Kinetics segregation effect

Stamenkovic V, Schmidt TJ, Ross PN, Markovic NM. 2003. Surface segregation effects in electrocatalysis Kinetics of oxygen reduction reaction on polycrystalline PtsNi alloy surfaces. J Electroanal Chem 554 191 -199. 

We have studied above a model for the surface reaction A + 5B2 -> 0 on a disordered surface. For the case when the density of active sites S is smaller than the kinetically defined percolation threshold So, a system has no reactive state, the production rate is zero and all sites are covered by A or B particles. This is quite understandable because the active sites form finite clusters which can be completely covered by one-kind species. Due to the natural boundaries of the clusters of active sites and the irreversible character of the studied system (no desorption) the system cannot escape from this case. If one allows desorption of the A particles a reactive state arises, it exists also for the case S > Sq. Here an infinite cluster of active sites exists from which a reactive state of the system can be obtained. If S approaches So from above we observe a smooth change of the values of the phase-transition points which approach each other. At S = So the phase transition points coincide (y 1 = t/2) and no reactive state occurs. This condition defines kinetically the percolation threshold for the present reaction (which is found to be 0.63). The difference with the percolation threshold of Sc = 0.59275 is attributed to the reduced adsorption probability of the B2 particles on percolation clusters compared to the square lattice arising from the two site requirement for adsorption, to balance this effect more compact clusters are needed which means So exceeds Sc. The correlation functions reveal the strong correlations in the reactive state as well as segregation effects. 

The kinetic equations are useful as a fitting procedure although their basis - the homogeneous system - in general does not exist. Thus they cannot deal with segregation and island formation which is frequently observed [27]. Computer simulations incorporate fluctuation and correlation effects and thus are able to deal with segregation effects but so far the reaction systems under study are oversimplified and contain only few aspects of a real system. The use of computer simulations for the study of surface reactions is also limited because of the large amount of computer time which is needed. Especially MC simulations need so much computer time that complicated aspects (e.g., the dependence of the results on the distribution of surface defects) in practice cannot be studied. For this reason CA models have been developed which run very fast on parallel computers and enable to study more complex aspects of real reaction systems. Some examples of CA models which were studied in the past years are the NH3 formation [4] and the problem of the universality class [18]. However, CA models are limited to systems which are suited for the description by a purely parallel ansatz. 

In this context, Berry [277] studied the enzyme reaction using Monte Carlo simulations in 2-dimensional lattices with varying obstacle densities as models of biological membranes. That author found that the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial concentration increase. In addition, the rate constant controlling the rate of the complex formation was found to be, in essence, a time-dependent coefficient since segregation effects arise due to the fractal structure of the reaction medium. In a similar vein, Fuite et al. [278] proposed that the fractal structure of the liver with attendant kinetic properties of drug elimination can explain the unusual... 

Experimental evidence showed compartmentalization in ATRP miniemulsions reduced polymerization rate (confined space effect), and more importantly, improved control over the polymerization " when the number of chains was small (high target Mn) for the system CuBr/EHAeTREN-n-butyl methacrylate. While in a conventional emulsion polymerization, segregation effects cause an increase in the rate, in ATRP, the confined space effect dominates the kinetics and results in a decrease in rate. 

Surface composition. The principle of surface segregation in ideal systems is easy to understand and to derive thermodynamically the equilibrium relations (surface concentration Xg as a function of the bulk concentration Xb at various temperatures) is also very easy (4,8). Even easier is a kinetic description which can also comprise some of the effects of the non-ideality (9). We consider an equilibrium between the surface(s) and the bulk(b) in the exchange like ... 

The segregation or demixing is a purely kinetic effect and the magnitude depends on the cation mobility and sample thickness, and is not directly related to the thermodynamics of the system. In some specific cases, a material like a spinel may even decompose when placed in a potential gradient, although both potentials are chosen to fall inside the stability field of the spinel phase. This was first observed for Co2Si04 [39]. Formal treatments can be found in references [37] and [38],... 

Effect of kinetics, or reaction order. Segregation and earliness of mixing affect the conversion of reactant as follows... 

Equation (8.14) demonstrates once more that the cation flux caused by the oxygen potential gradient consists of two terms 1) the well known diffusional term, and 2) a drift term which is induced by the vacancy flux and weighted by the cation transference number. We note the equivalence of the formulations which led to Eqns. (8.2) and (8.14). Since vb = jv - Vm, we may express the drift term by the shift velocity vb of the crystal. Let us finally point out that this segregation and demixing effect is purely kinetic. Its magnitude depends on ft = bB/bA, the cation mobility ratio. It is in no way related to the thermodynamic stability (AC 0, AG go) of the component oxides AO and BO. This will become even clearer in the next section when we discuss the kinetic decomposition of stoichiometric compounds. 

Sometimes, as in the case of particle segregation on fractals (e.g., the planar Sierpinski gasket discussed in Section 6.1) this effect indeed is self-evident [88-90]. Its analytical treatment for particle accumulation was presented in [91, 92] we reproduce here simple mesoscopic estimates following these papers. Particle concentrations obey the kinetic equations... 

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