Phase transition models, oscillatory

Phase transition models, oscillatory reactions, 39 92-97 Phenanthrene... 

Fig. 6. General representations of heterogeneous oscillatory mechanisms, (a) Buffer-step model (b) coverage-dependent activation energy (c) empty-site model (d) Sales-TUrner-Maple model (e) Pt(lOO) phase transition model (f) Dagonnier model (g) blocking/ reactivation model (h) bulk-phase transition model.

These models consider the mechanisms of formation of oscillations a mechanism involving the phase transition of planes Pt(100) (hex) (lxl) and a mechanism with the formation of surface oxides Pd(l 10). The models demonstrate the oscillations of the rate of C02 formation and the concentrations of adsorbed reactants. These oscillations are accompanied by various wave processes on the lattice that models single crystalline surfaces. The effects of the size of the model lattice and the intensity of COads diffusion on the synchronization and the form of oscillations and surface waves are studied. It was shown that it is possible to obtain a wide spectrum of chemical waves (cellular and turbulent structures and spiral and ellipsoid waves) using the lattice models developed [283], Also, the influence of the internal parameters on the shapes of surface concentration waves obtained in simulations under the limited surface diffusion intensity conditions has been studied [284], The hysteresis in oscillatory behavior has been found under step-by-step variation of oxygen partial pressure. Two different oscillatory regimes could exist at one and the same parameters of the reaction. The parameters of oscillations (amplitude, period, and the... 

The inherently nonisothermal models that require temperature variations for oscillatory behavior fall into two groups. In both cases, the reaction is blocked and reactivated at different temperatures. The blockage is caused either by a surface blocking or by a bulk-phase transition of the catalyst. 

A third Pt surface on which oscillations of the CO/O2 reaction have been observed is the (210) plane (75,78). In this case, a surface-phase transition was again proposed as an explanation for the oscillations. The (210) surface was observed to facet into (310) and (110) orientations during an induction period, after which oscillations began to occur on the (110) facets (78). An alternative model for the oscillatory behavior has been proposed by Ehsasi et al. (76). 

The oscillatory structure just mentioned has been clearly demonstrated to result from quantum-mechanical phase-interference phenomena. The necessary condition264,265 for the occurrence of oscillatory structure in the total cross section is the existence in the internuclear potentials of an inner pseudocrossing, at short internuclear distance, as well as an outer pseudo-crossing, at long internuclear distance. A schematic illustration of this dual-interaction model, proposed by Rosenthal and Foley,264 is shown in Fig. 37. The interaction can be considered to involve three separate phases, as discussed by Tolk and et al. 279 (1) the primary excitation mechanism, in which, as the collision partners approach, a transition is made from the ground UQ state to at least two inelastic channels U, and U2 (the transition occurs at the internuclear separation 7 , the inner pseudocrossing, in Fig. 37), (2) development of a phase difference between the inelastic channels,... 

The concept of the phase response in biological context has been thoroughly explored by Winfree [58], Ruoff et al. [59] report phase response experiments in which the oscillatory BZ reaction is perturbed with NaBr02. They experimentally determined relations between perturbation size and the phase of perturbation at which a transition is seen between phase advances and phase delays. These observations were compared to four different models of the BZ reaction and proved useful in ruling some of them out and identifying the best one. Phase response techniques were used to study forced oscillators... 

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