Chemistry Reference
In-Depth Information
C14OH
KT
0.10
C15OH
0
1000
4000
Area
FIGure 4.5
Π versus
A
plot for an ideal monolayer film: (a) ideal film (Π
A
= 411 = k
B
T);
(b) C
15
OH; (c) C
14
OH (Π: mN/m; A: Å
2
/molecule).
between the amphiphiles and the float from the two degrees of freedom of the trans-
lational kinetic energy in the two dimensions. It is thus seen that the ideal gas film
obeys the relation
Π A = k
B
T
[“ideal film”]
(4.1)
Π (mN/m) A(Å
2
per molecule) = 411 (T = 298 K) [“ideal film”]
(4.2)
In Figure 4.5, the Π A versus A is plotted for an ideal monolayer film. Various mol-
ecules have been found to give such ideal films (such as C
14
H
29
OH, valinomycin,
proteins). This is analogous to the three-dimensional gas law (i.e.,
PV
= kT). At
25°C, the magnitude of (k
B
T
) = 411 10
16
erg. If Π is in mN/m, and
A
in Å
2
, then
the magnitude of k
B
T
= 411. In other words, if one has a system with A = 400 Å
2
/
molecule, then the value of Π = 1 mN/m for the ideal gas film.
In general,
ideal gas
behavior is only observed when the distances between the
amphiphiles are very large, and thus the value of Π is very small, that is, <0.1 mN/m.
It is also noticed that, from such sensitive data, one can estimate the molecular weight
of the molecule in the monolayer. This has been extensively reported for protein
monolayers (Adamson and Gast, 1997; Birdi, 1989, 1999).
The latter observation requires an instrument with very high sensitivity, ±0.001
mN/m. The Π versus A isotherms of
n
-tetradecanol (Figure 4.5), pentadecanol, pen-
tadecyclic acid, and palmitic acid are typical data in the low Π region. Similar data
for isotherms were reported from other lipid monolayers by other workers.
The various forces that are known to stabilize the monolayers are mentioned as
Π = Π
kin
+ Π
vdw
+ Π
electro
(4.3)
where
Π
kin
arises from kinetic forces,
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