B2. Thermodynamic requirements for Solutions

For discussing Shacklette's contribution [47] to the question of this part we have to consider the basics of the term "solubility parameter": For transferring a liquid into the gas phase we need to invest half of the interaction energy between the molecules per molecule, or NL times per Mol. This energy (the negative inner molar vaporization enthalpy) defined per molar volume is the so-called "cohesion energy density e":

(2) e = - 0.5 * NL * z *  / Vm = ( Evap)/Vm

The "solubility parameter " is defined as the square root of this cohesion energy density.

For the dissolution of a chemical species A, one has to disrupt an interaction between the species molecules A and A', A'' and so forth, and to replace it by an interaction between A and the solvent molecules. For each disrupted A - A' interaction a new interaction A - S will be generated.

In the case of polymers, all intramolecular interactions (hence those between the monomer units) and all intermolecular interactions have to be replaced by polymer (= monomer unit) / solvent interactions, otherwise the polymer was not truly dissolved.

The use of a solubility parameter in characterizing an interaction between a species is only in accordance with its definition, if all monomer unit / monomer unit interactions have been replaced by monomer unit / solvent interactions. And only with the assumption, that the molar volume of the solvent and the molar volume of the monomer unit are of comparable size, one can work with solubility parameters when describing polymer solutions. Then one can derive for discussing compatibility between solvents and polymers:

(3) 0.5 * NL * z *  / Vm = - 0.5 (pol - solv)2

The general approach to use the difference of the solubility parameter as a measure for the interaction between the solvent and the material to be dissolved (in comparison to the interactions between the molecules of the solvent, and the material, resp.) is only productive, if the basic assumptions for the definition of the solubility parameter and the a.m. equation are fulfilled, i.e., the solvent molecules have replaced all interactions between all the monomer units.

The experimental determination of solubility parameters for polymers is generally made either by measuring it for lower molecular weight analogues, or by measuring the swelling degree of comparable cross-linked polymers. In the latter case, one plots the swelling degree versus the solubility parameter of the solvent used. The solubility parameter of the solvent with the maximum swelling effect is then equivalent with the one of the polymer.

It is important to consider, that for the dissolution of (partially) crystalline polymers one has to invest the crystal melting enthalpy as a part of H, see eqn. (1), which is not considered in the solubility parameter theory. Crystalline polymers are therefore soluble only above their melting point in the solvent having the right solubility parameter, if the solvent itself cannot invest more solvation enthalpy Hsolv than melt enthalpy Hmelt is necessary.

From eqn (1) it can be understood, that if the melt enthalpy, which is part of H, is too high, the (negative) entropic term cannot over-compensate the (positive) enthalpic term - in this case the polymer would be insoluble.

These considerations are clarifying that the solubility parameter concept is only applicable in the case of interactions of the solvent with all polymer segments (monomer units). There is a drastic difference when not dealing with "solutions" but "dispersions". Then we do not have a polymer / solvent interaction at the molecular level, but on a higher organization level: between surfaces: the polymer particle surface interacts with the solvent surface. Any colloidal dispersion is the result of a surface / surface interaction.

Solubility parameters cannot be derived from wetting and dispersion interactions in colloidal systems.

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