Branching in Continuous Polymerizations

LCB affects the properties of LDPE, low density polyethylene made by free-radical polymerization see Section 10. The continuous polymerization is carried out in stirred reactors or in tubes several authors (5, 90, 92) have considered the effects of LCB on MWD in perfectly-stirred tank reactors. 

Beasley (5) succeeded in obtaining an expression for the MWD in closed form, assuming termination to be exclusively by disproportionation  

Beasley s derivation contains, however, as well as some probably trivial mathematical approximations, certain implicit assumptions that make this conclusion doubtful. He did not present a detailed kinetic scheme for the polymerization reaction, but it is implied by his Eq. (2) that the formation of branches is instantaneous after a new radical site has been produced on the dead polymer. That is, no account is taken of the fact that some growing radicals will be removed from the reactor before the growth of the new branch is completed. The mean time for growth of a branch is 1 /akp(M) and the ratio t of the mean residence time V/q to this time, Le.  

Nicolas has also considered batch and tubular reactors and a cascade of stirred vessels he finds, in agreement with other workers, that a batch process produces narrower distributions than perfectly-stirred continuous reactors, but he finds that tubular reactors (assuming no axial or radial mixing) always produce material of infinite Pw, i.e. gel. 

Jadcson and co-workers (92) have used a variant of the method of generating functions to obtain moments of the MWD for the product from a perfectly-stirred continuous tank reactor. In its simplest form, this method consists in setting up a function (the generating function ) of a dummy variable, u say, having a power series expansion near u — 0 in which the coefficient of k is the concentration of n-mer in more elaborate forms of the method, other dummy 

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