Zeta potential
Encyclopedia
Zeta potential is a scientific term for electrokinetic potential
in colloidal systems
. In the colloidal chemistry literature, it is usually denoted using the Greek letter zeta
, hence ζ-potential. From a theoretical viewpoint, zeta potential is electric potential
in the interfacial double layer
(DL) at the location of the slipping plane versus a point in the bulk fluid away from the interface. In other words, zeta potential is the potential difference between the dispersion medium and the stationary layer of fluid attached to the dispersed particle.
A value of 25 mV (positive or negative) can be taken as the arbitrary value that separates low-charged surfaces from highly-charged surfaces.
The significance of zeta potential is that its value can be related to the stability of colloidal dispersions (e.g., a multivitamin syrup). The zeta potential indicates the degree of repulsion between adjacent, similarly charged particles (the vitamins) in a dispersion. For molecules and particles that are small enough, a high zeta potential will confer stability, i.e., the solution or dispersion will resist aggregation. When the potential is low, attraction exceeds repulsion and the dispersion will break and flocculate. So, colloids with high zeta potential (negative or positive) are electrically stabilized while colloids with low zeta potentials tend to coagulate or flocculate
as outlined in the table.
Zeta potential is widely used for quantification of the magnitude of the electrical charge at the double layer. However, zeta potential is not equal to the Stern potential or electric surface potential in the double layer. Such assumptions of equality should be applied with caution. Nevertheless, zeta potential is often the only available path for characterization of double-layer properties. Zeta potential should not be confused with electrode potential
or electrochemical potential (because electrochemical reactions are generally not involved in the development of zeta potential).
.
Electrokinetic phenomena
and electroacoustic phenomena
are the usual sources of data for calculation of zeta potential.
is used for estimating zeta potential of particulates
, whereas streaming potential/current is used for porous bodies and flat surfaces.
In practice, the Zeta potential of dispersion is measured by applying an electric field across the dispersion. Particles within the dispersion with a zeta potential will migrate toward the electrode of opposite charge with a velocity proportional to the magnitude of the zeta potential.
This velocity is measured using the technique of the Laser Doppler
Anemometer
. The frequency shift or phase shift of an incident laser beam caused by these moving particles is measured as the particle mobility, and this mobility is converted to the zeta potential by inputting the dispersant viscosity and dielectric permittivity, and the application of the Smoluchowski theories (see below).
and in details in many books on colloid and interface science. There is an IUPAC Technical Report prepared by a group of world experts on the electrokinetic phenomena
.
From the instrumental viewpoint, there are two different experimental techniques:
Both these measuring techniques may require dilution of the sample. Sometimes this dilution might affect properties of the sample and change zeta potential. There is only one justified way to perform this dilution - by using equilibrium supernatant. In this case the interfacial equilibrium between the surface and the bulk liquid would be maintained and zeta potential would be the same for all volume fractions of particles in the suspension. When the diluent is known (as is the case for a chemical formulation), additional diluent can be prepared. If the diluent is unknown, equilibrium supernatant is readily obtained by centrifugation.
and electric sonic amplitude
, see reference. There are commercially available instruments that exploit these effects for measuring dynamic electrophoretic mobility
, which depends on zeta potential.
Electroacoustic techniques have the advantage of being able to perform measurements in intact samples, without dilution. Published and well-verified theories allow such measurements at volume fractions up to 50%, see reference. Calculation of zeta potential from the dynamic electrophoretic mobility requires information on the densities for particles and liquid. In addition, for larger particles exceeding roughly 300 nm in size information on the particle size required as well.
in 1903. This theory was originally developed for electrophoresis
; however, an extension to electroacoustics
is now also available. Smoluchowski's theory is powerful because it is valid for dispersed particles of any shape
and any concentration
. However, it has its limitations:
The development of electrophoretic and electroacoustic theories with a wider range of validity was a purpose of many studies during the 20th century. There are several analytical theories that incorporate surface conductivity
and eliminate the restriction of the small Dukhin number
for both the electrokinetic and electroacoustic applications.
Early pioneering work in that direction dates back to Overbeek and Booth.
Modern, rigorous electrokinetic theories that are valid for any zeta potential and often any κa, stem mostly from the Ukrainian (Dukhin, Shilov and others) and Australian (O'Brien, White, Hunter and others) schools. Historically, the first one was Dukhin-Semenikhin theory. A similar theory was created 10 years later by O'Brien and Hunter. Assuming a thin double layer, these theories would yield results that are very close to the numerical solution provided by O'Brien and White. There are also general electroacoustic theories that are valid for any values of Debye length
and Dukhin number
.
All these theories predict electrophoretic mobility and zeta potential to be equal in sign. Recent molecular dynamics simulations, though, suggest that the main contribution to the zeta potential can arise from anisotropic water dipole at the interface not included in the traditional continuum theories and that electrophoretic mobility and zeta potential may in fact be opposite in sign.
Potential
*In linguistics, the potential mood*The mathematical study of potentials is known as potential theory; it is the study of harmonic functions on manifolds...
in colloidal systems
Colloid
A colloid is a substance microscopically dispersed evenly throughout another substance.A colloidal system consists of two separate phases: a dispersed phase and a continuous phase . A colloidal system may be solid, liquid, or gaseous.Many familiar substances are colloids, as shown in the chart below...
. In the colloidal chemistry literature, it is usually denoted using the Greek letter zeta
Zeta
-Science:* Zeta functions, in mathematics** Riemann zeta function* Zeta potential, the electrokinetic potential of a colloidal system* Tropical Storm Zeta , formed in December 2005 and lasting through January 2006* Z-pinch, in fusion power...
, hence ζ-potential. From a theoretical viewpoint, zeta potential is electric potential
Electric potential
In classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...
in the interfacial double layer
Double layer (interfacial)
A double layer is a structure that appears on the surface of an object when it is placed into a liquid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The DL refers to two parallel layers of charge surrounding the object...
(DL) at the location of the slipping plane versus a point in the bulk fluid away from the interface. In other words, zeta potential is the potential difference between the dispersion medium and the stationary layer of fluid attached to the dispersed particle.
A value of 25 mV (positive or negative) can be taken as the arbitrary value that separates low-charged surfaces from highly-charged surfaces.
The significance of zeta potential is that its value can be related to the stability of colloidal dispersions (e.g., a multivitamin syrup). The zeta potential indicates the degree of repulsion between adjacent, similarly charged particles (the vitamins) in a dispersion. For molecules and particles that are small enough, a high zeta potential will confer stability, i.e., the solution or dispersion will resist aggregation. When the potential is low, attraction exceeds repulsion and the dispersion will break and flocculate. So, colloids with high zeta potential (negative or positive) are electrically stabilized while colloids with low zeta potentials tend to coagulate or flocculate
Flocculation
Flocculation, in the field of chemistry, is a process wherein colloids come out of suspension in the form of floc or flakes by the addition of a clarifying agent. The action differs from precipitation in that, prior to flocculation, colloids are merely suspended in a liquid and not actually...
as outlined in the table.
| Zeta potential [mV] | Stability behavior of the colloid |
|---|---|
| from 0 to ±5, | Rapid coagulation or flocculation |
| from ±10 to ±30 | Incipient instability |
| from ±30 to ±40 | Moderate stability |
| from ±40 to ±60 | Good stability |
| more than ±61 | Excellent stability |
Zeta potential is widely used for quantification of the magnitude of the electrical charge at the double layer. However, zeta potential is not equal to the Stern potential or electric surface potential in the double layer. Such assumptions of equality should be applied with caution. Nevertheless, zeta potential is often the only available path for characterization of double-layer properties. Zeta potential should not be confused with electrode potential
Electrode potential
Electrode potential, E, in electrochemistry, according to an IUPAC definition, is the electromotive force of a cell built of two electrodes:* on the left-hand side is the standard hydrogen electrode, and...
or electrochemical potential (because electrochemical reactions are generally not involved in the development of zeta potential).
Measurement of zeta potential
Zeta potential is not measurable directly but it can be calculated using theoretical models and an experimentally-determined electrophoretic mobility or dynamic electrophoretic mobilityDynamic electrophoretic mobility
Dynamic electrophoretic mobility is a parameter that determines intensity of electroacoustic phenomena, such as Colloid Vibration Current and Electric Sonic Amplitude in colloids. It is similar to electrophoretic mobility, but at high frequency, on a scale of megahertz...
.
Electrokinetic phenomena
Electrokinetic phenomena
Electrokinetic phenomena are a family of several different effects that occur in heterogeneous fluids or in porous bodies filled with fluid. The term heterogeneous here means a fluid containing particles...
and electroacoustic phenomena
Electroacoustic phenomena
Electroacoustic phenomena arise when ultrasound propagates through a fluid containing ions. The associated particle motion generates electric signals because ions have electric charge. This coupling between ultrasound and electric field is called electroacoustic phenomena. Fluid might be a simple...
are the usual sources of data for calculation of zeta potential.
Electrokinetic phenomena
ElectrophoresisElectrophoresis
Electrophoresis, also called cataphoresis, is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. This electrokinetic phenomenon was observed for the first time in 1807 by Reuss , who noticed that the application of a constant electric...
is used for estimating zeta potential of particulates
Particulates
Particulates – also known as particulate matter , suspended particulate matter , fine particles, and soot – are tiny subdivisions of solid matter suspended in a gas or liquid. In contrast, aerosol refers to particles and/or liquid droplets and the gas together. Sources of particulate matter can be...
, whereas streaming potential/current is used for porous bodies and flat surfaces.
In practice, the Zeta potential of dispersion is measured by applying an electric field across the dispersion. Particles within the dispersion with a zeta potential will migrate toward the electrode of opposite charge with a velocity proportional to the magnitude of the zeta potential.
This velocity is measured using the technique of the Laser Doppler
Doppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...
Anemometer
Anemometer
An anemometer is a device for measuring wind speed, and is a common weather station instrument. The term is derived from the Greek word anemos, meaning wind, and is used to describe any airspeed measurement instrument used in meteorology or aerodynamics...
. The frequency shift or phase shift of an incident laser beam caused by these moving particles is measured as the particle mobility, and this mobility is converted to the zeta potential by inputting the dispersant viscosity and dielectric permittivity, and the application of the Smoluchowski theories (see below).
Electrophoresis
Electrophoretic velocity is proportional to electrophoretic mobility, which is the measurable parameter. There are several theories that link electrophoretic mobility with zeta potential. They are briefly described in the article on electrophoresisElectrophoresis
Electrophoresis, also called cataphoresis, is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. This electrokinetic phenomenon was observed for the first time in 1807 by Reuss , who noticed that the application of a constant electric...
and in details in many books on colloid and interface science. There is an IUPAC Technical Report prepared by a group of world experts on the electrokinetic phenomena
Electrokinetic phenomena
Electrokinetic phenomena are a family of several different effects that occur in heterogeneous fluids or in porous bodies filled with fluid. The term heterogeneous here means a fluid containing particles...
.
From the instrumental viewpoint, there are two different experimental techniques:
- MicroelectrophoresisMicroelectrophoresisMicroelectrophoresis is a method of studying electrophoresis of various dispersed particles using optical microscopy. This method provides image of moving particles, which is its unique advantage....
. It has the advantage of yielding an image of the moving particles. On the other hand, it is complicated by electro-osmosisElectro-osmosisElectroosmotic flow is the motion of liquid induced by an applied potential across a porous material, capillary tube, membrane, microchannel, or any other fluid conduit...
at the walls of the sample cell.
- Electrophoretic light scatteringElectrophoretic light scatteringElectrophoretic light scattering is based on dynamic light scattering. The frequency shift or phase shift of an incident laser beam depends on the dispersed particles mobility. In the case of dynamic light scattering, Brownian motion causes particle motion...
. It is based on dynamic light scatteringDynamic light scatteringthumb|right|350px|Hypothetical Dynamic light scattering of two samples: Larger particles on the top and smaller particle on the bottomDynamic light scattering is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers...
. It allows measurement in an open cell which eliminates the problem of electro-osmotic flow for the case of an Uzgiris, but not a capillary cell. And, it can be used to characterize very small particles, but at the price of the lost ability to display images of moving particles.
Both these measuring techniques may require dilution of the sample. Sometimes this dilution might affect properties of the sample and change zeta potential. There is only one justified way to perform this dilution - by using equilibrium supernatant. In this case the interfacial equilibrium between the surface and the bulk liquid would be maintained and zeta potential would be the same for all volume fractions of particles in the suspension. When the diluent is known (as is the case for a chemical formulation), additional diluent can be prepared. If the diluent is unknown, equilibrium supernatant is readily obtained by centrifugation.
Electroacoustic phenomena
There are two electroacoustic effects that are widely used for characterizing zeta potential: colloid vibration currentColloid vibration current
Colloid vibration current is an electroacoustic phenomenon that arises when ultrasound propagates through a fluid that contains ions and either solid particles or emulsion droplets ....
and electric sonic amplitude
Electric sonic amplitude
Electric sonic amplitude is an electroacoustic phenomenon that is the reverse to colloid vibration current. It occurs in colloids, emulsions and other heterogeneous fluids under the influence of an oscillating electric field...
, see reference. There are commercially available instruments that exploit these effects for measuring dynamic electrophoretic mobility
Dynamic electrophoretic mobility
Dynamic electrophoretic mobility is a parameter that determines intensity of electroacoustic phenomena, such as Colloid Vibration Current and Electric Sonic Amplitude in colloids. It is similar to electrophoretic mobility, but at high frequency, on a scale of megahertz...
, which depends on zeta potential.
Electroacoustic techniques have the advantage of being able to perform measurements in intact samples, without dilution. Published and well-verified theories allow such measurements at volume fractions up to 50%, see reference. Calculation of zeta potential from the dynamic electrophoretic mobility requires information on the densities for particles and liquid. In addition, for larger particles exceeding roughly 300 nm in size information on the particle size required as well.
Calculation of zeta potential
The most known and widely-used theory for calculating zeta potential from experimental data is that developed by Marian SmoluchowskiMarian Smoluchowski
Marian Smoluchowski was an ethnic Polish scientist in the Austro-Hungarian Empire. He was a pioneer of statistical physics and an avid mountaineer.-Life:...
in 1903. This theory was originally developed for electrophoresis
Electrophoresis
Electrophoresis, also called cataphoresis, is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. This electrokinetic phenomenon was observed for the first time in 1807 by Reuss , who noticed that the application of a constant electric...
; however, an extension to electroacoustics
Electroacoustics
Electroacoustics may refer to:*Electroacoustic music*Electroacoustic phenomena* Acoustical engineering, the interdisciplinary branch of Acoustics, electronics and electrical engineering dealing with electronic devices...
is now also available. Smoluchowski's theory is powerful because it is valid for dispersed particles of any shape
Shape
The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...
and any concentration
Concentration
In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration...
. However, it has its limitations:
- Detailed theoretical analysis proved that Smoluchowski's theory is valid only for a sufficiently thin double layer, when the Debye lengthDebye lengthIn plasma physics, the Debye length , named after the Dutch physicist and physical chemist Peter Debye, is the scale over which mobile charge carriers screen out electric fields in plasmas and other conductors. In other words, the Debye length is the distance over which significant charge...
, 1/κ, is much smaller than the particle radius a:
- The model of the "thin double layer" offers tremendous simplifications not only for electrophoresis theory but for many other electrokinetic and electroacoustic theories. This model is valid for most aqueous systems because the Debye length is typically only a few nanometers in water. The model breaks only for nano-colloids in a solution with ionic strengthIonic strengthThe ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions. The total electrolyte concentration in solution will affect important properties such as the dissociation or the solubility of different salts...
approaching that of pure water.
- Smoluchowski's theory neglects the contribution of surface conductivitySurface conductivitySurface conductivity is an additional conductivity of an electrolyte in the vicinity of charged surfaces. Close to charged surfaces a layer of counter ions of opposite polarity exists which is attracted by the surface charges. This layer of higher ionic concentration is a part of the interfacial ...
. This is expressed in modern theories as the condition of a small Dukhin numberDukhin numberDukhin number is a dimensionless quantity that characterizes the contribution of the surface conductivity to various electrokinetic and electroacoustic effects, as well as to electrical conductivity and permittivity of fluid heterogeneous systems....
:
The development of electrophoretic and electroacoustic theories with a wider range of validity was a purpose of many studies during the 20th century. There are several analytical theories that incorporate surface conductivity
Surface conductivity
Surface conductivity is an additional conductivity of an electrolyte in the vicinity of charged surfaces. Close to charged surfaces a layer of counter ions of opposite polarity exists which is attracted by the surface charges. This layer of higher ionic concentration is a part of the interfacial ...
and eliminate the restriction of the small Dukhin number
Dukhin number
Dukhin number is a dimensionless quantity that characterizes the contribution of the surface conductivity to various electrokinetic and electroacoustic effects, as well as to electrical conductivity and permittivity of fluid heterogeneous systems....
for both the electrokinetic and electroacoustic applications.
Early pioneering work in that direction dates back to Overbeek and Booth.
Modern, rigorous electrokinetic theories that are valid for any zeta potential and often any κa, stem mostly from the Ukrainian (Dukhin, Shilov and others) and Australian (O'Brien, White, Hunter and others) schools. Historically, the first one was Dukhin-Semenikhin theory. A similar theory was created 10 years later by O'Brien and Hunter. Assuming a thin double layer, these theories would yield results that are very close to the numerical solution provided by O'Brien and White. There are also general electroacoustic theories that are valid for any values of Debye length
Debye length
In plasma physics, the Debye length , named after the Dutch physicist and physical chemist Peter Debye, is the scale over which mobile charge carriers screen out electric fields in plasmas and other conductors. In other words, the Debye length is the distance over which significant charge...
and Dukhin number
Dukhin number
Dukhin number is a dimensionless quantity that characterizes the contribution of the surface conductivity to various electrokinetic and electroacoustic effects, as well as to electrical conductivity and permittivity of fluid heterogeneous systems....
.
All these theories predict electrophoretic mobility and zeta potential to be equal in sign. Recent molecular dynamics simulations, though, suggest that the main contribution to the zeta potential can arise from anisotropic water dipole at the interface not included in the traditional continuum theories and that electrophoretic mobility and zeta potential may in fact be opposite in sign.