Reactions circular

OS 92] [R 32] [P 72] For radial movement from a center position, wave splitting was found [68]. Two new reaction zones were formed from a part of the circular reaction zone (Figure 4.100). 

Microscopic reversibility" as used in chemical kinetics is a classic misnomer. The name stems from a complicated derivation based on Onsager s axiom of reversibility at the molecular level [13-17] At that level there is no preferential direction of time and, therefore, all events are in principle reversible. What is called microscopic reversibility in chemical kinetics is the statement that there can be no net circular reaction in a loop at equilibrium. For example, at equilibrium there can be no net circulation A — B — C — D — A in the loop 2.9 ... 

The argument leading to the conclusion that there can be no net circular reaction in a closed loop is based on the free energies of the members. As thermodynamic quantities, these are independent of whether or not the species involved also undergo other reactions. Accordingly, the rule is valid also for loops that are parts of larger networks, say, for ABC in... 

In contrast to the traditional derivation based on microscopic reversibility, that given here does not invoke equilibrium. It thus shows that no net circular reaction is possible even under non-equilibrium conditions. However, there is one very important qualification A net circular reaction does occur if it entails the conversion of co-reactants to co-products of lower Gibbs free energy. For example, the cycle 2.13 (next page) converts reactants A and B to product P while undergoing a net circular reaction K— L— M — N — K. This is a typical catalytic cycle. Such a cycle is not a loop, a term to be reserved for circular pathways in which any... 

The principle of no net circular reaction in a loop, even under non-equilibrium conditions, has an important corollary ... 

The reverse reaction is not allowed to take a different path, even if only partially, because that would create a loop with net circular reaction. 

The complex 0 contains nothing at all and is a mathematical artifice, not a species. [The pseudo-steps and thus the augmented network are not subject to the rules of stoichiometry and thermodynamics. For example, the CSTR network 14.1 violates microscopic reversibility in that it allows net circular reactions.]... 

Successive concentration maxima are normal behavior in reactions with sequential steps (see Section 5.4). However, their patterns do not repeat themselves. To achieve a repetition, the last step of the pathway must restore the original reactant, and in order to sustain a net circular reaction, the cycle must convert external reactants to products (see Section 2.5.2) ... 

The experimental observation of concentrical wave fronts has been ascribed to structural defects in the surface . On these defects, oxygen dissociates faster, and they therefore act as a periodic pulse generator for reaction fronts. With each pulse, a new front is generated, which then grows continuously. This behavior is indeed reproduced by our simulations when such a defect is included. Nonetheless, concentrical circles can also be simulated on a perfectly homogeneous surface. A circular reaction wave front is initiates spontaneously, e.g. by oxygen adsorption on a site that is vacated by CO desorption, at a position we will call the primary center. Inside this front, at a position different from the primary center, a new front is initiated. Structural defects form a stabilizing, rather than a necessary factor for spatio-temporal pattern formation in the form of concentrical circles. 

A second area of possible improvements of the protocol concerns modifications allowing the substitution of different circularization reactions, possibly increasing circularization efficiencies. One possible modification could, for example. 

Investigations on Taylor flow in non-circular chatmels originated from flows in porous materials, for instance in enhanced oil recovery. They are also relevant to microstructured reactors and to the many monolithic systems which in many cases have non-circular reaction channels. 

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