Polymer Molecular Weight Distributions: A Tutorial on Transformations between Number Density, Mass Density, and Linear/Logarithmic Axes

The demand for plastic has made nonbiodegradable plastic waste a global environmental problem. Chemical processes for polymer upcycling aim to convert plastic waste into value-added products. Many research efforts draw insights about the kinetics and mechanism of depolymerization reactions from the evolving molecular weight distribution (MWD). However, MWDs are reported in several different representations: as fractional-mass distributions or fractional-molar distributions, and on linear or logarithmic molecular mass scales. Conversion from one representation to another can dramatically change the appearance of the MWD. This tutorial discusses some common techniques for molecular weight characterization and quantitative interpretations for the raw data. We provide formulas to transform between representations of the MWD data, to change variables within population balance equations that predict time evolution of the MWD, and to create composite MWDs (with uncertainty estimates) from experiments in different but overlapping molecular weight ranges.