Low Frequency Vibrations and Diffusion in Disordered Polymers Bearing an Intrinsic Microporosity as Revealed by Neutron Scattering

The microscopic diffusion and the low frequency density of states (VDOS) of PIM-EA-TB(CH₃) are investigated by inelastic and quasi-elastic neutron scattering where also the demethylated counterpart of PIM-EA-TB(H₂) is considered. These intrinsic microporous polymers are characterized by large BET surface area values of several hundred m²/g and pore sizes between 0.5 and 2 nm. Detailed comparison is made to the archetype of polymers of intrinsic microporosity, PIM-1, and polynorbornenes also bearing a microporosity. Due to the wavelength of neutrons, the diffusion and vibrations can be addressed on microscopic length and time scales. From the inelastic neutron scattering experiments the low frequency density of states (VDOS) is estimated which shows excess contributions to the Debye-type VDOS known as Boson peak. It was found that the maximum frequency of the Boson peak decreases with increasing microporosity characterized by the BET surface area. However, besides the BET surface area, additional factors such as the backbone stiffness govern the maximum frequency of the Boson peak. Further the mean squared displacement related to microscopic motions was estimated from elastic fixed window scans. At temperatures above 175 K, the mean squared displacement PIM-EA-TB(CH₃) is higher than that for the demethylated counterpart PIM-EA-TB(H₂). The additional contribution found for PIM-EA-TB(CH₃) is ascribed to the rotation of the methyl group in this polymer because the only difference between the two structures is that PIM-EA-TB(CH₃) has methyl groups where PIM-EA-TB(H₂) has none. A detailed comparison of the molecular dynamics is also made to that of PIM-1 and the microporous polynorbornene PTCNSi1. The manuscript focuses on the importance of vibrations and the localized molecular mobility characterized by the microscopic diffusion on the gas transport in polymeric separation membranes. In the frame of the random gate model localized fluctuations can open or close bottlenecks between pores to enable the diffusion of gas molecules.