Page 580 - Handbook of Battery Materials

554 17 Liquid Nonaqueous Electrolytes

Table 17.6 Molar conductivities of LiBF 4 in DME at zero
◦
concentration and their standard deviations at 25 C accord-
ing to different methods.

−1
−1
2
2
Method Λ 0 (S cm ·mol ) σ(Λ 0 )(S cm ·mol )
Equations 17.9 and 17.19 139.3 ±2.2
Equation 17.18 140 ±10
Equation 17.9 63.2 ±4.3

This procedure is especially useful when the temperature coefficient of viscosity is
small and the temperature coefficient of the association constant is large.
Solvents of class 6 generally show this behavior. At low temperatures, say T 1 ,
both quantities K A and Λ 0 are small, and they can be determined with the help of
the conductivity equation, Equation 17.9 Equation 17.19 is then used to estimate
Λ 0 values at other temperatures T 2 . Table 17.6 shows that the results obtained with
this procedure for LiBF 4 in DME at 25 C are significantly more precise than those
◦
obtained from use of Equation 17.18 or direct evaluation of the data, Equation 17.19
[197].

17.3.3
Triple-Ion Association Constants

17.3.3.1 Bilateral Triple-Ion Formation
Conductivity curves (Λ vs c 1/2 ) of salts in solvents of low dielectric permittivity
commonly show a weakly temperature-dependent minimum around 0.02 mol·L −1
−1
followed by a strongly temperature-dependent maximum at about 1 mol·L .
According to Fuoss and Kraus [198, 199] the increase of conductivity behind the
minimum is due to the formation of new charge carriers from the ion pairs.
They assume that Coulombic forces suffice to form bilateral triple ions, cationic
− −
+ +
−
+
[C A C ] S and anionic [A C A ] , in solvents of low dielectric permittivity
+
−
S
(ε< 15) if the ions have approximately equal radii.
The conductivity functions of such electrolytes can be evaluated at the level of
limiting laws with the help of Equation 17.20 , permitting the determination of the
(T)
triple-ion dissociation constant K D and the ion-pair association constant K A .
√
√ (T) K A
g(c) c = 0 K A + c 1 − (17.20)
0 (T)
K D 0
1/2 −1
√
−3/2
g(c) = y 1 − S c 1 − (17.21)
± 0
0
(T)
The experimentally nonaccessible limiting conductivity of the triple ion Λ must
0
(T)
be estimated with the help of ion-size considerations yielding Λ = Λ 0 /3 [198,
0
199] or 2Λ 0 /3 [200], with preference for the latter value.