Single Particle Models - Mass- and Heat-transfer Resistances

Notice that the average number of LCBs per chain can vary from 0 when a = 0 to infinity when a = 1. Since most long-chain-branched polyolefins made with coordination catalysts are only sparsely branched, with values of B rarely exceeding unity, the upper limit of the paramter a should be considered only as a theoretical possibility never to be reached in practical situations. 

Chain length averages and polydispersity index for the whole polymer can also be related to the parameters a or B via Eqs. (36)-(38). 

These equations demonstrate that the polydispersity index of long-chain-branched polyolefins is always greater than 2 and that the chain length averages increase with an increasing number of LCBs per chain. 

It is also interesting to calculate the mass fraction of polymer populations containing i LCBs per chain, m , by Eq. (39). 

Similarly, an extension [Eq. (40)] of Stockmayer s distribution can be derived for binary copolymers containing LCBs formed by terminal branching [45]. 

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Single Particle Models - Mass- and Heat-transfer Resistances 399... 

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