Handbook of Solvents - George Wypych - ChemTech - Ventech!

4.1 Simple solvent characteristics 103
D ( ) ( )
Vm
2 2
= δ′ p − δ′ s 1 −ϕp
[4.1.6]
RT
⎡ K
H = ln⎢1+ ⎣⎢
( 1−ϕp) V
s
⎤
⎥
⎦⎥
+ ( Kpp / Vm)
( Kpp p / Vm)
1
C = ln
1+ ϕ
[4.1.7]
[4.1.8]
where:
α constant depending on the choice of the equation for the entropy of mixing.
Usually it equals 0.5.
b constant depending on the structure of solvent. b=1 for unstructured solvents, b=-1 for
solvents with single H-bond (e.g. alcohols) and b=-2 for solvents with double
H-bonds chains such as water.
Vm the molar volume of a repeating segment
Vs the molar volume of solvent
ϕp the volume fraction of polymer
δp, δs modified solubility parameters without regard to H-bonds.
K the stability constant of the corresponding solvent-polymer hydrogen bond
Kpp the constant of the self-association of polymer segments
Several polymers such as polyethylmethacrylate, polyisobutylmethacrylate and
polymethylmethacrylate were studied according to Huyskens-Haulait-Pirson approach.
The main advantage of this approach is that it accounts for entropy factors and other essential
parameters affecting solubility. The disadvantages are more numerous, such as lack of
physical meaning of some parameters, great number of variables, and insufficient coordination
between factors influencing solubility that have reduced this approach to an approximate
empirical scheme.
4.1.2 ONE-DIMENSIONAL SOLUBILITY PARAMETER APPROACH
The thermodynamic affinity between components of a solution is important for quantitative
estimation of mutual solubility. The concept of solubility parameters is based on enthalpy of
the interaction between solvent and polymer. Solubility parameter is the square root of the
cohesive energy density, CED:
δ= = ⎛
( ) ⎜
⎝
/ 12 ΔE
CED
Vi
i
12 /
⎞
⎟
⎠
[4.1.9]
where:
ΔEi cohesive energy
Vi molar volume
Solubility parameters are measured in (MJ/m 3 ) 1/2 or (cal/sm 3 ) 1/2 (1 (MJ/m 3 ) 1/2 =2.054
(cal/sm 3 ) 1/2 ). The cohesive energy is equal in magnitude and opposite in sign to the potential
energy of a volume unit of a liquid. The molar cohesive energy is the energy associated with
all molecular interactions in one mole of the material, i.e., it is the energy of a liquid relative
to its ideal vapor at the same temperature (see Chapter 5).