Page 60 - Lindens Handbook of Batteries

ELECTROCHEMICAL PRINCIPLES AND REACTIONS 2.17

Concentration of electroactive species Bulk

electrolyte

δ
Distance from electrode surface
FIGURE 2.15 Boundary-layer thickness at an electrode surface.

where L is the boundary-layer thickness at the limiting condition. It tells us that to increase i , one
L
needs to increase the bulk concentration, the electrode area, or the diffusion coefficient. In the design
of a battery, an understanding of the implication of this expression is important. Specific cases can be
analyzed quickly by applying Eq. (2.36), and parameters such as discharge rate and power densities
of new systems can be estimated.
Assume that the thickness of the diffusion boundary layer does not change much with concentra-
tion. Then δ = δ and Eq. (2.36) may be rewritten as
L
 C 
i =- E i  (2.38)
1

 C B  L

The difference in concentration existing between the electrode surface and the bulk of the electrolyte
results in a concentration polarization. According to the Nernst equation, the concentration polariza-
tion or overpotential produced from the change of concentration across the diffusion layer may be
written as
RT C
η = ln B (2.39)
c
C
nF
E
From Eq. (2.38) we have
RT  i 
η = nF ln    i L L -i  (2.40)

c

This gives the relation of concentration polarization and current for mass transfer by diffusion.
Equation (2.40) indicates that as i approaches the limiting current i , theoretically the overpotential
L
should increase to infinity. However, in a real process the potential will increase only to a point
where another electrochemical reaction will occur, as illustrated in Fig. 2.16. Figure 2.17 shows
the magnitude of the concentration overpotential as a function of i/i , with n = 2 at 25°C based on
L
Eq. (2.40).