Ensemble size

Geometrical effects, related to the number and geometrical arrangement of the surface metal atoms participating in the formation of the essential surface intermediates of the reaction in question. For these, number of atoms (ensemble size) appeared to be particularly crucial. 

Sachtler WMH, Somoijai GA. 1983. Influence of ensemble size on CO chemisorption and catalytic n-hexane conversion by Au-Pt(l 11) bimetallic single-crystal surfaces. J Catal 81 77. 

The interface can be charged by adding an excess number of cations to one phase, and an equal number of anions to the other phase. For certain purposes extra particles may be added to the basic setup. The Monte Carlo method is quite flexible, and for reasonable ensemble sizes such as 100 x 20 x 20 particles, it is also quite fast, a typical run taking no more than a few hours on a decent computer. 

Another way of investigating structure is through the classical method on metals of varying catalyst particle size. The key to this method is to measure active catalyst surface areas in order to determine changes in turnover rates with ensemble size. In recent years several chemisorption techniques have been developed to titrate surface metal centers on oxides (25). In this volume Rao and Narashimha and Reddy report on the use of oxygen chemisorption to characterize supported vanadium oxide. 

By alloying a metal A is dispersed (more or less, it depends on the type of alloys) in a metal B. If a certain reaction requires a big ensemble of contiguous atoms A in the surface of alloys, this reaction will be suppressed strongly by alloying. This may lead to selectivity changes, if other potential reactions in the system can occur on smaller ensembles or even individual atoms. This is true for systems when B is much less active than A. If both components are active, one has to consider also the possibility that a big ensemble required can be formed by a mixture of A and B. In some cases (Pt/Ir, Pd/Ni, Pt/Re,. . . ) the mixed ensembles may even be suspected to be more active than the one-component ensembles. In the literature, this kind of effect is called an ensemble size effect (1-5). 

Having all these possible complications in mind, we can start a cautious discussion on the ensemble size requirements of various reactions and their... 

Since various reactions evidently differ in their requirements with regard to ensemble size, the size (in alloys of an active metal with an inactive metal) and composition (in alloys of two active metals) of ensembles of active sites are responsible for the changes of selectivity due to alloying. 

Considerable progress has been made in accumulating information on the electronic structure of metals and alloys, on some aspects of the structure of hydrocarbon adsorption complexes, etc. Also, information on the relative importance of the electronic structure effects of alloying—as contrasted to the geometric, ensemble size effects—has grown appreciably. 

Fig. 2 B(t) = (az)(t) versus time for the asymmetric spin-boson model with (3 = 25, = 0.13 and Q = 0.4, e = 0.4. (Top) Comparison of exact quantum results (filled circles), ILDM simulations (small open circles), and QCL dynamics (filled triangles). Both ILDM and QCL simulations were carried out for an ensemble of 2 X 106 trajectories and no filters are employed. (Bottom) Convergence of TQCL dynamics with ensemble size 2 X 104 (filled squares) and 1 x 106 (filled triangles). Exact quantum results (filled circles). A filter parameter of Z = 500 is used for these calculations. ...

Xu M, Lill MA (2012) Utilizing experimental data for reducing ensemble size in flexible-protein docking. J Chem Inf Model 52(1) 187-198... 

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