Random graph approach to multifunctional molecular networks

TL;DR

This paper introduces a random graph model for multifunctional molecular networks that naturally predicts phenomena like gelation and micro-gelation, providing new insights into network topology evolution.

Contribution

It presents a novel random graph approach that models reactivity based on topology, predicting key phenomena without prior assumptions and introducing new descriptors for network analysis.

Findings

Predicts gelation and micro-gelation phenomena naturally

Analyzes non-homogeneous network topologies and their properties

Introduces new descriptors for network evolution understanding

Abstract

Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The random graph model favours reactivity for monomers that are positioned close in the network topology, and disfavours reactivity for those that are obscured by the surrounding. The phenomena of conversion-dependant reaction rates, gelation, and micro-gelation are thus naturally predicted by the model and do not have to be imposed. Resulting non-homogeneous network topologies are analysed to extract such descriptors as: size distribution, crosslink distances, and gel-point conversion. Furthermore, new to the molecular simulation community descriptors are invented. These descriptors are especially useful for understanding evolution of pure gel, amongst them: cluster coefficient, network modularity, cluster size distribution.