Page 53 - Lindens Handbook of Batteries
P. 53
2.10 PRINCIPLES OF OPERATION
and
RT RT
n = ln i - ln i (2.24)
α nF o α nF
which is the Tafel equation introduced earlier in a generalized form as Eq. (2.7). It can now be
seen that the kinetic treatment here is self-consistent with both the Nernst equation [see Eq. (2.19)]
(for equilibrium conditions) and the Tafel relationship [see Eq. (2.7)](for unidirectional processes).
To present the kinetic treatment in its most useful form, a transformation into a net current flow
form is appropriate. Using
i = i - f i (2.25)
b
substitute Eqs. (2.10), (2.13), and (2.18),
o
o
- α nFE (1 - )α nFE
i = nFAk C exp C - C exp C (2.26)
O
R
T
RT RT
When this equation is applied in practice, it is very important to remember that C and C are
R
O
concentrations at the surface of the electrode, or are the effective concentrations. These are not
necessarily the same as the bulk concentrations. Concentrations at the interface are often (almost
always) modified by differences in electric potential between the surface and the bulk solution. The
effects of potential differences that are manifest at the electrode-electrolyte interface are given in
the following section.
2.4 ELECTRICAL DOUBLE-LAYER CAPACITY AND
IONIC ADSORPTION
When an electrode (metal surface) is immersed in an electrolyte, the electronic charge on the metal
attracts ions of opposite charge and orients the solvent dipoles. There exist a layer of charge in the metal
and a layer of charge in the electrolyte. This charge separation establishes what is commonly known
5
as the “electrical double layer.” Experimentally, the electrical double-layer effect is manifest in the
phenomenon named “electrocapillarity.” The phenomenon has been studied for many years, and there
exist ther modynamic relationships that relate interfacial surface tension between electrode and elec-
trolyte solution to the structure of the double layer. Typically the metal used for these mea surements is
mercury since it is the only conveniently available metal that is liquid at room temperature (although
some work has been carried out with gallium, Wood’s met al, and lead at elevated temperature).
Determinations of the interfacial surface tension between mercury and electrolyte solution can
be made with a relatively simple apparatus. All that is needed are (1) a mercury-solution interface
that is polarizable, (2) a nonpolarizable interface as reference potential, (3) an external source of
variable potential, and (4) an arrangement to measure the surface tension of the mercury-electrolyte
interface. An experimental system that will fulfill these requirements is shown in Fig. 2.7. The inter-
facial surface tension is measured by applying pressure to the mercury-electrolyte interface by rais-
ing the mercury “head.” At the interface, the forces are balanced, as shown in Fig. 2.8. If the angle of
contact at the capillary wall is zero (typically the case for clean surfaces and clean electrolyte), then
it is a relatively simple arithmetic exercise to show that the interfacial surface tension is given by
ρ
γ = hgr (2.27)
2
where γ = interfacial surface tension, ρ = density of mercury, g = force of gravity, r = radius of capil-
lary, and h = height of mercury column in capillary.
