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Solubility correlation and thermodynamic analysis of two forms of Metaxalone in different pure solvents
Fluid Phase Equilibria 409 (2016) 1e6
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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Solubility correlation and thermodynamic analysis of two forms of Metaxalone in different pure solvents Minghuang Hong 1, Shiwang Wu 1, Minghui Qi, Guobin Ren* Laboratory of Pharmaceutical Crystal Engineering & Technology, School of Pharmacy, East China University of Science and Technology, Shanghai, 200237, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 May 2015 Received in revised form 26 August 2015 Accepted 6 September 2015 Available online 15 September 2015
The solubility data of two forms of MTX in ethanol, isopropanol, ethyl acetate and toluene was measured over the temperature range from 283.15 K to 323.15 K using shake flask method under atmospheric pressure. The experimental results indicated that the solubility of both forms of MTX increased as the temperature increased. And it was clear that the solubility of form B was lower than the solubility of form A at the same state. The experimental data was correlated by the modified Apelblat equation, the polynomial equation and the BuchowskieKsiazczak lh equation. All these thermodynamic models gave satisfactory correlation results, with the polynomial equation showing better fitting degree than the other two equations. The results of thermodynamic parameters (△Hd > 0, △Sd > 0, △Gd > 0) indicated an endothermic, entropy driven and nonspontaneous dissolution process of MTX in selected pure solvents. © 2015 Elsevier B.V. All rights reserved.
Keywords: Solubility Thermodynamic models Endothermic Entropy driven Nonspontaneous
1. Introduction Metaxalone (MTX) is a muscle relaxant used to relax muscles and relieve pain caused by strains, sprains, and other musculoskeletal conditions. Chemically, it is 5-[(3, 5-dimethylphenoxy) methyl]-1, 3-oxazolidin-2-one (Fig. 1) [1]. New therapeutic applications of MTX have been recently reported for the treatment of diabetic neuropathy and chronic daily headache [2]. Crystallization is important in the pharmaceutical industry as a separation process for intermediates and often servers as the final step in the manufacture of active pharmaceutical ingredients (APIs) [3]. The solubility of a crystalline compound provides vital thermodynamic information required to design crystallization processes, engineer the crystal size distribution and understand the phases which nucleate in the case of multiple-phase systems. Polymorphs are solid phases of the same compound but with different crystal structures. These different crystal structures exist
* Corresponding author. Laboratory of Pharmaceutical Crystal Engineering & Technology, School of Pharmacy, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237, China. E-mail addresses: [email protected] (M. Hong), [email protected] (S. Wu), [email protected] (M. Qi), [email protected] (G. Ren). 1 These authors contributed equally to this work. http://dx.doi.org/10.1016/j.fluid.2015.09.013 0378-3812/© 2015 Elsevier B.V. All rights reserved.
due to the different molecular arrangements of the molecules giving rise to differences in free energy and thus solubility [4]. Hence, it is necessary to study the solubility properties of polymorph for the purpose of separation and purification through crystallization process. The existence of polymorphism in MTX has been reported in the patent literature, which revealed two forms (A and B) that are characterized by powder X-ray diffraction (PXRD), differential scanning calorimetry (DSC), and Fourier transform infrared (FT-IR) spectroscopy [5]. Aitipamula et al. [6] reported the relative stability information of the two polymorphs of MTX. DSC thermograms of Form A and Form B were recorded at the heating rate of 5 C min1. Both forms showed a single sharp endotherm in the temperature range of 121e123 C, with the melting endotherms observed at 121.9 ± 0.1 C (△Hfus ¼ 137.1 J g1) and 122.2 ± 0.1 C (△Hfus ¼ 119.3 J g1) for Form A and Form B respectively. It was suggested that the polymorphs of MTX were enantiotropically related according to the Burger and Ramberger's heat of fusion rule, as the higher melting form showed a lower heat of fusion [7]. For expanding the fields of usage and purification of MTX, and considering the solubility studies of MTX has not been reported, in this work, the solubility data of two forms of MTX in ethanol, isopropanol, ethyl acetate, and toluene was measured from 283.15 K to 323.15 K using shake flask method.
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M. Hong et al. / Fluid Phase Equilibria 409 (2016) 1e6 Table 2 Experimental (xexptl) and correlated (xcal) mole fraction solubility of Metaxalone (Form A) in four different pure solvents (p ¼ 0.1 Mpa).a,b,c T/K
Fig. 1. Molecular structure of Metaxalone.
2. Experimental 2.1. Materials MTX was provided by Jiawei Pharmaceutical Co.,Ltd., which is a white crystalline powder with crystal gloss in the light. It's form was proved to be form A, which was characterized by powder X-ray diffraction (XRPD). Another form of MTX, form B, was prepared by our lab through crystallization process. The pure form B was confirmed by comparing its XRPD pattern with that from Ref. [6]. Each form of MTX's mass fraction was more than 99.5% determined by HPLC. All of the reagents used in this work were obtained from Shanghai Lingfeng Chemical Reagent Co.LTD with analytical reagent grade. More detailed information about the material used in this work was listed in Table 1.
2.2. Apparatus and procedure The saturated equilibrium solubility of the two forms of MTX was determined by shake flask method at atmospheric pressure and temperature range from 283.15 K to 323.15 K. An excess amount of MTX was added to known amount of various pure solvent in triplicate. The concentrated suspensions of MTX in each solvent were shaken continuously in a biological shaker at 100 rpm for 72 h. After 72 h, all the samples were taken out from the biological shaker and the solute particles were allowed to settle for 2 h. Then, the supernatant solutions were filtered through a 0.45 mm Millipore membrane filter, added to a volumetric flask, and diluted with methanol to an appropriate concentration for HPLC analysis [8e10]. The experimental mole fraction solubility (xexptl) of the two forms of MTX then calculated as reported in literature [11,12]. In order to identify the polymorph of solid phase has not changed in the measurement of solubility, the X-ray powder diffraction was used to characterise the solid residue. Data collection was performed on Rigaku D/MAX2550VB/PC using Cu Ka radiation in the 2-theta range of 5 e50 and scanning rate 20 $min1. According to the XRPD patterns, the samples' polymorph did not change during the measurement.
103xexptl
Ethanol 283.15 4.3635 288.15 5.7360 293.15 6.8088 298.15 8.2065 303.15 10.2513 308.15 11.8620 313.15 13.5296 318.15 16.4856 323.15 18.8753 2 b 10 RAD Isopropanol 283.15 3.1516 288.15 3.9603 293.15 5.0726 298.15 6.1817 303.15 7.5254 308.15 9.3560 313.15 11.1737 318.15 13.7009 323.15 16.8236 102RADb Ethyl acetate 283.15 7.7555 288.15 8.6796 293.15 10.7840 298.15 11.9599 303.15 13.6528 308.15 15.3066 313.15 17.6808 318.15 19.2608 323.15 23.1281 102RADb Toluene 283.15 1.2432 288.15 1.5741 293.15 1.9188 298.15 2.3179 303.15 2.8875 308.15 3.5686 313.15 4.2125 318.15 5.1181 323.15 6.3476 2 b 10 RAD a b c
lh
Modified apleblat
Polynomial
103xcal
102RDa
103xcal
102RDa 103xcal
102RDa
4.5100 5.5900 6.8400 8.3000 9.9500 11.8300 13.9400 16.2900 18.8800
3.3583 2.5451 0.4585 1.1390 2.9391 0.2695 3.0334 1.1867 0.0247 1.6616
4.4000 5.6100 6.9200 8.3600 9.9800 11.8000 13.8800 16.2400 18.9300
0.8374 2.1964 1.6335 1.8701 2.6465 0.5224 2.5899 1.4900 0.2896 1.5640
4.7900 5.7600 6.9000 8.2300 9.7900 11.6100 13.7400 16.2300 19.1700
9.7753 0.4187 1.3397 0.2860 4.4999 2.1242 1.5551 1.5507 1.5611 2.5679
3.2300 4.0100 4.9700 6.1300 7.5400 9.2400 11.3000 13.7800 16.7500
2.4876 1.2545 2.0223 0.8359 0.1937 1.2398 1.1307 0.5773 0.4372 1.1310
3.1500 3.9900 5.0100 6.2100 7.6000 9.2400 11.2300 13.7000 16.8200
0.0508 0.7495 1.2337 0.4583 0.9910 1.2398 0.5042 0.0066 0.0211 0.5839
3.1800 3.9900 4.9600 6.1400 7.5600 9.2700 11.3200 13.7800 16.7300
0.9011 0.7495 2.2194 0.6741 0.4595 0.9192 1.3097 0.5773 0.5561 0.9296
7.8700 9.0300 10.3400 11.8200 13.5000 15.4100 17.5600 19.9800 22.7100
1.4763 4.0366 4.1172 1.1695 1.1190 0.6754 0.6832 3.7339 1.8076 2.0910
7.7200 8.8700 10.4400 12.1200 13.7700 15.4100 17.2400 19.6100 23.0400
0.4578 2.1932 3.1899 1.3389 0.8587 0.6754 2.4930 1.8129 0.3808 1.4890
7.9100 9.0600 10.3500 11.8200 13.4800 15.3600 17.5100 19.9600 22.7800
1.9921 4.3823 4.0245 1.1695 1.2654 0.3487 0.9660 3.6301 1.5050 2.1426
1.2700 1.5600 1.9100 2.3400 2.8600 3.4900 4.2600 5.1800 6.3000
2.1524 0.8966 0.4598 0.9523 0.9517 2.2022 1.1269 1.2102 0.7498 1.1891
1.2600 1.5400 1.9200 2.3700 2.8900 3.5000 4.2300 5.1500 6.3300
2.1524 0.2614 1.1037 2.6780 0.7799 6.7738 2.3139 1.9917 0.5923 2.0719
1.2600 1.5700 1.9400 2.3800 2.9100 3.5500 4.3100 5.2200 6.3100
1.3481 0.2614 1.1037 2.6780 0.7799 0.5209 2.3139 1.9917 0.5923 1.2878
RD is the relative deviation. RAD is the relative average deviation. Standard uncertainties u are u(T) ¼ ±0.02 K, ur(xexptl) ¼ ±0.0012.
3. Results and discussion 3.1. Solubility data of two forms of MTX The solubility data of the two forms of MTX was listed in Tables 2 and 3, respectively. Fig. 2 showed the corresponding solubility curves. Combining the data in Table 2, Table 3 and Fig. 2, it could be
Table 1 Description of materials used in this paper. Chemical name
Mass fraction purity
Formula weight
Source
MTX(Form A) MTX(Form B) Ethanol Isopropanol Ethyl acetate Toluene
99.5 99.5 99.7 99.7 99.5 99.5
221.25 221.25 46.07 60.10 88.11 92.14
Donated by Jiawei Pharmaceutical Co.,Ltd. Prepared by our lab Shanghai Lingfeng Chemical Reagent Co.LTD Shanghai Lingfeng Chemical Reagent Co.LTD Shanghai Lingfeng Chemical Reagent Co.LTD Shanghai Lingfeng Chemical Reagent Co.LTD
M. Hong et al. / Fluid Phase Equilibria 409 (2016) 1e6
found that the solubility of both forms of MTX increased as the temperature increased. And it was obvious that the solubility of form B was lower than the solubility of form A at the same state. Both forms of MTX were slightly soluble in toluene while quite soluble in isopropanol, ethanol and ethyl acetate. The solubility order of both forms was: ethyl acetate > ethanol > isopropanol > toluene. This sequence was not consistent with the polarity and the solubility parameter order: ethanol > isopropanol > ethyl acetate > toluene [13]. It could be said that the polarity of the solvents might not be the only factor that determines the solubility of different form of MTX in the selected solvents. The hydrogen bonding might also contribute to soluteesolvent interactions, thereby influence the solubility of MTX. To sum up, the overall strength of soluteesolvent interaction will determine the solubility orders and great soluteesolvent interactions will give higher solubility [14].
Table 3 Experimental (xexptl) and correlated (xcal) mole fraction solubility of Metaxalone (Form B) in four different pure solvents (p ¼ 0.1 Mpa).a,b,c T/K
103xexptl Modified Apleblat
Ethanol 283.15 3.5626 288.15 4.3399 293.15 5.0140 298.15 6.2127 303.15 7.8857 308.15 9.0682 313.15 10.7605 318.15 12.9335 323.15 15.2587 102RADb Isopropanol 283.15 2.4616 288.15 3.2529 293.15 3.7186 298.15 4.5684 303.15 5.5790 308.15 7.0235 313.15 7.9346 318.15 9.8791 323.15 12.2170 2 b 10 RAD Ethyl acetate 283.15 5.8634 288.15 6.9074 293.15 7.5143 298.15 8.5084 303.15 10.0179 308.15 11.3760 313.15 12.1973 318.15 14.4771 323.15 17.0051 102RADb Toluene 283.15 0.9157 288.15 1.0767 293.15 1.1965 298.15 1.4292 303.15 1.7327 308.15 2.0981 313.15 2.4534 318.15 2.9863 323.15 3.5626 102RADb a b c
Polynomial
lh
103xcal
102RDa
103xcal
102RDa 103xcal
102RDa
3.5000 4.2900 5.2100 6.3100 7.6000 9.1000 10.8600 12.9000 15.2600
1.7579 1.1494 3.9100 1.5669 3.6232 0.3503 0.9250 0.2589 0.0087 1.5056
3.6000 4.2100 5.1400 6.3100 7.6500 9.1500 10.8500 12.8500 15.2800
1.0490 2.9928 2.5139 1.5669 2.9891 0.9017 0.8321 0.6455 0.1398 1.5145
3.7500 4.4900 5.3500 6.3500 7.5200 8.8900 10.4800 12.3500 14.5400
5.2593 3.4590 6.7022 2.2108 4.6376 1.9654 2.6064 4.5114 4.7099 4.0069
2.5800 3.1200 3.7800 4.5800 5.5500 6.7400 8.1900 9.9700 12.1300
4.8085 4.0844 1.6512 0.2543 0.5199 4.0366 3.2193 0.9200 0.7124 2.2452
2.5200 3.0900 3.8100 4.6600 5.6200 6.7400 8.1200 9.8800 12.2000
2.3711 5.0067 2.4580 2.0054 0.7348 4.0366 2.3371 0.0090 0.1394 2.1220
2.4400 3.0200 3.7200 4.5600 5.5700 6.7800 8.2200 9.9400 11.9900
0.8787 7.1587 0.0377 0.1835 0.1614 3.4671 3.5974 0.6164 1.8583 1.9955
6.0300 6.7400 7.5800 8.5700 9.7300 11.1000 12.7000 14.5900 16.8200
2.8420 2.4240 0.8744 0.7236 2.8742 2.4266 4.1217 0.7796 1.0886 2.0172
5.9400 6.6600 7.6500 8.7400 9.8700 11.0900 12.5200 14.3800 17.0000
1.3070 3.5822 1.8060 2.7217 1.4767 2.5145 2.6460 0.6710 0.0301 1.8617
5.8200 6.6500 7.5900 8.6600 9.8600 11.2300 12.7900 14.5800 16.6500
0.7396 3.7269 1.0075 1.7814 1.5765 1.2838 4.8596 0.7105 2.0883 1.9749
0.9000 1.0500 1.2400 1.4600 1.7300 2.0600 2.4700 2.9700 3.5800
1.7098 2.4838 3.6367 2.1526 0.1543 1.8173 0.6747 0.5463 0.4872 1.5181
0.9200 1.0500 1.2200 1.4400 1.7200 2.0700 2.4800 2.9800 3.5600
0.4744 2.4838 1.9652 0.7533 0.7314 1.3407 1.0823 0.2114 0.0742 1.0130
0.8600 1.0200 1.2100 1.4300 1.6900 1.9800 2.3300 2.7300 3.2100
6.0782 5.2700 1.1294 0.0536 2.4629 5.6302 5.0315 8.5830 9.8984 4.9041
RD is the relative deviation. RAD is the relative average deviation. Standard uncertainties u are u(T) ¼ ±0.02 K, ur(xexptl) ¼ ±0.0015.
3
3.2. Correlation of the experimental data To more quantitatively describe the solideliquid equilibrium, the dependence of the solubility data of different polymorphs of MTX on temperature and their thermodynamic properties, the following three equations were selected to correlate the experimental solubility data. 3.2.1. Modified Apelblat equation The solubility of MTX (Form A and Form B) in different pure solvents at the temperature ranging from 283.15 K to 323.15 K can be correlated by the modified Apelblat equation, which is a semiempirical model and deduced from the solideliquid phase equilibrium. The modified Apelblat equation is described as Eq. (1).
lnx ¼ A þ
B þ ClnT T
(1)
where x is the mole fraction solubility of MTX at the system temperature T. A, B, and C are the empirical constants, with A and B reflecting the non-idealities of the real solution in term of variation of activity coefficient in the solution, and C representing the effect of temperature on the fusion enthalpy. All the three empirical constants were determined by multivariate regression analysis [15,16]. 3.2.2. Polynomial equation When the variable factors such as solute, solvent and pressure are defined, the solubility will change only when the temperature changes. Under the proposition that the solubility changes continuously with temperature, the solubility of solute in solvents can be described by a 4th-order polynomial equation of absolute temperature as follows:
x ¼ B0 þ B1 T þ B2 T 2 þ B3 T 3 þ B4
(2)
where B0, B1, B2, B3 and B4 are the semi-empirical constants from nonlinear regression by least square method via Eq. (2) [17,18]. 3.2.3. BuchowskieKsiazczak lh equation The Buchowski-Ksiazczak equation (lh) gives an excellent explanation for behavior of various (solid þ liquid) systems giving
Fig. 2. Experimental and modeling solubility of MTX (Form A and Form B) in different solvents based on modified Apelblat equation. Experimental data: (Form A: -, Ethanol; C, Isopropanol; :, Ethyl acetate; A, Toluene), (Form B: ,, Ethanol; B, Isopropanol; △, Ethyl acetate; >, Toluene). Modeling data: (d,Form A; ---,Form B).
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M. Hong et al. / Fluid Phase Equilibria 409 (2016) 1e6
Table 4 The regressed parameters of modified Apeblat equation in the 283.15e323.15 K temperature range.a,b 102Aa
Solvent
104Ba
102Ca
104RMSDb
102Aa
R2
Form A Ethanol Isopropanol Ethyl acetate Toluene
102Ca
104RMSDb
R2
0.1916 0.4668 0.7120 0.8756
0.0479 0.2715 0.3132 0.3937
1.2971 1.4853 2.4176 0.2435
0.9988 0.9977 0.9952 0.9992
Form B 0.7214 0.0382 0.1047 0.2253
0.1304 0.1372 0.1148 0.1956
1.9735 0.8394 3.4819 0.4214
0.2596 1.7571 2.0710 2.6024
0.9982 0.9996 0.9947 0.9993
A, B, C are the parameters of modified Apeblat equation. RMSD is the root-mean-square deviation.
good correlation results using only by two variable parameters l and h. The Buchowski equation can be written as:
" RMSD ¼
jxcal xi j xi
i¼1
jxcal xi j xi
n
100%
#1 2 (6)
3.3. Thermodynamic properties of solutions
(4)
Thermodynamic properties play an important role in solideliquid equilibrium. The van't Hoff analysis is a significant research method in the thermodynamic field, the dissolution enthalpy, DHd, and the dissolution entropy, DSd can be estimated by plotting the lnx versus reciprocal of temperature [23]. The GibbseHelmholtz equation can be used to obtain Gibbs energy for the dissolution of MTX in different solvents at various temperatures:
The relative average deviation (RAD) is defined as follows:
RAD ¼
xi Þ 2 n
where n is the number of experimental points, and xi, cal and xi represent the calculated and the experimental solubility values, respectively [21,22]. The correlation results of both equations were presented in Tables 2e7 and graphically in Figs. 2e4. These indicate that both three equations were suitable for correlation of the solubility of both forms of MTX in different solvents with temperature variation. Comparing of the total average RD, RAD, RMSD and R2, it could be said that the polynomial equation was little better than the other equations.
(3)
where x is the molar solubility of MTX at the system temperature T, Tm is the melting temperature of the specific sample [19,20]. 1stOpt software was used to evaluate the multidimensional unconstrained nonlinear minimization of parameters. The relative deviation (RD), the relative average deviation (RAD) and the rootmean-square deviation (RMSD) were also given. The relative deviation (RD) is defined as follows:
Pn
cal
i¼1
1x 1 1 ¼ lh ln 1 þ l x T Tm
RD ¼
n X ðx
=
a b
0.9369 0.8485 0.7336 1.2505
104Ba
(5)
The root-mean-square deviation (RMSD) is defined as follows:
Table 5 The regressed parameters of polynomial equation in the 283.15e323.15 K temperature range.a,b Solvent Form A Ethanol Isopropanol Ethyl acetate Toluene Form B Ethanol Isopropanol Ethyl acetate Toluene a b
B0a
B1a
103B2a
106B3a
109B4a
104RMSDb
R2
0.8072 18.5858 89.043 11.8487
0.0076 0.2525 1.1889 0.1591
0.0208 1.2880 5.9505 0.8015
0.0035 2.9249 13.2306 1.7966
0.0395 2.4973 11.0295 1.5126
1.8739 0.5474 2.4250 0.3428
0.9984 0.9998 0.9975 0.9996
26.1087 22.5165 50.3433 0.4722
0.3453 0.3039 0.6740 0.0064
1.7132 1.5393 3.3833 0.0337
3.7820 3.4677 7.5470 0.0804
3.1367 2.9335 6.3144 0.0737
1.1773 1.3431 1.9730 0.1990
0.9984 0.9998 0.9975 0.9996
B0, B1, B2, B3 and B4 are the parameters of polynomial equation. RMSD is the root-mean-square deviation.
Table 6 The regressed parameters of BuchowskieKsiazczak lh equation in the 283.15e323.15 K temperature range.a,b Solvent
la
Ethanol Isopropanol Ethyl acetate Toluene
0.0801 0.1153 0.0450 0.0387
104ha
104RMSDb
R2
la
3.5415 3.0984 4.1619 8.8189
2.7126 0.8186 3.4103 1.0204
0.9967 0.9996 0.9950 0.9961
0.0547 0.0709 0.0308 0.0108
Form A
a b
104ha
104RMSDb
R2
4.9869 4.7764 5.9233 24.0285
3.7889 2.8667 2.6583 2.0144
0.9943 0.9914 0.9942 0.9924
Form B
l and h are the parameters of BuchowskieKsiazczak lh equation. RMSD is the root-mean-square deviation.
M. Hong et al. / Fluid Phase Equilibria 409 (2016) 1e6
5
Table 7 The regressed parameters of Van't Hoff equation in the 283.15e323.15 K temperature range.a,b,c,d Solvent Form A Ethanol Isopropanol Ethyl acetate Toluene Form B Ethanol Isopropanol Ethyl acetate Toluene a b c d
△Hda (KJ mol1)
△Sdb (J mol1 K1)
△Gdc (KJ mol1)
R2
102RMSDd
27.3693 31.5127 20.2996 30.6000
51.8512 63.4087 31.2536 52.3902
11.9099 12.6074 10.9814 14.9798
0.9980 0.9965 0.9961 0.9921
2.5417 1.1378 2.3595 2.7476
27.9096 29.6392 19.6029 26.1076
51.5292 54.7862 26.3826 33.5348
12.5461 13.3047 11.7369 16.1092
0.9980 0.9965 0.9961 0.9921
2.1240 2.9602 2.9414 3.9400
△Hd is the molar dissolution enthalpy. △Sd is the molar dissolution entropy. △Gd is the molar dissolution Gibbs free energy. RMSD is the root-mean-square deviation.
Fig. 3. Experimental and modeling solubility of MTX (Form A and Form B) in different solvents based on polynomial empirical equation. Experimental data: (Form A: -, Ethanol; C, Isopropanol; :, Ethyl acetate; A, Toluene), (Form B: ,, Ethanol; B, Isopropanol; △, Ethyl acetate; >, Toluene). Modeling data: (d,Form A; ---,Form B).
Fig. 5. Experimental and modeling solubility of MTX (Form A and Form B) in different solvents based on Van't Hoff equation. Experimental data: (Form A: -, Ethanol; C, Isopropanol; :, Ethyl acetate; A, Toluene), (Form B: ,, Ethanol; B, Isopropanol; △, Ethyl acetate; >, Toluene). Modeling data: (d,Form A; ---,Form B).
DHd DSd þ RT R
(7)
DGd ¼ DHd TDSd
(8)
lnx ¼
Fig. 5 illustrated the linear Van't Hoff plots of lnx versus 1/T. Table 7 presents the molar dissolution enthalpy and entropy determined using the least-squares and Gibbs energy calculated at 298.15 K. From Table 7, it could be seen that the molar dissolution enthalpy and entropy of both forms of MTX were positive (△Hd > 0, △Sd > 0), thereby indicating the course of MTX dissolving in each selected solvent at the experimental temperature range was endothermic and entropy-driven. Furthermore, the curves in Figs. 2 and 5 and the data in Tables 2, 3 and 7 revealed that the △Gd values were positive, which indicated that the dissolution process was nonspontaneous. And also we could find that the △Gd values trended in an opposite direction from solubility [24e26]. 4. Conclusions Fig. 4. Experimental and modeling solubility of MTX (Form A and Form B) in different solvents based on BuchowskieKsiazczak lh equation. Experimental data: (Form A: -, Ethanol; C, Isopropanol; :, Ethyl acetate; A, Toluene), (Form B: ,, Ethanol; B, Isopropanol; △, Ethyl acetate; >, Toluene). Modeling data: (d,Form A; ---,Form B).
The solubility data of two forms of MTX in four different pure solvents was determined by shake flask method at temperature ranging from 283.15 K to 323.15 K. In the selected pure solvents, the
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M. Hong et al. / Fluid Phase Equilibria 409 (2016) 1e6
solubility of both forms of MTX showed a strong dependence on temperature except in toluene. The modified Apelblat equation, polynomial equation and BuchowskieKsiazczak lh equation were used to describe the experimental data. It turned out that all the selected thermodynamic models could give satisfactory correlation results, with the polynomial equation showing the best fitting degree. Finally, the dissolution molar enthalpy, entropy and the molar Gibbs free energy were calculated based on the Van't Hoff equation. The results indicated that the dissolving course of MTX in each selected solvent at the experimental temperature range was endothermic, entropy-driven and nonspontaneous. Acknowledgment This work was supported by National Natural Science Foundation of China (No. 81102391) and the Shanghai Committee of Science and Technology (Grant 12DZ1930702). References [1] V.K. Marothu, R.N. Dash, S. Vemula, S. Donkena, R. Devi, M. Gorrepati, J. Pharm. Anal. 2 (2012) 431e436. [2] H.-L. Lin, T.-K. Wu, S.-Y. Lin, Thermochim. Acta 575 (2014) 313e321. [3] J. Chen, B. Sarma, J.M.B. Evans, A.S. Myerson, Cryst. Growth Des. 11 (2011) 887e895. [4] M.A. O'Mahony, D.M. Croker, Å.C. Rasmuson, S. Veesler, B.K. Hodnett, Org. Process Res. Dev. 17 (2013) 512e518.
[5] J. Chattopadhyay, S. Sarkar, J.S. Mahanty, S. Hazra, M. Mitra, M.K. Singh, US 2007/0185177 A1. [6] S. Aitipamula, P.S. Chow, R.B.H. Tan, Cryst. Growth Des. 11 (2011) 4101e4109. [7] A. Burger, R. Ramberger, Mikrochim. Acta II (1979) 259e272. [8] A.-G. Zeng, X.-L. Pang, N. Wu, D. Wang, G.-J. Nan, G.-D. Yang, X.-L. Bian, Fluid Phase Equilib. 366 (2014) 127e133. [9] F. Shakeel, N. Haq, F.K. Alanazi, I.A. Alsarra, J. Chem. Thermodyn. 82 (2015) 156e160. [10] F. Shakeel, F.K. Alanazi, I.A. Alsarra, N. Haq, J. Mol. Liq. 188 (2013) 28e32. [11] L. Song, H. Guo, Y. Xu, Z. Wei, X. Zhang, J. Ji, C. Yang, Fluid Phase Equilib. 384 (2014) 143e149. [12] G.-M. Yu, L.-S. Wang, C.-J. Du, J. Sun, Fluid Phase Equilib. 388 (2015) 6e15. [13] I.M. Smallwood, in: I.M. Smallwood (Ed.), Handbook of Organic Solvent Properties, Butterworth-Heinemann, Oxford, 1996, pp. 301e303. [14] H. Sun, P. Liu, Y. Xin, B. Liu, S. Wu, Fluid Phase Equilib. 388 (2015) 123e127. [15] J. Zhang, J. Ouyang, H. Zhang, X. Huang, H. Hao, Y. Wang, Q. Yin, W. Fang, Fluid Phase Equilib. 387 (2015) 95e102. [16] S. Wang, X. Cheng, B. Liu, Y. Du, J. Wang, Fluid Phase Equilib. 390 (2015) 1e6. [17] L. Wang, T.-T. Lv, J. Mol. Liq. 181 (2013) 29e33. [18] L. Wang, J. Mol. Liq. 188 (2013) 55e60. [19] K.D. Bhesaniya, K. Nandha, S. Baluja, J. Chem. Thermodyn. 74 (2014) 32e38. [20] Y. Kai, Y. Hu, Y. Liu, M. Liang, W. Yang, Y. Xi, Fluid Phase Equilib. 361 (2014) 282e288. [21] Y. Shen, Z. Liu, T. Li, B. Ren, J. Chem. Thermodyn. 80 (2015) 128e134. [22] F. Shakeel, N. Haq, F.K. Alanazi, I.A. Alsarra, J. Mol. Liq. 200 (2014) 398e403. [23] X. Zhang, G. Qian, R. Wang, X. Yang, L. Hao, H. Wei, X. Zhou, Fluid Phase Equilib. 388 (2015) 59e65. [24] L. Wang, X. Wang, T. Zuo, Q. Sun, P. Liu, S. Yao, H. Song, J. Chem. Thermodyn. 72 (2014) 48e53. [25] X. Shao, H. Ge, Z. Li, C. Ren, J. Wang, Fluid Phase Equilib. 390 (2015) 7e13. [26] Y. Cao, Q. Yang, H. Xing, Z. Bao, B. Su, Y. Yang, Q. Ren, Chin. J. Chem. Eng. 22 (2014) 1141e1144.
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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Solubility correlation and thermodynamic analysis of two forms of Metaxalone in different pure solvents Minghuang Hong 1, Shiwang Wu 1, Minghui Qi, Guobin Ren* Laboratory of Pharmaceutical Crystal Engineering & Technology, School of Pharmacy, East China University of Science and Technology, Shanghai, 200237, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 May 2015 Received in revised form 26 August 2015 Accepted 6 September 2015 Available online 15 September 2015
The solubility data of two forms of MTX in ethanol, isopropanol, ethyl acetate and toluene was measured over the temperature range from 283.15 K to 323.15 K using shake flask method under atmospheric pressure. The experimental results indicated that the solubility of both forms of MTX increased as the temperature increased. And it was clear that the solubility of form B was lower than the solubility of form A at the same state. The experimental data was correlated by the modified Apelblat equation, the polynomial equation and the BuchowskieKsiazczak lh equation. All these thermodynamic models gave satisfactory correlation results, with the polynomial equation showing better fitting degree than the other two equations. The results of thermodynamic parameters (△Hd > 0, △Sd > 0, △Gd > 0) indicated an endothermic, entropy driven and nonspontaneous dissolution process of MTX in selected pure solvents. © 2015 Elsevier B.V. All rights reserved.
Keywords: Solubility Thermodynamic models Endothermic Entropy driven Nonspontaneous
1. Introduction Metaxalone (MTX) is a muscle relaxant used to relax muscles and relieve pain caused by strains, sprains, and other musculoskeletal conditions. Chemically, it is 5-[(3, 5-dimethylphenoxy) methyl]-1, 3-oxazolidin-2-one (Fig. 1) [1]. New therapeutic applications of MTX have been recently reported for the treatment of diabetic neuropathy and chronic daily headache [2]. Crystallization is important in the pharmaceutical industry as a separation process for intermediates and often servers as the final step in the manufacture of active pharmaceutical ingredients (APIs) [3]. The solubility of a crystalline compound provides vital thermodynamic information required to design crystallization processes, engineer the crystal size distribution and understand the phases which nucleate in the case of multiple-phase systems. Polymorphs are solid phases of the same compound but with different crystal structures. These different crystal structures exist
* Corresponding author. Laboratory of Pharmaceutical Crystal Engineering & Technology, School of Pharmacy, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237, China. E-mail addresses: [email protected] (M. Hong), [email protected] (S. Wu), [email protected] (M. Qi), [email protected] (G. Ren). 1 These authors contributed equally to this work. http://dx.doi.org/10.1016/j.fluid.2015.09.013 0378-3812/© 2015 Elsevier B.V. All rights reserved.
due to the different molecular arrangements of the molecules giving rise to differences in free energy and thus solubility [4]. Hence, it is necessary to study the solubility properties of polymorph for the purpose of separation and purification through crystallization process. The existence of polymorphism in MTX has been reported in the patent literature, which revealed two forms (A and B) that are characterized by powder X-ray diffraction (PXRD), differential scanning calorimetry (DSC), and Fourier transform infrared (FT-IR) spectroscopy [5]. Aitipamula et al. [6] reported the relative stability information of the two polymorphs of MTX. DSC thermograms of Form A and Form B were recorded at the heating rate of 5 C min1. Both forms showed a single sharp endotherm in the temperature range of 121e123 C, with the melting endotherms observed at 121.9 ± 0.1 C (△Hfus ¼ 137.1 J g1) and 122.2 ± 0.1 C (△Hfus ¼ 119.3 J g1) for Form A and Form B respectively. It was suggested that the polymorphs of MTX were enantiotropically related according to the Burger and Ramberger's heat of fusion rule, as the higher melting form showed a lower heat of fusion [7]. For expanding the fields of usage and purification of MTX, and considering the solubility studies of MTX has not been reported, in this work, the solubility data of two forms of MTX in ethanol, isopropanol, ethyl acetate, and toluene was measured from 283.15 K to 323.15 K using shake flask method.
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M. Hong et al. / Fluid Phase Equilibria 409 (2016) 1e6 Table 2 Experimental (xexptl) and correlated (xcal) mole fraction solubility of Metaxalone (Form A) in four different pure solvents (p ¼ 0.1 Mpa).a,b,c T/K
Fig. 1. Molecular structure of Metaxalone.
2. Experimental 2.1. Materials MTX was provided by Jiawei Pharmaceutical Co.,Ltd., which is a white crystalline powder with crystal gloss in the light. It's form was proved to be form A, which was characterized by powder X-ray diffraction (XRPD). Another form of MTX, form B, was prepared by our lab through crystallization process. The pure form B was confirmed by comparing its XRPD pattern with that from Ref. [6]. Each form of MTX's mass fraction was more than 99.5% determined by HPLC. All of the reagents used in this work were obtained from Shanghai Lingfeng Chemical Reagent Co.LTD with analytical reagent grade. More detailed information about the material used in this work was listed in Table 1.
2.2. Apparatus and procedure The saturated equilibrium solubility of the two forms of MTX was determined by shake flask method at atmospheric pressure and temperature range from 283.15 K to 323.15 K. An excess amount of MTX was added to known amount of various pure solvent in triplicate. The concentrated suspensions of MTX in each solvent were shaken continuously in a biological shaker at 100 rpm for 72 h. After 72 h, all the samples were taken out from the biological shaker and the solute particles were allowed to settle for 2 h. Then, the supernatant solutions were filtered through a 0.45 mm Millipore membrane filter, added to a volumetric flask, and diluted with methanol to an appropriate concentration for HPLC analysis [8e10]. The experimental mole fraction solubility (xexptl) of the two forms of MTX then calculated as reported in literature [11,12]. In order to identify the polymorph of solid phase has not changed in the measurement of solubility, the X-ray powder diffraction was used to characterise the solid residue. Data collection was performed on Rigaku D/MAX2550VB/PC using Cu Ka radiation in the 2-theta range of 5 e50 and scanning rate 20 $min1. According to the XRPD patterns, the samples' polymorph did not change during the measurement.
103xexptl
Ethanol 283.15 4.3635 288.15 5.7360 293.15 6.8088 298.15 8.2065 303.15 10.2513 308.15 11.8620 313.15 13.5296 318.15 16.4856 323.15 18.8753 2 b 10 RAD Isopropanol 283.15 3.1516 288.15 3.9603 293.15 5.0726 298.15 6.1817 303.15 7.5254 308.15 9.3560 313.15 11.1737 318.15 13.7009 323.15 16.8236 102RADb Ethyl acetate 283.15 7.7555 288.15 8.6796 293.15 10.7840 298.15 11.9599 303.15 13.6528 308.15 15.3066 313.15 17.6808 318.15 19.2608 323.15 23.1281 102RADb Toluene 283.15 1.2432 288.15 1.5741 293.15 1.9188 298.15 2.3179 303.15 2.8875 308.15 3.5686 313.15 4.2125 318.15 5.1181 323.15 6.3476 2 b 10 RAD a b c
lh
Modified apleblat
Polynomial
103xcal
102RDa
103xcal
102RDa 103xcal
102RDa
4.5100 5.5900 6.8400 8.3000 9.9500 11.8300 13.9400 16.2900 18.8800
3.3583 2.5451 0.4585 1.1390 2.9391 0.2695 3.0334 1.1867 0.0247 1.6616
4.4000 5.6100 6.9200 8.3600 9.9800 11.8000 13.8800 16.2400 18.9300
0.8374 2.1964 1.6335 1.8701 2.6465 0.5224 2.5899 1.4900 0.2896 1.5640
4.7900 5.7600 6.9000 8.2300 9.7900 11.6100 13.7400 16.2300 19.1700
9.7753 0.4187 1.3397 0.2860 4.4999 2.1242 1.5551 1.5507 1.5611 2.5679
3.2300 4.0100 4.9700 6.1300 7.5400 9.2400 11.3000 13.7800 16.7500
2.4876 1.2545 2.0223 0.8359 0.1937 1.2398 1.1307 0.5773 0.4372 1.1310
3.1500 3.9900 5.0100 6.2100 7.6000 9.2400 11.2300 13.7000 16.8200
0.0508 0.7495 1.2337 0.4583 0.9910 1.2398 0.5042 0.0066 0.0211 0.5839
3.1800 3.9900 4.9600 6.1400 7.5600 9.2700 11.3200 13.7800 16.7300
0.9011 0.7495 2.2194 0.6741 0.4595 0.9192 1.3097 0.5773 0.5561 0.9296
7.8700 9.0300 10.3400 11.8200 13.5000 15.4100 17.5600 19.9800 22.7100
1.4763 4.0366 4.1172 1.1695 1.1190 0.6754 0.6832 3.7339 1.8076 2.0910
7.7200 8.8700 10.4400 12.1200 13.7700 15.4100 17.2400 19.6100 23.0400
0.4578 2.1932 3.1899 1.3389 0.8587 0.6754 2.4930 1.8129 0.3808 1.4890
7.9100 9.0600 10.3500 11.8200 13.4800 15.3600 17.5100 19.9600 22.7800
1.9921 4.3823 4.0245 1.1695 1.2654 0.3487 0.9660 3.6301 1.5050 2.1426
1.2700 1.5600 1.9100 2.3400 2.8600 3.4900 4.2600 5.1800 6.3000
2.1524 0.8966 0.4598 0.9523 0.9517 2.2022 1.1269 1.2102 0.7498 1.1891
1.2600 1.5400 1.9200 2.3700 2.8900 3.5000 4.2300 5.1500 6.3300
2.1524 0.2614 1.1037 2.6780 0.7799 6.7738 2.3139 1.9917 0.5923 2.0719
1.2600 1.5700 1.9400 2.3800 2.9100 3.5500 4.3100 5.2200 6.3100
1.3481 0.2614 1.1037 2.6780 0.7799 0.5209 2.3139 1.9917 0.5923 1.2878
RD is the relative deviation. RAD is the relative average deviation. Standard uncertainties u are u(T) ¼ ±0.02 K, ur(xexptl) ¼ ±0.0012.
3. Results and discussion 3.1. Solubility data of two forms of MTX The solubility data of the two forms of MTX was listed in Tables 2 and 3, respectively. Fig. 2 showed the corresponding solubility curves. Combining the data in Table 2, Table 3 and Fig. 2, it could be
Table 1 Description of materials used in this paper. Chemical name
Mass fraction purity
Formula weight
Source
MTX(Form A) MTX(Form B) Ethanol Isopropanol Ethyl acetate Toluene
99.5 99.5 99.7 99.7 99.5 99.5
221.25 221.25 46.07 60.10 88.11 92.14
Donated by Jiawei Pharmaceutical Co.,Ltd. Prepared by our lab Shanghai Lingfeng Chemical Reagent Co.LTD Shanghai Lingfeng Chemical Reagent Co.LTD Shanghai Lingfeng Chemical Reagent Co.LTD Shanghai Lingfeng Chemical Reagent Co.LTD
M. Hong et al. / Fluid Phase Equilibria 409 (2016) 1e6
found that the solubility of both forms of MTX increased as the temperature increased. And it was obvious that the solubility of form B was lower than the solubility of form A at the same state. Both forms of MTX were slightly soluble in toluene while quite soluble in isopropanol, ethanol and ethyl acetate. The solubility order of both forms was: ethyl acetate > ethanol > isopropanol > toluene. This sequence was not consistent with the polarity and the solubility parameter order: ethanol > isopropanol > ethyl acetate > toluene [13]. It could be said that the polarity of the solvents might not be the only factor that determines the solubility of different form of MTX in the selected solvents. The hydrogen bonding might also contribute to soluteesolvent interactions, thereby influence the solubility of MTX. To sum up, the overall strength of soluteesolvent interaction will determine the solubility orders and great soluteesolvent interactions will give higher solubility [14].
Table 3 Experimental (xexptl) and correlated (xcal) mole fraction solubility of Metaxalone (Form B) in four different pure solvents (p ¼ 0.1 Mpa).a,b,c T/K
103xexptl Modified Apleblat
Ethanol 283.15 3.5626 288.15 4.3399 293.15 5.0140 298.15 6.2127 303.15 7.8857 308.15 9.0682 313.15 10.7605 318.15 12.9335 323.15 15.2587 102RADb Isopropanol 283.15 2.4616 288.15 3.2529 293.15 3.7186 298.15 4.5684 303.15 5.5790 308.15 7.0235 313.15 7.9346 318.15 9.8791 323.15 12.2170 2 b 10 RAD Ethyl acetate 283.15 5.8634 288.15 6.9074 293.15 7.5143 298.15 8.5084 303.15 10.0179 308.15 11.3760 313.15 12.1973 318.15 14.4771 323.15 17.0051 102RADb Toluene 283.15 0.9157 288.15 1.0767 293.15 1.1965 298.15 1.4292 303.15 1.7327 308.15 2.0981 313.15 2.4534 318.15 2.9863 323.15 3.5626 102RADb a b c
Polynomial
lh
103xcal
102RDa
103xcal
102RDa 103xcal
102RDa
3.5000 4.2900 5.2100 6.3100 7.6000 9.1000 10.8600 12.9000 15.2600
1.7579 1.1494 3.9100 1.5669 3.6232 0.3503 0.9250 0.2589 0.0087 1.5056
3.6000 4.2100 5.1400 6.3100 7.6500 9.1500 10.8500 12.8500 15.2800
1.0490 2.9928 2.5139 1.5669 2.9891 0.9017 0.8321 0.6455 0.1398 1.5145
3.7500 4.4900 5.3500 6.3500 7.5200 8.8900 10.4800 12.3500 14.5400
5.2593 3.4590 6.7022 2.2108 4.6376 1.9654 2.6064 4.5114 4.7099 4.0069
2.5800 3.1200 3.7800 4.5800 5.5500 6.7400 8.1900 9.9700 12.1300
4.8085 4.0844 1.6512 0.2543 0.5199 4.0366 3.2193 0.9200 0.7124 2.2452
2.5200 3.0900 3.8100 4.6600 5.6200 6.7400 8.1200 9.8800 12.2000
2.3711 5.0067 2.4580 2.0054 0.7348 4.0366 2.3371 0.0090 0.1394 2.1220
2.4400 3.0200 3.7200 4.5600 5.5700 6.7800 8.2200 9.9400 11.9900
0.8787 7.1587 0.0377 0.1835 0.1614 3.4671 3.5974 0.6164 1.8583 1.9955
6.0300 6.7400 7.5800 8.5700 9.7300 11.1000 12.7000 14.5900 16.8200
2.8420 2.4240 0.8744 0.7236 2.8742 2.4266 4.1217 0.7796 1.0886 2.0172
5.9400 6.6600 7.6500 8.7400 9.8700 11.0900 12.5200 14.3800 17.0000
1.3070 3.5822 1.8060 2.7217 1.4767 2.5145 2.6460 0.6710 0.0301 1.8617
5.8200 6.6500 7.5900 8.6600 9.8600 11.2300 12.7900 14.5800 16.6500
0.7396 3.7269 1.0075 1.7814 1.5765 1.2838 4.8596 0.7105 2.0883 1.9749
0.9000 1.0500 1.2400 1.4600 1.7300 2.0600 2.4700 2.9700 3.5800
1.7098 2.4838 3.6367 2.1526 0.1543 1.8173 0.6747 0.5463 0.4872 1.5181
0.9200 1.0500 1.2200 1.4400 1.7200 2.0700 2.4800 2.9800 3.5600
0.4744 2.4838 1.9652 0.7533 0.7314 1.3407 1.0823 0.2114 0.0742 1.0130
0.8600 1.0200 1.2100 1.4300 1.6900 1.9800 2.3300 2.7300 3.2100
6.0782 5.2700 1.1294 0.0536 2.4629 5.6302 5.0315 8.5830 9.8984 4.9041
RD is the relative deviation. RAD is the relative average deviation. Standard uncertainties u are u(T) ¼ ±0.02 K, ur(xexptl) ¼ ±0.0015.
3
3.2. Correlation of the experimental data To more quantitatively describe the solideliquid equilibrium, the dependence of the solubility data of different polymorphs of MTX on temperature and their thermodynamic properties, the following three equations were selected to correlate the experimental solubility data. 3.2.1. Modified Apelblat equation The solubility of MTX (Form A and Form B) in different pure solvents at the temperature ranging from 283.15 K to 323.15 K can be correlated by the modified Apelblat equation, which is a semiempirical model and deduced from the solideliquid phase equilibrium. The modified Apelblat equation is described as Eq. (1).
lnx ¼ A þ
B þ ClnT T
(1)
where x is the mole fraction solubility of MTX at the system temperature T. A, B, and C are the empirical constants, with A and B reflecting the non-idealities of the real solution in term of variation of activity coefficient in the solution, and C representing the effect of temperature on the fusion enthalpy. All the three empirical constants were determined by multivariate regression analysis [15,16]. 3.2.2. Polynomial equation When the variable factors such as solute, solvent and pressure are defined, the solubility will change only when the temperature changes. Under the proposition that the solubility changes continuously with temperature, the solubility of solute in solvents can be described by a 4th-order polynomial equation of absolute temperature as follows:
x ¼ B0 þ B1 T þ B2 T 2 þ B3 T 3 þ B4
(2)
where B0, B1, B2, B3 and B4 are the semi-empirical constants from nonlinear regression by least square method via Eq. (2) [17,18]. 3.2.3. BuchowskieKsiazczak lh equation The Buchowski-Ksiazczak equation (lh) gives an excellent explanation for behavior of various (solid þ liquid) systems giving
Fig. 2. Experimental and modeling solubility of MTX (Form A and Form B) in different solvents based on modified Apelblat equation. Experimental data: (Form A: -, Ethanol; C, Isopropanol; :, Ethyl acetate; A, Toluene), (Form B: ,, Ethanol; B, Isopropanol; △, Ethyl acetate; >, Toluene). Modeling data: (d,Form A; ---,Form B).
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M. Hong et al. / Fluid Phase Equilibria 409 (2016) 1e6
Table 4 The regressed parameters of modified Apeblat equation in the 283.15e323.15 K temperature range.a,b 102Aa
Solvent
104Ba
102Ca
104RMSDb
102Aa
R2
Form A Ethanol Isopropanol Ethyl acetate Toluene
102Ca
104RMSDb
R2
0.1916 0.4668 0.7120 0.8756
0.0479 0.2715 0.3132 0.3937
1.2971 1.4853 2.4176 0.2435
0.9988 0.9977 0.9952 0.9992
Form B 0.7214 0.0382 0.1047 0.2253
0.1304 0.1372 0.1148 0.1956
1.9735 0.8394 3.4819 0.4214
0.2596 1.7571 2.0710 2.6024
0.9982 0.9996 0.9947 0.9993
A, B, C are the parameters of modified Apeblat equation. RMSD is the root-mean-square deviation.
good correlation results using only by two variable parameters l and h. The Buchowski equation can be written as:
" RMSD ¼
jxcal xi j xi
i¼1
jxcal xi j xi
n
100%
#1 2 (6)
3.3. Thermodynamic properties of solutions
(4)
Thermodynamic properties play an important role in solideliquid equilibrium. The van't Hoff analysis is a significant research method in the thermodynamic field, the dissolution enthalpy, DHd, and the dissolution entropy, DSd can be estimated by plotting the lnx versus reciprocal of temperature [23]. The GibbseHelmholtz equation can be used to obtain Gibbs energy for the dissolution of MTX in different solvents at various temperatures:
The relative average deviation (RAD) is defined as follows:
RAD ¼
xi Þ 2 n
where n is the number of experimental points, and xi, cal and xi represent the calculated and the experimental solubility values, respectively [21,22]. The correlation results of both equations were presented in Tables 2e7 and graphically in Figs. 2e4. These indicate that both three equations were suitable for correlation of the solubility of both forms of MTX in different solvents with temperature variation. Comparing of the total average RD, RAD, RMSD and R2, it could be said that the polynomial equation was little better than the other equations.
(3)
where x is the molar solubility of MTX at the system temperature T, Tm is the melting temperature of the specific sample [19,20]. 1stOpt software was used to evaluate the multidimensional unconstrained nonlinear minimization of parameters. The relative deviation (RD), the relative average deviation (RAD) and the rootmean-square deviation (RMSD) were also given. The relative deviation (RD) is defined as follows:
Pn
cal
i¼1
1x 1 1 ¼ lh ln 1 þ l x T Tm
RD ¼
n X ðx
=
a b
0.9369 0.8485 0.7336 1.2505
104Ba
(5)
The root-mean-square deviation (RMSD) is defined as follows:
Table 5 The regressed parameters of polynomial equation in the 283.15e323.15 K temperature range.a,b Solvent Form A Ethanol Isopropanol Ethyl acetate Toluene Form B Ethanol Isopropanol Ethyl acetate Toluene a b
B0a
B1a
103B2a
106B3a
109B4a
104RMSDb
R2
0.8072 18.5858 89.043 11.8487
0.0076 0.2525 1.1889 0.1591
0.0208 1.2880 5.9505 0.8015
0.0035 2.9249 13.2306 1.7966
0.0395 2.4973 11.0295 1.5126
1.8739 0.5474 2.4250 0.3428
0.9984 0.9998 0.9975 0.9996
26.1087 22.5165 50.3433 0.4722
0.3453 0.3039 0.6740 0.0064
1.7132 1.5393 3.3833 0.0337
3.7820 3.4677 7.5470 0.0804
3.1367 2.9335 6.3144 0.0737
1.1773 1.3431 1.9730 0.1990
0.9984 0.9998 0.9975 0.9996
B0, B1, B2, B3 and B4 are the parameters of polynomial equation. RMSD is the root-mean-square deviation.
Table 6 The regressed parameters of BuchowskieKsiazczak lh equation in the 283.15e323.15 K temperature range.a,b Solvent
la
Ethanol Isopropanol Ethyl acetate Toluene
0.0801 0.1153 0.0450 0.0387
104ha
104RMSDb
R2
la
3.5415 3.0984 4.1619 8.8189
2.7126 0.8186 3.4103 1.0204
0.9967 0.9996 0.9950 0.9961
0.0547 0.0709 0.0308 0.0108
Form A
a b
104ha
104RMSDb
R2
4.9869 4.7764 5.9233 24.0285
3.7889 2.8667 2.6583 2.0144
0.9943 0.9914 0.9942 0.9924
Form B
l and h are the parameters of BuchowskieKsiazczak lh equation. RMSD is the root-mean-square deviation.
M. Hong et al. / Fluid Phase Equilibria 409 (2016) 1e6
5
Table 7 The regressed parameters of Van't Hoff equation in the 283.15e323.15 K temperature range.a,b,c,d Solvent Form A Ethanol Isopropanol Ethyl acetate Toluene Form B Ethanol Isopropanol Ethyl acetate Toluene a b c d
△Hda (KJ mol1)
△Sdb (J mol1 K1)
△Gdc (KJ mol1)
R2
102RMSDd
27.3693 31.5127 20.2996 30.6000
51.8512 63.4087 31.2536 52.3902
11.9099 12.6074 10.9814 14.9798
0.9980 0.9965 0.9961 0.9921
2.5417 1.1378 2.3595 2.7476
27.9096 29.6392 19.6029 26.1076
51.5292 54.7862 26.3826 33.5348
12.5461 13.3047 11.7369 16.1092
0.9980 0.9965 0.9961 0.9921
2.1240 2.9602 2.9414 3.9400
△Hd is the molar dissolution enthalpy. △Sd is the molar dissolution entropy. △Gd is the molar dissolution Gibbs free energy. RMSD is the root-mean-square deviation.
Fig. 3. Experimental and modeling solubility of MTX (Form A and Form B) in different solvents based on polynomial empirical equation. Experimental data: (Form A: -, Ethanol; C, Isopropanol; :, Ethyl acetate; A, Toluene), (Form B: ,, Ethanol; B, Isopropanol; △, Ethyl acetate; >, Toluene). Modeling data: (d,Form A; ---,Form B).
Fig. 5. Experimental and modeling solubility of MTX (Form A and Form B) in different solvents based on Van't Hoff equation. Experimental data: (Form A: -, Ethanol; C, Isopropanol; :, Ethyl acetate; A, Toluene), (Form B: ,, Ethanol; B, Isopropanol; △, Ethyl acetate; >, Toluene). Modeling data: (d,Form A; ---,Form B).
DHd DSd þ RT R
(7)
DGd ¼ DHd TDSd
(8)
lnx ¼
Fig. 5 illustrated the linear Van't Hoff plots of lnx versus 1/T. Table 7 presents the molar dissolution enthalpy and entropy determined using the least-squares and Gibbs energy calculated at 298.15 K. From Table 7, it could be seen that the molar dissolution enthalpy and entropy of both forms of MTX were positive (△Hd > 0, △Sd > 0), thereby indicating the course of MTX dissolving in each selected solvent at the experimental temperature range was endothermic and entropy-driven. Furthermore, the curves in Figs. 2 and 5 and the data in Tables 2, 3 and 7 revealed that the △Gd values were positive, which indicated that the dissolution process was nonspontaneous. And also we could find that the △Gd values trended in an opposite direction from solubility [24e26]. 4. Conclusions Fig. 4. Experimental and modeling solubility of MTX (Form A and Form B) in different solvents based on BuchowskieKsiazczak lh equation. Experimental data: (Form A: -, Ethanol; C, Isopropanol; :, Ethyl acetate; A, Toluene), (Form B: ,, Ethanol; B, Isopropanol; △, Ethyl acetate; >, Toluene). Modeling data: (d,Form A; ---,Form B).
The solubility data of two forms of MTX in four different pure solvents was determined by shake flask method at temperature ranging from 283.15 K to 323.15 K. In the selected pure solvents, the
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solubility of both forms of MTX showed a strong dependence on temperature except in toluene. The modified Apelblat equation, polynomial equation and BuchowskieKsiazczak lh equation were used to describe the experimental data. It turned out that all the selected thermodynamic models could give satisfactory correlation results, with the polynomial equation showing the best fitting degree. Finally, the dissolution molar enthalpy, entropy and the molar Gibbs free energy were calculated based on the Van't Hoff equation. The results indicated that the dissolving course of MTX in each selected solvent at the experimental temperature range was endothermic, entropy-driven and nonspontaneous. Acknowledgment This work was supported by National Natural Science Foundation of China (No. 81102391) and the Shanghai Committee of Science and Technology (Grant 12DZ1930702). References [1] V.K. Marothu, R.N. Dash, S. Vemula, S. Donkena, R. Devi, M. Gorrepati, J. Pharm. Anal. 2 (2012) 431e436. [2] H.-L. Lin, T.-K. Wu, S.-Y. Lin, Thermochim. Acta 575 (2014) 313e321. [3] J. Chen, B. Sarma, J.M.B. Evans, A.S. Myerson, Cryst. Growth Des. 11 (2011) 887e895. [4] M.A. O'Mahony, D.M. Croker, Å.C. Rasmuson, S. Veesler, B.K. Hodnett, Org. Process Res. Dev. 17 (2013) 512e518.
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