The role of free volume, hydrogen bonds, and crosslinks on physical aging in polymers of intrinsic microporosity (PIMs) †

Physical aging is a slow structural relaxation process characteristic of glassy polymers that results in reduced membrane permeabilities. In this study, PIM-1, the archetypal polymer of intrinsic microporosity (PIM), was post-synthetically modi ﬁ ed to introduce components that are known to in ﬂ uence physical aging, such as hydrogen bonds and crosslinks. The e ﬀ ects of physical aging were monitored by permeation and sorption experiments, and structural changes were examined by positron annihilation lifetime spectroscopy (PALS) and other characterization techniques. The results suggest that higher initial fractional free volume is the primary factor contributing to higher rates of physical aging and that the introduction of hydrogen bonds and crosslinks reduces the initial free volume of PIM-1. In contrast, structural factors such as hydrogen bonds and crosslinks were the key factors in determining how permselectivity changed with physical aging. This study provides useful structure – property correlations and design principles related to free volume, hydrogen bonds, and crosslinks on physical aging behavior of microporous polymer membranes.


Introduction
Molecular separations play a critical role in a wide variety of chemical processes and engineering applications, making up nearly 50% of total energy consumption in the industrial sector. 1 Implementing more energy-efficient separation technologies has the potential to reduce energy consumption and carbon emissions that have reached a new global high in 2022. 2 In this regard, the use of membranes is a promising unit operation that could eventually supplement or replace existing energy-intensive industrial processes such as distillation.4][5] In the context of gas separations, membranes have multiple attractive features in addition to energy efficiency, such as modularity, small footprints, the absence of toxic mass separating agents, continuous operation, and potentially lower cost. 6,7major thrust of gas separation membrane research in the last four decades has been the development of new polymeric materials. 4][10] Based on Freeman's theory, the overall separation performance of polymeric materials can be improved by increasing backbone stiffness while simultaneously increasing free volume, and such features are the dening characteristics of polymers of intrinsic microporosity (PIMs). 11,12When this type of polymer is cast from solution, polymer chains pack inefficiently to generate some of the highest free volume structures known within the eld of gas separation membranes. 13IMs are attractive materials in the gas separation eld because their micropores allow for high gas sorption capacity while their rigid backbone structures hinder diffusion of larger gas penetrants, making them highly diffusion-selective materials especially when considering their high free volume. 14As a result, PIMs typically have orders-of-magnitude higher permeabilities than conventional polymers that are deployed as commercial gas separation membranes. 15,161][32][33][34][35] PIMs show promise because many compositions surpass the Robeson upper bound, yet they have never been deployed in large-scale industrial settings, in part due to challenges with scaling and stability, including phenomena such as plasticization and physical aging. 4,13,36,37f the two major stability issues, this paper focuses on physical aging behavior of PIMs.Physical aging is the long timescale structural relaxation process of glassy polymers moving towards an equilibrium state that results in changes in membrane property sets over time.This phenomenon is ubiquitous among all glassy materials. 38Mechanistically, kinetically trapped conformations of polymer segments gradually relax towards equilibrium packing structures, thereby reducing the free volume of the polymer. 38Physical aging obeys an exponential relationship between permeability and free volume, and hence, physical aging has the most pronounced effect on permeability right aer a polymer is formed into a lm; 39 however, this process persists throughout the lifetime of a polymer membrane used in the eld and results in membranes "aging out", requiring operators to discard and replace membrane modules. 37Because stable long-term performance is an important factor in commercial operations, more work is required to understand the underlying mechanisms of this phenomenon.
Some of the seminal studies on physical aging demonstrated that this feature is dependent on the amount of excess free volume and segmental mobility. 40,41Generally, polymers with high free volume are expected to age faster since the amount of excess free volume is the driving force for physical aging, 42 while polymers with high glass transition temperatures (T g s) are considered to be more resistant to physical aging since T g is correlated with chain mobility. 38,43,446][47] In this sense, PIMs have the dual attributes of low segmental mobility and high free volume, the former of which is expected to retard physical aging and the latter of which is expected to accelerate it.
Early PIM research anticipated that these polymers would have high physical aging resistance since PIMs generally lack a detectable T g by standard techniques and contain permanent micropores arising from their backbone congurations (i.e., congurational free volume) that are theoretically unaffected by physical aging. 48,49In terms of T g , we note that a study using fast scanning calorimetry has determined a T g of 715 K for PIM-1, which surpasses its degradation temperature of 673 K in an inert atmosphere. 50However, multiple studies have shown that PIMs exhibit physical aging behavior that is oen atypical of traditional polymers.For example, Swaidan et al. observed that TPIM-1, a triptycene-based ladder polymer, aged faster and more extensively than PIM-1, although the backbone of TPIM-1 has fewer exible dioxane moieties and contains triptycene units that incorporate congurational free volume. 48Recently, Lai et al. reported a stark difference in the aging behavior of two different catalytic arene-norbornene annulation (CANAL) polymers, which are microporous polymers consisting of conformationally restricted fused rings. 51The CANAL polymer with 2D contortions showed a slight gain in selectivity and a larger decrease in permeability with time, while the CANAL polymer with 3D contortions showed a high gain in selectivity and a small decrease in permeability with time. 51The results from such studies suggest that the physical aging characteristics that are accepted for conventional polymers do not always translate to the emerging PIM subclass.Therefore, systematic studies of physical aging in PIM materials are required to glean insights into this important yet poorly understood phenomenon.
Recently, our lab demonstrated a solid-state deprotection strategy for PIMs that resulted in simultaneous enhancements of permeability and selectivity relative to pre-protected PIM analogues. 29,52This method, called free volume manipulation (FVM), uses labile functional groups, such as a tert-butoxycarbonyl group (tBOC), to alter physical packing structures and hence transport properties of the deprotected polymers. 29,52By introducing bulky functional groups to the polymer backbone, the intersegmental distances are intentionally widened when the polymer is processed into a solid-state lm.Then, aer removing these labile functional groups through simple heat treatment in the solid-state, free volume increases.This method was highly effective for amine-functionalized PIM-1 (PIM-NH 2 ). 29Fig. 1 shows the FVM approach for PIM-NH 2 .In short, the archetypal PIM-1 is converted into its amine-functional counterpart, PIM-NH 2 , which signicantly decreases free volume due to hydrogen bonding. 29Next, the amine groups in PIM-NH 2 are protected with tBOC groups to yield PIM-tBOC.PIM-tBOC subsequently undergoes thermal treatment to yield free volume manipulated PIM-NH 2 (PIM-NH 2 -FVM), which has slightly larger average free volume element (FVE) diameters along with the potential for light urea crosslinks. 29This approach results in enhancements of both permeability and selectivity for PIM-NH 2 . 29n the context of long-term stability, the effect of FVM on physical aging is difficult to predict.FVM increases FVE size and drives the polymer further from its theoretical chain packing equilibrium, which can potentially accelerate the aging rate.However, it also introduces crosslinks that can reduce translational motions of the polymer segments.In previous comparisons of fresh and aged PIM-NH 2 and PIM-NH 2 -FVM permeability data, 29 both polymers showed similar permeability reductions, suggesting that FVM may stabilize the polymer matrix from accelerated physical aging despite introducing the additional free volume.
In this study, we investigate this phenomenon in greater depth, studying the inuence of amine functionalization and the subsequent free volume manipulation on archetypal PIM-1 lms by monitoring pure-gas transport properties over approximately 10 000 hours using non-plasticizing gases (H 2 , O 2 , N 2 , and CH 4 ).In addition to providing a baseline comparison for the aging behaviors of these post-synthetically modied PIMs, this study aims to bridge the guiding principles already established for conventional polymers on the role of free volume, hydrogen bonds, and crosslinks on physical aging behaviors of microporous polymers.By maintaining identical dioxane backbone structures while modifying hydrogen bonding, crosslinking, and free volume, this set of polymers provides a unique system to directly compare the effect of these features on physical aging.

Materials
PIM-1, PIM-NH 2 , and PIM-NH 2 -FVM polymer lms with thicknesses of 37.6 ± 0.9, 51.3 ± 1.1, and 51.2 ± 2.0 mm, respectively were prepared as previously reported. 29A detailed procedure is outlined in Section 1 of the ESI.† While thin lms generally below 1 mm in thickness are of great interest for commercial gas separation membranes, we consider thick lms here for broader comparisons with the open literature and because PIMs have easily observable aging behavior at these length scales. 23,29hysical aging studies of the post-synthetically modied PIMs at industrially relevant thicknesses will be the focus of our future work.

Characterization
Density was measured with a Mettler Toledo density measurement kit (ME-DNY-4) using Archimedes' principle.Room temperature water was used as the reference liquid, and the density for each sample was taken as the average of at least four different lm pieces.The error is reported as the standard deviation of the measurements performed.The fractional free volume (FFV) of all samples tested was calculated using the group contribution method: 53 where V is the experimental specic volume of the polymer and V w is the van der Waals volume of the polymer determined by the updated group contribution method from Wu et al. 53 Wide-angle X-ray scattering (WAXS) patterns were collected under 0.08 mbar vacuum using a SAXSLAB machine equipped with a DECTRIS PILATUS3 R 300K detector and Rigaku 002 microfocus X-ray source.All patterns were collected for 1200 s, and the resulting pattern was plotted as intensity I(q) versus scattering wavevector q: where q is Bragg's angle and l is the wavelength of the X-ray beam.Each peak from the resulting patterns was tted using "Gaussian peak + slope background" from the SAXSGUI soware program.
Positron annihilation lifetime spectroscopy (PALS) data were collected using an automated EG&G ORTEC fast-fast coincidence system.A Mylar envelope containing a 22 Na radioisotope source was sandwiched between two small stacks of polymer lms, each stack approximately 1.5 mm thick.All tests were performed under vacuum (10 −6 torr) at room temperature, and a minimum of 5 les with 4.5 × 10 6 integrated counts were collected for each polymer sample.Aer each measurement, least squares optimization was performed with the LT v9 program using a four-component (para-positronium, free positron, and ortho-positronium) tted model. 54In the model, the para-positronium lifetime was xed to s 1 = 0.125 ns and free positron (s 2 ) and two ortho-positronium lifetimes (s 3 and s 4 ) were tted, indicating bimodal free volume distributions, which typically result in better statistical tting for high free volume glassy polymers. 55Intensities (I i ) for all of these components were also determined. 56The PAScual soware was adapted to calculate pore size distributions, 57 and the Tao-Eldrup equation was used to calculate the average FVE size using the obtained ortho-positronium lifetimes: 56,58 where R is the radius of the FVE, R 0 = R + DR, and DR is an empirical parameter (1.66 Å). 59 In addition to FFV group in eqn (1), FFV PALS of all samples tested was calculated using the FVE radii and the corresponding intensities: 59 where c is an empirical scaling constant of 0.0018 Å −3 (R i is in Å and I i is in %). 60The scaling constant is known to vary between 0.001 and 0.002 Å −3 depending on polymer, 61 but 0.0018 Å −3 is used here because it is the most widely used approximation in the literature, 55,[62][63][64] and the constant does not affect the order of FFV PALS for the PIM lms studied in this work.

Pure-gas permeability measurements for physical aging
Before any physical aging experiments, all membrane samples were kept submerged in methanol.At the beginning of the physical aging experiments, the membranes were dried in a vacuum oven at 130 °C for 12 h under dynamic vacuum.PIM-NH 2 and PIM-NH 2 -FVM samples underwent additional thermal treatment, as described in Section 1.3 of the ESI.† The end of the drying or thermal treatment procedure was considered the initial physical aging time (t 0 ).During aging, all lms were kept inside a desiccator at ambient temperature (approximately ranging from 20-25 °C).Pure-gas permeabilities of four gases (H 2 , CH 4 , N 2 , and O 2 ) were tested for each aging sample using a constant volumevariable pressure automated permeation testing apparatus (Maxwell Robotics).All samples were masked with epoxy glue on brass supports to ensure no leakage from upstream to downstream.Further details of the testing setup can be found elsewhere. 20,29,52Before any permeation test, the entire apparatus was held under vacuum for 8 h.When changing to a different testing gas, the upstream was ushed with high pressure He, and the entire apparatus was held under vacuum between 0.5 and 1 h depending on the prior gas tested.All permeation tests for physical aging curves were performed at 35 °C with an upstream pressure of 15 psia and a downstream pressure <9.5 torr.For the variable temperature permeation study, the testing conditions were kept similar to those in the previous description, but the tests were performed at 35, 45, 55, and 65 °C.
Permeability (P) was calculated using the following equation: where V d is the downstream volume, l is the lm thickness, p 2 is the upstream pressure, A is the active area of the lms, (dp/dt) ss is the downstream pressure change at steady-state operating conditions, and (dp/dt) leak is the leak rate measured at the beginning of the permeation test.The ideal gas selectivity (a i,j ) was calculated by taking the ratio of the pure-gas permeability of the more permeable gas, i, to that of the less permeable gas, j: 2.4 Pure-gas sorption measurements for physical aging Similar to permeation tests, all lms were kept submerged in methanol until the planned experiments were executed.The membranes were dried and thermally treated right before the sorption tests, marking t 0 of the experiments.During aging, all lms were kept inside a desiccator at ambient temperature (approximately ranging from 20-25 °C).Pure-gas sorption isotherms of CH 4 , N 2 , and O 2 were measured at 35 °C using an automated pressure decay sorption testing apparatus (Maxwell Robotics).All connections in the apparatus were sealed using VCR gaskets to limit uncertainty from leaks.For each sorption test, at least 0.1 g of polymer lms were loaded into a 3 cm 3 sample cell.At the beginning of the sorption measurement, the entire apparatus was degassed under full vacuum for 8 h.When changing to a different testing gas, the apparatus was ushed with high pressure He and held under vacuum for 3 h.The charge volume was held at each testing pressure for 0.3 h before dosing the gas into the sample chamber.Once the testing gas was dosed, the sample chamber was allowed to equilibrate at the testing pressure for 2.5, 2, and 1 h for CH 4 , N 2 , and O 2 , respectively.Each sorption isotherm was collected up to 700 psia and tted using the dual-mode sorption (DMS) model, which is commonly used to describe sorption in glassy polymers: 65 where C i is the concentration of gas i in the polymer (cm 3 STP cm −3 pol ), p i is the equilibrated pressure (atm), k D,i is Henry's law constant (cm 3 STP cm −3 pol atm −1 ), C ' H,i is the Langmuir sorption capacity (cm 3 STP cm −3 pol ), and b i is the Langmuir affinity constant (atm −1 ).During the nonlinear least squares ts of the isotherms, the slope of ln(k D,i ) versus critical temperature (T c ) was constrained to have the same slope as that of ln(S i ) versus T c at 10 atm, where S i is the pure-gas sorption coefficient. 66t each testing pressure, the amount of gas sorbed by the sample was calculated by mass balance using the pressure in the charge chamber and the equilibrated pressure aer the charge gas was dosed into the sample chamber.The pure-gas sorption coefficients were then calculated by dividing the gas concentration in the polymer by the testing pressure:

Physical aging monitored by permeation tests
Physical aging behavior can be affected by multiple factors, such as casting solvent, membrane thickness, previous thermal history, drying conditions, and the environment where samples are stored. 44,67These factors are especially important for samples that have high amounts of non-equilibrium free volume and are hence susceptible to intense aging, such as PIMs.Table 1 shows a summary of the polymers studied and their treatment conditions.All PIM-1 lm thicknesses were kept at approximately 40 mm during solution casting, but posttreatments (i.e., amine functionalization and FVM) resulted in slight increases in thickness.The density of PIM-1 in this study was higher compared to the values typically reported in the literature, 29,32,[68][69][70][71][72][73][74][75][76] as shown in Table S1.† To ensure internal consistency, the densities of the samples made for this study were used in the FFV group calculations, and the batch-to-batch variable for additional samples of PIM-1, PIM-NH 2 , and PIM-NH 2 -FVM from our lab is also provided for reference in Table S2.† The FFV group of polymers calculated from the group contribution method closely matched what was expected from the pore size investigations from our previous study of these polymers. 29As shown in the table, PIM-1 showed the largest initial FFV, followed by PIM-NH 2 -FVM and PIM-NH 2 , respectively.Similarly, the FFV PALS calculated from PALS indicated the largest initial FFV for PIM-1, while PIM-NH 2 and PIM-NH 2 -FVM showed the same initial FFV within the uncertainty of the measurements.As noted in the experimental section, all samples (i.e., PIM-1, PIM-NH 2 , and PIM-tBOC) were soaked in methanol prior to aging experiments to reset the thermal history of each polymer.At the beginning of the aging experiments, all samples went through the same drying conditions as indicated in Table 1, while PIM-NH 2 and PIM-NH 2 -FVM went through additional post-treatment steps.Fig. 2 depicts a graphical comparison of the pure-gas permeabilities of H 2 , O 2 , N 2 , and CH 4 for the three PIM polymers as a function of time to approximately 10 000 h.All data points in Fig. 2 are normalized to the rst data point for easier comparison of trends among polymers, but comparisons of aging behavior on an absolute scale are shown in Fig. S1 † and the tabulated values are in Table S4 † for reference.As shown in Table S4, † the permeability and selectivity of fresh lms are reasonably similar compared to the previously reported values. 29Given the need to understand uncertainty and reproducibility for membrane-based gas separation, 77 at least three total samples from different casting batches were tested up to 1000 h, and the results are shown in Fig. S5 and 6 † for comparison.The general trends remained the same within the tested 1000 h, conrming the reproducibility of our results shown in Fig. 2.
Physical aging of conventional polymer membranes manifests itself in permeability loss since polymers lose free volume as polymer chains relax toward their equilibrium packing structure. 38As shown in Fig. 2, all three PIM polymers showed this traditionally observed permeability loss with aging time, suggesting that neither the introduction of secondary interactions from amine groups nor the introduction of light crosslinks mitigates free volume reduction.The extent of permeability reduction (CH 4 > N 2 > O 2 > H 2 ) exactly followed the order of kinetic gas diameters (CH 4 : 3.80 Å; N 2 : 3.64 Å; O 2 : 3.46 Å; H 2 : 2.89 Å), indicating that the dependence of physical aging rate monitored via permeability correlated directly with the sizes of penetrants.Such a dependence is seen in many other studies in the literature, 47,78 and it is attributed to the strong effect of free volume loss on diffusivity, as will be further discussed later.Among the three polymers tested, in general, PIM-NH 2 -FVM showed the largest permeability decrease, resulting in a 75% decrease for the largest gas considered, CH 4 , followed by PIM-NH 2 (70%) and PIM-1 (50%), respectively.Interestingly, the extent of permeability decreases for the polymers considered switched order for the smallest gas considered, H 2 , as shown in Fig. 2a.In this case, PIM-1 had a 26% decrease from its initial permeability to the nal measured permeability at approximately 10 000 h, while PIM-NH 2 and PIM-NH 2 -FVM showed a 17% and a 9% decrease, respectively, from their initial hydrogen permeability.
To further elucidate these ndings, the permeability data in Fig. 2 have been tted to the following equation: 79,80 where P 0 is the initial permeability at t = 1 h and b P is the physical aging rate constant or the slope of the aging curves in Fig. 2. It should be noted that the b P in eqn (9) should gradually approach zero as the polymer structure reaches its equilibrium state, making the equation applicable only when membrane lms are far away from their equilibrium state.The continuous decreases in permeability up to 10 000 h, along with high R 2 values shown in Fig. 2, indicate that the lms are continuously undergoing an aging process and have not yet approached their near-equilibrium state.Additionally, the ts shown in the gure were not constrained to intercept the initial permeability data points because they do not represent the true starting time for physical aging, which is the end of the drying or thermal treatment procedure by our denition.Fig. 3 shows the b P of each polymer as a function of the kinetic diameter squared of gas penetrants.The strong correlations (R 2 > 0.968) for all polymers on a semi-log scale suggest that the aging rate is signicantly inuenced by the sizes of penetrants as previously discussed.The slope obtained by tting b P against squares of kinetic diameters demonstrates the sensitivity of the free volume change of a polymer to the increasing size of permeating gases.As shown in the inset table in Fig. 3, PIM-NH 2 -FVM had the steepest slope of 0.199 Å −2 , followed by PIM-NH 2 (0.137 Å −2 ) and PIM-1 (0.058 Å −2 ), which demonstrates that PIM-NH 2 -FVM has the highest sensitivity to penetrant size when observed physical aging rates are monitored by permeation.PIMs have a characteristic diffusion-selective nature provided by their stiffened polymer backbone structures, so the diffusive barrier is larger for larger gas molecules.Of note, both PIM-NH 2 and PIM-NH 2 -FVM have tighter packing structures induced by hydrogen bonding, and PIM-NH 2 -FVM also contains light urea crosslinks that preserve the narrow FVE distribution. 29For comparison, the slopes extracted from various aging data of PIM-1 available in the literature are shown in Table S6 and Fig. S4, † with values ranging from 0.039-0.098Å −2 .While some slopes extracted from the literature exhibit higher values compared to that of the PIM-1 lm investigated in this study,  the highest slope identied in the literature remains smaller than those of both PIM-NH 2 and PIM-NH 2 -FVM.This nding further suggests that the increased diffusion-selective properties from tighter packing structures and crosslinks result in higher sensitivity in observed aging rates for increasing gas sizes.
Regarding the observed change in the order of aging rates when testing H 2 for our samples as shown in Fig. 2a, we note that previous studies have proposed that small gases such as H 2 may have unique transport behavior relative to larger gases due to small, interconnected void spaces within the membrane matrix. 81We further note that the switch is also readily observed in Fig. 3.The higher relative change in permeability for H 2 in PIM-1 compared to PIM-NH 2 and PIM-NH 2 -FVM is simply a result of H 2 surveying a broader portion of the free volume distribution in PIM-1 compared to other gas molecules.From a simulation study of PIM-1 by Li et al., 78 the effective FFV of PIM-1 had a strong dependence on the size of the probe molecules surveying its accessible free volume.PIM-1 had an FFV of 0.255 when surveyed with an H 2 molecule (Connolly radius of 1.45 Å), while it had an FFV of 0.222 when surveyed with a CO 2 molecule (Connolly radius of 1.65 Å). 78 In the case of the PIMs studied in this work, PIM-1 had the largest FFV, and the addition of polar functional groups such as amines as well as thermal treatment reduced the amount of free volume inside the polymer matrix for PIM-NH 2 and PIM-NH 2 -FVM, as seen from the FFV values in Table 1.Hence, a more signicant effect of aging on the smallest penetrant is observed for PIM-1.Additionally, the stronger inuence of free volume loss on diffusivity dominates with increasing gas size for the postsynthetically modied counterparts.
Fig. 4 shows the ideal selectivity of two gas pairs, H 2 /CH 4 and O 2 /N 2 , monitored as a function of time.Analogous to the relative permeability aging plots, the selectivities were normalized to the rst data point for easier comparison, and the selectivities on an absolute scale are shown in Fig. S2.† The H 2 /CH 4 and O 2 /N 2 selectivities increased for all polymers with aging time.
This result is a typical permeability and selectivity trade-off response of physical aging since the reduction of free volume in polymer membranes affects larger molecules more signicantly. 38When compared across the samples, PIM-NH 2 -FVM showed the highest gain in selectivities for both gas pairs throughout the aging period, resulting in a 260% increase for H 2 /CH 4 , followed by 180% for PIM-NH 2 and 50% for PIM-1.Fig. 5 shows the comparison of selectivity gain and permeability loss with aging compared to other PIMs in the literature that reported aging data with a minimum of 100 days of aging.It is important to note that direct comparisons or correlations cannot be made because all data have different aging times and thicknesses, but a few interesting observations can be gleaned.First, PIMs that have hydrogen bonds without crosslinks (the blue data points in Fig. 5) did not have a particularly distinguishing gain in selectivity or loss in permeability with aging compared to other PIMs.This nding suggests the high sensitivity of the aging rate constant we observed for PIM-NH 2 in Fig. 3 may not be a generalizable feature for PIMs with hydrogen bonds.Introducing hydrogen bonds to polymer backbone structures may only tune the free volume structures of PIMs without giving a distinctive aging attribute, at least for noncondensable gases.Further analysis should be made for condensable gases such as CO 2 since polar functional groups that induce hydrogen bonds signicantly affect gas transport of condensable gases. 65Second, while there are limited aging data for crosslinked PIMs in the literature, crosslinked PIMs generally gained much higher selectivities with aging compared to non-crosslinked PIMs.In fact, the smallest gain in H 2 /CH 4 selectivity among the crosslinked PIMs was 143%, and this was the ninth highest gain among all PIMs considered (N = 58).Given these ndings, the high sensitivity of aging rate constants we observed for PIM-NH 2 -FVM in Fig. 3 may be a generalizable feature of crosslinked PIMs.
What is particularly interesting about PIM-NH 2 -FVM is that it showed the steepest slope from the origin of the H 2 /CH 4 plot even among the crosslinked PIMs in the literature, highlighting its remarkably large boost in selectivity without losing much permeability to hydrogen.This result suggests that there is unique stability towards smaller gas molecules and increasing molecular screening of large gas molecules with aging.We hypothesize that this observation is a result of the FVM method creating a larger number of small FVE pathways for small gas molecules such as hydrogen.From our previous report on PALS data, applying FVM to PIM-NH 2 resulted in a 19% increase in the intensity related to the smaller FVE (I 3 ) along with the narrowing of the FVE distribution, 29 indicating an increase in the number of small FVEs and a reduction of larger FVEs, which heavily impacts the diffusion of larger gas molecules.Thus, PIM-NH 2 -FVM exhibited a signicant permeability reduction for larger gas molecules while still permitting rapid and selective diffusion of small gas molecules such as hydrogen.

Detailed analyses of the physical aging results
Permeability in polymers can be decoupled into an effective diffusion coefficient, D i , and a sorption coefficient, S i , using the sorption-diffusion model: 82 This model states that permeation of penetrants through a polymer membrane is governed by both thermodynamic factors (i.e., sorption of penetrants into the polymer matrix) and kinetic factors (i.e., diffusion of penetrants through the polymer matrix).By using the ideal gas selectivity equation in eqn (6), diffusion and sorption selectivity can also be decoupled as follows: In order to obtain these parameters at particular time points, eqn (9) was used with the tting parameters obtained from the experimental data in Fig. 2 to estimate the permeabilities at the test times of sorption experiments.Then, effective diffusivity values were extracted using sorption coefficients from pure-gas sorption experiments and eqn (10).Fig. 6 presents the comparison of the percent change in permeability (6a), sorption (6b), diffusivity (6c), and O 2 /N 2 selectivities (6d) aer approximately 2230 h of aging, and Table S10 † shows the tabulated values.
As shown in Fig. 6b, the sorption coefficients did not signicantly change compared to permeability for all gases and polymers.The changes in sorption coefficients throughout the 2230 h aging period were less than −4% for PIM-1 and PIM-NH 2 -FVM for all gases.While PIM-NH 2 showed a larger decrease among the three polymers, the changes were still small compared to the permeability changes shown in Fig. 6a.As shown in Fig. S8-10, † sorption isotherms did not change signicantly even at high pressures for all polymers, and this result demonstrates that a decrease in sorption is not a signicant factor regardless of the type of functional groups and additional crosslinks that PIMs contain.Relatively small changes in sorption coefficients have also been observed for CO 2 in PIM-1 from a detailed physical aging study by Bernardo et al., 79 even though CO 2 has relatively higher sorption compared to the gases tested in this study.Thus, we believe our ndings are generalizable to various gases with PIMs.
In contrast to the sorption coefficients, the effective diffusivity decreased signicantly with aging, as shown in Fig. 6c.This nding suggests that the mechanism for aging of these PIMs is driven by changes to the packing structure of polymer segments.As expected, changes in both permeability and diffusivity followed identical trends, correlating closely with the size of penetrants, as shown in Fig. 6a and c.The densication of the polymer matrix impacts the diffusion of larger gas penetrants more signicantly compared to smaller gas penetrants, and this nding conrms our assertions in Section 3.1 that physical aging monitored by permeability has a large dependence on the kinetic gas diameter due to the diffusion selective nature of PIMs.Hence, the change in diffusion selectivity had a much larger contribution to the permselectivity, as shown in Fig. 6d, and H 2 /CH 4 separation had a much larger gain in selectivity compared to O 2 /N 2 due to the larger  According to the Brandt model, the activation energy of diffusion, E D , is directly proportional to the square of the penetrant diameter (d 2 ): where c and f are polymer-dependent constants. 83The diffusion of gases in polymers follows an Arrhenius relationship since it is an activated process: where D o is a front factor. 11Thus, the magnitude of slopes in a log-linear plot of diffusivity versus kinetic diameter squared serves as a proxy for the size-sieving ability of membranes.Fig. 7 shows this comparison for both the fresh and aged lms.Here, the unlled symbols show the linear ts for the fresh lms, while the lled symbols show the linear ts for the aged lms.
As shown in the gure, the effective diffusivities of the four gases tested were strongly correlated with the kinetic diameter squared (R 2 > 0.997), and the slopes of all polymers became steeper as they aged.For fresh lms, the order of size-sieving ability was PIM-NH 2 -FVM > PIM-NH 2 > PIM-1.When the changes are compared, PIM-1 had the smallest slope change of −19.6% compared to PIM-NH 2 (−32.4%) and PIM-NH 2 -FVM (−32.5%).This analysis agrees with the order of permeability and diffusivity selectivity changes in Fig. 4 and 6d.From these results, it is clear that the addition of an amine functionality and crosslinks initially resulted in lower diffusivities compared to their unfunctionalized counterparts, but these features also  accelerated apparent aging rates (i.e., permeability reduction rates) for larger gases.
To investigate the changes in energetics of gas transport, variable-temperature permeation tests were performed to obtain the activation energy of permeation, E p : 20 P = P 0 e −E p /RT (14)   where P 0 is a prefactor.The activation energies calculated are shown in Fig. S12, Table S12, † and Fig. 8 presents the change in activation energies of fresh samples and 710 h aged samples for PIM-NH 2 and PIM-NH 2 -FVM.As the lms aged, the activation energies increased for both polymers, which suggests that polymer segments have increased endothermic barriers for permeation.This nding is consistent with expected reductions in free volume with aging, which would increase the amount of energy required for an activated perturbation due to sterically hindered chain movements in constricted space. 41,84Moreover, the increasing changes in E P with increasing gas penetrant sizes clearly point to increasing size-sieving barriers, again highlighting the diffusion-dominant changes in the transport process in these PIMs.When comparing the changes in E P with aging, PIM-NH 2 -FVM generally had larger increases.This nding suggests that the network of crosslinks further increases the required energy for the permeation of gas molecules, in agreement with the large selectivity increases observed in Fig. 4. We further note that the small activation energy change for H 2 observed for PIM-NH 2 -FVM matches the aging rate constant trends shown in Fig. 3, suggesting that H 2 surveys a different free volume distribution compared to other larger gases.As previously mentioned, applying FVM to PIM-NH 2 creates a larger number of small FVEs and reduces the number of larger FVEs by narrowing free volume distribution.This free volume distribution change indicates that the FVM approach allows H 2 to access previously inaccessible small FVEs that locally have a smaller driving force for physical aging, and hence, the activation energy of hydrogen is less likely to be affected by aging.
3.3 Inuence of physical aging on the packing structure and free volume While permeation is a helpful property to quantify physical aging, permeability reduction is a function of both the initial FFV and the size of the gases, which makes it difficult to directly compare between permeability reduction and structural changes that result from aging.A detailed explanation of this complexity is outlined in Fig. S13 † and the surrounding text.In short, if two samples with different initial FFVs have the same amount of free volume reduction, the sample with the smaller initial FFV is likely to have a larger permeability reduction on a normalized scale.In other words, it cannot be simply assumed that PIM-NH 2 -FVM experiences more free volume contraction with aging since it generally experiences larger permeability reductions.Thus, detailed morphological and free volume analyses have to be made in addition to permeation tests to quantify aging behavior of glassy polymers.
The changes in the packing structure of the PIMs considered in this study were investigated using wide-angle X-ray scattering (WAXS).Fig. 9a presents the WAXS patterns for both fresh and aged PIM samples, where the dotted lines indicate the fresh lms.All patterns show four distinct peaks, and these peaks clearly resemble the WAXS patterns observed in our previous study. 29A study by McDermott et al. showed that the three peaks in the high-q region, highlighted by the gray background in Fig. 9a, represent characteristic distances of spiro centers on different chains, while the larger peak in the low-q region is closely related to the microporosity of PIMs. 85,86While the locations of the low-q peaks were nearly unchanged for the PIMs studied in this work, the three characteristic peaks in the high-q region showed non-negligible changes, which provides quantitative insights into polymer densication during the aging period.A magnied version of the WAXS patterns in the high-q region is shown in Fig. 9b, and Table S13 † presents the dspacing, which are the average interchain distances that were calculated from these three peaks.
As shown in Fig. 9c, the average interchain distances decreased for all polymers with aging.Interestingly, PIM-NH 2 had a comparable reduction for all peaks compared to PIM-1, and PIM-NH 2 -FVM had the largest reduction for all three peaks.While these are very small changes (∼1-2%) and the characteristic spiro center distances do not directly inform the actual free volume sizes in PIMs, we notice a few correlations that agree with the analysis in Fig. 4 and 6.First, the comparable d-spacing reductions for PIM-NH 2 and PIM-NH 2 -FVM with PIM-1 further support our assertion that neither the introduction of secondary interactions from amine groups nor the introduction of light crosslinks mitigates volume contraction.Even if the chain mobilities decrease due to reduced free volume from hydrogen bonding and crosslinks, the polymer packing structures still evolve towards their equilibrium conformations at an appreciable rate within the tested time frame.Thus, permeability reductions were observed for all polymers.Second, the reduction order for peak 3 (P 3 ), which is associated with the smallest d-spacing of around 3.8 Å, correlates with the order of selectivity gains in Fig. 4.This result suggests that d-spacing in the range of gas penetrant size has the largest effect on selectivity, a result that would be consistent with PIMs obeying the sorption-diffusion model, similar to other reports in the literature. 24,29,87iven the thickness of our lms for this study, we wanted to investigate ultra-long term aging behavior of our samples.9][90][91][92] During a PALS experiment, positrons (e + ) are naturally emitted from a radioactive source.These positrons "pick off" electrons in FVEs, forming a transient semi-stable particle ortho-positronium (o-PS) that is subsequently annihilated in the polymer matrix.The lifetimes of the o-PS atoms are correlated with average FVE sizes by using the Tao-Eldrup relationship, and FVE distributions can also be obtained by analyzing the lifetimes and the relative intensities of the model parameters. 93Two o-PS lifetimes (s 3 and s 4 ) were obtained from PALS for the samples in this work, indicating the presence of a bimodal distribution within the PIM lms.The total FFV for a bimodal FVE distribution is the sum of FFV calculated from each bimodal peak as shown in eqn (4).Thus, the amount of free volume contributed by each average FVE diameter (d i ) can be approximated using the following equation: 59,63 FFV PALS;si ¼ c Tables 2 and S14 † summarize the PALS parameters obtained for the samples from our previous study 29 that have been aged for approximately 20 000 h (833 days).Fig. 10a-c show the comparison of the average FVE size distributions (FSDs) obtained for fresh and aged samples.It is noted that our samples have the same chemistry and underwent the same drying conditions as the previous study, but earlier samples had been aged under atmospheric conditions instead of in a desiccator.As shown in Table 2 and Fig. 10a-c, PIM-1 showed the largest average FVE size reduction of −25.6 ± 5.2% and −3.6 ± 0.4% for the small and large FVEs, respectively, compared to PIM-NH 2 (−16.6 ± 4.3% and −3.0 ± 0.6%) and PIM-NH 2 -FVM (−17.5 ± 4.5% and −1.4 ± 0.7%) over this relatively long aging period.The notably larger changes in both FVE sizes for PIM-1 agree with our analysis in Section 3.1 in that PIM-1 had the largest b The presented time is the aging time at the start of PALS experiments.c PALS data for fresh samples are from a previous study. 29ermeability reduction for only H 2 but a smaller permeability reduction for larger gases.This interesting nding is related to H 2 being able to survey a broader portion of free volume distribution due to its small size.Remarkably, the reduction orders for both d 3 and d 4 were strongly correlated with the order of the corresponding initial FFV PALS,s i , as shown in Fig. 10d and  e.More detailed experiments are required to investigate the correlation between free volume and rates of free volume reduction, but the comparison of FSDs with long aging times suggests that the total extent of structural change is most strongly correlated with the initial amount of free volume and not with amines or light crosslinks.This nding matches known trends for conventional glassy polymers, 40,84 suggesting that the same mechanistic and theoretical phenomena for aging apply to PIMs.

Conclusions
In this study, physical aging behavior of PIM-1, aminefunctionalized PIM-1 (PIM-NH 2 ), and free volume manipulated PIM-NH 2 (PIM-NH 2 -FVM) were systematically investigated via gas transport and structural analyses to closely examine how each modication impacted physical aging.The investigation of free volume size distribution for lms aged ∼2 years showed that PIM-1, which had the highest initial free volume compared to its aminated and crosslinked counterparts, had the largest total free volume reduction.This result indicates that initial free volume is the largest driver of free volume relaxation.Gas transport studies revealed that permeability changes from the structural relaxation process are strongly correlated with factors that inuence diffusion, such as penetrant size, free volume distribution, and crosslinks.As a result, the aminated PIM-1 derivative with higher initial free volume and light crosslinks showed an accelerated reduction in permeability for larger gases compared to its lower free volume counterpart without crosslinks.Taken together, initial free volume is the primary driving force for reducing free volume, but hydrogen bonds and crosslinks can introduce attributes that strongly impact diffusion of large gas molecules, contributing to improved permselectivity changes in microporous membranes.

Fig. 1
Fig.1The free volume manipulation (FVM) approach for PIM-NH 2 starting with the precursor PIM-1.Note that light crosslinking in PIM-NH 2 -FVM is represented by a potential urea bond.

Fig. 2
Fig. 2 Comparison of aging behavior by tracking pure-gas permeabilities on a normalized scale for (a) H 2 , (b) O 2 , (c) N 2 , and (d) CH 4 .All data have been normalized to the first data point to show relative permeability.The linear fits of the experimental data on a log-log scale are shown in the dashed lines along with their R 2 values.

Fig. 3
Fig. 3 Comparison of permeability aging rate constants (b p ) extracted from the experimental permeability data as a function of the kinetic diameter squared of penetrants.The dashed lines are linear fits of b p on a semi-log scale, and the resulting slopes are shown in the inset table.

Fig. 4
Fig. 4 Comparison of selectivity as a function of time on a normalized scale for (a) H 2 /CH 4 and (b) O 2 /N 2 .All data have been normalized to the first data point to show relative selectivity.The linear fits of the experimental data on a log-log scale are shown in the dashed lines along with their R 2 values.

Fig. 5
Fig. 5 Comparison of long-term physical aging effects on (a) H 2 /CH 4 and (b) O 2 /N 2 separation for various PIMs reported in the literature. 13,19,89,94-105The star symbols are PIMs in this study, and only polymer films with a minimum of 100 days of aging are considered.The dotted orange line is a parity line, representing equal permeability loss and selectivity gain.

Fig. 6
Fig. 6 Percent changes in (a) permeability, (b) sorption, (c) diffusivity, and (d) O 2 /N 2 selectivities over approximately 2230 h of physical aging.The gases are ordered from smallest to largest kinetic diameters, and gray dashed lines separate the three tested gases (O 2 , N 2 , and CH 4 ) in figures a-c.

Fig. 7
Fig. 7 Comparison of effective diffusivity plotted against kinetic diameter squared for fresh and 2230 h aged samples.Unfilled symbols represent fresh samples, and filled symbols represent aged samples.R 2 values for all fittings were above 0.997.

Fig. 8
Fig. 8 Comparison of changes in activation energy of permeation (E p ) for PIM-NH 2 and PIM-NH 2 -FVM samples upon aging.The samples were aged for 710 h.

Fig. 9
Fig. 9 Comparison of wide-angle X-ray scattering patterns on a (a) full scale and (b) magnified scale for PIM-1, PIM-NH 2 , and PIM-NH 2 -FVM.The fresh samples are represented by dotted lines, while the samples that have been aged for approximately 1400 h are represented by solid lines.The red dotted lines in (b) represent the peak values used to calculate the d-spacing, and the changes in the d-spacing obtained from the patterns are shown in (c).Table2A summary of average FVE diameters (d i ) and the corresponding FFV contributions (FFV PALS,s i ) obtained from PALS.PALS experiments considered samples from our previous study 29 that had been aged for approximately 20 000 h (833 days), and the changes are compared with the PALS data from the previous study a

Table 1
A summary of information on the polymers studied in this paper, including thickness, density, fractional free volume calculated from the group contribution method (FFV group ) and PALS (FFV PALS ), drying conditions, and post-treatment conditions a Light urea crosslinks were not considered in the calculation.