Hydroxyapatite and Other Biomedical Coatings by Electrophoretic Deposition - Biological and Biomedical Coatings: Processing and Characterization - page 86

used. The starting point for the DLVO model is the interaction between two spheres, which
are subject to both van der Waals attractive potential energy and electrostatic repulsive
potential energy, as given by Equation 3.2:

V T = V A + V R (3.2)

where:
V T = total potential energy
V A = attractive potential energy (van der Waals)
V R = repulsive potential energy (double layer)

In simplified form, the van der Waals attractive potential energy is given by Equation 3.3:

A
D

r r

V = −

1 2

(3.3)

A

r r

6 +

1 2

where:
V A = attractive potential energy (van der Waals)
A = Hamaker constant of the particle in a medium
D = distance between particles
r 1 = radius of particle 1
r 2 = radius of particle 2

The double layer repulsive potential energy generally is given in terms of a single par-
ticle radius by Equation 3.4:

r

( )

εψ

− D

V = ln 1 + e

κ

(3.4)

R

2

where:
V R = Repulsive potential energy (double layer)
ε = Permittivity of medium
ψ = Surface potential
r

= Radius of particle

1
κ

= Debye length

D = Distance between particles

Using these equations, the potential energy of the interaction between particles can be
shown schematically, which is done in Figure 3.4. This can be interpreted in terms of the
following phenomena [22,29]:

• Point A. At D ≈ 0, the particles are in contact, with maximal attractive potential
energy ( V A ), which dominates the total potential energy ( V T ).
• As the distance between the particles increases, the balance between the attrac-
tive potential energy ( V A ) and repulsive potential energy ( V R ) shifts in favor of the
latter.
• Point B. At the maximal V T , an energy barrier ( E B ) to particle flocculation is estab-
lished, so deflocculation occurs.