Kinetic description

Syntheses of sterically modified biopolymers can clearly yield insights into the presuppositions and possibilities of biological self-organization processes of biopolymers far beyond general thermodynamic and kinetic descriptions of natural systems. 

Although the results presented in Fig. 5.2 appear to verify the predictions of Eq. (5.16), this verification is not free from controversy. This controversy arises because various workers in this field employ different criteria in evaluating the success of the relationships we have presented in fitting experimental polymerization data. One school of thought maintains that an adequate kinetic description of a process must apply to the data over a large part of the time of the experiment. 

Polymerization in two phases, the Hquid monomer phase and the swollen polymer gel phase, forms the basis for kinetic descriptions of PVC polymerization (79—81). The polymerization rate is slower in the Hquid monomer phase than in the swoUen polymer gel phase on account of the greater mobiHty in Hquid monomer, which allows for greater termination efficiency. The lack of mobiHty in the polymer gel phase reduces termination and creates a higher concentration of radicals, thus creating a higher polymerization rate. Thus the polymerization rate increases with conversion to polymer. 

In kinetic analysis of coupled catalytic reactions it is necessary to consider some specific features of their kinetic behavior. These specific features of the kinetics of coupled catalytic reactions will be discussed here from a phenomenological point of view, i.e. we will show which phenomena occur or may occur, and what formal kinetic description they have if the coupling of reactions is taking place. No attention will be paid to details of mechanisms of the processes occurring on the catalyst surface from a molecular point of view. 

A kinetic description of a heterogeneous catalytic reaction will in most cases be different when the reaction proceeds simultaneously with other reactions in a complex system, compared with the case where its kinetics was studied separately. The most important is the effect in the case where the reactions concerned take place on the same sites of the surface of a catalyst. Let us take, for example, the system of competitive reactions... 

It should be noted that the kinetic analysis of this system consisting of five reactions represents the limiting case which can be reliably solved by the current experimental technique, if we wish its kinetic description to be in agreement with the kinetics of single reactions and the corresponding... 

In kinetic theory, the macroscopic quantities are found as averages over the motion of many molecules each molecular event is assumed to take place over a microscopic time interval, so that a measurement that is made over a macroscopic time interval involves many molecules. The kinetic-description is, therefore, a probabilistic one in that assumptions are made about the motion of one molecule and the results of this motion are averaged over all of the molecules of the gas, giving proper weight to the probability that the various molecules of the gas can have the assumed motion. 

Reaction rates are related to a and to temperature, T, by different and independent functions and a complete kinetic description of behaviour... 

Figure 7. Theoretical polymer distributions, based on kinetic description of Tan-lak (14) for micro-mixed and totally segregated CFSTRS with polymer feed (CFSTRS CMO = 0.5M FT = O.OIM 6 = 20.0 min XM = 0.70)...

The molecular weight distribution (MWD) is of vital importance for polymers of all types. It determines the ease of manufacture, the ease of fabrication, and the end-use properties of the polymer. A proper kinetic description of a polymerization requires determination of the molecular weight distribution of the polymer in addition to the usual concepts of conversion and selectivity. 

Catalytic reactions (as well as the related class of chain reactions described below) are coupled reactions, and their kinetic description requires methods to solve the associated set of differential equations that describe the constituent steps. This stimulated Chapman in 1913 to formulate the steady state approximation which, as we will see, plays a central role in solving kinetic schemes. 

Whether a catalytic reaction proceeds via a Langmuir-Hinshel vood or Eley-Rideal mechanism has significant implications for the kinetic description, as in the latter case one of the reactants does not require free sites to react. However, Eley-Rideal mechanisms are extremely rare, and we will assume Langmuir-Hinshelwood behavior throughout the remainder of this book. 

The mechanism of the NO -1- CO reaction at realistic pressures is thus very complicated. In addition to the reaction steps considered above, one also has to take into account that intermediates on the surface may organize into islands or periodically ordered structures. Monte Carlo techniques are needed to account for these effects. Consequently, we are still far from a complete kinetic description of the CO -1- NO reaction. For an interesting review of the mechanism and kinetics of this reaction we refer to Zhdanov and Kasemo [V.P. Zhdanov and B. Kasemo, Suif. Sci. Rep. 29 (1997) 31],... 

Surface composition. The principle of surface segregation in ideal systems is easy to understand and to derive thermodynamically the equilibrium relations (surface concentration Xg as a function of the bulk concentration Xb at various temperatures) is also very easy (4,8). Even easier is a kinetic description which can also comprise some of the effects of the non-ideality (9). We consider an equilibrium between the surface(s) and the bulk(b) in the exchange like ... 

F Langenbucher. In vitro dissolution kinetics Description and evaluation of a column-type method. J Pharm Sci 58 1265, 1969. 

The kinetic description of chain branching is complex, because the probability of a chain branching event depends on many things that we cannot simplify for the model we are developing. Suffice it to say that chain branching slows down the polymerization process. This is because any reaction occurring between chains does not incorporate the free monomer, leading to a reduced rate of monomer consumption. 

The mechanisms by which coal is converted to soluble or liquid form and the nature of the products of such reactions have been the subjects of a great deal of effort throughout the world. In the last two sections, researchers from Australia, Japan, South Africa, and the United States describe their findings in these areas. The reader will note that no unanimous agreement exists on the chemical mode by which coal is converted although kinetic descriptions are often similar. 

The detailed kinetic description of a chemical process is a primary feature for both the industrial practice and the comprehension of the reaction mechanism. The development of a kinetic model able to predict at the same time the reactants conversion and the products distribution (i.e., a detailed kinetic model) is a prerequisite for the design, optimization, and simulation of the industrial process. Also, the detailed description of process kinetics allows the ex post evaluation of the goodness of the mechanistic scheme on the basis of which the model itself is developed, making possible the collection of further insight in the chemistry of the process. 

These assumptions are partially different from those introduced in our previous model.10 In that work, in fact, in order to simplify the kinetic description, we assumed that all the steps involved in the formation of both the chain growth monomer CH2 and water (i.e., Equations 16.3 and 16.4a to 16.4e) were a series of irreversible and consecutive steps. Under this assumption, it was possible to describe the rate of the overall CO conversion process by means of a single rate equation. Nevertheless, from a physical point of view, this hypothesis implies that the surface concentration of the molecular adsorbed CO is nil, with the rate of formation of this species equal to the rate of consumption. However, recent in situ Fourier transform infrared (FT-IR) studies carried out on the same catalyst adopted in this work, at the typical reaction temperature and in an atmosphere composed by H2 and CO, revealed the presence of a significant amount of molecular CO adsorbed on the catalysts surface.17 For these reasons, in the present work, the hypothesis of the irreversible molecular CO adsorption has been removed. 

A complex reaction requires more than one chemical equation and rate law for its stoichiometric and kinetics description, respectively. It can be thought of as yielding more than one set of products. The mechanisms for their production may involve some of the same intermediate species. In these cases, their rates of formation are coupled, as reflected in the predicted rate laws. 

It should be emphasized that clear-cut situations described in Schemes 1-3 are uncommon and typically the combination of these models needs to be considered for kinetic and mechanistic description of a real system. However, even when one of the limiting cases prevails, each of these models may predict very different formal kinetic patterns depending on where the rate determining step is located. For the same reason, different schemes may be consistent with the same experimental rate law, i.e. thorough formal kinetic description of a reaction and the analysis of the rate law may not be conclusive with respect to the mechanism of the autoxidation process. 

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