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Thermodynamics of pharmaceuticals: Prediction of solubility in pure and mixed solvents with PC-SAFT
Fluid Phase Equilibria 302 (2011) 331–337
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Thermodynamics of pharmaceuticals: Prediction of solubility in pure and mixed solvents with PC-SAFT Theodora Spyriouni a,b,∗ , Xenophon Krokidis a , Ioannis G. Economou b,c a
Scienomics, 17 square Edouard VII, 75009 Paris, France National Center for Scientific Research “Demokritos”, Institute of Physical Chemistry, Molecular Thermodynamics and Modelling of Materials Laboratory, GR-153 10 Aghia Paraskevi Attikis, Greece c The Petroleum Institute, Department of Chemical Engineering, PO Box 2533, Abu Dhabi, United Arab Emirates b
a r t i c l e
i n f o
Article history: Received 29 June 2010 Received in revised form 25 August 2010 Accepted 31 August 2010 Available online 15 September 2010 Keywords: Solubility Thermodynamics Pharmaceuticals PC-SAFT
a b s t r a c t A new scheme is presented for the parameterization of pharmaceuticals in the context of the perturbedchain statistical associating fluid theory (PC-SAFT). The pharmaceutical parameters are fitted to experimental solubility values in three different solvents, i.e., a hydrophilic, a polar, and a hydrophobic solvent. Subsequently, the solubility of the pharmaceuticals in other solvents is predicted without the need for additional interaction parameters. The approach is presented for six commonly used pharmaceutical compounds (paracetamol, naproxen, ibuprofen, flurbiprofen, ketoprofen, and lovastatin) in numerous pure and mixed solvents, and in different temperatures. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Thermodynamic models are increasingly used by the pharmaceutical industry at different stages of the product and process development and optimization processes. At the product development and formulation stage, various solvents are screened for new pharmaceutical molecules. At the later stage of process development and optimization, appropriate selection of a solvent or a mixture of solvents is critical for the crystallization and other processes. Most of the pharmaceutical molecules are significantly more complex than molecules encountered in oil and chemical industry, with multiple functional polar and hydrogen bonding groups. At the same time, experimental physical property data for most of the pharmaceutical molecules of interest are substantially more limited than data for hydrocarbons and other compounds of importance to oil and gas industries. Even more, experimental values for the same physical property and at the same conditions may vary significantly from one source to another. The situation as outlined above sets up a very challenging framework toward the development of a thermodynamic model able
∗ Corresponding author at: National Center for Scientific Research “Demokritos”, Institute of Physical Chemistry, Molecular Thermodynamics and Modelling of Materials Laboratory, GR-153 10 Aghia Paraskevi Attikis, Greece. Tel.: +30 2106503961; fax: +30 2106511766. E-mail address: [email protected] (T. Spyriouni). 0378-3812/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.08.029
to correlate/predict important properties of pharmaceuticals for product and process design. On one hand, a suitable model should account explicitly for the different types of inter- but also intramolecular interactions, that include weak dispersion and highly oriented strong polar, hydrogen bonding and long range electrostatic interactions. On the other hand, accurate parameterization of such a model is often based on few and system specific data. In this way, the applicability of the model becomes limited to the system(s) and conditions optimized without any possibility for transferability to other, even similar, systems. The popular non-random two liquid (NRTL) model that is widely used for mainstream chemical engineering applications was recently extended to pharmaceutical mixtures through the NRTL segment activity coefficient (NRTL-SAC) model [1]. The inherent empirical nature of NRTL-SAC results in a model that correlates accurately experimental solubility data for pharmaceuticals in various solvents using several adjustable non-transferrable parameters. Another well known approach is the universal functional activity coefficient model (UNIFAC) [2]. Like NRTL-SAC, in this model experimental data are needed for parameter regression and therefore its accuracy to molecules with new functional groups is limited. Furthermore, the model has limited success in predicting the solubility as a function of temperature and for high molecular compounds. In recent years, the conductor-like screening model (COSMO-RS) [3] has found substantial use in academia and in industry. The model uses as input the sigma profile, a molecule-specific distribution of the charge density. The generation of sigma profiles
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is the most time-consuming aspect of the method, and it becomes impractical for large flexible molecules with multiple conformations. The main advantage of the model is that it uses only data from quantum chemical calculations, thus enabling predictions when there are no available experimental data. Recently, equation of state (EoS) models rooted to statistical mechanics have been applied to pharmaceutical solubility calculations. A lattice model, the non-random hydrogen bonding theory (NRHB) [4] was applied to widely used pharmaceuticals. Parameter values were obtained from simpler molecules that contain the same functional groups as the pharmaceutical molecules of interest. NRHB was subsequently used to calculate the solubility of these pharmaceuticals in various liquid and supercritical fluid solvents and mixed solvents [4,5]. A well known equation of state that has found extensive application to the chemical industry, the perturbed-chain statistical associating fluid theory (PC-SAFT) [6] was applied for the first time to correlate and predict the solubility of typical pharmaceuticals in pure solvents and binary mixtures [7]. In this work, the predictive ability of the PC-SAFT EoS is demonstrated through a new empirical workflow for the parameterization of pharmaceuticals. The workflow requires a few experimental data such as the enthalpy of fusion and the melting temperature of the pharmaceutical along with the solubility in three selected solvents. The parameters are used subsequently to predict the solubility of the pharmaceuticals in different solvents, at various temperatures. This approach is shown to be accurate also in the case of mixed solvents. No fitted binary interaction parameters are used throughout this work, except for the aqueous systems for reasons related to the parameterization scheme as will be clarified later on. The purpose of this work has been to evaluate the predictive capabilities of PCSAFT using an appropriate parameterization of the model. Clearly, the use of binary interaction parameter(s) fitted to experimental data would result in accurate correlation of the data. The so-called predictive PC-SAFT is applied to six typical pharmaceutical compounds and the predictions are compared against available experimental data of solubility in various solvent systems and temperatures.
2. Theory Pharmaceutical compounds are crystalline solids at room temperature. Their solubility in a liquid solvent can be described using standard thermodynamic expressions for solid–liquid equilibria. Consequently, the mole fraction of pharmaceutical i in a solvent is given by the expression [8]: ln
1 H f = ln i + xi RTm
T
m
T
−1 −
cP R
T
m
T
−1 +
cP Tm ln R T
(1)
where xi and i are the mole fraction and the activity coefficient of the pharmaceutical in the liquid solvent. Hf and Tm are the enthalpy of fusion and the melting temperature of the pharmaceutical, cP is the difference of the heat capacity of the pharmaceutical in the solid and the liquid state, R is the gas constant and T is the temperature. Hf , Tm , and cP are pure component properties. For the derivation of Eq. (1) it has been assumed that we have pure pharmaceutical in the solid phase. It has also been assumed that the triple point temperature and the melting point temperature of the pharmaceutical are very close to each other. This assumption is very good for pharmaceuticals and many other solid compounds. In addition, the third and fourth terms on the right hand side of Eq. (1) are of similar magnitude and different sign; thus one may omit them without significant loss of accuracy. Tsivintzelis et al. examined the validity of this approximation for several pharmaceutical mixtures [4].
As a result, a simplified expression is obtained for the solubility of a pharmaceutical in a solvent: ln
H f 1 = ln i + xi RTm
T
m
T
−1
(2)
The activity coefficient i accounts for the non-idealities between pharmaceutical and solvent molecules and can be calculated from an appropriate model, such as NRTL-SAC [1], NRHB [4], or PC-SAFT [6]. PC-SAFT is based on perturbation theory. The reference fluid corresponds to the hard chain fluid while perturbations account for dispersion forces and hydrogen bonding. The model is written in terms of the residual Helmholtz energy ares as: ares = ahc + adisp + aassoc ahc ,
adisp
(3)
aassoc
where and represent the hard chain, dispersion and association terms. The functional forms for these terms can be found in the original publication [6]. PC-SAFT is extended to mixtures using standard mixing rules [6]. 3. Parameterization of pharmaceuticals PC-SAFT contains five component-specific parameters that include the segment number m, the segment diameter , the segment dispersion energy ε/kB , the association energy εhb /kB , and the association volume hb . The last two parameters are needed for components that form hydrogen bonds. For the case of solvents, these parameters are fitted to vapor pressure and saturated liquid density from low temperature up to close to the critical point. A different approach is necessary in order to model solid compounds when dissolved in liquid solvents. All of the pharmaceuticals examined here contain functional groups that hydrogen bond, either with other pharmaceutical molecules or with solvent molecules. For simplicity, all pharmaceutical molecules are assumed to have 4 associating sites of equal strength (two electron acceptor and two electron donor, Scheme 4A). A more complicated association scheme based on the differentiation of the various associating sites (for example, carbonyl groups, hydroxyl groups) would require additional fitted parameters. Furthermore, as Ruether and Sadowski pointed out [7], hb has a relatively little effect on the solubility calculations and it was set equal to 0.01. Thus, the number of pure component parameters for regression practically reduces to four. The four pure component parameters for each pharmaceutical are fitted to solubility data in three different solvents, namely a hydrophilic solvent, a polar solvent and a hydrophobic solvent. Water is always used as the hydrophilic solvent. As polar solvents the following 3 are suggested as suitable candidates: methanol (MeOH), methyl isobutyl ketone (MIBK), and methyl ethyl ketone (MEK). The hydrophobic solvent is either n-heptane or benzene. According to this approach the number of data points needed for a sufficient parameterization of the pharmaceutical is reduced to three solubilities at one temperature (not necessarily room temperature) and the melting data of the compound (melting temperature and fusion enthalpy), used in Eq. (2). The proposed scheme has been implemented to six known active pharmaceutical compounds, namely paracetamol, naproxen, ibuprofen, flurbiprofen, ketoprofen, and lovastatin, whose molecular structure is shown in Fig. 1. The molecular weight (MW), the melting temperature (Tm ) and the fusion enthalpy (Hf ) of these molecules are listed in Table 1. The experimental literature solubilities in the three solvents used for the regression of the pharmaceutical parameters are given in Table 2. The solubility values vary significantly from one solvent to the other. An empirical but highly successful approach is proposed here where the aqueous solubility is artificially increased up to several orders of magnitude. The so-called “target solubilities”
T. Spyriouni et al. / Fluid Phase Equilibria 302 (2011) 331–337
333
Fig. 1. Chemical structure of the pharmaceuticals examined in this work.
Table 1 Molecular weight (MW), melting temperature (Tm ), and enthalpy of fusion (Hf ) for the pharmaceutical compounds examined in this work. Compound a
Paracetamol Naproxenb Ibuprofenc Flurbiprofend Ketoprofene Lovastatinf a b c d e f
MW
Tm (K)
151.16 230.26 206.28 244.26 254.28 404.54
443.6 427.6 347.2 388.2 367.7 445.5
Hf (J/mol) 27,000 31,500 25,500 29,100 21,000 43,136
Granberg and Rasmuson [10]. Neau et al. [11]. Gracin and Rasmson [12]. Grzesiak and Matzger [13]. Espitalier et al. [14]. Nti-Gyabaah et al. [15].
are shown in Table 2. The water solubility affects basically the size parameters m and of the pharmaceutical. Increasing the water solubility decreases the size of the molecule. From a physical point of view, the pharmaceuticals are modeled as small compounds with high dispersion and association energy per segment and this mimics better their interactions with other fluids as highly polar
Table 3 Multiplying factors used to calculate the target solubility in water from the actual solubility as a function of the order of magnitude of the actual value. Aqueous solubility (mg/g)
Multiplying factor
1.E−04 1.E−03 1.E−02 1.E−01 >1
10,000 1000 500 100 10
and associative compounds. The proposed multiplying factors that one should use in order to scale up solubility values are shown in Table 3. In order to correct for this artificial increase in solubility, a binary interaction parameter, kij , is necessary between water and pharmaceutical in order that the model represents accurately the experimental value. The kij is used for the predictions in systems where water is one of the components. The solubilities in the polar solvent and benzene remain unchanged. The solubility in n-heptane (hydrophobic solvent) needs to be adjusted as well. Additional studies performed and not shown here revealed that the solubility in n-heptane should be scaled up to the upper closest power of 10, i.e., if the actual value is
Table 2 Experimental solubility of the examined pharmaceutical compounds in specific solvents and target solubility used in the parameterization scheme. For the polar solvents and for benzene, the experimental and target solubility are the same. The units of solubility are mg/g solvent. The temperature (if not checked otherwise) is 298.15 K. Compound
Experimental solubility in Water
Paracetamol Naproxen Ibuprofen Flurbiprofen Ketoprofen Lovastatin a b c d e f g h i j k l
a
14.9 0.0159c 0.021c 0.009c 0.124h , f 0.0004k
Target solubility in
Polar solvent a
MeOH: 332 MeOH: 79d MeOH: 1752e , i MeOH: 383g MeOH: 355j , i MeOH: 40l
Granberg and Rasmuson [10]. Barra et al. [16]. Yalkowsky and He [17]. Bustamante et al. [18]. Gracin and Rasmuson [12]. The data refer to temperature equal to 293.15 K. Perlovich et al. [19]. Espitalier et al. [14]. The data refer to temperature equal to 303.15. Daniels et al. [20]. Tung et al. [21]. Sun et al. [22].
Hydrophobic b
Benzene: 0.2 Benzene: 21.5d Benzene: 244 Benzene: 229g – –
Water
Polar solvent
Hydrophobic
149 7.95 10.5 9 12.4f 4
MeOH: 332 MeOH: 79 MeOH: 1752i MeOH: 383 MeOH: 355i MeOH: 40
Benzene: 0.2 Benzene: 21.5 Benzene: 244 Benzene: 229 Heptane: 10 Heptane: 10
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Table 4 Parameters of the pharmaceutical compounds and solvents mentioned explicitly in this work. The solvents have been parameterized against VLE data (vapor pressures and saturated densities). The temperature range of regression and the AAD (%) are also listed. Compounds a
Paracetamol Naproxena Ibuprofena Flurbiprofena Ketoprofena Lovastatina Solvents for regression Waterb Methanolb Methyl isobutyl ketonea Methyl ethyl ketonea Heptanec Benzenec Other solvents Acetoned Ethanolb 2-Propanolb Propylene glycole 1,4-Dioxanea Ethyl acetatea Isopropyl acetata n-Butyl axcetatea Isopropyl ethera 2-Methyltetrahydrofurana Isooctanef a b c d e f
m
(A)
ε/k (K)
Nassoc
hb /k (K)
Khb
2.1973 3.5462 4.1915 2.3253 4.6712 2.9952
4.2153 3.0960 3.7269 4.0212 3.3635 2.6542
397.27 242.59 313.88 332.57 298.96 154.51
4 4 4 4 4 4
2003.76 1263.04 1294.75 300.00 1465.55 1334.79
0.01 0.01 0.01 0.01 0.01 0.01
1.0656 1.5255 4.1064 3.5904 3.4831 2.4653
3.0010 3.2300 3.4154 3.1538 3.8049 3.6478
366.51 188.90 193.54 172.29 238.40 287.35
2 2 2 2 0 0
2500.67 2899.50 904.97 1220.61 -
0.0349 0.0352 1.3110 1.4 -
3.0925 2.3827 3.0929 2.3392 2.5763 3.1478 3.5364 3.9246 3.1896 2.4759 3.1413
3.0848 3.1771 3.2085 3.6351 3.5250 3.4595 3.5121 3.5644 3.8233 3.7986 4.0862
168.32 198.24 208.42 284.62 209.10 239.59 233.26 243.70 229.28 272.39 249.77
2 2 2 2 2 2 2 2 2 2 0
1321.20 2653.40 2253.90 2080.03 1681.36 737.22 473.47 732.74 475.92 205.92
0.9639 0.0324 0.0247 0.0235 0.4251 0.0533 0.0256 0.0070 0.0009 0.5593
T (K)
Psat (%)
pliq
240-390 240-520
0.54 0.074
0.004 0.003
290-450 240-500 240-420 240-460 240-400 311-430
0.027 0.14 0.15 0.09 0.32 0.09
0.003 0.01 0.008 0.008 0.002 0.002
This work. Gross and Sadowski [23]. Gross and Sadowski [6]. von Solms et al. [24]. Grenner et al. [25]. Sun et al. [22].
between 0.1 and 1, the target value is set to 1, if the actual value is between 1 and 10 the target value is set to 10 and so on. This might be the necessary counteraction of the increase in the hydrophilic solubility. However, the solubility in benzene (hydrophobic solvent) does not need to be scaled. This is probably due to the partially polar nature of the solvent that results to higher pharmaceutical solubility compared to n-heptane in almost all cases. For ketoprofen and lovastatin where no experimental data were available for the solubility in the hydrophobic solvent, n-heptane was chosen as the hydrophobic solvent with an arbitrary solubility of 10 mg/g. Validation of the parameters for the prediction of pharmaceutical solubility in n-octanol (long aliphatic part) gave good results. All calculations reported herein have been performed using the SciTherm module of the Scienomics’ MAPS platform [9]. The PCSAFT parameters for the pharmaceuticals are given in Table 4, together with the parameters for the solvents examined here. A number of polar solvents are modeled as associating components with two sites. Although these solvents do not hydrogen bond, the inclusion of associating sites aims to mimic the polar interactions exhibited by such molecules and that affect the pharmaceutical solubility significantly. A similar approach was used in NRHB [4]. Solvent parameters were fitted to experimental vapor pressure and liquid density data and deviations for the experimental values are reported in Table 4.
available temperature). The number of solvents for each pharmaceutical in Fig. 2 and the average root-mean-squared (rms) error are given in Table 5. Rms is calculated as:
⎛ ⎞ 2 N ⎝ 1 exp rms = (log Xi − log Xicalc ) ⎠ N
(4)
i=1
where Xi is the solubility of the compound i in g/g solvent and N is the number of data points (solvents). The solvents used for the parameterization of pharmaceutical molecules are excluded from Fig. 2 and from the calculation of rms in Table 5. The fairly good agreement achieved for all compounds in all solvents shows that the parameterization scheme provides a valid description of the compound solubility with PC-SAFT.
4. Results and discussion The solubility of the pharmaceuticals in the various solvents examined in this work span several orders magnitude. In Fig. 2, a comparison is made between experimental and PC-SAFT predicted values for the solubilities of paracetamol [10,16,26], naproxen [27,28], ibuprofen [12,29], flurbiprofen [19,30], ketoprofen [20,31], and lovastatin [15,22,32] in pure solvents at 298.15 K (or the closest
Fig. 2. Predicted versus experimental solubility (expressed in mass fraction) of six common pharmaceutical compounds in various pure solvents at 298.15 K.
T. Spyriouni et al. / Fluid Phase Equilibria 302 (2011) 331–337
1000
Solubility (mg / g solvent)
Solubility (mg / g solvent)
1000
100
10
100 10 1 Paracetamol-Exp Naproxen-Exp Paracetamol-PC-SAFT Naproxen-PC-SAFT
0.1 0.01
1 0
0.2
0.4
0.6
0.8
0
1
0.2
0.4
0.6
0.8
1
Ethanol weight fraction
Acetone weight fraction
Based on the extended range of solubility values for different solvents shown in Fig. 2, one expects that in an appropriately selected mixed solvent the solubility will vary substantially as a function of composition. In pharmaceutical process design, a mixed solvent is commonly used to tune solubility. In this respect, a thermodynamic model that can accurately predict the variation of solubility is highly desirable. Some representative examples using PC-SAFT are discussed below. Standard mixing rules were used in all cases [23]. In Fig. 3, experimental data [33] and PC-SAFT predictions for the solubility of paracetamol in acetone–water mixture at 296.15 K are shown. The solubility varies by more than an order of magnitude, going through a maximum at around 0.7 acetone weight fraction. A binary interaction parameter kij = 0.0352 is used for the water–paracetamol interactions in order to correct the higher aqueous solubility of paracetamol induced by the parameterization scheme. PC-SAFT provides an excellent prediction of the solubility over the entire solvent composition range. The solubility of paracetamol in the 1,4-dioxane–water mixture at 298.15 K is shown in Fig. 4. For paracetamol–water the same kij was used, as above. The variation of solubility with composition is similar to the data for acetone–water, although the solubility maximum is now shifted to higher 1,4-dioxane composition (around 0.8 weight fraction). Here again, PC-SAFT predictions capture reasonably accurately the change in solubility; although a lower maximum solubility value is predicted compared to experimental data [34].
1000
100
10
Fig. 5. Solubility of paracetamol and naproxen in ethanol–water mixture. Experimental data (points) for paracetamol at 298.15 K [34] and naproxen at 293.15 [35] are compared with the PC-SAFT predictions (lines).
1600
Solubility (mg/g solvent)
Fig. 3. Solubility of paracetamol in acetone–water mixture at 296.15 K. The experimental data (points) are from [33]. The line is the PC-SAFT prediction.
Solubility (mg / g solvent)
335
1200
800
400
0 0
0.2
0.4
0.6
0.8
1
Ethanol weight fraction Fig. 6. Solubility of ibuprofen in the binary mixture of ethanol–propylene glycol at 298.15 K. Comparison between experimental data [36] (points) and PC-SAFT predictions (line).
A different mixed solvent commonly used in pharmaceutical industry is ethanol–water. In Fig. 5, experimental data [34,35] and PC-SAFT predictions for paracetamol at 298.15 K and naproxen at 293.15 K in this solvent are shown. The paracetamol solubility varies by more than an order of magnitude while the naproxen solubility varies by almost three orders of magnitude, as a function of composition. PC-SAFT predictions are in excellent agreement with experiments. For naproxen–water interactions, kij = 0.09572. We turn our attention next to non-aqueous solvents. In Fig. 6, experimental data [36] and PC-SAFT predictions are shown for the solubility of ibuprofen in ethanol–propylene glycol mixture at 298.15 K. Predictions from PC-SAFT (all binary interaction parameters set equal to zero) are remarkably accurate. Although the majority of pharmaceutical processes take place at ambient temperature, the effect of temperature in solubility is Table 5 Number of solvents for which a solubility prediction was made and average error (rms) over these solvents for all pharmaceutical compounds examined in this work. The temperature is 298.15 K (or the closest available).
1 0
0.2
0.4
0.6
0.8
1
1,4-Dioxane weight fraction Fig. 4. Solubility of paracetamol in the binary mixture of 1,4-dioxane–water at 298.15 K. Comparison between experimental data [34] (points) and PC-SAFT predictions (line).
Compounds
Number of solvents
rms
Paracetamol Naproxen Ibuprofen Flurbiprofen Ketoprofen Lovastatin
25 24 20 12 11 13
0.32 0.48 0.36 0.23 0.29 0.27
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Solubility (mg / g solvent)
1000
100 EtOH-Exp Acetone-Exp
10
EtOAc-Exp EtOH-PC-SAFT Acetone-PC-SAFT EtOAc-PC-SAFT
1 0
10
20
30
40
In Fig. 8, the ibuprofen solubility in ethanol and in 2-propanol as a function of temperature is shown. PC-SAFT predictions compare favorably with the experimental data [12]. The increase in solubility is captured satisfactorily by PC-SAFT although the absolute value of solubility is overestimated by the model (except for the solubility in ethanol at 35 ◦ C). Also, the relative solubility in the two solvents is predicted correctly. Finally, the solubility of lovastatin in ethanol and ethyl acetate is presented in Fig. 9. PC-SAFT predictions agree remarkably well with experimental data [22] over the entire temperature range. For both sets of data, PC-SAFT predicts a slightly stronger temperature effect compared to experiments.
o
T ( C)
5. Conclusions
Fig. 7. Solubility of paracetamol in ethanol (EtOH), acetone, and ethyl acetate (EtOAc) as a function of temperature. Experimental data (points) [10] and PC-SAFT predictions (lines).
2400
Solubility (mg/g solvent)
EtOH-Exp 2-propanol-Exp
2000
EtOH-PC-SAFT 1600
2-propanol-PC-SAFT
1200 800 400
References
0 0
10
20
30
40
T (o C) Fig. 8. Solubility of ibuprofen in ethanol (EtOH) and 2-propanol as a function of temperature. Comparison of experimental data (points) [12] and PC-SAFT predictions (lines).
140 EtOH-Expt
Solubility (mg / g solvent)
In this work a new approach was presented for predicting the solubility of pharmaceutical molecules by using PC-SAFT. The predictive ability of the scheme was based on the appropriate parameterization of the pharmaceutical molecules. The regression of parameters was performed against the solubility of pharmaceuticals in three solvents, i.e., a hydrophilic solvent (water), a polar solvent, and a hydrophobic solvent. We demonstrated that following this scheme the resulting parameters describe adequately the solubility of pharmaceuticals in pure and mixed solvents. No adjustable parameter is required except for the aqueous systems where a non-zero kij is used to correct the high solubility in water imposed by the parameterization scheme. The temperature dependence of the solubility was also captured satisfactorily by PC-SAFT.
120
EtOAc-Expt EtOH - PC-SAFT
100
EtOAc-PC-SAFT
80 60 40 20 0 0
10
20
30
40
50
60
o
T ( C) Fig. 9. Solubility of lovastatin in ethanol (EtOH) and ethyl acetate (EtOAc) as a function of temperature. Experimental data (points) [22] and PC-SAFT predictions (lines).
often significant and a reliable thermodynamic model should be able to capture it accurately, preferably without the use of additional empirical parameters. In Fig. 7, experimental data [10] and PC-SAFT predictions are shown for the solubility of paracetamol in ethanol, acetone and ethyl acetate in the range 0–30 ◦ C. PC-SAFT predicts accurately the increase of solubility with temperature and with the solvent change from ethyl acetate to acetone to ethanol.
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Thermodynamics of pharmaceuticals: Prediction of solubility in pure and mixed solvents with PC-SAFT Theodora Spyriouni a,b,∗ , Xenophon Krokidis a , Ioannis G. Economou b,c a
Scienomics, 17 square Edouard VII, 75009 Paris, France National Center for Scientific Research “Demokritos”, Institute of Physical Chemistry, Molecular Thermodynamics and Modelling of Materials Laboratory, GR-153 10 Aghia Paraskevi Attikis, Greece c The Petroleum Institute, Department of Chemical Engineering, PO Box 2533, Abu Dhabi, United Arab Emirates b
a r t i c l e
i n f o
Article history: Received 29 June 2010 Received in revised form 25 August 2010 Accepted 31 August 2010 Available online 15 September 2010 Keywords: Solubility Thermodynamics Pharmaceuticals PC-SAFT
a b s t r a c t A new scheme is presented for the parameterization of pharmaceuticals in the context of the perturbedchain statistical associating fluid theory (PC-SAFT). The pharmaceutical parameters are fitted to experimental solubility values in three different solvents, i.e., a hydrophilic, a polar, and a hydrophobic solvent. Subsequently, the solubility of the pharmaceuticals in other solvents is predicted without the need for additional interaction parameters. The approach is presented for six commonly used pharmaceutical compounds (paracetamol, naproxen, ibuprofen, flurbiprofen, ketoprofen, and lovastatin) in numerous pure and mixed solvents, and in different temperatures. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Thermodynamic models are increasingly used by the pharmaceutical industry at different stages of the product and process development and optimization processes. At the product development and formulation stage, various solvents are screened for new pharmaceutical molecules. At the later stage of process development and optimization, appropriate selection of a solvent or a mixture of solvents is critical for the crystallization and other processes. Most of the pharmaceutical molecules are significantly more complex than molecules encountered in oil and chemical industry, with multiple functional polar and hydrogen bonding groups. At the same time, experimental physical property data for most of the pharmaceutical molecules of interest are substantially more limited than data for hydrocarbons and other compounds of importance to oil and gas industries. Even more, experimental values for the same physical property and at the same conditions may vary significantly from one source to another. The situation as outlined above sets up a very challenging framework toward the development of a thermodynamic model able
∗ Corresponding author at: National Center for Scientific Research “Demokritos”, Institute of Physical Chemistry, Molecular Thermodynamics and Modelling of Materials Laboratory, GR-153 10 Aghia Paraskevi Attikis, Greece. Tel.: +30 2106503961; fax: +30 2106511766. E-mail address: [email protected] (T. Spyriouni). 0378-3812/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.08.029
to correlate/predict important properties of pharmaceuticals for product and process design. On one hand, a suitable model should account explicitly for the different types of inter- but also intramolecular interactions, that include weak dispersion and highly oriented strong polar, hydrogen bonding and long range electrostatic interactions. On the other hand, accurate parameterization of such a model is often based on few and system specific data. In this way, the applicability of the model becomes limited to the system(s) and conditions optimized without any possibility for transferability to other, even similar, systems. The popular non-random two liquid (NRTL) model that is widely used for mainstream chemical engineering applications was recently extended to pharmaceutical mixtures through the NRTL segment activity coefficient (NRTL-SAC) model [1]. The inherent empirical nature of NRTL-SAC results in a model that correlates accurately experimental solubility data for pharmaceuticals in various solvents using several adjustable non-transferrable parameters. Another well known approach is the universal functional activity coefficient model (UNIFAC) [2]. Like NRTL-SAC, in this model experimental data are needed for parameter regression and therefore its accuracy to molecules with new functional groups is limited. Furthermore, the model has limited success in predicting the solubility as a function of temperature and for high molecular compounds. In recent years, the conductor-like screening model (COSMO-RS) [3] has found substantial use in academia and in industry. The model uses as input the sigma profile, a molecule-specific distribution of the charge density. The generation of sigma profiles
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is the most time-consuming aspect of the method, and it becomes impractical for large flexible molecules with multiple conformations. The main advantage of the model is that it uses only data from quantum chemical calculations, thus enabling predictions when there are no available experimental data. Recently, equation of state (EoS) models rooted to statistical mechanics have been applied to pharmaceutical solubility calculations. A lattice model, the non-random hydrogen bonding theory (NRHB) [4] was applied to widely used pharmaceuticals. Parameter values were obtained from simpler molecules that contain the same functional groups as the pharmaceutical molecules of interest. NRHB was subsequently used to calculate the solubility of these pharmaceuticals in various liquid and supercritical fluid solvents and mixed solvents [4,5]. A well known equation of state that has found extensive application to the chemical industry, the perturbed-chain statistical associating fluid theory (PC-SAFT) [6] was applied for the first time to correlate and predict the solubility of typical pharmaceuticals in pure solvents and binary mixtures [7]. In this work, the predictive ability of the PC-SAFT EoS is demonstrated through a new empirical workflow for the parameterization of pharmaceuticals. The workflow requires a few experimental data such as the enthalpy of fusion and the melting temperature of the pharmaceutical along with the solubility in three selected solvents. The parameters are used subsequently to predict the solubility of the pharmaceuticals in different solvents, at various temperatures. This approach is shown to be accurate also in the case of mixed solvents. No fitted binary interaction parameters are used throughout this work, except for the aqueous systems for reasons related to the parameterization scheme as will be clarified later on. The purpose of this work has been to evaluate the predictive capabilities of PCSAFT using an appropriate parameterization of the model. Clearly, the use of binary interaction parameter(s) fitted to experimental data would result in accurate correlation of the data. The so-called predictive PC-SAFT is applied to six typical pharmaceutical compounds and the predictions are compared against available experimental data of solubility in various solvent systems and temperatures.
2. Theory Pharmaceutical compounds are crystalline solids at room temperature. Their solubility in a liquid solvent can be described using standard thermodynamic expressions for solid–liquid equilibria. Consequently, the mole fraction of pharmaceutical i in a solvent is given by the expression [8]: ln
1 H f = ln i + xi RTm
T
m
T
−1 −
cP R
T
m
T
−1 +
cP Tm ln R T
(1)
where xi and i are the mole fraction and the activity coefficient of the pharmaceutical in the liquid solvent. Hf and Tm are the enthalpy of fusion and the melting temperature of the pharmaceutical, cP is the difference of the heat capacity of the pharmaceutical in the solid and the liquid state, R is the gas constant and T is the temperature. Hf , Tm , and cP are pure component properties. For the derivation of Eq. (1) it has been assumed that we have pure pharmaceutical in the solid phase. It has also been assumed that the triple point temperature and the melting point temperature of the pharmaceutical are very close to each other. This assumption is very good for pharmaceuticals and many other solid compounds. In addition, the third and fourth terms on the right hand side of Eq. (1) are of similar magnitude and different sign; thus one may omit them without significant loss of accuracy. Tsivintzelis et al. examined the validity of this approximation for several pharmaceutical mixtures [4].
As a result, a simplified expression is obtained for the solubility of a pharmaceutical in a solvent: ln
H f 1 = ln i + xi RTm
T
m
T
−1
(2)
The activity coefficient i accounts for the non-idealities between pharmaceutical and solvent molecules and can be calculated from an appropriate model, such as NRTL-SAC [1], NRHB [4], or PC-SAFT [6]. PC-SAFT is based on perturbation theory. The reference fluid corresponds to the hard chain fluid while perturbations account for dispersion forces and hydrogen bonding. The model is written in terms of the residual Helmholtz energy ares as: ares = ahc + adisp + aassoc ahc ,
adisp
(3)
aassoc
where and represent the hard chain, dispersion and association terms. The functional forms for these terms can be found in the original publication [6]. PC-SAFT is extended to mixtures using standard mixing rules [6]. 3. Parameterization of pharmaceuticals PC-SAFT contains five component-specific parameters that include the segment number m, the segment diameter , the segment dispersion energy ε/kB , the association energy εhb /kB , and the association volume hb . The last two parameters are needed for components that form hydrogen bonds. For the case of solvents, these parameters are fitted to vapor pressure and saturated liquid density from low temperature up to close to the critical point. A different approach is necessary in order to model solid compounds when dissolved in liquid solvents. All of the pharmaceuticals examined here contain functional groups that hydrogen bond, either with other pharmaceutical molecules or with solvent molecules. For simplicity, all pharmaceutical molecules are assumed to have 4 associating sites of equal strength (two electron acceptor and two electron donor, Scheme 4A). A more complicated association scheme based on the differentiation of the various associating sites (for example, carbonyl groups, hydroxyl groups) would require additional fitted parameters. Furthermore, as Ruether and Sadowski pointed out [7], hb has a relatively little effect on the solubility calculations and it was set equal to 0.01. Thus, the number of pure component parameters for regression practically reduces to four. The four pure component parameters for each pharmaceutical are fitted to solubility data in three different solvents, namely a hydrophilic solvent, a polar solvent and a hydrophobic solvent. Water is always used as the hydrophilic solvent. As polar solvents the following 3 are suggested as suitable candidates: methanol (MeOH), methyl isobutyl ketone (MIBK), and methyl ethyl ketone (MEK). The hydrophobic solvent is either n-heptane or benzene. According to this approach the number of data points needed for a sufficient parameterization of the pharmaceutical is reduced to three solubilities at one temperature (not necessarily room temperature) and the melting data of the compound (melting temperature and fusion enthalpy), used in Eq. (2). The proposed scheme has been implemented to six known active pharmaceutical compounds, namely paracetamol, naproxen, ibuprofen, flurbiprofen, ketoprofen, and lovastatin, whose molecular structure is shown in Fig. 1. The molecular weight (MW), the melting temperature (Tm ) and the fusion enthalpy (Hf ) of these molecules are listed in Table 1. The experimental literature solubilities in the three solvents used for the regression of the pharmaceutical parameters are given in Table 2. The solubility values vary significantly from one solvent to the other. An empirical but highly successful approach is proposed here where the aqueous solubility is artificially increased up to several orders of magnitude. The so-called “target solubilities”
T. Spyriouni et al. / Fluid Phase Equilibria 302 (2011) 331–337
333
Fig. 1. Chemical structure of the pharmaceuticals examined in this work.
Table 1 Molecular weight (MW), melting temperature (Tm ), and enthalpy of fusion (Hf ) for the pharmaceutical compounds examined in this work. Compound a
Paracetamol Naproxenb Ibuprofenc Flurbiprofend Ketoprofene Lovastatinf a b c d e f
MW
Tm (K)
151.16 230.26 206.28 244.26 254.28 404.54
443.6 427.6 347.2 388.2 367.7 445.5
Hf (J/mol) 27,000 31,500 25,500 29,100 21,000 43,136
Granberg and Rasmuson [10]. Neau et al. [11]. Gracin and Rasmson [12]. Grzesiak and Matzger [13]. Espitalier et al. [14]. Nti-Gyabaah et al. [15].
are shown in Table 2. The water solubility affects basically the size parameters m and of the pharmaceutical. Increasing the water solubility decreases the size of the molecule. From a physical point of view, the pharmaceuticals are modeled as small compounds with high dispersion and association energy per segment and this mimics better their interactions with other fluids as highly polar
Table 3 Multiplying factors used to calculate the target solubility in water from the actual solubility as a function of the order of magnitude of the actual value. Aqueous solubility (mg/g)
Multiplying factor
1.E−04 1.E−03 1.E−02 1.E−01 >1
10,000 1000 500 100 10
and associative compounds. The proposed multiplying factors that one should use in order to scale up solubility values are shown in Table 3. In order to correct for this artificial increase in solubility, a binary interaction parameter, kij , is necessary between water and pharmaceutical in order that the model represents accurately the experimental value. The kij is used for the predictions in systems where water is one of the components. The solubilities in the polar solvent and benzene remain unchanged. The solubility in n-heptane (hydrophobic solvent) needs to be adjusted as well. Additional studies performed and not shown here revealed that the solubility in n-heptane should be scaled up to the upper closest power of 10, i.e., if the actual value is
Table 2 Experimental solubility of the examined pharmaceutical compounds in specific solvents and target solubility used in the parameterization scheme. For the polar solvents and for benzene, the experimental and target solubility are the same. The units of solubility are mg/g solvent. The temperature (if not checked otherwise) is 298.15 K. Compound
Experimental solubility in Water
Paracetamol Naproxen Ibuprofen Flurbiprofen Ketoprofen Lovastatin a b c d e f g h i j k l
a
14.9 0.0159c 0.021c 0.009c 0.124h , f 0.0004k
Target solubility in
Polar solvent a
MeOH: 332 MeOH: 79d MeOH: 1752e , i MeOH: 383g MeOH: 355j , i MeOH: 40l
Granberg and Rasmuson [10]. Barra et al. [16]. Yalkowsky and He [17]. Bustamante et al. [18]. Gracin and Rasmuson [12]. The data refer to temperature equal to 293.15 K. Perlovich et al. [19]. Espitalier et al. [14]. The data refer to temperature equal to 303.15. Daniels et al. [20]. Tung et al. [21]. Sun et al. [22].
Hydrophobic b
Benzene: 0.2 Benzene: 21.5d Benzene: 244 Benzene: 229g – –
Water
Polar solvent
Hydrophobic
149 7.95 10.5 9 12.4f 4
MeOH: 332 MeOH: 79 MeOH: 1752i MeOH: 383 MeOH: 355i MeOH: 40
Benzene: 0.2 Benzene: 21.5 Benzene: 244 Benzene: 229 Heptane: 10 Heptane: 10
334
T. Spyriouni et al. / Fluid Phase Equilibria 302 (2011) 331–337
Table 4 Parameters of the pharmaceutical compounds and solvents mentioned explicitly in this work. The solvents have been parameterized against VLE data (vapor pressures and saturated densities). The temperature range of regression and the AAD (%) are also listed. Compounds a
Paracetamol Naproxena Ibuprofena Flurbiprofena Ketoprofena Lovastatina Solvents for regression Waterb Methanolb Methyl isobutyl ketonea Methyl ethyl ketonea Heptanec Benzenec Other solvents Acetoned Ethanolb 2-Propanolb Propylene glycole 1,4-Dioxanea Ethyl acetatea Isopropyl acetata n-Butyl axcetatea Isopropyl ethera 2-Methyltetrahydrofurana Isooctanef a b c d e f
m
(A)
ε/k (K)
Nassoc
hb /k (K)
Khb
2.1973 3.5462 4.1915 2.3253 4.6712 2.9952
4.2153 3.0960 3.7269 4.0212 3.3635 2.6542
397.27 242.59 313.88 332.57 298.96 154.51
4 4 4 4 4 4
2003.76 1263.04 1294.75 300.00 1465.55 1334.79
0.01 0.01 0.01 0.01 0.01 0.01
1.0656 1.5255 4.1064 3.5904 3.4831 2.4653
3.0010 3.2300 3.4154 3.1538 3.8049 3.6478
366.51 188.90 193.54 172.29 238.40 287.35
2 2 2 2 0 0
2500.67 2899.50 904.97 1220.61 -
0.0349 0.0352 1.3110 1.4 -
3.0925 2.3827 3.0929 2.3392 2.5763 3.1478 3.5364 3.9246 3.1896 2.4759 3.1413
3.0848 3.1771 3.2085 3.6351 3.5250 3.4595 3.5121 3.5644 3.8233 3.7986 4.0862
168.32 198.24 208.42 284.62 209.10 239.59 233.26 243.70 229.28 272.39 249.77
2 2 2 2 2 2 2 2 2 2 0
1321.20 2653.40 2253.90 2080.03 1681.36 737.22 473.47 732.74 475.92 205.92
0.9639 0.0324 0.0247 0.0235 0.4251 0.0533 0.0256 0.0070 0.0009 0.5593
T (K)
Psat (%)
pliq
240-390 240-520
0.54 0.074
0.004 0.003
290-450 240-500 240-420 240-460 240-400 311-430
0.027 0.14 0.15 0.09 0.32 0.09
0.003 0.01 0.008 0.008 0.002 0.002
This work. Gross and Sadowski [23]. Gross and Sadowski [6]. von Solms et al. [24]. Grenner et al. [25]. Sun et al. [22].
between 0.1 and 1, the target value is set to 1, if the actual value is between 1 and 10 the target value is set to 10 and so on. This might be the necessary counteraction of the increase in the hydrophilic solubility. However, the solubility in benzene (hydrophobic solvent) does not need to be scaled. This is probably due to the partially polar nature of the solvent that results to higher pharmaceutical solubility compared to n-heptane in almost all cases. For ketoprofen and lovastatin where no experimental data were available for the solubility in the hydrophobic solvent, n-heptane was chosen as the hydrophobic solvent with an arbitrary solubility of 10 mg/g. Validation of the parameters for the prediction of pharmaceutical solubility in n-octanol (long aliphatic part) gave good results. All calculations reported herein have been performed using the SciTherm module of the Scienomics’ MAPS platform [9]. The PCSAFT parameters for the pharmaceuticals are given in Table 4, together with the parameters for the solvents examined here. A number of polar solvents are modeled as associating components with two sites. Although these solvents do not hydrogen bond, the inclusion of associating sites aims to mimic the polar interactions exhibited by such molecules and that affect the pharmaceutical solubility significantly. A similar approach was used in NRHB [4]. Solvent parameters were fitted to experimental vapor pressure and liquid density data and deviations for the experimental values are reported in Table 4.
available temperature). The number of solvents for each pharmaceutical in Fig. 2 and the average root-mean-squared (rms) error are given in Table 5. Rms is calculated as:
⎛ ⎞ 2 N ⎝ 1 exp rms = (log Xi − log Xicalc ) ⎠ N
(4)
i=1
where Xi is the solubility of the compound i in g/g solvent and N is the number of data points (solvents). The solvents used for the parameterization of pharmaceutical molecules are excluded from Fig. 2 and from the calculation of rms in Table 5. The fairly good agreement achieved for all compounds in all solvents shows that the parameterization scheme provides a valid description of the compound solubility with PC-SAFT.
4. Results and discussion The solubility of the pharmaceuticals in the various solvents examined in this work span several orders magnitude. In Fig. 2, a comparison is made between experimental and PC-SAFT predicted values for the solubilities of paracetamol [10,16,26], naproxen [27,28], ibuprofen [12,29], flurbiprofen [19,30], ketoprofen [20,31], and lovastatin [15,22,32] in pure solvents at 298.15 K (or the closest
Fig. 2. Predicted versus experimental solubility (expressed in mass fraction) of six common pharmaceutical compounds in various pure solvents at 298.15 K.
T. Spyriouni et al. / Fluid Phase Equilibria 302 (2011) 331–337
1000
Solubility (mg / g solvent)
Solubility (mg / g solvent)
1000
100
10
100 10 1 Paracetamol-Exp Naproxen-Exp Paracetamol-PC-SAFT Naproxen-PC-SAFT
0.1 0.01
1 0
0.2
0.4
0.6
0.8
0
1
0.2
0.4
0.6
0.8
1
Ethanol weight fraction
Acetone weight fraction
Based on the extended range of solubility values for different solvents shown in Fig. 2, one expects that in an appropriately selected mixed solvent the solubility will vary substantially as a function of composition. In pharmaceutical process design, a mixed solvent is commonly used to tune solubility. In this respect, a thermodynamic model that can accurately predict the variation of solubility is highly desirable. Some representative examples using PC-SAFT are discussed below. Standard mixing rules were used in all cases [23]. In Fig. 3, experimental data [33] and PC-SAFT predictions for the solubility of paracetamol in acetone–water mixture at 296.15 K are shown. The solubility varies by more than an order of magnitude, going through a maximum at around 0.7 acetone weight fraction. A binary interaction parameter kij = 0.0352 is used for the water–paracetamol interactions in order to correct the higher aqueous solubility of paracetamol induced by the parameterization scheme. PC-SAFT provides an excellent prediction of the solubility over the entire solvent composition range. The solubility of paracetamol in the 1,4-dioxane–water mixture at 298.15 K is shown in Fig. 4. For paracetamol–water the same kij was used, as above. The variation of solubility with composition is similar to the data for acetone–water, although the solubility maximum is now shifted to higher 1,4-dioxane composition (around 0.8 weight fraction). Here again, PC-SAFT predictions capture reasonably accurately the change in solubility; although a lower maximum solubility value is predicted compared to experimental data [34].
1000
100
10
Fig. 5. Solubility of paracetamol and naproxen in ethanol–water mixture. Experimental data (points) for paracetamol at 298.15 K [34] and naproxen at 293.15 [35] are compared with the PC-SAFT predictions (lines).
1600
Solubility (mg/g solvent)
Fig. 3. Solubility of paracetamol in acetone–water mixture at 296.15 K. The experimental data (points) are from [33]. The line is the PC-SAFT prediction.
Solubility (mg / g solvent)
335
1200
800
400
0 0
0.2
0.4
0.6
0.8
1
Ethanol weight fraction Fig. 6. Solubility of ibuprofen in the binary mixture of ethanol–propylene glycol at 298.15 K. Comparison between experimental data [36] (points) and PC-SAFT predictions (line).
A different mixed solvent commonly used in pharmaceutical industry is ethanol–water. In Fig. 5, experimental data [34,35] and PC-SAFT predictions for paracetamol at 298.15 K and naproxen at 293.15 K in this solvent are shown. The paracetamol solubility varies by more than an order of magnitude while the naproxen solubility varies by almost three orders of magnitude, as a function of composition. PC-SAFT predictions are in excellent agreement with experiments. For naproxen–water interactions, kij = 0.09572. We turn our attention next to non-aqueous solvents. In Fig. 6, experimental data [36] and PC-SAFT predictions are shown for the solubility of ibuprofen in ethanol–propylene glycol mixture at 298.15 K. Predictions from PC-SAFT (all binary interaction parameters set equal to zero) are remarkably accurate. Although the majority of pharmaceutical processes take place at ambient temperature, the effect of temperature in solubility is Table 5 Number of solvents for which a solubility prediction was made and average error (rms) over these solvents for all pharmaceutical compounds examined in this work. The temperature is 298.15 K (or the closest available).
1 0
0.2
0.4
0.6
0.8
1
1,4-Dioxane weight fraction Fig. 4. Solubility of paracetamol in the binary mixture of 1,4-dioxane–water at 298.15 K. Comparison between experimental data [34] (points) and PC-SAFT predictions (line).
Compounds
Number of solvents
rms
Paracetamol Naproxen Ibuprofen Flurbiprofen Ketoprofen Lovastatin
25 24 20 12 11 13
0.32 0.48 0.36 0.23 0.29 0.27
336
T. Spyriouni et al. / Fluid Phase Equilibria 302 (2011) 331–337
Solubility (mg / g solvent)
1000
100 EtOH-Exp Acetone-Exp
10
EtOAc-Exp EtOH-PC-SAFT Acetone-PC-SAFT EtOAc-PC-SAFT
1 0
10
20
30
40
In Fig. 8, the ibuprofen solubility in ethanol and in 2-propanol as a function of temperature is shown. PC-SAFT predictions compare favorably with the experimental data [12]. The increase in solubility is captured satisfactorily by PC-SAFT although the absolute value of solubility is overestimated by the model (except for the solubility in ethanol at 35 ◦ C). Also, the relative solubility in the two solvents is predicted correctly. Finally, the solubility of lovastatin in ethanol and ethyl acetate is presented in Fig. 9. PC-SAFT predictions agree remarkably well with experimental data [22] over the entire temperature range. For both sets of data, PC-SAFT predicts a slightly stronger temperature effect compared to experiments.
o
T ( C)
5. Conclusions
Fig. 7. Solubility of paracetamol in ethanol (EtOH), acetone, and ethyl acetate (EtOAc) as a function of temperature. Experimental data (points) [10] and PC-SAFT predictions (lines).
2400
Solubility (mg/g solvent)
EtOH-Exp 2-propanol-Exp
2000
EtOH-PC-SAFT 1600
2-propanol-PC-SAFT
1200 800 400
References
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T (o C) Fig. 8. Solubility of ibuprofen in ethanol (EtOH) and 2-propanol as a function of temperature. Comparison of experimental data (points) [12] and PC-SAFT predictions (lines).
140 EtOH-Expt
Solubility (mg / g solvent)
In this work a new approach was presented for predicting the solubility of pharmaceutical molecules by using PC-SAFT. The predictive ability of the scheme was based on the appropriate parameterization of the pharmaceutical molecules. The regression of parameters was performed against the solubility of pharmaceuticals in three solvents, i.e., a hydrophilic solvent (water), a polar solvent, and a hydrophobic solvent. We demonstrated that following this scheme the resulting parameters describe adequately the solubility of pharmaceuticals in pure and mixed solvents. No adjustable parameter is required except for the aqueous systems where a non-zero kij is used to correct the high solubility in water imposed by the parameterization scheme. The temperature dependence of the solubility was also captured satisfactorily by PC-SAFT.
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EtOAc-Expt EtOH - PC-SAFT
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EtOAc-PC-SAFT
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T ( C) Fig. 9. Solubility of lovastatin in ethanol (EtOH) and ethyl acetate (EtOAc) as a function of temperature. Experimental data (points) [22] and PC-SAFT predictions (lines).
often significant and a reliable thermodynamic model should be able to capture it accurately, preferably without the use of additional empirical parameters. In Fig. 7, experimental data [10] and PC-SAFT predictions are shown for the solubility of paracetamol in ethanol, acetone and ethyl acetate in the range 0–30 ◦ C. PC-SAFT predicts accurately the increase of solubility with temperature and with the solvent change from ethyl acetate to acetone to ethanol.
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