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.