Sorption Isotherms - Transport and Fate of Chemicals in Soils: Principles and Applications - page 3

1.2.1 Two-Site Langmuir

Based on several retention data sets, the presence of two types of surface
sites responsible for the sorption of phosphate (P) in several soils was postu-
lated. As a consequence, the Langmuir two-surface isotherm was proposed
(Holford, Wedderburn, and Mattingly, 1974) such that:

S ω

+ω

C

+

ω
+ω

C

1 2

= F F

(1.4)

1 2

S 1 C 1 C

max 1 2

where F 1 and F 2 (dimensionless) are considered as fractions of type 1 and
type 2 sites to the total sites ( F 1 + F 2 = 1), and ω 1 and ω 2 are the Langmuir
coefficients associated with sites 1 and 2, respectively. Equation 1.4 is an
adaptation of the original equation proposed by Holford, Wedderburn, and
Mattingly (1974) and was used by Holford and Mattingly (1975) to describe P
isotherms for a wide range of soils.
A more recent adaptation of the two-surface Langmuir equation is the
incorporation of a sigmoidicity term, where

+

S ω

+ω +σ

C
CC F

ω
+ω +σ

C
CC

1 2

= F

/) .

1 2

(1.5)

S 1 ( /) 1 (

max 1 1 2 2

The terms σ 1 and σ 2 are the sigmodicity coefficients (μg cm -3 ) for type 1 and
type 2 sites, respectively. Schmidt and Sticher (1986) found that the introduc-
tion of this sigmoidicity term was desirable in order to adequately describe
sorption isotherms at extremely low concentrations. Although the Langmuir
approach has been used to model P retention and transport from renovated
wastewater, the two-surface Langmuir with sigmodicity has been rarely
used to describe heavy metal retention during transport in soils. It should be
emphasized that for both Langmuir and Freundlich isotherms, an implicit
assumption is always made, namely, that equilibrium conditions are domi-
nant. Therefore, these formulations do not take into consideration possible
time-dependent or kinetic sorption behavior. Such sorption behavior is com-
mon for most solutes and is considered in Chapter 2.

1.3 General Types of Isotherms
Giles, D'Silva, and Easton (1974) proposed four general types of isotherms (C,
L, H, and S), which are illustrated in Figure 1.1. The C-type isotherms indi-
cate partitioning of ions or molecules between the solution and sorbed phase
along the same lines as that of the linear model (Equation 1.2). The L-type