Interdisciplinary Applied Mathematics

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is the electrophoretic mobility (in m2/(V.s)), A is the surface area of the electrode (in m2), and C is the mass concentration of the colloidal particle in the suspension (in kg/m13). For cylindrical coaxial electrodes, a closed-form expression for the yield during EPD is provided in (Avgustinik et al., 1962). For more advanced models of the EPD, the reader is referred to (Biesheuvel and Verweij, 1999).

The majority of work in EPD has been concerned with measuring the deposition rate, and maximizing film thickness and porosity of the deposited film. However, very little attention was devoted to the microscopic dynamics that give rise to the resulting morphology of the deposited layers. For a long time, the dynamics of electrophoretically deposited layers was assumed to be analogous to particle sedimentation. (Hamaker and Verwey, 1940) theorized    that    the    primary action    of    the    electric    field    was    to move

the particles toward the electrode and to produce a force that pressed the particles together on    the    electrode    surface,    the    same    way    gravity    acts    on

particle sedimentation. However, systematic experimentation has revealed new interesting physics during electrophoretic deposition (Richetti et al., 1984; Bohmer, 1996; Trau et al., 1996; Trau et al., 1997). Particle motion transverse to the applied electric field was observed close to the electrode surface, when particles do not stick to the electrode. This resulted in particle aggregation to form densely packed self-ordered planar clusters. This phenomenon is unexpected from pure electrostatic considerations, since like-charged particles repel each other. Consequently, the attractive interaction between particles must be strong enough to overcome electrostatic repulsion to facilitate the aggregation. In the following, we discuss in detail the aggregation dynamics during EPD.

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