Membrane Gas Separation

α
  (M 
1
/M 
2
) = P (M 
1
)/ P (M 
2
) are compared in Table 
3.4 for PTMSN and some other high permeability polymers. It is seen that this polymer 
is more permselective than PTMSP and AF2400 in the most cases. However, the observed 

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Addition-type Polynorbornene with Si(CH
3
)
3
 Side Groups
47
Table 3.5  Permeability coeffi cients P (Barrer) of high free volume polymers with respect 
to hydrocarbons (at 1 atm) 
Polymer
CH 
4
C 
2
H 
6
C 
3
H 
8
C 
4
H 
10
Ref.
PTMSN
790
1430
1740
1 7500
This work
PTMSP
15 000
31 000
38 000
–
[22]
PMP
2900
3700
7300
26 000
[23]
AF2400
435
252
97
–
[20]
PMP, poly(methylpentyne).
separation factors of PTMSN are not high, hence common ‘ trade - off ’ behaviour takes 
place in this case.
Possibly, one of the most interesting peculiarities of PTMSN is the variation of the P
values along the n - alkane series in this polymer. It is well known that conventional glassy 
polymers reveal size sieving (or mobility) selectivity as a function of molecular mass of 
penetrant: permeability coeffi cients correlate with the diffusion coeffi cients in such poly-
mers. Opposite behaviour is typical for rubbery polymers, where the P values correlate 
with the solubility coeffi cients ( S ): solubility controlled permeation. However, some high 
free volume glassy materials, fi rst and foremost PTMSP, show solubility controlled selec-
tivity [19] , so the separation factors reveal higher permeation rates of heavier components, 
e.g. R(C 
4
H 
10
/CH 
4
)
<
1. 
In this regard, PTMSN behaves like PTMSP and some other highly permeable poly-
acetylenes, as Table 3.5 indicates.
It is seen that the trend observed for PTMSN is similar to that typical for polyacety-
lenes, while perfl uorinated material AF2400 having more or less the same permeability 
for light gases as PTMSN shows diffusivity controlled permeation; a decrease in P values 
with the size of the penetrant. However, bearing in mind the relatively high experimental 
pressure of 1 
atm, which in the case of n 
- 
butane permeation corresponds to activity 
p / p
s
= 0.4 ( p
s
is the saturated vapour pressure of n - butane at 22 ° C), the observed high 
value P (C 
4
H 
10
) can be partly affected by the concentration dependence of P . Solubility 
controlled permeation here, as in other cases, can be ascribed to an open porosity kind of 
free volume typical for these polymers. For PTMSP, it was confi rmed by a computer 
simulation study using molecular dynamics [24] . So it can be assumed that the nano-
structure of PTMSN also includes large and partly opened pores. This subject will be 
considered in more detail later in this chapter. From the practical viewpoint, this result 
means that membrane based on PTMSN can be used to remove higher hydrocarbons from 
natural and associated petroleum gas. 
Continuous decrease in permeability in time (so called ageing) is a well - known pecu-
liarity of PTMSP and some other polyacetylenes [25] . Such ageing can be considered as 
a shortcoming of potential membrane materials, so it is quite desirable to test the time 
stability of the permeation parameters for any high free volume, high permeability poly-
mers. Bearing this in mind, we undertook a study of the effects of ageing on permeability 
coeffi cients of PTMSN. The results are given in Figure 3.1 . It can be concluded that some 
ageing takes place also in the case of PTMSN, though the rate of ageing is much slower 
that that of PTMSP.
A feature of highly permeable polyacetylenes is a low (sometimes negative) value of 
activation energy of permeation. Since

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48
Membrane Gas Separation
P
DS
=
(3.1)
P
P
E
RT
D
E
RT
S
H RT
=
−
(
)
=
−
(
)
+
−
(
)
0
0
0
exp
exp
exp
P
D
s
Δ
(3.2)
the activation energy of permeation can be presented as the sum:
E
E
H
P
D
s
=
+
Δ
.
(3.3)
where E
D
is the activation energy of diffusion and  
Δ
 H
s
is enthalpy of sorption. 
Since in such polymers activation energy barriers for diffusion are low, the prevailing 
effects are exerted by negative  
Δ
 H values. The temperature dependence of the permeabil-
ity coeffi cients in PTMSN shows that such behaviour is typical also for this polymer 
(Figure 3.2 ).
200
500
800
0
20
40
60
time, days
Permeability, Barrer
O
2
N
2
Figure 3.1 Time dependence of the permeability coeffi cients of PTMSN (storing at room 
temperature)
8.5
7.5
CO
2
C
2
H
6
CH
4
N
2
In P (Barrer) 6.5
5.5
2.9
3.0
3.1
3.2
1000/T, k
–1
3.3
3.4
3.5
Figure 3.2 Arrhenius dependence of permeability coeffi cients in PTMSN

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Addition-type Polynorbornene with Si(CH
3
)
3
 Side Groups
49
Already a qualitative analysis of Figure 3.2 indicates that the activation energies of 
carbon dioxide and ethane are negative, while those of other gases have relatively small 
values (see also Table 3.6 ). This is one more feature that explains solubility controlled 
permeation in PTMSN and its large gas permeability.
Pressure also exerts effects on the permeability coeffi cients of gases in PTMSN. 
The strongest effects were observed for permeability of carbon dioxide, as Figure 3.3
indicates.
Such shape of the P ( p ) curves is typical for glassy polymers. The left, low pressure 
branch of the curve is explained by semi - empirical dual - mode sorption and mobility 
model. The right branch that shows increases in permeability with increasing pressure is 
usually explained by the plasticization effects (see Ref. 19, p. 24). There is, however, one 
interesting peculiarity of PTMSN: in conventional glassy polymers such as polyimides, 
polycarbonates, etc. the pressure p
min
where the curve passes through a minimum amount 
Table 3.6  Parameters of the Arrhenius dependence of permeability in PTMSN
Gas
P
0
(Barrer)
E
P
(kJ/mol)
H 
2
6700
3.1
He
5100
4.2
O 
2
1700
1.3
N 
2
2500
4.6
CO 
2
250
−
7.4
CH 
4
1390
0.63
C 
2
H 
6
620
−
2.3
3700
0
0.4
0.8
1.2
3900
4100
4300