**2. Theoretical models of composites electrodeposition**

#### **2.1. Models neglecting the hydrodynamics of fluids**

In 1972 Guglielmi [27] proposed the first mechanism on electrocodeposition of inert particles in the metal matrix, and later this mechanism has been adopted by various authors. The model proposed by Guglielmi does not consider mass transfer.

According to this mechanism the process involves a two-step mechanism, as follows;


The loose adsorption coverage, a ratio of the area covered by loosely adsorbed particles to the total electrode area, was expressed in terms of the concentration of suspended particles using the classical Langmuir adsorption isotherm. For the strong adsorption rate, the volume of particles strongly adsorbed was given by a Tafel-type exponential relationship at high over potentials that depended on kinetic constants. The volume of metal electrodeposited was obtained by Faraday's law. Thus, the volume fraction of incorporated particles was then formulated as a function of the bulk concentration and the electrode over potential. From this model the volume fraction of incorporated particles, α′, can be mathematically expressed by:

$$\frac{\alpha^{\prime}}{1 - \alpha^{\prime}} = \frac{zF\rho\_{m}V\_{0}}{M\_{m}i\_{0}}e^{(B-A)}\frac{KC\_{p,b}}{1 + KC\_{p,b}}\tag{1}$$

where Mm is the atomic weight, *ρ*<sup>m</sup> is and the density of electrodeposited metal respectively, *i*0 the exchanging current density, z the valence of the electrodeposited metal, F the Faraday constant, η the electrode reaction over potential, C p, b the particle concentration in the bulk electrolyte. *k* is the Langmuir isotherm constant, which is mainly determined by the intensity of interaction between particles and cathode. The parameters *V*<sup>0</sup> and B are related to particle deposition, and they play a symmetrical role with the parameters. In addition*, i*0 and A are related to metal deposition.

In 1987, in order to overcome the shortcoming in the Guglielmi's model Celis et al. [28] proposed another model. The model consists of five consecutive steps:


**•** Capability of manufacturing nanostructured multi-component films.

**•** Can be used for deposition of ceramics, glasses, polymers, composites.

**•** This process avoids the problems associated with high temperature and high pressure

Research into the preparation of nanocomposite coatings, by electrochemically co- deposition of fine particles with metal from electrolytic solutions, has been investigated by numerous

As in the case of micro-composites, nanocomposite materials can be classified, according to

**•** Metal Matrix Nanocomposites (MMNC) such as Cr/Al2O3 [13], Ni/Al2O3 [14], Co-TiO2 [15],

**•** Polymer Matrix Nanocomposites (PMNC), such as Thermoplastic/thermoset polymer/

Nanocomposite materials have been extensively investigated in bulk and thin film forms because of their wide range of applications, starting from traditional industries, such as general mechanics and automobiles, paper mills, textiles, and food industries, to high- technology industries, such as microelectronics and magnetoelectronics [24]. In addition, the applications of nanocomposite coatings include wear and abrasion-resistant surfaces, lubrication, high hardness tools, dispersion-strengthened alloys, and protection against oxidation and hot corrosion. It has been also used to produce high surface area cathodes that have been used as

In 1972 Guglielmi [27] proposed the first mechanism on electrocodeposition of inert particles in the metal matrix, and later this mechanism has been adopted by various authors. The model

electro catalysts for hydrogen electrodes in industrial water electrolysis [25, 26].

**•** Ceramic Matrix Nanocomposites (CMNC); such as Al2O3/ZrO2 [19], ceramic/CNT [20],

**•** Reduction of waste often encountered in dipping or spraying techniques [5, 6].

**•** Rigid control of the composition and microstructure of deposit.

**•** High purity of deposited materials.

2 Electrodeposition of Composite Materials

**•** Low cost of equipment and materials.

**•** Easy to be scaled up to industry level.

their matrix materials, in three different categories;

Zn-Ni/ TiO2 [16], Al/CNT [17], Mg/CNT [18].

layered silicates [21], polyester/ Fe2O3 [22], polyester/TiO2 [23].

**2. Theoretical models of composites electrodeposition**

**2.1. Models neglecting the hydrodynamics of fluids**

proposed by Guglielmi does not consider mass transfer.

processing.

authors [7-12].

**•** Applicable to substrates of complex shape.


In Celis model, an equation relating weight of particle (Wp), with the weight increase per unit time and surface area (∆Wp) due to particle incorporation. The weight fraction of particles embedded in percentage is;

$$\frac{\Delta W\_p}{\Delta W\_m + \Delta W\_p} \ge 100\tag{2}$$

One of the limitations of this model is that the data needed for probability coefficient are not available [29].

In 1995, a theoretical model was proposed by Fransaer et al. [30] to describe the variations in the flow of current to disk electrodes caused by a finite number of spherical and probate particles. They developed a boundary collocation method to calculate the resistance variations and the influence on current in the presence of particles and in their absence. The increase in resistance to the flow of particles was measured as a function of the diameter of the particle. The resistance is increased by larger particles to a greater degree than smaller particles. The primary current distribution around a particle was plotted as a function of the aspect ratio of the particle. The position of the particle was also determined, from its influence on the current as it flows past the electrode.
