Chemistry Reference
In-Depth Information
Π
vdw
is related to the van der Waals forces acting between the alkyl chains (or
groups), and
Π
electro
is related to polar group interactions (polar group-water interaction, polar
group-polar group repulsion, charge-charge repulsion).
When the magnitude of A is very large, the distance between molecules is large. If
there are no van der Waals or electrostatic interactions, then the film obeys the ideal
equation. As the area per molecule is decreased, the other interactions become sig-
nificant. The Π versus
A
isotherm can be used to estimate these different interaction
forces. These analytical procedures have been extensively described in the current
literature (Gaines, 1966; Adamson and Gast, 1997; Birdi, 1989, 1999).
The ideal equation has been modified to fit Π versus
A
data in those films where
the co-area,
A
o
, correction is needed (Birdi, 1989):
Π (
A
−
A
o
) =
k
B
T
(4.4)
In the case of straight-chain alcohols or fatty acids,
A
o
is almost 20 Å
2
, which is the
same as found from the x-ray diffraction data of the packing area per molecule of
alkanes. This equation is thus valid when
A
>>
A
o
. The magnitude of Π is 0.2 mN/m
for
A
= 2000 Å
2
, for ideal film. However, Π will be about 0.2 mN/m for
A
= 20 Å
2
for a solid-like film of a straight-chain alcohol.
Π versus
A
for a monolayer of valinomycin (a dodecacyclic peptide) shows that the
relation as given in Equation 4.1 is valid (Figure 4.6). In this equation, it is assumed
that the amphiphiles are present as monomers. However, if any association takes
place, then the measured values of (Π
A
) would be less than k
B
T
< 411, as has also
been found (Birdi, 1989, 1999). The magnitude of k
B
T
= 4 10
−21
J, at 25°C.
In the case of nonideal films, one will find that the versus data does not fit the rela-
tion in the equation. This deviation requires that other modified equations-of-state
50
Collapse
Solid
Solid
Lex
LCO
Gas
0
Area per Molecule
FIGure 4.6
Π versus
A
isotherms for different types of states: (a) gas film; (b) liquid-expanded
(L
ex
) and liquid-condensed (L
co
); solid films; collapse state.
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