Critical Retardation Effects and Slow Relaxations

From the viewpoint of experimental workers, slow relaxations are аЬ­ normally (i.e. unexpected) slow transition processes. The time of а transition process is determined ав that of the transition from the initial state to the limit (t --+ (0) regime. The limit regime itself сап Ье а steady state, а limit cycle (а self-oscillation process), а strange attractor (stochastic self-oscillation), etc. Inevitably, the "limit" regime of the process is observed in experiments with finite accuracy. It is possible that the experiment was too short in time, and if the period of this experiment is sufficiently long, the regime would change considerably. Strictly speaking the limit transition t -> 00 holds only for а mathematical model. Similarly, the achievement of the limit regime (the end of the transition process) is only determined with finite accuracy. This circumstance will Ье used constantly in what follows. The most difficult problem is the adequate determination ofthe "abnormаНу" (i.e. unexpected) slow transition process. For this purpose, we must imagine the simplest system of expectations. It is based оп the hypotheses about reaction mechanisms. А catalytic reaction is represented ав а сот­ bination of elementary steps (see Chap. 3). We admit воте hypotheses concerning values ofthe corresponding rate coefficients. Typical concentrations of gas-phase substances and of surface compounds are also assumed to Ье known. One сап also introduce а concept ofthe characteristic time of а step. For example, the characteristic time for the step А +± В сап Ье determined ав l/(k+ + k-), where k+ and kare the rate constants for the direct and reverse reactions. For the reaction А + В -> С one сап introduce two characteristic times: l/kCA and l/kCB , where СА and СВ are the characteristic concentrations of А and В. Hence, as а rule, the researcb. worker has воте knowledge (воте hypothesis) about the base steps and their characteristic times. One refinement is necessary here. If а transition process is examined for the reactor as а whole, the equations of the steps include аН the reacting substances. If the transition process is examined only оп the surface, the equations of the steps contain only surface compounds, and the concentrations of gas-phase substances аге included in the rate constants. Let some transition process proceed much slower than might have been expected in terms of the hypotheses about characteri§tic times for the steps