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Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface.

is a scientific term for electrokinetic
potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...
in
colloid A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others exte ...
al dispersions. In the
colloidal chemistry Interface and colloid science is an interdisciplinary intersection of branches of chemistry, physics, nanoscience and other fields dealing with ''colloids'', heterogeneous systems consisting of a mechanical mixture of particles between 1 nm ...
literature, it is usually denoted using the Greek letter zeta (ζ), hence ''ζ-potential''. The usual units are
volts The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). Definition One volt is defined as the electric potential between two point ...
(V) or, more commonly, millivolts (mV). From a theoretical viewpoint, the zeta potential is the
electric potential Electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as electric potential energy per unit of electric charge. More precisely, electric potential is the amount of work (physic ...
in the interfacial double layer (DL) at the location of the slipping plane relative to a point in the bulk fluid away from the interface. In other words, zeta potential is the
potential difference Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge ...
between the dispersion medium and the stationary layer of fluid attached to the dispersed particle. The zeta potential is caused by the net
electrical charge Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...
contained within the region bounded by the slipping plane, and also depends on the location of that plane. Thus, it is widely used for quantification of the magnitude of the charge. However, zeta potential is not equal to the Stern potential or electric surface potential in the double layer, because these are defined at different locations. Such assumptions of equality should be applied with caution. Nevertheless, zeta potential is often the only available path for characterization of double-layer properties. The zeta potential is an important and readily measurable indicator of the
stability Stability may refer to: Mathematics *Stability theory, the study of the stability of solutions to differential equations and dynamical systems ** Asymptotic stability ** Exponential stability ** Linear stability **Lyapunov stability ** Marginal s ...
of colloidal dispersions. The magnitude of the zeta potential indicates the degree of electrostatic repulsion between adjacent, similarly charged particles 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 small, attractive forces may exceed this repulsion and the dispersion may 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 can also be used for the pKa estimation of complex polymers that is otherwise difficult to measure accurately using conventional methods. This can help studying the ionisation behaviour of various synthetic and natural polymers under various conditions and can help in establishing standardised dissolution-pH thresholds for pH responsive polymers.


Measurement

Some new instrumentations techniques exist that allow zeta potential to be measured. The Zeta Potential Analyzer can measure solid, fibers, or powdered material. The motor found in the instrument creates an oscillating flow of electrolyte solution through the sample. Several sensors in the instrument monitor other factors, so the software attached is able to do calculations to find the zeta potential. Temperature, pH, conductivity, pressure, and streaming potential are all measured in the instrument for this reason. Zeta potential can also be calculated using theoretical models, and an experimentally-determined
electrophoretic mobility Electrophoresis is the motion of charged dispersed particles or dissolved charged molecules relative to a fluid under the influence of a spatially uniform electric field. As a rule, these are zwitterions with a positive or negative net ch ...
or dynamic electrophoretic mobility. Electrokinetic phenomena and electroacoustic phenomena are the usual sources of data for calculation of zeta potential. (See Zeta potential titration.)


Electrokinetic phenomena

Electrophoresis Electrophoresis is the motion of charged dispersed particles or dissolved charged molecules relative to a fluid under the influence of a spatially uniform electric field. As a rule, these are zwitterions with a positive or negative net ch ...
is used for estimating zeta potential of
particulates Particulate matter (PM) or particulates are microscopic particles of solid or liquid matter suspension (chemistry), suspended in the atmosphere of Earth, air. An ''aerosol'' is a mixture of particulates and air, as opposed to the particulate ...
, whereas streaming potential/current is used for
porous Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure ...
bodies and flat surfaces. In practice, the zeta potential of dispersion is measured by applying an
electric field An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...
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 In meteorology, an anemometer () is a device that measures wind speed and direction. It is a common instrument used in weather stations. The earliest known description of an anemometer was by Italian architect and author Leon Battista Alberti ...
. The frequency shift or
phase shift In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is expressed in such a s ...
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 In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
, and the application of the Smoluchowski theories.


Electrophoresis

Electrophoretic mobility is proportional to electrophoretic velocity, which is the measurable parameter. There are several theories that link electrophoretic mobility with zeta potential. They are briefly described in the article on electrophoresis and in details in many books on colloid and interface science. There is an
IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
Technical Report prepared by a group of world experts on the electrokinetic phenomena. From the instrumental viewpoint, there are three different experimental techniques: microelectrophoresis, electrophoretic light scattering, and tunable resistive pulse sensing. Microelectrophoresis has the advantage of yielding an image of the moving particles. On the other hand, it is complicated by electro-osmosis at the walls of the sample cell. Electrophoretic light scattering is based on dynamic light scattering. It allows measurement in an open cell which eliminates the problem of electro-osmotic flow except for the case of 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. Tunable resistive pulse sensing (TRPS) is an impedance-based measurement technique that measures the zeta potential of individual particles based on the duration of the resistive pulse signal. The translocation duration of
nanoparticles A nanoparticle or ultrafine particle is a particle of matter 1 to 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 100 nm in only two directions. At ...
is measured as a function of voltage and applied pressure. From the inverse translocation time versus voltage-dependent electrophoretic mobility, and thus zeta potentials are calculated. The main advantage of the TRPS method is that it allows for simultaneous size and
surface charge A surface charge is an electric charge present on a two-dimensional surface. These electric charges are constrained on this 2-D surface, and surface charge density, measured in coulombs per square meter (C•m−2), is used to describe the charge ...
measurements on a particle-by-particle basis, enabling the analysis of a wide spectrum of synthetic and biological nano/microparticles and their mixtures. All 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 an aqueous solution, precipitation is the "sedimentation of a solid material (a precipitate) from a liquid solution". The solid formed is called the precipitate. In case of an inorganic chemical reaction leading to precipitation, the chemic ...
. 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 A diluent (also referred to as a filler, dilutant or thinner) is a diluting agent. Certain fluids are too viscous to be pumped easily or too dense to flow from one particular point to the other. This can be troublesome, because it might not be ...
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 Centrifugation is a mechanical process which involves the use of the centrifugal force to separate particles from a solution according to their size, shape, density, medium viscosity and rotor speed. The denser components of the mixture migrate ...
.


Streaming potential, streaming current

The streaming potential is an electric potential that develops during the flow of liquid through a capillary. In nature, a streaming potential may occur at a significant magnitude in areas with volcanic activities. The streaming potential is also the primary electrokinetic phenomenon for the assessment of the zeta potential at the solid material-water interface. A corresponding solid sample is arranged in such a way to form a capillary flow channel. Materials with a flat surface are mounted as duplicate samples that are aligned as parallel plates. The sample surfaces are separated by a small distance to form a capillary flow channel. Materials with an irregular shape, such as fibers or granular media, are mounted as a porous plug to provide a pore network, which serves as capillaries for the streaming potential measurement. Upon the application of pressure on a test solution, liquid starts to flow and to generate an electric potential. This streaming potential is related to the
pressure gradient In hydrodynamics and hydrostatics, the pressure gradient (typically of air but more generally of any fluid) is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular locat ...
between the ends of either a single flow channel (for samples with a flat surface) or the porous plug (for fibers and granular media) to calculate the surface zeta potential. Alternatively to the streaming potential, the measurement of streaming current offers another approach to the surface zeta potential. Most commonly, the classical equations derived by Maryan Smoluchowski are used to convert streaming potential or streaming current results into the surface zeta potential. Applications of the streaming potential and streaming current method for the surface zeta potential determination consist of the characterization of surface charge of polymer membranes, biomaterials and medical devices, and minerals.


Electroacoustic phenomena

There are two electroacoustic effects that are widely used for characterizing zeta potential: colloid vibration current and electric sonic amplitude. 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%. 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

The most known and widely used theory for calculating zeta potential from experimental data is that developed by Marian Smoluchowski 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 A shape is a graphics, graphical representation of an object's form or its external boundary, outline, or external Surface (mathematics), surface. It is distinct from other object properties, such as color, Surface texture, texture, or material ...
and any
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', '' number 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 length In plasmas and electrolytes, the Debye length \lambda_\text (Debye radius or Debye–Hückel screening length), is a measure of a charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists. With each D ...
, 1/\kappa, is much smaller than the particle radius, a: :: \cdot a \gg 1 :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 An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, also known as sodium chloride (NaCl), in wat ...
systems because the Debye length is typically only a few
nanometers 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm), or nanometer (American and British English spelling differences#-r ...
in water. The model breaks only for nano-colloids in a solution with
ionic strength The 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 a ...
approaching that of pure water. *Smoluchowski's theory neglects the contribution of surface conductivity. This is expressed in modern theories as the condition of a small Dukhin number: ::Du \ll 1 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 \kappa a, stem mostly from Soviet 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 ten 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.


Henry's equation

When κa is between large values where simple analytical models are available, and low values where numerical calculations are valid, Henry's equation can be used when the zeta potential is low. For a nonconducting sphere, Henry's equation is u_e= \frac \zeta f_1(\kappa a), where ''f''1 is the Henry function, one of a collection of functions which vary smoothly from 1.0 to 1.5 as κa approaches infinity.


References

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