Environmental Engineering Reference
In-Depth Information
E w
KT
(
)
xx
e
a
xx
=
E w
(
)
E C
KT
+
(
)
xx
xx
e
where
A
xsx
E w
(
)
= −
xsx
12
π
⋅
z
m
.
.
(6.31)
and
2
d
z
x
E C
(
)
=
xx
4
π
⋅
⋅
e
⋅
e
0
s
and
=
∑
e
e
⋅
[ ]
i
⋅
MR
i
s
i
where.
MR
.is.the.molar.refractivity.(l/m).of.constituent.
i
.
Because. the. probabilities. are. based. on. the. energy. balance. at. the. point. of. col-
lision,. they. are. concentration. independent.. The. point. of. collision,. deined. as. the.
effective.particle.radius.(
z
).in.the.interaction.model,.represents.the.distance.where.
the. kinetic. energy. of. the. particles. is. equal. to. the. repulsive. forces.. Therefore,. the.
probability.of.interaction.is.equal.to.the.agglomeration.eficiency:
a
=
P X X
(
·
)
xx
.
and
.
(6.32)
P X H O
(
·
)
=
1
−
a
2
xx
6.3.5 s
ummary
The.approach.described.above.can.be.extremely.useful.in.assessing.the.possible.risks.
from.nanomaterials.because.it.permits.the.prediction.of.signiicant.nonequilibrium.
behavior. based. on. measurable. physical. properties.. Simple. qualitative. assessment.
will.enable.a.determination.of.the.stability.of.the.nanoparticles..Detailed.quantita-
tive.assessment.will.allow.the.prediction.of.the.particles'.behavior,.and.thereby.the.
extent.of.potential.distribution.within.the.environment.
Consider.the.example.of.dispersed.C60
.
fullerene..Materials.such.as.carbon.nano-
tubes.and.fullerenes.are.not.stable.in.the.environment.and.will.agglomerate.under.
conditions. where. the. van. der. Waals. attraction. can. overcome. electrostatic. forces..
When.dispersed.as.either.a.hydrosol.or.aerosol,.usually.as.the.result.of.mechanical.
agitation,. carbonaceous. nanoparticles. immediately. begin. to. agglomerate,. forming.
larger.and.larger.super-particles..The.rate.of.agglomeration.is.a.function.of.the.imme-
diate.concentration.of.the.materials..Because.the.particles.are.subject.to.diffusion,.a.
