Determination of the zeta potential of inorganic colloidal systems
by the ESA (electrokinetic sonic amplitude) effect
Theory:
Besides the particle sizing and zeta potential methods, one can find today a very
recent technique: the electroacoustic method. When a high frequency sound wave
moves through a colloidal suspension it causes the particles move backwards and
forwards at the same frequency as the wave. Even at frequencies of the order of 1
MHz, this particle motion can be detected because it gives rise to an electrical signal.
The signal arises because, in addition to the (very small) motion of the particle, there
is a larger movement of the ions in the double layer (Figure 1), the fluid can indeed
respond to the pressure wave more quickly than the particle. (The particle's inertia
makes it slower to respond). This generates a small dipole and the presence of many
such dipoles in the suspension, all pointing in the same direction, creates a
macroscopic electric field which can be detected by placing two electrodes in the
suspension. The so-called colloid vibration potential has been known for half a
century
but
has
been
exploited
with
difficulty.
Fig. 1: Colloidal particles, with their diffuse double layers, in a sound wave. The wave causes both the
particles and their surrounding layers to move as indicated by the arrows. The larger movement of the
charge in the double layer causes a dipole to be set up and the sum of a large number of those
dipoles (all pointing in the same direction) generates a measurable potential difference.
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More recently (since the mid 1980s) it has been shown that the opposite effect also
occurs: if an alternating electric field is applied to a colloidal suspension it generates
a sound wave of the same frequency, just like a piezoelectric crystal. That is called
the electrokinetic sonic amplitude (ESA) effect. The method is based on the fact
that there is a phase lag between the applied signal and the resulting response
because of the inertia of the particles. The bigger the inertia of the particles, the more
difficult it is for them to follow the electrical signal. The ions in the surrounding double
layer, however, are able to keep up with the signal even at 15 MHz. By measuring
the phase lag as a function of the frequency of the applied field it is possible to
determine the particle size and hence from the magnitude of the ESA signal, the zeta
potential.
The great advantage of the technique is that there are no limits to dilute suspensions.
In his 19881) paper O'Brien derived a formula linking dynamic mobility to particle size
and zeta potential.
The determination of the particle size and zeta potential from the ESA-spectrum is in
principle a two-step process: first the dynamic mobility spectrum is calculated from
the ESA, and then the determination of size and charge follows from that spectrum.
In fact the determination occurs by taking the Fourier Transformation for a sinusoidal
applied voltage. If the frequency of the field is high enough to cause significant inertia
forces, the particle will lag behind the field. If the inertia forces are significant there
will be a time delay t between the applied field and the particle motion. The applied
field is represented as the real part of E0eit and the particle velocity as V0eit.
If the applied field strength is small, V0 will be proportional to E0.
For spherical particles this relationship takes the simple form:
V0 = DE0
(1)
This is the relation which defines the dynamic mobility D. From this definition it
follows that D is a complex quantity with magnitude V/E and with argument t radii.
As the applied frequency tends to zero, the time delay between the field and particle
motion diminishes and D becomes a real quantity, equal to the electrophoretic
mobility  defined for a static applied field.
The assumed linear relation (equ.1) will not be valid if the applied field strength is too
large. The particle velocity-and so the ESA-will then be a non-linear function of field
strength.
2
For a spherical particle which has a very thin double layer compared to the radius,
O'Brien has shown that the dynamic mobility is given by a modified form of the
Smoluchowsky equation:
D = (/3) G (a2/)
(2)
Here a represents the particle radius,  the viscosity,  the kinematic viscosity, and 
the zeta potential. The quantity  is related to the double-layer conductance. The
factor G represents the effect of inertia forces on the dynamic mobility (correction
factor).
With the device used for that experiment (field ESA), only the measurement of the
zeta potential is possible.
1) R.W.,O'Brien,R.W.,J.Fluid
2)
Mech. 190 (1988), 71
R.W. O’Brien, D.W. Cannon, W.N. Rowlands, J. Coll. Interf. Sci. 173, (1995), 406-418
Experimental part:
Chemicals: TiO2-Dispersion (2%), kaolin dispersion (2%), pH-buffer for calibration of
the pH-electrode, 1M NaOH, 1M HCl, aqueous solution of the polycation
poly(diallyldimethylammonium chloride) (PDADMAC-1% by weight)
Procedure:
1) Determine the dependence of zeta potential on the pH of a TiO 2-dispersion in the
following way:
-
Give 250 ml of a 2%(by weight) TiO2-dispersion in the cell and add defined
amounts of 1M HCl to the TiO2-dispersion! Measure after 3 min stirring
(equilibrium!) pH and zeta potential.
Volume of HCl to be added: 0.1 ml, 0.1 ml, 0.1 ml, 0.3 ml, 0.6 ml, 0.6 ml, 0.6
ml, 1 ml, 3.5 ml
Measure 3 times after each dropping and use for the following discussion the
average values.
2) Determine the dependence of the zeta potential of a kaolin dispersion on the
addition of a cationic charged polymer in the following way:
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-
Give 250 ml of a 2%(per weight) kaolin-dispersion in the cell and add defined
amounts of the polymer solution to the kaolin-dispersion! Measure after 3 min
stirring (equilibrium!) pH and zeta potential.
Volume of PDADMAC to be added: 0.1 ml, 0.1 ml, 14 x 0.5 ml, 3 x 1.0 ml
Measure 3 times after each dropping and use for the following discussion the
average values.
Discussion:
1) Plot the zeta potential versus the pH and discuss the resulting curve!
2) Plot the zeta potential and the pH versus polymer concentration and determine
the isoelectric point! What is the surface charge density on the kaolin regarding
negative charges (in millimoles of negative univalent charges per gram of clay)?
Convert this to C cm-2 assuming that the clay has a surface area of 17.5 m² g-1.
(charge density for PDADMAC: 6.192 x 10-3 mol ionic groups/ g polymer)
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