Modeling emerging polymeric and biological networks with random graphs

The term polymer describes a large class of molecules with a wide range of physical and mechanical properties. In radical polymerization, a polymer starts from small radical-containing molecules that react with monomer molecules, creating larger molecules in the process. The pattern in which the monomer units are connected, the topology, is the most important determining factor for polymer properties The analysis and property prediction of these large molecules is a challenging task and requires specialized mathematical modeling tools. In this thesis, a random graph (RG) model is used to predict polymer network topologies. By assuming that monomers and crosslinks are represented as nodes and edges, the polymer is accurately described as a network. Hence, the topological properties of the network are representative for the polymer, such as the emergence of a giant component. The RG model is paired with an automated reaction network generation (ARNG) model, which provides the essential reaction kinetics based on experimental data or atomistic models. The combined ARNG-RG model is applied to several network forming processes: autoxidation polymerization of linseed oil and ethyl linoleate, mixtures of multi-acrylate polymerizations and the formation of biocondensates, or protein droplets. The RG methodology was extended with a two-dimensional approach, which enables the correlation of component size with other physical properties. This allows the compution of the mass distribution and perform a copolymer composition analysis. Finally, a method is developed that incorporates spatially dependent processes, such as cyclization reactions, in the RG model.