Membrane Gas Separation

(a) 
10
-9
10
-8
10
-7
10
-6
0.000
0.005
0.010
0.015
0.020
0.025
0.030
Teflon AF2400
Teflon AF2400 + 25% FS
Teflon AF2400 + 40% FS
Diffusivity (cm
2
/s)
Average concentration (g/g
pol
)
(b)
10
-9
10
-8
10
-7
10
-6
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Teflon AF2400
Teflon AF2400 + 25% FS
Teflon AF2400 + 40% FS
Diffusivity (cm
2
/s)
Average concentration (g/g
pol
)
n-C
4
n-C
5
Figure 7.6 Average diffusivity of (a) n - C 
4
and (b) n - C 
5
in Tefl on AF 2400 - based mixed 
matrices at 25 ° C, versus average penetrant concentration

---

138
Membrane Gas Separation
In the following section, we will present quantitative correlations for both infi nite 
dilution diffusion coeffi cients and  
β
  values as a function of the mixed matrix structural 
parameters.
7.4.3
Correlations for Diffusivity 
The FFV in the unpenetrated polymer phase of the MMM calculated from the sorption 
isotherm of the test penetrant (n - C 
4
) through the NELF model can also be used to correlate 
the diffusivity data collected during sorption tests. The infi nite dilution diffusion coeffi -
cient in the polymeric phase, D
P
(0) determined from the experimental diffusivity data can 
be related to the FFV initially present in the polymer matrix (
FFV
M
0
). As shown in Figure 
7.7 for diffusion of n - butane in AF 2400, there is a correlation between the infi nite dilu-
tion diffusion coeffi cient and
1 FFV
M
0
, that agrees with Equation (7.16) . Similar behaviour 
is observed for n - C 
5
, with different values of the parameters A and B , as it can be seen 
from the results reported in Table 7.2 . This is not surprising, because the values of these 
empirical parameters are expected to be a function of the penetrant nature and size.
Finally, it is found that the coeffi cient  
β
  appearing in the concentration dependence of 
diffusivity, Equation (7.12) , is related to the FFV of the polymer phase of the MMM at 
infi nite dilution (Figure 7.7 c) through an exponential law:
β = ⋅
− ⋅
(
)
E
F
exp
FFV
M
0
(7.20)
The parameters E and F are both positive, vary with the penetrant (Figure 7.7 d), and their 
values are reported in Table 7.2 . The correlation expressed by Equation (7.20) actually 
states that the higher the initial free volume of the matrix, the lower the effect of concen-
tration on diffusion, i.e. the lower the value of  
β
  .