Random graph approach to multifunctional molecular networks

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.