Biomedical Engineering Reference
In-Depth Information
P
V
P
(
V
-
V
)
_______
Z
i
1
_____________
Z
f
1
2
D
n
=
T
RT
-
T
RT
(1.2)
i,
f,
where
V
is the calibrated dosing volume,
V
is the sample cell
1
2
volume,
P
is the initial pressure in
V
,
P
is the final pressure in the
i
1
f
entire system (
are the gas compressibility
factors at the measurement temperature,
V
+
V
), and
Z
and
Z
1
2
i
,T
f
,T
T
, and the pressures
P
and
i
P
, respectively.
Following this initial adsorption step, the valve is then closed
and the pressure in the dosing volume increased again. The pressure
in the dosing volume is recorded and the valve opened in order to
dose the sample with a second aliquot. The equilibrium pressure is
again recorded and the amount of adsorbate for that particular step
calculated, while accounting for the quantity of fluid remaining in
the sample cell (the adsorbate plus the gas phase) from the initial
dose. This stepwise process continues until a full isotherm has been
recorded. Assuming constant temperature conditions, in order to
simplify the algebra, the amount adsorbed after the
f
m
th adsorption
step is given by,
[
]
P
V
P
j
V
P
(
V
+
V
)
m
∑
j
f,
j
- 1
2
i,
1
f,
j
1
2
___________
Z
_________
Z
______________
Z
n
m
=
T
RT
+
T
RT
-
T
RT
(1.3)
f,
j
- 1,
i,
j
,
f,
j
,
= 1
where
P
and
P
are the initial and final pressures at isotherm point
i
,j
f,
j
j
,
Z
and
Z
are the gas compressibility factors at pressures
P
and
i
,j,T
f
,j,T
i
,j
P
is the measurement temperature.
Following completion of the adsorption isotherm measurement,
a desorption isotherm can be measured by reversing the above
process. The pressure in the dosing volume is reduced, with the
separation valve closed, and then recorded. The valve is again
opened and the pressure monitored and recorded at equilibrium.
The procedure continues until vacuum or a sufficiently low pressure
has been reached.
There are various other types of volumetric method, which
will not be covered here for the sake of brevity; however, it is
worth noting one variation, in particular, which is the
, and
T
f
,j
differential
volumetric method
. This exploits the greater measurement accuracy
of differential pressure transducers in comparison to their absolute
pressure counterparts. A good example was presented by Zielinski
et al.
[9], although systems had previously been reported by
Browning
et al.
[10] and Blackman
et al.
[11]. All three systems
