thornton doherty falcaro buso amenitsch han lee hill2013

Architecturing Nanospace via Thermal Rearrangement for HighlyEfficient Gas SeparationsAaron W. Thornton,*,† Cara M. Doherty,† Paolo Falcaro,† Dario Buso,† Heinz Amenitsch,‡

Sang Hoon Han,† Young Moo Lee,§ and Anita J. Hill†

†Materials Science and Engineering, and Process Science and Engineering, Commonwealth Scientific and Industrial ResearchOrganization, Private Bag 33, Clayton South MDC, Victoria 3169 Australia‡Institute of Inorganic Chemistry, Graz University of Technology, Stemayerg, 9/IV, A-8010 Graz, Austria§School of Chemical Engineering, and WCU Department of Energy Engineering, Hanyang University, Seoul 133-791, Republic ofKorea

*S Supporting Information

ABSTRACT: The ability to monitor free volume formation during space-makingtreatments is critical for the ultrafine tuning of nanospace for efficient gasseparation. Here, investigating the polymer thermal rearrangement usingsynchrotron in situ small-angle X-ray scattering for the first time and combiningthis information with transport theory, we elucidate the evolution of nanospacefeatures in polymer-based gas separation membranes. The proposed nanospacemonitoring technique encompasses the structure−property relationships, thereforeoffering a powerful tool for tuning the polymer properties for particular gas-relatedclean energy applications. These results demonstrate that the fine control of thenanospace dimension and magnitude leads to a drastic improvement in gasseparation performance above any material to date.

■ INTRODUCTION

Advances in materials with improved perm-selective propertiesare essential to enable more efficient energy production and toreduce emissions.1−6 The thermal rearrangement (TR)method7 has provided a breakthrough in the production ofpolymer membranes with nanospace tuned for fast selectivetransport of small molecules. These TR polymers have set thebenchmark for energy-efficient carbon dioxide capture, hydro-gen purification, and natural gas processing applications.7 TheTR method has been shown to increase carbon dioxidepermeability by 3 orders of magnitude without significant lossin selectivity for CO2/CH4, CO2/H2, and CO2/N2 separations.

8

Despite the remarkable efficiency of TR polymers and theattribution of their performance to the unique hourglass-shapednanospace configuration, there is a lack of fundamental insightinto the evolution of nanospace architecture in these materials.Understanding the structure−property relationship through-

out the structure evolution during thermal rearrangement is thegoal of the present work. Understanding these relationships willfacilitate further development and broader adoption of TRpolymers to address the profound industrial challenge ofcarbon-free energy production.9,10 In work to date, thechemistry of TR polymers has been investigated via massspectroscopy and Fourier transform infrared (FTIR) spectros-copy confirming the proposed mechanism of thermal rearrange-ment from precursor hydroxyl-containing polyimide topolybenzoxazole. The structure has been characterized via

positron annihilation lifetime spectroscopy (PALS),7,11 small-angle X-ray scattering (SAXS),7,12 and molecular simulation,13

confirming the creation of nanospace elements (∼ 1 nm).High-temperature performance has been measured, confirmingthe remarkable enhancement in gas permeability and selectivityas well as the thermal robustness of these materials.8 However,the predictive relationship between structure and properties hasnot yet been provided. Here, for the first time, we elucidate theTR process by combining PALS and real-time SAXS measure-ments coupled with transport theory, consequently offeringinsights and strategies for fine-tuning nanospace taking fulladvantage of the thermal rearrangement process.

■ EXPERIMENTAL SECTION

Materials. Synthesis details for these materials have beenreported in the work of Park et al.7 The precursor polymer isPIOFG-1, synthesized from 4,4′-hexafluoroisopropylidene-diphthalic anhydride (6FDA) and 2,2′-bis(3-amino-4-hydrox-ylphenyl) hexafluoropropane (bisAPAF) prepared via thermalimidization up to 300 °C, and its corresponding thermallyrearranged polymers are named TR-1-350, TR-1-400, and TR-1-450 for thermal rearrangement temperatures of 350, 400, and450 °C respectively.

Received: October 9, 2013Revised: October 17, 2013Published: October 18, 2013

Article

pubs.acs.org/JPCC

© 2013 American Chemical Society 24654 dx.doi.org/10.1021/jp410025b | J. Phys. Chem. C 2013, 117, 24654−24661

pubs.acs.org/JPCC

Positron Annihilation Lifetime Spectroscopy (PALS).PALS uniquely probes nanospace including those free volumeelements that are inaccessible to surface adsorption techni-ques.14−19 The PALS technique utilizes the relationshipbetween the lifetime of the semistable orthopositroniumprobe (o-Ps, kinetic size ≈ 1.06 Å) and the local electrondensity of the regions where annihilation occurs.14 The o-Ps isformed as the positron from a radioactive source, in this case22Na, penetrates the sample, forming a bound state with anelectron of the same spin. The lifetime of this component τo‑Psis measured using an Ortec positron lifetime system (Ortec,Oak Ridge, TN, USA). The lifetime of this component τo‑Ps isrelated to the hole radius R using the Tao−Eldrup equation20,21

τπ

π= −+ Δ

++ Δ−

−⎜ ⎟

⎡⎣⎢

⎛⎝

⎞⎠⎤⎦⎥

RR R

RR R

0.5 11

2sin

2o Ps

1

where ΔR is the electron cloud thickness (1.656 Å).22 Throughdeconvolution algorithms such as CONTIN,23 MELT,24 LT,25

and PAScual,26 we can extract the number of o-Ps lifetimes τo‑Psand their relative intensities Io‑Ps, which can be related to thehole size and relative number of holes, respectively.27 PALS iscapable of detecting a wide range of hole sizes, 1.06−200 Å, andis also capable of detecting multimodal size distributions.28−30

In the case of microporous polymers, bimodal hole sizedistributions have been detected.31 Here we analyze the PALSdata using PAScual for the TR polymers to investigate thetransition between unimodal and bimodal nanospace morphol-ogies, summarized in Table S1 of the Supporting Information.In Situ Small Angle X-ray Scattering (SAXS). To

effectively heat the sample to thermal-rearrangement temper-atures ∼450 °C while allowing beam access for SAXSmeasurements, the sample was sandwiched between two piecesof mica (because of its weak scattering fingerprint) within ahigh-temperature stage (Linkam cell) and thermally treatedunder nitrogen atmosphere. Measurements were performed atthe Australian Synchrotron over a q range of 0.02−1 Å−1 with acamera length of 962.6 mm and beam wavelength of 1.0332 Å.Temperature calibration of the SAXS experimental setup

using the Linkam cell was performed ex situ with athermocouple located on the sample at the beam locationand another remote thermocouple located on the sampleoutside the beam location. In situ measurements wereperformed with the remote thermocouple located on thesample outside the beam location. For the in situ configuration,a thermocouple reading of 500 °C gave a sample temperature atthe beam location of 450 °C. A comparison is made betweenthe SAXS results for an oven-treated sample at 450 °C and anin situ beamline treated sample with a sample temperature of450 °C (thermocouple reading of 500 °C). The goodcomparison confirms that the treatments and the resultantstructures are the same, see Figure S1 of the SupportingInformation. The thermal procedure includes a ramp fromroom temperature to 300 °C at 10 °C min−1, then a ramp at 20°C min−1 to the annealing temperature.The measured scattering intensity is a function of the

structure factor and the form factor, from which informationabout the molecular structure and morphology can beextracted. Here we use an empirical Voigt function, definedas the convolution of a Gaussian profile and a Lorentzianprofile, to describe the scattering pattern of the precursorpolymer which has no dominant scattering features. Theparameters for this fit are then utilized in the sticky−hard

sphere (SHS) Schultz model to describe the feature arisingfrom TR, namely the nanospace holes (∼1 nm).32 The SHSSchultz model assumes that the scattering feature is a result ofhard spheres with a shell and a hollow core, corresponding tocavities with the surrounding bulk polymer as the shell. Furtherdetails of this model can be found by referring to the work ofPontoni et al.32

Thermal Gravimetric Analysis (TGA). TGA wasperformed in flowing nitrogen using a Pyris thermogravimetricanalyzer (PerkinElmer Product N5378101, Revision 2.05,Shelton, CT) and a ramp from room temperature to 300 °Cat 10 °C min−1, then a ramp at 20 °C min−1 to the annealingtemperature.

Molecular Visualization. Molecular representations ofpolymers with various chemical structures and free spacewere constructed and characterized using the Materials Studio5.5 package (Accelrys Inc., San Diego, CA, 2005). The PolymerBuilding tool was used to grow the polymer chains, theAmorphous Cell module to randomly pack the molecules withina cell to match the experimental density, and the Forcite moduleto equilibrate the structures based on the geometryoptimization routine with COMPASS as the forcefield. Freevolume and occupied volume were mapped out using theAtomic Surfaces tool based on a probe radius of 1.4 Å. Furtherdetails of this method can be found in Jiang et al.13

Transport Theory. Permeability through glassy nonporouspolymer membranes typically follows the solution−diffusionmodel in which permeability is defined as the product ofsolubility and diffusivity, a convenient equation for separatingpermeability into the “quantity” of the gas and the “speed” ofthe gas, respectively. Diffusivity, an activated process, can berepresented in the Arrhenius form where temperature is thedriving force and the energy barrier correlates with the gasdiameter squared σ2 (or the effective area necessary for a gasmolecule to move), while solubility is usually described byHenry’s law.33−35 However, a purely predictive equation forpermeability within polymers is yet to be established because ofthe complexity of chemistry and chain dynamics; therefore,here we adopt a theoretical framework which assumes that thetotal permeability Pi for gas i is a combination of permeabilitythrough the “bulk” or dense polymer Pbulk,i and the “nanoholes”Pcav,i which are created during thermal rearrangement. Thistheory assumes that the physical transformation “nanoholes” inthe material dominates the transport properties over thechemical change “bulk”, supported by the work of Jiang et al.13

and Han et al.8 According to the resistance in series (RIS)model, the total permeability is defined as

ϕ ϕ=

+ −P

P P

P P(1 )ii i

i i

bulk, cav,

bulk, cav, (1)

where ϕ is the void fraction (or the fraction of cavitiesencountered in the flow direction). As Pbulk,i cannot yet bepredicted from chain chemistry alone, we set it to theexperimentally determined permeability for the nonporousprecursor polymer in the work of Park et al.7 During thermaltreatment, nanoholes of approximately 1 nm in diameter areformed. These holes act as pathways similar to those foundwithin inorganic membranes such as carbons, silicas, andzeolites, where the RIS transport is appropriate.36−40 Therefore,permeability may be described as

=P D S , (permeability)i i icav, cav, cav, (2)

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp410025b | J. Phys. Chem. C 2013, 117, 24654−2466124655

στ

=−

Dd

u3

, (diffusivity)ii

icav, (3)

ϕ=⎛⎝⎜

⎞⎠⎟S

RT

Q

RTexp , (solubility)i

icav,

(4)

where ui̅ = (8RT/πmi)0.5 is the average molecular velocity of gas

i with molecular mass mi according the Boltzmann distribution,d the average cavity diameter, τ the tortuosity, σi the gas kineticdiameter, and Qi the enthalpy of adsorption approximated hereas the van der Waals well depth εi for gas i.

41 This formulationconsiders that the diffusivity depends on the effective cavity

Figure 1. Nanospace characteristics of various materials with oxygen permeability grouped into categories of high free volume polymers,conventional glassy polymers, and liquid crystallines. Highlighted polycarbonate (PC) (green), TR 450−1 (blue), and poly(trimethylsilyl-1-propyne)(PTMSP) (red). (a) Bondi fractional free volume (FFV) with dashed lines separating regions of nanospace morphology predicted by Hedstrom etal.45 (b) PALS nanospace element size derived from Tant et al.,46 Staiger et al.,29 Budd et al.,31 and Park et al.7 (analyzed using PAScual26). Arrowedlines emphasize the transition from a unimodal precursor polymer (PIOFG-1) to a bimodal TR polymer (TR 450−1). Inset depicts nanospace sizedistributions for PC (green), TR 450−1 (blue), and PTMSP (red). (c) Number of nanospace elements (or nanospace magnitude). (d) InversePALS free volume of the third component with the exception of high free volume polymers where the fourth component is used. (e) Molecularstructures emphasizing the morphology of occupied volume (red) and free volume (blue) that drastically effect transport. PIOFG is omitted in (c)and (d) because the o-Ps inhibition significantly affects the measured PALS intensity.14,27,50



diameter (d − σi), which treats the gas molecule as a hardsphere rather than a point mass, and has proven to be a moreaccurate description within cavities less than 1 nm indiameter.39 Similarly, the solubility is more accurately describedby incorporating the condensability of the gas according toHenry’s law.If the cavity diameter is set to the value detected by PALS,

the model offers two adjustable parameters that can be used tounderstand the evolution of cavity morphology during thermalrearrangement, namely, ϕ and τ, which can be reduced to oneadjustable parameter if we assume a relation such as τ = (1/vf,i)

1/2, which is from Friedman et al.42

■ RESULTS AND DISCUSSIONMembrane performance is known to strongly correlate with theamount and nature of the free volume available for gasdiffusion, termed here nanospace.35 Here we compare nano-space characteristics for a wide range of high free volumepolymers, conventional glassy polymers, and liquid crystallines(Figure 1).Fractional free volume (FFV) calculated using Bondi’s group

contribution theory43 is a quantifiable characteristic of nano-space with a strong correlation with gas permeability.44 InFigure 1a, oxygen permeability versus FFV data is plotted withnanospace morphology definitions, namely, bimodal, perco-lated, and isolated. The critical FFV values for each morphologyregime is predicted by Hedstrom et al.45 In general, it ispredicted from the model that liquid crystallines compriseisolated pockets of nanospace, conventional glass polymerscomprise percolated pathways, and high free volume polymerscomprise bimodal distribution of nanospace elements. Fromthis prediction, the precursor polymer (PIOFG-1) transitionsfrom a percolated network of nanospace with unimodaldistribution into a bimodal distribution (i.e., a separation oftwo phases, the dense bulk phase and the void phase congruentwith a bimodal nanospace size distribution) during thermaltreatment.Further analysis using PALS that uniquely probes nanospace

with antimatter particles reveals a nanospace dimension(approximated as a cylindrical free volume element). PALSdata for the range of materials7,29,46 are presented in Figure 1b(see details in Table S1 of the Supporting Information) alongwith oxygen permeability. The transition stages during thethermal evolution from the precursor polymer (PIOFG-1) tothe TR material (TR-1) are highlighted. The data furtherconfirm a unimodal nanospace size distribution for conven-tional polymers and a bimodal nanospace distribution for highlypermeable polymers. There is also general trend from a class ofpolymers with low permeabilities and small nanospace elementslike those of the liquid crystalline “barrier” polymers toward aclass of “permeable” polymers with high permeabilities andlarge nanospace elements (micropores according to the IUPACdefinition >1 nm). Other polymers lie between these twoclasses where the nanospace size distribution may be equallydescribed by a broad unimodal or bimodal distribution, as hasbeen illustrated by recent molecular simulations of the TRpolymer series.13 This free volume distribution is furtherexplored in the inset of Figure 1b where the ratio of small tolarge nanospace elements is compared for TR and poly(1-trimethysilyl-1-propyne) (PTMSP). The TR nanospaceelement populations are evenly distributed compared toPTMSP, which contains more large nanospace elements thansmall elements.29,47,48 If the polymer contains too many large

nanospace elements, as found in PTMSP, continuous nano-space pathways will form where nonselective Knudsen diffusionis the dominate transport mechanism. This point wasemphasized by Robeson where the Knudsen-expected perme-ability was achieved within PTMSP.49 These data suggest thatby controlling the nanospace element populations one canmaximize permeability without loss in selectivity.Further insight is gained through the deconvolution of

nanospace magnitude (or number of nanospace elements)shown in Figure 1c. There is a major separation of the classes ofmaterials here as the nanospace elements divide and coalesceinto distinct morphologies characterized earlier as isolated,percolated, and biomodal networks, depicted in Figure 1e.Finally, there is a strong correlation between the PALS freevolume and oxygen permeability in Figure 1d similar to thatfound with FFV, though amplified here with a power lawdependence rather than an exponential dependence.To monitor the evolution of nanospace structure during the

thermal treatment for temperatures up to 450 °C, weperformed in situ SAXS as depicted in Figure 2. X-rays scatter

depending on the electron density configuration within thematerial, and they scatter on different length scales rangingfrom 5 Å to 0.5 μm depending on the instrument’s power anddetection capabilities. When the appropriate camera length andbeam energy is chosen, the SAXS instrument can detectstructural changes in the range of interest ∼1−100 Å.The SAXS data are displayed in Figure 3. The scattering

intensity is a function of the structure factor and the formfactor, from which information about the molecular structureand morphology can be extracted. Here we use an empiricalVoigt function, defined as the convolution of a Gaussian profileand a Lorentzian profile, to describe the scattering pattern ofthe precursor polymer which has no dominant scatteringfeatures (i.e., no large nanospace elements). The parameters for

Figure 2. In-situ SAXS experimental set up monitoring nanospaceevolution during thermal rearrangement (TR), with spectra andcorresponding molecular representations before and after thermaltreatment.



this fit are then utilized in the sticky−hard sphere (SHS)Schultz model to describe the scattering feature arising from

TR, namely the large nanospace elements.32 The volumeintensity Ihs and the radius of the cavities Rhs are listed in Table1 with other relevant parameters. Scattering intensities during

thermal treatment are shown in Figure 3a,b, demonstrating thetransition from the polymer Voigt model to the combined SHSSchulz model plus polymer Voigt model. The SAXS analysisindicates an average nanospace diameter of 7 (±2) Å, which iscomparable to that measured by PALS of 9 Å7 (see Table S2 ofthe Supporting Information for the variance in the SAXSnanospace diameter parameter). The nanospace size did notchange significantly throughout the treatment, whereas themagnitude of the nanospace increased rapidly at a criticaltemperature of 450 °C for both PALS and SAXS measure-ments. These results suggest that the evolution of nanospacestructure involves the immediate creation of large nanospaceelements of uniform size and distribution.The structural factor, equal to the product of intensity and q

squared, is another good measure for monitoring significantstructural changes over the length scale of interest and isplotted in Figure 3c. Here we compare the structural changesand the mass loss during thermal treatment, measured bythermal gravimetric analysis (TGA). According to the model32

that describes the formation of nanospace elements, asignificant structural change is detected when 450 °C isreached (heating ramp at 20 °C/min). The mass loss is shownto also increase at the same critical transition temperature,suggesting that the chemical conversion is associated with thecreation of nanospace. Interestingly, this event is followed by agradual structural change during the annealing time which isnot attributable to the formation of extra nanospace. Wepropose that this gradual change is most likely due to thephysical aging mechanism (or configurational readjustment ofthe chains due to a change in chemical composition) which isaccelerated at temperatures close to the glass transitiontemperature. Previous studies propose explanations related toa narrowing of the nanospace element size distribution and agradual decrease of nanospace size and magnitude.19,23,29,30 Forthe first time, using SAXS, this transition has been clearlyobserved. The in situ SAXS technique is shown to be capable ofcharacterizing the evolution of nanospace morphology duringvarious thermal treatments, providing important parameterssuch as volume of spheres/nanospace elements (Ihs) and meansphere radius (Rhs). Combining this information with a modellinking nanospace architecture to transport properties,51 themembrane free space can be now efficiently tuned to optimizesmall molecule transport for separation, capture, and deliverytechnologies.The PALS and SAXS data give experimentally determined

parameters compatible with a resistance in series (RIS)transport model to link structure and properties. In this

Figure 3. (a) In-situ SAXS measurement during thermal treatmentfrom 25 to 450 °C. The solid black lines indicate the model fit with theempirical Voigt function for the polymer component and the Schulzsphere for the nanospace component. (b) Three-dimensionalrepresentation of the in situ SAXS data. Red arrow indicates the qposition for nanospace evolution and the dotted line emphasizes thefinal shape of the completely converted TR polymer at frame number60. The color gradient of the surface corresponds to intensity. (c) Insitu SAXS structure factor (product of intensity and q squared)throughout thermal treatment (red line) and TGA data (green line).Thermal treatment includes a ramp from room temperature to 300 °Cat 10 °C min−1, then a ramp at 20 °C min−1 to the annealingtemperature of 450 °C. Frame numbers correspond to the thermaltreatment procedure.

Table 1. Fitting Parameters for SAXS Analysis with theSticky−Hard Sphere (SHS) Schulz Model and VoigtPolymer Framework

frame temperature SHS intensity Ihs SHS radius Rhs

60 450 °C + 40 min 141 3.3950 450 °C+ 27 min 140 3.4240 450 °C + 14 min 155 3.4530 450 °C + 1 min 148 3.4620 380 °C 48 3.4210 300 °C 29 3.38



model, large free volume elements are introduced into a denseglassy polymer matrix. The aim of this approach is to model theTR process using the mass loss (TGA) from the chemicalconversion and the nanospace size and magnitude (SAXS andPALS) from the structure evolution to predict the gaspermeability and selectivity properties as they evolve duringthermal rearrangement. The correlation between SAXS nano-space magnitude, PALS nanospace size, fitted transport voidfraction, and TR temperature is shown in Figure 4. Each

parameter is correlated with the TR temperature TR (or TRtreatment recorded as frame numbers) as demonstrated inFigure 5a. The following correlation functions were used:

ϕ =+ − +

−

TT

Transport void fraction ( )1

1 exp( 47)

[ ]

RR

0.65

(5)

= −D T TPALS nanospace diameter ( ) 3.7 0.067 [Å]R R(6)

=+ − +

I TT

SAXS sphere intensity ( )100

1 exp( 47)sph RR

0.65

(7)

=+ − +

−

T

T

SAXS structural invariant SI( )0.428

1 exp( 47)1

R

R0.65

(8)

=+ − +

M TT

Mass loss ( )10

1 exp( 47)Rloss R 0.65

(9)

This approach conveniently encompasses the featuresobserved for chemistry, structure, and properties using theTGA, PALS, SAXS, and permeability measurements in thisstudy. The performance, here characterized by CO2/CH4selectivity as a function of CO2 permeability, is related to thecritical treatment parameter, namely the TR temperature,through the RIS transport model (solid black line),demonstrated in Figure 5b. The model qualitatively predictsthe direct consequence of nanospace introduction within thepolymer matrix. The most unique insight from the model isthat there is an optimum nanospace distribution for efficient gasseparation that is created by reaching a treatment temperatureof 450 °C. Any further temperature rise will cause too muchconnected nanospace that offers continuous “low-selective”Knudsen pathways, as indicated by the dashed line segmentcalculated for TR temperatures greater than 450 °C for TR-1.Note that the model assumes that nanospace creation is acontinuous function of TR temperature. Realistically, there willbe a temperature limit where the polymer will carbonize,rendering this assumption invalid. However, the modelimportantly correlates the nanospace formation to thetemperature for this particular polymer. Other polymers willhave slightly different correlations and further investigations are

Figure 4. In situ synchrotron SAXS intensity with PALS and transportmodel parameters during TR treatment.

Figure 5. (a) Correlation between each parameter during TRtreatment according to eqs 5−9. (b) Performance trade-off plot ofcarbon dioxide/methane selectivity versus carbon dioxide permeability.RIS transport model (black line: solid segment from 25 to 450 °C anddashed segment beyond 450 °C), see eq 1.



required. The connectivity of free volume elements (mapped inblue) is critical for achieving maximum transport rates whilemaintaining maximum selectivity via constrictive regions asdepicted in Figure 1e. The RIS transport model predicts ananospace architecture that is not too closed, not too open, but‘just right” for the Goldilocks nanospace developed during theTR method.

■ CONCLUSIONFor the first time the TR process has been directly monitoredexperimentally using SAXS. This investigation based on X-rayscattering has proven to be an effective analytical methodologyto follow the changes of the nanospace features as aconsequence of the thermal treatment.Using a synchrotron facility and a dedicated setup, the

evolution of nanospace architecture in TR polymers has beenelucidated, and the process−property relationship has beensuccessfully modeled. The methodology presented here willhelp to design perm-selective materials with features tuned forprecise applications.

■ ASSOCIATED CONTENT*S Supporting InformationDetails of positron annihilation lifetime spectroscopy (PALS)and in situ small angle X-ray scattering (SAXS). This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis research was undertaken on the SAXS beamline at theAustralian Synchrotron, Victoria, Australia. The authors thankDrs. Nigel Kirby, Stephen Mudie, and David Cookson for theirhelpful discussions and technical prowess. A.W.T., C.M.D.,S.H.H., P.F., and A.J.H. acknowledge CSIRO funding via theOffice of the Chief Executive Science Team, and the AdvancedMaterials and Computational Science and Simulation Trans-formational Capability Platforms. The Australia−Korea EarlyCareer Science and Technology Researchers Program isacknowledged for support of A.W.T. and C.M.D. Y.M.L.acknowledges the WCU program (R31-2008-000-10092-0) andKorea CCS 2020 project (2012-000-8606) through the KoreanMinistry of Science and Technology. P.F. acknowledges theARC for support from DECRA Grant DE120102451, and theAM-TCP CSIRO scheme.

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(45) Hedstrom, J. A.; Toney, M. F.; Huang, E.; Kim, H. C.; Volksen,W.; Magbitang, T.; Miller, R. D. Pore Morphologies in DisorderedNanoporous Thin Films. Langmuir 2004, 20, 1535−1538.(46) Hill, A. J.; Tant, M. R.; McGill, R. L.; Shang, R. R.; Stockl, D. L.;Murray, D. L.; Cloyd, J. D. Free Volume Distribution DuringConsolidation and Coalescence of Latex Films. J. Coat. Technol. 2001,73, 115−124.(47) Yampol’skii, Y. P.; Shantorovich, V. P.; Chernyakovskii, F. P.;Kornilov, A. I.; Plate, N. A. Estimation of Free Volume inPoly(trimethylsilyl propyne) by Positron Annihilation and Electro-chromism Methods. J. Appl. Polym. Sci. 1993, 47, 85−92.(48) Consolati, G.; Genco, I.; Pegoraro, M.; Zanderighi, L. PositronAnnihilation Lifetime (PAL) in Poly[1-(trimethyl-silyl)propine](PTMSP): Free Volume Determination and Time Dependence ofPermeability. J. Polym. Sci., Part B: Polym. Phys. 1996, 34, 357−367.(49) Robeson, L. M. The Upper Bound Revisited. J. Membr. Sci.2008, 320, 390−400.(50) Geise, G. M.; Willis, C. L.; Doherty, C. M.; Hill, A. J.; Bastow, T.J.; Ford, J.; Winey, K. I.; Freeman, B. D.; Paul, D. R. Characterizationof Aluminum-Neutralized Sulfonated Styrenic Pentablock CopolymerFilms. Ind. Eng. Chem. Res. 2013, 52, 1056−1068.(51) Thornton, A. W.; Hilder, T.; Hill, A. J.; Hill, J. M. Predicting GasDiffusion Regime within Pores of Different Size, Shape andComposition. J. Membr. Sci. 2009, 336, 101−108.



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