Uma introdução ao conceito de "potencial zeta", em uma nota técnica produzida pela Malvern, que é a fabricante do equipamento Zetasizer Nano Series.

1. Zeta Potential
An Introduction in 30 Minutes
2
Introduction deflocculation. Figure 1 schematically VA = -A/(12 π D )
represents some of these processes.
Zeta potential is a physical property where A is the Hamaker constant and
which is exhibited by any particle in D is the particle separation. The
suspension. It can be used to repulsive potential VR is a far more
optimize the formulations of complex function.
suspensions and emulsions.
Knowledge of the zeta potential can VR = 2 π ε a ζ2 exp(-κD)
reduce the time needed to produce where a is the particle radius, π is the
trial formulations. It is also an aid in solvent permeability, κ is a function of
predicting long-term stability.
the ionic composition and ζ is the zeta
potential.
Colloid Science
Three of the fundamental states of
matter are solids, liquids and gases. If
one of these states is finely dispersed Figure 1: Schematic diagram
in another then we have a ‘colloidal showing various mechanisms where
system’. These materials have special stability may be lost in a colloidal
properties that are of great practical dispersion
importance.
There are various examples of Colloidal Stability and
colloidal systems that include DVLO Theory
aerosols, emulsions, colloidal
suspensions and association colloids. The scientists Derjaguin, Verwey,
Landau and Overbeek developed a
In certain circumstances, the theory in the 1940s which dealt with
particles in a dispersion may adhere Figure 2(a): Schematic diagram of the
the stability of colloidal systems.
to one another and form aggregates variation of free energy with particle
DVLO theory suggests that the
of successively increasing size, which separation according to DVLO theory.
stability of a particle in solution is
may settle out under the influence of dependent upon its total potential
gravity. An initially formed aggregate energy function VT. This theory
is called a floc and the process of its recognizes that VT is the balance of DVLO theory suggests that the
formation flocculation. The floc may or several competing contributions: stability of a colloidal system is
may not sediment or phase separate. determined by the sum of these van
If the aggregate changes to a much VT = VA + VR + VS der Waals attractive (VA) and
denser form, it is said to undergo electrical double layer repulsive (VR)
VS is the potential energy due to the
coagulation. An aggregate usually forces that exist between particles as
solvent, it usually only makes a
separates out either by sedimentation they approach each other due to the
marginal contribution to the total
(if it is more dense than the medium) Brownian motion they are undergoing.
potential energy over the last few
or by creaming (if it less dense than This theory proposes that an energy
nanometers of separation. Much more
the medium). The terms flocculation barrier resulting from the repulsive
important is the balance between VA
and coagulation have often been used force prevents two particles
and VR, these are the attractive and
interchangeably. Usually coagulation approaching one another and
repulsive contributions. They
is irreversible whereas flocculation adhering together (figure 2 (a)). But if
potentially are much larger and
can be reversed by the process of the particles collide with sufficient
operate over a much larger distance
energy to overcome that barrier, the
1 Zetasizer Nano series technical note MRK654-01

2. attractive force will pull them into adsorbs, the thickness of the Origins of Surface Charge
contact where they adhere strongly coating is sufficient to keep
and irreversibly together. particles separated by steric Most colloidal dispersions in aqueous
repulsions between the polymer media carry an electric charge. There
Therefore if the particles have a layers, and at those separations are many origins of this surface
sufficiently high repulsion, the the van der Waals forces are too charge depending upon the nature of
dispersion will resist flocculation and weak to cause the particles to the particle and it’s surrounding
the colloidal system will be stable. adhere. medium but we will consider the more
However if a repulsion mechanism important mechanisms.
does not exist then flocculation or • Electrostatic or charge
coagulation will eventually take place. stabilization - this is the effect on Ionisation of Surface Groups
particle interaction due to the
Dissociation of acidic groups on the
distribution of charged species in
surface of a particle will give rise to a
the system.
negatively charged surface.
Each mechanism has its benefits for Conversely, a basic surface will take
particular systems. Steric stabilization on a positive charge (figure 4). In both
is simple, requiring just the addition of cases, the magnitude of the surface
a suitable polymer. However it can be charge depends on the acidic or basic
difficult to subsequently flocculate the strengths of the surface groups and
system if this is required, the polymer on the pH of the solution. The surface
can be expensive and in some cases charge can be reduced to zero by
the polymer is undesirable e.g. when suppressing the surface ionisation by
decreasing the pH in case of
negatively charged particles (figure
Figure 2(b): Schematic diagram of the 4(a)) or by increasing the pH in the
variation of free energy with particle case of positively charged particles
separation at higher salt concentrations (figure 4(b)).
showing the possibility of a secondary
minimum.
If the zeta potential is reduced (e.g. in
high salt concentrations), there is a Figure 3: Steric and electrostatic
possibility of a “secondary minimum” stabilization mechanisms of
being created, where a much weaker colloidal dispersions
and potentially reversible adhesion
between particles exists (figure 2 (b)).
These weak flocs are sufficiently a ceramic slip is cast and sintered, the
stable not to be broken up by polymer has to be ‘burnt out’. This Figure 4(a): Origin of surface
Brownian motion, but may disperse causes shrinkage and can lead to charge by ionisation of acidic
under an externally applied force such defects. groups to give a negatively
as vigorous agitation. charged surface
Electrostatic or charge stabilization
Therefore to maintain the stability of has the benefits of stabilizing or
the colloidal system, the repulsive flocculating a system by simply
forces must be dominant. How can altering the concentration of ions in
colloidal stability be achieved? There the system. This is a reversible
are two fundamental mechanisms that process and is potentially
affect dispersion stability (figure 3): inexpensive.
• Steric repulsion - this involves It has long been recognised that the
polymers added to the system zeta potential is a very good index of
Figure 4(b): Origin of surface
adsorbing onto the particle the magnitude of the interaction
charge by ionisation of basic
surface and preventing the between colloidal particles and
groups to give a positively charged
particle surfaces coming into measurements of zeta potential are
surface
close contact. If enough polymer commonly used to assess the stability
of colloidal systems.
2 Zetasizer Nano series technical note MRK654-01

3. Differential loss of ions from
the crystal lattice
As an example, consider a crystal of
silver iodide placed in water. Solution
of ions occurs. If equal amounts of
Ag+ and I- ions were to dissolve, the
surface would be uncharged. In fact
silver ions dissolve preferentially, Figure 6(b): Origin of surface
leaving a negatively charged surface charge by specific adsorption
(figure 5). If Ag+ ions are now added of an anonic surfactant. R =
the charge falls to zero. Further hydrocarbon chain
addition leads to a positively charged
surface. The Electrical
Double Layer
The development of a nett charge at
the particle surface affects the
distribution of ions in the surrounding
interfacial region, resulting in an
increased concentration of counter Figure 7: Schematic representation of
ions, ions of opposite charge to that of zeta potential
the particle, close to the surface. Thus
an electrical double layer exists round particles coming together and
Figure 5: Origin of surface charge
each particle. flocculating.
by differential solution of silver
ions from a AgI surface
Zeta Potential The general dividing line between
stable and unstable suspensions is
Adsorption of charged species The liquid layer surrounding the generally taken at either +30 or -30
(ions and ionic surfactants) particle exists as two parts; an inner mV. Particles with zeta potentials
region (Stern layer) where the ions
Surfactant ions may be specifically more positive than +30 mV or more
are strongly bound and an outer
adsorbed on the surface of a particle, negative than -30 mV are normally
(diffuse) region where they are less
leading, in the case of cationic considered stable. However, if the
firmly associated. Within the diffuse
surfactants, to a positively charged particles have a density different form
layer there is a notional boundary
surface (figure 6(a)) and, in the case the dispersant, they will eventually
inside which the ions and particles
of anionic surfactants, to a negatively sediment forming a close packed bed
form a stable entity. When a particle
charged surface (figure 6(b)). (i.e. a hard cake).
moves (e.g. due to gravity), ions
within the boundary move it. Those
ions beyond the boundary stay with Factors Affecting Zeta Potential
the bulk dispersant. The potential at
this boundary (surface of (1) pH
hydrodynamic shear) is the zeta In aqueous media, the pH of the
potential (figure 7). sample is one of the most important
The magnitude of the zeta potential factors that affects its zeta potential. A
gives an indication of the potential zeta potential value on its own without
Figure 6(a): Origin of surface defining the solution conditions is a
charge by specific adsorption stability of the colloidal system. If all
the particles in suspension have a virtually meaningless number.
of a cationic surfactant. R = Imagine a particle in suspension with
hydrocarbon chain large negative or positive zeta
potential then they will tend to repel a negative zeta potential. If more
each other and there will be no alkali is added to this suspension then
tendency for the particles to come the particles tend to acquire more
together. However, if the particles negative charge. If acid is added to
have low zeta potential values then this suspension then a point will be
there will be no force to prevent the reached where the charge will be
3 Zetasizer Nano series technical note MRK654-01

4. 3+
neutralised. Further addition of acid A trivalent ion such as Al will Streaming potential: the electric field
will cause a build up of positive compress the double layer to a generated when a liquid is forced to
charge. Therefore a zeta potential greater extent in comparison with a flow past a stationary charged surface
versus pH curve will be positive at low monovalent ion such as Na+.
pH and lower or negative at high pH. Sedimentation potential: the electric
There may be a point where the plot Inorganic ions can interact with field generated when charged
passes through zero zeta potential. charged surfaces in one of two particles sediment
This point is called the isoelectric distinct ways (i) non-specific ion
point and is very important from a adsorption where they have no effect Electrophoresis
practical consideration. It is normally on the isoelectric point. (ii) specific ion
When an electric field is applied
the point where the colloidal system is adsorption, which will lead to a
across an electrolyte, charged
least stable. change in the value of the isoelectric
particles suspended in the electrolyte
point. The specific adsorption of ions
are attracted towards the electrode of
A typical plot of zeta potential versus onto a particle surface, even at low
opposite charge. Viscous forces
pH is shown in figure 8. In this concentrations, can have a dramatic
acting on the particles tend to oppose
example, the isoelectric point of the effect on the zeta potential of the
this movement. When equilibrium is
sample is at approximately pH 5.5. In particle dispersion. In some cases,
reached between these two opposing
addition, the plot can be used to specific ion adsorption can lead to
forces, the particles move with
predict that the sample should be charge reversal of the surface.
constant velocity.
stable at pH values less than 4
(sufficient positive charge is present) 3. Concentration of a formulation The velocity is dependent on the
and greater than pH 7.5 (sufficient component strength of electric field or voltage
negative charge is present). Problems gradient, the dielectric constant of the
The effect of the concentration of a
with dispersion stability would be medium, the viscosity of the medium
formulation component on the zeta
expected at pH values between 4 and and the zeta potential.
potential can give information to assist
7.5 as the zeta potential values are
in formulating a product to give The velocity of a particle in a unit
between +30 and -30mV.
maximum stability. The influence of electric field is referred to as its
known contaminants on the zeta electrophoretic mobility. Zeta potential
potential of a sample can be a is related to the electrophoretic
powerful tool in formulating the mobility by the Henry equation:-
product to resist flocculation for
example. UE = 2 ε z f(κa)
3η
Electrokinetic Effects
where UE = electrophoretic mobility, z
An important consequence of the = zeta potential, ε = dielectric
existence of electrical charges on the
constant, η = viscosity and f(κa) =
surface of particles is that they
Henry’s function.
Figure 8: Typical plot of zeta potential interact with an applied electric field.
versus pH showing the position of the These effects are collectively defined The units of κ, termed the Debye
isoelectric point and the pH values as electrokinetic effects. There are length, are reciprocal length and κ-1 is
where the dispersion would be four distinct effects depending on the often taken as a measure of the
expected to be stable way in which the motion is induced. “thickness” of the electrical double
These are: layer. The parameter ‘a’ refers to the
Electrophoresis: the movement of a radius of the particle and therefore κa
charged particle relative to the liquid it measures the ratio of the particle
2. Conductivity radius to electrical double layer
is suspended in under the influence of
The thickness of the double layer (κ-1) an applied electric field thickness (figure 9). Electrophoretic
depends upon the concentration of determinations of zeta potential are
ions in solution and can be calculated Electroosmosis: the movement of a most commonly made in aqueous
from the ionic strength of the medium. liquid relative to a stationary charged media and moderate electrolyte
The higher the ionic strength, the surface under the influence of an concentration. F(κa) in this case is
more compressed the double layer electric field 1.5, and this is referred to as the
becomes. The valency of the ions will Smoluchowski approximation.
also influence double layer thickness. Therefore calculation of zeta potential
4 Zetasizer Nano series technical note MRK654-01

5. from the mobility is straightforward for electrophoresis in combination with passed to a digital signal processor 4
systems that fit the Smoluchowski M3-PALS. and then to a computer 5. The
model, i.e. particles larger than about Zetasizer Nano software produces a
0.2 microns dispersed in electrolytes The M3-PALS Technique frequency spectrum from which the
containing more that 10-3 molar salt. electrophoretic mobility and hence
The Zetasizer Nano Series uses a zeta potential is calculated. The
For small particles in low dielectric combination of laser Doppler intensity of the detected, scattered
constant media (eg non-aqueous velocimetry and phase analysis light light must be within a specific range
media), f(κa) becomes 1.0 and allows scattering (PALS) in a patented for the detector to successfully
an equally simple calculation. This is technique called M3-PALS to measure it. This is achieved using an
referred to as the Huckel measure particle electrophoretic attenuator 6, which adjusts the
approximation. mobility. Implementation of M3-PALS intensity of the light reaching the
enables even samples of very low sample and hence the intensity of the
mobility to be analysed and their scattering. To correct for any
mobility distributions calculated. differences in the cell wall thickness
PALS can give an increase in and dispersant refraction,
performance of greater than 100 compensation optics 7 are installed
times that associated with standard to maintain optimum alignment.
measurement techniques. This allows
the measurement of high conductivity
samples, plus the ability to accurately
measure samples that have low
particle mobilities, such as samples
Figure 9: Schematic illustrating dispersed in non-aqueous solvents.
Huckel and Smoluchowski's Low applied voltages can now be
approximations used for the used to avoid any risk of sample
conversion of electrophoretic mobility effects due to Joule heating.
into zeta potential Further information discussing the
techniques of laser Doppler
electrophoresis and M3-PALS can be
Measuring Electrophoretic found in various articles available on
Mobility the Malvern Instruments web-site
The essence of a classical micro-
electrophoresis system is a capillary Optical Configuration of a
cell with electrodes at either end to Zeta Potential Instrument
which a potential is applied. Particles Figure 10: Optical configuration of
move towards the electrode, their A zeta potential measurement system the Zetasizer Nano series for zeta
velocity is measured and expressed in comprises of six main components potential measurements
unit field strength as their mobility. (figure 10). Firstly, a laser 1 is used
to provides a light source to illuminate
Early methods involved the process of the particles within the sample. For
directly observing individual particles zeta potential measurements, this References
using ultra-microscope techniques light source is split to provide an Derjaguin, B.V. and Landau, L. (1941)
and manually tracking their progress incident and reference beam. The Acta Physiochim. URSS, 14, 633.
over a measured distance. This incident laser beam passes through
procedure, although still being used the centre of the sample cell 2, and Verway, E.J.W. and Overbeek, J. Th.
by many groups world wide, suffers the scattered light at an angle of G. (1948) Theory of the Stability of
from several disadvantages, not least about 13o is detected 3. When an Lyophobic Colloids, Elsevier,
that of the strenuous effort required to electric field is applied to the cell, any Amsterdam.
make a measurement, particularly particles moving through the
with small or poorly scattering measurement volume will cause the Hunter, R.J. (1988) Zeta Potential In
particles. The technique used in intensity of light detected to fluctuate Colloid Science: Principles And
Malvern’s Zetasizer Nano range of with a frequency proportional to the Applications, Academic Press, UK.
instruments is laser Doppler particle speed and this information is
5 Zetasizer Nano series technical note MRK654-01

6. Shaw, D.J. (1992) Introduction To
Colloid And Surface Chemistry,
Butterworth Heinemann, UK.
Everett, D.H. (1994) Basic Principles
Of Colloid Science, The Royal Society
of Chemistry, UK.
Ross, S. and Morrison, I.D. (1988)
Colloidal Systems and Interfaces,
John Wiley and Sons, USA.
Lyklema, J. (2000) Fundamentals of
Interface and Colloid Science: Volume
1 (Fundamentals), Academic Press,
UK.
Measuring Zeta Potential: Laser
Doppler Electrophoresis, Technical
Note available from
www.malvern.co.uk
Measuring Zeta Potential Using
Phase Analysis Light Scattering
(PALS), Technical Note available from
www.malvern.co.uk
Measuring Zeta Potential: A New
Technique, Technical Note available
from www.malvern.co.uk
Simplifying the Measurement of Zeta
Potential Using M3-PALS, Technical
Note available from
www.malvern.co.uk
Malvern Instruments Ltd
Enigma Business Park • Grovewood Road • Malvern • Worcestershire • UK • WR14 1XZ
Tel: +44 (0)1684 892456 • Fax: +44 (0)1684 892789
Malvern Instruments Worldwide
Sales and service centers in over 50 countries for details visit www.malvern.co.uk/contact
more information at www.malvern.co.uk
6 Zetasizer Nano series technical note MRK654-01