Handbook of Solvents - George Wypych - ChemTech - Ventech!

514 Y. Y. Fialkov, V. L. Chumak
i
=∑ i i
1
ε εV
or for binary solvent
( )
[9.24]
ε= εV + ε −V
[9.24a]
1 2 1
Vast experimental material on binary liquid systems 1,2,3 shows that the equation [9.24]
gives satisfactory accuracy for systems formed of components non-associated in individual
states. For example, dielectric permittivity describes exactly systems n-hexane-pyridine,
chlorobenzene-pyridine by equation [9.24a]. For systems with (one or some) associated
components, it is necessary to consider fluctuations, which depend on concentration, density,
orientation, etc. Consideration of ε fluctuations shows that calculation of dielectric
permittivity for mixture of two chemically non-interacting liquids requires Δε-values determined
from equation [9.24a] and substituted to equation:
2
( 1 1)
( ) [ ( 2 ) ]
Δε= ε − ε Δρ
/ ε + δε [9.25]
where:
Δρ fluctuation of density
δε =(∂εAdd/∂V)/(∂εexp/∂V) ε1, ε2 dielectric permitivities of individual components
εAdd additive value
εexp experimental value
The Δε value may be calculated from a simplified equation. For equal volume mixtures
(V=0.5) of two solvents:
( )
2
V= 05 . 1 2 V=
05 .
Δε = 0. 043 ε −ε/
ε
[9.25a]
Thus, permittivity of equivolume mixture of two chemically non-interacting solvents
can be calculated from the equation
( )
ε = 05 . ε − ε + ε −Δ
ε
[9.26]
V= 05 . 1 2 2 V=
05 .
Having ε values of both initial components and the ε value for the mixture, it is not difficult
to interpolate these values for mixtures for any given composition.
For systems formed of two associated liquids, there are no reliable methods of ε isotherms
calculation. An empirical method has been proposed, which is based on the assumption
that each associated component mixed with the other associated component that does
not interact chemically with the first one introduces the rigorously defined contribution into
ε deviation from the volume-fractional additivity. The extent of these deviations for the first
representatives of the series of aliphatic carbonic acids and alcohols of normal structure, as
well as for some phenols, are given elsewhere. 3
Permittivity of mixtures at different temperatures can be calculated with high accuracy
from absolute temperature coefficients of permittivity and their values using equations
identical in form to [9.24]- [9.26]. For example, the calculation of temperature coefficients