Electric potential decays almost exponentially,
which allows introduction "Debye length" as estimate of the DL
thickness. Electric potential drops by approximately 2.7 times at the distance
from the surface that equals to the Debye length. Debye length depends mostly on
an "ionic strength". It is approximately 1 nm at the ionic strength
0.1 M, and it increases as a reciprocal square root of the ionic strength
(electrolyte concentration), becoming, for instance, 10 nm at the ionic strength
There is another characteristic distance within DL - location
of a "slipping plane" associated with tangential motion of the
liquid relative to the surface. Liquid underneath of the slipping plane remains
attached to the surface. Electric potential corresponding to the slipping plane
is " Zeta potential ". It is measured in mV and cannot exceed
There is one more plane located even closer to the surface.
Some of the counter-ions might specifically
adsorb near the surface and build an inner sub-layer, or so-called "Stern
layer". The outer part of the screening layer is usually called the "diffuse layer". What about the difference
between the surface charge ions and the ions adsorbed in the Stern layer? Why
should we distinguish them? There is a thermodynamic justification  but we
think a more comprehensive reason is kinetic (ability to move). The surface
charge ions are assumed to be fixed to the surface (immobile); they cannot move
in response to any external disturbance. In contrast, the Stern ions, in
principle, retain some degree of freedom, almost as high as ions of the diffuse
In the general case of an electrolyte
mixture there is no analytical solution that relates surface charge with Zeta
potential or "Stern potential". However, some convenient
approximations have been suggested [3-5]. In real life application Zeta
potential is usually used as an estimate of Stern potential and the main
characteristic of the electrostatic repulsion preventing particles aggregation.
Calculation of Zeta potential from
the parameters measured by
Zeta potential analyzer
requires appropriate theory. There are two important asymptotic cases when
analytical theories exist. The most know is the case of a "thin DL",
which corresponds to particulates with DL that is much thinner than
particle radius. The vast majority of aqueous dispersions satisfy this
condition, except for very small particles and a low ionic strength media.
Calculation of Zeta potential can be performed using "Smoluchowski theory",
when surface conductivity is negligible.
The opposite case of a "thick DL"
corresponds to systems where the DL is much larger than the particle radius. The
vast majority of dispersions in hydrocarbon media, having inherently very low
ionic strength, satisfy this condition.
These two asymptotic cases allow one to
picture, at least approximately, the DL structure around spherical particles. A
general analytical solution exists only for low potential, the so-called Debye-Hückel
There is one more important factor affecting DL structure -
"overlap of DLs". Increasing volume fraction and/or reduction of the
particle size brings particles surfaces close and eventually diffuse layers
Overlap of Double Layers might become important for nano-particles, macromolecules, proteins.
It is definitely important in non-polar liquids with very expanded
There are more details can be found in JUPAC report on
Electrokinetic phenomena  and in Wikipedia .
Derjaguin , B.V. and Landau, L., "Theory of the
stability of strongly charged lyophobic sols and the adhesion of strongly
charged particles in solution of electrolytes", Acta Phys. Chim, USSR, 14,
Verwey, E.J.W. and Overbeek, J.Th.G., "Theory of the Stability of Lyophobic
Colloids", Elsevier (1948)
Lyklema, J. "Fundamentals of Interface and
Colloid Science", Volumes 1, Academic Press, (1993)
Hunter, R.J. "Zeta potential in Colloid Science", Academic Press, NY (1981)
Dukhin S.S. and Derjaguin B.V. "Electrokinetic
Phenomena", Surface and Colloid Science, Ed. E. Matijevic, John Willey &
Sons, NY, (1974)
Interpretation of Electrokinetic Phenomena (IUPAC Technical Report),