Random Graph Approach to Multifunctional Molecular Networks

Abstract

Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The process does not account for spatial positions of the monomers explicitly, yet the Euclidean distances between the monomers are derived from the topological information by applying self-avoiding random walks. This allows favoring reactivity of monomers that are close to each other, and to disfavor the reactivity for monomers obscured by the surrounding. As a result, the model is applicable to large time scales. The phenomena of conversion-dependent reaction rates, gelation, microgelation, and structural inhomogeneity are predicted by the model. Resulting nonhomogeneous network topologies are analyzed to extract such descriptors as: size distribution, crosslink distances, and gel-point conversion. Furthermore, new to the molecular simulation community descriptors are suggested that are especially useful when explaining evolution of the gel as being a single molecule: local clustering coefficient, network modularity, cluster size distribution.