Porous materials play an important role in many applications, e.g. fuel
cells, bone transplants and CO2 storage. The current thesis is motivated by
the challenges faced in fuel cell technology with regard to the design and
manufacture of porous electrodes.
The macroscopic, observable properties of porous materials are determined
by their microstructure. However, the challenge still remains in finding
and formulating relations between the microstructure and the macroscopic
properties. This work tests and develops further a recent method that aims
at deriving such relations. The method consists of first quantifying the microstructure
in terms of volume elements called quadrons. This description
is then used in an entropy-based statistical mechanical formalism that makes
it possible to derive macroscopic properties.
We apply the quadron description to numerically generated structures:
planar granular packs and 3D tetrahedral cellular structures. We find that
the quadron statistics are sensitive to the microstructure. Especially, they
capture information about the pores, a microstructural feature that grain-based
volumes such as Voronoi cells do not capture. We evaluate the compactivity
– an analog to temperature – of the planar packs using different
methods. All the methods give the right relation between the compactivities
of the packs. In addition, the volume distributions of the quadrons
decay exponentially. These results lend support to the statistical mechanical
formalism.
We compare the quadron statistics of different 3D cellular structures including
examples of relevant microstructural features such as the throats –
the openings between two pores. Applying the reciprocity defined within
the quadron description, we link between grain shapes, the number of grain
contacts and the length of the TPB, which is a key property of fuel cells
electrodes. This reproduces an established phenomenon in granular materials,
however, this result is obtained here using cellular structures and the
quadron description only.