Determination of the free volume of thermosetting polymers

Free volume is a crucial concept for discussing the mobility of chain segments and the glass transition temperature (Tg) of polymers. Despite the necessity for a convenient approach to determine the free volume of thermosetting polymers, particularly epoxy resins, a suitable method is currently absent. The classical locally correlated lattice (LCL) theory is a significant method for calculating the hardcore volume and free volume of polymers. Based on this theory, the LCL equation of state (EOS) has been employed to calculate the free volume of several thermoplastic polymers via pressure-volume-temperature (PVT) data. For thermosetting polymers, such confined sites as cross-linked points constrain the mobility of the segment, the nonbonding interactions parameter q in the EOS will influence the hardcore volume Vhc (EOS). However, the EOS rarely involves such a constraint effect, resulting in an excessive Vhc (EOS) compared with the hardcore volume Vhc (PVT) obtained via the PVT. In view of the impact of confined sites on the nonbonding interactions, herein we propose a modified EOS (M-EOS) within the framework of LCL theory and determine the molecular parameters and hardcore volume Vhc (M-EOS) of thermosetting polymers. Vhc (M-EOS) is calculated closer to Vhc (PVT) than Vhc (EOS). Since the linear polymers have no cross-linked points, Vhc (M-EOS) is underestimated by the M-EOS in comparison with Vhc (PVT) of linear polymers. Consequently, the M-EOS and EOS are suitable for calculating the hardcore volume and free volume of thermosetting polymers and linear polymers, respectively. In this sense, the present work extends the scope of the application of the LCL theory to thermosetting polymers.