Theoretically predicting the solubility of polydisperse polymers using Flory–Huggins theory

Polydispersity affects physical properties of polymeric materials, such as solubility in solvents. Most biobased, synthetic, recycled, mixed, copolymerized, and self-assembled polymers vary in size and chemical structure. Using solvent fractionation, this variety in molecular features can be reduced and a selection of the sizes and molecular features of the polymers can be made. The significant chemical and physical dispersity of these polymers, however, complicates theoretical solubility predictions. A theoretical description of the fractionation process can guide experiments and material design. During solvent fractioning of polymers, a part of the polydisperse distribution of the polymers dissolves. To describe this process, this paper presents a theoretical tool using Flory–Huggins theory combined with molecular mass distributions and distributions in the number of functional groups. This paper quantifies how chemical and physical polydispersity of polymers affects their solubility. Comparison of theoretical predictions with experimental measurements of lignin in a mixture of solvents shows that multiple molecular features can be described well using a single set of parameters, giving a tool to theoretically predict the selective solubility of polymers.