Chemical waves, reaction-diffusion process

The previous chapters have discussed the behaviour of non-linear chemical systems in the two most familiar experimental contexts the well-stirred closed vessel and the well-stirred continuous-flow reactor. Now we turn to a number of other situations. First we introduce the plug-flow reactor, which has strong analogies with the classic closed vessel and which will also lead on to our investigation of chemical wave propagation in chapter 11. Then we relax the stirring condition. This allows diffusive processes to become important and to interact with the chemistry. In this chapter, we examine one form of the reaction-diffusion cell, whose behaviour can be readily understood by comparison with the responses observed in the CSTR. 

The above description is of a thermally propagating steady-state wave. It must be emphasized, however, that the basic feature of a thermal mechanism is not altered by the superposition of molecular diffusion onto the diffusional transport of heat. This applies not only to interdiffusion of reactants and products but also to the diffusion of chain carriers participating in the chemical reaction, provided that the chains are unbranched. The reason for this is that in a wave driven by a diffusion process, the source strength of an entering mass element must continue to grow despite the drain by the adjacent sink region. This growth can occur only if the reaction rate is increased by a product of the reaction, which may be temperature as well as a material product. 

In a detonation wave the change of state—after equally rapid compression—depends on the process of chemical reaction and is extended in accordance with the kinetics of the reaction. The only restriction is that the wave (reaction zone) not be extended to a length which is many times larger than the tube diameter. Comparison with a shock wave shows only that the role of heat conduction and diffusion of active centers in a detonation wave is negligible. But they are not needed the mixture, which has been heated to a high temperature, enters the reaction and reacts under the influence of active centers created by the thermal motion and multiplying in the course of the reaction. Each layer reacts without exchanging heat or centers with other layers. 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

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... 

However, only a few organic compounds behave in a polarographically reversible manner although many may involve a reversible electron transfer step, this is often followed by irreversible chemical reactions. Irreversible processes are those for which the current is limited mainly by the kinetics of the process at the electrode surface and not by diffusion. The nature of such current-potential curves can be described by reference to Figure 6. If electrochemical equilibrium obtains at the electrode surface, then a reversible wave is obtained (curve a). The irreversible wave (curve b) is more drawn out, i.e., for a given current, say, /i or I2, a higher cathodic potential is required. 

Diffusion in solids does not ensure the experimentally observed velocity of combustion wave propagation in the systems which are traditionally considered as gasless and burned in the mode of solid flames (gasless solid-state combustion). The phenomenology of indirect interactions, the thermochemistp and dynamics of the gas-phase carriers formation, as well as their participation in the reactants transport are studied in the systems Mo-B and Ta-C. The distributions of the main species in the gas phase of the combustion wave are measured in situ with the use of a dynamic mass-spectrometry (DMS) technique which allows for high temporal and spatial resolution. The detailed chemical pathways of the processes were established. It was shown that the actual mechanism of combustion in the systems under study is neither solid state nor gasless and the reactions are fiilly accomplished in a narrow front. 

The first cathodic wave was studied by cycling the potential across it at various scan rates and the peak potentials were found to increase as indicative of a reversible, diffusion-controlled system, with ° = — 1.43 V vs. SCE. However, at sweep rates 20mV/s the peak anodic current is much smaller than expected which was interpreted by the authors as indicating that the reduced species undergoes a subsequent chemical reaction, i.e. an EC process. 

Waves of chemical reaction may travel through a reaction medium, but the ideas of important stationary spatial patterns are due to Turing (1952). They were at first invoked to explain the slowly developing stripes that can be exhibited by reactions like the Belousov-Zhabotinskii reaction. This (rather mathematical) chapter sets out an analysis of the physically simplest circumstances but for a system (P - A - B + heat) with thermal feedback in which the internal transport of heat and matter are wholly controlled by molecular collision processes of thermal conductivity and diffusion. After a careful study the reader should be able to ... 

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