Supporting information for Publication Experimental Pure gas permeation measurements with the Variable pressure setup and time-lag (TL) analysis Single gas permeation measurements were carried out at 25 C and at a feed pressure of 1 bar in a fixed volume pressure increase apparatus (GKSS, Germany) in the time lag mode [1]. The instrument is equipped with PC controlled pneumatic valves allowing response times of less than 0.5 s [2]. An alumina trap avoids oil contamination of the membrane from the rotary vacuum pump. Before each experiment, the membrane sample was carefully evacuated (10-2 mbar) to remove any dissolved gas species. The gases were tested in the following order: He, H 2, N 2, O 2, CH 4, and CO 2. Circular samples with an effective membrane area of 2.14 cm 2 were used. The films were tested as received and after soaking in alcohol overnight and then drying in air at room temperature. The permeability coefficient, P, and diffusion coefficient, D, were determined from the pressure increase rate on the permeate side of the membrane cell assembly in the quasi steady state: 2 RT A p f P l pt = p0+ ( dp / dt) t+ t 0 VP Vm l 6D (S1) in which p t is the permeate pressure at time t and p 0 is the starting pressure, typically less than 0.05 mbar. The baseline slope (dp/dt) 0 is usually negligible for a defect-free membrane. R is the universal gas constant, T is the absolute temperature, A is the exposed membrane area, V P is the permeate volume, V m is the molar volume of a gas in standard conditions (0 C and 1 atm), p f is the feed 1
pressure, S is the gas solubility, D the gas diffusion coefficient and l the membrane thickness. The last term in Eq. (2) accounts for the so-called permeation time lag, Θ, which is inversely proportional to the diffusion coefficient of the gas: 2 l Θ= (S2) 6 D The gas permeability is expressed in Barrer (1 Barrer = 10 10 cm 3 (STP) cm cm 2 s 1 cmhg 1 = 3.35 10 16 mol m m 2 s 1 Pa 1 ). Pure gas permeation in a flow setup with gas chromatographic (GC) analysis Permeability coefficients were determined at room temperature (20-22 C) and at a feed (upstream) pressure of 1 bar. A carrier gas was passed over the down-stream side. Downstream pressure was also 1 bar but it comprised mainly the pressure of sweep gases (He in most the cases and N 2 in the cases of He and H 2 as penetrants). The partial pressure of penetrants in the downstream part of the cell was negligible, so the penetrants pressure drops were virtually 1 bar. The apparatus was equipped with a gas chromatograph (Chrom 5) for the analysis of permeate gas composition. The permeability coefficients P were determined, after establishing a steady-state stream in the cell, by measuring the penetrant concentration in the carrier gas and the total flow of the mixture: P = c r l A p (S3) 2
where c is the penetrant concentration in the carrier gas/penetrant mixture (vol.%), r is the flow rate of gas mixture at the outlet of the cell (cm 3 [STP] s -1 ), l is the thickness of the film (cm), A is the exposed surface area of the film (cm 2 ), p is the partial pressure drop of the penetrant across the film (Pa). As cast films were masked with aluminium foil before measurements of permeability. In order to study the effect of alcohol treatment, the films were immersed in ethanol for a day, then removed and kept overnight (18 h) in the ambient atmosphere before starting the measurements. Aluminium foil masks were used and the exposed area of the samples was in the range 0.8-3.5 cm 2. Measurement started immediately after application of the mask and lasted for 1.5-2 days: O 2, N 2, CO 2, CH 4 were measured during the first day; whereas He, H 2 were tested during the second day The accuracy of determination of the permeability coefficients (usually 5-10%) implies the following statistical or systematic errors: errors related to the measurement and non-uniform character of film thickness, errors in determination of the concentration of penetrants in permeate streams, errors in measurement of the surface area of the film and errors in calibration of the instrument (the latter two are negligible). For a certain film, 5-7 sequential determinations of the concentration of the penetrant were made, and for as cast films the results did not differ more than 1%. The error of determination of the permeability coefficients was 5%. Pure and mixed gas permeation in a flow setup with mass spectrometric (MS) analysis Mixed gas permeation tests were carried out with Argon depleted compressed air (Pirossigeno, Italy) on a 129 µm PIM-EA-TB film. The membrane was aged for three days after methanol soaking. Experiments were carried out in a standard cross-flow cell at 25 C and at a total feed pressure up to 7 bar. The permeate was at ambient pressure and the effective membrane area was 2.14 cm 2. Helium sweep gas was introduced at a flow rate of 50 cm 3 (STP) min -1 into the permeate side of the cell by means of a thermal mass flow controller (Bronkhorst Hi-Tech). The feed pressure was controlled using a forward pressure controller (Swagelok). In order to keep the stage cut under 1% (fraction of the feed 3
moving into the permeate), the retentate flow rate was fixed at a relatively high value of 200 cm 3 (STP) min -1. Under these conditions, the retentate composition was almost equal to that of the feed and concentration polarization effects were negligible. The compositions of feed, retentate and permeate were determined with a mass spectrometer (Hiden Analytical, HPR-20 QIC Benchtop analysis system) equipped with a quadrupole mass analyzer. The electron ionization energy was 70 ev; a Faraday cup was used as ion detector. For the calibration procedure, the relative sensitivity of O 2 in He and of N 2 in He was determined over a range of different compositions. The mixed O 2 /N 2 selectivity was evaluated as the ratio of the individually calculated permeances of the gases in the mixture and the individual gas permeance, Π, of the i th species in the ternary mixture [m 3 m -2 s -1 bar -1 ] is obtained as the ratio of its volumetric permeate flux, Q Permeate [m 3 m -2 s -1 ], to the partial pressure difference between the feed and permeate sides, P i : Permeate Permeate Permeate Permeate xi Q xi Q Π = = P x P - x P i Feed Feed Permeate Permeate i i i (S4) where x i is the mole fraction of the i th species [mol mol -1 ]. P Feed and P Permeate are the total feed and permeate pressures [bar], respectively. Q Permeate is the permeate flow rate per unit area, defined as: Permeate J Q Permeate = (S5) A The volumetric permeate flow rate, J Permeate [m 3 m -2 s -1 ], is calculated from the known flow rate (permeate +sweep) and from the measured composition of the permeate/sweep mixture. Gas Sorption measurements 4
Sorption experiments were performed gravimetrically at 25 C and at selected gas pressures (0.5-7.5 bar). A robust home-built sorption apparatus was used [3]. It was equipped with a calibrated McBain quartz spiral balance and with automatic charge-coupled device (CCD) camera. The experimental setup and procedure are described in detail elsewhere [4]. A sample ( 0.1 g) was attached to the spiral balance in a glass tube that was evacuated before the measurement to a pressure lower than 10-3 mbar by a rotary oil pump (Trivac D4B, Oerlikon Leybold). A Leybold oil mist filter was used to eliminate (with 99.99% efficiency) the contamination of the measuring chamber with oil vapours from the pump. After exposure of the sample to a particular gas at known pressure, the elongation of the quartz spiral was monitored by the CCD camera until the equilibrium state was reached. Before each gas experiment, a buoyancy test of the quartz spiral without polymer sample was performed under the same experimental conditions. Proper sample buoyancy was calculated as: ρgas buoyancysample = Vsample ρgas = msample (S6) ρ sample where V sample is the sample volume [cm 3 ] and ρ gas is the density of the gas at the given pressure and temperature [g cm -3 ], m sample is the mass [g] and ρ sample is the density [g cm -3 ] of the polymer sample. The average error of mass determination of each experiment was approximately 30 micrograms [4] which at 1 bar of CO 2 corresponds to 2-3 % and at 7 bar less than 1 % of gas mass uptake in the studied samples. 129 Xe NMR experimental and data analysis Xenon NMR spectroscopy was performed at 25 C using a Bruker Avance 500 system with 138.45 MHz 129 Xe resonance, equipped with a 10 mm probe. Spectra were acquired with single pulse excitation with 17 µs π/2 pulse length, a minimum of 800 scans and recycle delay of 17 s. The gas 5
employed (Xenon 5.0, Sapio S.r.l., Italy) has a content of 26.44% (natural abundance) of the NMR sensitive 129 Xe isotope. PIM-EA-TB film was immersed for 12 h (overnight) in reagent grade methanol (Sigma Aldrich, >99.8%), dried for 12 h at ambient conditions. and cut in small (1-2 mm 2 ) pieces. These were loosely packed in a heavy-walled 10 mm NMR tube (with a 7 mm i.d.) in the sensitive volume in the NMR coil. Atmospheric gases were removed by applying a dynamic vacuum (< 10-1 mbar) in the tube overnight at room temperature, using a rotary pump with nitrogen trap. The xenon gas was transferred quantitatively from a reservoir of known volume (28.3 ml) into the sample tube via a Schlenk manifold by freezing the sample tube with liquid nitrogen. The tube with Xenon and the sample was hermetically sealed with a flame. From the ratio of the original Xenon reservoir volume and the tube volume (5.85 ml, neglecting the volume occupied by the sample), the nominal pressure was calculated for each of the several tubes prepared for the variable pressure study. For the detailed interpretation of the chemical shift, we followed the interpretation recently rationalized by de Menorval [5] with the equation δ = obs δ + 0 δ + S δ + X δ ( Xe Xe) ρ (S7) Where δ 0 is the resonance of the free gas, δ S the chemical shift of the Xe surface interaction and δ X the shift caused specifically by the presence of charged ions. The last term in the equation accounts for Xe Xe interactions within the constraints of micropores. Setting the gas resonance as reference (0 ppm), and considering the absence of charged ions in the material, the plot of chemical shift against xenon pressure can be interpolated with a line, whose intercept (chemical shift at 0 pressure) is the, δ S value. 6
Molecular modelling Model preparation A PIM-EA-TB polymer chain of 15 monomer units (653 atoms) was used as template chain for the adjacent initial packing with the Amorphous Cell module. In every packing model, five polymer chains with a total of 3265 atoms were grown together under periodic boundary conditions at 308 K and at an initial density of 0.1 g cm -3. Additionally, every simulation cell contained 800 randomly distributed CH 4 molecules as obstacles to avoid ring catenation during the chain growth. The procedure for packing and equilibration are described in detail elsewhere [6]. Amorphous polymer packings were constructed using the Theodorou/Suter method [7, 8] as implemented in the Amorphous-Cell module. The obstacle molecules were later removed. Each removal procedure was followed by the structure relaxation, applying a force field parameter-scaling scheme used by Heuchel et al. [6]. Several hundred-energy minimization iterations and several thousand NVT-MD steps (constant number of particles, volume and temperature) were used for each parameter set. After removing the obstacle molecules using a downscaling procedure, the packing models were equilibrated via a set of MD runs to increase the density. A long final NpT-MD run (constant number of particle, pressure and temperature) was applied in the final equilibration [6]. The procedure was repeated, eliminating the non-realistic boxes, until three realistic amorphous cells for each of the polymers were generated with side lengths of the packing cells of 33.7 Å and a final density of 1.03 + 0.03 g cm -3. The deviations from the experimental density of 1.08 g cm -3 is about 5%, which is quite usual for glassy stiff-chain polymer materials, particularly if the models are large. After equilibration, the NpT-MD simulation was performed at 306 K, pressure of 1 bar for 6 nanoseconds. Mean Squared Displacements (MSD) For enhanced sampling efficiency, ten gas molecules of the same kind were inserted into each polymer structure and then the polymeric boxes were equilibrated. After equilibration, the NpT-MD simulation 7
was performed at 300 K and at p = 1 bar for 6 ns. Diffusion coefficients were calculated from the slope of the plots of the mean square displacements, D α, of gases versus time, t, using the Einstein relation: = 0 (S8) Where N α is the number of diffusing molecules of type α, r i (0) and r i (t) are the initial and final positions, respectively, of molecules (mass centers of particle i) over the time interval t, and 0 is the MSD averaged over the possible ensemble. The Einstein relationship assumes Brownian dynamics for the diffusing particles [9]. Calculation of solubility coefficients The solubility coefficients, S, were obtained from Grand Canonical Monte-Carlo (GCMC) simulations by fitting the sorption isotherm obtained from every simulated box to a straight line through the origin and taking the slope to be the solubility coefficient. In GCMC, the two different algorithms Metropolis and configurational bias were applied. Metropolis algorithm was preferred because it considers the adsorption of sorbate molecules in porous frameworks without providing them with any internal degrees of freedom. In this method, each conformation is treated as a rigid body and the sorbate molecules, such as those considered in this study, do not have a high degree of torsional flexibility. The Metropolis algorithm [10] is used to accept or reject an insertion and deletion of a sorbate molecule. The probabilities of addition and deletion of a sorbate molecule, P add and P del, respectively, are given as: P add 1 pv U = min 1; exp (S9) Ns+ 1 kbt kbt 8
and P del N skbt U = min 1; exp (S10) pv kbt where U is the energy [J], calculated from the sum of nonbonded (i.e. Coulombic and van der Waals interaction) energies, Ns is the number of sorbate molecules [-] k b is the Bolzman constant [J K -1 ] and T the absolute temperature [K], p the pressure [Pa] and V the molar volume [m 3 mol -1 ]. The addition is accepted if the energy change U, is negative or if the Boltzmann factor is greater than a random number generated between 0 and 1. The infinite dilution solubility coefficient S 0, is then obtained from the initial slope of the sorption isotherm: dc S0= lim = kd+ CH b (S11) p 0 dp Free volume The size distributions of the free volume elements accessible for penetrants of certain radius were also calculated using the program developed by Hofmann and Heuchel [11]. Free volume was determined by first superimposing a fine grid over the cubic packing. Then a test was performed at every point of the grid to determine if an overlap occurs between a hard spherical test particle (representing the penetrating molecule) and any atom of the polymer (represented also by a corresponding hard sphere). The result was a classification of grid points as occupied or free. Subsequently, the connectivity of the free grid points was considered, and connected free grid points were collected into groups, which represented individual holes. This was done in two ways. In the first approach (named V connect), the topological criterion was that every point of a group had at least one next neighbour, 9
which was also member of this group. This approach identified holes, which may be of complex shape and of large size. In a second approach, for every grid point, the shortest distance to a polymer atom is used to group points, and, among these distances, local maxima are defined by calculating the related gradient. Then, each grid point of the free-volume regions is assigned to its nearest local maximum. This approach is referred to as R max. This method dissolves larger free-volume regions of elongated or highly complex shapes into smaller local regions, to come closer to the situation of PALS spectra, where the positron probe particle cannot completely sample very large holes of complex topology. In the present work, the calculation starts by the superimposition of a fine grid of about 0.5 Å over the cubic packing model. In both approaches, the number of lattice cells belonging to a hole times their cell volume was used as a measure for the volume of this hole. The obtained volume of each hole was converted to an equivalent sphere and the radius of this sphere is taken as a measure for the average linear dimensions of the respective hole. The positronium (Posi) particle is assumed to have the size of a hydrogen atom, i.e., the radius is assumed to be 1.10 Å. Results 10
A B C Figure S1. Relevant sections of the FTIR spectrum, demonstrating the effect of treatment of as cast PIM-EA-TB films with MeOH (A) and EtOH (B). Confirmation of the complete removal of residual chloroform by MeOH treatment (C). 11
Table S1. Comparison of the diffusive and the sorptive terms to the permselectivity of glassy polymers. Polymer α D (O 2 /N 2 ) α S (O 2 /N 2 ) Ref. PTMSP 1.2 1.2 13 Teflon AF2400 1.5 1.66 1.4 1.2 14 15 Polytricyclononene with 2 SiMe 3 side groups 1.5 (as cast) 1.4 16 1.3 (EtOH) 1.2 Poly(trimethylsilyl norbornene) 1.8 1.4 17 Metathesis polynorbornene with 2 CF 3 side groups 1.4 1.9 18 PIM-1 3.5 (as cast) 1.1 10 2.4 (MeOH) 1.1 PIM-EA-TB (190 kda) 2.7 (as cast) 1.2 This work 3.5 (MeOH) 1.0 12
Figure S2. Top: NMR spectrum of 129 Xe at 25 C at 108.4 kpa in the presence of MeOH treated PIM-EA-TB at. The free xenon gas was used as the 0 ppm reference. Bottom: Variable pressure plot of 129Xe chemical shift with linear extrapolation to 0 pressure. 13
A B Figure S3. Free volume element size distribution based on free-volume elements accessible for Positronium, calculated with the R max and V connect approaches from packing models of (a) PIM-1 (Adapted from ref. [6], with PALS data from [12] and (b) PIM-EA-TB (this work). The red dashed lines represent the PALS data, the blue dashed line represents the NMR data considering a spherical radius. 14
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