Page 391 - Organic Electronics in Sensors and Biotechnology

368 Chapter Ten

like charge (co-ions) are repelled from the surface. This leads to the
formation of a net electric charge of one sign on one side of the interface
and a charge of opposite sign on the other side, giving rise to what is
called the electrical double layer.
10.2.4 Parameters Influencing EPD
There are two groups of parameters that determine characteristics of the
electrophoretic process; one is related to the nature of the suspension and
the other to the physical parameters, such as the electrical nature of the
electrode and the amount and time for which the voltage is applied for
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the deposition. Hamaker and Avgustnik et al. were the first to describe
the correlation between the amount of material deposited during EPD
and the different influencing parameters. Hamaker’s law relates the
deposit yield (w) to the electric field strength E, the electrophoretic mobil-
ity μ, the surface area of the electrode A, and the particle mass concentra-
tion in the suspension C through the following equation:
t 2
w = ∫ μ EACdt (10.4)
t
1
Avgustinik’s law is based on cylindrical, co-axial electrodes, and
the electrophoretic mobility has been expanded and is represented in
terms of permittivity ε, the zeta potential ξ, and the viscosity of the
suspension η:
lEεξ Ct
w = (10.5)
3ln( ab η)/
where l = length of the deposition electrode
a = radius of the deposition electrode
b = radius of the co-axial counter electrode (b > a)
Biesheuval and Verweij have considered three different phases
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during the deposition process, namely, solid phase, suspension phase,
and phase having negligible or no solid particles. Both the deposit phase
and the particle-free liquid phase grow at the expense of the suspension
phase. By considering the movement of the boundary between the
deposit and the suspension phases with time along with the continuity
equation and expression for velocity of particles in the suspension, they 20
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derived the following equation based on that of Avgustinik et al. :
2πμ lEC φ
w = d . s t (10.6)
/
ln( ab) φ − φ
d s
where φ = volumetric concentration of particles in suspension
s
φ = volumetric concentration of particles in deposit
d
C = mass concentration of particles in the deposit
d
μ = electrophoretic mobility = εξ/6πη