Oscillator chemical

The essence of our approach to designing new oscillators is choose autocatalytic systems, keep them far from equilibrium, and look for multiple stationary states. Carrying out this program requires specialized experimental and theoretical tools . 

Obviously, to find a specific set of conditions for the onset of a concentration jump between stable states, or for the occurrence of oscillations, for that matter, would require the testing of a huge number of reaction mixtures under conditions maintained far from equilibrium. Since such an experiment is not easily accomplished in ordinary glassware, we conducted our studies of oscillatory reactions in continuous flow reactors patterned after those used at the Paul Pascal Research Center in Bordeaux, France35). 

The volume or space in which reaction occurs is called the reactor. Closed systems, for which matter is neither gained nor lost, are referred to in the engineering literature as batch reactors. An open, or flow reactor, which permits the flow of matter in and out of the system, allows for the continuous and convenient change of solution composition. Most importantly, the continuous flow of matter into and out of the flow reactor trivially solves the problem of maintaining the system far from equilibrium, while facilitating the detection and determination of the chemical properties of species in these states. 

If [A] and [P] are maintained constant, the Lotka mechanism (Table 2) can be described by two coupled, non-linear differential equations2  

A plot of [X] against [Y] is called a phase trajectory diagram or phase portrait39. Nonlinear, but non-oscillatory reaction schemes have phase trajectories that are open curve segments,whose form depends on initial conditions and rate constants37. The phase 

---

Gray P and Scott S K 1994 Chemical Oscillations and Instabilities (Oxford Oxford University Press)... 

Englman R (1981) Vibrations in Interaction with Impurities. 43 113-158 Epstein IR, Kustin K (1984) Design of Inorganic Chemical Oscillators. 56 1-33 firmer O (1976) Calculations of Molecular Properties Using Force Fields. Applications in Organic Chemistry. 27 161-211... 

Autocatalysis can cause sustained oscillations in batch systems. This idea originally met with skepticism. Some chemists believed that sustained oscillations would violate the second law of thermodynamics, but this is not true. Oscillating batch systems certainly exist, although they must have some external energy source or else the oscillations will eventually subside. An important example of an oscillating system is the circadian rhythm in animals. A simple model of a chemical oscillator, called the Lotka-Volterra reaction, has the assumed mechanism ... 

This reaction can oscillate in a well-mixed system. In a quiescent system, diffusion-limited spatial patterns can develop, but these violate the assumption of perfect mixing that is made in this chapter. A well-known chemical oscillator that also develops complex spatial patterns is the Belousov-Zhabotinsky or BZ reaction. Flame fronts and detonations are other batch reactions that violate the assumption of perfect mixing. Their analysis requires treatment of mass or thermal diffusion or the propagation of shock waves. Such reactions are briefly touched upon in Chapter 11 but, by and large, are beyond the scope of this book. 

A recent, comprehensive treatment of chemical oscillators and assorted esoterica is given in... 

This set of first-order ODEs is easier to solve than the algebraic equations where all the time derivatives are zero. The initial conditions are that a ut = no, bout = bo,... at t = 0. The long-time solution to these ODEs will satisfy Equations (4.1) provided that a steady-state solution exists and is accessible from the assumed initial conditions. There may be no steady state. Recall the chemical oscillators of Chapter 2. Stirred tank reactors can also exhibit oscillations or more complex behavior known as chaos. It is also possible that the reactor has multiple steady states, some of which are unstable. Multiple steady states are fairly common in stirred tank reactors when the reaction exotherm is large. The method of false transients will go to a steady state that is stable but may not be desirable. Stirred tank reactors sometimes have one steady state where there is no reaction and another steady state where the reaction runs away. Think of the reaction A B —> C. The stable steady states may give all A or all C, and a control system is needed to stabilize operation at a middle steady state that gives reasonable amounts of B. This situation arises mainly in nonisothermal systems and is discussed in Chapter 5. 

The dynamic behavior of nonisothermal CSTRs is extremely complex and has received considerable academic study. Systems exist that have only a metastable state and no stable steady states. Included in this class are some chemical oscillators that operate in a reproducible limit cycle about their metastable... 

Belouzov-Zhabotinsky reaction [12, 13] This chemical reaction is a classical example of non-equilibrium thermodynamics, forming a nonlinear chemical oscillator [14]. Redox-active metal ions with more than one stable oxidation state (e.g., cerium, ruthenium) are reduced by an organic acid (e.g., malonic acid) and re-oxidized by bromate forming temporal or spatial patterns of metal ion concentration in either oxidation state. This is a self-organized structure, because the reaction is not dominated by equilibrium thermodynamic behavior. The reaction is far from equilibrium and remains so for a significant length of time. Finally,... 

According to the literature [21], all reported electrochemical oscillations can be classified into four classes depending on the roles of the true electrode potential (or Helmholtz-layer potential, E). Electrochemical oscillations in which E plays no essential role and remains essentially constant are known as strictly potentiostatic (Class I) oscillations, which can be regarded as chemical oscillations containing electrochemical reactions. Electrochemical oscillations in which E is involved as an essential variable but not as the autocatalytic variable are known as S-NDR (Class II) oscillations, which arise from an S-shaped negative differential resistance (S-NDR) in the current density (/) versus E curve. Oscillations in which E is the autocatalytic variable are knovm as N-NDR (Class III) oscillations, which have an N-shaped NDR. Oscillations in which the N-NDR is obscured by a current increase from another process are knovm as hidden N-NDR (HN-NDR Class IV) oscillations. It is known that N-NDR oscillations are purely current oscillations, whereas HN-NDR oscillations occur in both current and potential. The HN-NDR oscillations can be further divided into three or four subcategories, depending on how the NDR is hidden. 

A chemical reaction can be designated as oscillatory, if repeated maxima and minima in the concentration of the intermediates can occur with respect to time (temporal oscillation) or space (spatial oscillation). A chemical system at constant temperature and pressure will approach equilibrium monotonically without overshooting and coming back. In such a chemical system the concentrations of intermediate must either pass through a single maximum or minimum rapidly to reach some steady state value during the course of reaction and oscillations about a final equilibrium state will not be observed. However, if mechanism is sufficiently complex and system is far from equilibrium, repeated maxima and minima in concentrations of intermediate can occur and chemical oscillations may become possible. 

P. Schnittker, On chemical oscillators responding a frequency switch, J. Non-Equilib. Thermodyn., 5,129-136 (1980). 

Noyes, R. M. (1989). Some models of chemical oscillators. J. Chem. Educ., 66, 190-1. 

The previous chapter has provided some indication of the behaviour which can be exhibited by the simple cubic autocatalysis model. In order to make a full analysis, it is convenient both for algebraic manipulation and as an aid to clarity to recast the rate equations in dimensionless terms. This is meant to be a painless procedure (and beloved of chemical engineers even though traditionally mistrusted by chemists). We aim wherever possible to make use of symbols which can be quickly identified with their most important constituents thus for the dimensionless concentration of A we have a, with / for the dimensionless concentration of B. Once this transformation has been achieved, we can embark on a quite detailed and comprehensive analysis of the behaviour of this prototype chemical oscillator. 

Kevrekidis, I. G., Schmidt, L.D., and Aris, R. (1986). Forcing an entire bifurcation diagram case studies in chemical oscillators. Physica, 23, 391-5. 

Schneider, F. W. (1985). Periodic perturbations of chemical oscillators experiments. Ann. Rev. Phys. Chem., 36, 347-78. 

P. Gray and S. K. Scott Chemical oscillations and instabilities non-linear chemical kinetics... 

Fig. 7. Variations in the near-edge fine structure at the Pt Lm edge of a Pt/zeolite catalyst during CO oxidation exhibiting chemical oscillations [adapted from Hagelstein et at. (45)).

---