B3. Semi-quantitative approach [1] for “normal” polymers

It is well known, that the surface tension (and the solubility parameter ) of polymers is significantly higher (and therefore their solubility significantly lower) than that for the corresponding monomers or oligomeric analogues, e.g.:
 

monomer/analogue /  polymer / 
hexane 18.4 / 14.9 PE 28 - 32 / 17.5
styrene 25.5 / 16.8 PS 30 - 36 / 
19.5 - 22
caprolactam * / 26.0 PA 6.6 41 / 28 - 31
diethylphthalate 37.5/20.5 PET 43 / ca 30
aniline 43 / 21.1 PAni ES 69.4 ? / ?
* not available

The reasons can be found in the entropic term of eqn (1), for which Flory and Huggins developed their theory, leading to eqn (4)

(4) S = - R (nS lnS + nP lnP)

(with S and P being the solvent and the polymer, resp.)

It is easy to see, that for a low molecular weight compound, like hexane, the term TS will reach rather high values, as there are many moles for a given concentration P. (The value at 250 K is about 115 J/Mol). So, hexane is easily soluble in decalin. But for a PE wax with a Mw of only 10.000, TS will decreases to about 33 J/Mol even at 400 K (where one tries to dissolve PE in hot decalin).

But in contrast to hexane, we also have to consider the melt enthalpy, which for PE is around 250 J/g. Then, for a 1% solution of PE in one mole of decalin, eqn (1) becomes:

(5) GPE/decalin = 33,400 - 33.2 [J/mol] >> 0

hence PE is not soluble in decalin, unless we heat the solvent just above the melt temperature of PE, whereby we introduce the melt energy from outside, not by solvation, not by solvent-polymer interactions, but by external heating. The entropic driving force of -33.2 J/g is rather low, from where we understand that the dissolution is going on slowly. For PE with increased Mw (as used in industry) this term is still smaller.

The reason for a higher solubility parameter and hence a much lower solubility of polymers is the drastically reduced entropy contribution to the free energy of dissolution.

Footnotes

[1] quantitative figures are generally rare in the field of solution or dispersion properties, and - if available - differing; as it is not the goal to calculate precisely but to support qualitative arguments by appropriate data; they are taken as average numbers from tables being found in

- R. Weast, M. Astle (eds.) Handbook of Chemistry and Physics, 62nd edition, CRC press 1981

- A. Barton, Handbook of Solubility Parameters and other Cohesion Parameters, CRC Press1985

- J. Brandrup, E. Immergut (eds.), Polymer Handbook 2nd edition, J. Wiley 1975

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