Simulation of size exclusion chromatography for branched polymers formed by simultaneous long-chain branching and random scission

Abstract

In free-radical olefin polymerization, polymer transfer reactions can lead to chain scission as well as to the formation of long-chain branches. The dimensions of branched polymers so formed are investigated theoretically, by focusing our attention on the effects of scission frequency that is often difficult to determine. Scission reactions decrease the weight-average molecular weight significantly. When the polymer molecules are fractionated by the degree of polymerization (DP), however, the averages of branching density ρP and the mean-square radius of gyration of polymers with DP = P, P, are essentially unchanged, as long as the scission frequency is not very large. In a simple relationship between the ratios g and g' of radii of gyration and hydrodynamic radii, g' = gb, the value of b may change as a function of DP, and a simplified model function b = A log P + B was used to investigate the elution curve of size exclusion chromatography (SEC). It is shown that, although the molecular weight distribution (MWD) calibrated relative to standard linear polymers in SEC is much narrower than the true MWD, the use of a light scattering photometer to determine the absolute weight-average molecular weight within the elution volume makes the obtained MWD very close to the true one. On the basis of the P vs. P relationship, the calibrated MWD can be converted reasonably well to the true MWD. This simplified transformation method can be applied without knowing the scission frequency or the DP dependence of b. Once the true MWD is successfully estimated, a reliable parameter for the scission reaction can be determined.