Environmental Engineering Reference
In-Depth Information
Dispersion.in.air.(aerosol).differs.from.hydrosol.formation.principally.because.
(1).the.luid.medium.has.a.lower.density.and.higher.particle.velocities;.(2).the.medium.
has.a.low.dipole.moment;.and.(3).the.medium.has.a.low.dielectric.constant..There-
fore,.the.primary.factors.in.air.dispersion.are.particle.size.and.inter-particle.afinities.
that.are.related.to.inducible.net.zeta.potential.in.air.
In. both. cases. —. dispersion. in. water. and. dispersion. in. air. —. the. fate. of. the.
nanoparticle.results.from.the.interplay.of.competing.interactions.at.the.nanoparticle.
interface..To.predict.the.probability.of.agglomeration.and.thereby.the.stability.of.the.
nanomaterial,.the.force.ields.at.this.interface.must.be.described.in.thermodynamic.
terms.that.then.can.be.converted.to.a.probability.density.function.
6.3.3 n
anOpartiCle
a
FFinity
and
i
nter
-p
artiCle
F
OrCe
F
ields
Interactions. between. nanoparticles. and. environmental. constituents. such. as. luid.
media.are.expected.to.result.predominantly.from.Coulomb.(electrostatic).forces.and.
van.der.Waals.interactions..That.is.not.to.say.that.nanomaterials.will.not.undergo.
covalent.reactions.within.the.environment..An.example.of.such.a.reaction.is.the.appli-
cation.of.zero-valent.iron.in.groundwater.remediation.where.the.iron.nanoparticles.
undergo.direct.redox.reactions.with.groundwater.contaminants.[8]..However,.this.is.
the.exception.and.speciic.to.the.type.of.nanoparticles.involved..Coulomb.forces.will.
occur.in.any.situation.where.the.particle/medium.system.permits.the.formation.of.a.
charge.imbalance..van.der.Waals.interactions.are.universal.to.nanoparticles.and.will.
differ.among.type.only.with.regard.to.their.magnitude.
...
Coulomb energy
In. agglomeration. reactions,. the. Coulomb. force. is. almost. always. repulsive.. This.
occurs.because.it.is.most.common.that.like.particles.in.the.same.medium.will.acquire.
the.same.type.of.charge,.although.the.charge.density.may.vary.with.the.particle.size..
Charges.can.arise.as.the.result.of.charge.separation.producing.a.dipole.situation,.but.
unlike.molecular.dipoles,.this.is.usually.aligned.between.the.outside.surface.of.the.
particle.and.its.interior..As.such,.steric.hindrance.inhibits.differential.charge.interac-
tions..The.potential.energy.(
E
(
C
)
xx´
).arising.from.the.Coulomb.forces.between.the.
two.particles,.
X
.and.
X
´,.can.be.deined.as.follows:
q
⋅
q
.
E C
(
)
=
x
x
′
.
(6.24)
xx
′
4
π
⋅
z
⋅
e
⋅
e
0
s
where.
q
.is.the.net.particle.charge.on.
X
.or.
X
´,.e
0
.is.the.electric.constant.(8.85.×.10
-12
.
C
2
·N
-1
·m
-2
),.e
s
.is.the.dielectric.constant.of.the.medium,.and.
z
.is.the.particle.separa-
tion.[9]..This.can.be.optimized.for.the.interaction.between.two.spheres.as.follows.
[10]:
−
k
q
⋅
q e
z
.
E C
(
)
=
x
x
′
.
(6.25)
xx
′
(
)
4
π e
⋅
⋅
e
⋅
z
⋅
1
+
2
k
z
0
s
0
where.k.is.the.inverse.Debye.screening.length.(≈.1.43.nm).
