Handbook of Solvents - George Wypych - ChemTech - Ventech!

120 Valery Yu. Senichev, Vasiliy V. Tereshatov
For both polymers and solvents, the values of solubility parameters can be obtained
experimentally (see Subchapters 5.1, 5.3). The surface tension of polymer can be calculated
using parahor:
4
γ= ( P / V)
where:
V molar volume of a repeated polymer unit
Then the value of Vp is calculated:
NA∑ΔVi Vp
=
i
k
av
[4.1.53]
[4.1.54]
where:
kav = 0.681
If the density of polymer dp is known, then Vp = M/dp, where M is the molecular mass
of a repeating unit. The values of parahors are given in Table 4.1.5.
Table 4.1.5. Values of parahors
Atom C H O O2 N S F Cl Br I
P 4.8 17.1 20.0 60.0 12.5 48.2 27.5 54.3 68.0 91.0
Increment
Double
bond
Triple
bond
3-member
ring
4-member
ring
5-member
ring
6-member
ring
P 23.2 46.4 16.7 11.6 8.5 6.1
The value of Φis calculated from Eq. [4.1.48]. Vp,Vsare defined from ratios Vp=M/dp and Vs=M/ds where dp,dsare the densities of polymer and solvent, respectively. Then μ is
calculated from Eq. [4.1.49]. The obtained value of μ from Eq. [4.1.49] is compared with
2 2
value of μ = δp / δs
if the last value is lower or equal to the value of μ calculated from Eq.
[4.1.49], polymer should dissolve in a given solvent with probability of 85 %.
4.1.7 SOLVENT SYSTEM DESIGN
One-component system. Solvents can be arranged in accordance to their solubility parameter
as shown in Figure 4.1.1. It is apparent that a set of compatible solvents can be selected
for polymer, determining their range based on the properties of polymer.
The simplest case is expressed by the Gee’s equation for equilibrium swelling: 41
2
[ ( ) ]
Q = qmax exp −Vs δs −δp
[4.1.55]
where:
δs, δp solubility parameters for solvent and polymer.
The value of solubility parameter of solvent mixture with components having similar
molar volumes is relative to their volume fractions and solubility parameters: