Page 249 - Environmental Nanotechnology Applications and Impacts of Nanomaterials

234 Principles and Methods

magnitudes of the attractive (negative energy potential) and repulsive
(expressed as a positive quantity) phenomena involved. In the first
case, the interaction between surfaces is attractive at all separation dis-
tances. In the second case, the interaction is repulsive as the surfaces
approach one another until a repulsive energy barrier is overcome, at
which point the interactions become attractive. In the third case
(depicted in Figure 7.1), interactions are at first attractive, then repul-
sive, and finally attractive once again (as in the second case) as the
approach distances became smaller. The features of the potential energy
curve in this last case are designated as an attractive secondary
minimum (I), a repulsive barrier (II), and an attractive primary mini-
mum (III). As separation distance between two surfaces increases, the
different components of the interaction energies diminish from their
corresponding values at near-contact following a unique decay pattern,
which affects the shape of the resulting energy plot [4]. For instance,
the secondary minimum develops because repulsive electrostatic inter-
actions decay exponentially with separation distance while attractive
van der Waals interactions decay somewhat more slowly over a longer
range. The magnitudes of different interaction energies depend on par-
ticle size and thus, so does the overall interaction energy curve. For
example, as particle size decreases, the height of the energy barrier, if
present, also decreases; similarly, the secondary minimum becomes
more shallow with decreasing particle size. This is particularly evi-
dent at separation distances greater than 5 nm. Below this separation
distance, shorter-range interactions tend to be less impacted by parti-
cle size. Nevertheless, size effects on interaction energies have conse-
quences with regards to the stability of particle dispersions and particle
mobility [6].
The components of interaction energy that are accounted for in the
DLVO and other similar theories are discussed in more detail in the
following sections. These discussions, however, are not meant to be exhaus-
tive reviews of these subjects; the reader is instead referred to other sources
[4, 7, 8] for such detailed overviews. The purpose here is to consider the
effect of diminishing particle size on those interaction energies as they may
be relevant in determining nanoparticle fate and transport in the
environment.

Van der waals interactions. Van der Waals interactions are in most
cases attractive and act universally between surfaces in aqueous media.
These interactions incorporate three different electrodynamic forces:
dispersion, induction, and orientation [4]. The three electrodynamic
forces may be summed together to equal the total van der Waals
interfacial energy term. Lifshitz-van der Waals interaction energies
2
decay according to L , where L represents the distance between two