Page 163 - Book Hosokawa Nanoparticle Technology Handbook

3.5 INTERACTIONS BETWEEN PARTICLES FUNDAMENTALS
3.5.2 Control of interactions between particles in it is important to know the degree of each con-
liquids tribution of the kinetic energy and interaction
potential to the dispersion stability [3].
Many colloidal particles in industrial processes are in
flow fields, where particles are flowing, colliding The most fundamental concept (1) described above is
with each other. The stability of these particles is explained below. The details of the concept (2) are
decided by the combination of hydrodynamic and given elsewhere [3].
static interactions between particles. In other words, it
depends on the balance between their kinetic energy 3.5.2.1 Charging mechanism of colloidal particles
and interaction potential whether the collision of par- When particles are dispersed in solutions, their sur-
ticles results into their coagulation or the dispersion faces are more or less charged. The charging mecha-
by their rebound. The relative motion of i particle nism is classified as follows: the charging by
against j particle are determined by the equation of functional groups on the particle surface, the charging
motion. by adsorbed ions and the charging by isomorphic sub-
stitution.
mdv dt) F F F F ij (3.5.41)
(
ij
B
ij I
ij
i
(1) Charging by functional groups
When the particle surface has the functional group,
where m is the mass of colliding particle i, v the rel- such as –OH, –COOH and –NH , the surface will be
ij
i
3
ative velocity of i and j particles, t the time and F , charged by the dissociation in an aqueous solution.
Iij
F , F Fij are the vectors which represent the static For oxide particles, such as SiO , TiO and Al O ,
Bij
2
3
2
2
interactions between particles, the time-averaged water molecules adsorb and form –OH groups on the
force due to the Brownian motion and the hydrody- surface, as shown below.
namic interactions, respectively. F Iij is called the
static interaction force independent of the fluid
OH
motion, such as the electrostatic and the van der M OH H M OH M O H O

Waals forces. On the other hand, F Bij and F Fij are 2 2
called the dynamic interaction force generated by the
motions of particles and fluids. There exist two con- where M indicates a metal atom. In the cases of oxide
cepts on the stability, that is, coagulation and disper- particles, as well as zwitterionic particles, the surface
sion, of colloidal particles. potential is always positive at low pH and becomes
negative at high pH. Hence there exists the point
(1) One is that the stability of dispersions is
of zero charge (pzc) (pH ) in-between as shown in
0
determined qualitatively only by the absolute Table 3.5.5.
magnitude of F . When the repulsive force of
Iij
F is large enough, the collisions of particles (2) Charging by ionic adsorption
Iij
do not result into their coagulations, so that For AgI crystal particle, the surface charge is deter-

mined by the excess amount of either Ag or I ions
the dispersion is regarded as stable. In this
adsorbed on the particle surface. This surface poten-
way, the stability of dispersions is able to be tial is able to be calculated by the so-called Nernst
0
determined without knowing the detailed rel- equation:
ative motion of particles. This kind of deci-
sion on the stability of dispersions is very ⎛ ⎜ 2.3kT ⎞ ⎟ (pAg pAg ) (3.5.42)
useful when either the absolutely stable dis- 0 ⎝ e ⎠ 0
persions or the absolutely unstable disper-
sions are needed. Studies of these kinds have where k is the Boltzmann constant, T the temperature,
been carried out extensively in the field of the e the elementary charge. A few other crystal particles,
such as AgBr, AgCl, Ag S, AgCNS, and BaSO , are
science of colloid chemistry [1, 2]. 2 4
charged by the same mechanism. Values of the point of
(2) The other concept is that the stability of dis-
zero charge, pAg , are given in Table 3.5.5.
0
persions should be determined quantitatively
by solving equation (3.5.41), including the (3) Charging by isomorphic substitution
dynamic interaction forces between particles. This charging mechanism is found particularly in clay
minerals. When there are defects in the crystal lattice
The dynamic behavior of particles is especially 4 3
of particles in which Si is substituted by Al , the
important in the particle processing, where the
deficit of charge results in charging particles. This
collision of particles always occurs. In this case, charge is not affected by the solution pH.
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