6.4.4 Gelation
In a polymer solution above the chain overlap concentration,entanglements
occur (Fig. 6.16). If such a solution is deformed, part of the polymer chain
sections between entanglements will become stretched, by which their
conformational entropy decreases. Each chain section tends to regain its
original conformation, which implies that the material behaves in an elastic
manner. If the deformation is very slow, the entangled chains can slide along
each other while continuously seeking a conformation of largest entropy,
and the main result of the entanglements is an increase in viscosity (Section
6.4.3). If the deformation is fast, considerable stretching of chain sections
will occur, and the elastic effect will be strong. We now have aviscoelasticor
memory fluid: see Section 5.1.3. Ifpermanent cross-linksare formed between
entangled chains, agelis obtained, as is discussed in Section 17.2.2.
6.5 PHASE SEPARATION
Polymers have, like all solid materials, a limited solubility, but if the
concentration becomes greater than the solubility, separation into liquid
phases occurs, not precipitation. The factors governing this are briefly
discussed below.
6.5.1 One Solute
Going back to Section 6.4.2, Figure 6.13 shows a (hypothetical) result for
the solubility of a homopolymer. One relevant relation is given in the figure,
the others are in Eq. (6.12), with some calculated examples in Table 6.4. It
follows that the important variables are the excluded volume parameterb
and the polymer–solvent molecular volume ratioq(proportional to the
degree of polymerizationn). It is also seen that the critical value ofbfor
solubility is close to zero for high molar mass polymers.
To explain these observations, it may be remembered that the
solubility of a substance is reached if its molar free energy is equal in the
undissolved and the dissolved states. This can be expressed as
DGmix¼Dd!uG¼DHTDS¼0, and since entropy generally decreases
when a solute goes from the dissolved to the undissolved stateðDS< 0 Þ,DH
must be negative (net attraction between solute molecules). For small
spherical molecules, the enthalpy change precisely equalsTtimes the mixing
entropy at the solubility limit. For a polymer the situation is more
complicated. The enthalpy term is directly related tob, and forb<0, there
is net attraction between polymer segments. The translational mixing
entropy is very small; it goes to zero whenqbecomes very large, since the