Page 224 - Introduction to Colloid and Surface Chemistry

Colloid stability 213

For the case of two spherical particles of radii a\ and a 2, Stern
potentials, 0 dl and 0 d2, and a shortest distance, H, between their
Stern layers, Healy and co-workers 195 have derived the following
expressions for constant-potential, V R, and constant-charge, V R,
double-layer interactions. The low-potential form of the Poisson-
Boltzmann distribution (equation 7.12) is assumed to hold and KU\
and K.ai are assumed to be large compared with unity:

(a,+a 2 )

r
l i n(1- exp[-2K//])l (8,2)
-exp[-K//]J j

where € is the permittivity of the dispersion medium and K is as
defined in equation (7.6)
Table 8.2 shows the signs of V R that accord with equations (8.1)
and (8.2) for different homocoagulation and heterocoagulation
situations. (N.B. Attraction is negative and repulsion positive.)
= a 2 = a and 0 dl = 0 d2 = </r d, equations
For equal spheres, with a t
(8.1) and (8.2) reduce to
(8.3)
and

For small electric double layer overlap, such that exp [-K//] < 1,
these expressions both reduce to

= 2ireai^ exp[-K//] (8.5)
V R