Environmental Engineering Reference
In-Depth Information
10
−
16
cm
2
. Therefore, the total surface area of the soil
values, we obtain
A
m
=
×
28
m
20 m
2
/g. For large polyatomic molecules,
S
a
= Γ
i
NA
m
=
ϕ
will be considerably
different from 1.091. Moreover, for ionic compounds the lateral interactions between
theadsorbateswillaffectthearrangementsinthemonolayer.Itisalsoknownthationic
compounds will affect the interlayer spacing in the soil, and hence will over-estimate
the surface areas. For these reasons, ideally, the BET surface areas are measured via
the adsorption of neutral molecules (e.g., nitrogen and argon).
3.5.3 A
DSORPTION AT
C
HARGED
S
URFACES
There are numerous examples in environmental engineering where charged (elec-
trified) interfaces are important. Most reactions in the soil-water environment are
mediated by the surface charges on oxides and hydroxides in soil. Colloids used for
settling particulates in wastewater treatment work on the principle that modifying
the charge distribution on particulates facilitates flocculation. Surface charges on air
bubbles and colloids help in removing metal ions by foam flotation. The aggregation
and settling of atmospheric particulates and the design of air pollution control devices
also involve charged interfaces. Most geochemical processes involve the adsorption
and/or complexation of ions and organic compounds at the solid/water interface. It
is therefore obvious that a quantitative understanding of adsorption at charged sur-
faces is imperative in the context of this chapter. Two notable topics deal extensively
with these aspects (Morel and Herring, 1993; Stumm, 1993). In this section, we shall
explore how the distribution of charges in the vicinity of an electrified interface will be
computed.The applications of this to the problems cited are delegated to Chapter 4. In
the aqueous environment, the problem of applying these simple principles of adsorp-
tion leads to a more complex theory that incorporates chemical binding to adsorption
sites besides the electrical interactions.This is called the
surfacecomplexationmodel
.
We shall discuss some of this in Chapter 4 and other reaction kinetics applications
in Chapter 6.
For the most part the approach is similar to the one used to obtain the charge
distribution around an ion. The Poisson equation from electrostatics is combined
with the Boltzmann equation from thermodynamics to obtain the charge distribution
function. This is known as the
Guoy-Chapman theory
. The essential difference is
that here we are concerned with the distribution of charged particles near a surface
instead of near an ion. For simplicity, we choose an infinite planar surface as shown
in Figure 3.20. The electrical potential at the surface,
Ψ
0
, is known. The planar
approximation for the surface holds in most cases when the size of the particles
near the charged surface is much larger than the distance over which the particle-
surface interactions occur in the solution. As shown in Figure 3.20, we have a double
layer of charges: a localized charge density near the surface compensated for by the
charge density in the solution. This is called the
diffuse-double-layermodel
. The final
equation for charge distribution is (Bockris and Reddy, 1970)
+
e
u
0
/
2
1
e
−κ
x
e
u
0
/
2
+
1
−
e
u/
2
=
−
e
u
0
2
1
e
−κ
x
,
(3.85)
e
u
0
/
2
+
1
−
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