Page 189 - Introduction to Colloid and Surface Chemistry

178 Charged interfaces

Counter-ions

1/K
Distance (x) Distance (x)
Figure 7.1 Schematic representation of a diffuse electric double layer

n + =n 0 exp and n_ = « 0 exp ±£5*1
kT
where n+ and n_ are the respective numbers of positive and negative
ions per unit volume at points where the potential is ^ (i.e. where the
electric potential energy is zeifi and — ze$, respectively), and n 0 is the
corresponding bulk concentration of each ionic species.
The net volume charge density p at points where the potential is $
is, therefore, given by
p = ze(n + -n_
-zetj/1 f-fze^l
-exp -\
HkT J L kT J
zetf/
= -2z£/i 0sinh (7.1)
kT