92168.pdf

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

kT

and n_ = « 0 exp±£5*1

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_

H

-zetj/1 f-fze^l

-exp -\

kT J L kT J

= -2z£/i 0 sinh

zetf/

kT

(7.1)