Page 577 - Handbook of Battery Materials

17.3 Intrinsic Properties 551

17.3.1
Chemical Models of Electrolytes
An efficient description of ion pairing is based on the chemical model of electrolytes.
Chemical models of electrolytes take into account local structures of the solution due
to the interactions of the ions and solvent molecules. The underlying information
stems from spectroscopic, kinetic, and electrochemical experiments, as well as
from dielectric relaxation spectroscopy. The postulated structures include ion
pairs, higher ion aggregates, and solvated and selectively solvated ions [183].
The formation of these structures is represented with the help of chemical
equilibria. The equilibrium constants can consistently be determined with the help
of experimental methods. The association of solvated ions can be described by the
overall equilibrium reaction
+ −
C + A ⇐⇒ IP S (17.4)
S
S
−
where C is the solvated cation, A is the solvated anion, and IP S is a solvated ion
+
S
S
(c)
pair. The association constant K A is given by the relationship
(c) (1 − α)y IP
K A = 2 2 (17.5)
α cy
±
(c)
where K A is the association constant in the molarity scale, α is the degree of
dissociation, y IP is the activity coefficient of the ion pair, and y is the mean activity

±
coefficient of the free ions.
According to Eigen and Tamm, ion-pair formation proceeds stepwise, starting
− 0
+
from separated solvated ions which form a solvent-separated ion pair [C SSA ] ,
− 0
− 0
followed by a solvent-shared ion pair [C SA ] and finally a contact ion pair [C A ]
+
+
[184, 185]. All these species are solvated. The types of ion pair formed depend on
the relative strength of the interaction of the involved species.
− 0
+
−
−
+
+
[C ·nS] + [A ·mS] [C SSA ] + [(n + m) − 2]S (17.6)
− 0
− 0
+
+
[C SSA ] [C SA ] + S (17.7)
− 0
− 0
+
+
[C SA ] [C A ] + S (17.8)
17.3.2
Ion-Pair Association Constants
The commonly used method for the determination of association constants is
conductivity measurement on symmetrical electrolytes at low salt concentrations.
The evaluation may be advantageously based on the ‘low concentration chemical
model’ (lcCM), which is a Hamiltonian model at the McMillanMayer level including
short-range nonelectrostatic interactions of cations and anions [183, 186]. It is a
feature of the lcCM that the association constants do not depend on the physical
property of the electrolyte used for their determination. Association constants of the
same electrolyte at approximately equal concentration ranges of the salt which are
determined from thermodynamic properties (heat of dilution, electromotive force