Adiabatic behaviour

Modify the program such that it models adiabatic behaviour and study the influence of varying feed temperature. 

This says simply that at complete reaction (ass - 0), the temperature excess attains its adiabatic value for 50 per cent reaction, 9SS = 0ad and so on. In fact, in this special adiabatic case the relationship between the extent of conversion and the temperature rise implied by eqn (7.20) holds for all conditions and not just at the stationary state. We will examine the adiabatic behaviour in some detail later, but first return to the more general case. 

The result of this comparison may be regarded as representative. The adiabatic behaviour of an n-th order chemical reaction is predicted with reasonable accuracy while the result of the estimation for the autocatalytic process is much too critical. However,... 

These results are a striking demonstration of the effects associated to the potential ridge couplings between states are localized there, and adiabatic behaviour holds on both sides far from it. 

The correlation of the potential surfaces to the product OH seems obvious. The asymmetric excited state correlates to the asymmetric A-doublet, whereas the symmetric ground state correlates to the symmetric A-doublet. Conservation of electronic symmetry in the fragmentation predicts the formation of OH exclusively in the asymmetric A-doublet state. Conservation of electronic symmetry implies that the motion proceeds along the same potential surface and that transitions to other potential surfaces are negligible. This so called adiabatic behaviour is expected to hold for most molecular processes. It seems immediately clear that the origin for the selective population of A-doublet states is due to adiabatic behavior. 

Selective population of A-doublet states is a rather general phenomenon, which is found in chemical reactions, inelastic collisions, photodissociation and surface scattering. In most cases the selective population of A-doublet states is indeed explained by adiabatic behaviour, i.e. by the adiabatic rule ... 

This implies formation of OH exclusively in the Il"-A-doublet state, as would be expected from the simple argument of adiabatic behaviour. 

The adiabatic behaviour for chemical reactions provides some sort of selection rules for some classes of chemical reactions. One of the simplest is the Wigner-Witmer rule concerning the conservation of spin. This rule is based upon the evidence that coupling of the electron spin to other types of motion (e.g. translational motion) is very small and, consequently, can be neglected. As a result, the spin angular momentum is considered constant, i.e. AS = 0. An example of a chemical reaction in which the spin is not conserved is CO oxidation ... 

An alternative formulation that uses classical trajectories to model non-adiabatic behaviour is the Ehrenfest approach [79, 80]. In this, each trajectory point (p, q) is driven by a mean-field force... 

This adiabatic behaviour has also been observed for the reverse (Q + OH -> HCl + O) triplet reaction [83]. The singlet reaction behaves differently in this respect, as will be described shortly. 

Our problem will therefore be to give the adiabatic proposition a quantitative elaboration firstly in the sense that we are interested in the size of the deviations from adiabatic behaviour, and secondly that we do not restrict ourselves to arbitrarily given parameter changes, but treat the full problem with R as dynamic variables. 

The simplicity of these systems permits a complete algebraic analysis of the stationary-state solutions and their stability. They yield an unexpected richness of behaviour, and provide striking insights into the physical origins of isolas and mushrooms. Strong analogies may be drawn between isothermal and non-isothermal examples. Isothermal autocatalysis with a stable catalyst resembles non-isothermal reaction under adiabatic conditions isothermal autocatalysis with an unstable catalyst resembles non-isothermal, non-adiabatic behaviour. Recognizing the finite lifetime of the catalyst adds another dimension to the problem just as does finite heat loss. 

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