Page 242 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Electrochemical Engineering 149

overpotential is 500 mV when the exchange-current den- In most corrosion processes passivity is desirable be-
2
sity is 10 −3 A/cm , whereas the overpotential is 1500 mV cause the rate of electrode dissolution is significantly re-
2
for i 0 = 10 −12 A/cm . This result has especially important duced. The rate of aluminum corrosion in fresh water is
consequences for electro-chemical energy conversion de- relativelylowbecauseoftheadherentoxidefilmthatforms
vices. From Table II we see that most hydrocarbon oxida- on the metal surface. A thicker film can be formed on the
tions and oxygen reductions are relatively irreversible. In surface by subjecting it to an anodic current in a process
general, the exchange-current density is highest on noble known as anodizing. In most electrochemical conversion
metal surfaces. Because of the irreversibility of these re- processes passive films reduce the reaction rate and are,
actions, a practical device for the production of electricity therefore, undesirable.
through the direct electrochemical oxidation of hydrocar-
bons has not been devised.
III. MASS TRANSPORT
H. Passivity
In an electrodeposition process, ions must be transported
The curve shown in Fig. 3 cannot proceed indefinitely in to the electrode surface and subsequently react by gaining
either direction. In the cathodic direction, the deposition electrons to form metal atoms. Mass transport and elec-
of copper ions proceeds from solution until the rate at trode kinetics are the individual rate processes that deter-
which the ions are supplied to the electrode becomes lim- mine the overall deposition rate. Since these rate processes
ited by mass-transfer processes. In the anodic direction, act in series, it is the slowest step that governs the overall
copper atoms are oxidized to form soluble copper ions. rate. For engineering calculations, it is useful to determine
While the supply of copper atoms from the surface is es- the rate-limiting step and to simplify the calculation by ne-
sentially unlimited, the solubility of product salts is finite. glecting or crudely approximating the remaining steps. If
Local mass-transport conditions control the supply rate; so an electrochemical process is limited by mass-transport
a current is reached at which the solution supersaturates, processes, we must calculate the flux of ions or molecules
and an insulating salt-film barrier is created. At that point at the electrode surface. If a gaseous, reactant, such as
the current drops to a low level; further increase in the po- oxygen, is the limiting species, we can calculate its flux
tential does not significantly increase the current density. from the ordinary laws governing diffusion and convec-
A plot of the current density as a function of the potential tion; however, for ionic species we must also account for
is shown in Fig. 5 for the zinc electrode in alkaline elec- the flux due to the influence of the electric field on the
trolyte. The sharp drop in potential is clearly observed at charged species.
−0.9 V versus the standard hydrogen electrode (SHE). At
more positive potentials the current density remains at a
A. Governing Equations
low level, and the electrode is said to be passivated.
A mathematical description of an electrochemical system
should take into account species fluxes, material conser-
vation, current flow, electroneutrality, hydrodynamic con-
ditions, and electrode kinetics. While rigorous equations
governing the system can frequently be identified, the si-
multaneous solution of all the equations is not generally
feasible. To obtain a solution to the governing equations,
we must make a number of approximations. In the previ-
ous section we considered the mathematical description
of electrode kinetics. In this section we shall assume that
the system is mass-transport limited and that electrode
kinetics can be ignored.
Species flux can be described by the Nernst-Planck
equation,

N i =−z i u i Fc i ∇φ − D i ∇c i + c i v, (17)
where N i is the flux of species i, z the charge on the ion,
FIGURE 5 Typical potential sweep diagram on a zinc electrode.
Current density decreases rapidly near −900 mV versus SHE u i the mobility, c i the concentration of i, ∇φ the potential
(standard hydrogen electrode) as reaction products cover the gradient, D i the diffusivity of i, and v the bulk veloc-
electrode surface and passivate the electrode. ity. The first term on the right represents the flux due to