Friday, December 1, 2006
2:00pm – 3:00pm
Professor Heinz Pitsch
Department of Mechanical
Engineering
Stanford University
ÒComputational
Chemistry Based Multi-Scale Simulations of Polymer
Electrolyte
Membrane Fuel Cells: Development of Models
and
Numerical Algorithms, and Application to Fuel CellsÓ
Abstract:
Computational chemistry presently is a rapidly evolving
field, because of recent improvements in computational power and theoretical
developments, and the great potential of computations to further the
understanding of chemical processes and the interactions of chemistry and
transport phenomena. These computational approaches include quantum chemistry
simulations, molecular dynamics simulations, and dynamic Monte Carlo
simulations (DMC).
Here we will present the development of a computational
chemistry based multi-scale model for computational fluid dynamics simulations
of polymer electrolyte membrane (PEM) fuel cells. The multi-scale model is
based on DMC simulations of the chemistry on the electrocatalyst surfaces.
Several advancements in numerical techniques for computational chemistry
simulations and their applications to real systems will be presented for the
example of the PEM fuel cell cathode.
Transition probabilities required for these simulations are
determined from quantum chemical simulations. For electrochemical simulations,
the local reaction center theory by Anderson is used. We present an efficient
mathematical framework to determine the potential-dependent transition states
of electron transfer reactions by quantum calculations. This method leads to
fast convergence, reliability, and robustness of the located transition states
for more complex systems with a larger number of degrees of freedom, and makes
these computations cost-efficient enough to study a large number of individual
reactions. As an example, adsorbent interactions relevant for electrochemical
steps of the oxygen reduction reactions are discussed.
Because of the possible importance of such adsorbent
interactions and other non-linear local chemical effects, DMC methods are
expected to describe the chemical behavior more accurately than
environment-averaged methods. In PEM fuel cells, carbon-particle supported
platinum nano-particles are often used as electrocatalyst. These Pt-particles
can be approximated to be of cubo-octahedral form. The specific topology of
these particles can lead to important features associated with the complex
surface structure. Specifically, the edge/corner sites can behave differently
from sites located on the faces. Environment-averaged approaches, such as the
mean-field approximation, often fail to accommodate the details of such local
phenomena. DMC is computationally much more demanding than conventional approaches,
and several different DMC simulations algorithms have been proposed in the
past. An example is the popular Variable Step Size Method (VSSM). VSSM has the
advantage that the computational cost of a single time step is independent of
the lattice size for problems with time-independent rate parameters, but scales
with the square of the number of lattice sites otherwise. Another method, the
First Reaction Method (FRM), can be applied for time-varying rate coefficients,
but the computational cost per time step depends still linearly on the
logarithm of the number of lattice sites. Here we present a new DMC algorithm
that can be applied for time-varying rate coefficients, and which has a
computational cost per time step that is independent of the lattice size. To
demonstrate the capabilities of the new method, DMC simulations of cyclic
voltammetry of PEM fuel cell electrochemistry will be presented and compared
with experimental observations.
Finally, the integration of the DMC simulation technology
into a multi-scale model will be presented. The model describes the interaction
of surface chemistry with gas diffusion in thin electrolyte layers surrounding
the platinum particles on the nano-scale and the transport in the porous
material of the catalyst layer on the mirco-scale. Simulation results will be
compared with experimental data of a fuel cell using single crystal Pt
electrodes.