Probability of chain growth

Various mechanisms have been proposed for the FT reaction (j ) (2) and (4- ). A generalized mechanism is illustrated in Figure T. Irrespective of which mechanism is correct, or is dominant, there is general agreement that stepwise chain growth is involved. This inevitably results in a wide carbon number distribution of products, the particular distribution being determined by the probability of chain growth (<1). The calculated effect of different values on... 

Many studies address the effect of promoters such as K and Mn on Fe-based catalysts. Dry et al (23) suggest that the alkali promoter weakens the C-O bond and enhances its rate of dissociation it also strengthens the metal-C bond, the surface residence time of adsorbed chains, and the probability of chain growth. In the presence of Mn, termination to olefins predominates (24-26). Our results suggest that we must also consider the effect of promoters and of catalyst treatment on a-olefin readsorption. Perhaps the presence of alkali also enhances a-olefin readsorption reactions leading to heavier products whereas Mn does not. 

Table I. The Reaction Rate Constants for Propagation and Termination Expressed as a Function of Turnover Frequencies, Probability of Chain Growth, Steady-State Surface Coverage of the Precursor A, and the Equilibrium Constant K.

Table II. Minimum Reaction Rate Constants for Propagation Caknlated from the Data of Turnover Frequency and Probability of Chain Growth Published in the...

For anionic polymerizations in protic media, you get the same expressions as those obtained for free radical polymerization with termination by disproportionation (p is still the probability of chain growth, but now 1 -p is the probability of chain transfer). Again, the averages and distributions you can obtain are only valid for low degrees of conversion. For cationic polymerization, there are several types of transfer and termination reactions that occur m most reactions, so you... 

Fig. 13. The Fischer-Tropsch reaction produces homologous series in logarithmic distribution, as illustrated here by alcohols (Anders et al, 1974). From C2 upward, successive homo-logues form in fixed, molecular ratio C +t/C = a, where a is the probability of chain growth, typically 0.6-0.9. Interstellar cyanoacetylenes in the Taurus Molecular Cloud 1 likewise show a logarithmic distribution, of very similar slope (0.52 vs 0.59 for the FTT alcohols). Presumably they, too, formed by surface catalysis, rather than by gas-phase reactions...

Krishna and Bell (299) described the results of their steady-state tracing experiments by the model shown in Fig. 31. The scheme is in accord with the Anderson-Schulz-Flory distribution of products, based on chain growth by the successive addition of monomers s to chain fragments C s- is different from Ci,s. ft is assumed that the probability of chain growth a is not a function of n, where... 

It has been shown that surface basicity of iron-based catalysts greatly affects probability of chain growth.5 7 Alkali metal incorporation promotes the formation of higher carbon number molecules. As described in Dry s review,7 iron-based catalysts are prepared by precipitation techniques and promoted with Cu, K20, and Si02 (typical composition 5 g of K20, 5 g of Cu, and 25 g of Si02 per lOOg of Fe). This type of catalyst is well suited for heavy liquid fuels produced from a low-temperature... 

Fig. 9 Fischer-Tropsch chain growth mechanism (selectivity as a function of the probability of chain growth). (View this art in color at www.dekker.com.)...

The chain growth mechanism of the FT reaction appears to involve stepwise addition of primary carbon atom surface complexes (ref. 2-3). A wide product spectrum is hence inevitable. The probability of chain growth can, however, be manipulated by changing the catalyst formulation, or the temperature, or the gas composition (ref. 2). Thus it is possible to vary the CH selectivity from 1 to 100% or that of the "hard" wax from zero to over 50%. (The IBP of "hard" wax is 500 °C and it contains molecules with carbon numbers up to at least 250.) As the probability of chain growth increases, the intermediate products pass through maxima, about 50 % for gasoline and about 25 % for diesel fuel (ref. 2). 

The first stage, Heavy Paraffin Synthesis (HPS), converts hydrogen and carbon monoxide into heavy paraffins by the Fischer-Tropsch process. The product distribution is in accordance with Schultz-Flory polymerization kinetics, which is characterized by, the probability of chain growth. 

If it is assumed that the probability of chain growth (a) is independent of the hydrocarbon chain length, then the product distribution can be calculated for different values of a. The results of such calculations ((7), p. 215, (20)) show that as observed in practice (Figs. 5 and 6), all the intermediate carbon number cuts go through maximum as the probability of chain growth increases. There is a reasonable agreement between the calculated maximum and the experimental maximum but not in the case of the C2 hydrocarbons (the calculation predicts a maximum selectivity of about 30%, whereas in practice, it never exceeds about 20%). This misfit is discussed in the section FT Surface Reactions and Mechanisms. ... 

The temperatures indicate the boiling points of the respective product fractions at 1 bar. Alcohols, aldehydes, ketones, and acids dissolved in the water phase. Anderson-Schulz-Flory probability of chain growth. 

Cobalt Catalysts. For Co catalysts, it has been reported that when the P 2/Pco ratio was lowered, the FT selectivity shifted to higher molecular mass products (14,87). This is similar to LTFT Fe catalysts (see the section Iron Catalysts under Gas Composition and Pressures ). However, contrary to LTFT Fe catalysts, but similar to HTFT Fe catalysts, increasing the pressure over Co catalysts increased the probability of chain growth (88). In a more recent study with Co supported on alumina, it was fovmd that the wax selectivity increased from about 0% at 0.2 MPa to about 60% at 4.0 MPa (52). The effect of pressure on a Ru catalyst is similar (48). Combining the observed effects of the Pna/ co ratios and total pressures, the selectivity of Co catalysts might be proportional to a factor such as P jPco, where r < 1. 

As is mentioned in the section Overall Product Distributions, the C2 compounds and methane invariably do not fall on the ASF plots. The C2 falls below the line, and the Ci, particularly so for Co catalysts, falls above the line. (The ASF deviations have been discussed in chapters 3 and 8 of Reference 7). An isolated CH2 monomer (see Fig. 12a) is likely to be rapidly hydrogenated and this could explain the higher than expected methane 3delds. One of the reasons for the low levels of C2 compounds could be their reincorporation into growing chains. Alternatively, if the C2 surface specie is taken as the adsorbed ethylene, the addition of another CH2 could occur on either side of it, which would increase the probability of chain growth (see Fig. 12b). For C3 and higher adsorbed alkenes, however, a CH2 group, for steric hindrance reasons, is more likely to attach to the open side of the adsorbed alkene (see Fig. 12c). 

The probability of chain growth of a species with carbon number n is defined... 

Figure 6.11.2 Product distribution of Fischer-Tropsch synthesis as calculated by Eq. (6.11.15) for different values of the probability of chain growth a. ...

The FTS product distribution is determined by the probability of chain growth, which is the ratio of the rate of propagation to the overall reaction rate. 

Ethylene oligomerization catalyzed by AI-, Zr-, and Ni-complexes follows a so-called insertion/elimination mechanism that results in the production of 1-alkene mixtures of different chain lengths. The mechanistic reason for this product distribution is the fact that each metal-alkyl complex shows the same probability of chain growth independent of the chain length of the attached alkyl group. 

In order to derive the expression of the probability of chain growth from a diamine unit to next diepoxy unit is considered in terms of the states of diamine unit and the count of the... 

The paraffinic hydrocarbons produced via the FT reaction are highly linear. This implies that the synthesis reaction can be regarded as a stepwise addition of a Ci segment to the end of an existing chain. Since atoms of the alkyl chain remote from the end will hardly be capable of influencing this reaction, it is plausible that the relative probabilities of chain growth and chain termination (a and 1 - a, respectively) will be independent of the... 

Sie et al. (1988) have derived a relation that gives the maximum a value permissible, and the limits of operating pressure, temperature and conversion level, ensuring trouble-free fluid-bed operation. For the synthesis of a product following AFS kinetics with a probability of chain growth a, the condition for operation above the hydrocarbon dew point can be stated as... 

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