Prediction of Solubility

The success of any given method can vary enormously from system to system. Some can only be used for rough assessment while others can occasionally yield data of comparable precision to those attained by careful experimental measurement. Each system must be considered independently. 

Prediction methods using theoretical relationships based on the assumption of solution ideality can be very unreliable, as shown by the example in section 3.6 which indicates that an assumption of ideality for the simple case of naphthalene dissolved in an organic solvent can result in an error of up to 200% in estimating the solubility. 

The number of solubility measurements necessary for the construction of a multicomponent phase diagram increases enormously as the number of components is increased. It is in this area, therefore, that the demand for prediction method most often lies. The methods range from the entirely empirical, generally based on geometrical concepts, to the semi-theoretical, i.e. partly based on thermodynamic descriptions. A comprehensive account of some of these methods, together with several detailed worked examples, is given by NHt (1977). 

Several thermodynamie approaches have been made to the problem of solubility predietions in multieomponent aqueous salt solutions over the past 30 years or so, with varying degrees of success. Most methods are based to some extent on modified Debye Huekel equations (section 3.6.1) and require the predietion of aetivity eoeffieients, enthalpies and entropies of solution, and speeifie heat eapaeities. Within the eonfines of this chapter, however, it is not possible to give more than a flavour of the relevant literature in this area. 

For example, Marshall and Slusher (1966) made a detailed evaluation of the solubility of ealeium sulphate in aqueous sodium chloride solution, and suggested that variations in the ion solubility product could be described, for ionic strengths up to around 2 M at temperatures from 0 to 100 °C, by adding another term in an extended Debye Hiickel expression. Above 2 M and below 25 °C, however, further correction factors had to be applied, the abnormal behaviour being attributed to an increase in the complexity of the structure of water under these circumstances. Enthalpies and entropies of solution and specific heat capacity were also reported as functions of ionic strength and temperature. 

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Prediction of solubility for simple ionic compounds is difficult since we need to know not only values of hydration and lattice enthalpies but also entropy changes on solution before any informed prediction can be given. Even then kinetic factors must be considered. 

An extensive series of studies for the prediction of aqueous solubility has been reported in the literature, as summarized by Lipinski et al. [15] and jorgensen and Duffy [16]. These methods can be categorized into three types 1 correlation of solubility with experimentally determined physicochemical properties such as melting point and molecular volume 2) estimation of solubility by group contribution methods and 3) correlation of solubility with descriptors derived from the molecular structure by computational methods. The third approach has been proven to be particularly successful for the prediction of solubility because it does not need experimental descriptors and can therefore be applied to collections of virtual compounds also. 

Several research groups have built models using theoretical desaiptors calculated only from the molecular structure. This approach has been proven to be particularly successful for the prediction of solubility without the need for descriptors of experimental data. Thus, it is also suitable for virtual data screening and library design. The descriptors include 2D (two-dimensional, or topological) descriptors, and 3D (three-dimensional, or geometric) descriptors, as well as electronic descriptors. 

Multiple linear regression analysis is a widely used method, in this case assuming that a linear relationship exists between solubility and the 18 input variables. The multilinear regression analy.si.s was performed by the SPSS program [30]. The training set was used to build a model, and the test set was used for the prediction of solubility. The MLRA model provided, for the training set, a correlation coefficient r = 0.92 and a standard deviation of, s = 0,78, and for the test set, r = 0.94 and s = 0.68. 

Abraham, N., Lee, J. The correlation and prediction of solubility of compounds in water using an amended solvation energy relationship, J. Pharm. Sci. 1999, 88, 858-880. 

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]. 

In a recent study of twenty disperse and solvent dyes, data for water solubility, octanol/ water partition coefficient, entropy of fusion and melting point were subjected to regression analysis. Complicating factors such as impurities, polymorphism, tautomerism, polarisation and hydrogen bonding precluded the development of reliable predictions of solubility and partition coefficient. Anthraquinone dyes exhibited much lower entropy of fusion than many of the azo dyes [64,65]. 

SMARTS expression [42]. From Table 15.3, it is clear that the compounds in our test set are significantly different in size, polar surface area and complexity, compared to the kinds of molecules that are often used in the generation of algorithms for the prediction of solubility. 

More and better solubility data for simple and complex oxides (glasses, UO2 matrices) at elevated temperatures and pressures and improved techniques for measuring small solubilities. Solubility data for simple oxides provide thermochemical data, free energies in particular, which allow prediction of solubilities for complex oxides. Solubility data for some complex oxides are also necessary in order to verify the methods of predictions for complex oxides and establish key points. 

Yu X, Wang X, Wang H et al. (2006) Prediction of solubility parameters for polymers by a QSPR model. QSAR Comb Sci 25 156-161... 

The solubility parameter is therefore a measure of the energy density holding the molecules in the liquid state. Note that regular solution theory can only predict positive AH. Thus, with this approach, prediction of solubility involves matching the solute and solvent solubility parameters as closely as possible to minimize AH. As a very rough mle of thumb 61 — 62 must be less than 2 (f/cm3)1 /2 for solubility. 

In this chapter, new approaches developed in recent years for the prediction of solubility of organic compounds in solutions, both theoretical and empirical, will be discussed. It is intended to update readers on the methods for prediction of solubility and to provide tools for the design and study of new molecules in pharmaceutical research and development. 

Similar to many other empirical relationships, the coefLcients in Equation 3.45 are speciLc for different classes of solutes. The effect of functional group surface area on solubility would also vary for different functional groups. Hence, equations for the prediction of solubility in water will be different for compounds with different functional groups. 

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