Environmetal Soil Properties and Behaviour

Environmetal Soil Properties and Behaviour


DisciplinaControle e Remediação da Poluição dos Solos5 materiais18 seguidores
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the clay particles. Of the various kinds of electrochemical mod-
els proposed to explain and determine the nature and distribution of ions 
adjacent to the clay particle surfaces (Stern, 1924; Grahame, 1947; Kruyt, 1952; 
Sposito, 1984; Ritchie and Sposito, 2002), there is common agreement on the 
diffuse double-layer concept. The model that exemplifies this concept is gen-
erally identified as the diffuse double-layer (DDL) model, as shown in the 
schematic illustration in Figure 3.5. The partly hydrated cations and anions 
in the inner Helmholtz plane shown in the figure are potential determining 
ions (pdis) which are bonded to the reactive surfaces by ionic and covalent 
bonds. They contribute directly to the net electric charge and potential on 
the surfaces of reactive particles. The structured water adjacent to the surface 
of the particle is due to the specifically adsorbed ions at the interface. Values 
of up to 1.14 g/cm3 for water density have been measured for the first layer of 
water molecules, decreasing as the layers are added to 0.917 g/cm3 at about 
four water layers before increasing to 1.0 g/cm3 for free water. The viscosity 
of the hydration layer as measured by diffusion of ions near the surface is 
89Soil\u2013Water Systems
much greater than that of free water\u2014about 2.5 × 10\u22123 Pa s\u2014and the dielec-
tric constant decreases as one approaches the surface of the particle.
The complexes that are formed between the surface functional groups and 
the ions at the electrified interface are inner sphere complexes, and they have 
direct contact between them without interruption from any water molecule 
(Ritchie and Sposito, 2002). When a layer of water molecules interrupts con-
tact between these, the complexes are classified as outer sphere complexes. 
The inner Helmholtz plane (ihp) and outer Helmholtz plane (ohp) shown in 
Figure 3.5 identify the positions of the inner sphere and outer sphere com-
plexes with corresponding distances of \u3c7 and \u3b2, respectively. The thickness 
of the Stern layer \u3b4, which includes the ihp and the ohp, according to the 
Grahame (1947) model, is obtained by summing up the distances as \u3b4 = \u3c7 + 
\u3b2. According to the DDL model, the diffuse ion layer consists of the counter-
ions beyond the Stern layer needed to satisfy the net negative charge of the 
reactive particles.
3.3.1.1 Diffuse Double Layers
The interactions of diffuse double layers between adjacent and proximal 
clay particles are responsible, to a large extent, for the properties of swelling, 
plasticity, water retention, and other processes involving aqueous solution 
Inner Helmholtz plane (ihp)
Outer Helmholtz plane (ohp)
Diffuse ion-layer
\u3c7 \u3b2
\u3b4 Distance x from particle surface
Potential \u3c8
\u3c8oh = \u3c8\u3b4
\u3c8s
\u3c8
Edge view 
of particle
Clay mineral particle
\u3c8ih
Stern layer
FIguRE 3.5
Generalized DDL model showing electrified interface with aqueous solution containing dis-
solved solutes.
90 Environmental Soil Properties and Behaviour
interaction with the clay particles. This makes it important for one to have a 
better appreciation of what constitutes the diffuse double layers and how these 
double layers feature in the development of the various properties of soils.
The exchangeable cations (counterions) in the diffuse double layer shown 
in Figure 3.5 are located at some distance from the surface of the clay particle. 
Whilst the electrical forces between the net negatively charge surface and the 
positively charged ions serve to attract the cations to the particle surface, the 
thermal energy forces them to diffuse away from the surface. The balance of 
Coulomb electrical attraction and thermal diffusion leads to a diffuse layer 
of cations, with decreasing concentration as one moves further away from 
the particle surface. The theoretical distribution of cations in the diffuse dou-
ble layer can be calculated using some simplifying assumptions, namely: (a) 
clay particles can be considered as simple charged plates for which the elec-
tric field is described by the Poisson equation, and (b) the distribution of ions 
is described by the Boltzmann equation. Yong and Warkentin (1975) show 
that with these assumptions, the relationship for n+, the number of cations 
per unit volume at a distance x from the clay particle surface, is obtained as
 
n n
x z e n
Ti
i i
+ =
\uf8eb
\uf8ed\uf8ec
\uf8f6
\uf8f8\uf8f7coth 2
8 2 2
2
pi
\u3b5\u3ba
 (3.1)
where ni and zi are the concentration and valence of the ith species of ion in 
the bulk solution; and \u3b5, e, \u3ba, and T represent the dielectric constant, electronic 
charge, Boltzmann constant, and temperature, respectively. Calculations 
using Equation (3.1) for n+ for a 0.001 M salt with monovalent ions (Yong and 
Warkentin, 1975) give a value of n+ at x = 5 nm as 0.016 M. This shows that 
the concentration of cations at this distance of 5 nm from the particle surface 
is at least 16 times that of the concentration of cations in the bulk solution.
The extent of the diffuse double layer is related to the concentration and 
valence of the cations in the bulk solution. The lower the concentration and 
valence, the larger the ratio of n+ / ni. Monovalent ions at low concentrations 
provide the largest diffuse double layers. Increasing either the valence or 
the salt concentration in the porewater will reduce the extent of the diffuse 
double layers (Figure 3.6). For a divalent ion at the same concentration of 
0.001 M used in the previous calculation example, the value of n+ at x = 5 
nm is 0.004 M, showing that the concentration of cations at this distance is 
one-fourth that of the monovalent ions as shown in Figure 3.6.
3.3.1.2 Electric Potential \u3c8
The electric potential \u3c8s at the surface of the clay particle, which is defined as 
the surface potential and which varies with electrolyte concentration and the 
nature of the charge of the clay particle, decreases to a potential of \u3c8\u3b4 at the 
91Soil\u2013Water Systems
outer Helmholtz plane (ohp). Although this is shown as a linear drop from \u3c8s 
to \u3c8\u3b4 in Figure 3.5, there is considerable discussion as to the exact nature of 
this potential drop. Electrokinetically, \u3c8\u3b4 is considered to be equal (or almost 
equal) to the zeta potential \u3b6 \u2013 the electric potential in the slipping plane 
between the fixed and flowing liquid.
At distances beyond the ohp, the electric potential \u3c8 is described by the 
Gouy Chapman diffuse double-layer (DDL) model. With this model, one 
can compute the electric potential \u3c8 as a function of the distance x from the 
charged particle surface. Because of chemical bonding processes and com-
plexation in the \u3b4 region shown in Figure 3.5, simple electrostatic interaction 
calculations do not apply in this region. To determine \u3c8 in relation to x, the 
following assumptions and conditions are prescribed:
\u2022	 Coulombic interaction occurs between the charged ions (cations and 
anions) in solution and the charged clay particle surfaces.
\u2022	 The interactions between ions in solution and clay particles are deter-
mined in terms of the electric potential \u3c8 and are described by the 
Poisson relationship in respect to variation of \u3c8 with distance x away 
Distance x, nm
0 5 10 15
n +
/n
i
20
15
10
5
1
Divalent
cations
Monovalent
cations
Anions
An
io
ns Cations
Cations
Distance x
0.1 molar
0.001 molar
n/
n i
FIguRE 3.6
The bottom-left diagram shows the theoretical distribution of ions at a charged clay particle 
surface in relation to the influence of valence on the thickness of the diffuse double layer. Top 
right shows the influence of salt concentration on the theoretical distribution of cations and 
anions (n refers to the number of cations or anions).
92 Environmental Soil Properties and Behaviour
from the particle surface, as shown in Figure 3.5 as d2\u3c8 / dx2 = \u2013 4\u3c0\u3c1 /\u3f5, 
where