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1 Polymer 50 (009) Contents lists ville t ScienceDirect Polymer journl homepge: Physicl ging of ultrthin glssy polymer films trcked y gs permeility Brndon W. Rowe, Benny D. Freemn, Donld R. Pul * Deprtment of Chemicl Engineering, Texs Mterils Institute nd Center for Energy nd Environmentl Resources, The University of Texs t Austin, Austin, Texs 7871, United Sttes, USA rticle info strct Article history: Received 10 July 009 Received in revised form 7 Septemer 009 Accepted 13 Septemer 009 Aville online 1 Octoer 009 Keywords: Physicl ging Gs permeility Memrnes Memrne-sed seprtions ply key role in energy conservtion nd reducing greenhouse gs emissions y providing low energy routes for wide vriety of industrilly-importnt seprtions. For resons not completely understood, memrne permeility chnges with time, due to physicl ging, nd the rte of permeility chnge cn ecome orders of mgnitude fster in films thinner thn one micron. The gs trnsport properties nd physicl ging ehvior of free-stnding glssy polysulfone nd Ò films s thin s re presented. Physicl ging persists in glssy films pproching the length scle of individul polymer coils. The films studied rnged from 18 5 thick. They exhiited reductions in gs permeility, some more thn 50%, fter w1000 h of ging t 35 C, nd increses in selectivity. The properties of these ultrthin films devite drmticlly from ulk ehvior, nd the nture of these devitions is consistent with enhnced moility nd reduced T g in ultrthin films. The Struik physicl ging model ws extended to ccount for the influence of film thickness on ging rte, nd it ws shown to dequtely descrie the ging dt. Ó 009 Elsevier Ltd. All rights reserved. 1. Introduction The multitude of thin polymer film pplictions in, for exmple, microelectronics, cotings, seprtions, nd optics, hs stimulted gret interest in understnding polymer properties t the nnoscle [1 8]. Behvior of the glss trnsition temperture, T g, (which is typiclly ssocited with long-rnge coopertive moleculr motion nd is often referred to s the softening point of rigid, morphous glssy polymer) in ultrthin polymer films is n re of intensive reserch nd dete [3,9 14]. Typiclly, s film thickness decreses, free stnding films nd films supported on non-ttrctive sustrtes exhiit decresing T g, while films on ttrctive sustrtes show incresing T g [13]. These devitions from ulk ehvior re generlly ttriuted to enhnced moility t the free surfce nd ttrctive sustrte-polymer interctions, respectively [3,13]. However, the genesis of these property chnges is not completely understood ecuse different experimentl techniques cn revel pprently conflicting results, such s the divergent thickness-dependence of the diltometric nd dielectric T g of hyperrnched polyesters reported y Serghei et l. [1,14]. Additionlly, Forrest et l. hve shown tht the sme polystyrene smples which exhiit decresing T g with film thickness, indicting tht moleculr motion is fster in thinner films, lso show n increse in the time constnt for * Corresponding uthor. Tel.: þ ; fx: þ E-mil ddress: drp@che.utexs.edu (D.R. Pul). interfcil heling, which would typiclly suggest tht moleculr motion of the polymer chin segments is slower in thinner films [14]. Clerly, mny questions remin to fully understnd the fscinting, complex dynmics of ultrthin, highly confined glssy polymers. While the influence of film thickness on T g hs een n ctive re of scientific study, much less effort hs focused on the influence of ultrthin-film confinement effects on physicl ging in glssy polymers [9,15 17]. Physicl ging rises from the inherent nonequilirium nture of glssy polymers nd cuses mteril properties to drift over time towrds seemingly unttinle equilirium [18 0]. The effects of physicl ging re thermo-reversile, i.e., chnges cused y physicl ging cn e ersed y heting ove the glss trnsition. Thin film glssy polymers re used, or proposed for use, in wide vriety of importnt technologicl pplictions (e.g., gs nd liquid seprtion memrnes, fuel cells, solr cells, lithogrphy, nd opticl mterils) [6,7,1 3], nd the performnce of these thin films over time cn significntly influence enduse properties (e.g., gs flux through ultrthin memrnes used for gs seprtions) [4], so it is criticl to enhnce the fundmentl understnding of physicl ging in thin films. Polystyrene films s thin s undergo physicl ging, s evidenced y volumetric overshoot upon heting in ellipsometry mesurements; however, no informtion regrding the extent or rte of ging in such thin films hs een reported [16]. The fluorescence intensity of chromophore-leled poly(isoutyl methcrylte) films s thin s 10 nm hve een studied s function of ging; however, thickness dependent ging rte ws not clerly oserved [9]. Similr work y /$ see front mtter Ó 009 Elsevier Ltd. All rights reserved. doi:1016/j.polymer

2 5566 B.W. Rowe et l. / Polymer 50 (009) Priestley et l. hve shown reduced ging rtes in supported poly(methyl methcrylte) films s compred to 500 nm films [5]. The reduced ging rte ws ttriuted to ttrctive interctions etween the polymer nd silicon sustrte restricting polymer chin moility. As first step towrds understnding the ging ehvior of gs seprtion memrnes, which hve complex, symmetric hollow fier structure produced vi phse inversion processes,[6] welldefined free-stnding films of known thickness in the relevnt thickness rnge were studied. Reltive to ulk (i.e., thick film) ehvior, gs permeility exhiits drmticlly fster physicl ging in free-stnding glssy polymer films s thin s 400 nm thick [4,7 9]. However, to give high productivity, the selective lyer of modern gs seprtion memrnes is on the order of nm thick, nd it hs not een cler, until now, how ging ehvior evolves with thickness elow 400 nm, especilly when pproching length scles similr to tht of the polymer coil size [3]. Fig. 1 chrcterizes the relevnt thickness rnges nd the generl knowledge out physicl ging in ech regime. Studies of physicl ging in ultrthin films should provide insight regrding the mechnisms which cuse ccelerted ging in thin films nd yield etter understnding of the influence of free surfces nd confinement on polymer films. Moreover, such informtion would e of fundmentl importnce in developing predictive models of the long-term permetion properties of gs seprtion memrnes. This study presents the gs permeility nd physicl ging ehvior of polysulfone (PSF) nd Ò films s thin s. Lrge devitions from ulk ehvior were oserved nd re discussed in reltion to the influence of the free surfce on polymer moility. The physicl ging model developed y Struik is extended to include the influence of film thickness nd ccurtely descries the oserved ging ehvior. The results of this study re consistent with the notion of enhnced moility t the polymer/ir interfce.. Experimentl Fig. 1. Schemtic defining length scles of interest. Bisphenol A-sed polysulfone (PSF) from Solvy Advnced Polymers (UDEL PSF-3500 NT LCD) nd the polyimide commercilly known s Ò 518 from Huntsmn Advnced Mterils were used s received in this study. PSF nd Ò were chosen ecuse they re widely used gs seprtion memrne mterils, nd they hve T g s(186 C nd 317 C, respectively) well ove the temperture of use (pproximtely mient in mny cses), so they re deep within the glssy stte during use [3,4]. Thin polymer films were prepred y spin csting solutions of the polymers in cyclopentnone onto silicon wfers t 1000 rpm for 60 s; film thickness ws controlled y vrying the solution concentrtion. A vrile ngle spectroscopic ellipsometer mnufctured y J.A. Woollm Co., model 000D, ws used to mesure film thickness. A mjor rodlock to studying gs permeility in ultrthin films is the presence of microscopic pinhole defects, which form with incresing frequency s film thickness is reduced [4]. While this issue my hve little influence on results from studies using ellipsometry, fluorescence spectroscopy, nd other techniques, these trns-memrne defects destroy selectivity nd msk permeility of mteril under study, therey rendering the smple useless for gs trnsport studies. Indeed, defect frction of 10 6 on n re sis is enough to prevent memrne from performing gs seprtion [30]. A coting technique hs een pplied to circumvent this prolem. After spin-coting n ultrthin glssy film of morphous PSF or Ò, thin lyer of highly permele, ruery poly(dimethylsiloxne) (PDMS) ws coted directly on top of the glssy film. The PDMS overcot ws creted y spin csting PDMS solution in cyclohexne directly on the glssy film supported on silicon wfer. The PDMS solution consisted of Dehesive 940A with proprietry crosslinker (V4) nd ctlyst (OL) system provided y Wcker Silicones Corportion, Adrin, MI; cyclohexne ws dded to crete 1 wt.% silicon solution. The film ws then nneled t 110 C for 15 min to crosslink the PDMS nd remove residul solvent. Fig. presents crtoon of the structure of the films used in this study. The thickness of the PDMS lyer ws mesured using Dektk 6 M stylus profilometer. The PDMS lyer effectively locks convective flow through ny pinhole defects of the glssy lyer nd, t mient conditions, PDMS is more thn 150 C ove its T g,soit does not undergo physicl ging; consequently, its properties do not chnge with time [7]. Historiclly, the development of similr coting technique for hollow fier memrnes initilly enled the industril development of these mterils for gs seprtion [30,31]. However, until now, this pproch hs never een hrnessed to study physicl ging, s proed vi gs permeility, in ultrthin (i.e., <100 nm) films. The two lyer film ws then lifted from the silicon support using thin metl wire frme nd heted 15 C ove the ulk T g of the glssy lyer for 0 min to erse the therml history nd define strting point for the ging studies. The smple preprtion techniques re sed on those descried for single lyer films y Hung nd Pul[4]. The gs permeility coefficients of the films were mesured using stndrd constnt volume, vrile pressure method [3]. Mesurements were conducted t 35 C, n upstrem pressure of tm nd mximum downstrem pressure of 10 Torr. When not eing tested, smples were ged in dry environment t 35 C. 3. Results nd discussion 3.1. Influence of PDMS coting on gs trnsport nd ging ehvior The mss trnsfer resistnce from the PDMS lyer, which is constnt with time,[7] is significntly less thn tht from the glssy lyer due to the much higher gs permeility of PDMS thn PSF nd Ò, nd it cn e ccounted for using the following resistnce model, llowing one to ccess the ntive properties of the glssy film: [33] l composite P composite ¼ l PDMS P PDMS þ l Glssy P Glssy (1) where l PDMS nd l Glssy re the thicknesses of the PDMS nd glssy polymer (i.e., PSF or Ò ) lyers, respectively; P PDMS nd Highly permele lyer (e.g. PDMS) Ultrthin glssy polymer lyer Microscopic pinhole defects Fig.. Digrm of film structure used in this study (not to scle).

3 B.W. Rowe et l. / Polymer 50 (009) Tle 1 Bulk mteril properties. Polymer T g P O P N P CH4 186 C Polysulfone 317 C.1 8 Ò CH 3 Si CH 3 O n 13 C Poly(dimethylsiloxne) Permeility vlues re given in Brrers; 1 Brrer ¼ [cm 3 (STP) cm/(cm sec cmhg)]. P Glssy re the permeility coefficients of the PDMS nd glssy polymer, respectively. The totl thickness of the composite structure (i.e., the glssy polymer overcoted with PDMS) is l composite ¼ l PDMS þ l Glssy, nd the permeility of the composite structure is P composite. By mesuring the thickness of ech lyer nd knowing the PDMS permeility, Eqution (1) cn e used to clculte the permeility of the glssy polymer lyer from permeility mesurements on the composite structure. The structure, glss trnsition temperture, nd ulk permeility of the polymers of interest re recorded in Tle 1 [4,34,35]. The PDMS lyer ws typiclly 3 4 mm thick. In the thicker films studied in this work (>100 nm), the mss trnsfer resistnce from the PDMS lyer ws only few percent or less of the resistnce due to the glssy lyer. In the thinnest films studied (w), the contriution from PDMS ws w0% of the totl mss trnsfer resistnce. The PDMS lyer is not strongly dhered to the glssy film; it is esily seprted from the glssy lyer, so the PDMS lyer should not permeility (Brrer ) PSF 415 nm PSF no coting PSF Fig. 3. Comprison of PSF ging ehvior with nd without PDMS coting. significntly influence the ehvior of the underlying glssy polymer. To investigte ny influence the PDMS coting might hve on the ging response of these glssy films, the ging ehvior of PSF films of similr thicknesses with nd without PDMS coting is shown in Fig. 3. The error rs in this figure represent the verge stndrd devition for permeility mesurements of three different films of ech cse. The ging ehvior of film prepred y coting PSF with thin PDMS lyer is identicl, within experimentl error, to tht of PSF film of similr thickness ut without PDMS coting, so the presence of the PDMS lyer does not perceptily lter the ging response. 3.. Gs permeility nd ging in PSF films Figs. 4,, nd c show the oxygen, nitrogen, nd methne permeility, respectively, s function of ging time for PSF films with thicknesses rnging from down to. The ulk ging response of 60 mm thick film is included for comprison. The films were ged t 35 C in dry environment etween mesurements. Despite eing 150 C elow the ulk T g of PSF, drmtic ging effects on permeility re evident in the ultrthin films. The gs permeility rpidly decreses with ging time in ll films s the mteril evolves towrds the more dense, equilirium stte, nd the permeility for most of the thin films is less thn tht of the ulk PSF. The permeility of these films decreses to w50% of the initil vlue fter 1000 h, significntly more thn the 10% decrese reported for ulk-like films t similr ging times [4]. The higher permeility of these films, s compred to the ulk oxygen permeility of 1.4 Brrer reported y McHttie et l. [34], for instnce, is elieved to result from the rpid quench from ove T g, which cptures dditionl free volume in the polymer. Differences in reported permeilities for glssy polymers re common, ecuse gs trnsport properties depend strongly on the therml history of glssy polymer [36]. The /N nd /CH 4 pure gs selectivity s function of ging time for ech PSF film studied is shown in Fig. 5 nd, respectively; the ulk ging response is shown for comprison. The selectivity in ll films is ner or ove the ulk vlue, so the ultrthin films ehve s effectively defect-free films. The /N nd /CH 4 selectivity increses s the mteril ges; the polymer densifiction ccompnying physicl ging reduces the free volume of the polymer

4 5568 B.W. Rowe et l. / Polymer 50 (009) CH 4 c 0.6 Bulk N Bulk Bulk Fig. 4. Influence of physicl ging on oxygen permeility (), nitrogen permeility (), nd methne permeility (c) in PSF films rnging from to in thickness. Lines re provided to guide the eye O / N selectivit y Bulk Bulk selectivity 4 /C H Fig. 5. Influence of physicl ging on /N pure gs selectivity () nd /CH 4 pure gs selectivity () in PSF films rnging from to in thickness s function of ging time. Lines re provided to guide the eye.

5 B.W. Rowe et l. / Polymer 50 (009) permeility (Brrer ) N permeility (Brrer ) 5 C H 4 permeility (Brrer ) c 5 Fig. 6. Influence of physicl ging on oxygen permeility (), nitrogen permeility (), nd methne permeility (c) in Ò films rnging from 5 to in thickness. Lines re provided to guide the eye. which, in turn, mkes the mteril more size selective y reducing the diffusion of the lrger N nd CH 4 molecules more thn tht of smller molecules [4]. The N /CH 4 selectivity lso increses with physicl ging of PSF (e.g., from 0.85 to 0.90 in the film fter 1000 h); however these smll chnges led to more sctter of the dt nd re not shown for revity. Interestingly, the initil permeility, t 1 h of ging time, decreses with decresing film thickness for films less thn w100 nm thick. Additionlly, the initil /N selectivity increses s film thickness decreses, consistent with the permeility results. Superficilly, these results pper to contrdict reports of incresed moility ner the surfce of polymer films, since lower permeility nd higher selectivity would typiclly e ssocited with decresed chin moility. However, we elieve the initilly lower gs permeility in the ultrthin films is cused y ging occurring in the very first hour fter the quench from ove T g (when it is not fesile to perform gs permeility mesurements due to the time needed to prepre smples for study). If so, the enhnced moility t the free surfces llows ultrthin films to chieve low free volume stte (nd, consequently, lower permeility nd higher selectivity t one hour, when permeility cn first e mesured) more quickly thn ulk mteril [5]. This hypothesis is consistent with the results from the modelling study, which re descried in more detil elow Gs permeility nd ging in Ò films The influence of ging time on oxygen, nitrogen, nd methne gs permeility in Ò films with thicknesses rnging from 5 down to is presented in Fig. 6,, nd c respectively. The ging response of these films is more pronounced thn tht of the PSF films with some films exhiiting permeility decrese to w30% of the originl vlue fter 1000 h of ging. The fster ging in Mtrmid Ò s compred to PSF hs een shown previously, nd it is elieved to result from the higher frctionl free volume of Ò reltive to tht of PSF [4]. Fig. 7 nd illustrte the impct of physicl ging on the pure gs /N nd N /CH 4 selectivity of Ò films. Incresing selectivity with ging time is seen, s expected. Anlogous to the PSF ehvior, Ò exhiits decresed permeility nd incresed selectivity t one hour of ging s film thickness is reduced. These differences re elieved to

6 5570 B.W. Rowe et l. / Polymer 50 (009) O / N selectivit y selectivity 4 N /C H Fig. 7. Influence of physicl ging on /N pure gs selectivity () nd N /CH 4 pure gs selectivity () in Ò films rnging from 5 to in thickness s function of ging time. Lines re provided to guide the eye. e relted to the physicl ging tht occurs in the first hour fter the quench from ove T g Comprison to the upper ound Roeson presented the trde-off etween permeility nd selectivity in polymer memrnes, descriing this reltionship s the upper ound [37]. The theoreticl sis for this reltionship ws lter developed y Freemn [38]. Generlly, this reltionship descries the connection etween permeility nd selectivity in polymeric mterils [39]. Fig. 8 shows the evolution of gs trnsport chrcteristics of the films studied, s result of physicl ging, reltive to the upper ound. As the polymer ges, the trend of decresing permeility nd incresing selectivity move the film properties essentilly prllel to the upper ound. The rnge of permeility nd selectivity vlues exhiited y the sme mterils s function of physicl ging shows the significnt effect prior history cn hve on gs trnsport properties of glssy polymers. O /N selectivity PSF Oxygen Upper Bound Fig. 8. Influence of physicl ging in comprison with upper ound [36] Modelling Considertions The rte of physicl ging, which is often modeled s shown in eqution (), depends on the rtio of the driving force, i.e., the displcement of the specific volume from its equilirium vlue, nd the relxtion time for the smple, which is function of temperture nd the mteril s current free volume stte [18]. Aging Rteh dv dt ¼ ðv v NÞ s v; T g T () where v nd v N re the polymer specific volumes t time t nd t equilirium, respectively, T is temperture, nd s is chrcteristic relxtion time. Becuse the T g in ultrthin PSF films is elow the ulk vlue, s reported y Kim et l., these films should hve enhnced moility (i.e., lower s) s compred to the ulk [10]. Therefore, lthough ultrthin films my hve smller deprture from equilirium (i.e., lower v v N ) thn thicker films, s indicted y lower gs permeilities nd higher selectivities thn thick films, enhnced chin moility due to lower glss trnsition temperture in ultrthin films decreses the chrcteristic relxtion time (i.e., decreses s) [40]. The net effect of these two competing fctors (i.e., lower v v N nd lower s) on the rte of physicl ging is to ccelerte the physicl ging response of these films, consistent with the experimentl results shown in Figs While no report on the effect of film thickness on T g in Ò Tle Struik model prmeters for PSF nd Ò. Polymer g f i f e s N (sec) l (nm) N CH 4 PSF Ò

7 B.W. Rowe et l. / Polymer 50 (009) Tle 3 Vlues for permeility correltion (eqution (5)). exists, the similrity in the permeility results suggest similr ehvior could e expected. To mthemticlly descrie the influence of thickness-dependent relxtion times on physicl ging-induced chnges in permeility in ultrthin films, the self-retrding ging model developed y Struik to descrie the vrition in mny physicl properties (e.g., specific volume, impct strength, nd creep complince) of ulk glssy polymers with time is pplied [18]: ddf dt ¼ Df s ¼ Df s N expð g Df Þ where Df is the excess frctionl free volume (i.e., the difference etween the frctionl free volume in the polymer, f, nd the frctionl free volume of the sme mteril in the fully relxed, equilirium stte, f e ) (i.e., Df ¼ f f e ), s is the relxtion time t time t, s N is the relxtion time t equilirium (i.e., t t / N), nd g is constnt chrcterizing the sensitivity of the relxtion time to the excess frctionl free volume. This model ws developed for nd vlidted using dt from ulk polymers, where thickness effects on physicl ging re not oserved, so here s N is llowed to depend on film thickness s strightforwrd method to cpture thicknessdependent ging ehvior. The cse of thickness-dependent g ws lso exmined; however, the fit improvement did not justify llowing g to depend on thickness, ccording to n F-test [41]. Free volume is relted to the specific volume of the polymer, v, y f ¼ v v o v N CH 4 A (Brrer) B A (Brrer) B A (Brrer) B Prk & Pul [44] PSF Ò (3) (4) Oxygen t = 1hr Struik model Fig. 10. Influence of ging time nd film thickness on the predicted oxygen permeility ehvior of the PSF films studied sed on the modified Struik model. where v o is the occupied volume of the polymer (not needed in this nlysis) which cn e estimted y the Bondi method (i.e., v o ¼ 1.3v w ), nd v w is the vn der Wls volume estimted using the group contriution method [4]. The initil frctionl free volume, f i, used in the model ws sed on reported free volume vlues for PSF [34] nd Ò smples [43]. While the reported vlue of f i for Ò ws determined for rpidly quenched thin film smples, the vlue for PSF ws reported for ulk smples nd required n increse from the reported 56 to 60 to ccount for the initilly higher free volume in the rpid quenched stte s compred to the ulk stte. This chnge ws sed on mtching the predicted initil permeility, using eqution (5), with the experimentl results for the ulk PSF films studied here. For oth PSF nd Ò, the frctionl free volume t the fully relxed, T g (sec) Relxtion time PSF Relxtion time: Struik Model 435 Thin film T : Kim et l. Δ p = tm g Film thickness (nm) τ T g (K) Fig. 9. The influence of film thickness on physicl ging nd relxtion rtes. () Effect of ging time on oxygen permeility in PSF films rnging from to in thickness. Lines were generted from the modified Struik model. () Dependence of s N () nd T g (,), from Kim et l. 10, on PSF film thickness. The lines were drwn to guide the eye.

8 557 B.W. Rowe et l. / Polymer 50 (009) PSF Struik Model PSF Struik Model (sec) τ τ/τ Decresing film thickness Fig. 11. Influence of ging time nd film thickness on s (), nd the pproch to the equilirium relxtion time (), sed on the modified Struik model. equilirium stte, f e, ws given y Hung et l. sed on extrpoltion of the experimentl pressure-volume-temperture dt in the melt stte [43]. This ging model ws solved numericlly using MATLAB softwre. The frctionl free volume, f, clculted s function of ging time from eqution (3) ws used in the following correltion to clculte gs permeility: P ¼ Ae B=f (5) where A nd B re constnts sed upon permeility mesurements in smples of ulk thickness from the literture [44]. The permeility dt were fit to the Struik model y llowing s N nd g to vry to otin the est fit in lest squres nlysis. g ws not llowed to vry with film thickness, nd s N ws llowed to depend on film thickness. The resulting Struik model prmeters re shown in Tle, while the A nd B constnts used in the permeility correltion re shown in Tle 3. The comintion of the correltion in eqution (5) nd the thickness-dependent Struik model will e referred to herefter s the modified Struik model Modelling PSF permeility nd ging ehvior The modified Struik model, with only one thickness-dependent prmeter, s N, effectively cptures the ging ehvior of the ultrthin PSF films s shown in Fig. 9. Fig. 9 illustrtes the thickness dependence of s N from the permeility results; this ehvior suggests tht ccelerted ging in thinner films is chieved y the chrcteristic relxtion time decresing y orders of mgnitude s film thickness decreses. The relxtion times, s N, deduced in this wy show remrkly similr trend with thickness s the reported thickness dependence of T g, given y Kim et l. [10]. Apprently, the sme mechnisms tht pper to reduce T g in ultrthin films contriute to ccelerted ging in these mterils y reducing the chrcteristic relxtion time s film thickness decreses [10]. N N Δ p = tm Fig. 1. Influence of ging time on nitrogen permeility in PSF films rnging from to in thickness. Lines were generted from the modified Struik model using the sme relxtion times from the modeling nd A ¼ 11 Brrer for N. Fig. 13. Influence of ging time on nitrogen permeility in PSF films rnging from to in thickness. Lines were generted from the modified Struik model using A ¼ 15 Brrer for N.

9 B.W. Rowe et l. / Polymer 50 (009) CH Fig. 14. Influence of ging time on methne permeility in PSF films rnging from to in thickness. Lines were generted from the modified Struik model. Fig. 10 presents the predicted permeility ehvior of the PSF films studied including times 1 h. By chnging only s N with film thickness, the initil conditions of ech film re identicl, i.e., t very short times following the therml quench, ll films hve the sme permeility. The verticl line drwn t 1 h of ging is included to illustrte why the initil permeility mesured experimentlly (i.e., permeility t one hour, when it first ecomes possile to mesure permeility) decreses with decresing film thickness. The vlues of s s function of film thickness nd ging time re shown in Fig.11. In ll films, s increses with ging time in this selfretrding model wherey ging slows s it progresses. It is interesting to note tht t short ging times the difference in s etween the films studied spns severl orders of mgnitude, ut fter w1000 h of ging, this difference is less thn one order of mgnitude. Fig. 11 illustrtes the pproch to s N s function of film thickness, demonstrting how the thin films pproch equilirium more rpidly thn the thicker films. Once the reduced relxtion time, i.e., s/s N, egins to increse linerly with log ging time, the slope of the pproch to unity is the sme for ech film thickness ecuse the model prmeters re the sme for ech cse, except for the equilirium relxtion time. This pproch shows tht ech film ges similrly, nd results in simply shifting the ging curve s function of film thickness. The sme model prmeters which descrie the oxygen permeility dt in PSF cn lso e used to estimte to the nitrogen permeility dt y pplying the pproprite vlues of A nd B in eqution (4). The results of this nlysis, using the Struik model prmeters from the modelling nd literture vlues of A nd B for N, re shown in Fig. 1. While the model does fir jo of cpturing the experimentl dt, there is some disgreement t erly ging times in the thicker films. This discrepncy is elieved to e relted to the initil moleculr relxtions tht ffect the lrger N molecules more thn the molecules. All glssy polymers will hve distriution of free volume element sizes, with the verge size eing considered in the Struik model. However, ccording to the Struik model, lrger free volume sites (i.e., those lrge enough to ccommodte either N or ) ge more rpidly thn smller free volume sites (i.e., those lrge enough only to ccommodte ) due to their inherently greter displcement from the equilirium stte. By llowing s N to chnge from gs to gs, n improved fit of the nitrogen permeility ging dt is chieved, shown in Fig. 13. It ws lso necessry to djust the A prmeter from 11 (i.e., the literture vlue [44]) to 15 Brrer to mtch the initil N permeility in the PSF films. Although the literture vlues of A nd B used in eqution (4) generlly predict permeility well, some chnges in A were required to etter mtch the ehvior of the specific polymers considered here. Some djustment of these prmeters is expected to closely mtch the ehvior of individul polymers. The intent here is not to mke prmeter djustments tilored to the dt; rther, it is to provide qulittive nlysis of the underlying physicl phenomen relted to ging. The s N vlues used to clculte the nd N permeility of the film re shown in Tle. The shorter relxtion time for the N permeility ehvior indictes tht the rte of relxtion of the free volume which ffects N permeility is greter thn for permeility, in qulittive greement with the expecttion from the Struik model (i.e., tht lrger free volume elements ge fster). Fig. 14 compres the methne permeility ehvior to predictions from the modified Struik model. For CH 4, the relxtion times were similr to those used for N, seen in Tle. Also, the vlue for A in the permeility correltion ws chnged from 114 (i.e., the literture vlue [44]) to 10 Brrer to etter mtch the CH 4 permeility in PSF Modelling Ò permeility nd ging ehvior The modified Struik model ws lso pplied to descrie the Ò permeility dt. Fig. 15,, nd c show the close greement etween the model nd the oxygen, nitrogen, nd methne permeility ehvior. The prmeters used in the modified Struik model re shown in Tle. The vlues used in the permeility correltions for Ò were the sme s those reported y Prk nd Pul[44], except the A vlue for N, which ws chnged from 11 to 95 Brrer, s shown in Tle 3. The s N vlues for the lrger gses (i.e., N nd CH 4 ) re somewht smller thn tht of the smller gs,, consistent with the results oserved in PSF. The relxtion times for the Ò films re shorter thn for the PSF films, consistent with fster ging in Ò. The lower vlue of g in Ò, s compred to PSF, indictes weker influence of free volume on the ging rte in Ò thn in PSF. The influence of free volume on locl chin moility importnt for physicl ging cn e expected to vry from one mteril to nother. Crudely speking, one might imgine two extreme cses, one eing the sitution where the limiting fctor for such locl motion is the energy required to overcome energy rriers etween covlently connected moieties long the chin ckone (i.e., the rrier to chin motion is entirely due to intrmoleculr restrictions on chin segment motion) nd the second eing the cse where the limiting fctor is the energy required to move neighoring chin segments out of the wy so tht gingrelted locl motion cn occur (i.e., the rrier to chin motion is entirely due to intermoleculr restrictions on chin motion). Free volume should predominntly influence chin pcking nd, in turn, intermoleculr energy rriers, ut not the energy rriers etween covlent linkges long given chin. Therefore, in the first cse, one would expect little to no effect of free volume on the timescle of moleculr motion (i.e., low vlues of g), nd in the second cse, one would expect mximum effect of free volume on the timescle for moleculr motion (i.e., high vlues of g). Thus, the experimentl result tht g is higher in PSF thn in Ò suggests tht intr-moleculr moility restrictions, such s tht due to rigid chin structure, re more influentil in Ò thn PSF, which is consistent with the considerly higher T g vlue of Ò reltive to PSF. Interestingly, this result of the more rigid, higher T g polymer exhiiting fster relxtion is reminiscent

10 5574 B.W. Rowe et l. / Polymer 50 (009) p = tm 5 N 5 p = tm c CH 4 p = tm 5 Fig. 15. Influence of physicl ging on oxygen permeility (), nitrogen permeility (), nd methne permeility (c) in Ò films rnging from 5 to in thickness. Lines were generted from the modified Struik model using gs-specific prmeters shown in Tles nd 3. (sec) τ Struik Model Film thickness (nm) Fig. 16. Influence of film thickness on s N in modeling the oxygen permeility of Ò films sed on the modified Struik model. The line is drwn to guide the eye. of the influence of structurl symmetry on polymer ehvior. For exmple, polysulfones with pr linkges cross phenol rings in the min chin consistently hve higher T g nd yet higher moility, s relted to penetrnt diffusion, s compred to their met linked nlogs [45]. The influence of film thickness on s N in Ò ccording to the modified Struik model is shown in Fig. 16. As seen in PSF, s N decreses y severl orders of mgnitude s film thickness is reduced. For the other gses studied, film thickness hd similr influences on s N, i.e., s film thickness decreses, s N decreses. 4. Conclusions Understnding the influence of nnoscle confinement on physicl ging, or structurl relxtion, is essentil for descriing glssy dynmics of confined polymer systems nd for predicting the long-term performnce of glssy mterils in vriety of technologies, including gs seprtion memrnes. Enled y newly pplied coting technique, the gs permeility nd physicl ging of PSF nd Ò films s thin s thick were studied. All films exhiited rpidly decresing permeility nd incresing selectivity with ging time. Additionlly, the initil permeility, mesured t one hour of ging, of the ultrthin films decresed with decresing film thickness. Anlysis of the permeility/selectivity chrcteristics exhiited during ging, compred with the upper

11 B.W. Rowe et l. / Polymer 50 (009) ound, shows the sensitivity of gs trnsport properties to previous history. The gretly ccelerted ging in ultrthin films, s compred to ulk ehvior, is consistent with the notion of enhnced moility t the polymer surfce, which is the sme mechnism thought to cuse T g reductions in ultrthin films. Struik s physicl ging model cn cpture the oserved trends in permeility ging if the chrcteristic relxtion time is llowed to vry with thickness. Smll model prmeter djustments led to more ccurte description of the ehvior of different gses; the results of these chnges re consistent with the model wherey lrger free volume elements ge more rpidly thn smller elements. Acknowledgements This reserch ws supported y Air Liquide/MEDAL, the Ntionl Science Foundtion (Grnt DMR dministered y the Division of Mteril Reserch Polymer Progrm), nd the NSF Science nd Technology Center for Lyered Polymeric Systems (Grnt DMR ). References [1] Bit I, Yng JKW, Jung YS, Ross CA, Thoms EL, Berggren KK. Science 008; 31(5891): [] Brumn JI, Szuromi P. Science 1996;73(577):855. [3] Forrest JA, Dlnoki-Veress K. Advnces in Colloid nd Interfce Science 001;94(1 3): [4] Frnk CW, Ro V, Despotopoulou MM, Pese RFW, Hinserg WD, Miller RD, et l. Science 1996;73(577):91 5. [5] Jerome B, Commndeur J. Nture 1997;386(665): [6] Ruiz R, Kng H, Detcheverry FA, Doisz E, Kercher DS, Alrecht TR, et l. Science 008;31(5891): [7] In Elhj M, Schdt M. Nture 001;410(6830): [8] Jones RL, Kumr SK, Ho DL, Brier RM, Russell TP. Nture 1999;400(6740): [9] Ellison CJ, Kim SD, Hll DB, Torkelson JM. The Europen Physicl Journl E Soft Mtter 00;V8(): [10] Kim JH, Jng J, Zin WC. Lngmuir 000;16(9): [11] Serghei A, Huth H, Schick C, Kremer F. Mcromolecules 008;41(10): [1] Serghei A, Mikhilov Y, Eichhorn KJ, Voit B, Kremer F. Journl of Polymer Science Prt B Polymer Physics 006;44(0): [13] Ellison CJ, Torkelson JM. Nture Mterils 003;(10): [14] Fkhri Z, Vldkhn S, Forrest J. The Europen Physicl Journl E Soft Mtter 005;18(): [15] Priestley RD, Ellison CJ, Brodelt LJ, Torkelson JM. Science 005;309(5733): [16] Kwn S, Jones RAL. Europen Physicl Journl E Soft Mtter 003;10(3): [17] Simon SL, Prk JY, McKenn GB. The Europen Physicl Journl E - Soft Mtter 00;8(): [18] Struik LCE. Physicl ging in morphous polymers nd other mterils. Amsterdm: Elsevier; [19] Hutchinson JM. Progress in Polymer Science 1995;0(4): [0] Kurchn J. Nture 005;433(703): 5. [1] Hickner MA, Ghssemi H, Kim YS, Einsl BR, McGrth JE. Chemicl Reviews 004;104(10): [] Hlls JJM, Wlsh CA, Greenhm NC, Mrsegli EA, Friend RH, Mortti SC, et l. Nture 1995;376(6540): [3] Bker RW. Industril nd Engineering Chemistry Reserch 00;41(6): [4] Hung Y, Pul DR. Polymer 004;45(5): [5] Priestley RD, Brodelt LJ, Torkelson JM. Mcromolecules 005;38(3): [6] Pinnu I, Koros WJ. Journl of Applied Polymer Science 1991;43(8): [7] McCig MS, Pul DR. Polymer 000;41(): [8] Pfromm PH, Koros WJ. Polymeric Mterils Science nd Engineering 1994;71:401. [9] Dorkenoo KD, Pfromm PH. Mcromolecules 000;33(10): [30] Henis JMS, Tripodi MK. Science 1983;0(459):11 7. [31] Henis JMS, Tripodi MK. Seprtion Science nd Technology 1980;15(4): [3] Koros WJ, Pul DR, Roch AA. Journl of Polymer Science Polymer Physics Edition 1976;14(4): [33] Henis JMS, Tripodi MK. Journl of Memrne Science 1981;8(3): [34] McHttie JS, Koros WJ, Pul DR. Polymer 1991;3(5): [35] Merkel TC, Bondr VI, Ngi K, Freemn BD, Pinnu I. Journl of Polymer Science Prt B Polymer Physics 000;38(3): [36] Enscore DJ, Hopfenerg HB, Stnnett VT, Berens AR. Polymer 1977;18(11): [37] Roeson LM. Journl of Memrne Science 1991;6(): [38] Freemn BD. Mcromolecules 1999;3(): [39] Roeson LM. Journl of Memrne Science 008;30(1 ): [40] Koh YP, Simon SL. Journl of Polymer Science Prt B Polymer Physics 008;46(4): [41] Bevington PR, Roinson DK. Dt reduction nd error nlysis for the physicl sciences. nd ed. New York: McGrw Hill, Inc.; 199. [4] Krevelen DWV. Properties of polymers. 3rd ed. Amsterdm: Elsevier; [43] Hung Y, Wng X, Pul DR. Journl of Memrne Science 006;77(1 ): [44] Prk JY, Pul DR. Journl of Memrne Science 1997;15(1):3 39. [45] Aitken CL, Koros WJ, Pul DR. Mcromolecules 199;5(13):