Membrane Gas Separation

FFV
of MM 
versus w
F
NELF 
model
-
Solubility
of any gas 
i
-Ideal Solubility Selectivity
Swelling
1
Diffusivity in MM 
for gas 
i
D
i
MM
/D
i
pol
versus w
F
P
i
MM
/P
i
pol
versus w
F
Figure 7.1 Scheme of the modelling approach used for the mixed matrices transport 
behaviour [4]

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Vapor Sorption and Diffusion in Mixed Matrices Based on Tefl on® AF 2400 
133
at 18000 rpm in a Waring two - speed laboratory blender and then cast onto a Petri dish 
and covered with an aluminium foil, allowing controlled solvent evaporation. It seems 
that solvent evaporation is the critical step to obtain good fi lms, while the stirring time 
has no infl uence on the resulting membranes structure. The fi lms were completely dried 
within about 48 h and were not treated further before sorption experiments. The fi nal 
thickness of the fi lms is in the range 60 – 140
μ
m. Mixed matrices were prepared with two 
different fi ller loadings, 25% and 40% wt of FS. 
The vapours used in the experiments, n - butane and n - pentane, were supplied by Sigma -
Aldrich, reactant grade, and were used as received.
7.3.2
Vapour Sorption 
The determination of penetrant solubility and diffusivity was performed at pressures 
below 1 bar using a pressure decay apparatus. A known amount of vapour is fed into the 
sample chamber and the mass uptake is evaluated by measuring the pressure decrease of 
the gaseous phase versus time; the equilibrium solubility is equal to the fi nal, asymptotic 
value of the mass uptake. Pressure is measured with an absolute capacitance manometer 
(FS value 1000 mbar, accuracy 0.15% of the reading), and vapour activity is calculated 
as the ratio between the equilibrium pressure and the penetrant vapour pressure at the 
temperature of the experiment. Subsequent sorption tests are performed by increasing the 
external pressure in a stepwise manner. The system is placed in an air - thermostated 
chamber where temperature is kept fi xed to within
±
0.1 ° C. A scheme of the equipment 
is shown in Figure 7.3 . The penetrant diffusivity in the fi lm can be evaluated from the 
sorption kinetics, which follows Fickian behaviour, taking into account the variation of 
interfacial concentration during the experiment, due to the decrease of the gas pressure. 
The expression for the mass uptake in step ( i ) as a function of time,
M
t
i
( )
, for the mass 
sorption from a limited volume where the variation of the interfacial concentration is due 
to mass sorption in the membrane, is given by the well - known expression [17] :
M
M
M
M
q
e
t
i
i
i
i
n
Dq t l
n
n
( )
( )
∞
( )
( )
−
=
∞
−
−
= −
+
(
)
+ +
∑
0
0
2
2
1
1
2
1
1
2
2
α
α
α α
(7.19)
O
O
F
F
F
3
C
CF
3
F
F
(a)
(b)
Non-treated silica
Treated silica
C
F
H
Si
Si
H
F
m
n
C
O
O
O
Si
CH
3
CH
3
CH
3
Figure 7.2 Molecular structure of (a) Tefl on 
 ® 
AF and (b) non - porous fumed silica before 
and after treatment to have a hydrophobic surface

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134
Membrane Gas Separation
where
M
i
0
( )
and
M
t
i
( )
are the initial and fi nal mass uptakes of step ( i ), respectively,  
α
  is 
the ratio between the volume of the chamber and that of the membrane, corrected for the