Correlation between fractional free volume and diffusivity of gas molecules in glassy polymers

Effects of Thermal Treatment and Physical Aging on the Gas Transport Properties in Matrimid®

“…where E P is the activation energy of permeation, properly obtained as the sum of the enthalpy of solution and of the activation energy for the diffusion of the gas molecule; P 0 is a pre-exponential factor, which can be related to the entropy of the permeation and to the jump length [11][12][13][14]: R is the ideal gas constant and T is absolute temperature. Finally, a useful quantity to evaluate the membrane performance is the selectivity a ij between penetrants i and j, generally defined as the ratio between the mole fraction in the downstream, y i /y j , divided by the ratio of the two mole fractions upstream, x i /x j .…”

“…The most common framework employed to address these effects is the "free volume" theory, according to which the diffusivity of low molecular weight species in a polymer phase depends on the available free volume in the membrane matrix [11][12][13]. Diffusivity of small size penetrants in a membrane depends on the free volume available in the polymer matrix (and its distribution), so that the larger is the void concentration, the higher is the diffusivity coefficient [14].…”

“…From this point of view, physical aging, which usually describes the slow evolution of the polymer structure over time towards its equilibrium configuration, results in a reduction of the void sizes and concentration and, according to some authors, also in a decrease of polymer chain flexibility [13,33,34]. Consequently, these phenomena are usually accompanied by a decrease of gas permeability in the membrane and therefore by a reduction of its potential productivity in separation applications.…”

“…On the other hand, the influence of thermal treatment on transport properties requires a careful analysis in order to consider the different features that can be involved, as for instance, rearrangements of the macromolecules and their possible stiffening or softening, as well as the changes in polymer density. According to Struik [37], relaxation phenomena of the polymer macromolecules occur whenever the system is quenched from above to below T g , and the extent of volumetric rearrangements depends on the quenching conditions [13]. The relaxation process leads to a variation in the free volume of the polymer, and consequently in its transport properties.…”

Enhancement of Gas Permeability in HPC, CTA and PMMA under Microwave Irradiation

“…Gas transport properties in polymers are dependent on the amount of the space through which gas molecules diffuse and the mobility of polymeric chains, [4][5][6][7][8][9] that is, the high mobility of main chains and side groups leads to high gas permeability and diffusivity. Even in dense polymeric membranes, the enhancement and control of permeability due to accelerated molecular motion of polar functional groups by microwave irradiation could be expected.…”