Non‐Linear Dynamics: Oscillatory Kinetics and Spatio‐Temporal Pattern Formation

Abstract

The rate of a catalytic reaction is governed by the underlying mechanism, i.e. the sequence of elementary reaction steps, and depends on the external control parameters such as the concentrations (= partial pressures) p j of educt and product species and temperature T, if transport processes are excluded in this context. More specifically, usually the adsorbed species are assumed to be randomly distributed over the surface, and their concentrations (= coverages) θ i are described within a mean-field approximation so that the reaction rate (= number of molecules r formed per unit time, dn r /dt t ) is given by dn r dt = f θ i , T ( ) (1) whereby the coverages θ i are in turn determined by a set of differential equations (modeling the individual steps of adsorption, desorption and surface reaction) of the typeProper treatment then requires that additional constraints given by heat and mass balance are taken into consideration.Under flow conditions with the external control parameters being kept fixed, usually the reaction proceeds at steady state with constant rate, i.e., dn r /dt = constant and dθ i /dt = 0. Due to the nonlinear character of the quoted differential equations, this has, however, not necessarily to be the case; the kinetics may -for certain ranges of parameters -become oscillatory or even irregular (chaotic). Such systems are typically far away from equilibrium, and (i) By far the most detailed insights into the underlying mechanisms and the general phenomenology of spatio-temporal self-organization were obtained in studies with well-defined single crystal surfaces by applying the arsenal of modern surface physical methods.(ii) Single crystal studies are usually conducted with bulk samples under low pressure conditions (≤ 10 -4 mbar)where the temperature changes associated with varying reaction rate are negligible. In addition, the mean-free path of gaseous molecules is comparable or even larger than the dimensions of the reaction vessel, which is operated as a continuous flow reactor. Hence, concentration gradients in the gas phase are practically instantaneously (≤ 10 -3 s)transmitted. Analysis of such experiments is thus appreciably simplified.(iii) Experiments with polycrystalline, i.e. "real", catalysts are usually conducted at elevated partial pressures (≥ 1 mbar) under which the heat released by the reaction may lead to noticeable temperature variations. The resulting thermokinetic effects may become dominating, so that even the nonuniformity of the surface chemistry is masked and quite novel phenomena may arise. Ideally, the reaction is conducted in a way, which may be described by a continuously stirred tank reactor (CSTR), i.e., perfect mixing ensures that the concentrations are everywhere identical.However, frequently a concentration profile exists along the reactor, which is hence rather of the plug-flow type. It is thus evident that heat and mass transfer limitations may play important roles with such systems.Generally, an extended system such as a single crystal surface, or even more ...

Operando spatially and time-resolved X-ray absorption spectroscopy and infrared thermography during oscillatory CO oxidation

“…Both single-crystal surfaces and real exhaust gas catalysts have been extensively studied, especially with respect to Pt-catalyzed CO oxidation as model reaction [22,[31][32][33][34][35][36][37][38][39][40][41]. In particular, oscillatory CO conversion behavior has received growing attention [42][43][44][45]. Extensive research activities during the past decades led to a detailed understanding of its mechanism and origin for idealized systems (UHV and single-crystal surfaces) for which reversible surface phase transitions were identified as being responsible [46][47][48][49][50].…”

Low-Temperature Oxidation of CO in Smoke: A Review

“…The authors showed the influence of the metal cluster, indicating that the probability of oscillations diminishes with Pt crystal sized below 4 nm. The oscillation mechanism comes into play on Pd at low pressures, whereas on Pt it happens at higher pressures (46). This may provide some reference for design of the catalyst for a cigarette that would be less complicated with the rate oscillations.…”

“…Until then, oxygen was found to be atomized to some extent that also agreed with the fact that the oxygen adsorption heat decreased with increased O 2 pressure. The genesis of the oxygen atoms from CO and O 2 (air) was elucidated when Pt/CeO 2 was studied by ERTL (46) in CO combustion under the transient conditions of cold start of a car, and when oxidation on a similar catalyst was conducted in the presence of H 2 and H 2 O (16). During lowtemperature CO oxidation, the catalysts were covered predominantly with CO molecules.…”

“…Therefore, the kinetic oscillations, which are a well-known and thoroughly studied feature of CO catalytic oxidation in other than smoke environments, will be addressed in this review. The phenomenon is partially caused by a competitive sorption of O 2 and CO on a noble metal crystal and on the support, and involves interaction between chemisorbed molecules (46,62). The authors of (63,64) experimentally investigated the kinetics of the CO+O 2 reaction.…”

Entropic long-range ordering in an adsorption-desorption model

“…Having in mind formation of some adsorbate structures such as, for example, He on graphite [12] or on graphyne [13], or H on W [14,15], or O on Pt [16], we should take into account that equilibrium hard-core models provide only a very approximate description of these complex physical phenomena [17]. An important process, which often accompanies adsorption and affects, for example, a surface diffusion [18] or various surface chemical reactions, is desorption [19,20]. In certain statistical mechanics studies, the role of desorption in some equilibrium as well as nonequilibrium hard-core systems has already been examined [9].…”