Biomedical Engineering Reference
In-Depth Information
The presence of a surface film or monolayer on a pure liquid is expressed by
the surface pressure
,thatisdefinedas
Π
≡
σ
pure liquid surface
-
Π
σ
film covered surface
. (3)
It should be pointed out at this juncture that strict thermodynamics treat-
ment of the film-covered surfaces is not possible [18]. The reason is diffi-
culty in delineation of the system. The interface, typically of the order of a
1-2 nm thick monolayer, contains a certain amount of bound water, which
is in dynamic equilibrium with the bulk water in the subphase. In a strict
thermodynamic treatment, such an interface must be accounted as an open
system in equilibrium with the subphase components, principally water. On
the other hand, a useful conceptual framework is to regard the interface as
a “2-dimensional” (2D) object such as a 2D gas or 2D solution [19, 20]. Thus,
the surface pressure
is treated as either a 2D gas pressure or a 2D osmotic
pressure. With such a perspective, an analog of either
p
-
V
isotherm of a gas or
the osmotic pressure-concentration isotherm,
Π
-
c
, of a solution is adopted.
It is commonly referred to as the surface pressure-area isotherm,
Π
-
A
,where
A
is defined as an average area per molecule on the interface, under the pro-
vision that all molecules reside in the interface without desorption into the
subphase or vaporization into the air. A more direct analog of
Π
Π
-
c
of a bulk
solution is
is the mass per unit area, hence is the reciprocal
of A, the area per unit mass. The nature of the collapsed state depends on
the solubility of the surfactant. For truly insoluble films, the film collapses by
forming multilayers in the upper phase. A broad illustrative sketch of a
Π
-
Γ
where
Γ
Π
-
Γ
plot is given in Fig. 1.
For most monolayers, the range of surface pressures for which gas model
analogs are applicable, is quite low (
<
1 mN m
-1
). The simplest model one
could consider is an analog to an ideal gas or an ideal solution,
Π
Π
A
=
kT
,
(4)
or
=
Γ
RT
M
n
Π
(5)
that is the analog of the ideal gas equation of state,
pv
=
kT
,with
v
as the
molecular volume and
k
the Boltzmann constant, or that of ideal solution,
Π
M
n
,with
c
as the mass concentration and R the gas constant. Ex-
panding on the ideal solution analog into a virial form, we can add the second
virial coefficients
A
2
,suchthat
=
cRT
/
1+
A
2
Γ
+ ...
.
RT
Γ
M
n
Π
=
(6)
Such an expansion was employed by many in the early 1980s [21-27]. It
is, however, of little routine use for the static characterization of polymeric
monolayers since accurate measurements of surface pressure in this surface
