Long-Branching in LDPE

As mentioned in Section 9.3, Jackson (141) has obtained estimates of the chain-transfer coefficient of the growing radical with polymer in the free-radical polymerization of ethylene, C,p, by choosing the value so as to fit the MWD. As the polymerization conditions for the polymers mentioned in Table 10.1 are not disclosed, it is necessary to choose typical conditions 220° C and 2000 atm will be selected. Under these conditions Ctp, the ratio of the rate constant for attack on polymer (per monomer unit) to that for propagation, in a homogeneous phase, was found to be about 4.0 x 10 3. This is in good agreement with the known transfer coefficients for the lower alkanes (160), when allowance is made for the differences in pressure and temperature (100). The relation between Ctp and k is  

Even in well-stirred continuous reactors operating under single-phase conditions (/60) there is a distribution of residence times for polymer molecules, so that different molecules have different probabilities of growing branches thus there will be a distribution of values of X in the product. If the reactor is not well-stirred or is operating under two-phase conditions a wider distribution of X will result. For several reasons a correlation of X with MW is to be expected, so that fractions from the same polymer sample may have different, and sometimes very different, values of X, as has in fact been found by several authors (42, 152, 155, 157). The assumption that X is constant, made by several authors, is thus a dangerous one unless it is known that the polymer was made under conditions which justify it. 

It is satisfactory that a number of the values of X shown in Table 10.1 are of the order of magnitude expected from Jackson s result, though lower values occur, and some values, especially those obtained using g =g%, are considerably higher, by an order of magnitude or more. This fact tends to confirm the conclusion arrived at above that is too low a value for the exponent of g0 this confirmation is only rather weak, because of the lack of information about the polymerization conditions used. 

The conclusion that x is not surprising in view of the suggestion of Berry and Casassa (32) referred to in Section 4, according to which x will exceed for molecules having any form but that of a star, a shape unlikely to occur in a muchbranched polyethylene to any significant extent 

Despite the considerable effort that has been expended on studying branching in polyethylene, it can hardly be claimed that it is at present possible to determine the degree of LCB in this polymer unambiguously. 

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