Biomedical Engineering Reference
In-Depth Information
1.
Excess and Absolute Adsorption
Before discussing common sources of error in the next section, it
is worth briefly covering the different definitions of the adsorbed
quantity. In a gravimetric or volumetric adsorption measurement,
the experimentally determined quantity is the
.
This is the difference between the total quantity of a fluid in a fluid-
solid system and the quantity of fluid that would be present in the
absence of any adsorption. For storage applications, and for the
comparison of theoretical or simulated quantities with experiment,
it is of interest to determine the
excess adsorption
. This is the
total amount of adsorbate in the adsorbed phase. Unfortunately, it
is not possible to experimentally determine either the volume or
the density of this phase. An assumption must therefore be made
to perform the conversion. A number of assumptions are possible,
which Murata
absolute adsorption
et al.
[23] classified as either
constant volume
or
constant density
approximations.
The excess adsorbed mass,
m
, can be expressed as,
excess
m
m
V
(1.5)
excess
tot
F
a
where
m
is the total mass of the molecules in the adsorbate phase,
tot
ρ
is the density of the bulk fluid phase (far from the surface) and
F
V
is the volume of the adsorbed phase. The absolute adsorption is
therefore given by,
a
m
m
V
.
(1.6)
tot
excess
F
a
The conversion between these two quantities, using Eqs. (1.5) and
(1.6), clearly requires knowledge of
. Alternatively, however, we
can assume knowledge of the mean density of the adsorbate phase,
V
a
, so that
m
=
V
. This allows us to substitute
V
in Eq. (1.5),
tot
a
a
a
a
so that,
m
m
m
F
(1.7)
excess
tot
tot
a
And so,
m
.
(1.8)
m
excess
tot
1
F
a
