Page 612 - Handbook of Battery Materials

586 17 Liquid Nonaqueous Electrolytes

in order to obtain the maximum conductivity, κ max , attained at the concentration µ
of the electrolyte; a and b are empirical parameters without physical meaning. For
a discussion of the equation see Refs. [16, 105, 405].
PC solutions of LiClO 4 can be used as a suitable example to show that the
transition from low concentrations in lcCM to high electrolyte concentrations
in MSA theory can be based on the same continuum model, simultaneously
illustrating its limitations [406].
Figure 17.11a shows a representation of molar conductivity Λ of LiClO 4 /PC
−3
◦
(25 C) at low concentrations (c < 0.02 mol·dm ) by the use of Equation 17.9,
3
−1
2
Λ 0 = 26.7Scm ·mol −1 and K A = 5.2 mol ·dm . Figure 17.11b shows a repre-
sentation of concentrations up to 1 mol·dm −3 by the use of the MSA equation.
−1
3
K A = 4.2 mol ·dm , Λ 0 is taken from lcCM evaluation. Figure 17.11c shows
specific conductance κ. Full line: Equation 17.48, broken line: MSA equation.
(o = measured points in all three graphs.)
Just like integral equation techniques, the computer simulation methods cannot
treat all effects yielding electrolyte conductivity. A promising model consists in
combining the best possible structural information about the electrolyte solution
from simulation with integral equation techniques to treat frictional forces at
microscopic level [183] (H. Krienke, G. Ahn-Ercan, and A. Maurer, unpublished
results). The only parameter in this approach, the distance parameter of cation
and anion, is determined from the total correlation functions resulting from
computer simulations. Unfortunately, the method is time consuming and of
limited applicability. No battery-relevant systems have been investigated up to now.

17.4.5.2 Conductivity-Determining Parameters
The intrinsic properties of an electrolyte evaluated at low concentrations of the salt
and from viscosity and permittivity of the solvent also determine the conductivity
of concentrated solutions. Various systems were studied to check this approach.
The investigated parameters and items were:
−1
1) the dynamic viscosity η or the fluidity φ(= η ) of the solvent and its tempera-
ture dependence,
2) the radii of the ions,
3) the solvation of cations and anions, as accessible from Stokes radii R i of the
ions,
4) the association constant of the salt,
5) the role of selective solvation, and
6) the competition of solvation and association.
The main problem in the study of the role of these parameters on electrolyte
conductivity is their interdependence. The change in composition of a binary solvent
changes viscosity along with the dielectric permittivity, ion–ion association, and
ion salvation, which may be preferential for one of the two solvents and therefore
also changing the Stokes radii of ions.
A very old rule, the Walden rule, has been recently used to rationalize the
behavior of electrolytes.