As described in the previous chapter, intermodular interactions between solvent molecules are very important in determining the strength of the solvent in dissolving a polymer. The concept of a solubility parameter was introduced by Hildebrand for its application to mixtures of non-polar liquids. The concept was derived from considerations of cohesive energy density, which is the ratio of the energy required to vaporize 1 cm3 of liquid to its molar volume. The square root of the cohesive energy density is designated the solubility parameter 5.
Equation 4.1 5=^(AEv/Vm)
where AEv = heat of vaporization, Vm = molar volume of solvent
Solvents with similar values of 5 have comparable intermolecular forces and hence they are expected to be miscible in all proportions. On the other hand, if 5 values for two solvents are significantly different, it is unlikely that they will be miscible.
The above concept was restricted to non-polar solvents and hence was of little use in modern paint technology, where polymers and solvents with a wide range of polarity from non-polar to highly polar are used. Subsequently, Burrell recognized the potential of the solubility parameter concept and carried out work on solubility based on the swelling of polymers, which resulted in introduction of another parameter based on degree of hydrogen bonding by a solvent. He proposed a system in which solvents were classified, based on their hydrogen bonding capacity, into three categories: poorly, moderately, and strongly hydrogen bonding types. The resulting ranges of solubility parameters in these three groups of solvents permitted fairly good predictions of solubility based on which parameter can predict whether a solvent mixture will dissolve a resin. Plotting the solubility parameter against hydrogen bonding indices gives a solubility map, in which solvents are represented as single spots while polymers are contours.
The above theory proposed by Burrell was also moderately successful in prediction of solubility characteristics of resins in solvent mixtures. Therefore, one of the most widely used systems, especially in the paint industry, is the three dimensional Hansen solubility parameter system. Hansen divided the cohesive energy density into three components, related to dispersion forces, dipole forces and hydrogen bonding forces. The Hildebrand solubility parameter 5 is related to these components by the following Equation 4.2.
Equation 4.2: 52 = 5d2 + 5p2 + 5h2
Where 5d, 5p and 5h, are the solubility parameters corresponding to the non-polar (dispersion) contribution, polar contribution and hydrogen bond contribution respectively. Values of the Hansen solubility parameter 5 for some common solvents as well as their 5d, 5p and 5h values are shown in Table 4.1. In the Hansen system, solvents are represented as a single spot in the three dimensional model, while polymers are represented by a volume. Solvents that have their spot within this volume dissolve the polymer, while solvents lying outside the volume will not. For mixed solvents, a weighted average of the three partial solubility parameters can be calculated.
Table 4.1: Three dimensional solubility parameters of some common solvents (in units of MPa1/2)
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