*2.2.1. Two-step adsorption codeposition model*

Earlier codeposition mechanisms [68–70] suggested that two different phenomena should be taken into account to explain the deposition of inert particles: electrophoresis and adsorption. Although both possibilities can be supported by good arguments, there are also effective contradictions.

An electrophoretic effect could explain the observed effect of the current density on the coating. However, there are some difficulties to explain the effects of other parameters, such as, for example, the nonlinear dependence on the particle concentration. Two main objections can be made against the possibility of an electrophoresis effect controlling the codeposition of these particles. First, it should consider the fact that electroplating baths are high ionic strength media, thus presenting no electrophoretic effect. Second, as the mechanism considers only the inert particles (uncharged), they should not respond to a negatively charged electrode. On the contrary, it would be a mistake to consider only a mechanism based on particulate adsorption, because a simple adsorption mechanism could not give a satisfactory explanation for the effect of the current density on the coating [63,71].

Guglielmi [63] developed a hypothesis that used some concepts of the two previously described mechanisms, although the author tried to eliminate the earlier mentioned contra‐ dictions. The proposed model was based on two consecutive adsorption steps. The first step is substantially of physical nature and leads to the production of a layer of weakly adsorbed particles on the cathode, with a very high coverage; the second step was dependent on an auxiliary electric field, and thus substantially of electrochemical character, producing a strong adsorption of the particles on the electrode. The strongly adsorbed particles are then progres‐ sively covered by the metal growth and become incorporated to the coating.

This model presents a good physical meaning. It is possible to infer that, in the first step, the inert particles are surrounded by a thin layer of adsorbed ions and solvent molecules; these charged particles can then interact with the electrode. In the second step, the existing electric field at the interface between the substrate and the inert particles (charged by the electrolyte components) contributes to produce a strong adsorption field. There is a clear analogy between the two-step adsorption postulated for particles and the adsorption of ions on the external and internal Helmholtz plans, respectively [63].

Figure 1 shows a generic representation of the model proposed by Guglielmi [63]. It can be shown that the postulated mechanism is not affected by the above-mentioned contradictions and makes it possible to justify the influence of both the current density and the nonlinear particle concentration on the deposition process.

been carried out trying to propose models that could explain the influence of the deposition parameters on the codeposition phenomenon of inert particles in metallic matrix during the

The main problem faced by the authors who proposed such mechanisms was the physical explanation concerning the direct influence of deposition parameters, such as current density, particle concentration in the bath, stirring speed of the suspension, solution pH, and temper‐ ature, for example, on the codeposition phenomenon [38,47,48]. It is a very hard task, and only

Earlier codeposition mechanisms [68–70] suggested that two different phenomena should be taken into account to explain the deposition of inert particles: electrophoresis and adsorption. Although both possibilities can be supported by good arguments, there are also effective

An electrophoretic effect could explain the observed effect of the current density on the coating. However, there are some difficulties to explain the effects of other parameters, such as, for example, the nonlinear dependence on the particle concentration. Two main objections can be made against the possibility of an electrophoresis effect controlling the codeposition of these particles. First, it should consider the fact that electroplating baths are high ionic strength media, thus presenting no electrophoretic effect. Second, as the mechanism considers only the inert particles (uncharged), they should not respond to a negatively charged electrode. On the contrary, it would be a mistake to consider only a mechanism based on particulate adsorption, because a simple adsorption mechanism could not give a satisfactory explanation for the effect

Guglielmi [63] developed a hypothesis that used some concepts of the two previously described mechanisms, although the author tried to eliminate the earlier mentioned contra‐ dictions. The proposed model was based on two consecutive adsorption steps. The first step is substantially of physical nature and leads to the production of a layer of weakly adsorbed particles on the cathode, with a very high coverage; the second step was dependent on an auxiliary electric field, and thus substantially of electrochemical character, producing a strong adsorption of the particles on the electrode. The strongly adsorbed particles are then progres‐

This model presents a good physical meaning. It is possible to infer that, in the first step, the inert particles are surrounded by a thin layer of adsorbed ions and solvent molecules; these charged particles can then interact with the electrode. In the second step, the existing electric field at the interface between the substrate and the inert particles (charged by the electrolyte components) contributes to produce a strong adsorption field. There is a clear analogy between the two-step adsorption postulated for particles and the adsorption of ions on the external and

Figure 1 shows a generic representation of the model proposed by Guglielmi [63]. It can be shown that the postulated mechanism is not affected by the above-mentioned contradictions

sively covered by the metal growth and become incorporated to the coating.

two models, regarding the codeposition of inert particles, are well accepted [63,64].

electroplating of a cathodic composite coating [6,8,11,23,24,62–64].

*2.2.1. Two-step adsorption codeposition model*

162 Electrodeposition of Composite Materials

of the current density on the coating [63,71].

internal Helmholtz plans, respectively [63].

contradictions.

**Figure 4.** Schematic representation of the different stages of the electrochemical codeposition, as suggested by Gugliel‐ mi [63].

The proposed model was then validated by a mathematic treatment and submitted to an experimental evaluation [63]. It used a nickel sulfamate bath containing TiO2 particles (1 μm) and SiC (2 μm). It is important to mention, however, that none of these particles present inert electrical nature. The deposits were obtained at current densities of 2, 5, and 10 A dm-2, and the analysis of particle concentration in the coating was performed by gravimetric methods. The experimental data agreed with the codeposition proposed mechanism based on a twostep adsorption process. It was found that the concentration of the weakly adsorbed particles was twice the concentration of the particulate material in the suspension, thus justifying the premature saturation of the surface that was indicated by the first step model. However, in highly diluted suspensions, a fraction of the particles weakly adsorbed on the electrode was removed. The lowest concentration of the strongly adsorbed particles, as suggested by the second step model, was related to the reduction of the ions, which was relatively slow, compared to the rate of adsorption of the first step. The deposition of inert particles depended on the studied deposition parameters (current density and particle concentration in the bath). This model also explains the strong dependence on the particle concentration in the solution observed during codeposition, because the behavior of the particles strictly depended on the structure of molecules and ion layers adsorbed on the particle surface and indirectly on the electrolyte composition [62].

#### *2.2.2. Five-step codeposition model for inert particles [63]*

The groundings of Guglielmi's model [63] proved the importance of the mathematical treatment of the electrolytic bath in the codeposition process. However, some derivations and unexplained questions have arisen, and the generality of the model was questioned. Consid‐ ering only current density and particle concentration in the solution as the single parameters that control the process, this model ignored other important process parameters, such as hydrodynamics and the effect of bath constituents and its electrolytic conditions, such as pH and bath temperature. Therefore, the Guglielmi's model [62] was not considered able to predict how these other parameters affect the electrolytic codeposition of the particles [64].

The electrolytic codeposition mechanism of inert metal particles, proposed by Celis et al. [64], was based on two fundamental assumptions:


Thus, the incorporation of inert particles in the metal matrix proposed by Celis et al. [64] follows the next five stages and is schematically shown in Figure 5.

**Figure 5.** Model proposed by Celis et al. [64] to describe the incorporation of a particular material in composite coat‐ ings.


unexplained questions have arisen, and the generality of the model was questioned. Consid‐ ering only current density and particle concentration in the solution as the single parameters that control the process, this model ignored other important process parameters, such as hydrodynamics and the effect of bath constituents and its electrolytic conditions, such as pH and bath temperature. Therefore, the Guglielmi's model [62] was not considered able to predict

The electrolytic codeposition mechanism of inert metal particles, proposed by Celis et al. [64],

**1.** A layer of adsorbed ionic species is created around the inert particles when the particles are added to the solution or during pretreatment of the particles in ionic solutions, and

**2.** The reduction of some of these adsorbed ionic species is required for embedding particles

Thus, the incorporation of inert particles in the metal matrix proposed by Celis et al. [64] follows

**Figure 5.** Model proposed by Celis et al. [64] to describe the incorporation of a particular material in composite coat‐

**1.** Adsorption of ions and molecules occurs on the surface of the particles suspended in the

**2.** The particles are transferred to the hydrodynamic boundary by convection.

how these other parameters affect the electrolytic codeposition of the particles [64].

was based on two fundamental assumptions:

the next five stages and is schematically shown in Figure 5.

in the metal matrix.

164 Electrodeposition of Composite Materials

ings.

electrolyte.

**5.** The particles are trapped into the coating by the reduction of the ions adsorbed on their surface and the growth of the metallic matrix begins.

The model was constructed assuming the steady-state conditions, so that there are no varia‐ tions in concentration, pressure, temperature, or overpotentials during the process. It was also assumed that the cathode surface could be uniformly accessible by both the ionic solution and the inert particles. Finally, it was considered that a homogeneous suspension of particles in the coating solution was maintained [63]. In the diffusion layer, the ions move toward the cathode and carry the inert particles with them; simultaneously, a certain amount of ions is adsorbed. Once on the electrode surface, the ions are reduced to meet the demands of the reduction process [64].

This model showed that the codeposition process depends on many variables, although the most important are the current density and the overpotential. These two parameters influenced all the others, except those related to the particle (the nature of the particle, its weight, and its quantity in the suspension), the hydrodynamic conditions that influence the content of incorporated particles, and the probability that the codeposition occurs [64].

However, it is necessary to consider that particles of different nature can be used and differ‐ entiate the codeposition process of inert and conductive particles. Conductive particles are generally deposited in a greater amount than the inert particles and tend to cause dendrite growth of the metal matrix [5,11,44,45]. Neither the model proposed by Celis et al. [64] nor that suggested by Guglielmi [62] included the electrical nature of the particles as an important and influent parameter to be considered in their models. However, if all parameters are considered constant, there is a high probability of codeposition of conductive particles using the same mechanism proposed by Celis et al. [64].

Similar to what has been described for the first model, the present model was also validated by a mathematic treatment and submitted to an experimental evaluation [51]. In this case, it used CuSO4 or KAu(CN)2 solutions (pH 0.3 and 4.0, respectively), in which particles of γ-Al2O3 (0.05 μm; 20.0 g L-1) were added. The conditions of the experiments are shown in Table 2. The model proved to be valid for the codeposition of composite Cu/γ-Al2O3 coatings from sulfate acid baths and for Au/γ-Al2O3 coatings from cyanide acid baths.


**Table 2.** Conditions used to produce copper and gold matrix composite coatings containing γ-Al2O3 particles [64].
