Coverage-Dependent Adsorption
The adsorption energy of a species on a surface is generally not a constant: it changes as the surface fills, usually becoming weaker at higher coverage. Explanations include direct repulsion between adsorbates (dipole or Pauli repulsion), competition among adsorbates for bonding with the same surface atoms, and adsorbate-induced changes in the surface electronic structure. Because reaction, dissociation, desorption and diffusion barriers often scale with adsorption energies, coverage effects make kinetic parameters themselves coverage dependent. See also d-Band model and Adsorption scaling relations.
Oxygen on Ag- and Pd-terminated Ag3Pd(111) (2008)
On Ag3Pd(111), the average O binding energy weakens roughly linearly with coverage from 0.25 to 1 ML, by about 1 eV on Pd-terminated and about 1.5 eV on Ag-terminated configurations, and dissociative adsorption becomes endothermic above 0.25 ML on Ag-terminated surfaces (Kitchin et al. 2008). The steeper loss on Ag-rich terminations increasingly favors Pd at the surface at high oxygen load, so low-coverage binding data alone are not enough to predict adsorbate-induced segregation. Summary: kitchin2008.
C, N and O on Pd(111) and the principle of corresponding adsorption states (2009)
Using DFT (PW91) on 20 fcc-site configurations per adsorbate from 0.2 to 1 ML, Kitchin found that the most stable C, N and O adsorption energies on Pd(111) weaken nearly linearly with coverage, with slopes of 2.49, 1.88 and 1.29 eV/ML respectively. The trend is attributed to adsorbate-induced broadening and down-shift of the surface d band at nearly constant filling. Because all three adsorbates perturb the d band similarly, the energies of C and N in each configuration are linearly correlated with those of O in the same configuration, and after removing each fit’s intercept and slope the data collapse onto one line within about 100 meV/adsorbate. Exceptions arise only for reconstructed carbon structures and geometrically dissimilar sites (Kitchin 2009). Summary: kitchin2009.
Oxygen on Au(111) and Pt(111) through adsorbate-induced d-band changes (2009)
Using DFT on sixteen fcc-site oxygen configurations between 0.17 and 1.00 ML, this paper found that the oxygen adsorption energy weakens by about 1.5 eV/O on Au(111) and by more than 1.0 eV/O on Pt(111), nearly linearly for the most stable configuration at each coverage and leveling off toward a dilute limit at low coverage (Miller 2009). Atomistic thermodynamics placed only a p(2x2) phase on Au before bulk oxide formation, while p(2x2) and p(2x1) phases dominate on Pt. This is the first of the group’s studies that explains coverage dependence through adsorbate-induced surface electronic structure rather than direct adsorbate-adsorbate interactions. Summary: miller2009.
Oxygen on Au(111) and Pt(111) across the full configuration space (2009)
Miller and Kitchin used cluster expansions fit to DFT data to compute oxygen adsorption energies for all 8917 symmetry-distinct configurations in cells of up to 15 fcc sites on Au(111) and Pt(111). The lowest-energy configurations show some nonlinearity in coverage, particularly at high coverage, compared with the roughly linear trend in the original DFT set. The configurational correlation between Au and Pt adsorption energies seen in DFT holds across the whole expanded set, including high-energy configurations, which the authors attribute to a shared underlying mechanism such as the d-band behavior of both metals (Miller 2009). Summary: miller2009a. See also Cluster expansion.
Sulphur on low-index Cu facets (2009)
İnoğlu and Kitchin found with DFT that S adsorption on Cu(111), (100) and (110) generally weakens with coverage between 0.25 and 1.00 ML, becoming endothermic relative to H2S/H2 above 0.50 ML on Cu(111). As on Pd(111), the trend tracks adsorbate-induced d-band broadening at constant filling and the resulting down-shift of the d-band center. Exceptions include atop sites, dimer and trimer formation at 0.75 ML on bridge and atop sites of (100) and (110), and a coverage-independent energy on Cu(110) fourfold sites between 0.25 and 0.50 ML, attributed to the wide spacing between sites (İnoğlu 2009). Summary: inoglu2009a. See also Catalyst poisoning.
A tight-binding model for coverage-dependent adsorption energies (2010)
This paper generalizes the Pd(111) picture of coverage effects as adsorbate-induced d-band broadening to C, N, O and S on the (111), (100) and (110) facets of Cu, Rh, Pd, Ag, Ir, Pt and Au (İnoğlu 2010). Adsorption energies weaken linearly with surface d-band width, which itself grows linearly with coverage, and a tight-binding formula with a coverage-proportional adsorbate term predicts the widths with average error below 5 percent. Given one reference energy at 0.25 ML and the energy-width slope, the model estimated coverage-dependent adsorption energies on the (111) facets with average error below 4.3 percent, except for S on the noble metals Cu, Ag and Au. It ranks the adsorbate-induced electronic perturbation as S > N > C > O. Summary: inoglu2010.
Oxygen on seven late transition metal (111) surfaces (2011)
Miller, İnoğlu and Kitchin computed the same 20 fcc-site oxygen configurations (up to 1 ML) on Rh, Ir, Pd, Pt, Cu, Ag and Au(111) with PW91 DFT. On every surface the oxygen adsorption energy weakens roughly linearly with coverage, and the trend tracks adsorbate-induced d-band broadening at about constant filling and the resulting down-shift of the d-band center. Because the mechanism is shared, each metal’s configuration energies correlate linearly with those of the same configurations on Pd(111), with mean fit errors below 22 meV/O for Rh, Ir and Pt but larger for Ag, Au (55 meV/O) and Cu (120 meV/O), where reconstruction made the relaxed structures geometrically dissimilar (Miller et al. 2011). Summary: miller2011.
Coverage-dependent models as a trend in computational catalysis (2012)
In his preface to a Topics in Catalysis special issue, Kitchin identified the use of DFT to compute coverage-dependent adsorption properties, and to parameterize coarse-grained models such as lattice gas Hamiltonians for Monte Carlo simulation, as a growing trend in the field. He cited an example from the issue in which sulfur poisoning both reduced CO coverage and sharply lowered CO mobility (Kitchin 2012). Summary: kitchin2012.
Coverage dependence of site and adsorbate correlations across eight atoms and seven metals (2014)
Xu and Kitchin computed 896 PBE adsorption energies for H, C, N, O, F, S, Cl and Br on the (111) surfaces of Cu, Rh, Pd, Ag, Ir, Pt and Au at 0.25 to 1.0 ML in fcc, hcp, bridge and ontop sites. Energies on the geometrically similar fcc and hcp sites stayed strongly correlated at every coverage, but correlations of fcc with bridge and ontop sites were weaker, and coverage sometimes shifted ontop energies in the opposite direction from fcc energies, so higher coverage was identified as a key cause of the breakdown of correlations between dissimilar sites. Coverage also changed nearly every adsorbate-adsorbate correlation, which implies that coverage effects on a single site do not simply carry over from one adsorbate to another with a fixed slope (Xu 2014). Summary: xu2014a.
Coverage-dependent desorption barriers from DFT (2014)
The coverage dependence of oxygen adsorption on Pt(111) was carried through to an experimental observable by converting a DFT/cluster-expansion fit of the average adsorption energy into a differential adsorption energy and then, via a two-parameter Brønsted-Evans-Polanyi relation, into a coverage-dependent desorption barrier (Miller et al. 2013). Only configurations near the convex hull were treated as thermodynamically relevant, and a fourth-order polynomial with zero slope at zero coverage captured the nonlinear flattening toward the dilute limit. The resulting barrier is roughly linear between about 0.1 and 0.2 ML but clearly nonlinear below about 0.1 ML, showing that the common linear assumption fails at low coverage. Summary: miller2014.
Oxygen coverage on Pd(111) from a neural network potential (2017)
Boes and Kitchin computed DFT adsorption energies for 107 energy-unique oxygen configurations on 3 × 3 Pd(111) from 0 to 1 ML and fit a neural network potential to them. Oxygen formation energies became negative near 0.45 ML, and at 2/3 ML oxygen rows pulled a row of Pd out of the surface in a strong reconstruction. Grand-canonical MC with the network at μ(O2) = 0.75 eV and 600 K gave a mean fcc coverage of 0.50 ± 0.05 ML, 0.13 ML above a cluster-expansion prediction, a difference attributed mainly to the O2 reference energy. Two-oxygen NEBs showed adjacent fcc-hcp occupation to be strongly disfavored, and MD at 0.33 ML and above led to subsurface oxygen, consistent with the known ease of oxidizing Pd above about 0.5 ML (Boes 2017). Summary: boes2017a.