Membrane Gas Separation

7.2
Theoretical Background 
In gas separation, the performance of a membrane is usually evaluated through the 
selectivity  
α

i,j
  between two penetrants i and j , that is expressed as:
α
α α
i j
i
j
D
S
i
j
i
j
P
P
D
D
S
S
,
=
=
⋅
⋅
=
(7.1)
where P 
i
  is the permeability of the i 
th
  penetrant and can be calculated as the product of 
D 
i
  and S 
i
  if the solution - diffusion model holds true and Fick ’ s law is appropriate to rep-
resent the diffusive mass fl ux. 
The addition of nanoparticles in a polymeric matrix has been considered with the 
expectation of taking advantage of the specifi c qualities of the two materials, obtaining 
in fact a variety of unexpected behaviours which apparently demand an extensive experi-
mental analysis. Therefore, it would be highly desirable and useful to be able to predict 
the behaviour of a composite matrix from the properties of the pure constituents, glassy 
polymer and fi ller nanoparticles, while to our knowledge, there are no models available 
that can predict correctly the solubility and diffusivity behaviour of the mixed matrices 
under consideration. Only models for permeability are available and they all predict a 
decrease in permeability as rigid impermeable particles are added to the matrix, due to 
the increase in the tortuosity of the path that the penetrant molecules have to follow during 
diffusion through the membrane. One of the most commonly used is the Maxwell model 
[5] , initially derived for the permittivity of a dielectric medium, that states:

---

Vapor Sorption and Diffusion in Mixed Matrices Based on Tefl on® AF 2400 
127
P
P
i
i P
=
−
+
⎛
⎝⎜
⎞
⎠⎟
,
1
1
2
Φ
Φ
F
F
(7.2)
where  
Φ
 
F
is the volume fraction of the particles loaded. Even if suitable for some MMM 
with non - porous fi llers, this model is certainly not applicable to the case of amorphous 
Tefl on 
® 
loaded with FS nanoparticles. Thus a new method has been proposed [4] to 
calculate solubility and transport properties in MMM, based on the NELF model for solu-
bility, that can predict the behaviour of permeability through the separate calculation of 
penetrant solubility and diffusivity. The general features of the model are briefl y revised 
hereafter, before presenting the results of the experimental analysis.