Page 634 - Handbook of Battery Materials

608 17 Liquid Nonaqueous Electrolytes

be determined. Hence the transport of lithium salts in ILs is often observed by
pfg-NMR [463, 499, 501].

17.4.7.3 Moir´ e Pattern
Another nonelectrochemical method was developed by Nishikawa et al., who use
the creation of a Moir´ e pattern when two images of a laser beam, which are directed
through a diffusion cell, overlap on a screen [502]. Two solutions of different
concentrations are brought into contact, resulting in a two-way diffusion. The
Moir´ e patterns of ‘blind value,’ that is, the pattern of uniform concentration, and
the deviation of this blind value give the local refractive index gradient. With this
gradient the concentration profile can be determined and thus, with Fick’s law, the
diffusion coefficient. This method has the advantage that local diffusivities can be
observed.

17.4.7.4 Microelectrodes
Electrochemical methods for the determination of diffusion coefficients are not as
popular as nonelectrochemical methods. Compared to the number of references
with NMR data, the number of diffusion coefficients determined by electrochemical
methods is insignificant.
The spherical diffusion at microelectrodes [494] with no supporting electrolyte is
given by:

4nFD ± c
I sph = (17.75)
πr(1 − t ± )
where I sph is the diffusion-limited current density, n the number of electrons, F
the Faraday constant, D the diffusion coefficient of the electroactive ion, c the
concentration, and t ± the transference number of the electroactive ion.
The planar diffusion at macroelectrodes, described by the Cottrell equation [504]

1/2
nFD c
I pl = 1/2 ± 1/2 , (17.76)
π (1 − t ± )t
with t the time, can be combined with the spherical diffusion Equation 17.75 to
result in the transference number and the diffusion coefficient [494, 505]. Both
measurements have to be made to get suitable values.If one of the parameters is only
assumed [511], the calculated results cannot be taken as true data. Unfortunately
it has to be stressed that the boundary conditions for spherical diffusion are no
longer observed if lithium is deposited on the electrode.
17.4.7.5 Restricted Diffusion
Newman et al. [484] specified a method developed by Harned and French [508],
where the relaxation of a concentration gradient is measured in a vertical closed
cell, leading to the terminology ‘restricted’ diffusion. The relaxation at long times is
observed by determination of the potential difference between reversible electrodes
at the end of the cell [510]. The diffusion coefficient can now be calculated from the