Environmental Engineering Reference
In-Depth Information
aggregation.pathway.(
X
.+.
X
,.
XX
.+.
XX
,.
XXX
.+.
XXX
,.…)..Using.this.approach,.not.
only.is.the.range.recognized,.but.also.the.relative.probability,.which.is.a.function.of.
the.relative.collision.kinetics.of.the.intermediates,.is.retained.
6.3.2 p
rediCting
t
empOral
r
eaCtiOn
r
ates
: e
stimating
p
artiCle
a
FFinities
In. addition. to. a. method. to. determine. the. time. course. of. the. collision/diffusion.
kinetics,.prediction.of.the.fate.of.nanomaterials.requires.derivation.of.the.probabil-
ity. of. a. reaction. resulting. in. the. formation. of. a. product. per. collision. event,.
P
(
r
)..
Experimentally,. this. is. reasonably. easy. to. determine. within. the. conidence. of. the.
collision. kinetics. as. the. ratio. of. observed. product. formation. given. the. determined.
rate.of.collision:
k
k
x
′
X
+
X
→
Y
P r
( )
=
.
.
(6.23)
Dx
where.
k
´
Dx
.is.the.rate.of.collision.based.on.diffusion.and.
k
´
x
´
.is.the.rate.of.product.
formation..Deriving.
P
(
r
).from.thermodynamic.principles.is.dificult.because.of.the.
number.of.competing.forces.and.from.the.limited.knowledge.regarding.near-body.
interactions.in.solution..Hence,.the.methods.described.below.should.only.be.consid-
ered.a.means.of.estimation.
It. is. generally. true. that. the. more. thermodynamically. advantageous. a. reaction,.
the.more.likely.it.is.to.occur,.and.therefore.the.faster.the.rate.of.product.formation..
With.respect.to.the.agglomeration.of.nanoparticles,.product.formation.occurs.when.
the.forces.of.attraction.outweigh.the.forces.of.repulsion..This.summation,.however,.is.
not.straightforward.because.the.molecular.force.ields.around.each.nanoparticle.vary.
with.distance.from.the.particle..The.energy.required.to.overcome.these.force.ields.
depends.on.the.kinetic.energy.of.the.particles,.which.is.neither.constant.nor.uniform.
Derivation.of.predictive.values.for.the.free.energy.of.solvation.—.and.its.inverse,.
the.free.energy.of.precipitation.—.takes.into.account.the.afinity.of.the.solvent.(in.
this.case,.air.or.water).for.the.solute.relative.to.the.afinity.of.the.solute.particle.for.
other.solute.particles..These.afinities.are.chemical.speciic..However,.it.is.possible.
to.generalize.the.interactions.of.a.nanoparticle.with.its.solvent.medium.
Consider.an.example.of.a.nanoparticle.introduced.to.an.aqueous.medium:
•
If.the.nanoparticle's.surface.afinity.for.like.nanoparticles.is.low.relative.to.
the.afinity.for.the.water.molecules,.then.the.material.will.disperse.
If.the.nanoparticle.has.a.low.afinity.for.like.nanoparticles.but.its.afinity.
for.polar.water.molecules.is.insuficient.to.overcome.the.water-water.afin-
ity,.then.the.material.will.be.hydrophobic.and.will.not.disperse.in.water.but.
will.disperse.in.nonpolar.environments.at.the.solvent.interface.
If.the.nanomaterial.has.a.high.afinity.for.like.nanoparticles,.the.material.
will.not.disperse.in.either.aqueous.or.nonaqueous.environments.
•
•
These. situations. are. never. absolute.. In. general,. the. stronger. the. afinity. of. the.
nanoparticle.for.water,.the.higher.the.equilibrium.concentration.—.and.vice.versa..
(Recall.that.if.the.free.energy.of.solvation.is.less.than.zero,.then.a.material.will.dis-
perse.spontaneously.in.water.)
