Homogeneous model systems

This complex and structurally related molecules served as a functional homogeneous model system for commercially used heterogeneous catalysts based on chromium (e.g. Cp2Cr on silica - Union Carbide catalyst). The kinetics of the polymerization have been studied to elucidate mechanistic features of the catalysis and in order to characterize the potential energy surface of the catalytic reaction. 

In homogeneous model systems, this mechanism is scarcely realized because of proton exchange simplicity between the donor and the acceptor. It proceeds without substrate and, therefore, the efficiency of the push-pull mechanism in solution is reduced. Moreover, both the donor and the acceptor of protons are usually located far from the places required for proton transfer in solutions. This hinders the required alignment of reacting molecules being achieved. 

Kohn RD, Haufe M, Mihan S et al (2000) Triazacyclohexane complexes of chromium as highly active homogeneous model systems for the Phillips catalyst. Chem Commun 1927-1928... 

For solid samples forming homogeneous solutions the model system may be used if pure sample matrix materials are available otherwise, the standard additions method is used. 

The model is considered a generalized homogeneous model (Boure, 1976), and it seems to be well suited to system codes describing complex systems, such as nuclear reactors, which cannot take into account a detailed separate-phase flow model because of their complexity. 

The physical situation in a fluidized bed reactor is obviously too complicated to be modeled by an ideal plug flow reactor or an ideal stirred tank reactor although, under certain conditions, either of these ideal models may provide a fair representation of the behavior of a fluidized bed reactor. In other cases, the behavior of the system can be characterized as plug flow modified by longitudinal dispersion, and the unidimensional pseudo homogeneous model (Section 12.7.2.1) can be employed to describe the fluidized bed reactor. As an alternative, a cascade of CSTR s (Section 11.1.3.2) may be used to model the fluidized bed reactor. Unfortunately, none of these models provides an adequate representation of reaction behavior in fluidized beds, particularly when there is appreciable bubble formation within the bed. This situation arises mainly because a knowledge of the residence time distribution of the gas in the bed is insuf-... 

The ancient categories of water, earth, and air persist in classifying the phases that make up geochemical systems. For purposes of constructing a geochemical model, we assume that our system will always contain a fluid phase composed of water and its dissolved constituents, and that it may include the phases of one or more minerals and be in contact with a gas phase. If the fluid phase occurs alone, the system is homogeneous the system when composed of more than one phase is heterogeneous. 

Section 3 will deal with catalytic systems whose stereospecificity is mainly controlled by the chirality of the environment of the transition metal, independently of the possible chirality of the growing chain (chiral site stereocontrol). In particular, in Section 3.1 the chirality and stereospecificity of homogeneous catalytic systems based on metallocenes of different symmetries and in different experimental conditions will be reviewed. In Section 3.2 the chirality of model catalytic sites, which have been supposed for isospecific first-generation TiCl3-based and high-yield MgC -supported catalysts, is described. In Section 3.3 we will present a comparison between model catalytic sites proposed for heterogeneous and homogeneous stereospecific site-controlled catalysts. 

As an example, C2-symmetric isospecific models for homogeneous catalytic systems based on the (R, / -coordinated isopropyl-bis(l-indenyl) ligand and for heterogeneous catalytic systems based on TiCLt supported on MgCl2 are compared in Figure 1.19. These models correspond to minimum-energy preinsertion intermediates calculated to be suitable for primary propene insertion... 

J. M. Ziman, Models of Disorder the Theoretical Physics of Homogeneously Disordered Systems. Cambridge Cambridge University Press, 1979. 

SN2 reactions of primary organolithium compounds on PMMA in dilute homogeneous solution may be considered as a model system where all the important reaction parameters may be controlled they allow both a quantitative analysis of PMMA chain reactivity and the synthesis of well defined ketonic copolymers within a wide range of possible structural variations. The two homologous series of organolithium compounds and the corresponding reaction conditions we selected are given below ... 

All the model systems investigated by Bisschops et al. fell within the completely homogeneous fluidisation regime modelled by Gibilaro and Hossain126 . With the low-g rotor and... 

The solution procedure to this equation is the same as described for the temporal isothermal species equations described above. In addition, the associated temperature sensitivity equation can be simply obtained by taking the derivative of Eq. (2.87) with respect to each of the input parameters to the model. The governing equations for similar types of homogeneous reaction systems can be developed for constant volume systems, and stirred and plug flow reactors as described in Chapters 3 and 4 and elsewhere [31-37], The solution to homogeneous systems described by Eq. (2.81) and Eq. (2.87) are often used to study reaction mechanisms in the absence of mass diffusion. These equations (or very similar ones) can approximate the chemical kinetics in flow reactor and shock tube experiments, which are frequently used for developing hydrocarbon combustion reaction mechanisms. 

---