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:

  1. Using Hildebrand solubility parameters, if the polymer (p) and the solvent (s) have similar polar and hydrogen bonding parameters, following simple rule applies:1

    s - δp| ≤ 3.6 MPa1/2

  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:1

    [4(δd2 - δd1)2 + (δp2 - δp1)2 + (δh2 - δh1)2]1/2 ≤ R

    The interaction radius, R,  depends on the type of polymer. The R values are usually in the range of 4 to 15 MPa1/2.

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 solutions2 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:3,4

Δh1,2Δu1,2 = φ1 φ2 (δ1δ2)2

where Δu1,2 is the internal energy change of mixing per unit volume and φ1 and φ2 are the volume fractions of the solvent and the polymer in the mixture.

Notes & References
  1. Charles H. Hansen, Thesis: The Three Dimensional Solubility Parameter and Solvent Diffusion Coefficient, Danish Tech. Press (1967); Hansen Solubility Parameters: A User's Handbook, 2nd Ed., CRC Press. (2007)
  2. 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.
  3. Note that this equation always predicts positive heats of mixing which is only true for regular solutions.
  4. J.H. Hildebrand, R.L. Scott, The Solubility of Nonelectrolytes, 3rd ed., Dover, New York, 1964.
  • Summary

    Solubility Parameter

    Solubility parameters are frequently used in the paint and coating industry to aid in the selection of solvents and to predict the compatibility of polymers.

  • Compounds with similar chemical structure are more prone to dissolve than those with dissimilar structure. "Similia similibus solvuntar."

  • As a general rule, the lower the molecular weight of a polymer, the greater its solubility in a solvent.

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  • Hildebrand parameters are only useful for nonpolar and slightly polar mixtures in the absence of hydrogen bonding (dipole moment < 2 Debye).

  • The higher the molecular weight of a polymer, the closer the solubility parameter of the solvent needs to be to dissolve the polymer in the solvent.