Flory-Schulz

The production of hydrocarbons using traditional Fischer-Tropsch catalysts is governed by chain growth or polymerization kinetics. The equation describing the production of hydrocarbons, commonly referred to as the Anderson-Schulz-Flory equation, is ... 

The FTS mechanism could be considered a simple polymerization reaction, the monomer being a Ci species derived from carbon monoxide. This polymerization follows an Anderson-Schulz-Flory distribution of molecular weights. This distribution gives a linear plot of the logarithm of yield of product (in moles) versus carbon number. Under the assumptions of this model, the entire product distribution is determined by one parameter, a, the probability of the addition of a carbon atom to a chain (Figure 4-7). ... 

The catalytic single-step Alfen process has a good space-time yield, and the process engineering is simple. The molecular weight distribution of the olefins of the single-step process is broader (Schulz-Flory type of distribution) than in the two-step Alfen process (Poisson-type distribution) (Fig. 2). As a byproduct 2-alkyl-branched a-olefins also are formed, as shown in Table 6. About... 

A theoretical study of the m.w.d. broadening during the SPP of a semi-crystaline polymer showed that for linear structures, according to the Schulz-Flory relationship, no narrowing or broadening of the m.w.d. is to be expected (11). 

Reaction mechanisms and molar mass distributions The molar mass distribution of a synthetic polymer strongly depends on the polymerization mechanism, and sole knowledge of some average molar mass may be of little help if the distribution function, or at least its second moment, is not known. To illustrate this, we will discuss two prominent distribution functions, as examples the Poisson distribution and the Schulz-Flory distribution, and refer the reader to the literature [7] for a more detailed discussion. 

Figure 1 Poisson and Schulz-Flory distribution with identical (N)n = 50. The arrows indicate (,N)w = 51 (Poisson) and (N)w = 100 (Schulz-Flory).

From Table 2 it can also be observed that the selectivity towards different hydrocarbon groups strongly depended on the acid properties of solids. Large amounts of C4 and C6 olefins were obtained for the mesoporous NiMCM-41 and NiMCM-48 catalysts with the lowest acid site concentration. In this case, a near Schulz-Flory-type product distribution (C4>C6>C8>Cio) was observed. The increase in acid site density (for the catalysts NiY, NiMCM-36, NiMCM-22) results in decrease of C 6/C8 ratio. These results are in agreement with the reaction network proposed in Scheme 1. 

When determining the product selectivities, all compounds of equal carbon numbers (paraffines, olefins, isomers, and oxygen compounds) were summarized to one product fraction. The chain growth probability was determined by the Anderson-Schulz-Flory (ASF) distribution ... 

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... 

The carbon number distribution of Fischer-Tropsch products on both cobalt and iron catalysts can be clearly represented by superposition of two Anderson-Schulz-Flory (ASF) distributions characterized by two chain growth probabilities and the mass or molar fraction of products assigned to one of these distributions.7 10 In particular, this bimodal-type distribution is pronounced for iron catalysts promoted with alkali (e.g., K2C03). Comparing product distributions obtained on alkali-promoted and -unpromoted iron catalysts has shown that the distribution characterized by the lower growth probability a, is not affected by the promoter, while the growth probability a2 and the mass fraction f2 are considerably increased by addition of alkali.9 This is... 

The total product spectrum for a typical precipitated iron catalyst in an LTFT process is shown in Figure 13.3. Constructing an Anderson-Schulz-Flory (ASF) plot from the total product spectrum does not give a straight line and can conveniently be separated in two distinct regions, one from C, to C8 and another from C20 onward (as shown in Figure 13.4). The light olefins and... 

The product distribution frcm the Fischer-Tropsch reaction on 5 is shown in Table I. It is similar but not identical to that obtained over other cobalt catalysts (18-21,48, 49). The relatively low amount of methane production (73 mol T when compared with other metals and the abnormally low amount of ethane are typical (6). The distribution of hydrocarbons over other cobalt catalysts has been found to fit the Schulz-Flory equation [indicative of a polymerization-type process (6)]. The Schulz-Flory equation in logarithmic form is... 

Figure 1. A Schulz-Flory-type representation for catalysts derived from Curve 1, in situ decomposition of the Fe. (CO)I2-NaY adduct Curve 2, ex situ decomposition of the Fe3(CO)n-NaY adduct leading to large Fe crystallites (see text) initial pressure, 20 bar H2/CO = 4/1 reaction temperature, 250°C...

Figure 3. A Schulz-Flory-type plot for catalyst derived from CpFe(CO)2 2-NaY adduct initial pressure, 20 bar H2CO = 4/1 reaction temperature, 250°C...

Figure 9.4. Typical Schulz-Flory distribution fory=0.85...

Figure 9.5. Comparison of Poisson and Schulz-Flory distribution, see text...

The sensitivity of the product distribution for small changes of these parameters can also be exploited to our advantage the product distribution can be easily adjusted to changes of the demand for certain oligomers, but only within the limits of Schulz-Flory distributions ... 

For entries 3-5 the increase in molecular weight observed can be assigned to the increase in the rate of insertion and the rate of termination remains practically the same. An increase of the rate of polymerisation with the steric bulk of the ligand is usually ascribed to the destabilisation of the alkene adduct while the energy of the transition state remains the same. As a chain transfer reaction presumably P-hydride elimination takes place or traces of water might be chain transfer agents. Chain transfer does occur, because a Schulz-Flory molecular weight distribution is found (PDI 2, see Table 12.2). Shorter chains are obtained with a polar ortho substituent (OMe, entry 2) and in methanol as the solvent, albeit that most palladium is inactive in the latter case. 

Already in the study of linear chain molecules it has become evident that the shape of the molar mass distribution and its width provide a valuable guide to the mechanism of chain formation. Best known are the most probable (or Schulz-Flory) distribution and the narrow Poisson distribution. The former is often... 

Schaefgen and Flory [79] were the first to observe this effect. They prepared star-branched polyamides by co-condensation of A-B types of monomers with central units which carried/-functional A groups. By this technique star molecules were obtained in which the arms are not monodisperse in length. They rather obeyed the Schulz-Flory most probable length distribution with polydis-persity index However, the coupling of f arms onto a star center leads... 

The molar mass distribution of branched materials differ most significantly from those known for Hnear chains. To make this evident the well known types of (i) Schulz-Flory, or most probable distribution, (ii) Poisson, and (iii) Schulz-Zimm distributions are reproduced. Let x denote the degree of polymerization of an x-mer. Then we have as follows. 

Zirconia-modified silica impregnated with Co2(CO)s and activated under H2 at 300 °C renders a catalyst more active and selective to diesel fraction, in the CO hydrogenation reaction, than that conventionally prepared from a nitrate salt solution. The selectivity patterns followed a Schulz-Flory distribution and catalysts prepared from carbonyl precursor exhibited low water-gas shift activity [146]. 

Note 2 In the literature, this distribution is sometimes referred to as the Flory distribution or the Schulz-Flory distribution. 

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