W. Richard Bowen and Nidal Hilal 4

2.3 INTERACTION FORCES 55
separations, deviations did occur. This was attributed by the authors to
an effect of the roughness of the surfaces involved, leading to a deviation
from the assumed idealised geometry.
There are a number of examples of the AFM being used along with the
colloidal probe technique to probe van der Waals interactions between
surfaces in a variety of media. Whilst most such studies examine a combination
of van der Waals along with other surface forces, there are a few
that concentrate on van der Waals measurements. Milling and colleagues
[76] observed the interactions between colloidal gold spheres and poly(tetrafluoroethylene)
(PTFE) surfaces in a variety of different liquids. Hamaker
constants were found by fitting the appropriate force laws to the experimental
data. As noted by the authors, the experimentally determined
values for the Hamaker constant were only in agreement qualitatively
with those calculated from theory. In addition, theoretical values varied
significantly, depending upon whether an amorphous or crystalline form
of PTFE was considered. For the majority of liquids used, which were of
a polar nature (water, ethanol and dimethyl sulfoxide), only attractive
forces were measured. In the case of dimethyl formamide, which was also
a polar molecule, only repulsive interactions were observed. For these
interactions, only water had been expected to show an attractive interaction.
The authors concluded that in the case of the other polar liquids
studied that showed attraction, the surfaces must have become contaminated
by charged groups, leading to interactions that were not purely of
a van der Waals nature. For interactions taking place in the perfluoroalkanes
perfluorohexane and perfluorocyclohexane, as well as in air, shortrange
interactions were also attractive. This was as predicted from theory,
but the authors were unable to obtain experimentally determined values
for A H. In the other low-polarity solvents examined (cyclohexane, dodecane,
p-xylene and bromobenzene), all interactions were found to be repulsive,
which was qualitatively in accordance with theoretical A H values calculated
assuming amorphous PTFE surfaces.
Karamen et al. [77] studied the interactions between model aluminium
oxide surfaces in 1 mM solutions of potassium chloride as a function of
pH. At separation distances greater than 5 nm, interaction forces were
described very well by the traditional DLVO theory. From calculations
of the surface potential from forces measured using DLVO theory, it was
possible to calculate an isoelectric point at approximately pH 7, which
was in agreement with values obtained from the literature.
Many colloidal systems consist of particles with self-assembled monolayers
covalently bound to the surface. Such a system is inherently more
complex than those having interactions between single materials, as if the
outer layer is thin, then interactions between the underlying surfaces will
occur as well as between the monolayers. Kane and Mulvaney [78] studied
the interactions between gold spheres and surfaces before and after