Oscillations, Waves, and Interactions - GWDG

350 R. Pottel, J. Haller and U. Kaatze
Figure 14. Extrapolated static permittivity ɛ(0) versus volume fraction v of solute
for 1 mol/l aqueous solutions of alkali bromides [72] as well as tetraalkylammonium
and azoniaspiroalkane bromides at 25 ◦ C: Me4NBr, tetramethylammonium bromide;
Et4NBr, tetraethylammonium bromide; Pr4NBr, tetrapropylammonium bromide; Bu4NBr,
tetrabutylammonium bromide; 4:4NBr, 5-azoniaspiro[4,4]nonane bromide; 5:5NBr, 6azoniaspiro[5,5]undecane
bromide; 6:6NBr, 7-azoniaspiro[6,6]tridecane bromide [73]. The
dashed line is the graph of the Bruggeman mixture relation (Eq. (16)). The full line is
drawn to guide the eyes.
molecules are turned thereby in the direction opposed to the one given by the external
field. In the Hubbard-Onsager continuum theory a dielectric decrement
δɛHO = 2
3
ɛv(0) − ɛv(∞)
στv
ɛ0ɛv(0)
follows, where ɛv (∞) and τv denote the extrapolated high-frequency permittivity and
dielectric relaxation time of the solvent, respectively. In deriving Eq. (17) perfect slip
boundary conditions on the solvent flow at the ion surfaces have been assumed. The
large differences between the ɛ (0) data for the two series of LiCl solutions in Fig. 16
obviously reflect the different relaxation times of the solvent (τv = (8.27 ± 0.05) ps,
water [46]; τv = (48.7 ± 1) ps, methanol [46]; 25 ◦ C).
Equation (17) allows the kinetic depolarization decrement to be calculated and,
considering also the small reduction in the ɛ(0) values from the dilution of the dipolar
solvent (Eq. (16)), the remaining polarization deficiency to be evaluated in terms
of dielectric saturation. The degree of saturation is expressed by numbers Z ± of
(17)