Handbook of Solvents - George Wypych - ChemTech - Ventech!

130 Valery Yu. Senichev, Vasiliy V. Tereshatov
creases as does the contribution into χS (Figure
4.2.1). For example, polyvinylchloride with
dibutyl phthalate, tributylphosphate and some
other liquids have values β>0.
The dependence of solubility on pressure
can be described only by modern theories taking
into account the free volume of components.
28 The corresponding states theory
predicts 12 a pressure dependence of the χ1 parameter
through the effect on the free volume
of the solution components. This dependence
is predicted by the so-called solubility parameters
theory as well, 28 where the interaction between
solvent and solute is described by
Figure 4.2.3. A phase diagram with the lower critical solubility parameters with their dependencies
solution temperature (LCST).1-binodal, 2-spinodal;
I- zone of non-stable conditions, II- zone of on temperature and pressure (Fig. 4.2.2).
* *
metastable conditions, III- zone of the one phase con- When ε11 / ε22 ≤ 1then
δ1< δ2and
hence
ditions.
∂χ1 / ∂P δ2
and the
solvent becomes less compressible than the polymer. Then pressure can increase the
( δ1−δ2) value, giving ∂χ1 / ∂P>0.
4.2.6 METHODS OF CALCULATION OF SOLUBILITY BASED ON
THERMODYNAMIC PRINCIPLES
Within the framework of the general principles of thermodynamics of solutions, the evaluation
of solubility implies the evaluation of value of the Gibbs energy of mixing in the whole
range of concentrations of solution. However, such evaluation is difficult and for practical
purposes frequently unnecessary. The phase diagrams indicate areas of stable solutions. But
affinity of solvent to polymer in each of zone of phase diagram differs. It is more convenient
to know the value of the interaction parameter, possibly with its concentration dependence.
Practical experience from solvent selection for rubbers gives foundations for use of equilibrium
swelling of a crosslinked elastomer in a given solvent as a criterion of solubility. The
equilibrium swelling is related to χ1 parameter by Eq. [4.2.9]. As previously discussed in
Subchapter 4.1, the value of the χ1 parameter can be determined as a sum of entropy and
enthalpy contributions. In the one-dimensional solubility parameter approach, one may use
the following equation:
χ = χ +
1
S
( δ −δ)
1 2
RT
2
V
1
[4.2.10]
where:
χS the entropy contribution
In TDM approach, Eq. [4.1.45] can be used. Similar equations can be derived for the
Hansen approach. All existing systems of solubility imply some constancy of the entropy
contribution or even constancy in some limits of a change of cohesion characteristics of
polymers. Frequently χ1 = 0.34 is used in calculations.