Schulz-Flory-type distribution

The nickel concentration in the catalyst system is in the range 0.001-0.005 mol% (approx. 10-50 ppm). The oligomerization is carried out in a series of reactors at temperatures of 80-140°C and pressures of 7-14 MPa. The rate of the reaction is controlled by the rate of catalyst addition [19]. A high partial pressure of ethylene is required to obtain good reaction rates and high product linearity [11]. The linear a-alkenes produced are obtained in a Schulz-Flory-type distribution with up to 99% linearity and 96-98% terminal alkenes over the whole range from C4 to C+ (cf. Table 2) [23]. 

The oligomers obtained with these systems follow a Schulz-Flory type distribution. The nickel catalyst complexes can be divided into two groups nickel(ll) compounds modified with alkyl or hydride main-group metal derivatives (Ziegler-Natta type catalyst) and chelated nickel compounds with a Ni-C bond. 

Titanium and zirconium based catalysts oligomerize ethylene into a mixture of a-olefin ranging from C4 to C30 with a Schulz—Flory type distribution. The content of linear a-olefin is nearly 100% provided conversion is low enough (a high concentration of ethylene has to be maintained during the whole reaction). 

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... 

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. 

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... 

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... 

Metals such as Fe, Co, Ni, or Ru on alumina or other oxide supports convert CO and H2 to hydrocarbons. Using different catalysts and reaction conditions either CH4, liquid hydrocarbons, high molecular weight paraffins, methanol, higher alcohols, olefins, and aromatics can be obtained, though rarely (with the exception of CFL, and methanol) with high selectivity. Hydrocarbons typically exhibit a Schulz-Flory type molecular weight distribution. 

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. 

The catalysts belonging to the second class are especially reactive towards ethylene, and afford mixtures of nearly pure linear a-olefins ranging from C4 to C30 (chain length distribution of the Schulz—Flory type). These do not catalyze a double-bond shift. 

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... 

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. 

The termination step for 1-alkene formation is now the reaction of the surface alkenyl with surface H instead of the p-elimination step. Chain branching can proceed by the involvement of allylic intermediates. Since this new mechanism involves different types of reactions to form C2 and C2< hydrocarbons, it is not expected that the amounts of C2 products will lie on the normal curve of the Ander-son-Schulz-Flory distribution. 

Deviations from the Schulz-Flory distribution arc possible if secondary reactions such as cracking on acidic supports or insertion of product olefins into the growing chain occur [42]. It has been reported recently that the Schulz Flory constant a has a tendency to increase from C3 to C, [45]. This may be the reason why the values found are usually higher for methane and lower for Cj and C) j.)., as would be expected for an ideal Schulz-Flory distribution [40]. Investigations by Madon et at. on partly sulfur-poisoned iron/copper catalysts revealed a dual product distribution. This was explained by the assump tion of > 2 types of active sites for hydrocarbon chain formation, each with a slightly different value of the chain growth probability [46]. 

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). 

Another class of problems of which only the surface has been scratched is offered by mixed systems in which a Fischer-Tropsch type catalyst is combined with a solid acid such as a zeolite. Such systems have been used in recent attempts to produce narrower product distributions, and indeed deviations from the normal Schulz-Flory distribution have been reported (82-84). However, at the closing date of this review it was still unclear whether the results are characteristic of the running-in or of the steady-state behavior of the catalyst. In particular, the selective retention of the heavier products within the pores of the support might falsify the apparent catalyst selectivity. Only accurate mass-balancing and/or steady-state data can provide information on true product patterns unspoiled by this running-in phenomenon. 

This is the distribution which is expected of a single site type. It produces a polydispersity of MW/MN = 2.0. Metallocene catalysts usually produce such a distribution, as shown in Figure 1. It means that all of the sites behave identically, because they all have the same chemical structure. Ziegler catalysts usually produce a polydispersity of about 4.0, meaning that there is a greater variety of site types. To reproduce the Ziegler MW distribution, at least two to four Schulz-Flory distributions must be combined. Thus, one could say that Ziegler catalysts contain at least two to four unique site types. 

One can deconvolute these two MW distributions into seven Schulz-Flory distributions which might be thought of as contributed by seven distinct types of active sites, producing seven different MW polymers of PDI = 2.0. There is no basis for choosing seven components other than the fact that seven is the minimum number of MW curves needed to faithfully reproduce the original parent MW curve when the seven components are combined in the needed proportions. These seven components are shown in Figure 43, along with the thus reproduced 600 °C parent MW curve. 

Three types of polymer distribution are typically observed in samples obtained from polymerization logarithmic normal, Poisson, and Schulz-Flory distributions. The Poisson distribution can be very narrow and occurs when a constant number of polymer chains grow simultaneously and addition of the next monomeric unit is independent of previous units and is found in anionic polymerization (qv). The Schulz-Flory distribution, typical of radical polymerization (qv), arises when a constant number of chains growing ends exist and when termination and chain initiation processes are also active. This is in contrast to the Poisson distribution. A logarithmic-normal distribution is found for the polymerization of polyethylene and polypropylene (90,91). 

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