Predicting the mass spectrum of polymerizing linoleates using weighted random graph modeling

Biopolymers and biopolymer networks that form via autoxidation, like in drying of oil paint or fat degradation in food components, contain a large variety of monomeric building blocks. While the monomer variety complicates the modeling itself, obtaining experimental validation of infinite polymer networks is inherently difficult as well. A new model is developed, where an automated reaction network generation (ARNG) procedure is used to automatically generate the monomer components, structures and masses, and their reactions. This methodology is combined with random graph (RG) modeling to predict global polymer properties: distributions of numbers of monomer units and molar masses, gel point and gel fraction. This computational framework is applied to two model systems for linseed oil paint binder: the polymerization of ethyl linoleate (EL) and methyl linoleate (ML). A novel method was constructed to deal with the variability of monomer masses that complicates inferring molar mass from monomer number distribution. By modeling the polymer as a weighted random graph where the nodes contain information about the monomer masses in the system, the total weight of the finite connected components is computed. The predicted mass spectrum of finite connected components is used for validation with experimental data. A size exclusion chromatography (SEC) trace of ML is employed, which after calibration using the proposed framework, proves consistency between model and SEC data. The model provides a practical approach to both characterize complex biopolymers as polymers in terms of molar mass distribution and gel point, while preserving the information down to the level of monomeric units.