Chain-length-independent growth process

The FT growth mechanism implies that only methane (n = 1) and polymethylene (n — 00) can theoretically be obtained with 100% selectivity. Intermediate products of a specific carbon number range can only be made at substantially lower selectivities. A way to circumvent this limitation is to combine the chain-length-independent growth process with a selective cracking process, which has to meet the following two conditions ... 

Note that here both the probabilities of growth and the probability of termination are independent on the length of the chain. This is in fact an alternate notation of a Markov process and is a cascade. Each term 5... e is associated with the probability of the formation of a polymer chain of the respective degree of polymerization that is p P). It is immediately seen that because r = 1 the total probability for all the chains generated becomes 1. On the other hand, from the second equation in the set (17.1), r can be calculated to be r = e/ — m). This can be inserted into the first equation in the set (17.1). 

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