(732b) Defining and Counting Site Requirements for Reactions on Curved and Crowded Surfaces

Defining and counting site requirements for reactions on curved and
crowded surfaces.

David Hibbitts,^1,3 Abdulrahman Almithn,¹
David Flaherty,^2,3Jianwei Liu,³
Enrique Iglesia³

¹
Department
of Chemical Engineering, University of Florida, Gainesville, FL 32610

²Department of Chemical and Biomolecular Engineering, University of
Illinois Urbana-Champaign, Urbana, IL 61801

³Department of
Chemical and Biomolecular Engineering, University of California, Berkeley, CA
94720

Catalysis
by supported metal nanoparticles often occurs at conditions which result in
their curved surfaces being covered by one or more intermediate (MASI).
Counting the number of total exposed metal atoms on such surfaces is often done
by titration experiments (e.g. H₂ chemisorption) that assume a
specific (and often incorrect) saturation coverage of the titrant (e.g. H*).
Defining the number of sites required for a given surface reaction, however, is
more ambiguous and estimating site requirements from low- or fixed-coverage
calculations is fraught with error.

Density
functional theory (DFT) calculations are often used to model surface reactions
and the effects of coverage therein, typically by modeling metal nanoparticles
using flat periodic single-crystal surfaces. Common surfaces (for FCC metals)
include the close-packed (111) or (100) in addition to a variety of surfaces
that are ‘kinked’ to expose defect sites (under-coordinated metal atoms) such
as the (211). Reaction energetics are then calculated on these surfaces
independently—on surfaces either essentially bare or at ‘moderate’ (≤
0.75 ML) coverages—and from these data the effects of coverage are estimated,
and the effects of particle size are inferred by contrasting the behavior of
close-packed surfaces and defect sites on ‘kinked’ surfaces. These flat
periodic surface models, however, cannot allow for the lateral relaxation of
the adlayer that occurs when adlayer strain is created by repulsive
co-adsorbate interactions or by surface reactions that have a positive
activation area, meaning their transition states are larger than their relevant
precursors, analogous to activation volume in single-phase reactions. The
inability of the adlayer to laterally relax leads to inaccurate coverage
estimates and coverage effects.

Here,
we will demonstrate the necessity for curved catalyst models in estimating the
saturation coverage of H* or CO* species, the site-requirements for surface
reactions, and the rates and kinetic dependencies of high coverage reactions.
H* saturation coverages at H₂ chemisorption conditions will be
estimated by calculating H* adsorption energies on cubo-octahedral
Pt and Ir particles from 38 atoms (0.8 nm diameter)
to 586 atoms (2.4 nm) do demonstrate that H* to surface metal stoichiometries
can be as high as 2.9 ML (far above the 1 ML commonly used in the
interpretation of H₂ chemisorption isotherms).¹ Site
requirements for a well-studied probe reaction, ethane hydrogenolysis reactions
on H*-covered Ir surfaces^2–4, will be rigorously determined by
modeling the reaction at a variable number of H*-vacancies within the adlayer
on both Ir(111) and Ir₁₁₉ hemispherical particles (1.6 nm).⁵
These results demonstrate that the Ir(111) surface model incorrectly predicts ethane
hydrogenolysis rates and site requirements (and therefore H₂-pressure
dependencies) because the H*-adlayer cannot relax during formation of the
kinetically relevant transition state from the H*-covered surface (a positive
activation area reaction) while the Ir₁₁₉ model allows for H*
adlayer relaxation provides quantitative agreement with kinetic data.⁵
Furthermore, the Ir(111) surface model results in transition states which
communicate over long distances through the adlayer such that reaction
energetics vary with the choice of unit cell site (from 3×3 up to 9×9)
indicating severe artifacts of periodicity in these models.⁵ Activation
areas can also be negative, as in the case of CO–H₂ reactions on
CO*-covered Ru surfaces, and in such cases adlayer strain is relieved upon
formation of the kinetically relevant transition state therefore decreasing
activation energies as CO* coverage increases and ultimately mitigating CO
inhibition and allowing Fischer-Tropsch synthesis to occur at observed rates.⁶
These examples all demonstrate the necessity of curved and crowded particle
models in the use of theoretical techniques to determine reaction mechanisms,
estimate rates, and infer pressure-dependencies of reactions occurring at
conditions relevant to practical catalysis.

References

1.     
A. Almithn and D. Hibbitts, “Supra-monolayer coverages on small metal clusters
and their effects on H₂ chemisorption particle size estimates.” AIChE Journal, In
Press, (2018).

2.     
D. Flaherty, D. Hibbitts, E. Gurbuz, and E.
Iglesia, “Theoretical and kinetic assessment of the mechanism of ethane hydrogenolysis
on metal surfaces saturated with chemisorbed hydrogen.” Journal of Catalysis,
311 (2014) 350–356.

3.     
D. Flaherty and E. Iglesia, “Transition-state enthalpy and entropy
effects on reactivity and selectivity in hydrogenolysis of n-alkanes.” Journal
of the American Chemical Society, 49 (2013) 18586–18599.

4.     
D. Hibbitts, D. Flaherty, and E. Iglesia, “Effects of chain length on
the mechanism and rates of metal-catalyzed hydrogenolysis of n-alkanes.” Journal
of Physical Chemistry C, 120 (2016) 8125–8138.

5.     
A. Almithn and D. Hibbitts, “Effects of catalyst model and high adsorbate
coverages in ab initio studies of alkane hydrogenolysis.” ACS Catalysis, Submitted, (2018).

6.     
J. Liu, D. Hibbitts, and E. Iglesia, “Dense CO adlayers as enablers of
CO hydrogenation turnovers on Ru surfaces.” Journal of the American Chemical
Society, 139 (2017) 11789–11802.