Biomedical Engineering Reference
In-Depth Information
that are the constituents of the cellular membrane belong to this category. In a water
solution, the hydrocarbon tails minimize their interactions with the water, and the
molecules self-assemble into structures exposing only the hydrophilic headgroups
toward the water. In fact, they tend to aggregate into micelles such as the one de-
picted in Figure 8.8 as soon as their concentration is high enough.
We can write the equilibrium between a solubilized surfactant molecule
S
and a
micelle consisting of
n
of these molecules
S
n
(
n
>>1):
nS
«
S
n
whose equilibrium constant is:
] /[ ]
n
K [
S
S
(8.2)
we call c, the total concentration in surfactants:
c
=
[ ] n[
S
+
S
]
(8.3)
n
and we define c
*
as c
*
=(
nK
)
1/
n
Combining (8.2) and (8.3), we immediately find:
*
If c
<<
c , [ ]
S
∼
c
*
*
If c
>>
c , [ ]
S
∼
c
In other words, below c
*
called the “critical micellar concentration” (CMC),
surfactant molecules are individually solubilized; above this concentration, they
tend to aggregate in micelles. Micelles are very dynamic objects constantly exchang-
ing molecules with the free surfactant molecules in the solution [17] (Figure 8.9).
Figure 8.8
Schematic view of a micelle (2-D cross section).
