Biomedical Engineering Reference
In-Depth Information
and density of gas displaced by the sample. For a given mass, the
correction is dependent on the sample density, and the magnitude of
the correction will increase for a given sample mass as the density
decreases. The IUPAC guidelines [2] express the apparent change in
weight due to sorption,
Δw
, as,
V
D
s
w w w n
M
(1.10)
s
excess
g
where
w
is the apparent weight after sorption,
w
is the sample
s
weight in vacuum,
n
is the excess adsorption,
V
is the volume
excess
s
occupied by the sample,
υ
is the molar volume of the gas and
M
is its
g
molar mass. Therefore,
D
w
V
.
(1.11)
n
s
excess
M
g
The second term on the right hand side is the buoyancy
correction. It can be seen that as stated above, for a given sample
mass, the buoyancy effect correction will increase with decreasing
sample density; however, it will also increase with increasing gas
density. It is also clear that the buoyancy correction for a fixed
apparent weight change increases in significance in relation to the
apparent weight change for heavier adsorptives, although for a fixed
molar uptake this is counteracted by the increased molar mass of
the adsorbate.
In the case of carbon nanomaterials, which have a relatively
low density, these corrections can therefore be important and
must be applied carefully to avoid contributing significant errors
to the sorption measurement. Buoyancy effect corrections are the
analogue of the dead volume corrections required for volumetric
measurement (see Section 1.5.11), which also account for the
displacement of the gas phase by the sample; however, unlike the
dead volume corrections in volumetric measurement, the associated
error does not accumulate through the course of an isotherm
measurement because the correction is applied individually to
each weight versus pressure reading. Errors associated with the
knowledge of the sample density and hence volume (
), which
affect both buoyancy effect and dead volume corrections, were
discussed in Section 1.5.6.
V
s
