Membrane Gas Separation

p
Feed
 
238
119
mbar
p  / p
0 
0.41
0.71
–
P
3.35
4.85
10 
−
8
m 
3
STP
m m 
– 2
h 
– 1
bar 
−
1
12.4
17.9
Barrer
 
Θ
 
409
205
s
D
22.1
50.3
10 
−
10
cm 
2
s 
−
1
S
42.0
26.7
m 
3
STP
m 
−
3
bar 
−
1
160
38.1
10 
– 3
g cm 
−
3
bar 
−
1
C
10.0
3.18
cm 
3
STP
cm 
−
3
at p
Feed
38.0
4.53
10 
−
3
g cm 
−
3
at p
Feed
a
Effective values determined by the tangent method.

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Amorphous Glassy Perfl uoropolymer Membranes of Hyfl on AD®
77
lated time lag is about 200 s, the onset of permeation is only a few seconds for methanol. 
Surprisingly it then still takes at least 20 minutes to reach steady state permeation, 
about as long as it takes for the much larger DCM molecules to reach steady state 
permeation. 
The different behaviour between the two vapours is even more evident if we fi t the 
entire experimental curve directly with Equation (4.6) after expansion into 10 terms 
( n = 1, 2, 3, … 10). The DCM curve yields a nearly perfect fi t (Figure 4.8 , bottom), 
indicating that the DCM transport can be described well by the simple Fickian diffusion 
with a single diffusion constant, independent of time or concentration. In this case the 
values of D and S are directly obtained from the curve fi t and they agree within an error 
of a few percent with the values in Table 4.3 , obtained by the tangent method. 
In contrast, the methanol permeation curve cannot be fi tted satisfactorily. Nevertheless, 
if only the fi rst 150 s are considered the fi t is perfect, as shown in Figure 4.9 B. In this 
short time interval we can assume normal Fickian behaviour and the value of D is directly 
obtained from the curve fi t. For this case the corresponding time lag would be approx. 
65 s. At longer times the fi t (thin line delimiting area 1 in Figure 4.9 A) underestimates 
the experimental data (thick solid line in Figure 4.9 A). If we then take the difference 
between the fi rst fi t and the experimental curve (grey area 2), the shape is remarkably 
similar to a normal time lag curve (Figure 4.9 C). Indeed, this curve can again be fi tted 
satisfactorily with Equation (4.6) without the terms p
0
and (d p/ d t ) 
0
t , which have been 
taken into account in the fi rst step. The resulting time lag of the second step would approx. 
336 s. Still, the sum of the two fi ts (thin line delimiting area 2 in Figure 4.9 A) slightly 
underestimates the experimental curve. The same procedure can be repeated a third time 
(Figure 4.9 D) and again a nearly perfect fi t is obtained. The calculated time lag in the 
third step, approx. 1765 s but since it falls outside the window of the experimental data 
it should be considered with care. The sum of the three individual curves now coincides 
exactly with the experimental data.
This type of evaluation of the transient behaviour in the permeation of methanol vapour 
as the sum of three separate permeation curves suggest that methanol vapour transport is 
described by three independent diffusion phenomena. Given the polar character of metha-
nol, the presence of OH groups and the highly hydrophobic character of the polymer, 
in combination with the relatively large free volume elements, it speaks for itself that 
one would hypothesize that the formation of clusters of two, three or more methanol 
molecules, held together by hydrogen bridges between the hydroxyl groups could be 
responsible for the observed anomalies in the transport. It is worthwhile to note that 
evidence of the cluster formation in the process of methanol diffusion was obtained in 
the study of another PFP (AF2400) [38] . Molecular dynamics (MD) simulation studies 
have revealed that diffusion proceeds via a ‘ hopping ’ process, in which the penetrant 
molecules move around in a free volume element until their energy is high enough to 
overcome the energy barrier for jumping to the adjacent free volume element [21,23] . 
The required energy rapidly increases with increasing dimensions of the molecule and as 
a consequence the diffusion coeffi cient of larger molecules decreases, as observed for a 
series of permanent gases with different kinetic diameter
[24] 
. The same would be 
expected for clusters of more molecules in comparison with the single species. 
In this light it is too simplistic to assume that the three time lags are related to the 
presence of single, dimeric and trimeric species, each with its own characteristic diffusion 

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78
Membrane Gas Separation
A)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0
200
400
600
800
1000
1200