Schulz-Flory polymerization

Fig. 8 Fischer-Tropsch chain growth mechanism (Schulz-Flory polymerization mechanism). (View this art in color at WWW. dekker. com.)...

Selectivities. Hydrocarbon selectivity data were treated to test conformance to Schulz-Flory polymerization kinetics as outlined by Henrici-Olive and Olive (7) for Fischer-Tropsch catalysis. The pertinent correlation is ... 

A recent paper presented a Schulz-Flory polymerization mechanism for the synthesis (22). This scheme is a simplified form of SCG obtained by setting the branching parameter f equal to zero. 

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). ... 

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. 

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... 

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. 

Thus, Equation 27 is in this case a possible distribution function. It is of the type of the Schulz-Flory (25) distribution function. The expressions p and alternating polymerization (chain termination). The validity of the Schulz-Flory distribution function in this example of a polymerization with reversible propagation steps is evident. This type of distribution is always present if the distribution of the chain lengths... 

Flory polymerization kinetics (4). Henrici-Olive and Olivd (5) proposed the use of the related equation of Schulz (6). Over the last decade the Flory equation has been used frequently to describe product distributions in FT synthesis. The Friedel-Anderson (i) or Flory (4) approaches apply when the rates of propagation and termination are independent of carbon number. We do not attempt here to discuss all previous research on FT product distributions except to say that the literature contains many examples of product distributions that obey Flory kinetics within relative narrow carbon number ranges and many that do not. 

The F-T synthesis typically follows polymerization kinetics. The Anderson-Schulz-Flory equation describes the product distribution ... 

Figure 15 Anderson-Schulz-Flory plot for CO hydrogenation (dashed line theoretical plot for polymerization of Cj species solid line, experimentally observed values. See M. L. Turner, H. C. Long, A. Shenton, P. K. Byers, P. M. Maitlis, Chem. Eur. J., 1995, l,8j.

The experimentally obtained Anderson-Schulz-Flory (ASF) distribution (solid line) follows the theoretical values closely and was an early indication that the reaction to form the hydrocarbons was a type of polymerization, and indeed of Ci species. An interesting feature of the ASF plot is that it is not quite smooth but has a kink at A = 2 which comes below the curve (see Figure 15). The reason why substantially less ethane and ethylene than expected is formed has been widely debated it can occur if fewer free C2 species are produced or if the C2 fraction preferentially undergoes further reaction. The former explanation seems to be the more accepted one, in other words the rate at which surface-attached C2 undergoes further polymerization is faster than the rate of liberation of the free C2 hydrocarbons from the surface. 

These catalysts seem to be able to operate at low degrees of polymerization without giving the high yields of methane predicted by the Schulz Flory distribution. Activity maintenance and long-term catalyst performance remain to be proved. However, further research in this field may lead to stable catalysts giving a highly desirable distribution of liglit a olefin products [42]. 

Chains with monodisperse molecular weight distribution (Mw/Mn = 1.00) can occur in idealized conditions when all polymerizing centers initiate instantaneously and chain termination is absent. In these cases the catalyst is actually an initiator. These living polymerizations are quite rare among transition metal catalysts. More often, random chain termination leads to many chains formed per metal atom. A Schulz-Flory most probable distribution of polyalkene molecular weights (Mw/Mn = 2.00) is the result. In cases when more than one type of active site is present, bimodal or multimodal distributions of molecular weights result (Mw/Mn > 2.00). 

Free-radical polymerization with chain breaking exclusively by disproportionation or chain transfer yielding unreactive radicals produces a Schulz-Flory mole-fraction distribution. 

Any mechanistic proposal must comply with the following observations. (1) The Fischer-Tropsch hydrocarbon synthesis follows the formalism of polymerization kinetics with a Schulz-Flory distribution of the molecular weights. (2) a-Olefins and alcohols occur as the primary products. (3) The aliphatic final products are formed consecutively by hydrogenation of the olefins according to " C-labeling experiments [4 f, 30 b]. (4) Chain termination processes do not deactivate the catalyst centers because the chain-growth velocity stays constant for weeks. 

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