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Zeta potential

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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.

<a rel="nofollow" class="external text" href="https://www.wyatt.com/solutions/properties/charge-zeta-potential.html">Zeta potential</a> is a scientific term for <a href="Electrokinetic_phenomena" title="Electrokinetic phenomena">electrokinetic</a> <a href="Electric_potential" title="Electric potential">potential</a><a href="#cite_note-1">[1]</a><a href="#cite_note-2">[2]</a> in <a href="Colloid" title="Colloid">colloidal</a> <a href="Dispersion_(chemistry)" title="Dispersion (chemistry)">dispersions</a>. In the <a href="Colloidal_chemistry" class="mw-redirect" title="Colloidal chemistry">colloidal chemistry</a> literature, it is usually denoted using the Greek letter <a href="Zeta" title="Zeta">zeta (ζ)</a>, hence ζ-potential. The usual units are <a href="Volt" title="Volt">volts</a> (V) or, more commonly, millivolts (mV). From a theoretical viewpoint, the zeta potential is the <a href="Electric_potential" title="Electric potential">electric potential</a> in the interfacial <a href="Double_layer_(interfacial)" class="mw-redirect" title="Double layer (interfacial)">double layer</a> (DL) at the location of the <a href="Slipping_plane" class="mw-redirect" title="Slipping plane">slipping plane</a> relative to a point in the bulk fluid away from the interface. In other words, zeta potential is the <a href="Potential_difference" class="mw-redirect" title="Potential difference">potential difference</a> between the <a href="Dispersion_medium" class="mw-redirect" title="Dispersion medium">dispersion medium</a> and the stationary layer of fluid attached to the <a href="Dispersed_particle" class="mw-redirect" title="Dispersed particle">dispersed particle</a>.

The zeta potential is caused by the net <a href="Electric_charge" title="Electric charge">electrical charge</a> contained within the region bounded by the slipping plane, and also depends on the location of that <a href="Plane_(geometry)" class="mw-redirect" title="Plane (geometry)">plane</a>. Thus, it is widely used for quantification of the magnitude of the charge. However, zeta potential is not equal to the <a href="Stern_potential" class="mw-redirect" title="Stern potential">Stern potential</a> or <a href="Electric_surface_potential" class="mw-redirect" title="Electric surface potential">electric surface potential</a> in the double layer,<a href="#cite_note-Lyklema1995-3">[3]</a><a href="#cite_note-russel1992-4">[4]</a><a href="#cite_note-Dukhin-5">[5]</a><a href="#cite_note-Kirby-6">[6]</a> 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 <a href="Dispersion_stability" title="Dispersion stability">stability</a> of colloidal dispersions. The magnitude of the zeta potential indicates the degree of <a href="Electrostatic_repulsion" class="mw-redirect" title="Electrostatic repulsion">electrostatic repulsion</a> 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 <a href="Flocculation" title="Flocculation">flocculate</a>. 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.<a href="#cite_note-7">[7]</a>

Zeta potential can also be used for the <a href="Acid_dissociation_constant" title="Acid dissociation constant">pKa</a> 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.<a href="#cite_note-:0-8">[8]</a>

<caption>Stability behaviour of a colloid depending on zeta potential<a href="#cite_note-9">[9]</a>

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<th>Magnitude of Zeta potential (mV)

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<th>Stability behavior

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<td>0 to 5

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<td>Rapid coagulation or flocculation

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<td>10 to 30

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<td>Incipient instability

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<td>30 to 40

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<td>Moderate stability

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<td>40 to 60

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<td>Good stability

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<td>>61

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<td>Excellent stability

</td></tr></tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Measurement">Measurement</h2></div>

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 <a href="Electrophoretic_mobility" class="mw-redirect" title="Electrophoretic mobility">electrophoretic mobility</a> or <a href="Dynamic_electrophoretic_mobility" title="Dynamic electrophoretic mobility">dynamic electrophoretic mobility</a>.

<a href="Electrokinetic_phenomena" title="Electrokinetic phenomena">Electrokinetic phenomena</a> and <a href="Electroacoustic_phenomena" title="Electroacoustic phenomena">electroacoustic phenomena</a> are the usual sources of data for calculation of zeta potential. (See <a href="Zeta_potential_titration" title="Zeta potential titration">Zeta potential titration</a>.)

<div class="mw-heading mw-heading3"><h3 id="Electrokinetic_phenomena">Electrokinetic phenomena</h3></div>

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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Electrokinetic_phenomena" title="Electrokinetic phenomena">Electrokinetic phenomena</a></div>

<a href="Electrophoresis" title="Electrophoresis">Electrophoresis</a> is used for estimating zeta potential of <a href="Aerosol" title="Aerosol">particulates</a>, whereas <a href="Streaming_potential/current" class="mw-redirect" title="Streaming potential/current">streaming potential/current</a> is used for <a href="Porous" class="mw-redirect" title="Porous">porous</a> bodies and flat surfaces.

In practice, the zeta potential of dispersion is measured by applying an <a href="Electric_field" title="Electric field">electric field</a> 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 <a href="Doppler_effect" title="Doppler effect">Doppler</a> <a href="Anemometer" title="Anemometer">anemometer</a>. The frequency shift or <a href="Phase_shift" class="mw-redirect" title="Phase shift">phase shift</a> 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 <a href="Dielectric_permittivity" class="mw-redirect" title="Dielectric permittivity">dielectric permittivity</a>, and the application of the Smoluchowski theories.<a href="#cite_note-10">[10]</a>

<div class="mw-heading mw-heading4"><h4 id="Electrophoresis">Electrophoresis</h4></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Electrophoresis" title="Electrophoresis">Electrophoresis</a></div>

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.

<a href="#cite_note-Lyklema1995-3">[3]</a><a href="#cite_note-russel1992-4">[4]</a><a href="#cite_note-Dukhin-5">[5]</a><a href="#cite_note-Hunter-11">[11]</a> There is an <a href="International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a> Technical Report<a href="#cite_note-Delgado_2005-12">[12]</a> prepared by a group of world experts on the electrokinetic phenomena.

From the instrumental viewpoint, there are three different experimental techniques: <a href="Microelectrophoresis" title="Microelectrophoresis">microelectrophoresis</a>, <a href="Electrophoretic_light_scattering" title="Electrophoretic light scattering">electrophoretic light scattering</a>, and <a href="Tunable_resistive_pulse_sensing" title="Tunable resistive pulse sensing">tunable resistive pulse sensing</a>. Microelectrophoresis has the advantage of yielding an image of the moving particles. On the other hand, it is complicated by <a href="Electro-osmosis" title="Electro-osmosis">electro-osmosis</a> at the walls of the sample cell. Electrophoretic light scattering is based on <a href="Dynamic_light_scattering" title="Dynamic light scattering">dynamic light scattering</a>. 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. <a href="Tunable_resistive_pulse_sensing" title="Tunable resistive pulse sensing">Tunable resistive pulse sensing</a> (TRPS) is an impedance-based measurement technique that measures the zeta potential of individual particles based on the duration of the resistive pulse signal.<a href="#cite_note-Zeta_Potential_Measurement_-_Izon_Science-13">[13]</a> The translocation duration of <a href="Nanoparticle" title="Nanoparticle">nanoparticles</a> 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 <a href="Surface_charge" title="Surface charge">surface charge</a> measurements on a particle-by-particle basis, enabling the analysis of a wide spectrum of synthetic and biological nano/microparticles and their mixtures.<a href="#cite_note-14">[14]</a>

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 <a href="Supernatant" class="mw-redirect" title="Supernatant">supernatant</a>. 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 <a href="Diluent" title="Diluent">diluent</a> 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 <a href="Centrifugation" title="Centrifugation">centrifugation</a>.

<div class="mw-heading mw-heading4"><h4 id="Streaming_potential,_streaming_current">Streaming potential, streaming current</h4></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Streaming_current" title="Streaming current">Streaming current</a></div>

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.<a href="#cite_note-15">[15]</a> 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 <a href="Pressure_gradient" title="Pressure gradient">pressure gradient</a> 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 <a href="Marian_Smoluchowski" title="Marian Smoluchowski">Maryan Smoluchowski</a> are used to convert streaming potential or streaming current results into the surface zeta potential.<a href="#cite_note-16">[16]</a>

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,<a href="#cite_note-17">[17]</a> biomaterials and medical devices,<a href="#cite_note-18">[18]</a><a href="#cite_note-19">[19]</a> and minerals.<a href="#cite_note-20">[20]</a>

<div class="mw-heading mw-heading3"><h3 id="Electroacoustic_phenomena">Electroacoustic phenomena</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Electroacoustic_phenomena" title="Electroacoustic phenomena">Electroacoustic phenomena</a></div>

There are two electroacoustic effects that are widely used for characterizing zeta potential: <a href="Colloid_vibration_current" title="Colloid vibration current">colloid vibration current</a> and <a href="Electric_sonic_amplitude" title="Electric sonic amplitude">electric sonic amplitude</a>.<a href="#cite_note-Dukhin-5">[5]</a> 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.

<div class="mw-heading mw-heading2"><h2 id="Calculation">Calculation</h2></div>

The most known and widely used theory for calculating zeta potential from experimental data is that developed by <a href="Marian_Smoluchowski" title="Marian Smoluchowski">Marian Smoluchowski</a> in 1903.<a href="#cite_note-21">[21]</a> This theory was originally developed for electrophoresis; however, an extension to electroacoustics is now also available.<a href="#cite_note-Dukhin-5">[5]</a> Smoluchowski's theory is powerful because it is valid for <a href="Dispersed_particles" class="mw-redirect" title="Dispersed particles">dispersed particles</a> of any <a href="Shape" title="Shape">shape</a> and any <a href="Concentration" title="Concentration">concentration</a>. However, it has its limitations:

<ul><li>Detailed theoretical analysis proved that Smoluchowski's theory is valid only for a sufficiently thin double layer, when the <a href="Debye_length" title="Debye length">Debye length</a>, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1/\kappa }">

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<annotation encoding="application/x-tex">{\displaystyle 1/\kappa }</annotation>

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</math><img src="./b79eb229e228a09333c5e2f7893cb359ebb2dc48.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.664ex; height:2.843ex;" alt="{\displaystyle 1/\kappa }" loading="lazy">, is much smaller than the particle radius, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}">

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<annotation encoding="application/x-tex">{\displaystyle a}</annotation>

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</math><img src="./ffd2487510aa438433a2579450ab2b3d557e5edc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}" loading="lazy">:</li></ul>

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<annotation encoding="application/x-tex">{\displaystyle {\kappa }\cdot a\gg 1}</annotation>

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</math><img src="./9fc968d6c5cb9feae182d20ab088a5ca02264561.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.024ex; height:2.176ex;" alt="{\displaystyle {\kappa }\cdot a\gg 1}" loading="lazy"></dd></dl></dd></dl>

<dl><dd>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 <a href="Aqueous" class="mw-redirect" title="Aqueous">aqueous</a> systems because the Debye length is typically only a few <a href="Nanometers" class="mw-redirect" title="Nanometers">nanometers</a> in water. The model breaks only for nano-colloids in a solution with <a href="Ionic_strength" title="Ionic strength">ionic strength</a> approaching that of pure water.</dd></dl>

<ul><li>Smoluchowski's theory neglects the contribution of <a href="Surface_conductivity" title="Surface conductivity">surface conductivity</a>. This is expressed in modern theories as the condition of a small <a href="Dukhin_number" title="Dukhin number">Dukhin number</a>:</li></ul>

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<annotation encoding="application/x-tex">{\displaystyle Du\ll 1}</annotation>

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</math><img src="./d2d9cb92c5a510e18e077b1dd71f671141e9a16a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.03ex; height:2.176ex;" alt="{\displaystyle Du\ll 1}" loading="lazy"></dd></dl></dd></dl>

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 <a href="Surface_conductivity" title="Surface conductivity">surface conductivity</a> 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<a href="#cite_note-22">[22]</a> and Booth.<a href="#cite_note-23">[23]</a>

Modern, rigorous electrokinetic theories that are valid for any zeta potential, and often any <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \kappa a}">

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<annotation encoding="application/x-tex">{\displaystyle \kappa a}</annotation>

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</math><img src="./d74d948c33e77dfeb4b7cd7d91075cd527925cd3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.569ex; height:1.676ex;" alt="{\displaystyle \kappa a}" loading="lazy">, 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 href="#cite_note-24">[24]</a> A similar theory was created ten years later by O'Brien and Hunter.<a href="#cite_note-25">[25]</a> Assuming a thin double layer, these theories would yield results that are very close to the numerical solution provided by O'Brien and White.<a href="#cite_note-26">[26]</a> There are also general electroacoustic theories that are valid for any values of Debye length and Dukhin number.<a href="#cite_note-Dukhin-5">[5]</a><a href="#cite_note-Hunter-11">[11]</a>

<div class="mw-heading mw-heading3"><h3 id="Henry's_equation">Henry's equation</h3></div>

<div role="note" class="hatnote navigation-not-searchable">"Henry's equation" redirects here. For the gas law, see <a href="Henry's_law" title="Henry's law">Henry's law</a>.</div>

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 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{e}={\frac {2\varepsilon _{rs}\varepsilon _{0}}{3\eta }}\zeta f_{1}(\kappa a)}">

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<annotation encoding="application/x-tex">{\displaystyle u_{e}={\frac {2\varepsilon _{rs}\varepsilon _{0}}{3\eta }}\zeta f_{1}(\kappa a)}</annotation>

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</math><img src="./52254bb287537ad675e098708a8cff77e40be794.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.058ex; height:5.676ex;" alt="{\displaystyle u_{e}={\frac {2\varepsilon _{rs}\varepsilon _{0}}{3\eta }}\zeta f_{1}(\kappa a)}" loading="lazy">, where f1 is the Henry function, one of a collection of functions which vary smoothly from 1.0 to 1.5 as κa approaches infinity.<a href="#cite_note-Delgado_2005-12">[12]</a>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<li id="cite_note-1"><a href="#cite_ref-1">^</a> <a href="International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a>, <a href="IUPAC_books" class="mw-redirect" title="IUPAC books">Compendium of Chemical Terminology</a>, 5th ed. (the "Gold Book") (2025). Online version: (2006–) "<a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/E01968.html">electrokinetic potential, ζ</a>". <style data-mw-deduplicate="TemplateStyles:r1238218222">

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</style><a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.E01968">10.1351/goldbook.E01968</a>

</li>

<li id="cite_note-2"><a href="#cite_ref-2">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.iso.org/standard/52807.html">"Colloidal systems – Methods for Zeta potential determination"</a>. ISO International Standard 13099, Parts 1,2 and 3. International Organization for Standardization (ISO). 2012.</cite>

</li>

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</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q196823#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata950" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q196823#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata950" style="font-size:114%;margin:0 4em">Authority control databases </div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4190765-6">Germany</a></li><li><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85149765">United States</a></li><li><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00576521">Japan</a></li><li><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007534242005171">Israel</a></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><a rel="nofollow" class="external text" href="https://lux.collections.yale.edu/view/concept/5857d5f9-2889-48b3-9f58-2fa73de03db6">Yale LUX</a></li></ul></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

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