Phenomenological kinetics

After an introductory chapter, phenomenological kinetics is treated in Chapters 2, 3, and 4. The theory of chemical kinetics, in the form most applicable to solution studies, is described in Chapter 5 and is used in subsequent chapters. The treatments of mechanistic interpretations of the transition state theory, structure-reactivity relationships, and solvent effects are more extensive than is usual in an introductory textbook. The book could serve as the basis of a one-semester course, and I hope that it also may be found useful for self-instruction. 

The stochastic problem is to describe properly the time evolution of the Heisenberg operator d(t) averaged over all the realizations of collisional process in the interval (0,t). The averaging, performed in the impact theory, results in the phenomenological kinetic equation [170, 158]... 

Basic studies on the kinetics of swelling have been performed [1699]. Pure clays (montmoiillonite, illite, and kaolinite) with polymeric inhibitors were investigated, and phenomenologic kinetic laws were established. 

E. Temkin, Phenomenological kinetics of the motion of a phase boundary, Sov. Phys. Cryst., 15,1971, 767-72... 

A detailed discussion of the statistical thermodynamic aspects of thermally stimulated dielectric relaxation is not provided here. It should suffice to state that kinetics of most of the processes are again complicated and that the phenomenological kinetic theories used to described thermally stimulated currents make use of assumptions that, being necessary to simplify the formalism, may not always be justified. Just as in the general case, TSL and TSC, the spectroscopic information may in principle be available from the measurement of thermally stimulated depolarization current (TSDC). However, it is frequently impossible to extract it unambiguously from such experiments. 

Because of the wide application of these resins to diverse industries and their very different kinetic models and mechanisms of cross-linking and reactions, phenomenological kinetic models for epoxy, vinyl ester, and phenolic resins are presented in the next three subsections. 

Erdey-Gruz and Volmer contribution in 1930 form the basis of phenomenological kinetic electrochemistry. 

The first aim of this chapter is to analyze the significant implications associated with the mere statement of a rate equation. Limitations of phenomenological kinetic equations are discussed and more rigorous analysis based on the reaction pathway, for both stepwise and chainwise polymerizations, is presented. The effect of vitrification on polymerization rate is... 

In this section, constitutive equations describing the polymerization kinetics when the system is in the liquid or rubbery state are analyzed. The influence of vitrification on reaction rate is considered in a subsequent section. First, phenomenological kinetic equations are analyzed then, the use of a set of kinetic equations based on a reaction model is discussed in separate subsections for stepwise and chainwise polymerizations. 

Equation (5.4) is usually referred to as the Kamal equation (Kamal, 1974 Sourour and Kamal, 1976), and is one of the most popular phenomenological kinetic equations used in the literature to fit experimental data for thermosetting polymers. 

As stated in the previous section, the use of a phenomenological kinetic equation derived from Eq. (5.1), for a system that does not verify the required restrictions for its use, may lead to different kinetic expressions when trying to fit experimental results obtained under isothermal and nonisothermal conditions. In particular, it may be observed that different kinetic parameters result by varying the heating rates in nonisothermal experiments. 

The concept of reaction mechanism is very broad and its exact meaning depends to considerable extent on the point of view from which a given problem is to be analysed. Thus, for example, reaction mechanisms can be understood differently by a chemical physicist analysing a given reaction at the level of elementary collisions in crossed molecular beams, and by an organic chemist analysing the reaction course by the formalism of phenomenological kinetics. This implies that if one wants to speak about the mechanism of the reaction it is always necessary to specify also the point of view, from which the reaction is analysed. Thus, for example, in the case of usual reactions performed on the preparative scale, the term reaction mechanism is used to denote the detailed specification of whether the reaction proceeds in one elementary step or whether some, more or less stable, intermediates intervene. 

Volmer turned his attention to processes at - nonpo-larizable electrodes [iv], and in 1930 followed the famous publication (together with - Erdey-Gruz) on the theory of hydrogen - overpotential [v], which today forms the background of phenomenological kinetics of electrochemistry, and which resulted in the famous - Butler-Volmer equation that describes the dependence of the electrochemical rate constant on applied overpotential. His major work, Kinetics of Phase Formation , was published in 1939 [v]. See also the Volmer reaction (- hydrogen), and the Volmer biography with selected papers [vi]. 

A phenomenological kinetics profile for the formation of MCM-41 (CAT 16) was also obtained by monitoring the time dependence of the intensity of the central signal of the superhyperfine triplet of CAT 16 by EPR spectroscopy. A fast intensity loss was observed within the first 10 min of reaction, whereas between 10 and 120 min the signal intensity decreased much more slowly, reaching its final line shape after about 90 min. This result was interpreted in terms of a change from a liquid-like to a solid-like EPR spectrum of CAT 16. 

The self-inhibition effect [106,127] means that the conversion may be incomplete when definite restrictions are superimposed on the mobility of the elements of the reactive system [128]. Phenomenological kinetics of such processes may be described by the following equation ... 

Rudzinski W. and Panczyk T., Phenomenological Kinetics of Real Gas-Adsorption-Systems Isothermal Adsorption, Journal of Non-EqmHbrium Thermodynamics, 27 (2002)pp.l49-204. 

For example, to identify a potential hazard that is caused by changing the catalyst shape an equipment-based approach must include surface area as a process parameter to be searched a piece of information embedded in the phenomenological kinetic rate expression and not explicitly available. Thus,... 

Phenomenological Kinetic Model of Non-Thermal Plasma Sterilization of Air Streams... 

Comparison of the phenomenological kinetic model with experiments... 

The phenomenological kinetic analysis of the oscillatory reactions used for the examination of a catalyst is of essential importance for its characterization. However, the phenomenological kinetics of oscillatory reactions has specific properties based on their specific features. Thus, the amplitude of oscillations, the periods between them (At), their number (n), the preoscillatory period (rO, the duration from the beginning of the reaction to the end of the oscillatory state (Tend), and the duration of oscillatory state (Tosc = Tend t ) are all the kinetic parameters specific for kinetic and dynamic states of the system [47,48,51,54,66,69,70]. 

A phenomenological kinetic model of this process has been developed by Chang (47). The catalysts are zeolites of ZSM-5 type which have some unusual properties. The largest hydrocarbons which can penetrate the channel structure of ZSM-5 are in Cio range as, for in-... 

The Smoluchowski equation may be regarded as a phenomenological tool for describing the fluctuation of physical quantities, and can be applied to more general situations for example the equation can be used to describe the fluctuation of thermodynamic variables (such as concentration). In such cases, the potential U(x) must be regarded as the free energy which determines the equilibrium distribution of those variables, and the relation (3.17) must be replaced by phenomenological kinetic equations. We shall see such applications in Chapter 5. 

Here L is a phenomenological kinetic coefficient and A is a free energy. Near the transition point, S p is small so that A can be expanded with respect to S p as in the series... 

Doi and Ohta [249], and then Doi and Onuki [259], considered a simplifled model of two immiscible liquids at 0j = 02 = /2> having the same viscosity and density, focusing primarily on the interface and the flow-induced evolution of the interfadal area and orientation. Instead of the interphase the authors assumed an interface without thickness - consequently, postulating that the interface does not perturb the flow field (the passively advected interface). Thus, a semi-phenomenological kinetic equation describes the time evolution in a given flow field of the interfadal area per unit volume, Q, and its anisotropy, tensor... 

Thus, this approach determines the spinodal by a phenomenological kinetic principle v —> oo). How closely this obtained curve (perhaps, a quasispinodal) may fit to the thermodynamic spinodal can be determined only from experience in studying a number of systems. One particular case is dealt with below. 

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