Membrane Gas Separation

2.3
Gas Adsorption 
The sorption of nitrogen at liquid nitrogen temperature (77 
K) has long been used 
to characterize porous materials
[17] 
. Figure
2.2 
compares the low temperature N 
2
adsorption/desorption behaviour of PIM - 1 with that of a typical activated carbon [18]
HO
HO
OH
OH
F
F
CN
CN
F
F
+
O
O
O
O
CN
CN
n
PIM-1
K
2
CO
3
DMF
(a)
(b)
Figure 2.1 (a) Preparation of PIM - 1. (b) Molecular model of a fragment of PIM - 1 
showing the contorted structure
0
2
4
6
8
10
12
14
16
18
20
0
0.2
0.4
0.6
0.8
1
p/p
o
N
2
 adsorbed / (mmol g
–1
)
Figure 2.2 Nitrogen adsorption (fi lled symbols) and desorption (open symbols) isotherms 
at 77 K for PIM - 1 ( 
•
 ,
䊊
 ) and for Darco 20 - 40 mesh activated carbon ( 
䊏
 ,
䊐
 )

---

32
Membrane Gas Separation
(Darco 20 – 40 mesh). The data were obtained using a Micromeritics ASAP 2020 instru-
ment. The amount of gas adsorbed is plotted against equilibrium relative pressure ( p / p
0
), 
where p
0
is the saturation pressure of the gas at the temperature of measurement, in this 
case atmospheric pressure. For both materials, high uptake is seen at very low relative 
pressure. It is the very smallest pores (micropores, dimensions
<
2 nm) that fi ll fi rst, 
because multi - wall interactions give rise to strong adsorption. For the carbon, there is 
further adsorption associated with a hysteresis (the desorption curve lies above the adsorp-
tion curve) that closes at a relative pressure above 0.4. This is typical of a material 
that includes mesopores (dimensions 2 – 50 nm), which fi ll by a capillary condensation 
mechanism. PIM - 1 also shows hysteresis, but it differs in that the hysteresis extends 
down to low relative pressures. This cannot be explained by mesoporosity, but it may be 
attributed to swelling of the material on adsorption, or possibly to the tortuosity of the 
micropores. Thus the carbon sample has both micropores and mesopores, whilst PIM - 1 
is essentially microporous. Superimposed on the
‘ 
microporous material 
’ 
behaviour, 
however, is polymer behaviour, since rearrangement of polymer chains and swelling can 
occur, despite large - scale changes of polymer conformation being forbidden.
Brunauer, Emmet, Teller (BET) analysis of adsorption isotherms allows a surface area 
to be calculated [17,19] . The BET model is for multilayer adsorption on a fl at surface, so 
when applied to a porous material the surface area obtained is an apparent value. 
Nevertheless, BET surface area provides a useful comparison between materials. PIM - 1 
shows a higher BET surface area than the activated carbon in Figure 2.2 , a value of 
780 m 
2
g 
– 1
for PIM - 1 as compared to 545 m 
2
g 
– 1
for the carbon. 
Since the smallest pores are fi lled fi rst, the very low pressure region of the adsorption 
isotherm contains information about micropores. A method for determining the distribu-
tion of micropore size was developed by Horvath and Kawazoe [17,20] . The method 
assumes that all pores of a certain size will be fi lled at a particular relative pressure. The 
original Horvath – Kawazoe equation assumed the pores to be slit - shaped, but models for 
alternative pore geometries, such as cylinders [21] , have been developed. A pore size 
distribution for PIM - 1, calculated by the Horvath – Kawazoe method, can be seen in Figure 
2.3 . When interpreting data such as these, one should be aware of anomalies that arise 
because one is operating near the limits of the technique. The micropore distribution 
extends down to below the size corresponding to the lowest pressure that can be achieved 
experimentally. The data in Figure 2.3 are for a sample that was thoroughly outgassed 
at elevated temperature prior to measurement at liquid nitrogen temperature. The fi rst 
few data points are therefore infl ated by a contribution from smaller pores, giving an 
artifi cially sharp peak in the early part of the distribution. Despite this distortion of the 
distribution, low temperature N 
2
adsorption data support the concept that PIM - 1 behaves 
like a molecular sieve, with pore sizes in the micropore ( 
<
2 nm) region.
The Horvath – Kawazoe method can also be applied to adsorption of carbon dioxide at 
273 K. This gives information about smaller micropores than does nitrogen adsorption. 
A partial micropore distribution for PIM - 1 from CO 
2
adsorption is compared with the 
result from N 
2
adsorption in Figure 2.3 . Extension of the distribution to higher pore widths 
requires higher pressures than were possible on the instrument used to obtain these data. 
The apparent distribution from CO 
2
adsorption may be affected by the presence of specifi c 
adsorption sites. Nevertheless, the data support the idea that the material is essentially 
microporous. 

---

Gas Permeation Parameters and Other Physicochemical Properties
33
Computer simulation may be used to visualize the microporosity of PIM - 1. A pore size 
distribution derived by Heuchel et al. [22] from atomistic modelling of packed PIM - 1 is 
included in Figure 2.3 . This distribution was obtained using an approach that subdivides 
very elongated regions of free volume into smaller elements. The simulation, like the 
experimental gas adsorption results, indicates PIM - 1 to contain pores or spaces with 
widths in the nanometre and sub 
- 
nanometre range, i.e. microporosity as defi ned by 
IUPAC. A simulated N 
2
adsorption isotherm may be obtained from the computer model. 
Since the model is a purely static system, the predicted isotherm is what would be 
expected for a rigid microporous material, reaching a plateau at low relative pressure [22] . 
An apparent surface area of 435 m 
2
g 
– 1
may be calculated, lower than the experimental 
value of about 750 m 
2
g 
– 1
. The additional adsorption and hysteresis observed experimen-
tally may be attributed to the effects of polymer dynamics. 
Further information about the sizes of free volume elements or micropores can be 
obtained from inverse gas chromatography and positron annihilation lifetime spectros-
copy (PALS), as is discussed later.