Competitive Sorption and Transport - Transport and Fate of Chemicals in Soils: Principles and Applications - page 200

concentration in solution. Harmsen (1977) and Bond and Phillips (1990)
expressed the Rothmund-Kornfeld selectivity coefficient as:

n

ν
ν

j ν

ν

j

()
()

()
()

s
s

c
c

i i

=

R

( 7. 8)

K ij

i i

j j

where n is a dimensionless empirical parameter associated with the ion pair
i - j and R K ij is the Rothmund-Kornfeld selectivity coefficient. The above equa-
tion is best known as a simple form of the Freundlich equation, which applies
to ion exchange processes. As pointed out by Harmsen (1977), the Freundlich
equation may be considered as an approximation of the Rothmund-Kornfeld
equation valid for s i << s j and c i << c j , where:

R n

()

s =

K c ( 7. 9)

i ij

The ion exchange isotherms in Figure 7.6 show the relative amount
of Zn and Cd adsorbed as a function of relative solution concentration
along with best-fit isotherms based on the Rothmund-Kornfeld equation
for two acidic soils (Hinz and Selim, 1994). The diagonal line represents
a non-preference isotherm ( R K ij = 1, n = 1) where competing ions (Ca-Zn
or Ca-Cd) have equal affinity for exchange sites. The sigmoidal shapes of
the isotherms reveal that Zn and Cd sorption exhibit high affinity at low
concentrations, whereas Ca exhibits high affinity at high heavy metal con-
centrations. This behavior is well described by the Rothmund-Kornfeld
isotherm with n less than one. Isotherms in Figure 7.6 are consistent with
those of Bittel and Miller (1974), Harmsen (1977), and Abd-Elfattah and
Wada (1981). However, Abd-Elfattah and Wada obtained much larger
selectivities for low heavy metal concentrations on exchange surfaces com-
pared to the results shown.

7.3 Kinetic Ion Exchange
Numerous studies have indicated that ion exchange is a kinetic process in
which equilibrium is not instantaneously reached. Observed kinetic or time-
dependent ion exchange behavior is most likely a result of the transport of
initially sorbed ions from exchange sites to the bulk solution and the reverse
process of the transport of replacing ion from bulk solution to exchange sites.
Specifically, the rate of ion exchange is dependent on the following processes:
(1) diffusion of ions in the aqueous solution, (2) film diffusion at the solid-
liquid interface, (3) intraparticle diffusion in micropores and along pore wall
surfaces, and (4) interparticle diffusion inside solid particles (Sparks, 1989).
Due to the complexity of the kinetic processes, over the last three decades