POLYMER SOLUBILITY AND SOLUBILITY PARAMETER

Solubility parameters were initially developed to guide solvent selection in the paint and coatings industry. Today, they are widely used in in many other fields to predict miscibility and solubility of polymers, chemical resistance, and permeation rates.

One of the most important application of solubility parameters is the prediction of polymer solubility in solvents. The closer the solubility parameters of the solute and the solvent are, the more likely the solubility of the solute in the given solvent. 
In the case of polymers, there are several rules of thumb for selecting suitable solvents:

• Using Hildebrand solubility parameters, if the polymer (p) and the solvent (s) have similar polar and hydrogen bonding parameter, following simple rule applies: 

a. |δ_s - δ_p| ≤ 3.6 MPa^1/2

· Using Hansen solubility parameters, an approximate spherical "volume" of solubility with radius R can be drawn up for each solute. Only solvents that have Hansen solubility parameters within this volume are likely to dissolve the polymer in question:

a. [4(δ_d2 - δ_d1)² + (δ_p2 - δ_p1)² + (δ_h2 - δ_h1)²]^1/2 ≤ R

b. The interaction radius, R,  depends on the type of polymer. The R values are usually in the range of 4 to 15 MPa^1/2.

It is important to note that the higher the molecular weight of a polymer, the closer the solubility parameter of the solvent and polymer need to be to dissolve the polymer in the solvent. For linear and branched polymers, a plot of solubility versus solubility parameter for a range of solvents will peak when the (Hansen / Hildebrand) solubility parameters of the solute and solvent match. In the case of a cross-linked polymer, the swell volume, i.e. the solvent uptake, will peak when the solubility parameters of the solvent match those of the polymer.

As a general rule, the solubility parameters of polymers do not change much with temperature, whereas those of low molecular weight compounds often decrease noticeably with increasing temperature. In some cases, a solvent passes through soluble conditions to once more to become a non-solvent as the temperature increases.

For regular solutions¹ in which intermolecular (specific) attractions are minimal and the solution diverges only moderately from the ideal solution*, the enthalpy of mixing can be estimated from the solubility parameters as proposed by Hildebrand and Scott:²

ΔH_1,2 ≈ ΔU_1,2 = φ₁ φ₂ (δ₁ – δ₂)²

where ΔU_1,2 is the internal energy change of mixing per unit volume and φ₁ and φ₂are the volume fractions of the solvent and the polymer in the mixture.

Notes

• The word regular implies that all molecules (or repeat units) mix in a completely random manner, that is, in a regular solution of composition φ₁ and φ₂, the probability that a neighbor of a given molecule is of species 1 is given by its volume fraction φ₁ in the mixture.
• Note that this equation always predicts positive heats of mixing which is only true for regular solutions