232
7 Composites
in which α is the volume fraction of the particles in the deposit and i 0 is the exchange
current density of the metal being deposited. The molar weight M and the density
ρ also refer to the metal. From the discussion of Eq. 7.4, it can be seen that the
volume fraction of the particles in the deposit increases with the particle concentration and is expected to achieve saturation. Equation 7.4 implies the dependence of the
incorporation rate on the electrode potential, and, indirectly, on the current density,
too. The sign in the exponential term, (i.e., the value of A–B) determines whether
the increase in the current density promotes or hinders the particle codeposition. In
spite of the huge leap in the electrolytic codeposition theory, Guglielmi’s approach
cannot reveal explicitly the dependence of the codeposition rate on many experimental parameters (e.g., pH, temperature, hydrodynamic conditions); rather, the key
parameters can only be determined from the deposit analysis. Another shortcoming
of Guglielmi’s theory is that the metal deposition is treated as being totally analogous
to the particle-free case, which is not right.
The next important step in the mathematical description of the particle codeposition was made by Celis, Roos and Buelens [67]. They took into account five
consecutive subprocesses of the particle codeposition:
1. Formation of an ionic cloud around the particles including also the electroactive
metal ions that will later make the coating;
2. Transport of the particles from the bulk solution to the electrode side of the
hydrodynamic boundary layer by forced convection;
3. Transport of the particles through the diffusion layer by diffusion;
4. Weak adsorption of the particles with the retention of their ionic cloud;
5. Strong adsorption of the particles, loss of the ionic cloud and the reduction of
the ions previously adsorbed, leading to irreversible particle incorporation.
The first step may occur independently of the deposition process and hence, its
kinetic parameters are not included into the improved model either. The last two
steps are nearly analogous to those in Guglielmi’s model with the extension that
the reduction of the ions carried by the particles is also considered (though treated
the same way as the reduction of the solvated ions). The incorporation ratio of the
particles, w, is expressed first as weight per cent with a simple stoichiometric ratio:
w =
W P N P P
M i
z F
+ W P N P P
(7.5)
In the above equation, W P is the weight of a single particle, N P is the number of
particles crossing the diffusion layer around the working electrode per unit of time
and surface area, while P is a probability factor of the particle codeposition. The
P factor was assumed to be related to the ratio of the reduced (k) vs. the total (K)
number of electroactive metal ions adsorbed on a particle (where obviously k ≤ K).
Hence, the particle incorporation was approached in a totally different manner than
in the Guglielmi model. The particle incorporation can take place if the reduction
ratio of the adsorbed ions achieves a large enough proportion. Still, the K parameter
7 Composites
in which α is the volume fraction of the particles in the deposit and i 0 is the exchange
current density of the metal being deposited. The molar weight M and the density
ρ also refer to the metal. From the discussion of Eq. 7.4, it can be seen that the
volume fraction of the particles in the deposit increases with the particle concentration and is expected to achieve saturation. Equation 7.4 implies the dependence of the
incorporation rate on the electrode potential, and, indirectly, on the current density,
too. The sign in the exponential term, (i.e., the value of A–B) determines whether
the increase in the current density promotes or hinders the particle codeposition. In
spite of the huge leap in the electrolytic codeposition theory, Guglielmi’s approach
cannot reveal explicitly the dependence of the codeposition rate on many experimental parameters (e.g., pH, temperature, hydrodynamic conditions); rather, the key
parameters can only be determined from the deposit analysis. Another shortcoming
of Guglielmi’s theory is that the metal deposition is treated as being totally analogous
to the particle-free case, which is not right.
The next important step in the mathematical description of the particle codeposition was made by Celis, Roos and Buelens [67]. They took into account five
consecutive subprocesses of the particle codeposition:
1. Formation of an ionic cloud around the particles including also the electroactive
metal ions that will later make the coating;
2. Transport of the particles from the bulk solution to the electrode side of the
hydrodynamic boundary layer by forced convection;
3. Transport of the particles through the diffusion layer by diffusion;
4. Weak adsorption of the particles with the retention of their ionic cloud;
5. Strong adsorption of the particles, loss of the ionic cloud and the reduction of
the ions previously adsorbed, leading to irreversible particle incorporation.
The first step may occur independently of the deposition process and hence, its
kinetic parameters are not included into the improved model either. The last two
steps are nearly analogous to those in Guglielmi’s model with the extension that
the reduction of the ions carried by the particles is also considered (though treated
the same way as the reduction of the solvated ions). The incorporation ratio of the
particles, w, is expressed first as weight per cent with a simple stoichiometric ratio:
w =
W P N P P
M i
z F
+ W P N P P
(7.5)
In the above equation, W P is the weight of a single particle, N P is the number of
particles crossing the diffusion layer around the working electrode per unit of time
and surface area, while P is a probability factor of the particle codeposition. The
P factor was assumed to be related to the ratio of the reduced (k) vs. the total (K)
number of electroactive metal ions adsorbed on a particle (where obviously k ≤ K).
Hence, the particle incorporation was approached in a totally different manner than
in the Guglielmi model. The particle incorporation can take place if the reduction
ratio of the adsorbed ions achieves a large enough proportion. Still, the K parameter