**2.2 Deposition models**

Unlike the kinetic models regarding electrophoresis, the second step of EPD, that is the deposition, is still matter of discussion, especially for the arrangement of particles on the electrode surface. After arriving at the working electrode, particles are packed onto its surface reproducing the electrode shape. The aggregation and the arrangement of the particles on the electrode surface depend on surface chemistry of particles and on interactions between particles in suspension and between particles and substrate.

The fundamental condition for a performing EPD process is to use a stable suspension where particles are keep well dispersed in the liquid medium and can move towards the electrode without influencing or being influenced by other particles. Here, particles can be rearranged on the electrode surface during packing under the action of electric field.

Of course, from the electrical point of view, the suspension composition is critical because the presence of deflocculants, binders or dispersants influences the surface charge of particles and their electrical response.

The interactions between particles inside a liquid medium is largely described by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. When an external force exists, as the driving force of an electric field, the minimum of the energy curve is shifted towards an higher value (Fig. 5). If the applied field exerts a force so great as to overcome the mutual repulsion force, two particles coagulate. Similar phenomenon occurs when a particle moves toward an electrode in an EPD cell.

Some deposition mechanisms are proposed to explain the phenomenon of particles accumulation:


The last, proposed by Sarkar and Nicholson (Sarkar & Nicholson, 1996), is the most diffused and accepted. This theory affirms that when a positive charge moves toward an electrode together oppositely charged ions, its shell is distorted, thinning ahead and thickening behind, due to fluid dynamics. As a consequence, the particle feels a weak attraction toward another positively charged particle, so together they can move under the electric field. The EDL of the two particles is less wide than that of a single particle, so when another particle

where *i0*, current density at time *t=0,* K, the deposited mass-passed charge ratio, V, the external applied voltage, d and Dd, resistivity and density of the deposited layer,

Therefore, this resistive model is able to describe the EPD process both at regime and during the transient of the deposition current, provided that suspension contains such dispersant or binder as the electroactive chemical species are available for all the deposition time, making

Unlike the kinetic models regarding electrophoresis, the second step of EPD, that is the deposition, is still matter of discussion, especially for the arrangement of particles on the electrode surface. After arriving at the working electrode, particles are packed onto its surface reproducing the electrode shape. The aggregation and the arrangement of the particles on the electrode surface depend on surface chemistry of particles and on

The fundamental condition for a performing EPD process is to use a stable suspension where particles are keep well dispersed in the liquid medium and can move towards the electrode without influencing or being influenced by other particles. Here, particles can be

Of course, from the electrical point of view, the suspension composition is critical because the presence of deflocculants, binders or dispersants influences the surface charge of

The interactions between particles inside a liquid medium is largely described by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. When an external force exists, as the driving force of an electric field, the minimum of the energy curve is shifted towards an higher value (Fig. 5). If the applied field exerts a force so great as to overcome the mutual repulsion force, two particles coagulate. Similar phenomenon occurs when a particle moves

Some deposition mechanisms are proposed to explain the phenomenon of particles

The last, proposed by Sarkar and Nicholson (Sarkar & Nicholson, 1996), is the most diffused and accepted. This theory affirms that when a positive charge moves toward an electrode together oppositely charged ions, its shell is distorted, thinning ahead and thickening behind, due to fluid dynamics. As a consequence, the particle feels a weak attraction toward another positively charged particle, so together they can move under the electric field. The EDL of the two particles is less wide than that of a single particle, so when another particle

interactions between particles in suspension and between particles and substrate.

rearranged on the electrode surface during packing under the action of electric field.

�(�) � ����� (6)

respectively. This equation at short deposition time is approximated by:

deposition a diffusive control process.

particles and their electrical response.

toward an electrode in an EPD cell.




accumulation:

**2.2 Deposition models** 

is approaching, it can be close enough to interact through van der Waals attractive forces and so coagulates. Similar mechanism occurs at the electrode surface where the high particles concentration allows the formation of a particles deposit.

Fig. 5. Potential energy vs. separation distance for particles in absence () and in presence (- - -) of an electric field.

This model was integrated by Fukada (Fukada et al., 2004) with a further consideration based on the experimental observation of De (De & Nicholson, 1999). According to De, Fukada verified that H+ are depleted at the cathode because of particle discharge, through the reaction:

$$H\_{\text{x=co}}^{+} \xrightarrow{transport \, process} H\_{\text{x=0}}^{+} + e^{-} \xrightarrow{charge \, transfer} \frac{1}{2}H\_{2} \tag{7}$$

This implies an increase of local pH toward the isoelectric point and then the coagulation is facilitated. Fukada found an analytical expression for the variation of the H+ concentration with time, validated by experimental results for alumina suspension in ethanol. This expression, generally suitable for suspensions containing H+ or H3O+, shows that the steady state with respect to diffusion and charge transfer of H+ ions corresponds to a reduction of zeta-potential at the cathode and consequently to coagulation.

Other deposition mechanisms, mentioned above, although explain experimental results in some conditions, are not valid in general. In fact, flocculation by particles accumulation suggests a deposit formation by electrophoresis similar to gravitation, so that the pressure exerted by the arriving particles at the electrode makes the particles close to form a deposit, overcoming the repulsion forces between particles. This hypothesis does not explain why the deposition occurs on a membrane which does not act as an electrode.

Similarly, particles charge neutralization at the electrode suggests the charged particles are neutralized by the contact with the electrode surface, but it does not explain the deposition mechanism when the deposit is thicker than a monolayer.

With respect to electrochemical coagulation of particles, the hypothesis is that an increase of electrolyte concentration around particles produces a reduction of the repulsion between particles near the electrode, where particles can coagulate. However, time required to have an increased electrolyte concentration is not negligible, experimentally estimated as

Ceramic Coatings Obtained by Electrophoretic Deposition:

on the quality of the deposit.

based on silicon carbide and Nextel 720 fibres.

density and the quality of coatings.

Fundamentals, Models, Post-Deposition Processes and Applications 53

thickness is lower than a critical value which depends on the powders used for deposition. Van der Biest (Van der Biest et al., 2004) obtained coatings on stainless steel with WC-5Co, Al2O3, TiC, and TiB2 powders, having an average particle size and a surface area equal to 1, 0.3, 2, and 1.5-2 µm, and 2.47, 10, 1-2 and 0.5-1.5 m2/g, respectively. The thickness below which no cracking was observed was 125, 316 and 56 µm, for the first three powders, whereas surprisingly a layer 5 mm thick was deposited without observing cracks in the case of TiB2. This result supports the influence of the powder characteristics

Generally, an EPD coating is deposited on a metal substrate that can be non resistant to high temperature which is necessary to sinter ceramics. Two approaches exist to limit damages of substrate: to use some method to lower the sintering temperature, such as powders with a fine grain or a low melting additive, or to use a different sintering treatment, such as microwave or irradiation. In the following, some of the methods cited before are reported. In order to lower the sintering temperature, a first stratagem that could be used is the choice of precursors suitable to form a ceramic material. Some examples were those of Boccaccini (Boccaccini et al., 1996, 1997) and Kooner (Kooner et al., 2000) who prepared EPD sols based on boehmite (-AlOOH), fumed amorphous silica, and fumed -alumina with appropriate concentrations, as precursors of mullite. Mullite has a number of attractive properties for high-temperature structural applications, but its sintering temperature is higher than 1600°C. The use of nano-particles and fine mullite seeds lowered the sintering temperature by up to 1300-1400°C, making possible the formation of mullite matrix by EPD in fabrics

Reaction bonding (RB) is a forming technique developed to produce near net-shape ceramics and to overcome problems caused by shrinkage during sintering. It consists of introducing some elements or compounds that, by reacting with an oxidant or reducing atmosphere at a temperature higher than room temperature, can produce a ceramic matrix. Aluminium particles were added to PSZ suspensions by Wang (Wang et al., 2000b; Wang et al., 2002). During heat treatment in air at low temperature (600°C), metal powder was converted to nanometer sized oxide crystals, that subsequently were sintered and bonded to PSZ at 1200°C. The volume expansion associated with the AlAl2O3 reaction partially compensated the sintering shrinkage. The combined use of EPD with the reaction bonding process allowed to fabricate crack-free and relatively dense ceramic coatings, maintaining the sintering temperature lower than that usual one (1350-1500°C). However, as the oxidation of the Al powder in the green form is affected by the thermal processing profile, the oxidation and sintering temperature has to be appropriately chosen to optimise the

Another candidate for reaction bonding is ZrN due to its low reaction temperature. Baufel (Baufel et al., 2008) utilised a suspension with zirconia and zirconium nitride to obtain an EPD coating on Ni alloys. Two different contents of ZrN were mixed together with YSZ in ethanol and milled in order to reduce the grain size of powders. After deposition and drying in ambient conditions, a heat treatment was performed in air at 1000 °C for 6 h. In XRD spectra, the treated samples showed only pronounced peaks of zirconia without evidence of ZrN peaks, so they concluded that all ZrN transformed into zirconia, within the detection limit of XRD. As a result, combining EPD and reaction bonding, Baufel obtained zirconia

inversely proportional to the square of applied voltage. Moreover, this mechanism is invalid when there is no increase of electrolyte concentration near the electrode.

Recently, new models considering particles flow from an electro-dynamic point of view are developed (Guelcher et al., 2000; Ristenpart et al., 2007). Experimental results of Guelcher confirmed a numerical prediction of clustering of colloidal particles deposited in a DC electric field by considering an electro-osmotic particles flow. By analysing the long-range attraction force intra-particles, Ristenpart demonstrated the flow direction of a particle depends on the sign of its dipole coefficient. Under particular conditions, the electro-osmotic component and the electrohydrodynamic component of flow can have the same direction and so can produce aggregation.

This overview demonstrates that the discussion on models and mechanisms of electrophoresis and deposition of ceramic particles in presence of an electric field is still open, and that many efforts have been made for some decades, from Hamaker to today, to explain and understand the large amount of experimental results.
