Page 149 - Book Hosokawa Nanoparticle Technology Handbook

3.2 SINGLE NANOPARTICLE MOTION IN FLUID FUNDAMENTALS
(b) Smoluchowski equation
When the double layer is very thin compared with the
particle radius, a 1/ , the double layer is effectively
flat and may be treated as such. Under those condi-
tions, the forces imparted to the liquid by the applied stationary plane
electric field are transmitted to the particle as the liq-
uid flows along its surface. The electrophoresis is
given by

u r0 (3.2.29) Figure 3.2.5

The electro-osmosis in a quartz cell for zeta potential
measurement.
Smoluchowski equation is applicable in aqueous
media.
is observed in the wide range of pH. The magnitude
(c) Henry equation of the electro-osmotic mobility is usually much larger
Henry showed that the two equations could be recon- than the mobility of other species. As a result, the
ciled by taking account of the effect of the particle electro-osmotic flow carries any species toward cath-
shape and size on the electric field. His equation is ode through the capillary regardless of the polarity of
surface charge of the species. This phenomenon has
2 f ( a) been utilized to separate ionic species by their charge
u r 0 (3.2.30) and frictional forces. This technique is well-known as
3 capillary electrophoresis. More recently, the electro-
osmosis has been applied to the transportation,
where the function f( a) varies as 1 f( a) 3/2 for manipulation and patterning of nano particles [1].
0 a . Figure 3.2.5 shows the schematic structure of an elec-
The equations of electrophoresis are very important trophoresis cell for the zeta potential measurement. It is
since they are connected to the electrophoretic mobil- composed of a quartz glass capillary with electrodes at
ity with the -potential. The conventional method for both ends. The capillary is sealed by valves to form a
measuring zeta potential is to observe the migration closed tube. The inside wall of the cell has negative
of particles in a liquid with a microscope and measure charge and this leads to a liquid flow in the cell due to
their velocity using a stopwatch. The technique of electro-osmosis. In a closed capillary, the fluid flow
laser Doppler velocimetry (LDV) has mostly replaced along the cell wall is cancelled at a special position
this laborious measurement procedure. called the stationary layer or stationary plane because of
the return flow in the center of the cell. Measurements
(2) Electro-osmosis of the particle’s motion at this position give the true
Electro-osmosis is the motion of liquid which is adja- electrophoretic mobility. The position of the stationary
cent to a flat, charged surface under the influence of plane is dependent on the cell geometry and can be cal-
an electric field applied parallel to the surface. If the culated for symmetrical shapes of capillary.
surface is negatively charged, there will be a net
excess of positive ions in the adjacent liquid and as (3) Dielectrophoresis
they move under the influence of the applied field The motion of a particle, with a dielectric permittivity
they draw the liquid along them. different from that of a surrounding liquid medium, is
The electro-osmotic velocity v eo under an electric termed “dielectrophoresis”. This force does not
field strength E is defined as follows: require the particle to be charged and all particles
exhibit dielectrophoretic activity in the presence of
v u E (3.2.31) electric fields. However, the strength of the force
eo eo
depends strongly on the dielectric properties of the
particles and the medium, on the particle shape and
where u eo is the electro-osmotic mobility which is size, as well as on the frequency of the electric field.
given by Consequently, fields of a particular frequency can
manipulate particles with great selectivity. This has

u r 0 allowed, for example, the separation of cells or the
eo
(3.2.32) orientation and manipulation of nanoparticles and
nanowires. The dielectrophoretic behavior of a single
In a fused silica capillary whose inside walls is nega- particle has been characterized using a hyperbolic
tively charged, considerably fast flow toward cathode quadrupole microelectrode [2].

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