Ensemble size effects

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). 

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. 

In contrast to these cases, for the Rhir heterometallic cluster catalysts inside NaY zeolite the dramatic suppression of hydrogenolysis by increasing the Ir contents is interpreted in terms not of a simple ensemble size effect but of an electronic state associated with the electron deficiency, namely, d-hole orbital of the clusters, as discussed for the Xe NMR chemical shifts on the series Rhe- tlr /NaY (245). The remarkable difference in hydrogenolysis activity between Rh and Ir crystallites inside NaY arises from their electron-deficient sites, which favor C—C bond scission via the alkane carbonium intermediate (177). The C2/C3 selectivity is defined as the ratio of the rates of butane conversion to ethane (k ) to the rates of butane conversion to methane plus propane (k,) ... 

Chandler BD, Schnabel AB, Pignolet LH (2001) Ensemble size effects on toluene hydrogenation and hydrogen chemisorption by supported bimetaUic particle catalysts. J Phys Chem B 105 149... 

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. 

An apparent particle size effect for the hydrodechlorination of 2-chlorophenol and 2,4-dichlorophenol was observed by Keane et al. [147], Investigating silica supported Ni catalysts (derived from either nickel nitrate or nickel ethane-diamine) with particles in the size range between 1.4 and 16.8 nm, enhanced rates for both reactions were observed with increased size over the full range (Figure 13). As electronic factors can be ruled out in this dimension, the observed behavior is traced back to some sort of ensemble effect, known from CFC transformations over Pd/Al203... 

Mon, K. K. Binder, K., Finite size effects for the simulation of phase coexistence in the Gibbs ensemble near the critical point, J. Chem. Phys. 1992, 96, 6989-6995... 

There are several commercial packages that realise the above strategy for molecularly realistic systems. It is useful to discuss some of the limitations. Ideally, one would like to do simulations on macroscopic systems. However, it is impossible to use a computer to deal with numbers of degrees of freedom on the order of /Vav. In lipid systems, where the computations of all the interactions in the system are expensive, a typical system can contain of the order of tens of thousands of particles. Recently, massive systems with up to a million particles have been considered [33], Even for these large simulations, this still means that the system size is limited to the order of 10 nm. Because of this small size, one refers to this volume as a box, although the system boundaries are typically not box-like. Usually the box has periodic boundary conditions. This implies that molecules that move out of the box on one side will enter the box on the opposite side. In such a way, finite size effects are minimised. In sophisticated simulations, i.e. (N, p, y, Tj-ensembles, there are rules defined which allow the box size and shape to vary in such a way that the intensive parameters (p, y) can assume a preset value. 

Computationally, polydispersity is best handled within a grand canonical (GCE) or semi-grand canonical ensemble in which the density distribution p(a) is controlled by a conjugate chemical potential distribution p(cr). Use of such an ensemble is attractive because it allows p(a) to fluctuate as a whole, thereby sampling many different realizations of the disorder and hence reducing finite-size effects. Within such a framework, the case of variable polydispersity is considerably easier to tackle than fixed polydispersity The phase behavior is simply obtained as a function of the width of the prescribed p(cr) distribution. Perhaps for this reason, most simulation studies of phase behavior in polydisperse systems have focused on the variable case [90, 101-103]. 

The particle-size effect is for both supports the largest for the selectivity towards the roll-over mechanism (via the di-G-T)1 intermediate, Figure ID), which is strongly increased with the larger particles. Hence, also the roll-over mechanism is a clearly structure-sensitive reaction. It is facilitated by large particles, and probably an ensemble of catalytically active, empty sites is needed for the formation of the di-G-r)1 intermediate. 

Also the mode of adsorption (e.g. of CO, hydrocarbons, etc.) can depend on the available ensemble size or given composition of the surface [64—68]. It appears that the heat of adsorption of various modes of CO adsorption is only marginally influenced when the required ensemble (1,2 or 3 and more) is transferred from a pure metal into a matrix of another metal (for instance alloys with Cu, Au and Ag). When a CO molecule, monitored by IR spectroscopy, is taken as a probe of the local electronic structure of atoms (or ensembles of atoms), no pronounced effects of alloying are found 69-71]. 

For the molecules investigated, the MD and MC methods furnish similar adsorption energies although the MD results are slightly better when compared to the experiments. Since the MC and MD simulations have been performed in different ensembles but with the same force field, the difference in the results of the two simulations may be partly due to finite size effects. However, temperature fluctuations during the MD simulations in the NVE ensemble may also contribute to this difference. For the linear alkanes the MM results are qualitatively correct but only when a specific force field is used to describe the zeolite. However, for the branched alkane the MM results are comparable to the MD and MC ones even when a generic force field, such as Dreiding n, is used to represent the zeolite. 

V. Mayagoitia, F. Rojas, V. Pereyra and G. Zgrablich, Surf. Sci. 221 (1989) R. H. Ldpez, A. M. Vidales and G. Zgrablich, Correlated site-bond ensembles statistical equilibrium and finite-size effects , Langmuir 16,7 (2000). 

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