Membrane Gas Separation

8.3.3
O 
2
 /N 
2
and CO 
2
 /CH 
4
Selectivities of HBPI – Silica Hybrid Membranes 
The ideal gas selectivity for the combination of gases A and B (  
α
  (A/B)) is defi ned by the 
following equation [28] ;
α
α
α
A B
A
B
A
B
A
B
A B
A B
(
)
=
( )
( )
=
( )
( )
×
( )
( )
=
(
)
×
(
)
P
P
D
D
S
S
D
S
(8.5)
where  
α
 
D
(A/B) is the diffusivity selectivity and  
α
 
S
(A/B) is the solubility selectivity. The 
O 
2
/N 
2
and CO 
2
/CH 
4
selectivities of the hybrid membranes are listed in Tables 8.2 – 8.4

---

152
Membrane Gas Separation
Table 8.2  Permeability coeffi cients and ideal selectivity of HBPI – silica hybrid membranes 
at 76 cmHg and 25 ° C 
Sample
P
×
10 
10
, (cm 
3
(STP)cm/cm 
2
s cmHg)
 
α
  (O 
2
/N 
2
)
 
α
  (CO 
2
/CH 
4
)
CO 
2
O 
2
N 
2
CH 
4
6FDA - TAPOB
7.4
1.5
0.23
0.098
6.8
75
TMOS, 10 wt% SiO 
2
10
2.0
0.31
0.13
6.6
79
TMOS, 20 wt% SiO 
2
13
2.1
0.32
0.16
6.7
82
TMOS, 30 wt% SiO 
2
23
3.0
0.46
0.24
6.6
95
TMOS/MTMS, 10 
wt% SiO 
2
13
2.7
0.41
0.20
6.6
65
TMOS/MTMS, 20 
wt% SiO 
2
28
5.4
0.89
0.45
6.0
62
TMOS/MTMS, 30 
wt% SiO 
2
44
7.9
1.3
0.74
5.9
59
TMOS/MTMS, 40 
wt% SiO 
2
72
12
2.3
1.4
5.2
53
TMOS/MTMS, 50 
wt% SiO 
2
133
22
4.5
2.8
5.0
48
MTMS, 10 wt% SiO 
2
23
4.4
0.75
0.45
5.9
51
MTMS, 20 wt% SiO 
2
53
9.5
1.9
1.5
4.9
34
MTMS, 30 wt% SiO 
2
99
18
4.1
4.1
4.3
24
MTMS, 40 wt% SiO 
2
158
28
7.6
10
3.7
15
MTMS, 50 wt% SiO 
2
251
46
14
20
3.4
12
ODPA - TAPOB
0.63
0.13
0.013
0.0064
10
98
TMOS, 10 wt% SiO 
2
0.93
0.18
0.017
0.0094
11
98
TMOS, 20 wt% SiO 
2
0.88
0.17
0.017
0.0078
10
112
TMOS, 30 wt% SiO 
2
1.2
0.22
0.024
0.011
9.0
111
TMOS/MTMS, 10 
wt% SiO 
2
1.3
0.27
0.029
0.022
9.1
58
TMOS/MTMS, 20 
wt% SiO 
2
2.6
0.48
0.062
0.038
7.7
68
TMOS/MTMS, 30 
wt% SiO 
2
6.7
1.2
0.16
0.11
7.3
62
MTMS, 10 wt% SiO 
2
1.8
0.37
0.052
0.036
7.2
51
MTMS, 20 wt% SiO 
2
3.9
0.85
0.13
0.092
6.7
43
MTMS, 30 wt% SiO 
2
17
3.1
0.61
0.64
5.1
26
PMDA - TAPOB
3.3
0.59
0.088
0.066
6.7
50
TMOS, 10 wt% SiO 
2
4.1
0.69
0.11
0.069
6.4
60
TMOS, 20 wt% SiO 
2
4.6
0.71
0.10
0.063
7.0
73
TMOS, 30 wt% SiO 
2
7.1
1.0
0.15
0.073
6.8
97
TMOS/MTMS, 10 
wt% SiO 
2
4.8
0.76
0.12
0.081
6.5
59
TMOS/MTMS, 20 
wt% SiO 
2
13
1.9
0.31
0.22
6.1
58
TMOS/MTMS, 30 
wt% SiO 
2
33
4.9
0.89
0.68
5.5
48
MTMS, 10 wt% SiO 
2
9.3
1.5
0.25
0.21
5.9
44
MTMS, 20 wt% SiO 
2
30
4.8
1.0
1.0
4.6
30
MTMS, 30 wt% SiO 
2
55
8.8
2.2
2.5
4.0
22

---

Physical and Gas Transport Properties
153
Table 8.3  Diffusion coeffi cients and diffusivity selectivity of HBPI – silica hybrid 
membranes at 76 cmHg and 25 ° C 
Sample
D
×
10 
8
(cm 
2
/s)
 
α
 
D
(O 
2
/N 
2
)
 
α
 
D
(CO 
2
/CH 
4
)
CO 
2
O 
2
N 
2
CH 
4
6FDA - TAPOB
0.30
1.4
0.25
0.028
5.8
11
TMOS, 10 wt% SiO 
2
0.35
1.5
0.29
0.026
5.2
13
TMOS, 20 wt% SiO 
2
0.37
1.3
0.25
0.030
5.3
12
TMOS, 30 wt% SiO 
2
0.57
1.7
0.29
0.040
5.8
14
TMOS/MTMS, 10 
wt% SiO 
2
0.59
2.1
0.46
0.060
4.7
9.9
TMOS/MTMS, 20 
wt% SiO 
2
1.2
4.0
0.90
0.090
4.4
13
TMOS/MTMS, 30 
wt% SiO 
2
1.7
5.9
1.2
0.17
5.1
10
TMOS/MTMS, 40 
wt% SiO 
2
2.6
7.9
1.8
0.25
4.4
11
TMOS/MTMS, 50 
wt% SiO 
2
5.2
14
3.7
0.63
3.7
8.2
MTMS, 10 wt% SiO 
2
1.0
3.8
0.83
0.13
4.5
8.1
MTMS, 20 wt% SiO 
2
2.6
8.7
2.2
0.42
4.0
6.0
MTMS, 30 wt% SiO 
2
5.4
16
4.8
1.2
3.4
4.4
MTMS, 40 wt% SiO 
2
9.9
28
9.3
3.7
3.0
2.7
MTMS, 50 wt% SiO 
2
17
46
17
6.8
2.6
2.5
ODPA - TAPOB
0.030
0.16
0.021
0.0019
7.7
16
TMOS, 10 wt% SiO 
2
0.039
0.19
0.025
0.0025
7.6
16
TMOS, 20 wt% SiO 
2
0.033
0.17
0.022
0.0021
7.6
16
TMOS, 30 wt% SiO 
2
0.040
0.19
0.024
0.0026
7.6
15
TMOS/MTMS, 10 
wt% SiO 
2
0.071
0.36
0.060
0.011
6.1
6.3
TMOS/MTMS, 20 
wt% SiO 
2
0.13
0.54
0.10
0.016
5.2
8.4
TMOS/MTMS, 30 
wt% SiO 
2
0.34
1.3
0.24
0.027
5.4
13
MTMS, 10 wt% SiO 
2
0.12
0.54
0.11
0.012
5.0
9.4
MTMS, 20 wt% SiO 
2
0.33
1.1
0.23
0.037
4.6
9.1
MTMS, 30 wt% SiO 
2
1.1
3.6
0.89
0.25
4.1
4.3
PMDA - TAPOB
0.14
0.57
0.11
0.020
5.0
6.9
TMOS, 10 wt% SiO 
2
0.16
0.64
0.11
0.023
5.9
7.1
TMOS, 20 wt% SiO 
2
0.14
0.53
0.090
0.012
5.9
12
TMOS, 30 wt% SiO 
2
0.19
0.61
0.11
0.019
5.3
10
TMOS/MTMS, 10 
wt% SiO 
2
0.17
0.70
0.13
0.019
5.4
9.4
TMOS/MTMS, 20 
wt% SiO 
2
0.45
1.6
0.34
0.071
4.6
6.4
TMOS/MTMS, 30 
wt% SiO 
2
1.1
3.2
0.77
0.13
4.1
8.5
MTMS, 10 wt% SiO 
2
0.43
1.0
0.35
0.066
2.9
6.5
MTMS, 20 wt% SiO 
2
1.5
4.8
1.5
0.40
3.2
3.8
MTMS, 30 wt% SiO 
2
2.8
9.0
3.6
0.71
2.5
4.0

---

154
Membrane Gas Separation
and  
α
  (O 
2
/N 
2
) and  
α
  (CO 
2
/CH 
4
) are plotted against O 
2
and CO 
2
permeability coeffi cients 
in Figures 8.6 and 8.7 , respectively.
In Figure 8.6 ,  
α
  (O 
2
/N 
2
) values of the hybrid membranes slightly decrease with increas-
ing O 
2
permeability along with the upper bound trade - off line for O 
2
/N 
2
separation dem-
onstrated by Robeson [29] . Nevertheless, the hybrid membranes show relatively high 
 
α
  (O 
2
/N 
2
) values just below the upper bound. 
Table 8.4  Solubility coeffi cients and solubility selectivity of HBPI – silica hybrid membranes 
at 76 cmHg and 25 ° C 
Sample
S
×
10 
2
(
cm STP cm
cmHg
polym
3
3
(
)
)
 
α
 
S
(O 
2
/
N 
2
)
 
α
 
S
(CO 
2
/
CH 
4
)
CO 
2
O 
2
N 
2
CH 
4
6FDA - TAPOB
25
1.1
0.92
3.5
1.2
7.0
TMOS, 10 wt% SiO 
2
30
1.4
1.1
5.0
1.3
5.9
TMOS, 20 wt% SiO 
2
35
1.7
1.3
5.2
1.3
6.8
TMOS, 30 wt% SiO 
2
41
1.8
1.6
6.0
1.1
6.7
TMOS/MTMS, 10 wt% SiO 
2
22
1.3
0.90
3.3
1.4
6.6
TMOS/MTMS, 20 wt% SiO 
2
24
1.4
1.0
4.9
1.4
4.9
TMOS/MTMS, 30 wt% SiO 
2
26
1.3
1.2
4.4
1.2
5.9
TMOS/MTMS, 40 wt% SiO 
2
27
1.5
1.3
5.5
1.2
5.0
TMOS/MTMS, 50 wt% SiO 
2
26
1.6
1.2
4.4
1.3
5.8
MTMS, 10 wt% SiO 
2
23
1.2
0.90
3.6
1.3
6.3
MTMS, 20 wt% SiO 
2
21
1.1
0.90
3.7
1.2
5.6
MTMS, 30 wt% SiO 
2
19
1.1
0.86
3.4
1.3
5.4
MTMS, 40 wt% SiO 
2
16
1.0
0.82
2.7
1.2
5.8
MTMS, 50 wt% SiO 
2
15
1.0
0.79
3.0
1.3
4.9
ODPA - TAPOB
21
0.81
0.60
3.3
1.3
6.3
TMOS, 10 wt% SiO 
2
24
0.98
0.70
3.8
1.4
6.2
TMOS, 20 wt% SiO 
2
26
1.0
0.78
3.6
1.3
7.2
TMOS, 30 wt% SiO 
2
29
1.2
1.0
4.0
1.2
7.3
TMOS/MTMS, 10 wt% SiO 
2
18
0.74
0.49
2.0
1.5
9.1
TMOS/MTMS, 20 wt% SiO 
2
20
0.90
0.61
2.4
1.5
8.1
TMOS/MTMS, 30 wt% SiO 
2
20
0.92
0.69
4.0
1.3
5.0
MTMS, 10 wt% SiO 
2
16
0.69
0.48
2.9
1.4
5.4
MTMS, 20 wt% SiO 
2
12
0.80
0.54
2.5
1.5
4.7
MTMS, 30 wt% SiO 
2
16
0.85
0.69
2.6
1.2
5.9
PMDA - TAPOB
24
1.0
0.77
3.3
1.3
7.3
TMOS, 10 wt% SiO 
2
26
1.1
1.0
3.1
1.1
8.5
TMOS, 20 wt% SiO 
2
32
1.3
1.1
5.3
1.2
6.0
TMOS, 30 wt% SiO 
2
38
1.7
1.3
4.0
1.3
9.7
TMOS/MTMS, 10 wt% SiO 
2
27
1.1
0.89
4.4
1.2
6.3
TMOS/MTMS, 20 wt% SiO 
2
29
1.2
0.93
3.1
1.3
9.2
TMOS/MTMS, 30 wt% SiO 
2
29
1.5
1.1
5.1
1.3
5.7
MTMS, 10 wt% SiO 
2
22
1.4
0.71
3.2
2.0
6.7
MTMS, 20 wt% SiO 
2
20
1.0
0.69
2.5
1.5
7.9
MTMS, 30 wt% SiO 
2
19
1.0
0.60
3.5
1.6
5.5

---

Physical and Gas Transport Properties
155
Figure 8.5 CO 
2
permeability (a), diffusion (b) and solubility (c) coeffi cients of 6FDA -
 TAPOB HBPI – silica hybrid membranes plotted against silica content
Figure 8.6 Ideal O 
2
 /N 
2
selectivity (  
α
 (O 
2
 /N 
2
 )) of HBPI – silica hybrid membranes plotted 
against O 
2
permeability coeffi cient
For CO 
2
/CH 
4
separation, more attractive behaviour is observed (Figure 8.7 ). The values 
of
 
α
  (CO 
2
/CH 
4
) of the hybrid membranes prepared solely with TMOS increase with 
increasing silica content in connection with increased CO 
2
permeability. The remarkable 
CO 
2
/CH 
4
separation behaviour of the HBPI 
– 
silica hybrid membranes prepared with 
TMOS is considered to be due to the characteristic distribution and interconnectivity of 
free volume elements created by the incorporation of silica, which provides a size 
-
selective CO 
2
/CH 
4
separation ability [11] . On the other hand,  
α
  (CO 
2
/CH 
4
) values of the 

---

156
Membrane Gas Separation
MTMS systems decrease with increasing CO 
2
permeability in connection with increased 
silica content as similar as the cases of conventional polymeric membranes. The distinc-
tive difference between TMOS and MTMS systems is considered to be due to the differ-
ences in mean size and total amount of free volume elements created by the incorporation 
of silica. The size - selective CO 
2
/CH 
4
separation ability of the hybrid membranes prepared 
with MTMS is sacrifi ced by excess enhancements of mean size and total amount of free 
volume elements although CO 
2
permeability of the MTMS systems is markedly increased. 
It should be noted the CO 
2
/CH 
4
separation ability of the TMOS/MTMS combined systems 
shows an intermediate behaviour between those of TMOS and MTMS systems. As shown 
in Figure 8.7 ,  
α
  (CO 
2
/CH 
4
) of the TMOS/MTMS combined systems have high values and 
tend to exceed the upper bound for CO 
2
/CH 
4
separation [29] with increasing CO 
2
perme-
ability or silica content. Especially, 6FDA 
- 
TAPOB HBPI 
– 
silica hybrid membranes 
contain more than 20 wt% of silica show high  
α
  (CO 
2
/CH 
4
) values, exceeding the upper 
bound. Although a similar tendency of improvement of CO 
2
/CH 
4
separation ability has 
been reported for some linear - type polyimide – silica hybrid membranes [9] , such unique 
improvements of both CO 
2
permeability and CO 
2
/CH 
4
separation ability for the TMOS/
MTMS combined system observed in this study have not been yet reported. This fact 
indicates that mean size and distribution of free volume elements in the TMOS/MTMS 
combined systems are successfully controlled for effi cient CO 
2
/CH 
4
separation and, as a 
result, the TMOS/MTMS combined systems show simultaneous large enhancements of 
CO 
2
permeability and CO 
2
/CH 
4
separation ability.
Figure 8.7 Ideal CO 
2
 /CH 
4
selectivity (  
α
 (CO 
2
 /CH 
4
 )) of HBPI – silica hybrid membranes 
plotted against CO 
2
permeability coeffi cient

---

Physical and Gas Transport Properties
157