Active centre , homogenous

The comparable values of the polydispersity index for both isotactic and atactic polymers led Keii to conclude that the same active centre distribution exists according to the ratio between propagation and transfer rate constants. Furthermore, the low values of the polydispersity index would suggest good active centre homogeneity. 

Let a be the fraction of the surface covered with adsorbed gas. Then (1 — cr) is the fraction left uncovered. In view of the possibility that the surface is not homogeneous and that adsorption only occurs on active centres, fraction of surface covered must be understood to mean the fraction of the available surface which is actually covered. Thus, from the point of view of adsorption, the surface might be covered when certain patches only were completely occupied by adsorbed molecules, and the rest of the surface might be incapable of taking up gas at any pressure. 

In the case of olefin polymerisation in the presence of homogeneous metallocene-based catalysts, the individual polymerisation stages have not been very thoroughly investigated. However, kinetic studies have helped, among others, to define the nature of the active centres and to establish the occurrence of some polymerisation elementary steps in a quantitative way. 

The mechanism and theory of bioelectrocatalysis is still under development. Electron transfer and variation of potential in the electrodeenzyme-electrolyte system has therefore to be investigated. Whether the enzyme is soluble and the electron transfer process occurs through a mediator, or whether there is direct enzyme immobilization on the electrode surface, the homogeneous process in the enzyme active centre has to be described by the laws of enzyme catalysis, and the heterogeneous processes on the electrode surface by the laws of electrochemical kinetics. Besides this there are other aspects outside electrochemistry or... 

A first step towards acquiring such knowledge is the work of Chien who polymerized ethylene with homogeneous bis cyclopentadienyltitanium dichloride (cp2TiCl2) and Et2AlCl. He assumes termination to be a bimolecular reaction of the active centres... 

Furthermore, soluble catalytic systems containing homogeneous active centres yield polymers with very narrow MWD (Q 2) even when they are used in hetero-phasic processes (see Section 4.1.1). 

By solving a differential equation system which describes the above polymerization model for homogeneous active centres (kp = const.), a polydispersity Q value between 1 and 2 was obtained, which cannot explain the MWD of the experimentally obtained polymers (Q = 2.5-5.0). On the other hand, even an exponential distribution... 

Analogously with MWD broadening, even the composition heterogeneity observed for ethylene-propylene copolymers, obtained with either homogeneous or heterogeneous catalytic systems, has often been attributed to the plurality of active centres... 

Cozewith and Ver Strate examined fractionation data of ethylene-propylene copolymers obtained with homogeneous or apparently homogeneous systems, based on vanadium compounds such as VCl and aluminum trialkyl, or VOCI3 and AKCjHjljCl. While some catalytic systems gave the expected narrow MWD with Q 2 and high composition uniformity concerning monomeric units distribution, others gave a wider composition distribution and multimodal and broader MWD with Q even >10. The authors attributed this last result to different active centres. 

For example, Soga et al. > found, by examining propylene polymerization in toluene in the temperature range 0-65 °C with an apparently soluble catalyst such as tetrabenzylzirconium, that the isotactic index and the polydispersity of the polymer increased as the polymerization temperature increased. Furthermore, the value of Q > 30 was much greater than that predicted for homogeneous active centres. From these results the authors concluded that the catalyst should be made up of small invisible colloid-type particles. The same interpretation is valid for the surprising results (Q 40) obtainedfor polyethylene, in Isopar solution at 200 °C, with the originally soluble tetrabenzylzirconium-water catalyst. 

Accordingly, a broadening of MWD should be possible only by creating inhomogeneity in the active centre valences so as to promote different capabilities of monomer coordination and insertion and, thus, different propagation constants. The correspondence between narrow MWD and a unique oxidation state of the transition metal has been also pointed out by Christman for the ethylene polymerization with vanadium compounds-aluminum alkyls homogeneous systems. In this case, addition of a promoter causes re-oxidation of the deactivated sites (V") to the same identical initial ones (V "). 

This seems valid both for homogeneous and heterogeneous catalytic systems, remembering that, in the last case, the crystalline lattice could be sufficient to stabilize the active centre. 

With the TiCl —MgO catalyst polyethylene polydispersity was not influenced by either the type or concentration of the aluminum-alkjd, while the use of an aluminum alkyl with a higher reducing power, in the case of some MgClj-supported catalysts, tended to make active centres more homogeneous and to give a narrower MWD in the following order... 

As a consequence, a pseudo-homogeneous isothermal model has been assumed, consisting of mass balance equations on the gas phase and on the active centres The model equations are the following ... 

Van Koten and coworkers examined the permeabihty of nanofiltration membranes (SelRO-MPF-60 MWCO 400 g mol ) using coloured metalloden-drimers ([G0]-[G3]) of increasing molecular weight and size (=0.6-1.0 nm) in CHjClj [87]. The retention times were measured via UV-Vis spectroscopy ([Gl] fi/2=108 h [G2] fi/2=300 h [G3] fi/2>60 days). In this way the authors showed that dendrimers do not have to be exceptionally large for successful retention. Subsequently they fimctionahsed the support of choice with a catalyt-ically active centre instead of the dye. Nanofiltration membrane-capped immersion vials were developed and used to compartmentahse homogeneous dendritic catalysts. These catalytic systems could be regenerated and stored for months without losing their activity. 

We shall proceed with this review in the following way. First, we present the main facts known about the catalysts. Then at the end of this section we shall formulate those features of the active catalysts which are common to particular cases, in the hope that this can later help us to select from the published ideas the most probable explanation of the activity of catalysts for oxygenates, the most likely nature of active centres, and the most acceptable mechanism. However, before taking this last step, we shall discuss some relevant facts about CO adsorption, CO homogeneous reactions, and methanol synthesis. 

The closed sequence radical reaction introduces a multiplicative kinetic factor with respect to the initiation so that there is a certain analogy with homogeneous and heterogeneous catalysis, which is also characterized by the existence of closed sequences. However, a big difference exists between chain reactions and so-called catalytic reactions. In fact, in catalytic reactions, the total number of active centres is fixed, whereas that of chain reactions is determined by the competition between the initiation and termination reactions. The rate of a chain reaction is therefore a function of both the kinetic characteristics of the initiation, propagation and termination reactions. 

The kinetic model developed in [83] describes the dependence of the conversion on time and MW for butadiene polymerisation on homogeneous catalysts. Compounds with Co, Al, and H2O are assumed to participate in the formation of AC. Computational and experimental data for the conversion of butadiene are proved to correlate well with each other when polymerisation is carried out with the cobalt octanoate -diethylaluminium chloride - water catalytic system. However, this model considers only one type of active centre and does not provide an explanation for the increase of polybutadiene polymerisation with conversion growth. The polymerisation diagram and mathematical model with two types of AC have been proposed for butadiene polymerisation in the presence of a Li(H-C4H9) - diethylene glycol dimethyl ether catalytic system [84], This approach is suitable for the calculation of changes... 

There have been several theoretical studies on the olefin metathesis reaction and the structures of homogeneous catalysts [1-5]. However, we have not found examples of theoretical modelling of olefin metathesis active sites on heterogeneous catalysts. In the case of the heterogeneous molybdena catalysts, the active centres contain probably Mo [6,7], but other Mo valences are also possible (e.g., Mo [8]). 

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