Zeta potential

Diagram showing the ionic concentration and potential difference as a function of distance from the charged surface of a particle suspended in a dispersion medium.

Zeta potential is a scientific term for electrokinetic potential^[1] in colloidal dispersions. In the colloidal chemistry literature, it is usually denoted using the Greek letter zeta (ζ), hence ζ-potential. From a theoretical viewpoint, the zeta potential is the electric potential 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 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 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,^[2] 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 a key indicator of the stability 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.^[3][4]

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

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 mobility.

Electrokinetic phenomena and electroacoustic phenomena are the usual sources of data for calculation of zeta potential.

Electrokinetic phenomena

Electrophoresis 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).^[5]

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 electrophoresis and in details in many books on colloid and interface science.^[6][7][8][9] There is an IUPAC Technical Report^[10] prepared by a group of world experts on the electrokinetic phenomena.

From the instrumental viewpoint, there are two different experimental techniques: microelectrophoresis and electrophoretic light scattering. 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 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 current and electric sonic amplitude, see reference.^[8] 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.

Calculation of zeta potential

The most known and widely used theory for calculating zeta potential from experimental data is that developed by Marian Smoluchowski in 1903.^[11] This theory was originally developed for electrophoresis; however, an extension to electroacoustics is now also available.^[8] Smoluchowski's theory is powerful because it is valid for dispersed particles of any shape and any concentration. However, it has its limitations:

• Detailed theoretical analysis proved that Smoluchowski's theory are valid only for a sufficiently thin double layer, when the Debye length, 1/κ, is much smaller than the particle radius a:

${\kappa} \cdot a \gg 1$

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 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 strength 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^[12] and Booth.^[13]

Modern, rigorous electrokinetic theories that are valid for any zeta potential and often any κa, 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.^[14] A similar theory was created 10 years later by O'Brien and Hunter.^[15] Assuming a thin double layer, these theories would yield results that are very close to the numerical solution provided by O'Brien and White.^[16] There are also general electroacoustic theories that are valid for any values of Debye length and Dukhin number.^[8][9]

References

1. Definition of electrokinetic potential in "IUPAC. Compendium of Chemical Terminology", 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.
2. Kirby, B.J. (2010). Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices. Cambridge University Press. ISBN 978-0-521-11903-0.
3. Greenwood, R; Kendall, K (1999). "Electroacoustic studies of moderately concentrated colloidal suspensions". Journal of the European Ceramic Society 19 (4): 479–488.
4. Hanaor, D.A.H.; Michelazzi, M.; Leonelli, C.; Sorrell, C.C. (2012). "The effects of carboxylic acids on the aqueous dispersion and electrophoretic deposition of ZrO₂". Journal of the European Ceramic Society 32 (1): 235–244. doi:10.1016/j.jeurceramsoc.2011.08.015.
5. Zeta Potential Using Laser Doppler Electrophoresis - Malvern.com
6. Lyklema, J. "Fundamentals of Interface and Colloid Science", vol.2, page.3.208, 1995 ISBN 0-12-460529-X
7. Russel, W.B., Saville, D.A. and Schowalter, W.R. "Colloidal Dispersions", Cambridge University Press, 1992 ISBN 0-521-42600-6
8. Dukhin, A.S. and Goetz, P.J. "Ultrasound for characterizing colloids", Elsevier, 2002 ISBN 0-444-51164-4
9. Hunter, R.J. "Foundations of Colloid Science", Oxford University Press, 1989 ISBN 0-19-855189-4
10. A. V. Delgado; F. Gonzalez-Caballero; R. J. Hunter; L. K. Koopal; J. Lyklema (2005). "Measurement and Interpretation of Electrokinetic Phenomena" (IUPAC Technical Report). Pure Appl. Chem. 77 (10): 1753–1850. doi:10.1351/pac200577101753.
11. M. von Smoluchowski, Bull. Int. Acad. Sci. Cracovie, 184 (1903)
12. Overbeek, J.Th.G., Koll. Bith, 287 (1943)
13. Booth, F. (1948). "Theory of Electrokinetic Effects". Nature 161 (4081): 83–6. doi:10.1038/161083a0. PMID 18898334.
14. Dukhin, S.S. and Semenikhin, N.M. Koll. Zhur., 32, 366 (1970)
15. O'Brien, R.W. and Hunter, R.J. Can. J. Chem., 59, 1878 (1981)
16. O'Brien, Richard W.; White, Lee R. (1978). "Electrophoretic mobility of a spherical colloidal particle". Journal of the Chemical Society, Faraday Transactions 2 74: 1607. doi:10.1039/F29787401607.