24
2 Electrochemistry and Electrodeposition
consecutive electron transfer steps, the apparent Tafel slope can be obtained by the
analysis of the complete kinetic scheme. In this case, the relative hindrance of the
consecutive charge transfer processes is a crucial parameter.
2.8.2 Influence of Reactant Transport on the Electrode
Processes
Transport of various components in an electrochemical system may take place by
three main transport processes: diffusion, migration and convection. If the rate of
the transport process is determined by the gradient of the chemical potential of the
reactant, the transport is pure diffusional. When the driving force of the transport
process is provided by the electric field in the media, we can speak about migration.
Finally, if the transport is provided by the displacement of the elemental volume of
a fluid media by external mechanical forces, the transport is convective. Whichever
means of the transport dominates in a particular system, the transport process must
be regarded as a process in series with the electron transfer step.
It is common in the electrochemical laboratory practice that the number of transport processes concerning the reactant is reduced. When a supporting electrolyte is
used in basic laboratory experiments and the concentration of the reactant is small,
the migration of the reactant(s) can be neglected. However, it should be remembered
that this case practically never happens in an industrial plating system where the
reactant is a major constituent of the bath. Convective transport can be provided by
either gas bubble agitation or mechanical stirring, but well-defined convection can
be achieved mostly by the rotation of the electrode (rotating disc or cylinder electrode), for which exact mathematical description is also available. Diffusion is always
to be considered. Even for an approximate and qualitative picture on the transport
processes prevailing around an electrode, one must deal with at least Fick’s first law,
simply written in a one-dimensional form as follows:
J =
1
A
dn
dt
= −D
dc
dx
(2.13)
with the usual meaning of the variables (J: flux of the reactant, A: surface area of the
electrode, D: diffusion coefficient).
From the point of view of the thickness of the electrolyte solution layer where
the reactant concentration is different from its bulk value, one can speak about either
a finite or an infinite diffusion layer, which belong to controlled hydrodynamics
(stirred solution or rotating electrode) and stagnant solution, respectively. In the next
chapter, various examples will be shown for measurements performed under either of
these circumstances. Here, the evaluation of the formulae will refer to a well-defined
diffusion layer thickness, similarly to the general approach of many textbooks, also
for sake of simplicity. First, the electrode will be planar and macroscopic that makes it
2 Electrochemistry and Electrodeposition
consecutive electron transfer steps, the apparent Tafel slope can be obtained by the
analysis of the complete kinetic scheme. In this case, the relative hindrance of the
consecutive charge transfer processes is a crucial parameter.
2.8.2 Influence of Reactant Transport on the Electrode
Processes
Transport of various components in an electrochemical system may take place by
three main transport processes: diffusion, migration and convection. If the rate of
the transport process is determined by the gradient of the chemical potential of the
reactant, the transport is pure diffusional. When the driving force of the transport
process is provided by the electric field in the media, we can speak about migration.
Finally, if the transport is provided by the displacement of the elemental volume of
a fluid media by external mechanical forces, the transport is convective. Whichever
means of the transport dominates in a particular system, the transport process must
be regarded as a process in series with the electron transfer step.
It is common in the electrochemical laboratory practice that the number of transport processes concerning the reactant is reduced. When a supporting electrolyte is
used in basic laboratory experiments and the concentration of the reactant is small,
the migration of the reactant(s) can be neglected. However, it should be remembered
that this case practically never happens in an industrial plating system where the
reactant is a major constituent of the bath. Convective transport can be provided by
either gas bubble agitation or mechanical stirring, but well-defined convection can
be achieved mostly by the rotation of the electrode (rotating disc or cylinder electrode), for which exact mathematical description is also available. Diffusion is always
to be considered. Even for an approximate and qualitative picture on the transport
processes prevailing around an electrode, one must deal with at least Fick’s first law,
simply written in a one-dimensional form as follows:
J =
1
A
dn
dt
= −D
dc
dx
(2.13)
with the usual meaning of the variables (J: flux of the reactant, A: surface area of the
electrode, D: diffusion coefficient).
From the point of view of the thickness of the electrolyte solution layer where
the reactant concentration is different from its bulk value, one can speak about either
a finite or an infinite diffusion layer, which belong to controlled hydrodynamics
(stirred solution or rotating electrode) and stagnant solution, respectively. In the next
chapter, various examples will be shown for measurements performed under either of
these circumstances. Here, the evaluation of the formulae will refer to a well-defined
diffusion layer thickness, similarly to the general approach of many textbooks, also
for sake of simplicity. First, the electrode will be planar and macroscopic that makes it