Schulz-Flory statistics

The nickel-catalyzed Shell higher olefin process (SHOP) is of major industrial importance [9,11]. Ethylene is converted to a-olefins with a statistical distribution in which the lower oligomers are favored (so-called Schulz Flory distribution). This is carried out at 80-120 °C and 70 140 bar in the presence of a nickel catalyst with phosphine ligands such as Ph2PCH2COOK. The product mixture is separated into C4 io, C12-18, and C20+ fractions by distillation. 

The polycondensation processes generally produce polyamides that are mixtures of polymer molecules of different molecular weights, the distribution of which usually follows a definite continuous function according to the most probable distribution model by Schulz-Flory [3]. This distribution function may, in principle, be derived from the kinetics of polymerization process, but is more readily derived from statistical considerations. In this case, the extent... 

The chain lengths of the hydrocarbons obey a statistical distribution named after Anderson, Schulz, and Flory, given by... 

A single polymer particle contains a statistically large number of polymers, of the order of 1013. The corresponding MWD can be described with the Flory-Schulz equation only if the single-site type is guaranteed, and under constant reaction conditions, i.e., constant temperature, pressure, and concentrations near the active sites. However, in an industrial polymerization process, a particle often encounters different conditions over its lifetime. In... 

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