Gas Permeation Parameters and Other Physicochemical Properties
37
0
500
1000
1500
0
10
20
30
40
Time / days
P
/ Barrer
Figure 2.5 Dependence of oxygen permeability (
䊊
) and nitrogen permeability (
䉭
) on
time for PIM - 1 membrane (state 3, methanol - treated) kept at ambient temperature in air
Table 2.3 Activation energies of permeation, E
p
, for water - free (state 2) PIM - 1
membranes, determined by the pressure increase method (GKSS) and by the gas
chromatographic method (TIPS)
Gas
E
p
/(kJ mol
−
1
)
GKSS
TIPS
CO
2
−
4.5
−
1.5
H
2
3.2
3.6
He
5.4
5.0
O
2
3.3
1.1
CH
4
10.9
10.9
N
2
10.5
7.5
Table 2.4 Values of diffusion coeffi cient, D
, and solubility coeffi cient, S
, at 30 ° C for
PIM - 1 in various states (1 = water - treated; 2 = water - free; 3 = methanol - treated)
Gas
D /(10
−
7
cm
2
s
−
1
)
S /(10
−
3
cm
3
[STP] cm
−
3
cmHg
−
1
)
State 1
State 2
State 3
State 1
State 2
State 3
CO
2
3.5
4.5
16
270
770
700
H
2
100
290
500
2.7
6.9
6.6
He
190
360
680
0.82
2.6
1.9
O
2
9.3
15
39
14
40
39
CH
4
–
1.3
7.1
–
160
163
N
2
5.7
4.3
16
9.1
35
37
investigated in this work included
n - alkanes (C
3
– C
10
),
n - alcohols (C
1
– C
4
), acetone, chlo-
roform, tetrachloromethane, tetrahydrofuran, cyclohexane, benzene, perfl uorobenzene,
toluene, perfl uorotoluene, 4 - fl uorotoluene and 2,3,4,5,6 - pentafl uorotoluene. PIM - 1 was
coated from solution
in THF onto a large pore, low surface area support (Inerton AW),
which was packed into a stainless steel column (internal diameter = 3 mm; length = 1.5 m).
The proportion of polymer in the dry packing material was determined by back - extracting
38
Membrane Gas Separation
in a Soxhlet apparatus and found to be 8.3% by mass. Experiments were carried out using
a LKhM - 8MD chromatograph with thermal conductivity detector, over the temperature
range 45 – 250 ° C. Helium was used as the carrier gas. The retention
time for an air peak
was used to correct for the dead volume of the chromatograph. Knowing the fl ux of carrier
gas, the pressure drop in the column and the mass of polymer in the column, a specifi c
retention volume for each solute was calculated, from which the infi nite dilution solubility
coeffi cient,
S , was determined. The
temperature dependence of S allowed the enthalpy of
sorption,
Δ
H
s
to be determined, and hence the partial molar enthalpy of mixing,
Δ
H
m
=
Δ
H
s
–
Δ
H
c
, where
Δ
H
c
is the enthalpy of condensation of the solute [5] .
It has been found, for a wide range of solutes in glassy and rubbery polymers, that
S
varies with
T
c
2
, where
T
c
is the critical temperature of the solute [31] . This
correlation
was found to apply for PIM - 1, as can be seen in Figure 2.6 , which includes
S values from
IGC and
S values derived from gas permeation experiments. Figure 2.6 also includes data
for the previous ‘ champion ’ amongst membrane polymers, PTMSP [32] , and the results
show that PIM - 1 exhibits the largest solubility coeffi cients of all
polymers studied in this
way. This confi rms the exceptional affi nity that PIM - 1 has for small molecules.
Enthalpies of sorption and partial molar enthalpies and entropies of mixing for PIM - 1
with a selection of solutes are listed in Table 2.5 . Values of
Δ
H
s
are more strongly nega-
tive than is generally observed for other glassy polymers, refl ecting strongly negative
Δ
H
m
values (exothermic mixing). Values of
Δ
S
m
are also large and negative, showing that for
the solute in the polymer there is considerable restriction in the degrees of freedom. The
mixing process is thus entropically unfavourable, but driven by a large enthalpy term.
The size of free volume elements in a glassy polymer can be
estimated from the depend-
ence of
Δ
H
m
on solute size [31] . A plot of
Δ
H
m
against
V
c
, where
V
c
is the critical volume
of the solute, generally passes through a minimum at a value of
V
c
that corresponds to a
mean size of free volume elements. The data for
n - alkanes in Table 2.5
show increasingly
negative values of
Δ
H
m
up to decane. Unfortunately, temperature limitations meant that
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