Heterogeneous systems kinetics

The traditional cocatalyst, diethylaluminumchloride or triethylaluminum, shows only a pure polymerization activity and was used as a homogeneous system to understand the polymerization, which is simpler in soluble than in heterogeneous systems. Kinetic studies and applications of various methods have helped to define the nature of the active centers, to explain aging effects, to establish the mechanism of the interaction with olefins, and to obtain quantitative evidence of some elementary steps [12,13]. 

Statistical mechanical Monte Carlo as well as classical molecular dynamic methods can be used to simulate structure, sorption, and, in some cases, even diffusion in heterogeneous systems. Kinetic Monte Carlo simulation is characteristically different in that the simulations follow elementary kinetic surface processes which include adsorption, desorption, surface diffusion, and reactivity . The elementary rate constants for each of the elementary steps can be calculated from ab initio methods. Simulations then proceed event by event. The surface structure as well as the time are updated after each event. As such, the simulations map out the temporal changes in the atomic structure that occur over time or with respect to processing conditions. 

Chemical reactions obey the rules of chemical kinetics (see Chapter 2) and chemical thermodynamics, if they occur slowly and do not exhibit a significant heat of reaction in the homogeneous system (microkinetics). Thermodynamics, as reviewed in Chapter 3, has an essential role in the scale-up of reactors. It shows the form that rate equations must take in the limiting case where a reaction has attained equilibrium. Consistency is required thermodynamically before a rate equation achieves success over tlie entire range of conversion. Generally, chemical reactions do not depend on the theory of similarity rules. However, most industrial reactions occur under heterogeneous systems (e.g., liquid/solid, gas/solid, liquid/gas, and liquid/liquid), thereby generating enormous heat of reaction. Therefore, mass and heat transfer processes (macrokinetics) that are scale-dependent often accompany the chemical reaction. The path of such chemical reactions will be... 

The first of these factors pertains to the complications introduced in the rate equation. Since more than one phase is involved, the movement of material from phase to phase must be considered in the rate equation. Thus the rate expression, in general, will incorporate mass transfer terms in addition to the usual chemical kinetics terms. These mass transfer terms are different in type and number in different kinds of heterogeneous systems. This implies that no single rate expression has a general applicability. 

It is obvious that the effect of mixing must be taken into account in order to get reliable kinetic data. Such factors as k%a and kia, the mass transfer coefficients, are largely determined by mixing efficiency, especially in heterogeneous systems. 

Although the major objective of this paper has been to illustrate the concepts involved in the development of detailed chemical kinetic mechanisms for reactions taking place in the gas phase, a very short introduction is provided here to illustrate the application of the foregoing concepts to heterogeneous systems. 

Chapter 1 reviews the concepts necessary for treating the problems associated with the design of industrial reactions. These include the essentials of kinetics, thermodynamics, and basic mass, heat and momentum transfer. Ideal reactor types are treated in Chapter 2 and the most important of these are the batch reactor, the tubular reactor and the continuous stirred tank. Reactor stability is considered. Chapter 3 describes the effect of complex homogeneous kinetics on reactor performance. The special case of gas—solid reactions is discussed in Chapter 4 and Chapter 5 deals with other heterogeneous systems namely those involving gas—liquid, liquid—solid and liquid—liquid interfaces. Finally, Chapter 6 considers how real reactors may differ from the ideal reactors considered in earlier chapters. 

Billingham, N. C. and A. D. Jenkins, Free Radical Polymerization in Heterogeneous Systems, Chap. 6 in Comprehensive Chemical Kinetics, Vol. 14A, C. H. Bamford and C. F. H. Tipper, eds., American Elsevier, New York, 1976. 

The concept of micro- and macrofluids is of particular importance in heterogeneous systems because one of the two phases of such systems usually approximates a macrofluid. For example, the solid phase of fluid-solid systems can be treated exactly as a macrofluid because each particle of solid is a distinct aggregate of molecules. For such systems, then, Eq. 2 with the appropriate kinetic expression is the starting point for design. 

Giovanoli, R. Briitsch, R. (1974) Dehydration of y-FeOOH Direct observation of the mechanism. Chimia 28 188-191 Giovanoli, R. Briitsch, R. (1975) Kinetics and mechanisms of the dehydration of y-FeOOH. Thermochim. Acta 13 15-36 Giovanoli, R. Cornell, R.M. (1992) Crystallization of metal substituted ferrihydrites. Z. Pflanzenemahr. Bodenk. 155 455-460 Giovanoli, R. Briitsch, R. Stadelmann, W. (1975) Thermal decomposition of y- and a-FeOOH. In Barrett, P. (ed.) Reaction kinetics in heterogeneous systems. Elsevier Amsterdam, 302-313... 

Description of polymerization kinetics in heterogeneous systems is complicated, even more so given that the structure of complex formed is not very well defined. In template polymerization we can expect that local concentration of the monomer (and/or initiator) can be different when compared with polymerization in the blank system. Specific sorption of the monomer by macromolecular coil leads to the increase in the concentration of the monomer inside the coil, changing the rate of polymerization. It is a problem of definition as to whether we can call such a polymerization a template reaction, if monomer is randomly distributed in the coil on the molecular level but not ordered by the template. 

In this chapter we provide the fundamental concepts of chemical and biochemical kinetics that are important for understanding the mechanisms of bioreactions and also for the design and operation of bioreactors. First, we shall discuss general chemical kinetics in a homogeneous phase and then apply its principles to enzymatic reactions in homogeneous and heterogeneous systems. 

In heterogeneous systems, the rate expressions have to be developed on the basis of (a) a relation between the rate and concentrations of the adsorbed species involved in the rate-determining step and (b) a relation between the latter and the directly observable concentrations or partial pressures in the gas phase. In consequence, to obtain adequate kinetic rate expressions it is necessary to have a knowledge of the reaction mechanism, and an accurate means of relating gas phase and surface concentrations through appropriate adsorption isotherms. The nature and types of adsorption isotherm appropriate to chemisorption processes have been discussed in detail elsewhere [16,17] and will not be discussed further except to note that, in spite of its severe theoretical limitations, the Langmuir isotherm is almost invariably used for kinetic interpretations of surface hydrogenation reactions. The appropriate equations are... 

Because reactions in solids tend to be heterogeneous, they are generally described by rate laws that are quite different from those encountered in solution chemistry. Concentration has no meaning in a heterogeneous system. Consequently, rate laws for solid-phase reactions are described in terms of a, the fraction of reaction (a = quantity reacted -r- original quantity in sample). The most commonly encountered rate laws are given in Table 1. These rate laws and their application to solid-phase reactions are described elsewhere. 1 4 10-12 Unfortunately, it is often merely assumed that solid-phase reactions are first order. This uncritical analysis of kinetic data produces results that must be accepted only with great caution. 

The production of species i (number of moles per unit volume and time) is the velocity of reaction,. In the same sense, one understands the molar flux, jh of particles / per unit cross section and unit time. In a linear theory, the rate and the deviation from equilibrium are proportional to each other. The factors of proportionality are called reaction rate constants and transport coefficients respectively. They are state properties and thus depend only on the (local) thermodynamic state variables and not on their derivatives. They can be rationalized by crystal dynamics and atomic kinetics with the help of statistical theories. Irreversible thermodynamics is the theory of the rates of chemical processes in both spatially homogeneous systems (homogeneous reactions) and inhomogeneous systems (transport processes). If transport processes occur in multiphase systems, one is dealing with heterogeneous reactions. Heterogeneous systems stop reacting once one or more of the reactants are consumed and the systems became nonvariant. 

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