Chain growth probability factor

The description of the product distribution for an FT reaction can be simplified and described by the use of a single parameter (a value) determined from the Anderson-Schulz-Flory (ASF) plots. The a value (also called the chain growth probability factor) is then used to describe the total product spectrum in terms of carbon number weight fractions during the FT synthesis. In the case... 

As indicated in Figure 10.2, there is a distinct change in the slope of the line at carbon numbers 8 to 12, and this has also been observed by other researchers.2-3 This change in the slope cannot be explained by the ASF model, which is based on the premise that the chain growth probability factor (a) is independent from the carbon number. Some further developments of the ASF model by Wojciechowski et al.3 made use of a number of abstract kinetic parameters for the calculation of a product spectrum. Although it still predicts a straight line for the a plot, they suggested that the break in the line is due to different mechanisms of chain termination and could be explained by the superposition of two ideal distributions. This bimodal distribution explained by two different mechanisms... 

There is practically no difference in the polydispersity between PMMA samples prepared in the presence of the diamagnetic (18-electron) and paramagnetic (17-electron) closo complexes 4 and 5, respectively. On the contrary, steric factors have a quite noticeable effect on the chain propagation step and the macromolecular characteristics of the samples. Thus, if the phosphine groups at the metal center are linked via methylene bridges (complexes 4 and 5), favorable steric conditions for controlling the polymer chain growth probably occur that lead to the formation of polymers with MWDs much narrow than in the case of complex 2. 

One of the best of these schemes (10, II), SCG (simple chain growth), involved one-carbon addition to one end of the growing chain at the first carbon with a probability a and to the second carbon with a probability af, if addition had not already occurred on this carbon. The SCG scheme assumed that the growth constants were independent of carbon number and structure of the growing chain, a situation that is fortuitous rather than expected. For a given carbon number, the ratios of branched to normal hydrocarbons are f or 2f for monoethyl isomers and P or 2P for dimethyls the factor one or two depends on whether the species can be produced in one or two ways. This simple mechanism predicted carbon number and isomer distributions moderately well and also seemed consistent with the tagged alcohol incorporation studies of Emmett, Kummer, and Hall (12,13,14). SCG does not produce ethyl-substituted carbon chains, which were subsequently found to be present in about the same concentration as dimethyl species (15,16). 

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. 

The nuclear chain reaction can be modeled mathematically by considering the probable fates of a typical fast neutron released in the system. This neutron may make one or more coUisions, which result in scattering or absorption, either in fuel or nonfuel materials. If the neutron is absorbed in fuel and fission occurs, new neutrons are produced. A neutron may also escape from the core in free flight, a process called leakage. The state of the reactor can be defined by the multiplication factor, k, the net number of neutrons produced in one cycle. If k is exactly 1, the reactor is said to be critical if / < 1, it is subcritical if / > 1, it is supercritical. The neutron population and the reactor power depend on the difference between k and 1, ie, bk = k — K closely related quantity is the reactivity, p = bk jk. i the reactivity is negative, the number of neutrons declines with time if p = 0, the number remains constant if p is positive, there is a growth in population. 

The growth scheme used in this work is a modification of growth scheme B from Anderson et al. (I) Addition of the carbon atom is permitted on the first two carbon atoms on one end of the growing chain and on substituents on the first three carbon atoms. Results are not very different if branching is allowed on the first three carbon atoms of a chain (8). The chain branching factor is /, as usual, except in the formation of quaternary carbons in which case 0.1 / is used because of the low probability of substitution on tertiary carbon atoms. 

There is a striking resemblance between Permeation (Chap. 18) and Crystallisation. Just as Permeability is the product of Solubility and Diffusivity (P = SD), the rate of crystallisation is the product of Nucleability (or probability of Nucleation, also called "nucleation factor") and Transportability (Self-diffusivity of chains or chain fragments, also called "transport factor"). This statement is valid as well for the primary nucleation in melt or solution, as for the growth of the crystallites (which is a repeated sequence of surface nucleation and surface growth). 

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