Fluctuations of the order parameter in chemical reactions

The rain was so heavy that it made all pigs clean and people - dirty. 

Consider now the fluctuations of the order parameter in the system possessing the chemical reaction this problem could be perfectly illustrated by computer simulations on lattices. We start with the bimolecular A -1- B — 0 reaction discussed above, and first of all froze particle diffusion. Let the recombination event happen instantly when a pair AB of dissimilar particles occupies the nearest lattice sites (assume lattice to be squared). Immobile particles enter into reaction as a result of their creation with the equal probabilities in empty lattice sites from time to time a newly created particle A(B) finds itself nearby pre-created B(A) and they recombine. (Since this recombination event is instant, the creation rate is of no importance.) This model describes, in particular, Frenkel defect accumulation in solids under 

The presented stationary distributions of particles could be statistically developed the corresponding correlation functions x( ) are shown in Fig. 1.19. It shows that the ordering within AB pairs not only propagated to the longer distances (at r a number of AB pairs is less than that for a random distribution of particles) but also changed - non-interacting similar particles are now spatially correlated as if they efficiently attract each other, which has clear analogy with quantum ideal boson gas discussed above. 

The existence of the (quasi) steady-state in the model of particle accumulation (particle creation corresponds to the reaction reversibility) makes its analogy with dense gases or liquids quite convincing. However, it is also useful to treat the possibility of the pattern formation in the A + B 0 reaction without particle source. Indeed, the formation of the domain structure here in the diffusion-controlled regime was also clearly demonstrated [17]. Similar patterns of the spatial distributions were observed for the irreversible reactions between immobile particles - Fig. 1.20 [25] and Fig. 1.21 [26] when the long range tunnelling) recombination takes place (recombination rate a r) exponentially depends on the relative distance r and could 

Undoubtedly, it means that the chemical kinetics being a kind of the mean-field theory, should be improved through an introduction of the fluctuations in the order parameter. 

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