Hydrogen Chemisorption Isotherms on Platinum Particles at Catalytic Temperatures: Langmuir and Two-Dimensional Gas Models Revisited

Abstract

Density functional theory (DFT) and dihydrogen chemisorption uptakes at temperatures relevant to catalysis are used to determine and interpret adsorption enthalpies and entropies over a broad range of chemisorbed hydrogen (H*) coverages (0.1 ML to saturation) on Pt nanoparticles (1.6, 3.0, and 9.1 nm mean diameters) and Pt(111) surfaces. Heats of adsorption decrease by 30 kJ mol −1 as H 2 coverage increases from nearly bare (0.1 ML) to saturated (∼1 ML) surfaces, because of the preferential saturation of lowcoordination surface atoms by H* at low coverages. Such surface nonuniformity also leads to stronger binding on small Pt particles at all coverages (e.g., 47 kJ mol −1 on 1.6 nm, 40 kJ mol −1 on 3.0 nm, and 37 kJ mol −1 on 9.1 nm particles all at 0.5 ML), because their surfaces expose a larger fraction of low-coordination atoms. As H* approaches monolayer coverages, H*−H* repulsion leads to a sharp decrease in binding energies on all Pt particles. Measured H* entropies decrease with increasing H* coverage and decreasing particle size, but their values (35−65 J mol −1 K −1 ) are much larger than for immobile H* species at all coverages and particle sizes. Two-dimensional gas models in which mobile H* adsorbates move rapidly across uniform (ideal), excluded-area, or DFT-predicted nonuniform potential energy surfaces all give H* entropies ≥30 J mol −1 K −1 , qualitatively consistent with measured values. Larger H* entropies are predicted for uniform (ideal) PES while smaller H* entropies are predicted using nonuniform PES. DFT-derived barriers for H* diffusion between hcp and fcc 3-fold sites on Pt( 111) surface are about 6 kJ mol −1 , a value similar to thermal energies (kT) at temperatures of catalytic relevance, consistent with fast diffusion in the time scale of adsorption−desorption events and isotherm measurements. Mobile adsorbate entropy models are therefore essential for accurate estimates of adsorbate coverages, particularly because vibrational frequencies analyzed by harmonic oscillator approximations lead to large underpredictions of entropies, resulting in DFT-predicted adsorption free energies that are too large to result in high coverageseven at conditions where H* is known to cover the surface. The nonuniformity of Pt surfaces, repulsion among coadsorbates, and high adsorbate mobility starkly contrast with the requirements for Langmuirian descriptions of binding and reactions at surfaces, despite the ubiquitous use and success in practice of the resulting equations in describing adsorption isotherms and reaction rates on surfaces. Such fortuitous agreement is a likely consequence of the versatility of their functional form, taken together with the limited range in pressure and temperature in adsorption and kinetic measurements. The adsorption and kinetic constants derived from such data, however, would differ significantly from theoretical estimates that rigorously account for surface coordination, adsorbate mobility, and coadsorbate repulsion.

Kinetics of NH3 Desorption and Diffusion on Pt: Implications for the Ostwald Process

“…The temperature ranges (1050–1250 K) and associated step densities of our experimental (solid box) and Ostwald process (dashed box) conditions are indicated in the plot. The step densities for the Ostwald catalyst are not known, but we consider typical step/edge densities found on catalytic nanoparticles 42 , 43 as representative for real catalysts.…”

Controlling the Surface Functionalization of Ultrasmall Gold Nanoparticles by Sequence‐Defined Macromolecules

“…DFT calculations have also shown that the adsorption energy of sulfur on the surface of different fcc metals like Au, Ag, Cu and Pt follows the general trend (100) ≈ (110) > (111) [27] . In addition to the strong covalent and ionic metal‐sulfur bonds, van der Waals dispersive forces provide further possibilities which is especially interesting for S‐carrying ligands by bringing more atoms of a ligand molecule to the gold surface [26a] . In general, attractive or repulsive forces, for example, based on van der Waals forces, hydrogen bonding, or electrostatic interactions between the ligands influence the number of molecules that can be accommodated on the gold nanoparticle surface.…”

Identification of stable adsorption sites and diffusion paths on nanocluster surfaces: an automated scanning algorithm

“…Entropies, vibrational frequencies, and pre-exponential factors for diffusion events may also be obtainable from the PES. 23 The automated collection of all thermodynamic and kinetic data, when interfaced with codes to perform kinetic modeling, can then enable high-throughput screening of both monometallic and alloy clusters for catalysis and materials science In summary, we presented an automated, highly parallelizable approach-the ACSS method-to generate approximate 2D PESs of 3D nanocluster surfaces. These PESs fully characterize the stable adsorption sites and diffusion paths of adsorbates on the surfaces of nanoclusters with minimal human workload.…”

“…Because PESs are rich in information, researchers increasingly employ them in catalysisrelated problems. 23,24 Until now however, PESs have mainly been used to study two-dimensional (2D) surfaces such as extended slab models.…”