their intrinsic ionisation constants from potentiometric and conductometric titra-
tions. Two types of ionisable sites with intrinsic ionisation constants pK
s1
¼ 2:6 and
pK
s2
¼ 6:4 were distinguished. The total number of sites, N
1
þ N
2
¼ 4:8 10
17
(sites/m
2
), was calculated from the CEC of 0.59 meq/g (mont morillonite of Kuz-
mice). The ratio of weak and strong acid groups was N
2
=N
1
¼ 0:41, i.e. 29% of all
sites were weak acidic centres. The most acidic sites were the H
3
O
+
ions replacing
exchangeable Na
+
ions (Janek and Lagaly, 2001 ). The surface potential as a func-
tion of pH was calculated from the charge densities. At 10
3
M NaCl and above pH
4, the surface potential showed a plateau at 185 mV. This value decreased to 70 mV
in 10
–1
M NaCl and to 30 mV in 1 M NaCl, and the plateau extended to pHE6. On
the basis of these surface potentials, the total interaction curves (Hamaker co nstant
A ¼ 0:5 10
20
J) were hypothetical at small distances (see remark above), but they
clearly showed that the maximum of the total interaction energy disappears at about
0.1 M NaCl (pH ¼ 2), 0.3 M NaCl (pH¼ 4), and 0.4 M NaCl (pH¼ 8). These results
agree with the experimental data for samples treated with sodium hexametaphos-
phate (0.1, 0.20.25, and 0.350.40 M at pH¼ 2, 4, and 8, respectively (Tomba
´
cz
et al., 1990)) and diphosphate (0.360.44 M at pH¼ 9, Frey and Lagaly, 1979b).
A quite different (and, for a colloid scientist, strange) view was put forward by
Low and co-workers (Sun et al., 1986; Low, 1987; Miller and Low, 1990) on the basis
of extensive studies on the clay–water system. They suggested that hydration of the
clay mineral surface was the primary cause of swelling. This ‘non-specific interaction
of water’ ( undefined term) with the clay surface cou ld not be fully explained. Hy-
dration of the interlayer cations was assumed to be of minor importance. However,
Delville and Las zlo (1989) showed that the Poisson-Boltzman n formalism correctly
reproduces the relation between interlayer distance and swelling pressure. The driv-
ing force is the stabilisation of water molecules within the interlayer force field. In all
cases, the Poisson- Boltzmann approximation, modified to incorporate ion/polyion-
excluded volume effects, led to a concentration profile in agreement with Monte
Carlo calculations. Quirk and Marc
ˇ
elja (1997) examined published data on the ex-
tensive swelling of Li
+
-montmorillonite as revealed by d
(00l)
spacings over the pres-
sure 0.050.9 MPa and 110
4
M LiCl. Both the Poisson–Boltzmann and DLVO
double layer theories satisfactorily predict surface separations over the range
1.812.0 nm. The DLVO theory with a 0 .55 nm-thick Stern layer indica ted Stern
potentials of 58 to 224 mV (for 110
4
M LiCl) and a constant Gouy plane
charge of 0.038 C/m
2
(about 30% of the layer charge). There was no additional
pressure contributing to hydration forces (Israelachvili, 1994) for surface separations
of about 1.8 nm or larger. (The hydration force was considerable for muscovite, with
a surface charge density about three times that of mon tmorillonite (Pashley and
Quirk, 1984)).
In the presence of Ca
2+
(and other di- and tri valent metal) ions, the particles
remain coagulated and cannot be dispersed even in pure water. Fitzsimmons et al.
(1970) showed that, just after contact of Na
+
-montmorillonite dispersions with cal-
cium-saturated exchange resins, Ca
2+
-montmorillonite exists as single layers like the
Chapter 5: Colloid Clay Science188