General kinetic model

In a series of papers, Jin and Bethke (2002 2003 2005 2007) and Jin (2007) derived a generalized rate expression describing microbial respiration and fermentation. They account in their rate model for an electron-donating half-cell reaction, 

The redox reaction that supplies the microbe with energy from the environment, 

The kinetic factors, which can vary from zero to one, are given by, 

The /) values can be determined formally only through careful experiments. Significantly, however, /) values are needed only for species whose concentrations change under the conditions of interest for other species, the quantities can be folded into the corresponding kinetic constant, or the kinetic constant and rate constant. For species whose concentrations are likely to change, such as the reaction substrates, /3 is commonly taken to be one, in the absence of contradictory information 

If the concentrations of only the electron donor and acceptor are considered to vary, each mD+ is invariant and the term ] [ n/ 1 in Equation 18.23 reverts to a half-saturation constant K[y Similarly, the corresponding term in Equation 18.24 may be represented by K A. Now, we see the dual Monod equation (Eqn. 18.16) is a specific simplification of the general rate law (Eqn. 18.22). 

Let S and 5f(t) be the total surface area and the area free from the adsorbate. Introducing the adatom density ni(t) on free area and the fractional coverage g of the free area yields 

The differentirJ form of this equation can be obtained using the condition m(t) 1  

The Kolmogorov model of crystalline growth couples g t) with the nucleation rate on a free part of the substrate a(t) (a t) = I(t), o —t 0) and velocity of linear growth of the crystalline phase v (Belen kiy 1980)  

For I(t) we shall use the expression (11.2.3). The growth velocity v t) can be evaluated in the following way. The coverage is changed via processes of evaporation lnd absorption. The corresponding rate of the coverage change is 

One can apply the Kolmogorov model provided a growing film has crystalline structure. It is known (Dash 1975) that mechanism gas-ciystall is involved in a crystalline film formation at temperatures T 0.3T with T being the melting temperature of the deposit. This mechanism takes place almost always in technological processes of film deposition onto cold substrate (Dash 1975, Jaycock and Parfitt 1981). If 0.3 T 0.6 Tm, the intermediate regime occurs, while for 

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The corresponding reactions of transient Co(OEP)H with alkyl halides and epoxides in DMF has been proposed to proceed by an ionic rather than a radical mechanism, with loss of from Co(OEP)H to give [Co(TAP), and products arising from nucleophilic attack on the substrates. " " Overall, a general kinetic model for the reaction of cobalt porphyrins with alkenes under free radical conditions has been developed." Cobalt porphyrin hydride complexes are also important as intermediates in the cobalt porphyrin-catalyzed chain transfer polymerization of alkenes (see below). 

It occurs via two adjacent adsorbed NO molecules, leading to an adsorbed dinitrosyl species. These last two co-adsorbed NO species made the two N-O bonds weaker, and the successive two N-O bond scissions led to N2. According to a general kinetic model [12], the NzO intermediate can desorb before dissociating to N2, if the desorption rate constant, kdes, is higher than the reaction (dissociation) rate constant, k, as presented in the following set of rate constants (Figure 5.2) ... 

Various mechanisms and kinetics of coal liquefaction have been proposed and examined by many investiga tors(l,2,4-8). As a general kinetic model of coal lique-action, scheme 1 was assumed. The reaction rate of every reaction step in the scheme assumed to be first order with respect to reacting species and dissolved hydrogen. A few typical cases of a general kinetic model and the general characteristics for their cases are illustrated on Table 3. When compared these typical figures, the curves are apparently different in shape. 

Table 3 Typical Cases of a General Kinetic Model...

To illustrate the conditions under which a system that includes chain propagating, chain branching, and chain terminating steps can generate an explosion, one chooses a simplified generalized kinetic model. The assumption is made that for the state condition just prior to explosion, the kinetic steady-state assumption with respect to the radical concentration is satisfactory. The generalized mechanism is written as follows ... 

In order to estimate kinetic constants for elementary processes in template polymerization two general approaches can be applied. The first is based on the generalized kinetic model for radical-initiated template polymerizations published by Tan and Alberda van Ekenstein. The second is based on the direct measurement of the polymerization rate in a non-stationary state by rotating sector procedure or by post-effect in photopolymerization. The first approach involves partial absorption of the monomer on the template. Polymerization proceeds according to zip mechanism (with propagation rate constant kp i) in the sequences filled with the monomer, and according to pick up mechanism (with rate constant kp n) at the sites in which monomer is outside the template and can be connected by the macroradical placed onto template. This mechanism can be illustrated by the following scheme ... 

Fig. 15. Suggested general kinetic model for protein adsorption in the absence of any covalent bond formation or disruption. Any protein desorbed in a denatured state is assumed to rapidly renature in solution. If the surface is heterogeneous, then two or more such scenarios can be formulated, with appropriate account of the area fractions of each type of surface present...

Partial blocking effect was first identified for pure iron in contact with aerated sulphuric acid medium [55]. Corrosion of carbon steel in sodium chloride media clearly showed the porous layer effect (see Section 5.2) [74]. The same effect was found for zinc corrosion in sodium sulphate [75] and the properties of the layer which was demonstrated to be formed of an oxide/hydroxide mixture were further used for building a general kinetic model of anodic dissolution [76], usable for measurement of the corrosion rate from impedance data. 

Modern technological practice, particularly the various types of chemical processing, use a great variety of formulations for the synthesis of polyurethanes. Therefore it is nearly impossible to create a general kinetic model which would be valid for various polymerizing systems. However, the same general approach to creating such models can be used for different cases. Therefore, it is useful to demonstrate the method used to construct a model and its characteristic kinetic equations for some typical cases. 

Banerjee, S., P.H. Howard, A.M. Rosenberg, A.E. Dombrowski, H. Sikka, and D.L. Tullis. 1984. Development of a general kinetic model for biodegradation and its application in chlorophenols and related compounds. Environ. Sci. Technol. 18 416-422. 

A general kinetic model should accommodate all chemical processes known to affect the dechlorination process. These include (1) reductive dechlorination takes place on the iron surface, rather than in the aqueous phase, so adsorption must occur (2) other components in the system may affect the dechlorination reaction by competing for the reaction sites (3) surface sites for reduction and for sorption may not be the same, as for the system with PCE and TCE where dechlorination takes place on the reactive sites, but most of the adsorption is clearly on the nonreactive sites (Burris et al., 1995). In the following section we will first discuss a single-site model similar to the one used by Johnson et al. (1998), which has accounted for the first two observations, then develop a two-site model that will also take the third observation into consideration. We aim to illustrate how coadsorbates in the iron system will affect adsorption and reduction of chlorinated solvents. TCE will be used as an example since relevant adsorption and reduction data are available, from which the required parameters for simulation could be estimated. 

A program to construct kinetic models of heterogeneous catalytic reactions that would be similar to the generally accepted models of chemical kinetics. This general kinetic model has been implemented in the model of the ideal adsorbed layer. 

General kinetic model and prediction of critical effects... 

One of the most essential problems in the construction of a "general kinetic model is to describe both the high-vacuum and the normal pressure regions (we have discussed this problem more fully in Sect. 1). 

The relationship between the coal organic structure and the products of thermal decomposition has been incorporated into a general kinetic model. The model has proved successful in simulating the results of vacuum thermal decomposition experiments for a variety of bituminous coals and lignites (5,12,13). It has also proved to be successful in limited application to other conditions such as coal proximate... 

A generalized kinetic model of cure is developed from the aspect of relaxation phenomena. The model not only can predict modulus and viscosity during the cure cycle under isothermal and non-isothermal cure conditions, but also takes into account filler effects on cure behavior. The increase of carbon black filler loading tends to accelerate the cure reaction and also broadens the relaxation spectrum. The presence of filler reduces the activation energy of viscous flow, but has little effect on the activation energy of the cure reaction. 

A generalized kinetic model of cure has been developed from the aspect of relaxation phenomenon. The model not only can predict isothermal and non-isothermal cure curves using modulus and viscosity data, but also allows us to take into account the effect of filler on cure behavior. The prediction of viscosity and modulus values during the cure cycle allows one to preprogram cure in order to improve the material processing and end-product performance. The important findings of this study... 

This review covering the influence of polymerization parameters on MWD clearly shows how impossible it is to elaborate laws valid for all catalytic systems. Furthermore, numerous discrepancies among the experimental data prevent any attempt at their rationalization based on a general kinetic model, even for similar catalytic systems. However, at least qualitatively, the following conclusions can be reasonsably drawn ... 

General kinetic model have involved Monod s model. 

A general kinetics model for all photochemical reaction orders, and a photosystem designed to harvest visible light as a source of electrons for use in redox reactions applicable to organic synthesis have also been described. ... 

The equations used in our study of the thermodynamics and kinetics of thermal electron reactions using the ECD and NIMS are presented. The ECD and NIMS methods were developed in our laboratories. These are used to determine the rate constants, electron affinities, partition function ratios, and bond dissociation energies of molecules and energies for the formation of complexes of anions. The general kinetic model for the ECD and negative-ion mass spectrometry is presented. Molecules will be classified using example data. 

General kinetics modeling program with PK/PD support... 

Bhattacharya,A., General Kinetic Model for Liquid-Liquid Phase Transfer Catalyzed Reactions, Ind Eng. Cheat Res., 35, 645 (1996). 

A general kinetic model has been presented (23) which appears to be consistent with the data presently accumulated oir some 100 compounds. The electron attachment steps and negative ion dissociation reactions are as follows ... 

A general kinetic model framework for the description of mass transport and chemical reactions at the gas-particle interface has been developed by Poschl et al. (2005). 

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