Measuring the electrical field drop over a deposit during electrophoretic deposition

Problem statement

To predict the yield of deposition during electrophoretic deposition, the mass balance law of Hamaker is generally accepted to describe the kinetics of the EPD process.

[1]

with Y the yield (g), t the deposition time (s), µ the electrophoretic mobility (m²V^-1s^-1), E the electric field strength (V/m) at the deposition front, c the solids loading (g/m³) of the powder in suspension, S the electrode surface (m²), f is a factor which takes into account that not all powder brought to the electrode is incorporated in the deposit (f = 1 or less).

The value of the electric field strength E has to be known to solve equation [1]. E depends on the potential drops over the suspension, deposit and electrodes. Most authors claim the presence of a resistant deposit but have not measured it. Therefore, a procedure is explained here on how to measure possible potential drops during EPD.

Related article: G. Anné, K. Vanmeensel, J. Vleugels, O. Van der Biest, Influence of the suspension composition on the electric field and deposition rate during electrophoretic deposition, Colloids and Surfaces A: Physicochemical Engineering Aspects, 245 (2004) 35–39. (PDF)

Theory

The electrical field strength can be determined by solving an equivalent electrical scheme for the resistivity of the suspension and the deposit. The applied voltage U, is consumed in three steps: a potential drop at each electrode and an ohmic potential drop over the suspension. Moreover, during electrophoretic deposition, a deposit forms at one of the electrodes, and in principle, the ohmic drop over the deposit can differ from the ohmic drop over the suspension (fig. 1):

[2]

with d₁ the thickness of the deposit (m), r_dep the resistivity of the deposit (W/m), d the distance between the electrodes (m), r_susp the resistivity of the suspension (Wm). I is the current passing through the deposition cell (A). DU₁ and DU₂ are the potential drops over the electrodes (V).

Fig. 1. Schematic of the equivalent electrical circuit of an EPD cell.

From this electrical circuit the electrical field strength (E) in the suspension can be calculated by:

[3]

with I the current passing through the cell (A), L the specific conductivity of the cell (S/m) and S the electrode surface (m²).

The electric field strength can be calculated from this expression by measuring the current and conductivity as function of time during EPD.

Experimental procedure

Electrophoretic deposition at constant voltage can be performed in a set-up as schematically presented in Fig. 2. The system is composed of a suspension flow-through deposition cell and a suspension circulation system driven by a peristaltic pump. During deposition, the cell current should be automatically recorded, whereas the conductivity of the suspension has to be monitored by a conductivity electrode in the suspension circulating system outside the deposition cell to avoid interference from the applied electric field in the cell. In this way, the relationship between the conductivity of the suspension and the current in the deposition cell can be determined by eq. [3].

Fig. 2. Schematic view of the EPD set-up .

Results

Current and suspension conductivity measurements during EPD of Al₂O₃ powder from different organic suspensions revealed that the suspension composition determines whether a potential drop is generated at the deposition electrode or not.

An electrical resistive layer was formed during electrophoretic deposition of Al₂O₃ from ethanol with HNO₃, HCl, polyethyleneimine or CH₃COOH addition, whereas no potential drop was observed when depositing from a methylethylketone (MEK) + butylamine suspension. Fig. 3 shows the evolution of the electrical field strength during EPD.

In this way, a relationship can be found between the yield of deposition and the magnitude of the potential drop at the deposition electrode.

The experimental observations on different organic solvent systems also clearly illustrate that the electrophoretic deposition behaviour from one well defined suspension should not be generalised to other solvent-additive systems.

Fig. 3. The E-field strength, calculated according to eq. [3] as function of time for the ethanol with HCl, HNO₃, CH₃COOH or PEI and a MEK with n-butylamine suspensions.

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