Membrane Gas Separation

4.4
Molecular Dynamics Simulations 
Molecular dynamics (MD) simulation studies were carried out to get deeper insight into 
the free volume structure and its spatial arrangement in the polymers, and into the correla-
tion between the free volume and the transport properties of the materials. It is of crucial 
importance that MD simulations provide not only local characteristics of the free volume 
such as FVE size and FVE size distribution, but also information on its topology, enabling 
a complete visualization in 3D [1,27,32] . 
The construction of a correct model for the polymer structure is the prerequisite for 
obtaining accurate results and it is always the fi rst step in the FV modelling. Nowadays 
several well established simulation methods exist for the preparation of atomistic packing 
models, both for high and for low free volume polymers [33] . In molecular modelling of 
amorphous polymers, usually a cubic characteristic volume element is fi lled with polymer 

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72
Membrane Gas Separation
chain segments with or without small permeant molecules in a way that represents most 
closely the behaviour to be expected in reality. 
The analysis and visualization of the free volume of a polymeric model can be obtained 
in several ways, e.g. the Monte Carlo method [34] , geometrical sizing methods [35] and 
energetic sizing method using the cavity energetic sizing algorithm (CESA) method [36] . 
The free volume in the packing models can be described qualitatively but for comparison 
with experimental methods a more quantitative evaluation is necessary. 
A fi rst evaluation is often made by a direct visualization of the packed polymer chains, 
cut into thin slices. The slice representations give important qualitative differences in the 
amount and distribution of free volume in the polymer. Generally, a homogeneous dis-
tribution of free volume is typical for ‘ normal ’ amorphous polymers with small and 
medium amounts of free volume [33] , but polymers with high content of free volume 
such as PTMSP [32] and also glassy PFPs like Tefl ons AF [32] or Hyfl ons AD [27] , 
behave differently. These materials contain regions of high segmental packing density 
where the free volume distribution resembles that in low and medium free volume 
polymers. The other regions of the materials show rather large voids that may extend in 
three dimensions to form a partly continuous hole phase. The shape of such free volume 
elements is highly irregular and non - spherical. 
For the quantitative description of the free volume distributions, different methods have 
been developed, based on energetic [36] or geometric considerations [35] . In the fi rst case 
the cavity size distribution is defi ned using a spherical volume with variable dimensions 
and a well - defi ned centre, located at the minimum in a repulsive particle energy fi eld. In 
the second approach, used in the present work, the free volume is determined overlaying 
a tight three - dimensional grid on the polymer box and inserting a probe at every grid 
point. All grid points showing overlap with the van der Waals radius of the atoms in the 
polymer matrix are classifi ed as occupied. Those without overlap are part of the free 
volume. All neighbouring free grid points are grouped into single elements that represent 
the individual holes. This approach identifi es also cavities that are large and with an 
irregular shape. 
The results of this free volume analysis are visualized in Figure 4.7 for a representative 
slice of Hyfl on AD80X. Every free grid point is represented by a sphere of radius of 
1.1 Å , corresponding to a positronium - sized test particle. The individual FVEs are repre-
sented by the collection of adjacent and partially overlapping spheres. In this representa-
tion several large FVEs seem to be present but in reality most of them belong to a single 
very large interconnected free volume element which extends over the neighbouring 
slices. Due to the periodic boundary conditions the FVEs which reach one edge of the 
slice continue at the opposite side.
For the representation of the complex geometry in a quantitative way different sets of 
shape parameters have been introduced, for instance based on the void surface area, 
equivalent sphere volume, radius of gyration. Each of these methods introduces an over-
simplifi cation of the very complex nature of the voids. For the same reason the photo-
chromic probe method described above shows a much narrower distribution than one 
might expect on the basis of the clearly elongated voids displayed in Figure 4.7 . This is 
a common limit of all experimental probing methods, none of which can probe the 
complex void structure to its full extent.

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Amorphous Glassy Perfl uoropolymer Membranes of Hyfl on AD®
73