Brookhaven Instruments Corporation Technical Information

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Colloidal Stability in Aqueous Suspensions:
Two Variables
Why too much dispersant causes problems.

Abstract
Zeta potential in aqueous suspensions is a func-
tion of two variables: charge at the shear plane
and free salt ion concentration. [Free here
means not attached to the particle surface.] If a
dispersant that is added to increase the surface
charge density (increase stability) is too con-
centrated, the contribution it makes to the free
salt ion concentration is counterproductive
(promotes instability).
Introduction
Colloidal suspensions are stabilized in one of
two ways. Surface charge, naturally occurring
or added, enhances electrostatic stability. Ad-
sorption of nonpolar surfactants or polymers
enhances stability through steric stabilization.
Electrostatic stabilization gives rise to a mo-
bile, charged, colloidal particle whose electro-
phoretic mobility can be measured. Zeta poten-
tial is calculated from mobility.
The square of the zeta potential is proportional
to the force of electrostatic repulsion between
charged particles. Zeta potentials are, therefore,
measures of stability. Increasing the absolute
zeta potentials increases electrostatic stabiliza-
tion. As the zeta potential approaches zero,
electrostatic repulsion becomes small com-
pared to the ever-present Van der Waals attrac-
tion. Eventually, instability increases, which
can result in aggregation followed by sedimen-
tation and phase separation.
Electrostatic Potential Differences: Sur-
face Potential Defined
Imagine that you had two, infinitesimally small
metal probes attached to a voltmeter. Now
imagine one probe is attached to the surface of
a colloidal particle and the other one is in the
liquid in which the particle is suspended. The
reading on the meter is the electrostatic poten-
tial difference between these two points. It is
called the surface potential
o
. See Figure 1
where
o
= + 80 mV.
The y-axis in this figure also represents the
solid-liquid boundary. The x-axis, in nano-
metres, is the distance from the surface out into
the liquid, it being assumed there is no other
particle close by. There are two idealizations in
a figure like this one. First, real solid particles
are not smooth at the atomic level. They are
more like low lying, rough hills on the atomic
level. Second, the charge density on the surface
is not typically uniform, but often patchy. The
surface has lots of hydrophobic spaces charac-
terized by no charge and lots of hydrophilic
spaces characterized by charge.
Therefore, if we could attach a tiny voltmeter
probe at specific surface locations, the surface
potential would vary from place to place. But
we can neither freeze the particle motion in a
liquid nor are there probes small enough. Thus,
a cartoon like this one arises when we average
spatially (vertically) over the rough surface to
define an imaginary plane to call the surface.

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Figure 1: Electrostatic potential vs. distance
in nanometres from colloidal particle sur-
face. (Courtesy of David Fairhurst.)

In addition, we are averaging temporally over
the rotational diffusion time of the particle that
is much faster than the time to make an electro-
static measurement. Still, these idealizations
work well and have been the basis for using
zeta potential determinations to describe col-
loidal stability for more than 50 years.
Before describing the zeta potential, it is worth
noting a few special features of the curves in
Figure 1. If nothing is specifically adsorbed
onto the surface, the corresponding anions (the
suspension must be neutral overall), or the ani-
ons from added salts (or surfactants) preferen-
tially gather near the positive surface. Ther-
mally-driven diffusion increases the randomi-
zation of all ions as the distance from the sur-
face increases. The electrostatic potential dif-
ference thus decreases. Far enough away from
the surface, if the voltmeter probes are placed
in the liquid; the electrostatic potential differ-
ence is zero since the average charge density is
constant.
Depending on the sophistication of the theory
to describe what takes place close to the sur-
face, a variety of imaginary, but theoretically
useful planes or layers are defined. Here, the
simplest is shown. It is called the Stern plane.
The electrostatic potential difference is called

d
. It represents the average position of the
counterions that move with the surface.
Zeta Potential Defined
Any molecules covalently bonded to the sur-
face move with the particle when it diffuses or
is induced to move electrophoretically in an
applied electric field. When wetting, dispersing
or stabilizing agents are strongly adsorbed onto
the surface, they too move with the particle.
Counterions very near the surface, perhaps
within the first nanometre or two also move
with the particle. Finally, solvent molecules are
sometimes also strongly bound to the surface.
However, at some short distance from the sur-
face, the less tightly bound species are more
diffuse and do not move with the particle. So
another imaginary yet useful theoretical layer is
defined: the shear plane. Everything inside the
shear plane is considered to move with the par-
ticle; everything outside of the shear plane does
not. In other words, as the particle moves it
shears the liquid at this plane.
The zeta potential is defined to be the electro-
static potential difference between an average
point on the shear plane and one out in the liq-
uid away from any particles.
Zeta potential is important because, for most
real systems, one cannot measure the surface
potential. One cannot measure the zeta poten-
tial directly either; however, one can measure
the electrostatic mobility of the particles and
calculate zeta potential. Though strictly incor-
rect, it is common to hear the zeta potential
spoken of as a substitute for the surface poten-
tial. The surface potential is a function of the
surface charge density. The zeta potential is a
function of the charge density at the shear
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plane. The magnitude of the zeta potential is
almost always much smaller than the surface
potential. Even the sign of the zeta potential
can be different.
Figure 1 also shows the case of specific adsorp-
tion of an anionic dispersing agent onto the
positively charged surface. This may occur if
the hydrophobic, patchy surfaces that are un-
charged can firmly anchor the nonpolar tail of a
sufficiently long, anionic surfactant. The shear
plane is shifted further out (for simplicity, not
shown here) and is now negative. The zeta po-
tential is now negative; whereas, the original
zeta potential is positive.
Whether or not the sign of the zeta potential is
the same as that of the surface potential, it is
clear that the zeta potential is a measure of the
charge density ultimately arising from the sur-
face or species attached to it. There is another
contribution to zeta potential that is too often
ignored when trying to properly interpret col-
loidal stability.
Effect of Salt on Zeta Potential
Theories describing how the charge density
around a particle varies with distance always
use the concept of the diffuse double layer. In
the simplest theory, the electrostatic potential
decays exponentially with distance away from
the shear plane. The inverse of the decay con-
stant is a distance called the Debye double
layer thickness. It is a function of free salt ion
concentration (as embodied in the value of the
ionic strength): the higher the concentration,
the faster the decay, the smaller the double
layer thickness. At high enough salt, the double
layer collapses to the extent that the ever-
present attractive van der Waals forces over-
come the charge repulsion. This is one example
of the so-called salting out effect. Electro-
statically stabilized colloidal suspensions will
become unstable with the addition of enough
salt.

Figure 2: Effect of salt concentration on zeta
potential. (Courtesy of David Fairhurst.)

See Figure 2. The zeta potential decreases
when the concentration of free salt ions in-
creases. In the figure, c is the free salt ion con-
centration. Since c
2
>c
1
, it follows that
2
<
1
.
(For simplicity, the shift in the position of the
shear plane was not shown.)
Too Much Dispersant
Oxide surfaces often have an affinity for phos-
phates. Phosphate ions can increase surface
charge density, resulting in higher absolute zeta
potential. An example is shown in Figure 3.
Colloidal silica, SiO
2
, catalog no. 421553, ob-
tained from the Sigma-Aldrich Company is a
30% v/v aqueous suspension as received. It
was diluted about 100:1 for these measure-
ments. All the measurements were made with a
Brookhaven ZetaPALS zeta potential analyzer.
The zeta potential is approximately -30 mV di-
luted in just DI water.
When tetrasodium pyrophosphate, TSPP, is
added to water, it hydrolyzes completely to
form hydrogen phosphate. The hydrogen phos-
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phate hydrolyzes a little bit to form dihydrogen
phosphate plus hydroxide ion. For this reason,
solutions of TSPP are basic with pH around 10,
depending on the initial concentration of TSPP.
Zeta Potential vs TSPP Concentration
Concentration % wt/vol
0.0001 0.001 0.01 0.1 1 10
Z
e
t
a

P
o
t
e
n
t
i
a
l

(
m
V
)
-80
-70
-60
-50
-40
-30
-20
-10
0

Figure 3. Zeta potential of SiO
2
vs. Concen-
tration of added TSPP.

With the initial addition of TSPP, the zeta po-
tential decreases. This suggests that the hydro-
gen phosphate, the phosphate species in highest
concentration, adsorbs at the silica surface. The
negative surface charge density is increased,
and the zeta potential decreases to approxi-
mately -70 mV, a substantial change towards
greater electrostatic stability.
However, TSPP is a 4:1 electrolyte and for
every mole of TSPP added, the ionic strength
increases by a factor of 10. A lot of free ions
are created that begin to decrease the double
layer.
Initially, the decrease in the double layer thick-
ness that would result in a higher zeta potential
is insignificant compared to the effect of the
hydrogen phosphate adsorbing at the surface.
Yet, there is a competition and the two effects
strike a balance from 0.01 to 0.1% wt/vol. Be-
yond 0.1%, the particle surface is saturated and
additional TSPP now works against stability by
collapsing the double layer resulting in a sig-
nificant decrease in the zeta potential.
Clearly, for this particular distribution of SiO
2

surface areas, somewhere between 0.01 and
0.1% wt/vol is optimum for stability. Adding
more is counterproductive. Since the concen-
tration of SiO
2
in this case was 0.6% w/vol, the
optimum TSPP concentration varies from 1.7%
to 17% of the solids concentration. A rule of
thumb is 10% of the solids concentration for
the dispersant. Clearly, that rule depends on the
particle size distribution as that determines sur-
face area and coverage requirements. Yet, here,
it held up reasonably well.
Summary
Ionic dispersants can help stabilize oxide sur-
faces by adding surface charge density. Zeta
potential is a measure of the success of the ad-
dition. However, too much dispersant can be
counterproductive when the surface is saturated
and the ionic strength rises too much.

If you need more information on this subject, please con-
tact Dr. Bruce Weiner at Brookhaven Instruments.