Page 238 - Introduction to Colloid and Surface Chemistry

Colloid stability 227

2
2
(2e N cz 1
Substituting — for K (equation (7.6)) gives
v e ** J
5 5
x
___
9.85__ 10VA: F y
c,c.c.= (8.14)
N,e A z
For an aqueous dispersion at 25°C, equation (8.14) becomes

3.84x10 J _ 3
r
c.c.c.= - — — moldm

A number of features of the Deryagin-Landau-Verwey-Overbeek
(D.L.V.O.) theory emerge from these expressions:

1. Since y limits to unity at high potentials and to zet^^kT at low
potentials, critical coagulation concentrations are predicted to be
proportional to 1/z 6 at high potentials and to $j/z 2 at low
potentials (see Figure 8.6). For a typical hydrosol, t]/ d will have an
intermediate value in this respect. Taking 75 mV as a typical value
for $d (see Figure 7.4), critical coagulation concentrations of inert
electrolytes with z — 1, 2 and 3 are, for a given sol, predicted to be
in the ratio 100 : 6.7 : 0.8. This is broadly in accord with
experimental c.c.c. values, such as those presented in Table 8.1.
The experimental values, however, tend to show a significantly
stronger dependence on z than predicted above, and this probably
reflects increased specific adsorption of counter-ions in the Stern
109
layer with increasing z .
2. For a typical experimental hydrosol critical coagulation concen-
3
tration at 25°C of 0.1 mol dm" for z = 1, and, again, taking tfr d =
75 mV, the effective Hamaker constant, A, is calculated to be
equal to 8 x 10~ 20 J. This is consistent with the order of
magnitude of A which is predicted from the theory of London-van
der Waals forces (see Table 8.3).
3. Critical coagulation concentrations for spherical particles of a given
3
material should be proportional to e and independent of particle size.
The definitions of the term 'critical coagulation concentration' (a)
in relation to experimental measurements and (b) as a means for