Phenomenological rate parameters

In NR, dissociations of neutral intermediates and ions formed by collisional reionization are convoluted in the spectrum. An efficient deconvolution is achieved by varying step-wise the time scales for neutral and ion dissociations and using the measured temporal profiles of NR ion intensities to obtain phenomenological rate parameters for both neutral (kN) and ion dissociations (k) [61,62]. These variable-time measurements not only distinguish neutral and ion dissociations, but the measured rate parameters also provide quantitative information on the contribution of either process and can be used to assess branching... 

Table 2. Phenomenological rate parameters (chemisorpion rate UKyoK, desorption rate / jj and the rate of bimolecular interaction vroi) of the surface reaction typical for Sn02 based thin films gas sensors exposed to H2 gas (see Figure 11.).

If k is expressed in liters per mole per second, the standard state for the free energy and entropy of activation is 1 mole/liter. If the units of k are cubic centimeters per molecule per second, the corresponding standard state concentration is 1 molecule/cm3. The magnitudes of AG and AS reflect changes in the standard state, so it is not useful to say that a particular reaction is characterized by specific numerical values of these parameters unless the standard states associated with them are clearly identified. These standard states are automatically determined by the units chosen to describe the reactant concentrations in the phenomenological rate expressions. 

Most elementary chemical reactions can be categorized as unimolecular or bimolecular events. However, further phenomenological classification is useful for the development of detailed chemical kinetic models. This way, rate parameters for new reactions can be estimated rapidly and reliably by analogy to similar reactions in the same phenomenological class. In addition, the number of different elementary reactions that must separately be treated is reduced. It must be recognized, however, that exceptional cases... 

To distinguish between simultaneous or only consecutive epimerizations at CHD centers, kinetic experiments based on the four isomers of 1 -methyl-2,3-d2-cyclopropane were designed141. The phenomenological rate constants associated with the various reactions leading from one isomer to another employ subscripts to designate the carbon atom at which an epimerization occurs k, indicates a one-center epimerization at C(/), and /q is used for a two-center epimerization at C(i) and C(J) (Scheme 1). In this case, with all four isomers present in equal concentrations at equilibrium, the time dependence of each is governed by four rate constants kuk2- k2, kl2 = kl2 and /c23. But, at best, only three kinetic parameters may be found experimentally kt, k2i and (k2 + kl2). 

Given that the reaction kinetics of the forward and backward reactions are first order in Ox and Red, respectively, measurements of ks, kc, or ka, and a, AHf and/or AHf provide a detailed phenomenological description of the electrochemical kinetics for solution-phase reactants at a given electrode-electrolyte interface. It is also of fundamental interest, however, to evaluate rate parameters for adsorbed (or "surface attached ) reactants or reaction intermediates (Sect. 2.3). 

Table 1. The rate parameters of the surface reaction evaluated hy fitting of the phenomenology (2) to the experimental dependencies of r on gas concentration for various sensors modified by individual metallic impurity and exposed to H2 and CO gases in the air of the relative humidity RH= 33 %.

A novel method for the evaluation of the kinetic parameters of the sensor response to a gas is described in this section. The theoretical study of the phenomenological model described in Section 2 made it possible to propose this method. The core of the method is the controlled periodic variation of the gas composition in the atmosphere. It was theoretically demonstrated by [4] that the oscillations of the gas coverage on the surfaces are determined by the rate parameters of the chemical reaction. Since main characteristics of... 

In the remainder of this subsection, the goal is to relate these phenomenological rate constants to more fundamental parameters of the growing oxide layer. Table 7.1 lists the parabolic rate constants for a number of metals oxidized in pure oxygen at 1000°C. 

These results highlight a) Photodegradation reaction rates should be defined on the basis of phenomenologically meaningful parameters, case of W rr, b) Reaction rate evaluation is a task that should be developed carefully, accounting for possible nonidealities in the photocatalytic reactor such as particle wall fouling. 

Dynamic parameters such as diffusion coefficients and the phenomenological rate constant of ion transfer can also be evaluated. 

The usefulness of these rate parameters, i.e., their relevance to other experimental situations, depends on the validity of the three above assumptions. If they are invalid, the measured rate parameters are restrictively phenomenological, relevant solely to the conditions of the particular measurement. These considerations stress the need to test that validity, as indicated in the discussion of control experiments in the following section. 

The specific material constants were introduced earlier through eqs. (7.24c), with 9 = T/Tg and/(yP) being given by eqs. (7.41). In eq. (7.46) is an empirical rate parameter, to be chosen as a best fit to experimental results to complete the definition, and to replace the mechanistic expressions with the more convenient equivalent phenomenological forms introduced here. Through these choices, the power-law form of the kinetic law of eq. (7.43) becomes a flexible representation of the large-strain plastic flow of metallic glasses near Jg. 

Detailed kinetic studies of the thermal imidisation of polyisoimide by DSC are described. Both isothermal and dynamic methods were used to obtain kinetic parameters and a phenomenological rate equation for estimating the degree of imidisation as a function of time. 15 refs. KOREA... 

For tliis model tire parameter set p consists of tire rate constants and tire constant pool chemical concentrations l A, 1 (Most chemical rate laws are constmcted phenomenologically and often have cubic or otlier nonlinearities and irreversible steps. Such rate laws are reductions of tire full underlying reaction mechanism.)... 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

We now want to study the consequences of such a model with respect to the optical properties of a composite medium. For such a purpose, we will consider the phenomenological Lorentz-Drude model, based on the classical dispersion theory, in order to describe qualitatively the various components [20]. Therefore, a Drude term defined by the plasma frequency and scattering rate, will describe the optical response of the bulk metal or will define the intrinsic metallic properties (i.e., Zm((a) in Eq.(6)) of the small particles, while a harmonic Lorentz oscillator, defined by the resonance frequency, the damping and the mode strength parameters, will describe the insulating host (i.e., /((0) in Eq.(6)). 

From a catalytic viewpoint this is the most important phenomenological parameter for quantifying the promoting or poisoning effect of a given coadsorbed species i (e.g. 02 F, Na+, H+) on the rate of a catalytic reaction. Similarly to the case of classical promotion (eq. 2.19), it is defined from ... 

The random error arises from the measurement of y the true value of which is not known. The measurements are assumed to be free of systematic errors. The modeling equations contain adjustable parameters to account for the fact that the models are phenomenological. For example, kinetic rate expressions contain rate constants (parameters) the value of which is unknown and not possible to be obtained from fundamental principles. 

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