Determination of Monomer Transfer Constants from MWD

The traditional method of determining the monomer transfer constant is the Mayo method [294,295], where the inverse of the number average chain length Pn is extrapolated to zero polymerization rate. To obtain reliable values, one needs to measure rather large P values to high precision that can then be extrapolated to zero polymerization rate. In addition, linear extrapolation is not guaranteed if bimolecular termination reactions are chain-length-dependent [296]. 

A simple alternative method was proposed by Gilbert et al. [296, 297] to determine the chain transfer constants based on the chain length distribution (CLD). If the dominant chain termination mechanism is chain transfer to monomer, the instantaneous numerical MWD (the number fraction distribution) is given by  

In many emulsion polymerizations, the monomer/polymer ratio is kept constant during Interval II, and the accumulated MWD is approximately equal to the instantaneous distribution. Equation 84 shows that the Cm value can be determined from the slope of the InN(P) versus P plot. 

In a zero-one system in which a radical has just entered a polymer particle containing one polymer radical, and is terminated instantaneously, the number fraction distribution in the absence of a polymer transfer reaction is given by  

It is evident from Eq. 85 that the condition =l/(kp[M]pFe) Cm is needed to apply the CLD method to emulsion polymerization. Note that the radical entry rate may be increased through the radical exit. Even when these conditions are satisfied, a higher polymer concentration than for the corresponding bulk polymerization may result in more occurrences of the polymer transfer reaction. 

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