Membrane Gas Separation

4.5
Transport Properties 
4.5.1
Permeation Measurements 
Vapour permeation experiments were carried out at 25 ° C in a fi xed volume – pressure 
increase instrument constructed by GKSS (Germany) according to the procedure described 
before [24] . Circular membranes with an effective exposed area of 11.3 cm 
2
or 2.14 cm 
2
were used. Depending on the specifi c vapour to be tested, the permeation measurements 
were performed at feed pressures ranging from 35 mbar to almost saturation. The mem-
brane, mounted inside the permeation cell, was thoroughly evacuated for at least 1 h 
before the fi rst measurement in order to remove all absorbed species. Evacuation was 
continued until the baseline drift was signifi cantly below the expected steady state pres-
sure increase rate of the species to be tested. Between two subsequent measurements the 
system was evacuated for a period of at least fi ve times the time lag of the previous species 
in order to guarantee the complete removal of the penetrant from the membrane and from 
the rubber seals. 
Measurements were carried out in the time lag mode, starting to record the permeate 
pressure as a function of time as soon as the membrane was exposed to the vapour.
Figure 4.7 Representative slice of an atomistic packing model of Hyfl on AD80X. The 
polymer chains are represented by the small sticks. The free volume elements are shown 
as the darker continuous regions, represented by a collection of neighbouring and 
overlapping spheres. Slice thickness ca. 5 Å

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74
Membrane Gas Separation
4.5.2 Data Elaboration: Determination of the Time Lag and Steady 
State Permeability 
For the gas permeation measurements the diffusion coeffi cient was determined by the 
well - known time lag procedure, based on the penetration theory. If a penetrant - free mem-
brane is exposed to the penetrant at the feed side at t = 0 and the penetrant concentration 
is kept very low at the permeate side, then the total amount of penetrant, Q 
t
  , passing 
through the membrane in time t is given by [37] :
Q
l c
D t
l
n
D n
t
l
t
i
n
⋅
= ⋅ − −
−
( )
− ⋅ ⋅ ⋅
⎛
⎝⎜
⎞
⎠⎟
∞
∑
2
2
2
2
2
2
1
6
2
1
π
π
exp
l
(4.5)
in which c 
i
  is the penetrant concentration at the membrane interface at the feed side, l is 
the membrane thickness (in m) and D is the diffusion coeffi cient (in m 
2
s 
– 1
). 
For the barometric instrument used in the present work, the permeate volume is con-
stant and permeation results in an increase of the permeate pressure as a function of time, 
which is described by a similar equation:
p
p
dp dt
t
RT A l
V V
p
S
D t
l
n
D n
t
P
m
f
n
=
+
(
)
⋅ +
⋅ ⋅
⋅
⋅ ⋅
⋅ − −
−
( )
− ⋅
0
0
2
2
2
1
6
2
1
π
exp
2
2
2
2
⋅ ⋅
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜
⎞
⎠⎟
∞
∑
π
t
l
l
(4.6)
In which p 
t
  is the permeate pressure (in bar) at time t (in s), p
0
is the starting pressure (in 
bar), R is the universal gas constant (8.314
×
10 
−
5
m 
3
bar mol 
−
1
K 
−
1
), T is the absolute 
temperature (in K), A is the exposed membrane area (in m 
2
), V
P
is the permeate volume 
(in m 
3
), V 
is the molar volume of a gas at standard temperature and pressure 
(22.41
×
10 
−
3
m 
3
STP
mol 
−
1
at 0 ° C and 1 atm), p
f
is the feed pressure (in bar) and S is the 
gas solubility coeffi cient (m 
3
STP
m 
−
3
bar 
−
1
). The term (d p /d t ) 
0
represents the baseline slope 
(in bar s 
−
1
). Usually this should be negligible, but in the case of very slow permeating 
species it may be necessary to correct for this term. This is also the case if minor cracks 
are formed in these rather brittle perfl uoropolymers under the pressure of the sealing rings 
in the membrane cell, which may give rise to Knudsen - type of diffusion and apparent 
baseline drift. At very long times the exponential term approaches zero and Equation (4.6)
reduces to:
p
p
dp dt
t
RT A l
V V
p
S
D t
l
t
P
m
f
=
+
(
)
⋅ +
⋅ ⋅
⋅
⋅ ⋅
⋅ −
⎛
⎝
⎞
⎠
0
0
2
1
6
(4.7)
or
p
p
dp dt
t
RT A
V V
p
S D
l
t
l
D
t
P
m
f
=
+
(
)
⋅ +
⋅
⋅
⋅
⋅ ⋅
−
⎛
⎝⎜
⎞
⎠⎟
0
0
2
6
(4.8)
Thus, at long times a plot of p 
t
  versus time describes a straight line which, upon extrapo-
lation, intersects the baseline at t = l
2
/6 D , defi ned as the time lag,  
Θ
  (s)
Θ =
l
D
2
6
(4.9)

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Amorphous Glassy Perfl uoropolymer Membranes of Hyfl on AD®
75
Hyflon AD80X, 23.3 
μ
m 
Dichloromethane, p = 238 mbar, activity p/p
0
= 0.41 
Hyflon AD80X, 24.9 
μ
m
Methanol, p = 119 mbar, activity p/p
0
= 0.71 
409
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0
500
1000
1500
2000
2500