(265b) Crowding and Curvature: Nanoparticle Models Revisited for Chemisorption and Hydrogenolysis Reactions

Crowding
and Curvature: Nanoparticle Models Revisited for Chemisorption and
Hydrogenolysis Reactions

Abdulrahman Almithn, Ibrahim Alfayez, and David Hibbitts^*

Department
of Chemical Engineering, University of Florida, Gainesville, FL 32611, United States

*corresponding
author: hibbitts@ufl.edu

Bare periodic single-crystal surface
models are commonly used in density functional theory (DFT) calculations to
model catalytic reactions. However, metal-catalyzed reactions often occur at
near-saturation conditions where the catalytic surfaces are highly covered with
adsorbed species. The lack of curvature in these flat periodic models precludes
the adlayer from lateral relaxation to minimize repulsive co-adsorbate
interactions at high coverages, leading to inaccurate estimates of saturation
coverages and site requirements.

H₂ chemisorption measurements
are often used to estimate the size of supported metal clusters by assuming a
H-to-surface-metal (H*:M_surf) stoichiometry of unity at saturation (θ_sat
= 1 ML) and counting the number of exposed metal atoms. Transmission electron
microscopy (TEM) and X-ray diffraction (XRD) can also be used to confirm the
size obtained from chemisorption, however, small metal particles (< 5 nm in
diameter) are difficult to detect using these techniques. Supra-monolayer
coverages of H* (θ_sat > 1 ML) on small Ir, Pt, and Rh
clusters (2–5 nm), where low-coordinated corner
and edge atoms dominate the surfaces, have been reported in literature.¹ Therefore, the assumption of θ_sat
= 1 ML in chemisorption measurements would lead to underestimated particle size
and, consequently, inaccurate measured turnover rates in catalytic reactions. DFT
calculations were used to demonstrate that these low-coordinated atoms can
uptake more than a single H* atom, ruling out H* spillover to the support or
ingression into the bulk as explanations for the observed supra-monolayer
coverages. Cubo-octahedral Pt-group metal particles of varying size (38–586
atoms, 0.8–2.4 nm) were covered with H* gradually to determine the saturation
coverage of each metal and size. Calculated differential adsorption energies
show that Ir₅₈₆ particles, for example, saturate at 1.75 ML while
small Ir₃₈ particles can reach a saturation coverage of 2.88 ML, in
contrast to periodic Ir(111) surfaces that saturate at 1 ML. These findings
were used to establish correlations between saturation coverage and particle
size for Pt-group metals that can be used to accurately estimate saturation
coverages from chemisorption measurements.²

These saturated full particle models
were then simplified into half-particle models to examine the effects of high
co-adsorbate coverages on metal-catalyzed reactions and to accurately estimate
site requirements. Ethane hydrogenolysis was used as a prob reaction because it
is a well-studied reaction and typically occurs at high H* coverages. Measured
turnover rates over Ru, Rh, and Ir clusters show a H₂-pressure
dependence of ~[H₂]⁻³
but Pt shows a H₂-pressure dependence of ~[H₂]^−2.3,³ suggesting either differences in
mechanism or site requirements. Our DFT-calculated free energy barriers, using
bare periodic surface models, indicate that C–C bond cleavage in ethane occurs
via the *CHCH* intermediate which lost 4 H atoms through quasi-equilibrated
dehydrogenation steps on Group 8–10
metals (Ru, Os, Rh, Ir, Ni, Pd, and Pt).⁴ However, these bare surface models neglect
co-adsorbate interactions and cannot be used to estimate site requirements (the
number of H* atom that must be removed from the H*-saturated surface to
accommodate the transition state). H*-covered periodic surface models also
overestimate activation barriers and site requirements because ethane
hydrogenolysis is a reaction with a positive activation area (the transition
state is larger than the H* atoms it replaces) and thus repulsive co-adsorbate
interactions can only be relieved by increasing the number of vacant sites. For
example, DFT-predicted turnover rate on the H*-covered Ir(111) periodic surface
is 4 orders of magnitude lower than the measured rate and show a H₂-pressure
dependence of ~[H₂]⁻⁴.⁵ Curved nanoparticle models, on the
other hand, allow lateral relaxation of the adlayer that weakens co-adsorbate
interactions at high coverages, leading to quantitative agreement with kinetic
measurements (r ~ [H₂]⁻³
on Ir₁₁₉; r ~ [H₂]^−2.4 on Pt₁₁₉). These
findings, taken together, demonstrate the importance of using particle models
in DFT calculations to accurately estimate saturation coverages and site
requirements for catalytic reactions at these conditions.

References

(1)
    Kip, B., J. Catal. 1987, 105, 26–38.

(2)     Almithn,
A. and Hibbitts, D., AIChE J. 2018, 64, 3109–3120.

(3)     Flaherty,
D. and Iglesia, E., J Am Chem Soc 2013, 135, 18586–18599.

(4)     Almithn,
A. and Hibbitts, D., J. Phys. Chem. C 2019, 123,
5421–5432.

(5)     Almithn,
A. and Hibbitts, D., ACS Catal 2018, 8, 6375–6387.