Page 585 - Handbook of Battery Materials

17.3 Intrinsic Properties 559

Addition of strongly solvating ligands L to electrolytes with high ion pair
association constants entails a series of selective solvation reactions
+
+
C +L [C L] + (17.25)
S S
+
+
+
[C L] +L [C L 2 ] + (17.26)
S S
−
A + L [A L] − (17.27)
−
S S
− 0
− 0
[C A ] + L [C LA ] S (17.28)
+
+
S
shifting the equilibria of Equations 17.6–17.8 in the direction of the solvated free
ions. As a consequence, the properties of the electrolyte change; for example,
the addition of small amounts of ligands to a solution entails large conductivity
increases up to more than 100% [222]. Conductivity measurements in solvents
of very low dielectric constants therefore are strongly affected by traces of water,
which there acts as a ligand (see Section 17.2.4 and Ref. [20]).
The pioneering work of Gilkerson et al. [223–231] and Huyskens et al. [232,
233] allows the determination of the corresponding equilibrium constants from
conductivity measurements. If all equilibria, Equations 17.6–17.8, are involved, the
0
association constants of an electrolyte without (K ) and with (K A ) addition of the
A
ligand at concentration c L of the ligand L are given by the relationship [233]
+ 2
−
+
K 0 (1 + K c L + K c )(1 + K c L )
A 1 2 L 1
= (17.29)
K A (1 + K P c L )
where K + refers to the equilibrium Equation 17.25, K + to Equation 17.26, K −
1 2 1
to Equation 17.27, and K P to Equation 17.28 Studies of this type are very time
consuming because many series of conductivity measurements must be performed,
0
as K and K A (c L ) are needed along with their appertaining limiting values of
A
conductivity with and without added ligand.
At small salt concentrations and very large association constants, the ratio of
association constants can be approximated by

2

K A 0 L 1 − 0 1 − 0 κ L 2

= L = R G L ≈ R G ≈ (17.30)
K A 1 − L 1 − L κ
0 0
neglecting the difference in molar ionic conductivities due to selective Li -ion
+
L
solvation. and Λ L are the limiting molar conductivity and the molar conductivity
0
at finite concentration in presence of the ligand, Λ 0 and Λ are the limiting value
and the value at finite concentration before addition of ligand.
Salomon and coworkers investigated the role of ligands known to offer cavities
with diameters matching the radius of lithium ion such as, for example, 15-crown-5,
or the cryptand [222], 12-crown-4 (12C4) and derivatives such as 1-aza-12-crown-4
(1-A-12C4) and 1-benzoaza-12-crown-4 (1-BA-12C4) for various battery electrolytes
at moderate concentrations [234–238].
The conductometric titration, shown in Figure 17.5 (adapted from Ref. [236])
exhibits the expected conductivity increase for LiBF 4 and LiSO 3 CF 3 -solutions in
◦
PC/5-crown-5 mixtures at 25 C, that is, for salts which are known to be strongly
associated despite the relatively high dielectric permittivity of the solvent.