Gas Solubility, Diffusivity, Permeability, and Selectivity in Mixed Matrix Membranes Based on PIM-1 and Fumed Silica

The effects of adding fumed silica (FS) nanoparticles on the gas permeability, solubility, diffusivity and selectivity of a polymer of intrinsic microporosity (PIM-1) are modeled considering the density of the composite matrix as the key input information. PIM-1 is treated as a homogeneous glassy polymer endowed with a specific free volume that increases with the amount of nanoparticles loaded, as indicated by the experimental values of mixed matrix density. The solubility isotherms of H2, He, O2, N2, CH4 and CO2 in matrices of PIM-1 with different FS loadings are calculated with the Nonequilibrium Lattice Fluid (NELF) model. The gas diffusivity and permeability variation due to FS addition are related to the fractional free volume of the polymer phase according to the semiempirical free volume theory equation. Remarkably, the coefficient amplifying the free volume effect increases with the molecular size of the gas, expressed by the van der Waals volume, thus allowing to estimate the transport properties of gases not investigated experimentally, such as methane. The behavior inspected differs from the one observed in Mixed Matrix Membranes (MMM) formed by PIM-1 and porous selective fillers, that show higher selectivity towards smaller penetrants than the pure polymer, because the effect of silica nanoparticles is only represented by an enhancement of the large free volume domains. The model allows to estimate the ideal selectivity together with its solubility and diffusivity contributions, at various FS contents, for several gas pairs (O2/N2, CO2/N2, CO2/CH4, CO2/H2), which are then compared to the experimental trends available