Membrane Gas Separation

Penetrant
n - C 
4
0.720
430
290
n - C 
5
0.749
451
305
Penetrant
k 
ij
 
k 
sw
  (MPa 
−
1
) Matrix
n - C 
4
0.14
0.13 
0.20 
0.21
AF 2400 
AF 2400/25% wt FS 
AF 2400/40% wt FS
n - C 
5
0.14
0.85 
1.20 
2.00
AF 2400 
AF 2400/25% wt FS 
AF 2400/40% wt FS
a
Experimental value.
b
Value estimated based on the experimental solubility isotherms of n - C 
4
.
Table 7.2  Values of the coeffi cients A , B , E and F for the correlations of Equations (7.16)
and (7.20)
A
B
E
F
(cm 
2
/s)
(g/g 
pol
) 
−
1
n - C 
4
H 
10
2.28
×
10 
16
18.008
8.27
×
10 
9
57.08
n - C 
5
H 
12
5.06
×
10 
16
18.355
3
×
10 
18
118.93

---

Vapor Sorption and Diffusion in Mixed Matrices Based on Tefl on® AF 2400 
137
7.4.2
Diffusivity 
The diffusion coeffi cient was calculated in every sorption step of the pressure decay 
experiments, fi tting Equation (7.19) to the transient data of mass uptake. Results for pure 
polymers and MMM are reported in Figure 7.6 , where it can be seen that the addition of 
FS particles increases the diffusivity value, at fi xed penetrant concentration in the poly-
meric phase. This is against the common thought that the addition of impermeable parti-
cles decreases the diffusion coeffi cient by increasing the tortuosity of the path that the 
penetrant molecules have to follow inside the membrane. However, the observed behav-
iour is completely consistent with previous results obtained for several gases and vapours 
in mixed matrices based on fumed silica and PTMSP, PMP and amorphous Tefl on [2,3] . 
For those systems, the diffusivity enhancement was observed with every penetrant 
inspected, while the extent of the phenomenon varies with the specifi c penetrant. The 
same results are obtained considering diffusion coeffi cients obtained both from sorption 
and permeation experiments [2,3] . This trend has been considered as a direct consequence 
of the increase of the concentration of larger free volume elements with increasing fi ller 
content in Tefl on AF 2400, which was documented with positron annihilation lifetime 
spectroscopy technique [3] .
Also the variation of the apparent diffusivity with penetrant average concentration in 
the MMM shows a peculiar behaviour. Such a dependence is represented by the parameter 
 
β
  used in Equation (7.12) , and we can notice that its value decreases with increasing fi ller 
content. An analogous phenomenon was already evidenced by Merkel et al. , although no 
clear explanation was provided [2,3] . It appears that the matrices characterized by high 
fi ller loadings have rather high infi nite dilution diffusivities so that the favourable effect 
of swelling, which increases with penetrant concentration, results in smaller relative 
increases of diffusivity.