Page 629 - Handbook of Battery Materials

17.4 Bulk Properties 603

Combining Equations 17.65 and 17.66, the transference number for the cation is
I ss ( V − I 0 R 0 )
t + = (17.67)
I 0 ( V − I ss R ss )
This method is very popular for measuring transference numbers of lithium
electrolytes (see references in Table 17.18) because of the very easy procedure
and low time costs. But it must be taken into account that the measurement
was developed for binary and ideal solid electrolytes, which is often not the case,
especially for solid polymer electrolytes, where a large amount of ion-pairs is
probable.
17.4.6.5 Conductivity Measurement
Transference numbers for infinitely diluted electrolytes can be determined by
conductivity measurements, too, see Equation 17.59. A study on methanol solutions
of thiocyanate salts in dependence of concentration and temperature [457] shows
that electrolytes with a transference number lower than 0.5 yielded functions
decreasing with decreasing temperature and increasing concentration; electrolytes
with transference numbers larger than 0.5 showed the opposite behavior, but both
in agreement with Walden’s rule.

17.4.6.6 Galvanostatic Polarization Method
Another electrochemical method is more suited for concentrated solutions. Here,
a concentration gradient is established by a galvanostatic polarization, which is not
measured directly, but by observing the related cell potential during galvanostatic
polarization and determining the exact potential at the moment of current interrup-
tion. Ma et al. introduced this procedure for polymer electrolytes by combining three
different measurements to determine the cationic transference number [458]: the
measurement of the potential during galvanostatic polarization, the salt diffusion
coefficient, and the concentration dependence of the potential. The knowledge of
these parameters allows the calculation of the cationic transference number [459]:
√
z + ν + c ∞ Fm Dπ
t + = 1 − (17.68)
4 dU
dln c
with z + the charge number of the cation, ν + the stoichiometric moles of cations
added to a solution, c ∞ the bulk concentration, D the salt diffusion coefficient,
dU/dlnc the concentration dependence of the potential, and m the slope of a plot
of the potential at the time of current interruption against it 0.5 ,with i the current
i
density and t i the polarization time.
This way of determining the cation transference number involves some un-
derlying assumptions, too: binary electrolyte with the cation as active species, no
convection, semi-infinite diffusion, and one-dimensional cell geometry. Further-
more, the method combines the results of three different measurements, which is
very time-consuming. Nevertheless, the calculation of transference numbers does
not assume ideality or diluted solutions, making it more applicable for modelling
transport parameters of lithium-ion batteries.