Environmetal Soil Properties and Behaviour

Environmetal Soil Properties and Behaviour


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and the absolute temperature, 
respectively; cc and co are the ion concentrations midway between particles 
and in the outside porewater; and x is the distance. The swelling pressure P 
can be calculated from the Van\u2019t Hoff relationship, if the swelling pressure is 
defined with osmotic pressure, as
 P = RT(cc \u2013 co) (4.1)
where R is the gas constant and T is the absolute temperature. If one uses ther-
modynamic concepts, the swelling pressure P is expressed as P = (\u3bco \u2013 \u3bcin)/\u3bdw, 
according to the relationship \u3c0 = CRT = \u2013 \u394\u3bc/\u3bdw, where \u3bco and \u3bcin are the chemi-
cal potentials of the outside porewater and water between particles, respec-
tively \u3bdw is the specific volume of water \u3c0 is the osmotic pressure, C is the molar 
ion concentration, and \u394\u3bc is the chemical potential difference.
Figure  4.2 shows that calculations using the Van\u2019t Hoff relationship for 
high-swelling sodium montmorillonite at low salt concentrations match 
measured values. However, at higher salt concentrations, the measured 
swelling pressures exceed the calculated values. Whilst some minor floc-
culation might be expected, the major culprit contributing to the difference 
between theoretically calculated and measured values probably results from 
errors in using concentrations rather than activities of the exchangeable ions, 
and from neglecting the tactoid structure of the clay. Since the activity coef-
ficients are not obtainable for situations where the concentration of cations 
exceeds that of the anions, as compared to the case for the region between 
contiguous particles, the errors in using the Van\u2019t Hoff relationship can-
not be strictly quantified. Bolt (1956), however, states that the magnitude of 
error obtained by using the Van\u2019t Hoff relationship is about 10%. One could 
therefore expect that calculated swelling pressures would undercalculate 
pressures in the high-pressure region, and overcalculate pressures in the 
low-pressure region.
141Swelling Clays
Application of the theory of the diffuse double layer (DDL) to calculate 
swelling pressures requires acceptance of the ideal behaviour or the ions 
in the double layer (ion layer). The Boltzmann relationship discussed in 
Section 3.3.1 in Chapter 3 is based on the principle that the work needed to 
bring an ion from the bulk solution into the area of the charged clay particle 
can be attributed solely to the potential energy of the ion in the field of the 
charged particle. However, the following issues and factors are not consid-
ered: (a) the polarization energy of the ion in the electric field, (b) the energy 
of interaction between the ion and the surrounding ions or water molecules, 
(c) the energy of interaction between the ion and the particle surface, and (d) 
the influence of dielectric saturation in the diffuse ion layer.
The energies of interaction between ion and surrounding ions or water 
molecules, and the energy of interaction between the ion and particle sur-
face have been addressed in Section 3.3.2, insofar as inclusion into an energy 
interaction model for calculations of swelling pressure. In regard to dielec-
tric saturation, Grahame (1947) indicates that this will not materially affect 
calculations based on a constant dielectric constant\u2014a conclusion based on 
the agreements obtained between his capacity measurements of mercury 
and calculations using the Gouy-Chapman model.
4.2.3 Swelling\u2014Effect of Salt Concentration 
and Porewater Composition
4.2.3.1 Higher Valences and Mixtures of Cations
The use of the Gouy-Chapman theory and the Van\u2019t Hoff relationship for cal-
culations of osmotic pressure would predict that an increase in porewater salt 
concentration would decrease the swelling of high-swelling clays. This pre-
diction is in accord with calculations that take into account the reduction in 
the diffuse ion-layer thickness. However, increasing salt concentration does 
not have the quantitatively predicted effect in decreasing swelling pressure. 
This is thought to be the result of low swelling in water combined with errors 
in using concentrations rather than activities. Furthermore, because divalent 
ions and higher valence ions are present mainly in the Stern layer, it follows 
that calculations of swelling pressure using the DDL (diffuse double-layer) 
model will not accord with measured values. For montmorillonite, there is an 
uncertainty about the relevant surface area to use in the calculations because 
the particles are arranged or grouped together into tactoids, resulting thereby 
in swelling only between the tactoids and not between individual particles. 
The studies of Norrish (1954) and Blackmore and Miller (1961) show that diva-
lent cations tend to restrict the swelling of montmorillonite to a maximum 
of about 0.9 nm because of stabilization of particles into tactoids or domains. 
Attempts made to modify calculations by taking into account tactoid surface 
areas have produced some level of agreement between theoretically calcu-
lated and measured values. Shainberg et al. (1971) have suggested that DDL 
142 Environmental Soil Properties and Behaviour
calculations can account for such behaviour if one makes allowance for the 
interparticle water in the tactoids, and if the analysis is based on the external 
ion distributions.
Because the swelling potential of swelling clays containing mixtures of 
cations is closely related to the content of Na ions in the free water relative 
to the divalent species of cations in the same free water, quantification of 
swelling can be undertaken in terms of the exchangeable sodium percentage 
(ESP) on the clay particle surfaces, or the sodium adsorption ratio (SAR) in 
the porewater. The ESP and SAR are given as follows:
ESP = [(Exchangeable Na+)/CEC]·100, where the units for Na+ and CEC 
are Meq/100 g.
SAR = Na+/[(Ca2+ + Mg2+)/2]½, where all concentrations are in Meq/L.
Soils with low salt concentrations and high SAR and ESP values will show 
high swelling characteristics. Swelling is generally not significant unless the 
ESP is at least 25 or more (McNeal et al., 1968; Quirk, 1968; Aylmore and 
Quirk, 1959).
4.2.3.2 Influence of Exchangeable Cations
The influence of exchangeable ions on water uptake in the interlayer and swell-
ing of montmorillonites shows decreasing uptake in the order of Li > Na > K > 
Rb > Cs. The decrease in interlayer swelling with increasing atomic number of 
alkali ions has been explained by Michaels (1959) as being due to the increas-
ing polarisability of the cations. This means to say that swelling increases with 
increasing hydration capability of the cation. The individual lattice-layers of 
swelling clays in the anhydrous state are assumed to be bonded to one another 
by secondary valence-force interactions between adjacent lattice-layer surfaces, 
and also by bridging action due to the exchangeable cations. Exposure of the 
anhydrous clay to water will result in separation of the various lattice-layers, 
with the degree of separation being dependent on the affinity of the cations 
for water relative to their affinity for the lattice-layer surfaces. If the hydration 
tendency of the cation is high, there will be a cluster of molecules around the 
cation, resulting in minimizing or reducing the original bridging role of the 
cations. The outcome will be high water sorption and swelling of the clay. It 
appears that as the hydration energies of the cations increase, the degree of 
swelling of the corresponding montmorillonite also increases.
The reciprocal thickness K of the diffuse double-layer is a function of 
the ionic valence zi and concentration ni. Figure 4.5 shows the influence of 
changes in valence of the ions present the diffuse ion layer in relation to 
the development or determination of the total potential \u3c8 as a function of 
distance x from a negatively charged clay particle surface (left