Membrane Gas Separation

8.2.4
Measurements 
Infrared (IR) spectra were recorded on a JASCO FT/IR - 460 plus. UV/VIS optical trans-
mittances were investigated by a JASCO V - 530 UV/VIS spectrometer at a wavelength 
Scheme 8.1 Preparation of hyperbranched polyimide – silica hybrid membrane

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Physical and Gas Transport Properties
147
of 200 – 800 nm. Thermogravimetric – differential thermal analysis (TG - DTA) experiments 
were performed with a Seiko TG/DTA6300 at a heating rate of 10 ° C/min under air fl ow. 
Thermal mechanical analysis (TMA) measurements were carried out using a Seiko TMA/
SS6100 at a heating rate of 5 ° C/min under N 
2
fl ow. CO 
2
, O 
2
, N 
2
and CH 
4
permeation 
measurements were carried out by a constant volume/variable pressure apparatus at 
76 cmHg and 25 ° C. The permeability coeffi cient, P (cm 
3
(STP) cm/cm 
2
s cmHg), was 
determined by the following equation [15] ;
P
A
L
p
V
RT
p
t
=
22414
d
d
(8.1)
where A is the membrane area (cm 
2
), L is the membrane thickness (cm), p is the upstream 
pressure (cmHg), V is the downstream volume (cm 
3
), R is the universal gas constant 
(6236.56 cm 
3
cmHg/mol K), T is the absolute temperature (K), and d p /d t is the permeation 
rate (cmHg/s). The gas permeability coeffi cient can be explained on the basis of the 
solution - diffusion mechanism, which is represented by the following equation [16,17] ;
P
D S
= ×
(8.2)
where D (cm 
2
/s) is the diffusion coeffi cient and S (
cm STP cm
cmHg
polym
3
3
(
)
) is the solu-
bility coeffi cient. The diffusion coeffi cient was calculated by the time - lag method repre-
sented by the following equation [18] ;
D
L
=
2
6
θ
(8.3)
where  
θ
  (s) is the time - lag. Density of the pure HBPIs was measured by the fl oating 
method with bromoform and 2 - propanol at 25 ° C. According to the group contribution 
method, fractional free volume (FFV) of a polymer can be estimated by the following 
equation [19] ;
FFV
V
V
V
sp
w
sp
=
−
1 3
.
(8.4)
where
sp
(cm 
3
/mol) is the specifi c molar volume which can be calculated from the experi-
mental density,  
ρ
  (g/cm 
3
), and V 
w
(cm 
3
/mol) is the van der Waals volume of the repeat unit.