Size/Shape – Property Relationships of Non - Carbonaceous Inorganic Nanoparticles and their Environmental Implications - Environmental and Human Health Impacts of Nanotechnology - page 87

KC
KC

ads

ΓΓ

=

max

1 +

ads

where C is the activity (effective concentration) of the adsorbate in solution, K ads
is the adsorption reaction constant (related to the free energy change for the
adsorption reaction), max

is the adsorption capacity (the maximum number of molecules/ions per unit area
that can be adsorbed). These parameters are referred to in the studies when appli-
cable. (It should be noted that the Langmuir adsorption equation describes adsorp-
tion on a homogeneous surface. Because nanoparticle surfaces are relatively
heterogeneous by their very nature, parameters derived using this model should be
interpreted with caution.)
As with many studies in the emerging fi eld of nano-environmental science, inter-
pretation of the results for size dependent trends is complicated by variation within
and/or among the samples. The samples often not only vary in size but also in
morphology, aggregation state and even crystal phase. All of these variables can
affect particle behaviour. While these added variables can be accounted for via
careful characterization, it is not always simple to do, and in some cases may be
impossible. As synthetic methods advance further, it should become easier to syn-
thesize or purchase more homogeneous and well characterised nanoparticle
samples, and the results from such studies should become easier to interpret and
compare.

Γ is the number of molecules sorbed per unit area and Γ

3.5 Nanoparticle Fate: Dissolution and Solid State Cation Movement

Currently, the fate and degradation pathways of nanoparticles are unknown. One
possible fate for nanoparticles is for them to dissolve. As many nanoparticles may
contain toxic metals, this is a matter of concern. Here, what is known about nanopar-
ticle dissolution is discussed, especially with respect to size and shape. Solid state
cation movement and exchange processes are discussed as well, as these may also
alter nanoparticle fate in the environment.

3.5.1 Basic Energetic and Kinetic Considerations of Nanoparticle Dissolution

Classically, the dependence of solubility upon particle size, assuming a spherical
particle, can be expressed with a modifi ed form of the Kelvin equation:

S
S

2 V

RTr

γ

= exp

where S is the solubility of particles with inscribed radius r in m, S 0 is the solubility
of the bulk material,

0

is the surface free energy in mJ/m 2 , R is the gas constant in γ

K, T is the temperature in K and V - is the molecular volume in m 3 /mol
(Adamson, 1982). According to this relation, as the particle dimensions decrease,
the solubility increases exponentially relative to the bulk solubility. An example of

nJ/mol ⋅