Membrane Gas Separation

Probe/FVE Volume (A
3
)
Cumulative FVD (-)
-0.012
-0.010
-0.008
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
0.008
FVD (-)
AD60X
AD80X
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
3.5
4.0
4.5
5.0
5.5
6.0
Probe/FVE eq. radius (A)
Cumulative FVD (-)
-0.012
-0.010
-0.008
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
0.008
FVD
(-
)
AD60X
AD80X
Figure 4.6 FVE distribution curve in terms of probe or FVE volume (left) and in terms of 
probe or FVE equivalent radius, r
eq
(right). Fitting results: Hyfl on AD60X:  
μ
= 419 and 
  
σ
= 53 Å
3
( r
eq
= 4.64 Å ,  
σ
= 0.19 Å ); Hyfl on AD80X:  
μ
= 462 and  
σ
= 68 Å
3
( r
eq
= 4.79 Å , 
  
σ
= 0.24 Å ). The values between parentheses are based on the fi t of the radius

---

Amorphous Glassy Perfl uoropolymer Membranes of Hyfl on AD®
71
F
V
= +
−
⎛
⎝
⎞
⎠
1
2
1
2
2
erf
μ
σ
(4.3)
where V is the probe size or corresponding FVE size,  
μ
  is the mean value and  
σ
  is the 
standard deviation, a measure of the width of the distribution. The void size distribution 
is then described by the normal probability function:
f
V
=
−
−
(
)
⎛
⎝⎜
⎞
⎠⎟
1
2
2
2
2
σ π
μ
σ
exp
(4.4)
The latter describes a peak with a maximum at the average void volume V =  
μ
  . The two 
experimental data sets in the present work can be fi tted quite satisfactorily with the normal 
distribution function. The resulting quantitative data of the fi tting procedure are given in 
the caption of Figure 4.6 . 
The size of the free volume elements is in the range of about 250 – 560 Å
3
in Hyfl on 
® 
AD60X and ca. 280 – 640 Å
3
in Hyfl on 
® 
AD80X. This means that, if we assume a spherical 
shape of free volume elements, the equivalent radius is roughly between 4 Å and 5.4 Å , 
slightly lower in Hyfl on AD60X than in Hyfl on AD80X, with a maximum in the distribu-
tion of about 420 Å
3
and 460 Å
3
( r
eq
= 4.6 Å and 4.8 Å ), respectively. Recently, a compara-
tive study of various experimental and computational free volume probing techniques on 
Hyfl on AD was reported [27] and the results of photochromic probing were consistent 
with those of PALS, IGC and
129
Xe - NMR. Molecular dynamics (MD) simulations showed 
that the free volume distribution is much more complex than what can be described by a 
simple Gaussian distribution, due to a strongly interconnected three - dimensional void 
structure. Small discrepancies between the individual experimental probing techniques 
can all be traced back to this complex void structure and to the fundamentally different 
physicochemical interactions between the probes and the polymer matrix. For a qualita-
tive description of the difference between the two grades of Hyfl on the Gaussian distribu-
tion is more than satisfactory.