Correlation and Prediction of Drug Molecule Solubility in Mixed

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Ind. Eng. Chem. Res. 2006, 45, 4816-4824

Correlation and Prediction of Drug Molecule Solubility in Mixed Solvent Systems with the Nonrandom Two-Liquid Segment Activity Coefficient (NRTL-SAC) Model Chau-Chyun Chen* Aspen Technology, Inc., Ten Canal Park, Cambridge, Massachusetts 02141

Peter A. Crafts AstraZeneca Pharmaceuticals Ltd., Process R&D, Macclesfield, Cheshire, SK10 2NA, United Kingdom

The recently developed Nonrandom Two-Liquid Segment Activity Coefficient (NRTL-SAC) model [reported by Chen and Song, Ind. Eng. Chem. Res. 2004, 43, 8354] offers a practical thermodynamic framework to predict drug solubility in a wide range of solvents, based on a small initial set of measured solubility data. The model yields satisfactory results in first correlating drug solubility in a few representative pure solvents and then qualitatively predicting drug solubility in other pure solvents. Here, we investigate the applicability of the NRTL-SAC model for predicting drug solubility in mixed solvents for three molecules: acetaminophen, sulfadiazine, and cimetidine. The study shows that the model provides robust correlation and prediction of drug solubility in both pure and mixed solvents, with a qualitative level of accuracy. The model is a useful tool in support of the early stages of crystallization process development and other areas of drug process design. 1. Introduction Crystallization is the preferred method of purification in the pharmaceutical industry for both the final drug substance and the isolated intermediates in the synthesis. During the early stages of process development, the availability of drug substance for laboratory studies is often restrictive, because of the difficulty and cost of manufacture, as well as the competitive demands of formulation development and clinical trials. This problem is compounded by the high rate of attrition for new drugs and the large number of candidates that are cocurrently in development and competing for resource. It is typical for these constraints to restrict the experimental program of solvent selection, which may lead to a sub-optimal crystallization design in respect of yield, productivity, and manufacturability. Although highthroughput solubility measurement techniques are improving, they are still time- and labor-intensive, and, where crystallization requires a mixed solvent system, it is practically impossible to cover the full range of solvent combinations with sufficient detail to find the optimal solution. To overcome these obstacles, it is highly desirable to have a thermodynamically consistent model to correlate and predict drug solubility in pure and mixed solvent systems based on a small initial set of measured solubility data. The number of literature references in this area is currently small, particularly with respect to mixed solvent systems, where the solubility behavior can be highly nonideal. Recently, Chen and Song1 reviewed prior solubility modeling work and proposed the semiempirical Nonrandom Two-Liquid Segment Activity Coefficient (NRTL-SAC) model as a thermodynamic framework for the qualitative correlation and prediction of drug molecule solubility in pure and mixed solvent systems. They presented satisfactory results with NRTL-SAC in correlating drug solubility in a few representative pure solvents and then in * To whom correspondence should be addressed. Tel.: 617-9491202. Fax: 617-949-1466. E-mail: [email protected].

predicting drug solubility in other pure solvents. In this study, we extend the investigation to mixed solvent systems. We will obtain drug molecule parameters by correlating solubilities in a few pure solvents and then examine the solubility predictions in both pure and mixed solvents for three drug molecules: acetaminophen, sulfadiazine, and cimetidine. These three drug molecules were chosen because there is sufficient public literature solubility data available in both pure and mixed solvent systems. Figure 1 shows their molecular structures. 2. Thermodynamic Relationship The solubility of a solid organic nonelectrolyte can be approximated by the following simplified expressions:1,2

ln xSAT ) I

(

)

∆fusS Tm 1- ln γSAT I R T

γSAT )A+ ln Ksp ) ln xSAT I I

(2)

∆fusS R

(3)

Tm∆fusS ∆fusH )R R

(4)

A) B)

B T

(1)

where xSAT is the mole fraction of solute I dissolved in the I solvent phase at saturation, ∆fusS the entropy of fusion of the solute, R the ideal gas constant, T the temperature (K), Tm the the activity coefficient of the melting point of the solute, γSAT I solute in solution at saturation, Ksp the solubility product constant, and ∆fusH the enthalpy of fusion of the solute. The terms ∆fusS, ∆fusH, and Tm vary with the polymorphic forms of the solute. Given a polymorph and a temperature, the solute solubility is only a function of its activity coefficient in solution. The activity coefficient of the solute in solution determines the solute’s solubility as the solvent composition changes.

10.1021/ie051326p CCC: $33.50 © 2006 American Chemical Society Published on Web 05/26/2006

Ind. Eng. Chem. Res., Vol. 45, No. 13, 2006 4817

Because of the approximate nature of eq 1, in this work, we choose to treat the parameter A in eq 2 as an adjustable parameter while having the parameter B estimated from ∆fusH to account for the temperature effect on solubility. For rigid molecules, the value of parameter A in eq 2 is expected to be ∼6.8.2 Parameter A is expected to increase proportionally with the degree of conformational flexibility of the molecule. 3. NRTL Segment Activity Coefficient Model The NRTL-SAC model suggests that the activity coefficient for component I in solution is the sum of a combinatorial term γCI and a residual term γRI :

ln γI ) ln γCI + ln γRI

(5)

Here, the combinatorial term γCI is calculated from the FloryHuggins equation for the combinatorial entropy of mixing. The residual term γRI is calculated from the local composition (lc) interaction contribution γlcI of the Polymer NRTL model.3 The Polymer NRTL equation incorporates the segment interaction concept and computes the activity coefficient for component I in solution by summing up contributions to the activity coefficient from all segments that comprise component I. The equation is given as

ln γRI ) ln γlcI )

rm,I[ln Γlcm - ln Γlc,I ∑ m ] m

with

ln

Γlcm

)

∑j xjGjmτjm

+

∑k

xkGkm

ln

Γlc,I m

)

∑j xj,IGjmτjm ∑k xk,IGkm

xm′Gmm′

(

+

)

∑j xjGjmτjm′

τmm′ ∑ m′ x G ∑k k km′ ∑k xkGkm′ xm′,IGmm′

(6)

(

(7)

τmm′ ∑ m′ ∑k xk,IGkm′ ∑k xk,IGkm′

xj )

)

∑j xj,IGjm′τjm′

(8)

∑I xIrj,I ∑I ∑i xIri,I

xj,I )

(9)

rj,I

∑i ri,I

(10)

where I is the component index; the terms i, j, k, m, and m′ are the segment species index, xI is the mole fraction of component I, xj is the segment-based mole fraction of segment species j, rm,I is the number of segment species m that are contained only in component I, Γlcm is the activity coefficient of segment species m, and Γlc,I m is the activity coefficient of segment species m contained only in component I. G and τ in eqs 7 and 8 are local binary quantities related to each other by the NRTL nonrandomness factor parameter R:

G ) exp(-Rτ)

(11)

Figure 1. Molecular structure for (a) acetaminophen, (b) sulfadiazine, (c) cimetidine, and (d) sulfamerazine.

To account for various solvent-solvent, solvent-solute, and solute-solute molecular interactions, Chen and Song1 proposed four predefined conceptual segments, along with their corresponding segment-segment binary parameters (i.e., R and τ terms). The four predefined conceptual segments include one hydrophobic segment (x), one polar-attractive segment (y-), one polar-repulsive segment (y+), and one hydrophilic segment (z). The hydrophilic segment represents the molecular surface area with interactions characteristic of a hydrogen-bond donor or acceptor. The hydrophobic segment represents the molecular surface area that is adverse to hydrogen bonding. The polar segments represent the molecular surface area with interactions characteristic of an electron donor or acceptor. The polarattractive segment exhibits attractive interactions with a hydrophilic molecular surface, whereas the polar-repulsive segment exhibits repulsive interactions with a hydrophilic molecular surface. The molecule-specific model parameters of solvents and solutes, i.e., hydrophobicity X, polarity types Y- and Y+, and hydrophilicity Z, correspond to segment numbers of the four conceptual segments, i.e., rm,I (m ) x, y-, y+, z) in eq 6. Chen and Song1 reported molecular parameters for 62 solvents commonly used in the pharmaceutical industry. In this study, these parameters have been updated based on a more-extensive literature search and regression effort, with available vaporliquid and liquid-liquid-phase equilibrium data for solventsolvent binary pairs. The updated parameters for the 62 solvents plus those for n-octane are reported in Table 1. They represent minor refinements to the parameters reported by Chen and Song.1 4. Test Cases To test the effectiveness of the NRTL-SAC model, we investigate three drug molecules with ample literature solubility data in pure and mixed solvents. For each drug molecule, we first obtain experimental solubility data for the drug molecule in four to eight solvents with distinctive surface interaction characteristics at or near room temperature. These solvents should include hydrophobic solvents (such as hexane or heptane), hydrophilic solvents (such as water and methanol), and polar solvents (acetone, acetonitrile, dimethylsulfoxide

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Table 1. Updated NRTL-SAC Molecular Parameters for 63 Common Solvents

Table 2. NRTL-SAC Molecular Parameters for Solutes

solvent name

X

Y-

Y+

Z

acetic acid acetone acetonitrile anisole benzene 1-butanol 2-butanol N-butyl acetate methyl tert-butyl ether carbon tetrachloride chlorobenzene chloroform cumene cyclohexane 1,2-dichloroethane 1,1-dichloroethylene 1,2-dichloroethylene dichloromethane 1,2-dimethoxyethane N,N-dimethylacetamide N,N-dimethylformamide dimethyl sulfoxide 1,4-dioxane ethanol 2-ethoxyethanol ethyl acetate ethylene glycol diethyl ether ethyl formate formamide formic acid N-heptane N-hexane isobutyl acetate isopropyl acetate methanol 2-methoxyethanol methyl acetate 3-methyl-1-butanol methyl buty ketone methylcyclohexane methyl ethyl ketone methyl isobutyl ketone isobutanol N-methyl-2-pyrrolidone nitromethane N-pentane 1-pentanol 1-propanol isopropyl alcohol N-propyl acetate pyridine sulfolane tetrahydrofuran 1,2,3,4-tetrahydronaphthalene toluene 1,1,1-trichloroethane trichloroethylene M-xylene water triethylamine 1-octanol N-octane

0.048 0.131 0.018 0.536 0.615 0.425 0.343 0.317 0.483 0.739 0.727 0.393 1.161 0.892 0.394 0.529 0.188 0.459 0.277 0.160 0.180

0.222 0.109 0.131 0.010

0.195 0.513 0.883 0.653 0.281

0.206

0.154 0.251 0.179 0.339 0.387 0.256

1.152 1.000 0.620 0.552 0.090 0.082 0.239 0.419 0.673 1.053 0.261 0.673 0.566 0.252 0.122 0.898 0.458 0.374 0.332 0.514 0.135 0.209 0.235 0.924 0.604 0.548 0.552 0.758

0.004 0.069 0.030 0.105 0.027 0.024

0.030 0.778 0.752 1.114 0.086 0.030 0.121 0.058 0.343 0.028 0.305 0.089 0.090

0.183 0.154 0.139 0.095

0.224 0.095 0.224 0.790

0.490 0.393 0.330 0.142 0.142 0.484 0.167

0.691 0.208 0.832 0.427 0.077 0.193 0.254 0.401 0.106 0.441

0.089 0.040

0.021

0.630 0.323 0.852

0.177 0.341

0.252 0.420

0.541 0.498 0.180 0.338 0.538 0.469 0.246 0.463 0.469 0.067 0.281 1.032

0.024 0.013 0.134

0.038 0.057

0.594 0.361 0.314

0.485 0.051 0.491 0.530 0.636

0.587 0.305

0.249 0.708

0.320 0.865 0.304 0.287 0.262 0.316 1.000

0.403 0.867 1.253

0.030 0.534

(DMSO), dimethylformamide (DMF), etc.). From these drug solubility data, we identify drug molecular parameters including the conceptual segment numbers and the parameters needed to determine the solubility product constant Ksp. Given the parameters for solvents and solutes, we then perform solidliquid equilibrium calculations to identify the solute solubility for any mixture of solvents and solutes at a given temperature and pressure.

solute name

X

Y-

Y+

Z

A

acetaminophen sulfadiazine cimetidine

0.498 0.757 0.414

0.487

0.162

1.270 1.940 2.462

7.804 6.218 12.216

0.441

4.1. Acetaminophen. For acetaminophen (molecular weight of MW ) 151.16), Manzo and Ahumada4 reported a melting temperature of Tm ) 441.2 K, a heat of fusion of ∆fusH ) 26.0 kJ/mol, and an entropy of fusion of ∆fusS ) 59.0 J/(mol K). There are extensive sets of experimental solubility data available for acetaminophen. Granberg and Rasmuson5 reported acetaminophen solubility data in pure solvents. Subrahmanyam et al.6 reported acetaminophen solubility data for methanolwater and methanol-ethyl acetate binary solvents. Romero et al.7 reported data for ethanol-water, ethanol-ethyl acetate, and dioxane-water binary solvents. Bustamante et al.8 reported data for a dioxane-water binary solvent. Granberg and Rasmuson9 reported data for acetone-water and acetone-toluene binary solvents, and acetone-water-toluene ternary solvents. We first identify the NRTL-SAC molecular parameters for acetaminophen from its solubility data in eight solvents.5 Table 2 reports the identified molecular parameters including parameter A. Parameter B, which is not reported in Table 2, is computed from eq 4 to have a value of -3131. The identified value for parameter A, 7.804, is considered consistent with the value of 7.096 that is computed from eq 3. Among the acetaminophen solubility data in 26 pure solvents5 at 30 °C, three (1-hexanol, 1-heptanol, and diethylamine) are excluded from this study, simply because Table 1 does not include the molecular parameters for these three solvents. Eight of the remaining 23 solvents are used as representatives of hydrophilic (water and ethanol), polar-attractive (DMSO), polarrepulsive (acetone, acetonitrile and THF), and hydrophobic solvents (chloroform and toluene). Standard deviations of the data points are assumed to be constant (20%). The root-mean2 1/2 - ln scal square (rms) error in the term ln s, {∑Ni (ln sexp i i ) ]/N} , for the fit is 0.549 (here, s is the solubility of the solute in terms of milligrams per gram of solvent and N is the number of data points). We then use the identified molecular parameters to predict the acetaminophen solubility in the remaining solvents. The rms error in ln s for the 23 solvents is 1.075. As shown in Figure 2, the NRTL-SAC predictions are in qualitative agreement with the experimental data. The model predictions do show some systematic errors. The solubility predictions are consistently above the experimental data for alcohols and below the experimental data for associating polar solvents (DMF and DMSO). In addition, there are two significant outliers. The model prediction for 1,4-dioxane (139.9 mg/g solvent) is almost 1 order of magnitude larger than the data (17.1 mg/g solvent). We suspect the Granberg and Rasmuson data5 for 1,4-dioxane is in error, because the model prediction is, in fact, consistent with the experimental solubility data for 1,4-dioxane reported by Romero et al.7 (86.9 mg/g solvent at 25 °C). Dichloromethane is another outlier; the model prediction (5.62 mg/g solvent) for dichloromethane is 1 order of magnitude larger than the data (0.32 mg/g solvent). A possible explanation is that the solvent parameters for dichloromethane are not optimized. Excluding 1,4-dioxine and dichloromethane, the rms error for the remaining 21 solvents drops significantly to 0.814. The model parameters based on the eight pure-solvent regression cases are also used to predict the solubility of acetaminophen in mixed solvents. Figures 3-9 show the prediction results at 25 °C, compared to the experimental data.


Figure 5. Model prediction versus experimental data for acetaminophen solubility in acetone-water binary solvents at 298.15 K (solid squares (9) are experimental data,9 and solid line (s) represents model predictions). Figure 2. Model prediction versus experimental data5 for acetaminophen solubility in pure solvents at 303.15 K (solid squares (9) represent the eight pure-solvent solubility data points that were used to identify the solute parameters; empty diamonds (]) represent pure solvent solubility data, excluding the eight pure solvents).

Figure 6. Model prediction versus experimental data for acetaminophen solubility in 1,4-dioxane-water binary solvents at 298.15 K (solid squares (9) are experimental data of Romero et al.,7 empty squares (0) are experimental data of Bustamante et al.,8 and solid line (s) represents model predictions). Figure 3. Model prediction versus experimental data for acetaminophen solubility in methanol-water binary solvents at 298.15 K (solid squares (9) are experimental data,6 and solid line (s) represents model predictions).

Figure 4. Model prediction versus experimental data for acetaminophen solubility in ethanol-water binary solvents at 298.15 K (solid squares (9) are experimental data,7 and solid line (s) represents model predictions).

Figures 3 and 4 show the prediction results for mixed solvents of two hydrophilic solvents, i.e., methanol-water and ethanolwater binary solvents. The acetaminophen solubility in the methanol-water binary solvent is nonideal but without a peak. Ethanol is more hydrophobic than methanol and it brings significant hydrophobicity to the solvent mixture. As a result, the acetaminophen solubility in the ethanol-water binary solvent shows a solubility peak. Although the model overpredicts the

solubility in pure alcohols, the model mixed-solvent predictions clearly capture the alcohol-water binary solvent solubility trend. Figures 5 and 6 show the prediction results for mixed solvents of one polar solvent and one hydrophilic solvent, i.e., acetonewater and 1,4 dioxane-water binary solvents. The solubility behavior of acetaminophen in these two binary systems is extremely nonideal, with “bell”-shaped solubility behavior, as a function of solvent composition, and a 4-to-5-fold solubility increase in the binary solvents. The model predictions are excellent for both single solvent solubility and binary solvent solubility. It is interesting that, although the model predictions for the dioxane-water binary solvent are significantly lower than the data of Romero et al.,7 the model predictions are reasonably close to the later data reported by the same group.8 Figure 7 shows the prediction results for mixed solvents of one polar solvent and one hydrophobic solvent, i.e., acetonetoluene binary mixture. The solubility behavior of acetaminophen in the acetone-toluene binary solvent is relatively ideal. The model predictions are again excellent for both single solvent solubility and binary solvent solubility. Figures 8 and 9 show the prediction results for mixed solvents of one hydrophilic solvent and one hydrophobic solvents, i.e., methanol-ethyl acetate and ethanol-ethyl acetate binary solvents. The model overpredicts the solubilities in methanol and in ethanol. However, the model predictions for the two binary solvent systems are consistent with the trends exhibited by the experimental data. Given that Figures 3-9 represent predictions in binary solvents with molecular parameters identified from solubility

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Figure 7. Model prediction versus experimental data for acetaminophen solubility in acetone-toluene binary solvents at 298.15 K (solid squares (9) are experimental data,9 and solid line (s) represents model predictions). Figure 10. Model prediction versus experimental data11 for sulfadiazine solubility in pure solvents at 298.15 K (solid squares (9) represent the seven pure-solvent solubility data points that were used to identify the solute parameters, and empty diamonds (]) represent pure solvent solubility data excluding the seven pure solvents).

Figure 8. Model prediction versus experimental data for acetaminophen solubility in methanol-ethyl acetate binary solvents at 298.15 K (solid squares (9) are experimental data,6 and solid line (s) represents model predictions).

Figure 9. Model prediction versus experimental data for acetaminophen solubility in ethanol-ethyl acetate binary solvents at 298.15 K (solid squares (9) are experimental data,7 and solid line (s) represents model predictions).

data in just eight pure solvents, the model predictions for acetaminophen solubility are considered to be very satisfactory. 4.2. Sulfadiazine. For sulfadiazine (MW ) 250.28), Sunwoo and Eisen10 reported Tm values of 538.8 K, ∆fusH of 31.2 kJ/ mol, and ∆fusS of 57.9 J/(mol K). Solubility measurements of sulfadiazine in 26 pure solvents at 25 °C have been reported by Bustamante et al.11 In a separate paper, Bustamante et al.12 also reported sulfadiazine solubility in water-1,4-dioxane binary solutions at 25 °C. Elworthy and Worthington13 reported the solubility of sulfadiazine in waterdimethyl formamide (DMF) binary solutions at 20, 30, and 40 °C. In addition, Sunwoo and Eisen10 reported the solubility in N,N-dimethylacetamide. Martinez and Gomez14 reported the

solubility in octanol, water, and their mutually saturated solvents. Martinez et al.15 reported the solubility in cyclohexane at 20, 30, and 40 °C. Mauger et al.16 reported the solubility in alcohols at 25, 30, and 37 °C. Together, they represent another case to examine the robustness of the NRTL-SAC model predictions. We first identify the conceptual segment molecular parameters and the value of parameter A for sulfadiazine from the Bustamante et al.11 solubility data in seven pure solvents representing solvents of various types: hydrophilic (water), polar attractive (DMA, DMSO), polar repulsive (1,4-dioxane, acetone) and hydrophobic (toluene, benzene). Parameter B is estimated (-3752) from the experimental data for ∆fusH. Standard deviations of the data points are assumed to be constant (20%). The resulting molecular parameters for sulfadiazine are given in Table 2. The molecule has a high Z-value, which indicates significant hydrophilicity. The determined value for parameter A, 6.218, is consistent with the value of 6.964 that was computed from eq 3. The rms error in ln s for the fit is 0.844. Among the seven pure solvents, DMSO is a significant outlier. The model prediction for the DMSO solubility (135.6 mg/g solvent) is significantly lower than the experimental data (850.4 mg/g solvent). These model parameters are then used to predict sulfadiazine solubility in other pure solvents, water-dioxane binary solvents, and water-DMF binary solvents. Figure 10 shows the model predictions versus experimental data for the sulfadiazine room-temperature solubility in 19 pure solvents included in the Bustamante et al.11 data set. With the exception of ethylene glycol, the model systematically predicts much higher solubility than the experimental data, with respect to eight of the nine alcohols. The rms error in ln s for the 19 solvents is 2.950. With the eight alcohols excluded, the rms error in ln s for the remaining solvents drops to 0.750. Including some of the alcohols in the initial identification of the sulfadiazine molecule parameters improves the fit for the remaining alcohols. However, these fits would bring the value of parameter A far below 6.8. For example, adding methanol and ethanol to the seven-solvent list yields 4.207 for the parameter A value, which suggests the possibility of a different polymorph with lower solubility. Pending direct proof of a different polymorph in the alcohols for sulfadiazine, the difficulty with some of the sulfadiazine solubility data creates the possibility that the current NRTL-SAC model formulation


Figure 11. Model prediction versus experimental data for sulfadiazine solubility in 1,4-dioxane-water binary solvents at 298.15 K (solid squares (9) are experimental data,12 and solid line (s) represents model predictions).

and parameters may be sub-optimal for certain classes of solvents or solutes. Our literature search does confirm the existence of two polymorphs for sulfadiazine.17 Yang and Guillory18 reported a second sulfadiazine polymorph with Tm (K) and ∆fusH values (532.2 K and 40.8 kJ/mol, respectively) that are quite different from those reported by Sunwoo and Eisen.10 We found no direct literature evidence that a second sulfadiazine polymorph is formed in the alcohols. However, Caira and Mohamed19 positively identified two orthorhombic polymorphs of sulfamerazine, which is a derivative of sulfadiazine. Caira and Mohamed reported sulfamerazine polymorph I in a methanol solvent and polymorph II in an acetonitrile solvent. They also detected a phase transition from polymorph II to polymorph I, which suggests polymorph I is the less soluble and more stable polymorph. The molecular structure of sulfamerazine is shown in Figure 1. Figures 11 and 12 show the predicted sulfadiazine solubility in binary solvents of 1,4-dioxane-water and DMF-water, respectively. The predictions are in satisfactory agreement with trends exhibited by the available experimental data. With the sulfadiazine molecular parameters determined solely from the seven pure-solvent solubility data, the model correctly predict a significant solubility peak with the dioxane-water binary solvent at 25 °C and no solubility peak with the DMF-water binary solvent at 20 °C. 4.3. Cimetidine. Cimetidine (which has a molecular weight of MW ) 252.34) is a relatively complex molecule with two hydrogen-bond donor sites and six hydrogen-bond acceptor sites. The structure has seven rotatable bonds and nuclear magnetic resonance (NMR) studies20 have shown that cimetidine exists in two tautomeric forms when in solution. These occur across the cyanoguanidine group, as illustrated in Figure 13. Solubility measurements for cimetidine in 12 pure solvents and 9 binary solvent mixtures at 25 °C, together with differential scanning calorimetry (DSC) measurements of the enthalpy and temperature of melting are reported by Westwood.21 Further literature data on cimetidine solubility in mixed solvent systems have not been found. Polymorphism is important in the specification of active pharmaceutical ingredients, because of its impact on solubility,

Figure 12. Model prediction versus experimental data for sulfadiazine solubility in DMF-water binary solvents at 293.15 K (solid squares (9) are experimental data,13 and solid line (s) represents model predictions).

Figure 13. Diagram showing that cimetidine exists in two tautomeric forms. Table 3. NRTL-SAC Molecular Parameters for Cimetidine from Three Regression Cases case

X

six solvents all single solvents all single and mixed solvents

0.414 0.335 0.447

Y-

Y+

Z

A

0.441 0.580 0.447

2.462 2.559 2.665

12.216 12.364 12.283

dissolution rate, and the eventual drug release profile in patients. In the case of cimetidine there are five documented polymorphic forms (named A-E) together with two hydrated forms.21 The Westwood results further show that Forms A and B have almost identical lattice energies and their solubility behavior can thus be taken as equivalent. This assumption is important because some of the Westwood measurements were made with a solid phase that was a mixture of Forms A and B. Although Form A was used in the solubility experiments, it transformed in the slurry to Form B, which was determined to be thermodynamically more stable at 25 °C. Powder X-ray diffraction (XRD) and Fourier transform mid-infrared (FT-mid-IR) spectroscopy were used to characterize the solid phase both before and after each solubility experiment, and the analysis confirmed that only Forms A and B were present. Neither polymorph C or D were observed. Form A has a melting temperature of Tm ) 413.5 K, heat of fusion of ∆fusH ) 44.033 kJ/mol, and an entropy of fusion of ∆fusS ) 106.5 J/(mol K). Form B has a melting temperature of Tm ) 413.7 K, heat of fusion of ∆fusH ) 44.084 kJ/mol, and an entropy of fusion of ∆fusS ) 106.6 J/(mol K). The cimetidine molecular parameters were regressed for three subsets of the available data. The first set comprises six pure solvent solubility points, the second uses all of the pure solvent solubility data, and the final set includes all pure solvent and binary solvent data combined. The regression results are shown in Table 3 and Figure 14.

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Figure 14. Model prediction versus experimental data21 for cimetidine solubility in pure and mixed solvents at 298.15 K; solute parameters determined from six pure-solvent data (solid squares (9) represent the six pure-solvent solubility data points that were used to identify the solute parameters, empty diamonds (]) represent pure solvent solubility data excluding the six pure solvents, and empty triangles (4) represent mixedsolvent solubility data).

For the regression case involving six pure solvents, we select the following solvents of different types: hydrophilic (water and ethanol), polar-repulsive (acetonitrile and methyl ethyl ketone), and hydrophobic (n-octane and ethyl acetate). Note that the Westwood dataset does not contain any solubility data for polar-attractive solvents. Figure 14 shows the model predictions versus experimental data results for the six pure solvent - ln solubility data case. The rms error in ln w, {∑iN (ln wexp i 2/N}1/2, for the fit is 0.641 (here, w is the solubility of the wcal ) i solute in mass fraction and N is the number of data points). The rms errors in ln w for all pure solvent data (excluding diethyl ether) and for all pure solvent and binary solvent data as predicted from the six solvent case are 0.799 and 0.678, respectively. This shows that the parameters identified from the six solvents are able to predict the solubility in other pure solvents and binary solvents. Table 3 shows very similar molecular parameter estimates for the three regression cases with different subsets of the available data. The corresponding regression results for the case of all pure solvents and the case of all pure and binary solvents are virtually identical to Figure 14, generated from the sixsolvents case. This finding supports the argument that the NRTL-SAC framework is both a good correlative and predictive model for single and binary solvents. For all three cases, the identified values for parameter A are very similar to the ideal figure of 12.82, as calculated from eq 3, using the DSCderived data for Tm and ∆fusH of Form A. In all cases, parameter B is fixed at -5296, as calculated from the DSC data for Form A. The hydrophilicity, Z, has a relatively large value, as expected from the number of hydrogen bond donors and acceptors (eight in total) for cimetidine. The regression statistics indicate very good identification for both X and Z, with relative standard deviations of ∼ 15%. However, Y- was found to be zero and Y+ is somewhat less significant with a relative standard deviation of ∼90%. This may be a consequence of not having solubility data with polar-attractive solvents in the dataset. Generally, as shown in Figure 14, the model represents the data very well over the 10 orders of magnitude of solubility measurement. The correlation seems to be free from systematic error, and, in this case, the alcohols are fitted quite accurately.

Figure 15. Model prediction versus experimental data21 for cimetidine solubility in ethanol-water binary solvents at 298.15 K; cimetidine parameters determined from six pure-solvent data (solid squares (9) are experimental data, and solid line (s) represents the model prediction). Table 4. Model Predictions versus Experimental Data21 for Cimetidine Solubility in Three Binary Solvents at 298.15 K solvent

experimental

prediction

A. Ethanol-Methanol Binary ethanol 0.0469 ethanol:methanol, 50:50 (v/v) 0.0955 methanol 0.175

0.0479 0.105 0.162

B. Ethylene Glycol-Methanol Binary ethylene glycol 0.119 ethylene glycol:methanol, 50:50 (v/v) 0.175 methanol 0.175

0.054 0.101 0.162

C. Ethylene Glycol-Water Binary ethylene glycol 0.119 ethylene glycol:water, 75:25 (v/v) 0.0734 water 0.0061

0.054 0.030 0.0059

There is one significant outlier in the cimetidine dataset for diethyl ether, and this point was excluded from the regression. It is included as a predicted point in Figure 14 for completeness. This result suggests that further parameter optimization may be desirable for the diethyl ether solvent parameters. Figure 15 shows the predicted trend for cimetidine solubility in an ethanol-water binary system. The predictions are based on the molecular parameters identified in the six pure solvents case. The solubility behavior is highly nonideal with a maximum solubility of ∼0.0883 (mass fraction) for a 75% v/v ethanolwater mixture. This represents an almost 2-fold increase in solubility, compared to pure ethanol at mass fractions of 0.047. The model predicts the solubility trend satisfactorily, with a predicted solubility peak that is 60% of the experimental value. The experimental peak solubility occurs at 80% v/v ethanol, whereas the predicted peak is broader and occurs at a slightly lower composition of ∼70% v/v ethanol. Very limited cimetidine solubility data are available for other binary solvents. In the ethanol-methanol system, there is one measured data point for a 50% v/v mixture. In the ethylene glycol-methanol system, there is one measured data point in a 50% v/v mixture. In the ethylene glycol-water system, there is one measured data point in a 75% v/v mixture. These data points, and the corresponding NRTL-SAC prediction results, are given in Table 4. Again, the predictions are based on


molecular parameters identified in the six-solvent regression case. NRTL-SAC predicts solubility trends that are essentially linear for each of these systems. This is broadly consistent with the single-point experimental data for the binary mixtures, with the exception of the ethylene glycol-methanol binary result, where the experimental data seem to be too high. With such a small set of experimental data, it is not possible to show conclusively that the predicted trends are correct for these systems. In summary, the NRTL-SAC model predicts the solubility trend in binary solvent systems with moderate accuracy for cimetidine, which is a structurally complex and conformationally flexible molecule.

the knowledge of solubility data as related to polymorphism grows, there will be opportunities for further refinements to the model, perhaps in the definition of conceptual segments or the assignment of segment-segment binary interaction parameters. The goal of future work is to improve the predictive quality of the model from that of a qualitative one to a semiquantitative one. Although we do not investigate the relationship between temperature and solubility in this work, we have found that eq 2 provides a reasonable first approximation for the temperature effect. Generally, solute activity coefficients are weak functions of temperature, and we have observed minor departures from eq 2 for certain solute systems. Equation 2 is a reasonable choice for a qualitative model, and it makes use of parameters that are easy to derive from DSC data.

5. Discussions In this study, we show qualitative NRTL-SAC predictions of both pure solvent and mixed solvent solubilities for three drug molecules based on molecular parameters identified from solubility data in a representative set of pure solvents. In addition, in the case of cimetidine, we show the molecular parameters are relatively constant, regardless of whether pure solvent solubility data or binary solvent solubility data were used to identify the parameters. These qualitative predictions suggest that the NRTL-SAC conceptual segment approach and the underlying mixing rules provide a reasonable description of the liquid phase nonideality for the systems concerned. Although there is little solubility data in ternary solvent systems and higher-order solvent systems for us to examine, we expect the model to yield qualitatively correct predictions for multicomponent solvent systems. The selection of solubility data does impact the quality of molecular parameters identified for the solute. Generally, the model requires one or more solubility measurements from each of the four types of solvents: hydrophilic, hydrophobic, polar attractive, and polar repulsive. These solvents serve as “molecular sensors” that probe the molecular surface interaction characteristics of the solute. Many solvents may exhibit dual or multiple interaction characteristics. For example, ethanol may be considered both hydrophilic and hydrophobic. Chloroform may be considered both hydrophobic and polar repulsive. In selecting the solubility measurements for the solute parameter regression, we choose solvents that cover the four types of distinctive surface interaction characteristics. The solubility peak in mixed solvent systems represents a minimum in the activity coefficient of the solute in the solvent mixture. Specifically, the maximum solute solubility (in mole fraction) corresponds to the minimum solute activity coefficient in a given solvent system. The NRTL-SAC model suggests that the solute activity coefficient would approach that of the ideal solution, i.e., unity, as the conceptual segment makeup of the mixed solvent system approaches that of the solute. In other words, an ideal solvent or solvent mixture for a given solute would be one with the same hydrophobicity, polarity, and hydrophilicity as those of the solute molecule. It is also possible that the solute activity coefficient will become less than unity if the solvent system exhibits strong attractive interactions with the solute. The study indicates that some of the model predictions may be inadequate for certain solvents, which suggests a need to further optimize molecular parameters for the solvents. In the case of sulfadiazine, the model predictions are too high for alcohols and too low for DMF and DMSO. It is evident that, as the NRTL-SAC conceptual segment approach evolves and

6. Conclusions The Nonrandom Two-Liquid Segment Activity Coefficient (NRTL-SAC) model offers a simple and practical thermodynamic framework for solubility modeling of pharmaceutical molecules. By taking solubility measurements in just four to eight representative solvents, it is possible to characterize the surface interaction characteristics of the drug molecule, in terms of conceptual segments, and then to qualitatively predict solubility in any precharacterized solvent or mixture of solvents. This method quickly identifies both good solvent and antisolvent candidates for crystallization design and can provide a first estimate of yield and productivity. The simplicity of the model, the robustness of the predictions, and the applicability of the model to both organic nonelectrolytes and organic electrolytes22 make this a useful thermodynamic framework for solubility modeling in support of crystallization process design. The thermodynamic framework of NRTL-SAC applies equally to the prediction of vapor-liquid equilibrium and liquid-liquid equilibrium, in conjunction with solid-liquid equilibrium, and should increase the applications of solubility data to many areas of drug manufacturing process design. Acknowledgment The authors thank Clare Westwood and Gerry Steele of AstraZeneca for provision of the cimetidine dataset. The authors are grateful to Professor John Prausnitz for his critical review and warm comments regarding the manuscript. Literature Cited (1) Chen, C.-C.; Song, Y. Solubility Modeling with a Non-Random TwoLiquid Segment Activity Coefficient Model. Ind. Eng. Chem. Res. 2004, 43, 8354. (2) Frank, T. C.; Downey, J. R.; Gupta, S. K. Quickly Screen Solvents for Organic Solids. Chem. Eng. Prog. 1999, (December), 41. (3) Chen, C.-C. A Segment-Based Local Composition Model for the Gibbs Energy of Polymer Solutions. Fluid Phase Equilib. 1993, 83, 301. (4) Manzo, R. H.; Ahumada, A. A. Effects of Solvent Medium on Solubility. V: Enthalpic and Entropic Contributions to the Free Energy Changes of Di-substituted Benzene Derivatives in Ethanol: Water and Ethanol: Cyclohexane Mixtures. J. Pharm. Sci. 1990, 79, 1109. (5) Granberg, R. A.; Rasmuson, A. C. Solubility of Paracetamol in Pure Solvents. J. Chem. Eng. Data 1999, 44, 1391. (6) Subrahmanyam, C. V. S.; Reddy, M. S.; Rao, J. V.; Rao, P. G. Irregular Solution Behavior of Paracetamol in Binary Solvents. Int. J. Pharm. 1992, 78, 17. (7) Romero, S.; Reillo, A.; Escalera, B.; Bustamante, P. The Behavior of Paracetamol in Mixtures of Amphiprotic and Amphiprotic-Aprotic Solvents. Relationship of Solubility Curves to Specific and Nonspecific Interactions. Chem. Pharm. Bull. 1996, 44, 1061.

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ReceiVed for reView November 28, 2005 ReVised manuscript receiVed April 24, 2006 Accepted May 1, 2006 IE051326P

Correlation and Prediction of Drug Molecule Solubility in Mixed

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