Gas Solubility, Diffusivity, Permeability, and Selectivity in Mixed Matrix Membranes Based on PIM‑1 and Fumed Silica Maria Grazia De Angelis,* Riccardo Gaddoni, and Giulio C. Sarti Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali (DICAM), Alma Mater Studiorum Universita ̀ di Bologna, via Terracini 28, 40131 Bologna, Italy ABSTRACT: The effects that the addition of fumed silica (FS) nanoparticles has 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 H 2 , He, O 2 ,N 2 , CH 4 , and CO 2 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 an estimation of 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 toward 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 an estimation of the ideal selectivity together with its solubility and diffusivity contributions, at various FS contents, for several gas pairs (O 2 /N 2 , CO 2 /N 2 , CO 2 /CH 4 , CO 2 /H 2 ), which are then compared to the experimental trends available. ■ INTRODUCTION The family of polymers with intrinsic microporosity (PIMs) is based on non-network polymers that are soluble and can be processed easily with solvent-based methods, unlike conven- tional microporous materials, and possess open structures due to a rigid spirocyclic molecular scaffold. 1 The most studied polymer of this class is the product of condensation of 5,5′,6,6′- tetrahydroxy-3,3,3′,3′-tetramethyl-1,1′-spirobisindane and tetra- fluoroterephtalonitrile, named PIM-1. 2−5 Such a polymer shows outstanding properties for the gas separation of several industrial mixtures, for example, CO 2 /CH 4 and CO 2 /N 2 , for which they lie on or above the most recent Robeson trade-off curve. 6 In the last six years, authors have tried to further improve those features by adding various inorganic fillers to the polymer matrix, such as functionalized multiwalled carbon nanotubes (MWCNTs), 7 metal organic frameworks (MOFs), or micro- porous and mesoporous molecular sieves of different kinds, 8 zeolitic imidazolate frameworks (ZIF-8), 9 or fumed silica nanoparticles. 10 The latter case will be inspected and modeled in this work, and we will introduce also some considerations on other types of composite structures and properties. The solubility and transport behavior of different penetrants in mixed matrix membranes (MMM) obtained by adding fumed silica (FS) nanoparticles to high-free-volume glassy polymers shows rather unusual and unexpected features which make it very hard to obtain reasonable predictions or expectations for permeability, solubility, and diffusivity, simply based on the behavior shown by the unloaded polymer matrix. 11 Therefore, the importance of a reliable modeling approach for the transport properties of those MMM is apparent and of great impact in order to reduce the necessary experimental effort to the essential minimum required. The transport behavior of composite materials formed by glassy polymers and silica nanoparticles cannot be described with the conventional models for transport into “ideal” composite systems, such as the Maxwell model, unless the number of adjustable parameters is increased significantly to take into account size and distribution of a possible third phase, represented by the hypothetical additional void space between polymer and particles. 11 On the other hand, in 2008 a successful approach was proposed that allows a representation of solubility and transport properties of several gases in MMM obtained by adding dense nanoparticles of fumed silica in high free volume glassy polymers such as poly(1-trimethylsilyl-1- propyne) (PTMSP) and Teflon AF 1600 and 2400. 12−14 In the approach, the mixed matrix transport properties can be quantitatively described by considering only two phases, silica and polymer matrix, with the latter characterized by a different fractional free volume (average density) with respect to the pure unloaded polymer. The diffusion coefficients in the mixed matrix are estimated by means of the free volume theory applied to the polymer phase, accounting for the increased tortuosity of the diffusive path due to the presence of the impermeable filler particles. Special Issue: Enrico Drioli Festschrift Received: December 22, 2012 Revised: March 15, 2013 Accepted: March 20, 2013 Article pubs.acs.org/IECR © XXXX American Chemical Society A dx.doi.org/10.1021/ie303571h | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX