Handbook of Solvents - George Wypych - ChemTech - Ventech!

116 Valery Yu. Senichev, Vasiliy V. Tereshatov
δ
p
μ
= 501 .
/
V
34
1
[4.1.35]
Peiffer 11 proposed the expressions which separates the contributions of polar forces
and induction interactions to the solubility parameters:
where:
( 2 3 )( 1)
2 4
δ = K πμ / kTp N / V
[4.1.36]
p
( 2 )( )
3
2
δ = K παμ / i N / V
[4.1.37]
i
1
3
ε* interaction energy between two molecules at the distance r*
N number of hydroxyl groups in molecule
4
p =2μ / 3kTε*
[4.1.38]
2
i = 2αμ
/ ε * [4.1.39]
It should be noted that in Hansen’s approach these contributions are cumulative:
2 2 2
δ = δ + δ
[4.1.40]
p p i
For the calculation of hydrogen-bonding component, δ h, Hansen and Scaarup 28 proposed
an empirical expression based on OH-O bond energy (5000 cal/mol) applicable to alcohols
only:
( . N / V)
δh = 20 9 1
12 /
[4.1.41]
In Subchapter 5.3, the values of all the components of a solubility parameter are calculated
using group contributions.
4.1.5 THREE-DIMENSIONAL DUALISTIC MODEL
The heat of mixing of two liquids is expressed by the classical theory of regular polymer solutions
using Eq. [4.1.10]. This expression is not adequate for systems with specific interactions.
Such interactions are expressed as a product of the donor parameter and the acceptor
parameter. The contribution of H-bonding to the enthalpy of mixing can be written in terms
of volume units as follows: 21
( )( )
Δ H′ = A −A D −D
mix 1 2 1 2 1 2
ϕϕ [4.1.42]
where:
A1,A2 effective acceptor parameters
D1,D2 donor parameters,
ϕ1, ϕ2 volume fractions,
Hence enthalpy of mixing of two liquids per volume unit can be expressed by: 32
2
[ ( 1 2)
( )( ) ]
ΔH = δ′ − δ′ + A −A D − D ϕϕ = Bϕϕ
mix
1 2 1 2 1 2 1 2 [4.1.43]