Surface heterogeneity approach

Surface heterogeneity is difficult to remove from crystalline inorganic substances, such as metal oxides, without causing large loss of surface areas by sintering. Thus in Fig. 2.14 in which the adsorbent was rutile (TiO ) all three adsorbates show a continuous diminution in the heat of adsorption as the surface coverage increases, but with an accelerated rate of fall as monolayer completion is approached. 

The sketched examples represent just the tip of the iceberg called heterogeneous catalysis. An excellent account of the historical development as well as of the current state of the art can for example be found in a recent review by J. M. Thomas. [30] A few of the additional effects for which understanding can also be sought on the basis of file surface science approach will only be briefly listed ... 

Hemminger, J. C., Heterogeneous Chemistry in the Troposphere A Modern Surface Chemistry Approach to the Study of Fundamental Processes, Int. Rev. Phys. Chem., in press (1999). 

In the traditional surface science approach the surface chemistry and physics are examined in a UHV chamber at reactant pressures (and sometimes surface temperatures) that are normally far from the actual conditions of the process being investigated (catalysis, CVD, etching, etc.). This so-called pressure gap has been the subject of much discussion and debate for surface science studies of heterogeneous catalysis, and most of the critical issues are also relevant to the study of microelectronic systems. By going to lower pressures and temperatures, it is sometimes possible to isolate reaction intermediates and perform a stepwise study of a surface chemical mechanism. Reaction kinetics (particularly unimolecular kinetics) measured at low pressures often extrapolate very well to real-world conditions. 

Lajtar, L., J. Narkiewicz-Michalek, W. Rudzinski, and S. Partyka. 1993. A new theoretical approach to adsorption of ionic surfactants at water/oxide interfaces Effects of oxide surface heterogeneity, Langmuir 9, 3174-3190. 

Henry, C. R., Chapon, C., Giorgio, S., and Goyhenex, C., Size effects in heterogeneous catalysis A surface science approach, in Chemisorption and Reactivity on Supported Clusters and Thin Films, 331,117, NATO ASI Ser., Ser. E, Dordrecht (1997). 

The treatment of adsorption on a heterogeneous surface has constituted a topic of perennial interest, and this paper provides an extension, to the point of practical usefulness, of an approach for which the groundwork has been in existence for some time. Our interest in this matter developed out of work in this laboratory on the effects of radiation on the surfaces of solids, where changes in the nature of surface heterogeneities were obviously taking place. The results of these studies are given by Adamson, Ling, and Datta (2). 

At present we are beginning to understand the reaction mechanisms of many heterogeneous catalytic reactions at the molecular level. A major breakthrough came with the design of catalytic model systems, such as single crystal surfaces, enabling exhaustive structural characterization and model catalytic experiments. The surface science approach forms the basis of current developments of surface chemical reaction rate theory. 

The heterogeneous reactors with supported porous catalysts are one of the driving forces of experimental research and simulations of chemically reactive systems in porous media. It is believed that the combination of theoretical methods and surface science approaches can shorten the time required for the development of a new catalyst and optimization of reaction conditions (Keil, 1996). The multiscale picture of heterogeneous catalytic processes has to be considered, with hydrodynamics and heat transfer playing an important role on the reactor (macro-)scale, significant mass transport resistances on the catalyst particle (meso-)scale and with reaction events restricted within the (micro-)scale on nanometer and sub-nanometer level (Lakatos, 2001 Mann, 1993 Tian et al., 2004). 

When the adsorbate reaches a thickness of several molecular layers, the effects of surface heterogeneity are considerably reduced. If the temperature is not too low, some - but not all - multilayers appear to undergo a continuous increase in thickness as the pressure approaches saturation and bulk behaviour is gradually developed (Venables etal., 1984). With such systems, it seems reasonable to assume that the... 

Equation (4.47) and obtain an isotherm equation in which the distribution function, (B) was expressed in an analytical form (Huber et al., 1978 Bansal et al., 1988). In principle, f(fl) provides an elegant basis for relating the micropore size distribution to the adsorption data. However, it must be kept in mind that the validity of the approach rests on the assumption that the DR equation is applicable to each pore group and that there are no other complicating factors such as differences in surface heterogeneity. 

The determination of the energy of adsorption is the most direct way of studying surface heterogeneity, but as adsorption calorimetry is experimentally more demanding than the measurement of the isotherm, this approach has inevitably attracted less attention. However, as will become evident in subsequent chapters, there is much to be gained by employing the two experimental techniques in combination. 

A host of attempts have been made to Improve BET theory, but most approaches have only limited applicability. They include better statistics of the stacking of molecules, account of lateral Interaction, or adsorption limited to a certain number of layers to mimic sorption in pores. Regarding this last attempt. Isotherms of types IV and V in fig. 1.13 can be predicted, but this is a mathematical rather than physical exercise since limitation is in reality not caused by a spontaneous cessation of adsorption after a given number of layers has been completed. Also in view of the additional complication of surface heterogeneity, the insight gained tends to be proportional to rather than to n, where n is the number of publications. 

The examples discussed in the previous sections Illustrate models for deriving Isotherms for binary systems. A variety of variants (e.g. mobile adsorbates), alternatives (e.g. models based on computer simulations) and extensions (e.g. multimolecular adsorption. Inclusion of surface heterogeneity, can be, and have been, proposed. The extensions usually require more parameters so that agreement with experiment is more readily obtained, but as long as various models are not compared against the evidence, discrimination is impossible. As there are numerous theoretical (e.g. distinction between molecules in the first and second layer) and experimental (presence of minor admixtures, tenaciously adsorbing on part of the surface) variables one tends to enter a domain of diminishing returns. On the other hand, there are detailed models for certain specific, well-defined situations. Here we shall review some approaches for the sake of illustration. 

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