Solubility behavior, prediction

Much effort has been expended on models that can be used to predict the solubility behavior of solutes, with good success being attained using a semi-empirical, group contribution approach [75]. In this system, the contributions made by individual functional groups are summed to yield a composite for the molecule, which implies a summation of free energy contributions from constituents. This method has proven to be useful in the prediction of solubility in water and in water-cosolvent mixtures. In addition to the simplest methodology, a variety of more sophisticated approaches to the prediction of compound solubility have been advanced [68]. 

The extensions of the Hildebrand and Hansen approaches are both empirical. Afterthe solubility behavior has been evaluated in a series of solvent systems, regression analysis can be used to estimate the empirical coefLcients, including th fferm of the extended Hansen approach, and then the solubility can be estimated in a solvent system which has not been included in the experimental portion of the study. The problem with acknowledging the predictive power of these equations is that the solubility in many solvents must be determined before being able to predict the solubility in the solvent of choice. It is probably easier to simply perform the solubility study in the solvent of choice and eliminate the prediction equation altogether. On the other hand, in a study of binary solvent systems consisting of water and a cosolvent appropriate to parenteral products, the solubility maximum in that series can be readily estimated by the mathematical expression Lnally achieved. 

This discussion has been largely limited to solubility parameter approaches that some considerto be of limited application since they have quantitative limits. It should be appreciated that these theoretical approaches and their applications have led to a deeper understanding of solubility behavior and of predictive approaches to solubility estimations. More to the point, extrapolations and interpolations dramatically extend the applicability of these approaches to the estimation, albeit a crude estimation, of the solubility of a new compound in a well-studied solvent, or of a well-characterized compound in a new solvent. In 1949, Hildebrand stated ... 

In this dilemma of contradicting interests, COSMO-RS can be a valuable tool for the computational characterization of the solubility behavior of the drug candidate as well as of its dissociation constants. Both are of crucial interest since the small and very expensive amount of compound has to be dissolved and embedded in different solvents and environments for the various steps of purification, crystallization, analysis, and formulation. At present, empirical solubility parameter approaches are often used in order to classify and predict the solubility behavior of the new drug, but despite their poor physical foundation, they have the additional disadvantage that the experimental measurement of the solubility parameters of the new drug consumes time and compound. In contrast, the required DFT/COSMO calculations can be started before the compounds come to the development laboratory, and a COSMO-RS solubility and dissociation screening can be completed—even at optimal computational level— when the work in the development department starts. Furthermore, none of the valuable substance is wasted in this step. 

Dressman reviewed the methodologies used for simulating bio fluids. These methodologies focus on the solubility behavior and dissolution rate in solvents, which mimic the fluids in the gastro intestinal system like Fessif and Fassif. These dissolution tests were invented for better prediction the in vivo performance of drug products. They are barely comparable with solubilities in buffered aqueous media and have a limited throughput of a couple of compounds a day. 

Although most of the oils tested in this study show a similar solubility behavior, significant differences can occur, depending on the composition of the oils with respect to their hydrocarbon fraction and the chemical nature and the amount of additives. With the specifications given by the producers like density and viscosity at standard conditions (see Table 1) no correlation could be found to the experimental data. Further information about the composition is hardly available and an exact analysis is not only undesired but also nearly impossible. This lack of information also makes phase equilibrium calculations to be not very useful for the correlation or prediction of these solubility data. In every single case the solubility has to be determined experimentally. 

By now, nearly every chemist has had some introduction to the subject of supercritical extraction in one form or another, and it would seem that after scores of papers, newsreleases, and trade journal articles, only so much can be said about the background and early findings, the thermodynamic interactions between dissolved solutes and high pressure gases, the equations of state that can correlate and predict solubility behavior, the many applications of the technology (some of which are in flavors), the full scale coffee and hops extraction plants now in operation, etc. What, then, can a paper entitled "Supercritical Fluids - Overview and Specific Examples in Flavors Applications" give that s new -hopefully, a different development of the historical perspective... 

The premise of ideal solubility is that the system must be considered as a mixture of components that do not form mixed crystals (Wesdorp et al. 2005). If the assumption of ideality holds true, then the Hildebrand equation may predict the solubility behavior of a binary TAG mixture (Knoester et al. 1972) ... 

Pure-component vapor pressures can be used for predicting solubilities for systems in which Raoult s law is valid. For such systems Pa = Pa a, where pA is the pure-component vapor pressure of the solute and pA is its partial pressure. Extreme care should be exercised when attempting to use pure-component vapor pressures to predict gas-absorption behavior. Both liquid-phase and vapor-phase nonidealities can cause significant deviations from the behavior predicted from pure-component vapor pressures in combination with Raoult s law. Vapor-pressure data are available in Sec. 3 for a variety of materials. 

Does the above described complexity allow one to reliably predict thermodynamic solubility for drug candidates While we think that this is impossible at present, we believe it is realistic to make compound rankings for solubility behavior, provided that the model used is trained appropriately. VolSurf offers a solubility model developed with controlled literature data and in-house solubility data. Although the solubility error in the prediction phase can be evaluated in 0.7 log units (not suitable to rank the solubility of very similar compounds), the model can still be valid to filter compounds with calculated solubility below a certain threshold. 

Chrastil s equation was adopted in the systematic study of binary solubility behavior because it is easy to use and it does not require information on the properties of lipid components. Its parameters can then be used to interpret the effect of operating conditions on solubility. Its value, however, is limited for predictive modeling of solubility data, which should involve in-depth thermodynamic models (e.g., using an Equation of State (EOS) approach), describing all the phases present at equilibrium. 

MarshAt.i, W. L., and C. A. Chen. 1982. Amorphous silica solubilities. V. Prediction of solubility behavior in aqueous mixed electrolyte solutions to 300°C. Geochim. Cos-mochim. Acta 46 289-91. 

The values of the properties which will be fitted by using equations 2.9 and 2.10 will be selected from available and apparently reliable experimental data whenever there are sufficient amounts of such data. Some important properties of polymers, such as the van der Waals volume (Chapter 3) and the cohesive energy (Chapter 5), are not directly observable. They are inferred indirectly, and often with poor accuracy, from directly observable properties such as molar volume (or equivalently density) and solubility behavior. When experimental data are unavailable or unreliable, the values of the properties to be fitted will be estimated by using group contributions. The predictive power of such correlations developed as direct extensions and generalizations of group contribution techniques will then be demonstrated by using them... 

Finding an appropriate mixed solvent system should not be done on a strictly trial and error basis. It should be examined systematically based on the binary solubility behavior of the solute in solvents of interest. It is important to remember that the mixed solvent system with the solute present must be miscible at the conditions of interest. The observed maximum in the solubility of solutes in mixtures is predicted by Scatchard-Hildebrand theory. Looking at Eq. (1.50) we see that when the solubility parameter of the solvent is the same as that of the subcooled liquid solute, the activity coefficient will be 1. This is the minimum value of the activity coefficient possible employing this relation. When the activity coefficient is equal to 1, the solubility of the solute is at a maximum. This then tells us that by picking two solvents with solubility parameters that are greater than and less than the solubility parameter of the solute, we can prepare a solvent mixture in which the solubility will be a maximum. As an example, let us look at the solute anthracene. Its solubility parameter is 9.9 (cal/cm ). Looking at Table 1.8, which lists solubility parameters for a number of common solvents, we see that ethanol and toluene have solubility parameters that bracket the value of anthracene. If we define a mean solubility parameter by the relation... 

The nature of the dissolution medium can profoundly affect the shape of a dissolution profile. The relative rates of dissolution and the solubilities of the two polymorphs of 3-(3-hydroxy-3-methylbutylamino)-5-methyl-a5-triazino[5,6-Z)7indole were determined in USP artificial gastric fluid, water, and 50% ethanol solution [69]. In the artificial gastric fluid, both polymorphic forms exhibited essentially identical dissolution rates. This behavior has been contrasted in Fig. 6 with that observed in 50% aqueous ethanol, in which Form II has a significantly more rapid dissolution rate than Form I. If the dissolution rate of a solid phase is determined by its solubility, as predicted by the Noyes-Whitney equation, the ratio of dissolution rates would equal the ratio of solubilities. Because this type of behavior was not observed for this triazinoindole drug, the different effects of the dissolution medium on the transport rate constant can be suspected. 

Numerous sources with compiled solubility parameters are available for commercial solvents [1, 2] and polymers [2, 73] Although their use affords qualitative results, they are commonly used in industry to predict the miscibility of polymers in solvents [39, 77]. For solvents ranked according to their solubility parameter, those in close proximity may show a comparable solubility behavior, whereas those that are far apart may show substantial differences. 

Phase separation is frequently observed in polymer solutions and it is mainly due to their low entropy of mixing. At a state of equilibrium each species of the mixture is partitioned between two phases, namely, the supernatant (extremely dilute) and precipitated (moderately dilute) phases [78]. Theoretical models and experimental techniques have been developed to predict the solubility behavior of polymer solutions, polymer blends, and other related systems [79, 80]. Simple theories only permit a rather qualitative description of this phenomenon [78]. Refined and improved theoretical and semiempirical models allow a more accurate prediction of the demixing phenomena and related thermodynamic properties [57, 81]. 

Consider the three solvents ether, water, and toluene. (Look up their structures if you are unsure. Remember that ether is also called diethyl ether.) Based on your knowledge of polarity and solubility behavior, make your predictions. It should be clear that naphthalene is insoluble in water because naphthalene is a hydrocarbon that is nonpolar and water is very polar. Both toluene and ether are relatively nonpolar, so naphthalene is most likely soluble in both of them. One would expect naphthalene to be more soluble in toluene because both naphthalene and toluene are hydrocarbons. In addition, they both contain benzene rings, which means that their structures are very similar. Therefore, according to the solubility rule "Like dissolves like," one would predict that naphthalene is very soluble in toluene. Perhaps it is too soluble in toluene to be a good crystallizing solvent. If so, then ether would be the best solvent for crystallizing naphthalene. 

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