Spatio-temporal phenomenon

In the microscopic techniques discussed above, the challenge was to visualize the atomic detail. However, in catalysis one also encounters phenomena that occur on the scale of micrometers or millimeters which ask for imaging. In particular, the ordering of adsorbates in large islands and the development of spatio-temporal patterns in oscillating reactions [8], This spectacular phenomenon has stimulated the exploration of imaging techniques that provide information on patterns on the micrometer to millimeter scale. 

The phenomenon of self organization occurs at nonstabHities of the sta tionary state and leads to the formation of temporal and spatio temporal dissipative structures. Remember that oscillating instabilities of stationary states of dynamic systems can be observed for the intermediate nonlinear stepwise reactions only, when no fewer than two intermediates are involved (see Section 3.5) and at least one of the elementary steps is kinet icaUy irreversible. The minimal sufficient requirements for the scheme of a process with temporal instabilities are not yet strictly formulated. However, in aU known examples of such reactions, the rate of the kineti caUy irreversible elementary reaction at one of the intermediate steps is at least in a quadratic dependence on the intermediate concentrations. Among these reactions are autocatalytic steps. 

The spontaneous development of spatial or spatio-temporal nonuniformities under homogeneous external conditions is a characteristic feature of non-equilihrium systems. This phenomenon is called pattern formation [l]-[3]. 

Theoretically this phenomenon was studied in chains of self-oscillating cells with linear coupling [15]. The selection of a single frequency and formation of the phase waves was also shown in the Ginzburg-Landau equations which govern spatio-temporal dynamics near the Hopf bifurcation [16]. 

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