025.8 303.15 2160.0 308.15 2248.2 313.15 2381.2 318.15 2488.1 323.15 2598.0 Isopropyl ether 283.15 296.58 288.15 356.82 293.15 421.10 298.15 485.43
DmixS (J$K1$mol1)
DmixH (kJ$mol1)
43.700 51.133 59.484 69.492 80.224 91.440 102.73 118.00 137.92
11.803 14.076 16.683 19.852 23.336 27.072 30.944 36.161 43.002
62.632 73.880 88.388 101.23 115.63 134.55 153.16 172.06 193.52
17.123 20.579 25.082 29.247 33.999 40.262 46.622 53.258 60.900
64.875 75.703 87.387 99.957 114.31 133.02 151.44 168.63 193.61
17.743 21.093 24.797 28.877 33.609 39.804 46.094 52.190 60.931
3.4749 3.9330 4.4910 5.1905 6.0990 7.0099 7.9423 8.9350 10.250
0.51253 0.59884 0.70649 0.84469 1.0286 1.2218 1.4278 1.6550 1.9604
87.053 96.118 110.58 126.06 142.79 162.25 183.31 205.40 229.62
24.011 26.990 31.611 36.674 42.262 48.846 56.114 63.918 72.623
166.77 179.50 203.46 238.12 263.89 297.57 334.72 368.67 423.08
46.391 50.826 58.641 69.844 78.731 90.289 103.26 115.60 134.83
1101.2 1133.1 1151.8 1186.1 1232.1 1251.5 1288.0 1308.3 1324.1
310.04 324.66 335.74 351.61 371.34 383.41 400.96 413.74 425.27
56.393 68.334 81.257 93.935
15.671 19.334 23.400 27.521
Table 9 (continued ) T(K)
DmixG (J$mol1)
DmixS (J$K1$mol1)
DmixH (kJ$mol1)
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 N-octane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-heptane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-hexane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
573.43 670.38 780.40 897.17 1061.7
114.45 138.71 168.92 203.21 261.74
34.121 42.073 52.117 63.753 83.520
112.84 139.08 178.94 215.50 263.30 326.14 399.20 471.01 580.70
4.8713 6.8152 9.0559 11.303 13.144 13.286 10.395 5.2781 12.855
1.4921 2.1029 2.8337 3.5856 4.2478 4.4203 3.6543 2.1502 3.5734
3.9025 4.9270 6.2774 7.9366 10.008 12.182 14.952 17.921 22.234
4.5146 5.8576 7.7267 10.135 13.316 16.722 21.359 26.468 34.803
1.2822 1.6928 2.2714 3.0297 4.0467 5.1650 6.7037 8.4386 11.269
3.3304 4.2138 5.3633 6.5685 8.1356 10.063 12.812 15.590 19.677
4.0231 5.2283 6.8778 8.6186 11.012 14.109 18.968 24.006 32.385
1.1425 1.5107 2.0216 2.5762 3.3466 4.3578 5.9526 7.6531 10.485
2.9412 3.6998 4.9161 6.1664 7.6911 9.6114 11.554 14.186 17.459
3.5062 4.5227 6.3106 8.1843 10.581 13.792 17.073 21.929 28.474
0.99573 1.3069 1.8549 2.4463 3.2153 4.2595 5.3580 6.9908 9.2188
The values of DmixG, DmixH and DmixS were calculated by Eqs. (18-20). The combined expanded uncertainties U are Uc(DHm) ¼ 0.060DHm, Uc(DSm) ¼ 0.065DSm, Uc(DGm) ¼ 0.065DGm (0.95 level of confidence). a
b
"
N 2 1 X exp x RMSD ¼ xcal i N i¼1 i
#1=2 (34)
where xexp andxcal i denote the experimental and calculated mole i fraction solubility of flurbiprofen, respectively. N stands for the number of the experimental data points. The calculated model parameters of A, B, and C in the modified Apelblat equation, l and h in the lh equation, Dlij in the Wilson model, and Dgij in the NRTL model as well as the values of ARD% and RMSD are set out in Tables 5e8. As can be seen from the table, four equations can give satisfactory correlation results by reason that ARD% values of all the equations are under 5. The modified Apelblat model can give better correlation results than the other three models with a lower ARD% value. Furthermore, the calculated solubility data are also given in Table 3 and the values obtained using the modified Apelblat equation are presented graphically in Figs. 4e5, indicating that the differences between the experimental and calculated values are really small. 4.3. Mixing and dissolution thermodynamic properties Based on the experimental solubility values and the NRTL
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
B. Tian et al. / Journal of Molecular Liquids xxx (xxxx) xxx Table 10 The dissolution thermodynamic properties of flurbiprofen in pure solvents.a,b T(K)
DdisG (J$mol1)
N-propanol 283.15 139.04 288.15 169.37 293.15 205.00 298.15 246.39 303.15 293.42 308.15 346.93 313.15 406.31 318.15 471.11 323.15 531.92 Isopropanol 283.15 153.40 288.15 185.75 293.15 223.87 298.15 267.07 303.15 316.26 308.15 371.04 313.15 432.59 318.15 501.45 323.15 573.55 N-butanol 283.15 151.25 288.15 183.95 293.15 222.15 298.15 265.61 303.15 314.82 308.15 368.75 313.15 431.39 318.15 500.11 323.15 565.72 Isobutanol 283.15 111.15 288.15 137.01 293.15 167.21 298.15 202.19 303.15 242.56 308.15 288.66 313.15 341.12 318.15 400.40 323.15 460.40 Isopentanol 283.15 146.55 288.15 179.88 293.15 214.26 298.15 259.43 303.15 305.22 308.15 359.45 313.15 420.49 318.15 486.31 323.15 554.38 Isopropyl acetate 283.15 189.81 288.15 232.60 293.15 275.10 298.15 325.61 303.15 383.70 308.15 447.18 313.15 516.51 318.15 595.50 323.15 657.36 Methyl tert-butyl ether 283.15 519.32 288.15 574.64 293.15 659.06 298.15 729.07 303.15 791.20 308.15 868.27 313.15 957.05 318.15 1019.5 323.15 1118.4 Isopropyl ether 283.15 67.246 288.15 82.651 293.15 101.61 298.15 125.06
DdisS (J$K1$mol1)
DdisH (kJ$mol1)
47.784 55.986 65.226 76.332 88.291 100.85 113.56 130.86 153.69
13.391 15.963 18.916 22.512 26.472 30.730 35.155 41.162 49.133
66.973 79.076 94.719 108.61 124.21 144.79 165.14 185.92 209.70
18.810 22.600 27.543 32.115 37.338 44.246 51.281 58.649 67.191
69.374 81.034 93.642 107.24 122.80 143.16 163.30 182.21 209.88
19.492 23.166 27.229 31.708 36.912 43.746 50.706 57.470 67.257
6.8838 7.8810 9.1196 10.710 12.843 15.063 17.431 20.077 23.823
1.8380 2.1339 2.5062 2.9910 3.6508 4.3530 5.1174 5.9871 7.2380
91.706 101.36 116.75 133.28 151.18 172.08 194.79 218.75 245.20
25.820 29.027 34.011 39.478 45.525 52.667 60.578 69.109 78.682
172.83 186.11 211.08 247.24 274.19 309.47 348.48 384.27 441.83
48.747 53.395 61.603 73.389 82.737 94.916 108.61 121.66 142.12
1112.8 1145.6 1165.1 1200.5 1248.0 1268.5 1307.0 1328.9 1346.8
314.57 329.53 340.89 357.20 377.54 390.02 408.33 421.77 434.10
58.567 71.059 84.597 97.914
16.516 20.393 24.698 29.068
9
Table 10 (continued ) T(K)
DdisG (J$mol1)
DdisS (J$K1$mol1)
DdisH (kJ$mol1)
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 N-octane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-heptane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-hexane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
153.02 183.55 223.21 268.80 318.57
119.37 144.73 176.29 212.11 273.07
36.034 44.415 54.982 67.214 87.924
28.283 35.673 44.854 56.058 69.709 86.508 107.41 133.78 165.89
4.0714 5.7884 7.6546 9.5450 10.886 10.318 6.5387 0.50654 19.170
1.1811 1.7036 2.2888 2.9019 3.3698 3.2660 2.1550 0.29494 6.0289
0.93427 1.3060 1.7132 2.2351 3.0129 3.8552 5.0518 6.2643 7.8878
4.4869 5.8216 7.6793 10.073 13.234 16.619 21.228 26.305 34.588
1.2714 1.6788 2.2529 3.0055 4.0149 5.1250 6.6526 8.3752 11.185
0.86989 1.1404 1.4748 2.0104 2.4138 3.2881 4.2436 5.4684 6.8321
3.9994 5.1975 6.8372 8.5678 10.948 14.026 18.856 23.864 32.193
1.1333 1.4988 2.0058 2.5565 3.3213 4.3254 5.9090 7.5978 10.410
0.76067 0.97760 1.3528 1.7516 2.2652 3.1635 3.8051 5.0482 6.2161
3.4855 4.4960 6.2734 8.1360 10.519 13.710 16.973 21.799 28.306
0.98768 1.2965 1.8404 2.4275 3.1911 4.2279 5.3189 6.9404 9.1533
The values of DdisG, DdisH and DdisS were calculated by Eqs.(29-31). The combined expanded uncertainties U are Uc(DHd) ¼ 0.060DHd, Uc(DSd) ¼ 0.065DSd, Uc(DGd) ¼ 0.065DGd (0.95 level of confidence). a
b
model, the mixing thermodynamic properties of flurbiprofen in different pure solvents were calculated. The results are listed in Table 9. It can be seen from the data that the values of DmixH are positive while the values of DmixG are negative, suggesting that the mixing processes in all the investigated solvent systems are endothermic and spontaneous. In addition, the dissolution thermodynamic properties were calculated through Eqs. (29-31). The results are given in Table 10. From the results listed in Table 10, the positive DdisH values and the negative DdisG values demonstrate that the dissolution processes in the tested solvent systems are endothermic and spontaneous. The absolute values of DdisG are increasing as the temperature increases, which is consistent with the fact that the solubility data of flurbiprofen increase with the rising temperature. 5. Conclusions In this work, the solubility data of flurbiprofen in twelve pure solvents were determined from 283.15 to 323.15 K under atmospheric pressure using a gravimetric method. All the solubility data increase apparently with the increasing temperature, and the average solubility values over full temperature range are ranked as
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
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methyl tert-butyl ether > isopropyl acetate > isopropanol z nbutanol z isopentanol > n-propanol > isobutanol > isopropyl ether > acetonitrile > n-octane > n-heptane > n-hexane. The experimental solubility of flurbiprofen were correlated by four thermodynamic models. The modified Apelblat equation can give better correlation results with lower values of ARD%. In addition, mixing and dissolution thermodynamic properties of Gibbs energy, enthalpy and entropy were calculated and the results indicate that both the mixing and the dissolution processes are endothermic and spontaneous in the tested solvent systems. Acknowledgements This research is financially supported by Natural Science Foundation of Tianjin (No. 18JCYBJC40800). References [1] L. Cheng, T. Li, L. Dong, X. Wang, Q. Huo, H. Wang, Z. Jiang, X. Shan, W. Pan, X. Yang, Design and evaluation of bilayer pump tablet of flurbiprofen solid dispersion for zero-order controlled delivery, J. Pharm. Sci. 107 (2018) 1434e1442, https://doi.org/10.1016/j.xphs.2017.12.026. [2] D.H. Oh, Y.-J. Park, J.H. Kang, C.S. Yong, H.-G. Choi, Physicochemical characterization and in vivo evaluation of flurbiprofen-loaded solid dispersion without crystalline change, Drug Deliv. 18 (2011) 46e53, https://doi.org/ 10.3109/10717544.2010.509365. [3] A. Mantas, V. Labbe, I. Loryan, A. Mihranyan, Amorphisation of free acid ibuprofen and other profens in mixtures with nanocellulose: dry powder formulation strategy for enhanced solubility, Pharmaceutics 11 (2019) 68, https://doi.org/10.3390/pharmaceutics11020068. [4] I.M. Chalmers, B.J. Cathcart, E.B. Kumar, W.C. Dick, W.W. Buchanan, Clinicopharmacological studies and clinical evaluation of flurbiprofen. A new nonsteroidal antirheumatic agent, Ann. Rheum. Dis. 31 (1972) 319e324, https:// doi.org/10.1136/ard.31.4.319. [5] R. Williams, M. Jeffcoat, M. Kaplan, P. Goldhaber, H. Johnson, W. Wechter, Flurbiprofen: a potent inhibitor of alveolar bone resorption in beagles, Science 227 (1985) 640e642, https://doi.org/10.1126/science.3969553. [6] R.N. Brogden, R.C. Heel, T.M. Speight, G.S. Avery, Flurbiprofen: a review of its pharmacological properties and therapeutic use in rheumatic diseases, Drugs 18 (1979) 417e438, https://doi.org/10.2165/00003495-197918060-00001. [7] J.-O. Henck, M. Kuhnert-Brandstatter, Demonstration of the terms enantiotropy and monotropy in polymorphism research exemplified by flurbiprofen, J. Pharm. Sci. 88 (1999) 103e108, https://doi.org/10.1021/js9801945. [8] A.L. Grzesiak, A.J. Matzger, New form discovery for the analgesics flurbiprofen and sulindac facilitated by polymer-induced heteronucleation, J. Pharm. Sci. 96 (2007) 2978e2986, https://doi.org/10.1002/jps.20954. [9] J.W. Mullin, Crystallization, fourth ed., Butterworth-Heinemann, Oxford ; Boston, 2001. [10] S. Black, L. Dang, C. Liu, H. Wei, On the measurement of solubility, Org. Process Res. Dev. 17 (2013) 486e492, https://doi.org/10.1021/op300336n. cs-Nova k, Study of equilibrium solubility mea[11] E. Baka, J.E.A. Comer, K. Taka surement by saturation shake-flask method using hydrochlorothiazide as model compound, J. Pharm. Biomed. Anal. 46 (2008) 335e341, https://doi.org/ 10.1016/j.jpba.2007.10.030.
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Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K Beiqian Tian a, Yaoguang Feng a, Xin Li a, Jinyue Yang a, Zhiyong Ding a, Xin Huang a, b, **, Qiuxiang Yin a, b, Chuang Xie a, b, Hongxun Hao a, b, * a
National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin, 300072, China Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300072, China
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 July 2019 Received in revised form 10 September 2019 Accepted 13 September 2019 Available online xxx
In this work, solution thermodynamic properties including solubility, mixing thermodynamic properties and dissolution thermodynamic properties are investigated in detail. Gravimetric method was utilized for measuring the solubility data of flurbiprofen in twelve pure solvents including n-propanol, isopropanol, n-butanol, isobutanol, isopentanol, isopropyl acetate, methyl tert-butyl ether, isopropyl ether, acetonitrile, n-octane, n-heptane and n-hexane over the temperatures range from 283.15 to 323.15 K under atmospheric pressure. The results indicated that the solubility of flurbiprofen increased with the increasing temperature. Furthermore, the experimental solubility data were correlated by the modified Apelblat equation, lh equation, Wilson model and NRTL model. And the modified Apelblat equation can give better correlation results with lower values of ARD%. Moreover, mixing and dissolution thermodynamic properties of flurbiprofen in different solvents were calculated according to the experimental data and the NRTL model. © 2019 Elsevier B.V. All rights reserved.
Keywords: Flurbiprofen Solubility Mixing thermodynamic properties Dissolution thermodynamic properties
1. Introduction Flurbiprofen, whose molecular formula is C15H13FO2 and CAS Registry No. is 86-55-5, is a member of the phenylalkanoic acid series. The chemical structure of flurbiprofen is presented in Fig. 1. Flurbiprofen is a weakly acidic drug possessing poor aqueous solubility and gastrointestinal irritation, classified as Biopharmaceutical Classification System Type II drug [1e3]. It is widely used for treating rheumatoid arthritis, and moderating pain of migraine, osteoarthritis, and sore throat with analgesic, antipyretic and anti-inflammatory properties [4e6]. According to previous reports, three polymorphic forms (Forms I, II and III) of flurbiprofen have been reported [7,8]. Form I is the thermodynamically stable form under ambient condition and hence Form I flurbiprofen is used in clinic. During manufacture of Form I
* Corresponding author. National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin, 300072, China. ** Corresponding author. Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300072, China. E-mail addresses: [email protected] (X. Huang), [email protected] (H. Hao).
flurbiprofen, solution crystallization is the final step which will determine the final quality of the product. Thermodynamic solubility represents the saturation concentration of a compound in equilibrium with undissolved solid phase. It is undeniably true that the solid-liquid phase equilibrium is an important part of chemical thermodynamics, which is crucial to design and optimize a crystallization process for the fact that solution crystallization is generally used as the final process to obtain pure objective crystal form products industrially. However, from literature review, reports on solubility data of flurbiprofen in organic solvents is rare. In this study, the solubility data of flurbiprofen in twelve pure organic solvents (n-propanol, isopropanol, n-butanol, isobutanol, isopentanol, isopropyl acetate, methyl tert-butyl ether, isopropyl ether, acetonitrile, n-octane, n-heptane and n-hexane.) were systematically measured from 283.15 to 323.15 K under atmospheric pressure through gravimetric method. Four thermodynamic models including the Apelblat equation, lh equation, Wilson model and NRTL model were implemented to correlate the solubility data of flurbiprofen Form I. Furthermore, the mixing and dissolution thermodynamic properties including the enthalpy, the entropy, and the Gibbs free energy change were derived through the experimental data and the NRTL model.
https://doi.org/10.1016/j.molliq.2019.111744 0167-7322/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
2
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2.4. Solubility measurements
Fig. 1. Chemical structure of flurbiprofen.
2. Experimental 2.1. Materials Flurbiprofen with mass-based fraction of 0.990 was purchased from Wuhan Yuancheng Co-creation Technology Co., Ltd. Isopropyl acetate was purchased from Shanghai Macklin Biochemical Co., Ltd. N-butanol and isopentanol were purchased from Lianlong Bohua Chemical Co., Ltd. Isopropyl ether was purchased from Tianjin Kangkede Technology Co., Ltd. All other solvents like n-propanol, isopropanol, isobutanol, methyl tert-butyl ether, acetonitrile, noctane, n-heptane and n-hexane were purchased from Tianjin Kemiou Chemical Reagent Co., Ltd. All the materials of which more detailed information are listed in Table 1 were used without further purification. 2.2. Powder X-ray diffraction The powder X-ray diffraction (PXRD) was performed to characterize the crystal form of flurbiprofen before and after each experiment. And the data were collected on Rigaku D/max-2500 (Rigaku, Japan) with voltage of 40 kV, current of 100 mA, step size of 0.02 and scanning rate of 8 /min over diffraction angle (2q) from 2 to 40 .
In this work, the classical shake-flask method [9e11] was implemented to measure the solubility data of flurbiprofen in pure solvents including n-propanol, isopropanol, n-butanol, isobutanol, isopentanol, isopropyl acetate, methyl tert-butyl ether, isopropyl ether, acetonitrile, n-octane, n-heptane and n-hexane over the temperatures range from 283.15 to 323.15 K. In this method, approximately 25 mL of solvent was added to a conical flask (50 mL) which was kept at constant temperature under the control of a shaker with thermostatic bath (Tianjin Ounuo Instrument Co. Ltd., China). Subsequently, excess flurbiprofen was added to the solvent. Undissolved solid and solution were constantly shaken at a speed of 200 rpm for 12 h to ensure that the mixture reached complete equilibrium which has been demonstrated in the preliminary experiments. After the shaker was stopped, the system was remained still for 6 h at the experimental temperature so as to precipitate the undissolved solid. After that, the supernatant liquid was withdrawn by a pre-heated or pre-cooled syringe and then was filtered into a pre-weighed beaker through an organic membrane filter (0.45 mm, f13 mm, Tianjin Jinteng Experimental Equipment Co., Ltd). The beaker with saturated solution was weighted immediately and dried in an electronic oven at 318.15 K for 36 h until the total weight of the sample did not change any more. Finally, the residual solute together with the beaker was weighed again. All samples were measured by an electronic analytical balance (Mettler Toledo ML204, Switzerland) with an accuracy of ±0.0001 g. (The wet solids which did not dissolve were analyzed by XRPD. The XRPD patterns are shown in Fig. 2). The procedure above all was carried out three times in parallel and the average value was used to calculate the mole fraction solubility of flurbiprofen based on the following equations [12]:
x1 ¼
m1 =M1 m1 =M1 þ m2 =M2
(1)
where m1 and m2 represent the mass of flurbiprofen and solvent; M1 and M2 denote the respective molar mass of flurbiprofen and solvent, respectively.
2.3. Differential scanning calorimetry 3. Thermodynamic models The melting temperature (Tm) and fusion enthalpy (DfusH) of flurbiprofen were obtained using DSC instrument (DSC 1/500, Mettler-Toledo, Switzerland). The measurements were carried out at a heating rate of 10 K/min under protection of a nitrogen atmosphere. An empty pan was used as contrast while another 5e10 mg flurbiprofen was put into an aluminum pan scanning from 298.15 K to 403.15 K.
3.1. Modified apelblat equation Deduced from the Clausius-Clapeyron equation, the modified Apelblat equation is a commonly used semi-empirical model to correlate the absolute temperature and the solubility of solute. The formula is given as follows [13].
Table 1 The sources and mass-based fraction of experimental materials. Chemical name
CAS Registry No.
Source
Mass purity
Analysis method
N-propanol Isopropanol N-butanol Isobutanol Isopentanol Isopropyl acetate Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane
71-23-8 67-63-0 71-36-3 78-83-1 123-51-3 108-21-4 1634-04-4 108-20-3 75-05-8 111-65-9 142-82-5 110-54-3
Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Lianlong Bohua Chemical Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Lianlong Bohua Chemical Co., Ltd., Tianjin, China Shanghai Macklin Biochemical Co., Ltd., Shanghai, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Tianjin Kangkede Technology Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China
0.995 0.997 0.995 0.990 0.985 >0.990 0.995 0.950 0.995 0.995 0.995 0.995
GCa GCa GCb GCa GCb GCc GCa GCd GCa GCa GCa GCa
a b c d
Gas Gas Gas Gas
chromatography, chromatography, chromatography, chromatography,
conducted conducted conducted conducted
by by by by
Tianjin Kemiou Chemical Reagent Co., Ltd., Tianjin, China. Lianlong Bohua Chemical Co., Ltd., Tianjin, China. Shanghai Macklin Biochemical Co., Ltd., Shanghai, China. Tianjin Kangkede Technology Co., Ltd., Tianjin, China.
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
B. Tian et al. / Journal of Molecular Liquids xxx (xxxx) xxx
3
thermodynamic model, which is written as follows [17,18].
lnx1 ¼
DfusH
R
ðT ðT 1 1 1 1 DCp lng1 dT DCpdT þ Tm T RT R T Tm
Tm
(4) where x1, DfusH, R, Tm, g1, DCp, and T are the equilibrium mole fraction of the solute, the fusion enthalpy of solute, the gas constant, the melting point of the solute, the activity coefficient, the difference of heat capacities between subcooled liquid and solid, and the absolute temperature, respectively. In addition, the latter two items in Eq. (4) are generally much lower in value than the first two due to the diminutive value of DCp, Eq. (4) can be simplified as follows.
lnx1 ¼ Fig. 2. Powder X-ray diffraction patterns of residual solid in different solvents: (a) simulated from a single crystal structure; (b) raw flurbiprofen; (c) residual solid in npropanol; (d) residual solid in isopropanol; (e) residual solid in n-butanol; (f) residual solid in isobutanol; (g) residual solid in isopentanol; (h) residual solid in isopropyl acetate; (i) residual solid in methyl tert-butyl ether; (j) residual solid in isopropyl ether; (k) residual solid in acetonitrile; (l) residual solid in n-octane; (m) residual solid in n-heptane; (n) residual solid in n-hexane.
lnx1 ¼ A þ
B þ C ln T T
(2)
where x1 is the mole fraction solubility of flurbiprofen. T is the corresponding absolute temperature. A, B, and C are fitted model parameters. The values of A and B reveal the variation in the solution activity coefficient, and C is the indication of the influence of temperature on the enthalpy of fusion [14].
DfusH R
1 1 lng1 Tm T
(5)
The NRTL model can be used to calculate the solute activity coefficient (g1). In pure solvents, the activity coefficient can be calculated by Eqs. (6-10)
" lng1 ¼ x22
t21 G221 ðx1 þ G21 x2 Þ
þ 2
t12 G212
# (6)
ðx2 þ G12 x1 Þ2
G12 ¼ eðat12 Þ
(7)
G21 ¼ eðat21 Þ
(8)
t12 ¼
g12 g22 Dg12 ¼ RT RT
(9)
3.2. lh equation
t21 ¼
g21 g11 Dg21 ¼ RT RT
(10)
Another empirical formula, the lh equation proposed by H. Buchowski et al., can also be implemented to describe the equilibrium data [15]. The equation can be described as Eq. (3) [16].
where R is the gas constant (8.314 J mol1 K1). T refers to thermodynamic temperature. Dg12 and Dg21 are parameters of this model which represent the Gibbs free energy of intermolecular interaction. The parameter a is a regulable constant between 0 and 1 standing for the non-randomness of the system [19]. In this work, a ¼ 0.2 was chosen for the correlation of flurbiprofen solubility data in twelve different pure solvents.
1 x1 1 1 ¼ lh ln 1 þ l T Tm x1
(3)
where l and h are two model parameters in the equation, T is absolute temperature and Tm refers to the melting temperature of solute.
3.4. Wilson model 3.3. NRTL model The solubility of solute can be expressed by a general
The Wilson equation proposed by Wilson [20] can be used to determine the activity coefficients and is described as follows
Table 2 Density and molar volumes of flurbiprofen and all the organic solvents used. Substance
r(g/cm3)
V(cm3/mol)c
Substance
r(g/cm3)
V(cm3/mol)c
Flurbiprofena N-propanolb Isopropanolb N-butanolb Isobutanolb Isopentanolb Isopropyl acetateb
1.279 0.804 0.786 0.810 0.802 0.810 0.888
191 74.8 76.5 91.5 92.4 109 115
Methyl tert-butyl etherb Isopropyl etherb Acetonitrileb N-octaneb N-heptaneb N-hexaneb
0.741 0.725 0.790 0.703 0.680 0.660
119 141 52.0 162 147 131
a b c
The density of flurbiprofen was obtained by the tapping density tester. The density of solvents were obtained from literature [21]. The molar volume of flurbiprofen and solvents were calculated by Eq. (14).
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
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where x1 and x2 stand for the mole fraction of flurbiprofen and solvent respectively. The mixing thermodynamic properties of the real solution system can be calculated by using Eqs. (18-20).
Dmix G ¼ GE þ Dmix Gid
(18)
Dmix H ¼ HE þ Dmix Hid
(19)
Dmix S ¼ SE þ Dmix Sid
(20)
where DmixG, DmixH and DmixS refer to mixing properties of Gibbs energy, enthalpy and entropy respectively, and GE, HE and SE represent the excess mixing properties of Gibbs energy, enthalpy and entropy of the real solution, respectively. They can be deduced from Eqs. (21-23) [22].
GE ¼ RTðx1 lng1 þ x2 lng2 Þ Fig. 3. DSC plot of flurbiprofen. E
lng1 ¼ lnðx1 þ L12 x2 Þ þ x2
L12 L21 x1 þ L12 x2 x2 þ L21 x1
H ¼ T
l l V Dl V2 11 ¼ 2 exp 12 exp 12 V1 RT V1 RT
(12)
L21 ¼
l l V Dl V1 22 ¼ 1 exp 21 exp 21 V2 RT V2 RT
(13)
M
r
" E . # v G T vT
vlng1 vlng2 þ x2 ¼ RT 2 x1 vT vT p;x p;x
(11)
L12 ¼
V¼
2
(21)
(14)
where L12 and L21 represent Wilson parameters. Dl12 and Dl21 are two model parameters which represent the cross interaction energy parameters. V1 and V2 represent the molar volume of the solute and the solvent respectively, which can be determined by the molar mass and density by Eq. (14), where M represents the molar mass and r is the density. In addition, the density of the solvents were obtained from literature and the density of flurbiprofen was measured by the tapping density tester (ZS-201, Liaoning Instrumentation Research Institute Co. Ltd). In detail, pre-weighted flurbiprofen was put into a 25 mL graduated cylinder. Subsequently, the graduated cylinder was put on the tapping density tester shaking for 40 min at a frequency of 150 times/minute until the volume remained constant. The experiment was repeated three times to obtain the density of flurbiprofen. The values of molar volume and density are listed in Table 2. 3.5. Mixing and dissolution thermodynamic properties It is of great importance to investigate the mixing and dissolution properties of flurbiprofen in real solutions. For the ideal solution, its mixing properties including Gibbs energy, enthalpy, and entropy can be described as Eqs. (15-17)
Dmix Gid ¼ RTðx1 lnx1 þ x2 lnx2 Þ
(15)
Dmix Hid ¼ 0
(16)
Dmix Sid ¼ Rðx1 lnx1 þ x2 lnx2 Þ
(17)
(22) SE ¼
H E GE T
(23)
where g1 and g2 denote the activity coefficient of solute and solvent respectively, which can be calculated from the NRTL model. With regard to thermodynamic dissolution properties, they can be calculated on the basis of the mixed thermodynamic properties, since four processes including mixing can be considered to be the constitutive stages of dissolution process, which is expressed as follows [23]. heating fusion Solute(solid) at T!Solute(solid) at Tm ! Solute(liquid) at Tm cooling mixing !Solute(liquid) at T! Solute(solution) at T. Then the entire dissolution thermodynamic can be described as
Ddis M ¼ x1 Dheat M þ Dfus M þ Dcool M þ Dmix M
(24)
where M stands for enthalpy (H), entropy (S) and Gibbs energy (G) respectively. x1 is the mole fraction of solute. DdisM, DheatM, DfusM, DcoolM and DmixM mean the thermodynamic property of dissolution, heating, fusion cooling and mixing process respectively. The thermodynamic properties of the heating process and the cooling process can be calculated from Eqs. (25-30).
Dheat H ¼ CpðsÞ ðTm TÞ
(25)
Dcool H ¼ CpðlÞ ðT Tm Þ
(26)
Tm T
(27)
T Tm
(28)
Dheat S ¼ CpðsÞ ln Dcool S ¼ CpðlÞ ln
The Cp(s) and Cp(l) representing the constant pressure heat capacity of solid and liquid respectively, which are very close in most circumstances. Therefore, the values of (DheatH þ DcoolH) and (DheatS þ DcoolS) can be considered as zero. And the following equations can be used to calculate the dissolution thermodynamics:
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
B. Tian et al. / Journal of Molecular Liquids xxx (xxxx) xxx Table 3 Experimental and calculated mole fraction solubility of flurbiprofen in the twelve pure solvents from 283.15 K to 323.15 K under p ¼ 101.3 kPaa,b T/K
103xexp,a 1
N-propanol 283.15 60.3 288.15 71.7 293.15 84.8 298.15 101 303.15 119 308.15 139 313.15 160 318.15 190 323.15 233 Isopropanol 283.15 64.1 288.15 76.7 293.15 93.5 298.15 109 303.15 127 308.15 151 313.15 177 318.15 205 323.15 239 N-butanol 283.15 66.4 288.15 78.7 293.15 92.4 298.15 108 303.15 125 308.15 150 313.15 175 318.15 201 323.15 240 Isobutanol 283.15 50.3 288.15 58.3 293.15 68.3 298.15 81.5 303.15 100 308.15 119 313.15 140 318.15 165 323.15 200 Isopentanol 283.15 68.7 288.15 77.4 293.15 91.1 298.15 107 303.15 124 308.15 145 313.15 170 318.15 197 323.15 230 Isopropyl acetate 283.15 89.5 288.15 97.6 293.15 113 298.15 135 303.15 152 308.15 176 313.15 203 318.15 230 323.15 277 Methyl tert-butyl ether 283.15 172 288.15 185 293.15 196 298.15 212 303.15 236 308.15 251 313.15 280 318.15 305 323.15 335 Isopropyl ether 283.15 32.1 288.15 40.2
Apelblat
lh
Wilson
NRTL
103xcal 1
103xcal 1
103xcal 1
103xcal 1
60.7 71.6 84.6 100 118 139 164 193 227
57.3 69.6 83.9 100 120 141 166 194 225
56.6 69.2 83.9 101 120 142 167 194 222
60.3 72.6 86.7 103 121 142 166 192 220
64.3 77.1 91.8 109 129 151 176 205 238
63.5 76.6 91.7 109 129 152 177 206 237
61.9 75.8 91.9 110 131 153 178 205 234
66.1 79.2 94.1 111 131 152 176 203 233
66.7 78.3 91.9 108 127 148 174 204 238
63.6 76.6 91.6 109 128 151 176 204 235
65.9 78.9 93.8 111 130 151 175 202 231
65.5 78.5 93.4 111 130 151 175 203 231
49.7 58.7 69.4 82.4 98.0 117 140 167 200
46.2 56.7 69.0 83.5 100 120 142 167 196
46.2 56.6 68.9 83.3 100 120 142 167 196
48.6 58.9 71.1 85.1 101 120 141 166 193
67.8 78.6 91.3 106 124 144 169 197 231
64.3 76.8 91.1 108 126 147 171 197 227
64.2 76.9 91.3 108 126 147 171 197 226
63.9 76.6 91.1 108 126 148 171 197 226
87.8 100 114 131 151 175 203 235 274
82.2 97.2 114 133 155 179 206 235 268
82.5 97.9 115 134 156 180 206 235 265
82.2 97.9 115 134 156 180 206 235 264
172 184 198 214 232 253 277 305 336
166 182 199 217 236 257 280 304 330
160 178 201 221 237 262 280 303 325
161 179 201 221 237 262 280 303 325
32.5 39.7
29.6 37.7
30.7 38.5
31.5 39.0
5
Table 3 (continued ) Apelblat
lh
Wilson
NRTL
103xcal 1
103xcal 1
103xcal 1
103xcal 1
49.3 58.8 72.7 89.0 109 131 167
48.5 59.3 72.6 89.0 109 134 164
47.6 59.5 73.9 90.9 111 135 162
47.9 59.2 73.3 90.1 110 134 164
48.1 59.0 72.7 89.4 110 134 165
11.8 15.2 20.7 26.0 33.3 43.8 56.9 70.5 93.2
11.8 15.4 20.1 26.1 33.8 43.6 56.1 72.1 92.2
10.9 14.7 19.7 26.0 34.1 44.2 56.8 72.5 91.6
12.4 15.8 20.5 26.1 33.5 43.2 55.8 71.3 93.3
13.0 16.3 20.8 26.2 33.3 42.9 55.5 70.8 93.7
0.409 0.531 0.700 0.919 1.21 1.52 1.94 2.41 3.17
0.407 0.537 0.703 0.916 1.18 1.52 1.94 2.47 3.12
0.405 0.535 0.702 0.914 1.18 1.52 1.94 2.47 3.14
0.410 0.539 0.704 0.914 1.18 1.51 1.94 2.46 3.15
0.416 0.550 0.720 0.935 1.21 1.54 1.96 2.47 3.12
0.350 0.455 0.598 0.750 0.959 1.23 1.66 2.10 2.84
0.355 0.453 0.581 0.748 0.968 1.26 1.64 2.14 2.80
0.308 0.417 0.558 0.742 0.978 1.28 1.67 2.16 2.78
0.322 0.428 0.568 0.745 0.973 1.27 1.66 2.14 2.81
0.353 0.468 0.615 0.800 1.03 1.33 1.69 2.14 2.71
0.306 0.394 0.550 0.713 0.921 1.20 1.49 1.91 2.48
0.303 0.406 0.538 0.706 0.920 1.19 1.52 1.93 2.44
0.308 0.409 0.538 0.704 0.914 1.18 1.51 1.93 2.46
0.313 0.413 0.543 0.707 0.915 1.18 1.51 1.93 2.48
0.322 0.426 0.559 0.728 0.940 1.21 1.53 1.94 2.44
103xexp,a 1
T/K
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 N-octane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-heptane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-hexane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
a Standard uncertainties are u(T) ¼ 0.05 K and u(p) ¼ 0.3 kPa. Relative standard uncertainty is ur(x1) ¼ 0.05. b xexp is the experimental mole fraction solubility, xcal 1 1 is the calculated mole fraction solubility of flurbiprofen.
Ddis H ¼ xN Dfus H þ Dmix H
(29)
Ddis S ¼ xN Dfus S þ Dmix S
(30)
Ddis G ¼ Ddis H T Ddis S
(31)
As for the fusion process, the value of DfusG can be considered as zero now that the system is in equilibrium. The value of DfusH can be measured by DSC, and the value of DfusS can be calculated from Eq. (32).
Dfus S ¼
Dfus H Tm
(32)
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
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B. Tian et al. / Journal of Molecular Liquids xxx (xxxx) xxx
4. Results and discussion 4.1. Characterization of flurbiprofen The PXRD patterns of the raw material, wet solid recovered from the equilibrium solid phase after the solubility experiments and Form I by simulating from a single crystal structure (CCDC 1157849) [24] are shown in Fig. 2. It can be seen that there was no polymorphic transformation and crystal forms of all the samples remained unchanged during the experiments. The DSC analysis results of flurbiprofen are shown in Fig. 3. It can be seen from the curve that a clear endothermic peak is located at T ¼ 388.8 K, which is in accordance with data reported in the literature (Tm ¼ 389.3 K) [25]. And the molar enthalpy of fusion is 26.335 kJ/mol. These tiny deviations from the reported values might be resulted from the differences of instruments, measurement methods and environment of experiments. The standard uncertainties of the Tm and DfusH are 0.5 K and 0.02 kJ/mol, respectively. Fig. 4. Mole fraction solubility of flurbiprofen in nine pure solvents (n-propanol, isopropanol, n-butanol, isobutanol, isopentanol, isopropyl acetate, methyl tert-butyl ether, isopropyl ether, acetonitrile) at temperatures ranging from 283.15 K to 323.15 K.
Fig. 5. Mole fraction solubility of flurbiprofen in three pure solvents (n-octane, nheptane, n-hexane) at temperatures ranging from 283.15 K to 323.15 K.
Table 4 Physicochemical properties of some solvents used in this work. P b Solvent name pa a N-propanol Isopropanol N-butanol Isobutanol Isopentanol Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane a b c d e f
0.52 0.48 0.47 0.4 0.4 0.27 0.27 0.75 0.01 0.08 0.04
P
bc
4.2. Solubility data of flurbiprofen The mole fraction data of flurbiprofen in twelve pure solvents including n-propanol, isopropanol, n-butanol, isobutanol, isopentanol, isopropyl acetate, methyl tert-butyl ether, isopropyl ether, acetonitrile, n-octane, n-heptane, n-hexane at temperatures ranging from 283.15 K to 323.15 K are presented in Table 3 and graphically shown in Figs. 4e5. The data set can provide a reference for the selection of solvents and antisolvents in crystallization process of flurbiprofen. It can be found that all the solubility data increase apparently with the increasing temperature, and the average solubility values over full temperature range are ranked as methyl tert-butyl ether > isopropyl acetate > isopropanol z nbutanol z isopentanol > n-propanol > isobutanol > isopropyl ether > acetonitrile > n-octane > n-heptane > n-hexane. Futhermore, the solubility values in alkane solvents are approximately 102 times that in alcohol solvents, indicating that alkane solvents including n-octane, n-heptane and n-hexane should be suitable as anti-solvents. Solvent properties were collected to explain solubility data, as summarized in Table 4 [26,27]. The polarity of the chosen solvents is ranked as acetonitrile > n-propanol > isopropanol > nbutanol > isopentanol ¼ isobutanol > methyl tert-butyl ether > isopropyl ether > n-octane > n-heptane > n-hexane. The order of polarity is the same as the solubility order of alkane solvents, which are consistent with “like dissolves like” rules. However, the
Dipole momentd
Dielectric constante
Cohesive energy densityf
0.37 0.33 0.37 0.37
0.48 0.56 0.48 0.48
1.55 1.56 1.66 1.64
20.52 19.26 17.33 16.78
520.37 489.11 446.01 425.37
0 0 0.07 0 0 0
0.4 0.41 0.32 0 0 0
1.2 1.13 3.92 0 0 0
4.5 3.38 35.69 1.94 1.91 1.88
226.7 188.66 522.95 195.23 200.08 200.76
Polarity/dipolarity of the solvent. Summation of the hydrogen bond donor propensities of the solvent. Summation of the hydrogen bond acceptor propensities of the solvent. Dipole moment in the unit of debye. Dielectric constant. Cohesive energy density in the unit of J$cm3.
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7
Table 5 Parameters and deviations of the modified Apelblat equation for flurbiprofen in different solvents at p ¼ 101.3 kPaa,b,c Parameters
A
B
C
ARD%
104RMSD
N-propanol Isopropanol N-butanol Isobutanol Isopentanol Isopropyl acetate Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane Average ARD% Average 104RMSD
120.0008 8.723133 111.4824 185.4493 151.2062 185.4241 171.8818 177.4563 121.2018 43.85164 290.5385 1.819414 1.030 11.15
2735.926 2250.103 2447.088 5535.778 4330.283 6049.515 6367.543 4720.636 1300.659 2296.237 8753.383 4460.212
19.04660 2.466449 17.73520 28.85186 23.59599 28.62680 26.14818 27.87108 19.86686 7.820382 44.57698 1.032880
1.074 0.5546 0.7262 1.103 0.5343 1.449 0.6779 1.033 1.319 1.015 1.393 1.480
25.21 8.887 14.26 13.15 6.871 25.37 18.60 13.27 7.424 0.2852 0.2292 0.2106
a b c
The values of A, B, C were obtained by correlating the experimental data with the Apelblat equation. The values of the average relative deviation (ARD%) and the root-mean-square deviations (RMSD) were calculated by Eqs. (33-34). Standard uncertainty is u(p) ¼ 0.3 kPa.
solubility data of flurbiprofen in all selected solvents are not entirely in accordance with the principle, resulted from the fact that solvent effects usually depend on more than a single property of solvents. And the dissolution is a complicated process influenced by not only polarity, but also other factors, such as ability to form hydrogen bond, size of molecules, viscosity and solutesolvent interaction. For instance, there are both hydrogen donor and hydrogen acceptor in the molecular structure of flurbiprofen, which is beneficial to the formation of hydrogen bonds with solvent molecules. Alcohol solvents including isopropanol, nbutanol, isopentanol, n-propanol and isobutanol have smaller polarity and larger solubility values than acetonitrile. It can be interpreted by the larger hydrogen bond donor/acceptor propensities of the alcohol solvents. In order to expand its application, the experimental solubility data of flurbiprofen were correlated with four thermodynamic models, whose accuracy and credibility were evaluated by the average relative deviation (ARD%) and the root-mean-square deviations (RMSD) calculated by Eqs. (33-34) [28,29].
N exp cal 100 X x i x i ARD% ¼ N i¼1 xexp i
(33)
Table 6 Parameters and deviations of the lh equation for flurbiprofen in different solvents at p ¼ 101.3 kPaa,b,c
Table 7 Parameters and deviations of the Wilson model for flurbiprofen in different solvents at p ¼ 101.3 kPaa,b,c Parameters
Dl12
Dl21
ARD%
104RMSD
N-propanol Isopropanol N-butanol Isobutanol Isopentanol Isopropyl acetate Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane Average ARD% Average 104RMSD
1581.831 2870.684 3024.858 721.4851 3140.182 3909.440 1049.001 3213.852 990.5119 8880.201 9885.675 9074.320 2.097 26.29
150.0347 595.2338 2249.938 118.8022 2738.922 3117.037 1887.890 1006.763 2499.568 5129.523 2787.283 5134.956
2.756 1.593 1.686 2.288 1.640 2.647 2.959 2.229 1.754 0.9258 3.040 1.642
48.07 24.07 37.66 24.66 23.73 54.66 77.49 18.55 5.960 0.2166 0.2744 0.1482
a The values of Dl12, Dl21 were obtained by correlating the experimental data with the Wilson model. b The values of the average relative deviation (ARD%) and the root-mean-square deviations (RMSD) were calculated by Eqs. (33-34). c Standard uncertainty is u(p) ¼ 0.3 kPa.
Table 8 Parameters and deviations of the NRTL model for flurbiprofen in different solvents at p ¼ 101.3 kPaa,b,c
Parameters
l
h
ARD%
104RMSD
Parameters
103Dg12
103Dg21
ARD%
104RMSD
N-propanol Isopropanol N-butanol Isobutanol Isopentanol Isopropyl acetate Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane Average ARD% Average 104RMSD
1.262651 1.263332 1.218218 1.164163 1.041613 1.192716 0.4249432 1.347271 1.201529 0.02965729 0.03271015 0.02446566 2.108 20.28
2542.710 2456.439 2515.937 2882.661 2783.458 2325.463 2801.019 2947.024 4075.853 151361.0 148913.9 186958.4
2.290 0.7003 1.796 2.301 1.500 2.384 1.478 3.367 2.568 0.9714 4.380 1.555
38.36 11.29 25.93 24.48 21.29 45.78 38.92 26.33 10.13 0.2611 0.4018 0.1707
N-propanol Isopropanol N-butanol Isobutanol Isopentanol Isopropyl acetate Methyl tert-butyl ether Isopropyl ether Acetonitrile N-octane N-heptane N-hexane Average ARD% Average 104RMSD
5.476433 2.653021 1.365753 1.247220 1.485232 2.835769 0.08064158 4.700646 4.590171 1.153305 0.5321919 1.953050 2.345 26.90
3.369539 3.557660 2.057813 1.723598 2.127835 2.984171 0.1173505 8.378196 10.17783 10.14455 11.06854 10.13745
2.786 2.757 1.834 1.956 1.688 1.723 2.329 1.341 2.743 1.905 4.190 2.892
73.51 57.91 28.39 49.65 35.95 24.35 31.11 12.57 8.138 0.3262 0.6462 0.2715
a The values of l, h were obtained by correlating the experimental solubility data with the lh equation. b The values of the average relative deviation (ARD%) and the root-mean-square deviations (RMSD) were calculated by Eqs. (33-34). c Standard uncertainty is u(p) ¼ 0.3 kPa.
a The values of Dg12, Dg21 were obtained by correlating the experimental data with the NRTL model. b The values of the average relative deviation (ARD%) and the root-mean-square deviations (RMSD) were calculated by Eqs. (33-34). c Standard uncertainty is u(p) ¼ 0.3 kPa.
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
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Table 9 The mixing thermodynamic properties of flurbiprofen in pure solvents.a,b T(K)
DmixG (J$mol1)
N-propanol 283.15 570.77 288.15 658.35 293.15 754.68 298.15 866.43 303.15 984.02 308.15 1105.1 313.15 1226.0 318.15 1379.5 323.15 1567.3 Isopropanol 283.15 611.71 288.15 709.05 293.15 829.19 298.15 936.24 303.15 1053.2 308.15 1198.9 313.15 1340.3 318.15 1481.2 323.15 1634.8 N-butanol 283.15 626.71 288.15 720.55 293.15 820.18 298.15 925.63 303.15 1042.7 308.15 1187.7 313.15 1328.3 318.15 1459.6 323.15 1634.7 Isobutanol 283.15 471.39 288.15 534.45 293.15 610.04 298.15 702.85 303.15 820.29 308.15 938.32 313.15 1059.3 318.15 1187.6 323.15 1351.9 Isopentanol 283.15 638.27 288.15 706.52 293.15 806.11 298.15 911.80 303.15 1024.7 308.15 1152.4 313.15 1288.0 318.15 1428.3 323.15 1577.8 Isopropyl acetate 283.15 830.31 288.15 896.21 293.15 1005.0 298.15 1151.9 303.15 1265.7 308.15 1406.0 313.15 1555.7 318.15 1692.6 323.15 1887.4 Methyl tert-butyl ether 283.15 1753.1 288.15 1846.6 293.15 1920.6 298.15 2025.8 303.15 2160.0 308.15 2248.2 313.15 2381.2 318.15 2488.1 323.15 2598.0 Isopropyl ether 283.15 296.58 288.15 356.82 293.15 421.10 298.15 485.43
DmixS (J$K1$mol1)
DmixH (kJ$mol1)
43.700 51.133 59.484 69.492 80.224 91.440 102.73 118.00 137.92
11.803 14.076 16.683 19.852 23.336 27.072 30.944 36.161 43.002
62.632 73.880 88.388 101.23 115.63 134.55 153.16 172.06 193.52
17.123 20.579 25.082 29.247 33.999 40.262 46.622 53.258 60.900
64.875 75.703 87.387 99.957 114.31 133.02 151.44 168.63 193.61
17.743 21.093 24.797 28.877 33.609 39.804 46.094 52.190 60.931
3.4749 3.9330 4.4910 5.1905 6.0990 7.0099 7.9423 8.9350 10.250
0.51253 0.59884 0.70649 0.84469 1.0286 1.2218 1.4278 1.6550 1.9604
87.053 96.118 110.58 126.06 142.79 162.25 183.31 205.40 229.62
24.011 26.990 31.611 36.674 42.262 48.846 56.114 63.918 72.623
166.77 179.50 203.46 238.12 263.89 297.57 334.72 368.67 423.08
46.391 50.826 58.641 69.844 78.731 90.289 103.26 115.60 134.83
1101.2 1133.1 1151.8 1186.1 1232.1 1251.5 1288.0 1308.3 1324.1
310.04 324.66 335.74 351.61 371.34 383.41 400.96 413.74 425.27
56.393 68.334 81.257 93.935
15.671 19.334 23.400 27.521
Table 9 (continued ) T(K)
DmixG (J$mol1)
DmixS (J$K1$mol1)
DmixH (kJ$mol1)
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 N-octane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-heptane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-hexane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
573.43 670.38 780.40 897.17 1061.7
114.45 138.71 168.92 203.21 261.74
34.121 42.073 52.117 63.753 83.520
112.84 139.08 178.94 215.50 263.30 326.14 399.20 471.01 580.70
4.8713 6.8152 9.0559 11.303 13.144 13.286 10.395 5.2781 12.855
1.4921 2.1029 2.8337 3.5856 4.2478 4.4203 3.6543 2.1502 3.5734
3.9025 4.9270 6.2774 7.9366 10.008 12.182 14.952 17.921 22.234
4.5146 5.8576 7.7267 10.135 13.316 16.722 21.359 26.468 34.803
1.2822 1.6928 2.2714 3.0297 4.0467 5.1650 6.7037 8.4386 11.269
3.3304 4.2138 5.3633 6.5685 8.1356 10.063 12.812 15.590 19.677
4.0231 5.2283 6.8778 8.6186 11.012 14.109 18.968 24.006 32.385
1.1425 1.5107 2.0216 2.5762 3.3466 4.3578 5.9526 7.6531 10.485
2.9412 3.6998 4.9161 6.1664 7.6911 9.6114 11.554 14.186 17.459
3.5062 4.5227 6.3106 8.1843 10.581 13.792 17.073 21.929 28.474
0.99573 1.3069 1.8549 2.4463 3.2153 4.2595 5.3580 6.9908 9.2188
The values of DmixG, DmixH and DmixS were calculated by Eqs. (18-20). The combined expanded uncertainties U are Uc(DHm) ¼ 0.060DHm, Uc(DSm) ¼ 0.065DSm, Uc(DGm) ¼ 0.065DGm (0.95 level of confidence). a
b
"
N 2 1 X exp x RMSD ¼ xcal i N i¼1 i
#1=2 (34)
where xexp andxcal i denote the experimental and calculated mole i fraction solubility of flurbiprofen, respectively. N stands for the number of the experimental data points. The calculated model parameters of A, B, and C in the modified Apelblat equation, l and h in the lh equation, Dlij in the Wilson model, and Dgij in the NRTL model as well as the values of ARD% and RMSD are set out in Tables 5e8. As can be seen from the table, four equations can give satisfactory correlation results by reason that ARD% values of all the equations are under 5. The modified Apelblat model can give better correlation results than the other three models with a lower ARD% value. Furthermore, the calculated solubility data are also given in Table 3 and the values obtained using the modified Apelblat equation are presented graphically in Figs. 4e5, indicating that the differences between the experimental and calculated values are really small. 4.3. Mixing and dissolution thermodynamic properties Based on the experimental solubility values and the NRTL
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
B. Tian et al. / Journal of Molecular Liquids xxx (xxxx) xxx Table 10 The dissolution thermodynamic properties of flurbiprofen in pure solvents.a,b T(K)
DdisG (J$mol1)
N-propanol 283.15 139.04 288.15 169.37 293.15 205.00 298.15 246.39 303.15 293.42 308.15 346.93 313.15 406.31 318.15 471.11 323.15 531.92 Isopropanol 283.15 153.40 288.15 185.75 293.15 223.87 298.15 267.07 303.15 316.26 308.15 371.04 313.15 432.59 318.15 501.45 323.15 573.55 N-butanol 283.15 151.25 288.15 183.95 293.15 222.15 298.15 265.61 303.15 314.82 308.15 368.75 313.15 431.39 318.15 500.11 323.15 565.72 Isobutanol 283.15 111.15 288.15 137.01 293.15 167.21 298.15 202.19 303.15 242.56 308.15 288.66 313.15 341.12 318.15 400.40 323.15 460.40 Isopentanol 283.15 146.55 288.15 179.88 293.15 214.26 298.15 259.43 303.15 305.22 308.15 359.45 313.15 420.49 318.15 486.31 323.15 554.38 Isopropyl acetate 283.15 189.81 288.15 232.60 293.15 275.10 298.15 325.61 303.15 383.70 308.15 447.18 313.15 516.51 318.15 595.50 323.15 657.36 Methyl tert-butyl ether 283.15 519.32 288.15 574.64 293.15 659.06 298.15 729.07 303.15 791.20 308.15 868.27 313.15 957.05 318.15 1019.5 323.15 1118.4 Isopropyl ether 283.15 67.246 288.15 82.651 293.15 101.61 298.15 125.06
DdisS (J$K1$mol1)
DdisH (kJ$mol1)
47.784 55.986 65.226 76.332 88.291 100.85 113.56 130.86 153.69
13.391 15.963 18.916 22.512 26.472 30.730 35.155 41.162 49.133
66.973 79.076 94.719 108.61 124.21 144.79 165.14 185.92 209.70
18.810 22.600 27.543 32.115 37.338 44.246 51.281 58.649 67.191
69.374 81.034 93.642 107.24 122.80 143.16 163.30 182.21 209.88
19.492 23.166 27.229 31.708 36.912 43.746 50.706 57.470 67.257
6.8838 7.8810 9.1196 10.710 12.843 15.063 17.431 20.077 23.823
1.8380 2.1339 2.5062 2.9910 3.6508 4.3530 5.1174 5.9871 7.2380
91.706 101.36 116.75 133.28 151.18 172.08 194.79 218.75 245.20
25.820 29.027 34.011 39.478 45.525 52.667 60.578 69.109 78.682
172.83 186.11 211.08 247.24 274.19 309.47 348.48 384.27 441.83
48.747 53.395 61.603 73.389 82.737 94.916 108.61 121.66 142.12
1112.8 1145.6 1165.1 1200.5 1248.0 1268.5 1307.0 1328.9 1346.8
314.57 329.53 340.89 357.20 377.54 390.02 408.33 421.77 434.10
58.567 71.059 84.597 97.914
16.516 20.393 24.698 29.068
9
Table 10 (continued ) T(K)
DdisG (J$mol1)
DdisS (J$K1$mol1)
DdisH (kJ$mol1)
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 N-octane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-heptane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 N-hexane 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
153.02 183.55 223.21 268.80 318.57
119.37 144.73 176.29 212.11 273.07
36.034 44.415 54.982 67.214 87.924
28.283 35.673 44.854 56.058 69.709 86.508 107.41 133.78 165.89
4.0714 5.7884 7.6546 9.5450 10.886 10.318 6.5387 0.50654 19.170
1.1811 1.7036 2.2888 2.9019 3.3698 3.2660 2.1550 0.29494 6.0289
0.93427 1.3060 1.7132 2.2351 3.0129 3.8552 5.0518 6.2643 7.8878
4.4869 5.8216 7.6793 10.073 13.234 16.619 21.228 26.305 34.588
1.2714 1.6788 2.2529 3.0055 4.0149 5.1250 6.6526 8.3752 11.185
0.86989 1.1404 1.4748 2.0104 2.4138 3.2881 4.2436 5.4684 6.8321
3.9994 5.1975 6.8372 8.5678 10.948 14.026 18.856 23.864 32.193
1.1333 1.4988 2.0058 2.5565 3.3213 4.3254 5.9090 7.5978 10.410
0.76067 0.97760 1.3528 1.7516 2.2652 3.1635 3.8051 5.0482 6.2161
3.4855 4.4960 6.2734 8.1360 10.519 13.710 16.973 21.799 28.306
0.98768 1.2965 1.8404 2.4275 3.1911 4.2279 5.3189 6.9404 9.1533
The values of DdisG, DdisH and DdisS were calculated by Eqs.(29-31). The combined expanded uncertainties U are Uc(DHd) ¼ 0.060DHd, Uc(DSd) ¼ 0.065DSd, Uc(DGd) ¼ 0.065DGd (0.95 level of confidence). a
b
model, the mixing thermodynamic properties of flurbiprofen in different pure solvents were calculated. The results are listed in Table 9. It can be seen from the data that the values of DmixH are positive while the values of DmixG are negative, suggesting that the mixing processes in all the investigated solvent systems are endothermic and spontaneous. In addition, the dissolution thermodynamic properties were calculated through Eqs. (29-31). The results are given in Table 10. From the results listed in Table 10, the positive DdisH values and the negative DdisG values demonstrate that the dissolution processes in the tested solvent systems are endothermic and spontaneous. The absolute values of DdisG are increasing as the temperature increases, which is consistent with the fact that the solubility data of flurbiprofen increase with the rising temperature. 5. Conclusions In this work, the solubility data of flurbiprofen in twelve pure solvents were determined from 283.15 to 323.15 K under atmospheric pressure using a gravimetric method. All the solubility data increase apparently with the increasing temperature, and the average solubility values over full temperature range are ranked as
Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744
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methyl tert-butyl ether > isopropyl acetate > isopropanol z nbutanol z isopentanol > n-propanol > isobutanol > isopropyl ether > acetonitrile > n-octane > n-heptane > n-hexane. The experimental solubility of flurbiprofen were correlated by four thermodynamic models. The modified Apelblat equation can give better correlation results with lower values of ARD%. In addition, mixing and dissolution thermodynamic properties of Gibbs energy, enthalpy and entropy were calculated and the results indicate that both the mixing and the dissolution processes are endothermic and spontaneous in the tested solvent systems. Acknowledgements This research is financially supported by Natural Science Foundation of Tianjin (No. 18JCYBJC40800). References [1] L. Cheng, T. Li, L. Dong, X. Wang, Q. Huo, H. Wang, Z. Jiang, X. Shan, W. Pan, X. Yang, Design and evaluation of bilayer pump tablet of flurbiprofen solid dispersion for zero-order controlled delivery, J. Pharm. Sci. 107 (2018) 1434e1442, https://doi.org/10.1016/j.xphs.2017.12.026. [2] D.H. Oh, Y.-J. Park, J.H. Kang, C.S. Yong, H.-G. Choi, Physicochemical characterization and in vivo evaluation of flurbiprofen-loaded solid dispersion without crystalline change, Drug Deliv. 18 (2011) 46e53, https://doi.org/ 10.3109/10717544.2010.509365. [3] A. Mantas, V. Labbe, I. Loryan, A. Mihranyan, Amorphisation of free acid ibuprofen and other profens in mixtures with nanocellulose: dry powder formulation strategy for enhanced solubility, Pharmaceutics 11 (2019) 68, https://doi.org/10.3390/pharmaceutics11020068. [4] I.M. Chalmers, B.J. Cathcart, E.B. Kumar, W.C. Dick, W.W. Buchanan, Clinicopharmacological studies and clinical evaluation of flurbiprofen. A new nonsteroidal antirheumatic agent, Ann. Rheum. Dis. 31 (1972) 319e324, https:// doi.org/10.1136/ard.31.4.319. [5] R. Williams, M. Jeffcoat, M. Kaplan, P. Goldhaber, H. Johnson, W. Wechter, Flurbiprofen: a potent inhibitor of alveolar bone resorption in beagles, Science 227 (1985) 640e642, https://doi.org/10.1126/science.3969553. [6] R.N. Brogden, R.C. Heel, T.M. Speight, G.S. Avery, Flurbiprofen: a review of its pharmacological properties and therapeutic use in rheumatic diseases, Drugs 18 (1979) 417e438, https://doi.org/10.2165/00003495-197918060-00001. [7] J.-O. Henck, M. Kuhnert-Brandstatter, Demonstration of the terms enantiotropy and monotropy in polymorphism research exemplified by flurbiprofen, J. Pharm. Sci. 88 (1999) 103e108, https://doi.org/10.1021/js9801945. [8] A.L. Grzesiak, A.J. Matzger, New form discovery for the analgesics flurbiprofen and sulindac facilitated by polymer-induced heteronucleation, J. Pharm. Sci. 96 (2007) 2978e2986, https://doi.org/10.1002/jps.20954. [9] J.W. Mullin, Crystallization, fourth ed., Butterworth-Heinemann, Oxford ; Boston, 2001. [10] S. Black, L. Dang, C. Liu, H. Wei, On the measurement of solubility, Org. Process Res. Dev. 17 (2013) 486e492, https://doi.org/10.1021/op300336n. cs-Nova k, Study of equilibrium solubility mea[11] E. Baka, J.E.A. Comer, K. Taka surement by saturation shake-flask method using hydrochlorothiazide as model compound, J. Pharm. Biomed. Anal. 46 (2008) 335e341, https://doi.org/ 10.1016/j.jpba.2007.10.030.
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Please cite this article as: B. Tian et al., Solution thermodynamic properties of flurbiprofen in twelve solvents from 283.15 to 323.15 K, Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.111744