Chemistry Reference
In-Depth Information
system. The total interaction energy, V (h), is given as (Scheludko, 1966; Bockris et
al., 1980; Adamson and Gast, 1997; Chattoraj and Birdi, 1984; Birdi, 2002)
V(h) = V
el
+ V
vdw
(7.18)
where V
el
and V
vdw
are electrostatic repulsion and van der Waals attraction compo-
nents. Dependence of the interaction energy
V
(h) on the distance
h
between particles
has been ascribed to coagulation rates as follows:
a. During slow coagulation
b. When fast coagulation sets in
The dependence of energy on
h
and V(h),
V(h) = [(64 C RT ψ
2
)/
k
exp(−
k
h
) −
H/
(2 h
2
)
(7.19)
satisfies the requirements of this coagulation rate. For a certain ratio of constants, it
has the shape shown in Figure. 7.8. For large values of
h
, V(h) is negative (attraction),
following the energy of attraction V
vdw
, which decreases more slowly with increasing
distance (~ 1/h
2
). At short distances (small h), the positive component V
el
(repulsion),
which increases exponentially with decreasing
h
, (exp(−
k
h), can overcompensate
V
vdw
and reverse the sign of both dV(h)/dh and V(h) in the direction of repulsion. On
further reduction of the gap (very small h), V
vdw
should again predominate since
V
el
= 64 C RT ψ
2
/k, as h ≥0
(7.20)
whereas the magnitude of V
vdw
increases indefinitely when h > 0. There is thus a
repulsion maximum in the function V(h), which can be easily found from the condi-
tion dV(h)/dh = 0. The transition from stability (a) to instability (c) as the electrolyte
concentration, C, is increased as shown in Figure 7.8. Curve (b) corresponds to the
onset of rapid coagulation. The choice of solution (maximum or minimum) does
not present any difficulty since V(h) is positive for the maximum. The solution of
V(h)
a
h
b
c
FIGure 7.8
Variation of V(h) vs. h: (a) stable; (b) rapid coagulation; (c) unstable. (See text
for details.)
Search WWH ::
Custom Search