Handbook of Solvents - George Wypych - ChemTech - Ventech!

9.3 Physical properties of mixed solvents 513
9.3.1.1 Permittivity
In liquid systems with chemically non-interacting components, molar polarization, PM, according
to definition, is additive value; expressing composition in molar fractions:
i= i
M = ∑ Mi i
i=
1
P P x
where:
xi molar fraction of corresponding mixture component
In the case of binary solvent system:
( ) ( )
[9.21]
P = P x + P 1 − x = P − P x + P
[9.21a]
M M1 M2 M1 M2 M2
where:
x molar fraction of the first component.
Here and further definitions indices without digits relate to additive values of mixture properties
and symbols with digits to properties of component solvents. As
M () () /
then ()
i
=∑( )
1
P = f ε M ρ = f ε θ
or for binary solvent
f εθ f ε θx
i i i
() εθ= ( ε) θ + ( ε) θ(
− )
[9.22]
f f x f 1 x
[9.22a]
1 1 2 2
where:
M an additive molecular mass
ρ density
θ molar volume
f(ε) one of the permittivity functions, e.g., 1/ε or (ε - 1)/(ε +2)
In accordance with the rules of transfer of additive properties from one way of composition
expression to another 3 based on [9.22], it follows that
i
() ε =∑ ( ε )
1
f f V
i i
and for a binary system
() ε = ( ε ) + ( ε )( − )
[9.23]
f f V f 1 V
[9.23a]
1 2
where:
V the volume fraction.
Substituting f(ε) function into [9.23], we obtain volume-fractional additivity of
permittivity