Heterogeneity concept

We used the concept of sound velocity dispersion for explanation of the shift of pulse energy spectrum maximum, transmitted through the medium, and correlation of the shift value with function of medium heterogeneity. This approach gives the possibility of mathematical simulation of the influence of both medium parameters and ultrasonic field parameters on the nature of acoustic waves propagation in a given medium. 

On the other hand, as applied to the submonolayer region, the same comment can be made as for the localized model. That is, the two-dimensional non-ideal-gas equation of state is a perfectly acceptable concept, but one that, in practice, is remarkably difficult to distinguish from the localized adsorption picture. If there can be even a small amount of surface heterogeneity the distinction becomes virtually impossible (see Section XVll-14). Even the cases of phase change are susceptible to explanation on either basis. 

Somor]ai G A 1998 Molecular concepts of heterogeneous catalysis J. Moi. Struct (Theochem) 424 101... 

In this chapter we introduced the concept of shock waves, ignoring the features that distinguish solids from fluids. The properties include shear strength, polymorphic phase transformations, heterogeneous structure, anisotropy, and viscoplastic behavior. These topics make up the majority of the subject of shock compression of solids, and form a large portion of the rest of this book. 

The evolution of T, is just an exercise in mesoscale thermodynamics [13]. These expressions, in combination with (7.54), incorporate concepts of heterogeneous deformation into a eonsistent mierostruetural model. Aspects of local material response under extremely rapid heating and cooling rates are still open to question. An important contribution to the micromechanical basis for heterogeneous deformation would certainly be to establish appropriate laws of flow-stress evolution due to rapid thermal cycling that would provide a physical basis for (7.54). 

Horie and his coworkers [90K01] have developed a simplified mathematical model that is useful for study of the heterogeneous nature of powder mixtures. The model considers a heterogeneous mixture of voids, inert species, and reactant species in pressure equilibrium, but not in thermal equilibrium. The concept of the Horie VIR model is shown in Fig. 6.3. As shown in the figure, the temperatures in the inert and reactive species are permitted to be different and heat flow can occur from the reactive (usually hot) species to the inert species. When chemical reaction occurs the inert species acts to ther-... 

The rate (or kinetics) and form of a corrosion reaction will be affected by a variety of factors associated with the metal and the metal surface (which can range from a planar outer surface to the surface within pits or fine cracks), and the environment. Thus heterogeneities in a metal (see Section 1.3) may have a marked effect on the kinetics of a reaction without affecting the thermodynamics of the system there is no reason to believe that a perfect single crystal of pure zinc completely free from lattic defects (a hypothetical concept) would not corrode when immersed in hydrochloric acid, but it would probably corrode at a significantly slower rate than polycrystalline pure zinc, although there is no thermodynamic difference between these two forms of zinc. Furthermore, although heavy metal impurities in zinc will affect the rate of reaction they cannot alter the final position of equilibrium. 

The study of catalytic polymerization of olefins performed up to the present time is certain to hold a particular influence over the progress of the concepts of the coordination mechanism of heterogeneous catalysis. With such an approach the elementary acts of catalytic reaction are considered to proceed in the coordination sphere of one ion of the transition element and, to a first approximation, the collective features of solids are not taken into account. It is not surprising that polymerization by Ziegler-Natta catalysts is often considered together with the processes of homogeneous catalysis. 

His researches and those of his pupils led to his formulation in the twenties of the concept of active catalytic centers and the heterogeneity of catalytic and adsorptive surfaces. His catalytic studies were supplemented by researches carried out simultaneously on kinetics of homogeneous gas reactions and photochemistry. The thirties saw Hugh Taylor utilizing more and more of the techniques developed by physicists. Thermal conductivity for ortho-para hydrogen analysis resulted in his use of these species for surface characterization. The discovery of deuterium prompted him to set up production of this isotope by electrolysis on a large scale of several cubic centimeters. This gave him and others a supply of this valuable tracer for catalytic studies. For analysis he invoked not only thermal conductivity, but infrared spectroscopy and mass spectrometry. To ex-... 

It is apparent, from the above short survey, that kinetic studies have been restricted to the decomposition of a relatively few coordination compounds and some are largely qualitative or semi-quantitative in character. Estimations of thermal stabilities, or sometimes the relative stabilities within sequences of related salts, are often made for consideration within a wider context of the structures and/or properties of coordination compounds. However, it cannot be expected that the uncritical acceptance of such parameters as the decomposition temperature, the activation energy, and/or the reaction enthalpy will necessarily give information of fundamental significance. There is always uncertainty in the reliability of kinetic information obtained from non-isothermal measurements. Concepts derived from studies of homogeneous reactions of coordination compounds have often been transferred, sometimes without examination of possible implications, to the interpretation of heterogeneous behaviour. Important characteristic features of heterogeneous rate processes, such as the influence of defects and other types of imperfection, have not been accorded sufficient attention. 

Recently, with the improvement achieved in the preparation and control of surfaces, a number of approaches have been devoted to the estimation of the pzc of pt(lll).140 197 210 211 These are summarized in Table 29 for convenience of the reader. The value recommended for pc-Pt is also reported for comparison. In three cases the pzc has been estimated indirectly and the value is strikingly close to the pzc of poly crystalline Pt. In view of the heterogeneity of Pt surfaces, this closeness is puzzling and suggests that the phenomenon used to estimate the pzc does not conform to the concept of zero charge. 

The reader must have already identified some of the basic concepts which play a key role in understanding the electrochemical activation of heterogeneous catalysis catalysis, electrocatalysis, promotion, electrochemical promotion, spillover, backspillover. It is therefore quite important to define these terms unambiguously so that their meaning is clearly determined throughout this book. 

Chapter 7 introduces the concept of absolute electrode potential in solid state electrochemistry. This concept has some important implications not only in solid state electrochemistry but also, potentially, in heterogeneous catalysis of supported catalysts. 

The discussion is organized in the following order First the advantages of HRC scheme, relative to the industrial (i.e., heterogenous) process are briefly commented on second, the relevance of celMose activation and the physical state of its solution to optimization of esterification are discussed. Finally, the use of recently introduced solvent systems and synthetic schemes, designed in order to obtain new, potentially useful cellulose esters with controlled, reproducible properties is reviewed. A comment on the conformity of these methods with the concepts of green chemistry is also included. 

Using microkinetic expressions, we have discussed the most important catalytic concepts that describe heterogeneous catalytic reactions. We have related these concepts with the energies, entropies, and transition-state features that are accessible through current state-of-the-art DFT techniques. 

Whitaker, S, Transport Processes with Heterogeneous Reaction. In Concepts and Design of Chemical Reactors Whitaker, S Cassano, AE, eds. Gordon and Breach Newark, NJ 1986 1. Whitaker, S, Mass Transport and Reaction in Catalyst Pellets, Transport in Porous Media 2, 269, 1987. 

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