One-Dimensional A + B = O Reaction with One Immobile Species
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ONE-DIOHlIENSIlONAlL A + 1M= 0 REACTMION WITH ONE iMMOBILE SPECIES PANOS ARGYRAKIS* and RAOUL KOPELMAN** 0 Department of Physics, University of Thessaloniki, 54006 Thessaloniki, Greece **Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA A•3SIRACT The elementary batch reaction A + B = 0 is re-examined via Monte-Carlo simulations on a one-dimensional lattice. The relative mobility of the A and B species is varied in this model, but the initial densities of the A and B are always the same. We calculate the rates, the density profiles, and the particle distribution functions. The rate power law is conserved, i.e., the well-known 1/4 behavior is established for all mobilities. The rate coefficient is the only mobility-dependent quantity. The interparticle distribution functions show that the aggregation depends on the relative mobility but the segregation does not. This subtle difference has no effect on the asymptotic reaction order, which is close to 5. HI. ]INTR•ODUCT]ION
Non-classical reaction kinetics has been of much interest over the last decade. I The most striking anomaly is the spontaneous reactant segregation for the A + B = 0 reaction. This segregation and the corresponding anomalous rate law was first suggested 15 years ago 2 for a diffusion limited batch reaction. It was shown later to hold even for steady state reactions 3 .4 .5 in low dimensional media. In most of the early literature it was assumed that the species A and B have strictly the same concentration (density) and the same diffusion constant (mobility). This was followed by treatments for unequal concentrations. 6 ,7 There were also treatments of unequal mobilities. 7-10 While at steady state the mobility affects both the degree of segregation and the rate law, 8 it was recently indicated 7 that this is not the case for the power law in batch reactions. 7 How the immobility affects segregation and aggregation is still an open question. This question is addressed below for batch reactions. It is interesting to notice that as of today there are no published experimental results that confirm these striking non-classical anomalies for the A + B = 0 reaction. The reported experiments cover the A + A -+ Products (annihilation, homofusion, coagulation), and the A + B = B (i.e., trapping, quenching reactions). These reactions only result in subtle, mesoscopic spatial self-ordering. 1 -13 The first step in this new direction was recently presented by Koo et al.14 .15 in reactions that startunder segregation (separation of the A's from the B's, but no aggregation of A's or B's). Here the surprise is the preservation of the segregation and, concomitantly, its nonclassical effects on the rate laws. 16.17 Furthermore, neither the concentration nor the mobility of the A's and B's are equal. Such unequal mobilities have some unexpectedly dire consequences, 15 -18 affecting both the segregation and the rate laws. In all A + B --t 0 experimental reaction studies, it is easy to assure effectively equal concentrations of species A a
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