Handbook of Solvents - George Wypych - ChemTech - Ventech!

2.3 Basic physical and chemical properties 59
A universal approach was developed by Hildebrand who assumed that the mutual solubility
of components depends on the cohesive pressure, c. The square root of cohesive
pressure is the Hildebrand’s solubility parameter, δ:
δ= c =
ΔHv
−RT
V
m
[2.3.12]
where:
ΔHv heat of vaporization
R gas constant
T temperature
Vm molar volume of solvent = M/d
M molecular mass of solvent
d density of solvent
Frequently, the term RT is neglected because it accounts for only 5-10% of the heat of
vaporization. This equation explains the reasons for the correlation between the Hildebrand
solubility parameter and heat of vaporization as given in Figure 2.3.1.
The Hildebrand model takes into account only the dimensions of molecules or of the
molecular segments participating in the process of solvation and dispersion interactions.
The model is useful, therefore, in predicting the solubility of non-polar substrates. The solubility
parameters of solvents and solutes are compared and if they are similar there is high
probability (exceptions exist) that the solvents are miscible that a solute is soluble in a solvent.
Two solvents having the same solubility parameters should have the same dissolving
capabilities. If one solvent has solubility parameter slightly below the solubility parameter
of solute and the second solvent has solubility parameter above the solute, the mixture of
both solvents should give better results than either solvent alone. This model is an experimental
and mathematical development of the simple rule of “like dissolves like”.
Solvents and solutes also interact by donor-aceptor, electron pair, and hydrogen bonding
interactions. It can be predicted that the above concept is not fully universal, especially
in the case of solutes and solvents which may apply these interactions in their solubilizing
action. Hansen developed a three-dimensional scale with parameters to expand theory in order
to include these interactions. Hansen defined solubility parameter by the following
equation:
δ = δ + δ + δ
2 2 2 2
d p h [2.3.13]
where:
δd dispersion contribution to solubility parameter
δp polar contribution to solubility parameter
δh hydrogen bonding contribution to solubility parameter
Hansen defined solvent as a point in three-dimensional space and solutes as volumes
(or spheres of solubility). If a solvent point is within the boundaries of a solute volume space
then the solute can be dissolved by the solvent. If the point characterizing the solvent is
outside the volume space of a solute (or resin) such a solvent does not dissolve the solute.
The solubility model based on this concept is broadly applied today by modern computer
techniques using data obtained for solvents (the three components of solubility parameters)
and solutes (characteristic volumes). A triangular graph can be used to outline the limits of