A Simple Mathematical Model for the Structural Description of Polyesters Based on Glycerol

Glycerol is a low-cost and biobased monomer widely used in the production of polyesters for applications such as surfactants and tissue engineering scaffolds, for example. However, the description of the structure of these polyesters remains challenging. This study presents a kinetic study of the polymerization of glycerol and dicarboxylic acids for the correlation of the ratio of the conversions of primary and secondary hydroxy groups of glycerol to their relative reactivity, the regioselectivity of the catalyst, and the occurrence of acyl migration. A mathematical model based on probability theory was used to estimate the molar fraction of the repetitive units of the polyesters, and key structural parameters such as the number-average degree of polymerization and the degree of branching as a function of conversion as well as the gel point were effectively described. These structural parameters were compiled into a theoretical structural map to provide a direct means of graphically understanding how the structure of the polyester changes as a function of hydroxy group conversion.