Mathematical Modeling of Hydrogen Spillover on Metal-Doped Carbon Materials

1
Mathematical Modeling of Hydrogen Spillover on
Metal-Doped Carbon Materials

• Qixiu Li
• Prof. Derek Elsworth
• EGEE 520
• 04-29-2008

2
Introduction

• Hydrogen spillover is defined as the
  dissociative chemi-sorption of hydrogen on the
  metal and the subsequent migration of atomic
  hydrogen onto the surface of the support such as
  alumina, carbon and so on that would not
  typically adsorb active species under the same
  conditions.

• Three steps
• Hydrogen molecules dissociate on metal and then
  diffuse from metal to metal.
• Hydrogen atoms diffuse from metal to carbon
  surface (spillover).
• Hydrogen atoms diffuse from carbon to carbon and
  be adsorbed.

???
3
Governing equation and formulation
The fluid flow and diffusion equation (Ficks law)
A time-scaling coefficient c concentration D
diffusion coefficient R adsorption rate
Arrehenius expression for surface diffusion
Do surface diffusivity at zero loading Ea
activation energy for surface diffusion k
Boltzmann constant T absolute temperature
4
Comsol model
Setting Graphite surface cell containing 50 x
50 carbon atoms ( Diameter 12.2 nm) Metal one
single Pt particle (Diameter 2nm)
Graphite
metal
5
Parametric study
Parameters Equation used Calculation result
D on metal surface 3.6 x 10-10 m2/s
D on carbon surface 7.58 x 10-20 m2/s
Adsorption rate mol/m3s
A m T Ea (on metal) Ea(on carbon)
1 3 298.15 K 0.40 eV 0.78 eV
Constants
6
Comsol solution
1x10-4 s
1x10-1 s
10 s
200 s
7
Comsol solution (cont.)
t 200 s
Hydrogen spillover diffusion coefficient 1.1 x
10-16 m2/s
t 0 s
8
Validation
Literature
Example Grid for the Monte Carlo simulations at
steady state
Comsol sulotion for the infinite element analysis
at steady state
9
Conclusion

• Infinite element analysis is an useful method for
  the analysis of hydrogen spillover process.
  Comsol diffusion model (transient analysis) can
  be applied to this process.
• In our modeling, the whole hydrogen diffusion
  process takes about 150 seconds.
• Hydrogen diffusion (from metal to carbon)
  coefficient has been calculated to be1.1 x 10-16
  m2/s which is reasonable.
• The modeling result agrees well with the
  literature result.