One-dimensional solubility parameter approach

The thermodynamic affinity between components of a solution is important for quantitative estimation of mutual solubility. The concept of solubility parameters is based on enthalpy of the interaction between solvent and polymer. Solubility parameter is the square root of the cohesive energy density, CED  

Solubility parameters are measured in (MJ/m ) or (cal/sm ) (1 (MJ/m ) =2.054 (cal/sm ) °). The cohesive energy is equal in magnitude and opposite in sign to the potential energy of a volume unit of a liquid. The molar cohesive energy is the energy associated with all molecular interactions in one mole of the material, i.e., it is the energy of a liquid relative to its ideal vapor at the same temperature (see Chapter 5). 

Sis a parameter of intermolecular interaction of an individual liquid. The aim of many studies was to find relationship between energy of mixing of liquids and their 5 The first attempt was made by Hildebrand and Scatchard who proposed the following equation  

AU internal energy of mixing, that is a residual between energies of a solution and 

X2 molar fractions of components V, V2 molar volumes of components 

The free energy of mixing of solution can be calculated from the equation 

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This subchapter is devoted to the evaluation of one-dimensional solubility parameters. The methods of the evaluation of components of solubility parameters in multi-dimensional approaches are given in the Subchapter 4.1. 

In addition, the theoretical equations in the Hildebrand and Hansen approaches can be effectively applied to predicting the solubility of a new compound by employing the experimental solubility data of a structurally related compound. The predicted values for the new compound would be based on the experimental one- or three-dimensional solubility parameter of the structurally related compound, and the group additivity principles would be applied to estimate the respective solubility parameter of the second compound. Solubility parameters associated with the Hildebrand and Hansen approaches have proved useful in the selection of not only solvents, but also of other excipients found in formulations (Belmares et al., 2004). 

One-dimensional approaches to the determination or calculation of solubility parameters were derived for non-polar substances. For substances capable of taking part in polar and donor-acceptor interactions these methods became inaccurate. This led to attempts to improve the methods by adding parameters. Several approaches were taken. 

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