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Mathematical Modeling of Hydrogen Spillover on Metal-Doped Carbon Materials

Mathematical Modeling of Hydrogen Spillover on Metal-Doped Carbon Materials. Qixiu Li Prof. Derek Elsworth EGEE 520 04-29-2008. Introduction.

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Mathematical Modeling of Hydrogen Spillover on Metal-Doped Carbon Materials

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  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. 1 2 3 • 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. H2 molecules ??? Metal Support

  3. Governing equation and formulation The fluid flow and diffusion equation (Fick’s 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 Constants

  6. Comsol solution 1x10-1 s 1x10-4 s 10s 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.

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