Page 633 - Handbook of Battery Materials

17.4 Bulk Properties 607

slowly through the solvent. The fact that the diffusion coefficient decreases markedly
with increasing concentration leads to the question whether the Stokes–Einstein
relation can be used for concentrated electrolytes. Corrections can be made by
introducing the activity coefficient or empirical estimates. However, the corrections
also have to be treated with care [475]. Nonetheless, the relationship to the viscosity
can be helpful in determining the diffusion coefficient because it is easy to measure.
Measurements of diffusion coefficients are experimentally a difficult field. Cus-
sler wrote about his work [475]: ‘.. . that measurement of diffusion is a Holy Grail
requiring noble knights who dedicate their lives to the quest.’
First of all, a more detailed definition of diffusion coefficients has to be made.
There is a difference between the binary, chemical or salt diffusion coefficient
and the tracer and self-diffusion coefficient. As can be seen, different citations use
different terms for the parameters [475, 483, 484]. The mathematical relationship
of these diffusion coefficients is [485]

c T dln γ ±
∗
D = D · 1 + (17.73)
c 0 dln m
with D the binary, chemical, or salt diffusion coefficient, D* the tracer or
self-diffusion coefficient, c T the total concentration, c 0 the solvent concentration,
γ ± the mean molal activity coefficient, and m the molality.
There are many descriptions of the methods available for the measurement
of diffusion and their theoretical background. Even in standard textbooks of
electrochemistry useful information can be found. Special monographs cover this
topic including its mathematical background [475, 486–493]. For liquids, methods
such as the diaphragm cell [496], Taylor dispersion [495], Gouy diffractometry and
interferometry [487], and dynamic light scattering [497] are often utilized for the
determination of diffusion coefficients. For nonaqueous liquid lithium electrolytes
other methods are preferred, such as pfg-NMR, Moir´ e patterns, microelectrodes,
or setups based on restricted diffusion. These methods are described in later
subsections.

17.4.7.2 Pfg-NMR
For lithium salts in liquid battery electrolytes the most commonly used method is
pfg-NMR. A large magnetic field is applied to the sample, changing in time and
space, resulting in a spin echo signal of the nuclei with amplitude A. If there occurs
any diffusion in a time interval, the amplitude A reduces to amplitude A 0 and the
ratio of the two amplitudes gives the so-called tracer diffusion coefficient [498]:

A 0 2 2 2 δ
ln =−γ g δ D − (17.74)
A 3
with γ the gyromagnetic ratio, g the magnitude of the gradient pulses with duration
δ, the time interval between the gradient pulses, and D the diffusion coefficient.
This procedure is so popular because it directly gives the self-diffusion coefficients
of the anions and cations, respectively. The disadvantage is the impossibility
of distinguishing between ions and ion associates. However, the number of
components is not restricted and the diffusion in very viscous systems can also