Page 119 - Introduction to Transfer Phenomena in PEM Fuel Cells
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108 Introduction to Transfer Phenomena in PEM Fuel Cells
Kreuer et al. [KRE 04] synthesized simulation tools and proton transfer
mechanisms in membranes.
3.6.2.1. Statistical mechanics
Explaining the behavior of macroscopic systems from their microscopic
characteristics is the subject of statistical mechanics. It thus makes it
possible to study the Brownian motion of the particles (individually
monitoring their position in a fluid) and it is based on a main assumption that
the equations of classical mechanics are still valid (Langevin principle).
It is then possible to study the interactions between the different
molecules present in the membrane pores.
Paul and Paddison [PAU 04] used this simulation technique to evaluate
the relative permittivity of water (ε r) in a cylindrical pore filled with water
and ions by formulating a hypothesis of local thermodynamic equilibrium.
They deduced radial variations for (ε r) in the pore. It should be noted that a
study based on statistical mechanics requires the introduction of probability
densities, thus making the overall study more complex [COL 08].
3.6.2.2. Molecular dynamics
This is another very small-scale modeling technique that simulates the
evolution of a particle system over time (hence, “dynamics”).
The trajectory of a molecule is calculated by applying the laws of
Newtonian classical mechanics.
These simulations are carried out for a few nanoseconds, during which
the time is discretized. The system is composed of a hundred molecules;
each molecule is considered as a dynamic entity for which the position of
atoms evolves over time. At each time step, Newton’s second law makes it
possible to know the speed and position of each atom by knowing the forces
acting on it.
In the case of Nafion membranes, there are four types of forces: the
interactions between the atoms, the forces at the interfaces, the permanent
stresses (e.g. the temperature) and the driving forces (gravity, gradients of
pressure and concentration) [DIN 98].
