Solubility prediction thermodynamic basis

In this work we derive simple relationships between temperature, solute solubility and retention. The simple thermodynamic models developed predict the trend in retention as a function of pressure, given the solubility of the solute in the fluid mobile phase at constant temperature and the trend in k as a function of temperature at constant pressure. Our aim is to examine the complicated dependence of retention on the thermodynamic and physical properties of the solute and the fluid, providing a basis for consideration of more subtle effects in SFC. 

In this work solubility data of biological compounds taken from literature were considered. Different thermodynamic models based on cubic equations of state (EOS) are used in the correlation of experimental data. The interaction parameters are described on the basis of group contribution (G.C.) approach in order to establish correlations suitable for the prediction of the solubility of compounds of similar molecular structure. 

Thermodynamics is the basis of all chemical transformations [1], which include dissolution of chemical components in aqueous solutions, reactions between two dissolved species, and precipitation of new products formed by the reactions. The laws of thermodynamics provide conditions in which these reactions occur. One way of determining such conditions is to use thermodynamic potentials (i.e., enthalpy, entropy, and Gibbs free energy of individual components that participate in a chemical reaction) and then apply the laws of thermodynamics. In the case of CBPCs, this approach requires relating measurable parameters, such as solubility of individual components of the reaction, to the thermodynamic parameters. Thermodynamic models not only predict whether a particular reaction is likely to occur, but also provide conditions (measurable parameters such as temperature and pressure) in which ceramics are formed out of these reactions. The basic thermodynamic potentials of most constituents of the CBPC products have been measured at room temperature (and often at elevated temperatures) and recorded in standard data books. Thus, it is possible to compile these data on the starter components, relate them to their dissolution characteristics, and predict their dissolution behavior in an aqueous solution by using a thermodynamic model. The thermodynamic potentials themselves can be expressed in terms of the molecular behavior of individual components forming the ceramics, as determined by a statistical-mechanical approach. Such a detailed study is beyond the scope of this book. 

DSC analysis represents a superior method of thermal analysis, in that the area under a DSC peak is directly proportional to the heat absorbed or evolved by the thermal event, and integration of these peak areas yields the enthalpy of reaction (in units of calor-ies/gram or Joules/gram). Even though conclusions reached on the basis of enthalpies of fusion are possibly compromised by their omission of the entropy contribution, an indication of the thermodynamic trends inherent in the system is often possible. For instance, the same polymorphic form of moricizine hydrochloride was deduced on the basis of thermal analysis and equilibrium solubility measurements. On the other hand, auranofin represents a compound for which one anhydrous polymorphic form is predicted to be the most stable by virtue of its melting point and heat of fusion but for which solubility measurements demonstrate that the other polymorph was in fact the thermodynamically stable form. ... 

The predictions that can be made for solvent mixtures on the basis of the solubility diagram are not strictly valid because they involve thermodynamic simplifications and empirical parameters, and disregard temperature effects [14.29], [14.33]. A strong warning must therefore be given against the uncritical use of solubility parameters. Nevertheless, description of the solvents with the aid of the solubility parameter concept often provides useful information about their solvency and reveals similarities which can otherwise only be characterized empirically (e.g., latent solvents or dilutability). 

Prior to Harwood s work, the existence of a Bootstrap effect in copolymerization was considered but rejected after the failure of efforts to correlate polymer-solvent interaction parameters with observed solvent effects. Kamachi, for instance, estimated the interaction between polymer and solvent by calculating the difference between their solubility parameters. He found that while there was some correlation between polymer-solvent interaction parameters and observed solvent effects for methyl methacrylate, for vinyl acetate there was none. However, it should be noted that evidence for radical-solvent complexes in vinyl acetate systems is fairly strong (see Section 3), so a rejection of a generalized Bootstrap model on the basis of evidence from vinyl acetate polymerization is perhaps unwise. Kratochvil et al." investigated the possible influence of preferential solvation in copolymerizations and concluded that, for systems with weak non-specific interactions, such as STY-MMA, the effect of preferential solvation on kinetics was probably comparable to the experimental error in determining the rate of polymerization ( 5%). Later, Maxwell et al." also concluded that the origin of the Bootstrap effect was not likely to be bulk monomer-polymer thermodynamics since, for a variety of monomers, Flory-Huggins theory predicts that the monomer ratios in the monomer-polymer phase would be equal to that in the bulk phase. 

Although it is not strictly a molecular simulation method, we mention the GSE here since it can be derived from the thermodynamic cycle of crystal to supercooled liquid to solution provided that some assumptions are made about the entropy of melting, AS. The GSE provides useful estimates of solubihty when experimental melting point and AS data are available [34], However, the GSE is not usually applicable to unsynthesized molecules as the best empirical methods for predicting melting point give predictive errors of 40-50°C [35, 36], The GSE has provided the basis of empirical methods to predict solubility such as the Solubihty Forecast Index [37]. 

In this respect, the in silico prediction of the thermodynamic mixing behavior of different polymer-drug/excipient mixtures is of central interest. A common approach to cope with this problem is the calculation of the solubility parameters according to Hildebrand or Hansen [9-12], which is standard in the development of polymer mixtures [13]. The use of highly developed force fields as the basis of any MD simulation software enables the calculation of solubility parameters with accuracy comparable to those measured experimentally by inverse gas chromatography [14], and an increasing number of other statistical quantitative property relationships between simulated and experimental values are established [15-18]. 

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