A Method for Following Changes in Molecular Weight Distributions of Polymers on Degradation: Development and Comparison with Ultrasonic Degradation Experiments

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Abstract
When polymers are degraded by submitting them to shearing action, neither the probability of scission of a macromolecule, as a function of molecular weight (MW), nor the probability distribution of the lengths of the resulting fragments is known a priori. Information about these probabilities can be obtained by comparing observed changes in the molecular weight distributions (MWD) of degrading polymer with changes calculated from models. These models are based on assumed functions relating the probabilities mentioned to the MW of the polymer and that of the fragments. In order to make this comparison, equations are derived for various moments of the MWDs in terms of arbitrary initial MWDs and probability functions. Some simplified forms of these equations arising from chosen simple functions for the probabilities are also given. Data are presented to show that the precision of the weight-average MW calculated from gel-permeation chromatography (GPC) is about twice that of the number-average and z-average MW. On the basis of this observation, a particular index is recommended to indicate the shape of MWDs derived from GPC. This index, calculated from the experimental MWDs of degrading polystyrene as a function of degree of degradation, is compared with index curves computed from models with specified forms for the two probability functions. These comparisons suggest that this polymer has a minimum degradable MW of about 40,000. Finally experimental MWDs are shown to agree well with those calculated.