Environmental Engineering Reference
In-Depth Information
defi ned as their electrophoretic mobility,
= v/E. From measurements of electro-
phoretic mobility, the potential at the particles hydrodynamic slipping plane (or
shear plane) called zeta potential (
µ
ζ
), is calculated from:
µη
εκ
3
(6.10)
ζ
=
2
fr
(
)
where
a) is
Henry's function, which is simple and well defi ned for two extreme cases. Henry' s
function is defi ned by the Smoluchowski approximation as 3/2 for situations where
the diffuse layer thickness (Debye length, 1/
η
is the viscosity of the medium,
ε
is the dielectric constant and f(
κ
) is much smaller than the particle
radius (r), while it is defi ned by the Hűckel approximation as 1 for situations where
the Debye length is larger than the particle radius. For commercial instruments
either of the two approximations or customized values for Henry's function can be
selected. The Hűckel approximation is mainly valid in organic solvents or pure
water. The Smoluchowski approximation is not valid for NPs in water with some
ionic strength. Therefore, there have been several theories developed to more
accurately parameterize the electrokinetics of small particles in ionic media, and
these have been reviewed recently (Delgado
et al.
, 2005). In addition to the old
fashioned method of measuring particle velocity in an electrical fi eld by means of
a microscope and a stop-watch, modern instruments have been developed that use
laser doppler velocimetry (e.g. light scattering phase analysis). Zeta potential mea-
surements are very suitable to study dispersion properties and ionic strength and
pH regions of electrostatic stabilization (Figure 6.9). As a rule of thumb a colloidal
dispersion that has either a zeta potential that is less than
κ
30 mV or above 30 mV
can be considered electrostatically stable. For this particular case in Figure 6.9 that
would apply to a pH below four or above 7.5. The maximum agglomeration usually
occurs at the isoelectric point.
−
60
Isoelectric point
Stable
40
20
Unstable
0
-20
-40
Stable
-60
2
4
6
8
10
12
pH
Figure 6.9
Illustration of a typical zeta potential pH titration curve. The pH where the
zeta potential is zero is defi ned as the isoelectric point and is a characteristic of each
nanomaterial.
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