Page 54 - Handbook of Battery Materials

20 1 Thermodynamics and Mechanistics

• Diffusion overpotential: When high current densities j at electrodes (at the boundary
to the electrolyte) exist, depletion of the reacting substances is possible, resulting
in a concentration polarization. In this case the reaction kinetics is determined
only by diffusion processes through this zone, the so-called Nernst layer. Without
dealing with its derivation in detail, the following formula is obtained for the
occurring diffusion overpotential (j limit being the maximum current density):

RT j

η diff =
· ln 1 −
(1.29)
zF j limit

As expected, the value of η diff increases with increasing current densities.
• Reaction overpotential: Both the overpotentials mentioned above are normally
of greater importance than the reaction overpotential. But sometimes it may
happen that other phenomena which occur in the electrolyte or during elec-
trode processes such as adsorption and desorption are the rate-limiting fac-
tors.
• Crystallization overpotential: This can occur as a result of the inhibited intercalation
of metal ions into their lattice. This process is of fundamental importance when
secondary batteries are charged, especially during the metal deposition at the
negative side.

Open Circuit
IR - drop Ohmic Polarization
Charge Transfer Polarization
E - Cell Potential [V]
Concentration Polarization

I - Current [A]
Figure 1.8 Cell polarization as a function of operating current.

Corresponding to the change in the potential of the single electrodes, which
is related to their different overpotentials, a shift in the overall cell voltage is
observed (see Figure 1.8). Moreover, an increasing cell temperature can be noticed.
Besides joulic heat, caused by voltage losses due to the internal resistance R i
(electrolyte, contact to the electrodes, etc.) of the cell, thermal losses W K (related to
overpotentials) are the reason for this phenomenon.
2
W J = I · R i · t (1.30)

W K = I · η i · t (1.31)