Fluctuations and critical phenomena in catalytic CO oxidation on nanoscale Pt facets

Abstract

Local fluctuations and fluctuation-induced transitions in catalytic CO oxidation are studied with field electron microscopy on the (112) facets of a [100]-oriented Pt field emitter tip. The reaction is investigated in the bistable range close to the cusp point (critical point) that terminates the bistability range in pCO, T-parameter space. The amplitude and the spatial coherence of the fluctuations increase on approaching the critical point. The fluctuations are spatially well correlated on each flat (112) facet, but their correlation decays rapidly across stepped regions that terminate the flat facets. On smaller (112) facets, an onset of fluctuation-induced transitions is observed earlier (i.e., further away from the critical point) than for larger (112) facets. The behavior of the reaction system near the cusp point appears to be similar to that of an equilibrium system near the critical point. The observed fluctuations are mimicked in a simple reaction model for CO oxidation on surfaces that incorporates both rapid diffusion of adsorbed CO, and superlattice ordering of adsorbed immobile oxygen. The steady states of the model exhibit a cusp bifurcation, from a regime of bistability to one of monostability. The fluctuations increase near this cusp point, as in experiment. This behavior is analyzed via kinetic Monte Carlo simulations and analytic procedures, focusing on the consequences for fluctuationinduced transitions. Local fluctuations and fluctuation-induced transitions in catalytic CO oxidation are studied with field electron microscopy on the ͑112͒ facets of a ͓100͔-oriented Pt field emitter tip. The reaction is investigated in the bistable range close to the cusp point ͑critical point͒ that terminates the bistability range in p CO , T-parameter space. The amplitude and the spatial coherence of the fluctuations increase on approaching the critical point. The fluctuations are spatially well correlated on each flat ͑112͒ facet, but their correlation decays rapidly across stepped regions that terminate the flat facets. On smaller ͑112͒ facets, an onset of fluctuation-induced transitions is observed earlier ͑i.e., further away from the critical point͒ than for larger ͑112͒ facets. The behavior of the reaction system near the cusp point appears to be similar to that of an equilibrium system near the critical point. The observed fluctuations are mimicked in a simple reaction model for CO oxidation on surfaces that incorporates both rapid diffusion of adsorbed CO, and superlattice ordering of adsorbed immobile oxygen. The steady states of the model exhibit a cusp bifurcation, from a regime of bistability to one of monostability. The fluctuations increase near this cusp point, as in experiment. This behavior is analyzed via kinetic Monte Carlo simulations and analytic procedures, focusing on the consequences for fluctuation-induced transitions. Disciplines Mathematics | Physical Chemistry

Fluctuations and bistability in a “hybrid” atomistic model for CO oxidation on nanofacets: An effective potential analysis

“…The population model and its master equations treatment are described in more detail in Ref. 12. Here we recap some essential ingredients.…”

“…12, we have given the explicit form of the ME using pair approximations. Here suffice it to note that W ␣ can be approximately given by ⍀w ␣ in Eqs.…”

“…1 Recently it has been applied to the CO oxidation problem. 7,12 The population model is essentially a MF approximation of the atomistic model. Instead of microscopic configurations and processes of adsorbates, one only tracks the total numbers ͑or equivalently coverages͒ of adsorbates of different species and their increment and decrement.…”

“…[8][9][10][11] Recent experiments on FET's, where fluctuations play a critical role due to the nanoscale system size, provide tremendous new possibilities for modeling of surface reactions and for comparison with stochastic theories including those going beyond MF treatments. 10,[12][13][14] For surface reactions, one generally expects significant spatial correlations ͑e.g., due to reactant islanding induced by adspecies interactions͒, and thus the MF description will be inadequate. Indeed, simple models for CO oxidation with limited CO mobility produce discontinuous transitions between reactive and inactive states, 15,16 reminiscent of firstorder phase transitions in equilibrium systems ͑where a complicated nucleation theory rather than the MF theory is needed to describe the detailed dynamics of transitions between these states͒.…”

From atomistic lattice-gas models for surface reactions to hydrodynamic reaction-diffusion equations

“…16 Thus, we shall also consider a modified model where O 2 (gas) adsorbs at diagonally adjacent empty sites, provided the six additional neighbors are also free of O͑ads͒. 21,25,29,30 See Fig. 1.…”