Hansen approach

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. 

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). 

A. Beerbower and J.R. Dickey ( ) were also concerned with the interactions of solvents and polymers as they were working in an area concerning the effects of hydraulic fluids on hoses and linings. In applying the Hansen approach to their particular set of polymers and solvents, they found that accurate predictions required the addition of a correction factor ... 

This approach has become a constituent of the Hansen approach and has not received a separate development. 

Chen implied that was the enthalpy contribution to the Flory-Huggins parameter and plotted the solubility data in a 5 -%jj diagram where 4 was the H-bond parameter in the Hansen approach. In these diagrams sphere-like volumes of Hansen s solubility have degenerated to circles. 

Using the Hansen approach, the solubility of any polymer in solvents (with known Hansen s parameters of polymer and solvents) can be predicted. The determination of polymer parameters requires evaluation of solubility in a great number of solvents with known values of Hansen parameters. Arbitrary criteria of determination are used because Hansen made no attempts of precise calculations of thermodynamic parameters. 

In TDM approach, Eq. [4.1.45] can be used. Similar equations can be derived for the Hansen approach. All existing systems of solubility imply some constancy of the entropy contribution or even constancy in some limits of a change of cohesion characteristics of polymers. Frequently = 0.34 is used in calculations. 

Hereinafter this approach has become a component of Hansen approach and did not develop independently. 

The Hansen approach provides extensive information on the nature of solubility and interactions of solvents and polymers. " But it has its own set of difficulties related to estimating the correct values of the parameters and generating graphical interpretation of results. " ... 

Barra J, Lescure F, Doelkcr E, Bustamante P (1997) The expanded Hansen approach to solubility parameters. Paracetamol and citric acid in individual solvents. J Pharm Pharmacol 49 644-651... 

Alternatively to the work of the Flory-Huggins theory, other methods like the Hansen solubility parameter can be used to estimate the solvent quality [51]. In the Hansen approach, the polar, hydration, and dispersion components are considered separately and the contribution of each parameter is considered [46, 51, 52]. 

The Hansen approach assumed that the cohesive energy can be divided into contributions of dispersion interactions, polar interactions, and hydrogen bonding. 

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