Membrane Gas Separation

0.1
1
10
100
1000
10000
100000
1000000
10000000
100000000
0
10
20
30
40
T
c
2
 / (10
4
 K
2
)
S /
 (cm
3
 [STP] cm
-3
 atm
-1
)
Figure 2.6 Dependence of solubility coeffi cient at 35 ° C on T
c

2
 , where T
c
is the critical 
temperature of the solute, for PIM - 1 ( 
•
 ) and PTMSP [32] ( 
䉭
 )

---

Gas Permeation Parameters and Other Physicochemical Properties
39
n - alkanes larger than decane could not be studied, so a clear minimum is not observed 
for PIM - 1. However, this suggests a minimum at a value of V
c
≥
600 cm 
3
mol 
– 1
, which 
translates into a sphere of radius
≥
0.6 nm, or an equivalent pore width in the region of 
1.2 nm. This supports the evidence from adsorption analysis and computer simulation, 
discussed earlier, that PIM - 1 contains cavities of dimensions in the micropore region, as 
defi ned by IUPAC. Yet further evidence of this comes from PALS, as discussed below.
2.6
Positron Annihilation Lifetime Spectroscopy 
Reaction of a positron with an electron gives a metastable positronium (Ps) particle, which 
may have antiparallel spins ( para - positronium, p - Ps) or parallel spins ( ortho - positronium, 
o - Ps). Within a polymer, the longer lifetimes of o - Ps may be related to the size, concen-
tration and distribution of free volume elements. There have been a number of studies of 
PIM - 1 by positron annihilation lifetime spectroscopy (PALS) [33 – 36] . 
This work investigated PIM - 1 membranes in the three ‘ states ’ discussed above. Nickel -
foil supported
22
NaCl was used as a positron source and stacks of fi lm samples, each 
about 1 mm thick, were placed either side of the source. Annihilation lifetime decay 
curves were measured with an EG & G Ortec ‘ fast - fast ’ lifetime spectrometer. Measurements 
were made both in air and under an inert atmosphere (N 
2
). However, o - Ps lifetimes in air 
were reduced due to quenching by oxygen, so only results obtained under N 
2
are discussed 
here. Results were analysed in terms of a four component lifetime distribution, which 
allowed obtaining better statistical fi t. The two longest lifetimes,  
τ
 
3
and  
τ
 
4
, for PIM - 1 in 
Table 2.5  Enthalpy of sorption,
Δ
H
s
 , partial molar enthalpy of mixing,
Δ
H
m
 , and partial 
molar entropy of mixing,
Δ
S
m
 , determined by IGC for a selection of solutes in PIM - 1 
Solute
 
Δ
 H
s
/(kJ mol 
( 
−
1
)
 
Δ
 H
m
/(kJ mol 
−
1
)
 
Δ
 S
m
/(J K 
−
1
mol 
−
1
)
propane
−
43
−
24
−
56
n - butane
−
51
−
21
−
51
n - pentane
−
61
−
26
−
58
n - hexane
−
64
−
28
−
61
n - heptane
−
69
−
30
−
62
n - octane
−
80
−
38
−
77
n - nonane
−
87
−
40
−
77
n - decane
−
88
−
40
−
72
methanol
−
43
−
7
−
32
ethanol
−
51
−
16
−
44
n - propanol
−
59
−
21
−
54
n - butanol
−
64
−
24
−
56
acetone
−
58
−
27
−
60
chloroform
−
60
−
25
−
50
tetrachloromethane
−
60
−
26
−
50
tetrahydrofuran
−
60
−
27
−
56
benzene
−
57
−
25
−
48
toluene
−
71
−
33
−
66

---

40
Membrane Gas Separation
Table 2.6  Long o - Ps lifetimes,
τ

3
and
τ

4
 , and corresponding radii of free volume elements, 
 R
3
and R
4
 , for PIM - 1 in various states (1 = water - treated; 2 = water - free; 3 = methanol -
 treated) under a nitrogen atmosphere 
State
 
τ
 
3
/ns
 
τ
 
4
/ns
R
3
/nm
R
4
/nm
1
1.4
5.6
0.22
0.51
2
2.1
5.8
0.30
0.52
3
1.8
7.1
0.27
0.58
each state are listed in Table 2.6 , along with the corresponding radii of free volume 
elements, calculated according to the Tao - Eldrup model [37,38] . It can be seen that the 
longest lifetime suggests free volume elements with a radius of about 0.5 nm, or equiva-
lent pore widths in the vicinity of 1 nm. This once again confi rms the ‘ microporosity ’ of 
PIM - 1. Furthermore, there is arguably a detectable increase in R
4
in going from the lower 
permeability ‘ water - treated ’ state 1 to the high permeability ‘ methanol - treated ’ state 3.