Handbook of Solvents - George Wypych - ChemTech - Ventech!

4.1 Simple solvent characteristics 119
4.1.6 SOLUBILITY CRITERION
The polymer superstructure influences its solubility. Askadskii and Matveev proposed a
new criterion of solubility for linear polymers based on interaction of forces of a surface
tension on wetting. 38 The solubility parameter of polymer should be lower or equal to the
work of rupture by solvent of a bond relative to a volume unit of the bond element. The condition
of solubility can be expressed as follows:
where:
⎛γ
⎞
μ ≤2ρΦ⎜
⎟
⎜
⎝ γ ⎟
⎠
p
s
ρ
12 /
2 2
μ = δp / δs
δp, δs solubility parameters for polymer and solvent accordingly.
ε
ε
r
= max
p
s
s
maxrp
Φ=
12 /
4(
VV p s)
12 / 12 / ( Vp + Vs
)
2
[4.1.46]
[4.1.47]
[4.1.48]
where:
p s
εmax, εmax
maximum deformations of polymer and solvent at rupture
rs,rp characteristic sizes of Frenkel’s swarms for solvent and and small radius of globule of
bond for polymer, respectively
Vp,Vs molar volumes of polymer and solvent (per unit)
Φ≈1
ρ≈const
The above expression was obtained with neglecting the preliminary swelling. Consideration
of swelling requires correction for surface tension of swelled surface layers:
where:
2 ( )
μ < 2ρΦ⎡Φ− Φ − 1+
a
⎣⎢
/
12
⎤
⎦⎥
[4.1.49]
a =γps / γp
[4.1.50]
( )
γ = γ + γ −2Φγ
γ
ps p s p s
12 /
[4.1.51]
For practical purposes, the magnitude of ρ estimated graphically is 0.687. Thus
μ