Page 257 - Environmental Nanotechnology Applications and Impacts of Nanomaterials

242 Principles and Methods

Implications of the continuum approximation for nanoparticles. The fore-
going discussion of the configuration of water on surfaces underscores a
key limitation in our ability to describe many interactions at the nanome-
teric scale. DLVO and other theories describing particle behavior in
aqueous media typically treat the intervening fluid (water) as a uni-
form, structureless medium that is well described in terms of its bulk
properties [4] such as density, viscosity, and dielectric constant. As illus-
trated in the case of ordered water near surfaces, a molecular view of
interactions between particles, surfaces, and fluid molecules may be
required to adequately describe phenomena that affect nanoparticle
aggregation and deposition. A primary challenge in this regard lies in
bridging phenomena that apply at the atomic or molecular scale with
those observed in the larger scale system. Given the size and complex
composition of any real system, it is not possible to simply calculate and
sum all of the interactions that occur at the molecular scale. The prob-
lem remains computationally intractable. Approaches for bridging this
gap in length-scales include averaging across many molecular interac-
tions at a given scale, or using bulk properties as boundary conditions
for performing detailed calculations at a given location at the molecular
scale.
Limitations on theories that assume that particles and ions exist in
a fluid described as a continuum are particularly apparent when sepa-
ration distances between two surfaces approach 5 nm or less. When
considering particles with dimensions similar to that of ions, molecular
interactions, such as steric repulsion, become significant. Similar limi-
tations exist in describing particle surfaces. Errors may be introduced
in averaging over many functional groups on a surface as is typically
done in surface complexation modeling.

Aggregation
Particle dispersions are thermodynamically unstable if the total free
energy of the systems may be lowered through a reduction in interfa-
cial area via aggregation. Aggregation involves the formation and
growth of clusters and is controlled by both the reaction conditions and
interfacial chemical interactions [12, 14, 22]. The propensity of
nanoparticles to aggregate, particularly in natural systems, is an
important consideration in determining not only their mobility, fate,
and persistence, but also their toxicity. Nanoparticles will have negli-
gible settling rates. However, aggregation may result in a growth in
mean particle size to the extent that settling rates increase. The per-
sistence of the aggregated nanomaterial in suspension may therefore
decrease as these aggregates settle or flow toward collector surfaces,
due to favorable attachment conditions. This reduction in persistence