Hydroxyapatite and Other Biomedical Coatings by Electrophoretic Deposition - Biological and Biomedical Coatings: Processing and Characterization - page 85

Slipping plane

Negative surface charged particle

Double layer

Stern layer

Diffuse layer

Surface potential ( ψ )

Stern potential ( ψ s )

Zeta potential ( ζ )

Electrical forces ≈
random thermal motion

δ 1/ κ

Distance from particle surface

FIGURE 3.3
Schematic of a particle and associated surface charge. (Adapted from Van der Biest, O.O. and Vandeperre, L.J.,
Annu. Rev. Mater. Sci. , 29 [1] 327-52 (1999); Usui, S., Electric Charge and Charge Neutralization in Aqueous
Solutions, pp. 432-39 in Powder Technology Handbook . Marcel Dekker, New York, 1991; Cazes, J. (ed.)., Encyclopedia
of Chromatography , 3rd Edition, CRC Press, Boca Raton, FL, 2005.)

k = Boltzmann constant
T = absolute temperature
e = electron charge
n i = concentration of ions
z i = valence of ions
k ′ = dielectric constant of medium ( ε / ε o [28])

A high surface charge on a particle, regardless of the charge type, results in the forma-
tion of a thick double layer [29]. This condition prevents particles from approaching closely
to one another owing to electrostatic repulsion. This condition typically results in sus-
pensions of low viscosities, deflocculation, and high stability. With lower surface charges
and thinner double layers, suspensions typically exhibit high viscosities, flocculation, and
rapid gravitational settling.

Derjaguin, Landau, Verwey, and Overbeek Theory

The most commonly applied theoretical model describing the force between charged sur-
faces in a liquid medium is the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory,
which is applicable for dilute suspensions [19,21,22,29,30]. However, the Gouy-Chapman
(GC) theory [31] and the Gouy-Chapman-Stern-Grahame (GCSG) theory [26] also are