W. Richard Bowen and Nidal Hilal 4

54 2. MEASUREMENT OF PARTICLE ANd SURFACE INTERACTIONS
where the total interaction energy V T is expressed in terms of the repulsive
double layer interaction energy V R and the attractive London–van
der Waals energy V A. For a measurement made between a spherical colloid
probe and a plain surface, this can be adapted to give the relationship
for a normalised force:
F
R
�2π( V � V )
A R
(2.55)
Contrary to the double layer interaction, the van der Waals interaction
energy is mostly insensitive to variations in electrolyte strength and pH.
Additionally, the van der Waals attraction must always be greater than
the double layer repulsion at extremely small distances since the interaction
energy satisfies a power law (i.e. V A � � D �n ), whereas the double
layer interaction energy remains finite or increases far more slowly
within the same small separation range.
DLVO theory was challenged by the existence of long-range attractive
electrostatic forces between particles of like charge. The established theory
of colloidal interactions predicts that an isolated pair of like-charged
colloidal spheres in an electrolyte should experience a purely repulsive
screened electrostatic (Coulombic) interaction. The experimental evidence,
however, indicates that the effective interparticle potential can
have a long-range attractive component in more concentrated suspensions
[67, 68] and for particles confined by charged glass walls [69, 70].
The explanations for the observation are divided and debatable. One of
the arguments [71] demonstrated that the attractive interaction measured
between like-charged colloidal spheres near a wall can be accounted for
by a non-equilibrium hydrodynamic effect, which was proved by both
analytical results and Brownian dynamics simulations.
2.3.3.1 Measurement of DLVO Forces Using Atomic Force Microscopy
The following section will review a number of papers describing
experiments to measure van der Waals and electrostatic double layer
forces between particles using the colloidal probe technique, but should
not be considered as a complete coverage of published information. For
further reading, there are a number of excellent reviews that may be recommended
[13, 21, 72–74].
The first use of AFM to measure interactions between a colloidal particle
and a surface was reported by Ducker and colleagues, where a silica
sphere was allowed to interact with a silica surface in aqueous NaCl
solutions [4, 75]. Force measurements were fitted with theoretical force
laws for DLVO theory, combining van der Waals and electrostatic double
layer interactions. For separations greater than 3 nm, observations agreed
favourably with the conventional DLVO theory. However, at closer