Page 166 - Book Hosokawa Nanoparticle Technology Handbook

FUNDAMENTALS CH. 3 CHARACTERISTICS AND BEHAVIOR OF NANOPARTICLES AND ITS DISPERSION SYSTEMS

V V B

V R

V T
0
( r 2− a) a /
Secondary minimum
V A

Primary
(a)
minimum

V B
V B
-3
V C e = 10 mol/l V = 65 mV
0
-2
10 mol/l 50 mV
-1
10 mol/l 35 mV
0 0
−
−
( r 2 a) a / ( r 2 a) a /
V A ( = 0 mV)
0
V A
-2
= 65 mV C e = 10 mol/l
0
(b) (c)
Figure 3.5.11
Typical interaction potentials V between charged particles in solutions given by DLVO theory (a), the dependence on the
electrolyte concentration (b), and the dependence on the surface potential (c).
3.5.2.3 Control of dispersion stability using DLVO theory where the temperature and Hamaker constant are
As known from equations (3.5.50) and (3.5.52), the given by T(K) and A(J), respectively. This indicates
variable parameters in these equations are and C e that the value of CCC for trivalent cations is 1/729 of
0
(or ) only, because the others belong to the specific CCC value for mono-valent cations. This dependence
properties of dispersions. The value of C may be of CCC on z is confirmed experimentally, and the
e
altered by adding salts, and that of by the solution relation is known as the Schulze–Hardy law. This
0
pH. As illustrated in Fig. 2(b), (c), the dispersion coincidence between the prediction by the DLVO
becomes unstable, as C increases or decreases. theory and experimental results is one of the reasons
e
0
When the value of C increases, the electrostatic why the DLVO theory has been widely accepted as
e
repulsive potential disappears and the potential nearly the fundamental theory for hydrophobic colloids. In
coincides with the van der Waals potential at the so- the many real colloids, the following relation may
called critical coagulation concentration (CCC). At be used.
C CCC, the coagulation rate becomes constant. This
e
region is called the rapid coagulation region, and that of CCC
z n ( n 2 ) 6 (3.5.55)
C CCC is called the slow coagulation region. It is
e
known that the value of CCC depends on z. According This rule indicates that stable dispersions are obtain-
to the theoretical prediction, CCC(mol/l) for particles of able by reducing the concentration of multi-valent
high surface potential is expressed by the following ions, while the addition of multi-valent ions is very
equation: effective to promote the coagulation and the
solid–liquid separation. The stability of dispersions is

5
2
6
CCC 72 10 57 3 T z A (3.5.54) controllable also by the surface potential . At the
.
r 0
142