Biomedical Engineering Reference
In-Depth Information
7.3.3 Adsorption and the Langmuir Model
7.3.3.1 Langmuir Model
Another very important class of reactions in biotechnology is the adsorption of mol-
ecules on a solid functionalized surface. In particular, it is the case of DNA hybrid-
ization. In such a reaction, there are three components: first, a “free” substrate in
a buffer fluid sometimes called “target” or “analyte,” in concentration [
S
]; second,
a surface concentration [G]
0
of ligands—or capture sites—immobilized on a func-
tionalized surface; third a product which is the surface concentration of adsorbed
targets, that we denote [G] (Figure 7.22). Note that [
S
] is a
volume concentration
(unit mole/m
3
) whereas [G] and [G]
0
are surface concentration (unit mole/m
2
). Such
a kinetic is called a Langmuir-Hinshelwood mechanism.
The reaction is weekly reversible because targets are constantly captured by ligands
and they constantly dissociate (at a smaller rate). The reaction may be symbolized by
S
® G
G ®
S
In the case of adsorption, the reaction rates are somewhat different to the defi-
nition of the usual chemical rates, mainly because the rate the immobilization of the
substrate
S
depends not only on the volume concentration at the wall, but also on
the available sites for adsorption. Thus, we can write
d S
[ ]
v
= -
=
k
([
G - G
]
[
])[ ]
S
on
0
w
d t
(7.35)
d
[
G
]
v
¢
= -
=
k
[
G
]
off
d t
where
k
on
and
k
off
are called respectively the adsorption and dissociation rates and
[
S
]
w
is the concentration at the wall. For simplicity we will note G
=
[G],
c =
[
S
] and
c
0
= [
S
]
w
. The net rate of adsorption is then
d
G
=
k c
(
G - G -
)
k
G
(7.36)
0
0
on
off
dt
Figure 7.22
Adsorption of targets on a surface functionalized with immobilized ligands.
