Extended ZGB-model

The extended ZGB-model incorporating diffusion and desorption processes... 

We have introduced in this Section a stochastic model for the A+ 2B2 —> 0 reaction which is equivalent to the ZGB-model [2] and thus remedies a deficiency of a previously presented model [13]. In this model we obtain for the case of no diffusion for the phase transition points y = 0.395 and y2 = 0.565, which are in good or fair agreement with the results of the ZGB-model (y = 0.395 and yi = 0.525). In the model [13] where the reaction occurs only if A particle jumps to active site occupied by a B particle, we obtain y — 0.27 and 7/2 = 0.65 (for D — 10). Because the reaction occurs only due to diffusion, we cannot directly compare this model with the ZGB-model in which no diffusion exists. But the value of t/2 is in agreement with computer simulations of the extended ZGB-model including diffusion (t/2 = 0.65 for a high diffusion rate) [3]. The value of y should not be influenced by the additional aspect of A-diffusion because too few A particles... 

To demonstrate this, in Section 9.2.2 we have studied a stochastic model for an extended ZGB-model including diffusion, desorption and energetic interactions as additional steps. We have used different values of the diffusion and the desorption rates and different values for the energetic parameters. In the case of repulsive interactions the system s behaviour is strongly influenced by. Eaa for large values of Yqo and by for small values of kco-The former parameter leads to a smooth phase transition at yi and the latter to a sharp transition at 2/1 The sharpness and the location of the phase transitions depend also on the diffusion and desorption rate of the A particles. The A-diffusion leads to an increase of the value of 2/2 due to the higher reactivity of the A particles. At lower values of Yco the system behaviour is nearly not influenced by the diffusion. The A-desorption increases the values of the critical points and smoothes the phase transition at 2/2- This effect becomes very important if Ca is large. 

In order to get a more realistic description of surface reactions energetic interactions must be taken into account. We introduced in Section 9.2.1 a general model which is able to handle systems which include mono- and bimolecular steps like adsorption, desorption, diffusion and reaction [38]. Here we apply this model to an extended version of the ZGB-model which incorporates particle diffusion and desorption [41]. 

C0(ads)+0(ads)— C02(ads)+, 4.C02(ads) — C02(gas)+. The probabilities of steps 1 and 2 are between 0 and 1, while probabilities of other steps are P(3) = 1, P 4) = 1, P(-l)= 0 P(-2)= 0, P(-4)=0. The ZGB-model shows the effect of heterogeneity in the adlayer because of the infinitely fast formation of C02, there is a segregation of the reactants in CO and oxygen islands. The original model has later been extended and modified by numerous people to include desorption of the reactants, diffusion, an Eley Rideal mechanism for the oxidation step, physisorption of the reactants, lateral interactions, an oxidation step with a finite rate constant, surface reconstruction and additional poisoning adsorbates. 

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