424
12 Localized or Spatially Selective Electrodeposition Methods
flow could be visualized with the help of a solution containing tracer particles [2,
3]. The second period called the “diffusion-hindered regime” is effective at later
times. The theoretical approach to the transport means was quantitatively verified by
copper electrodeposition studies in thin-layer cells. The spatial and temporal concentration variation was nearly symmetrical at the anode and the cathode. However, the
depletion near the cathode along with the occurrence of a small-conductivity layer
around the cathode surface may give rise to electroconvection, unlike at the (sacrificial) anode where the concentration increases. The complete formulation of the
phenomena can be found in [1] and in the literature cited therein.
For vertical thin-layer cells with horizontal electrode at the top and the bottom
of the cell, it was shown that a stable transport and constant concentration gradient
can be achieved if the cathode is the upper electrode (the anode in these studies was
a sacrificial electrode of the same material as the cathode) [4]. If the metal salt is
consumed at the upper part of the cell, the density of the solution decreases there,
and the solution layering eliminates any buoyancy-driven convection. If the current
density is below the diffusion-limited value, the concentration gradient observed
along the vertical cross section of the cell increases approximately proportionally
to the current density [5]. As the diffusion-limited current density is approached,
instability occurs, and oscillation starts (cell voltage oscillation under galvanostatic
conditions and vice versa) [5]. Even if the deposition at the top-situated cathode
becomes dendritic near the limiting current, the growth front remains fairly straight
across the cell, even though the solution between the dendrites is fully depleted for the
reactant. This situation is completely the opposite if the cathode is the bottom electrode. Then, the buoyancy force gives rise to the occurrence of turbulence-looking
fluid motion. The vortex tubes detaching from the electrodes expand towards each
other and later merge. This leads to a mixing much exceeding the concentration
equalization effect of diffusion, and the concentration gradients tend to be attenuated. Experimental observations based on two-dimensional light absorption maps
were strongly supported with numerical simulations leading to essentially the same
concentration gradients and fluid motion.
Ramification of the growing metal is particularly common in thin-layer cells,
especially when two conditions are fulfilled: (i) the cell is operated at deposition rates
close to the mass transport-limited one; and (ii) no supporting electrolyte is used.
As dendrites start growing, the solution between the dendrites becomes practically
depleted with respect to the electrolyte. Concerning the solution concentration along
the direction of the mean electrical field (i.e., perpendicular to the edges which
comprise the electrodes), various zones follow each other from the cathode to the
anode [6]. Due to the nearly complete depletion and the difference between ion
migration rates, there is a space charge layer with a thickness of at most 10 µm,
which is followed by a quasi-neutral (~100 µm thick) and a bulk neutral solution
layer. At the close vicinity of the tip of the growing dendrites, electroconvection is
the major force acting. Between the growing end zones of the dendrites, the electrical
forces give rise to counter-rotating fluid vortices, whose relative contribution to the
overall transport much exceeds that of the diffusion if the growth rate is high as
compared to the classical diffusion-limited current density.
12 Localized or Spatially Selective Electrodeposition Methods
flow could be visualized with the help of a solution containing tracer particles [2,
3]. The second period called the “diffusion-hindered regime” is effective at later
times. The theoretical approach to the transport means was quantitatively verified by
copper electrodeposition studies in thin-layer cells. The spatial and temporal concentration variation was nearly symmetrical at the anode and the cathode. However, the
depletion near the cathode along with the occurrence of a small-conductivity layer
around the cathode surface may give rise to electroconvection, unlike at the (sacrificial) anode where the concentration increases. The complete formulation of the
phenomena can be found in [1] and in the literature cited therein.
For vertical thin-layer cells with horizontal electrode at the top and the bottom
of the cell, it was shown that a stable transport and constant concentration gradient
can be achieved if the cathode is the upper electrode (the anode in these studies was
a sacrificial electrode of the same material as the cathode) [4]. If the metal salt is
consumed at the upper part of the cell, the density of the solution decreases there,
and the solution layering eliminates any buoyancy-driven convection. If the current
density is below the diffusion-limited value, the concentration gradient observed
along the vertical cross section of the cell increases approximately proportionally
to the current density [5]. As the diffusion-limited current density is approached,
instability occurs, and oscillation starts (cell voltage oscillation under galvanostatic
conditions and vice versa) [5]. Even if the deposition at the top-situated cathode
becomes dendritic near the limiting current, the growth front remains fairly straight
across the cell, even though the solution between the dendrites is fully depleted for the
reactant. This situation is completely the opposite if the cathode is the bottom electrode. Then, the buoyancy force gives rise to the occurrence of turbulence-looking
fluid motion. The vortex tubes detaching from the electrodes expand towards each
other and later merge. This leads to a mixing much exceeding the concentration
equalization effect of diffusion, and the concentration gradients tend to be attenuated. Experimental observations based on two-dimensional light absorption maps
were strongly supported with numerical simulations leading to essentially the same
concentration gradients and fluid motion.
Ramification of the growing metal is particularly common in thin-layer cells,
especially when two conditions are fulfilled: (i) the cell is operated at deposition rates
close to the mass transport-limited one; and (ii) no supporting electrolyte is used.
As dendrites start growing, the solution between the dendrites becomes practically
depleted with respect to the electrolyte. Concerning the solution concentration along
the direction of the mean electrical field (i.e., perpendicular to the edges which
comprise the electrodes), various zones follow each other from the cathode to the
anode [6]. Due to the nearly complete depletion and the difference between ion
migration rates, there is a space charge layer with a thickness of at most 10 µm,
which is followed by a quasi-neutral (~100 µm thick) and a bulk neutral solution
layer. At the close vicinity of the tip of the growing dendrites, electroconvection is
the major force acting. Between the growing end zones of the dendrites, the electrical
forces give rise to counter-rotating fluid vortices, whose relative contribution to the
overall transport much exceeds that of the diffusion if the growth rate is high as
compared to the classical diffusion-limited current density.