  Many research fields, reaching from social networks and epidemiology to
biology and physics, have experienced great advance from recent developments in
random graphs and network theory. In this paper we propose to view percolation
on a directed random graph as a generic model for step-growth polymerisation.
This polymerisation process is used to manufacture a broad range of polymeric
materials, including: polyesters, polyurethanes, polyamides, and many others.
We link features of step-growth polymerisation to the properties of the
directed configuration model, and in this way, obtain new analytical
expressions describing the polymeric microstructure. Thus, the molecular weight
distribution is related to the sizes of connected components, gelation to the
emergence of the giant component, and the molecular gyration radii to the
Wiener index of these components. A model on this level of generality is
instrumental in accelerating the design of new materials and optimizing their
properties.
