Page 296 - Environmental Nanotechnology Applications and Impacts of Nanomaterials

Nanoparticle Transport, Aggregation, and Deposition 281

mixtures of polysaccharides, proteins, and nucleic acids. This process is
collectively called biofilm formation [93]. The bioavailability of nanopar-
ticles to aquatic organisms, and in turn their access to the chain food, is
likely to depend on the filtering properties of the biofilms that surround
various microbes. Attractive interactions between the nanoparticles and
biofilms are expected to favor retention [94–96], while repulsive interac-
tions will prevent nanoparticle diffusion in the organic network.

Diffusion in biofilms and gel-like structures. In porous and disordered media
such as soil, biofilms, or bacterial flocs, the random movement of diffus-
ing particles is constrained. Diffusion in these disordered gel-like systems
is often modeled as transport through a fractal structure [97]. In uniform
Euclidean systems, for every number of dimensions, the random diffusion
motion of a nanoparticle denoted by superscript A is described as [98]:

2
A
A
x std 5 2dD t (29)
2
where x std A is the mean square displacement of the diffusing solute at
time t; D is the nanoparticle diffusion coefficient; and d is the dimen-
sionality of space. The diffusion properties of small particles in gels has
been related to three distinct parameters [99–101] that affect the dis-
tribution of particles in a gel saturated with water described by a global
partition coefficient
[99]:

[A] g
5 ap 5 (30)
[A] w

where [A] and [A] are the nanoparticle concentrations in the gel and
w
g
in the bulk solution, respectively; and , , and are the respective con-
tributions of purely steric, chemical, and electrostatic effects.
Steric obstruction. Steric interactions arise in disordered systems when
the nanoparticle approaches the size of the interconnected pores in the
media. (This is different from the steric interactions affecting particle
stability discussed earlier.) The potential for collisions with the pore
walls in the media reduces the degrees of freedom for particle movement,
with a resultant reduction in the macroscopic diffusion coefficient of
the particle in the disordered media compared with unconstrained dif-
fusion in the bulk fluid. These obstructions may be characterized in
terms of a steric obstruction coefficient [102]:

R A 2
5 s1 2 fd 3 a1 2 b (31)
R p