Membrane Gas Separation

time (s)
permeate pressure (mbar)
Exp.
1
2
3
D)
Step 3 
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0
200
400
600
800
1000
0
100
200
300
0
50
100
150
400
500
600
1200
time (s)
permeate pressure (mbar)
C)
Step 2 
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
time (s)
permeate pressure (mbar)
B)
Step1
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
time (s)
permeate pressure (mbar)
Figure 4.9 Left side: Experimental permeation curve of methanol vapour in the Hyfl on 
AD80X membrane of Figure 8 (thick dark line). The shaded areas and the thin brighter 
lines represent the different steps of the fi tting procedure according to Eq. (4.6) . Right 
side, B, C, D: experimental data or residual experimental data (noisy dark lines), with the 
corresponding fi t of the individual steps in the three different time intervals (thin brighter 
lines). The sum of the three fi ts coincides perfectly with the experimental data. In most 
cases the fi t is nearly perfect and only one curve can be distinguished. See further 
explanation in the text

---

Amorphous Glassy Perfl uoropolymer Membranes of Hyfl on AD®
79
Table 4.4  Van der Waals volume and (apparent) diffusion coeffi cient of dichloromethane 
and of hydrogen bonded methanol clusters of different size
a

Species
van der Waals volume ( Å ) 
3
D (10 
−
10
cm 
2
s 
−
1
)
Method
MeOH
37.4
160
Fit with eq. (4.6)
(MeOH) 
2
71.6
30.7
Fit
(MeOH) 
3
105.8
5.9
Fit
MeOH Average
–
50.3
Tangent
CH 
2
Cl 
2
56.9
22.1
Tangent
a
Calculated with the ‘ Materials Studio ’ software package, Accelrys, Inc. (San Diego, CA).
coeffi cient. It is reasonable to assume that the fi rst part of the curve indeed corresponds 
to the diffusion of relatively fast, single methanol molecules which are not delayed by 
interaction with other molecules. The situation is more complex for the rest of the per-
meation curve. Since hydrogen bonds are relatively weak bonds, the formation of clusters 
is a dynamic process of continuous aggregation and dissociation. The clusters may there-
fore diffuse either as a whole or they may fi rst dissociate and then diffuse as single 
molecules. If the average lifetime of a cluster is shorter than the corresponding jump 
frequency of the cluster, then it is more likely that methanol diffuses as the single mol-
ecules. In that case the observed ‘ slower ’ diffusion constants must be interpreted as a 
temporary ‘ immobilization ’ of the methanol molecules in larger clusters. The procedure 
described above then becomes a potential method to analyze the average cluster size. 
Further evaluation of this possibility is in progress [39] .