Page 94 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Molecular Weight of Polymers 57

3.2 SOLUBILITY

Polymer mobility is an important aspect helping determine a polymer’s physical, chemical, and
biological behavior. Lack of mobility, either because of interactions that are too swift to allow the
segments within the polymer chain some movement or because there is not suffi cient energy (such
as a high enough temperature) available to create mobility or because of a lack of available free
volume, results in a brittle material. Many processing techniques require the polymer to have some
mobility. This mobility can be achieved through application of heat and/or pressure and through
dissolving the polymer. Because of its size, the usual driving force of entropy increase for the mix-
ing and dissolving of materials (entropy) is smaller for polymers in comparison to small molecules.
Traditional molecular weight determinations require that the polymer be dissolved. Here, we will
focus on the general topic of polymer solubility and the factors that influence polymer solubility.

The first attempts at predicting solubility were largely empirical. Paint technologists employed
various approaches. In one approach Kauri-butanol values were equal to the minimum volume of test
solvent that produced turbidity when added to a standard solution of Kauri-Copal resin in 1-butanol.
The aniline point is the lowest temperature where equal volumes of aniline and the test solvent are
completely miscible. Both tests are really measures of the relative aromaticity of the test solvent.
Mixing can be described in terms of free energy. Free energy has two terms, an energy-related
term and one related to order/disorder. The energy-related term is called enthalpy, H, and the order/
disorder term called entropy, S.
For mixing to occur and for polymers to be dissolved it is essential that the change in free energy,
∆G, which is the driving force in the solution and mixing processes, decrease to below zero, that is,
be negative. ∆H and ∆S are equal to the change in enthalpy and change in entropy and for constant
temperature the relationship is the classical Gibbs equation.

∆G = ∆H − T ∆S (3.1)

“Like-likes-like best of all” is a description that is useful at appropriate times in science. It is
true of solubility. Thus, water-likes-water best of all and is infinitely soluble in itself. Hexane-likes-

hexane best of all and is infinitely soluble in itself. Hexane and water are not soluble in one another

because hexane is nonpolar and water is polar; thus they are not “like one another.” In solubility,
and in fact all of mixing, the ∆H term is always unfavorable when mixing or when solubility occurs.
(Shortly, we will deal with attempts such as the CED and solubility parameter to minimize the unfa-
vorable aspect of the ∆H term.) Thus, it is the ∆S term that allows mixing and solubility to occur. As
seen in Figure 3.3 the amount of randomness or disorder gain is great when pure materials such as
water and ethanol is changed from the ordered pure materials to the disordered mixture.
By comparison, the increase in randomness, ∆S, is much smaller if one of the materials is a
polymer since the possible arrangement of the polymer chains is much more limited because the
polymer units are attached to one another and not free to simply move about on their own. Figure 3.4
illustrates this with water and poly(ethylene glycol), PEG. We notice several aspects. First, as noted
above, the number of arrangements of the PEG units is limited. Second, as in the case of an onion,
each layer of PEG chains must be peeled back allowing water molecules to approach inner layers
before entire solubility occurs and causes swelling. This results in polymer solubility often requir-
ing a longer period of time, sometimes hours to week to months, in comparison to the solubility of
smaller molecules where solubility can occur in seconds.
Polymer solubility, in comparison to small molecules, is

a. More limited with respect to the number of solvents as a result of the lower increase in
randomness;
b. It is more limited with respect to the extent of solubility; and
c. Takes a longer time to occur.

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