Coloured random graphs explain the structure and dynamics of cross-linked polymer networks

Verena Schamboeck,Piet D Iedema,Ivan Kryven

doi:10.1038/s41598-020-71417-9

Verena Schamboeck, Piet D Iedema + Show 1 more

Open Access

https://doi.org/10.1038/s41598-020-71417-9

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Journal: Scientific Reports	Publication Date: Sep 3, 2020
Citations: 8	License type: open-access

Affiliation: University of Amsterdam, Utrecht University

Abstract

Step-growth and chain-growth are two major families of chemical reactions that result in polymer networks with drastically different physical properties, often referred to as hyper-branched and cross-linked networks. In contrast to step-growth polymerisation, chain-growth forms networks that are history-dependent. Such networks are defined not just by the degree distribution, but also by their entire formation history, which entails a modelling and conceptual challenges. We show that the structure of chain-growth polymer networks corresponds to an edge-coloured random graph with a defined multivariate degree distribution, where the colour labels represent the formation times of chemical bonds. The theory quantifies and explains the gelation in free-radical polymerisation of cross-linked polymers and predicts conditions when history dependance has the most significant effect on the global properties of a polymer network. As such, the edge colouring is identified as the key driver behind the difference in the physical properties of step-growth and chain-growth networks. We expect that this findings will stimulate usage of network science tools for discovery and design of cross-linked polymers.

Highlights

Step-growth and chain-growth are two major families of chemical reactions that result in polymer networks with drastically different physical properties, often referred to as hyper-branched and crosslinked networks
We introduce an evolving network model with an arbitrary degree distribution to show that the different effects induced by the two most common polymerisation processes on the resulting materials are provoked by the presence or absence of memory in the underlaying network structures
The nodes represent the monomer units and the edges correspond to the covalent bonds, which are formed during the polymerisation process

Summary

Introduction

Step-growth and chain-growth are two major families of chemical reactions that result in polymer networks with drastically different physical properties, often referred to as hyper-branched and crosslinked networks. In contrast to step-growth polymerisation, chain-growth forms networks that are history-dependent Such networks are defined not just by the degree distribution, and by their entire formation history, which entails a modelling and conceptual challenges. We show that the structure of chain-growth polymer networks corresponds to an edge-coloured random graph with a defined multivariate degree distribution, where the colour labels represent the formation times of chemical bonds. These models represent a monomer unit as a vertex with a defined number of half-edges, and rely on the assumption that any pair of half-edges has independent and identical probability to be connected (the i.i.d. assumption) Such models predict molecular size distributions and the gelation time for several special cases of monomer functionality. Successful such a technique proves to be for step-growth polymer networks, it cannot explain the networks produced by chain-growth procedure due to history dependence of the latter

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