Kinetics homogenity, definition

In deterministic theory we started with the definition of a compartment as a kinetically homogeneous amount of material. The equivalent definition in stochastic theory is that the probability of a unit participating in a particular transfer out of a compartment, at any time, is the same for all units in the compartment. 

The reactions considered in the TC4 model are shown in Table 2. The model involves 6 adjustment parameters associated with heterogeneous kinetic constants (see reactions 1 to 6 in Table 2). The differential equations associated to the rate laws of the elementary reactions proposed in this study were solved by using a Fortran program developed by Braum and coworkers [3]. The kinetic constants from the homogeneous phase reactions were obtained from the National Institute of Standards and Technology (NIST) database [4] which the following kinetic constant definition holds ... 

Let us start with some definitions. A compartment is an amount of material that acts as though it is well-mixed and kinetically homogeneous. A compartmental model consists of a finite number of compartments with specified interconnections among them. The interconnections represent fluxes of material which physiologically represent transport from one location to another or a chemical transformation, or both, or control signals. An example of a simple two-compartment model is Ulustrated in Figure 9.1 where the compartments are represented by circles and the interconnections by arrows. 

Given the introductory definitions, it is useful before explaining well-mixed and kinetic homogeneity to consider possible candidates for compartments. Consider the notion of a compartment as a physical space. Plasma is a candidate for a compartment a substance such as plasma glucose could be a compartment. 

Definition of a method for obtaining samples for a source of kinetic data on this reactive extmsion must take several factors into account o Extremely small initiator to polymer ratios are involved, o The rate of dispersion of the initiator and the degree of dispersion obtained is likely itiq>ortant to both the homogeneity of the product and the efficiency of the initiator. 

Only visual inspection of the reaction solution was made. Since the metals used, i.e., Ru, Os, Ir, Co, are heterogeneous Fischer-Tropsch catalysts, definite proof of the homogeneity of these systems must await detailed spectroscopic and kinetic measurements. 

We adopt this kinetic definition of reaction order without reference to the actual number of molecules involved in each act of chemical transformation. In homogeneous reactions the kinetically determined order is equal to the number of molecules participating in the actual change of which the rate is being measured. In heterogeneous reactions this equality is not necessarily preserved. It will be convenient to call the order inferred from the effect of pressure on the time of half-change the apparent order, and to refer to the number of molecules involved as the true order of the reaction. We have now to consider the relation of the true and the apparent order in various cases. ... 

Kinetic data for the ox heart preparation are included even though definitive data regarding homogeneity are not available. 

The application of chemical kinetics to even homogeneous solutions is often arduous. When kinetic theories are applied to heterogeneous soil constituents, the problems and difficulties are magnified. With the latter in mind, one must give definitions immediately for two terms—kinetics and... 

By definition of a homogeneous scalar field, one has the following relation between the kinetic and the potential terms ... 

Argon and Salama have demonstrated that this form of the expression accoimts for the measured craze growth kinetics in homogeneous glassy polymers very well, giving for values in the range of 1.5-2.0, which is quite consistent with the definition of this quantity in Eq. (51) and the known extension ratio of 4 in craze matter and back stresses that correspond to this extension ratio. 

This chapter is divided into three parts. In the first, basic definitions and their consequences for homogeneous chemistry are presented. The second deals with the fundamental aspects of electrode phenomena, whereas the third discusses the problem of mass transfer at electrodes and its consequences for electrochemical kinetics. The particular problems and concepts associated with preparative-scale electrolysis are presented in a special chapter (Chapter 3). 

Adsorption on a solid catalyst surface, complex formation in homogeneous catalysis with metallo-organic complexes and in biocatalysis with enzymes share the same principle, i.e. the total number of sites is constant. Therefore, the rate expressions for reactions on heterogeneous, homogeneous and biocatalysts have a similar form. The constant number of active sites results in rate expressions that differ from homogeneous gas phase kinetics. Partial pressures are usually used in rate expressions for gas-phase reactions, while concentrations are used when the reactions take place in the liquid phase. It appears that definitions and nomenclature of particular kinetics constants in the different sub-communities differ sometimes. In the following sections the expressions used by the different subdisciplines will be compared and their conceptual basis outlined. 

The rate equation specifies the mathematical fimction (g(ur) = ktox AodAt = k f(ur)) that represents (with greatest statistical accuracy. Chapter 3) the isothermal yield a) - time data for the reaction. For reactions of solids these equations are derived from geometric kinetic models (Chapter 3) involving processes such as nucleation and growth, advance of an interface and/or diflEusion. f( ir) and g(ar) are known as conversion functions and some of these may resemble the concentration functions in homogeneous kinetics which give rise to the definition of order of reaction. 

---