Rubbery Polymer-Inorganic Nanocomposite Membranes: Free VolumeCharacteristics on Separation Property

Ben Li, Dan Xu, Xiongfei Zhang, Zhongyi Jiang,* Yu Wang, Jing Ma, Xiao Dong, and Hong Wu

Key Laboratory for Green Chemical Technology of Ministry of Education, School of Chemical Engineering andTechnology, Tianjin UniVersity, Tianjin 300072, China, and China State Key Laboratory of Materials-OrientedChemical Engineering, Nanjing UniVersity of Technology, Nanjing 210009, China

The rational design of polymer-inorganic nanocomposite membranes relies heavily on the precise insightand elaborate control of the interface. Presently, the direct exploration of the hierarchical structure ofnanocomposite membranes still remains elusive. In the present study, we propose a facile and genericmethodology to quantitatively probe the interfacial structure by complementary positron annihilation lifetimespectroscopy (PALS) and molecular dynamics simulation (MDS) techniques. MDS is used to acquire themolecular level information such as the polymer-inorganic interface interaction energy, chain mobility withinthe nanocomposite membranes, whereas PALS is used to acquire the free volume characteristics of thenanocomposite membranes. As proof-of-principle, we choose anisotropic inorganic nanotube embedded rubberypolymer membrane as a model, which generates the interface between soft polymer and rigid inorganic.PALS reveals that incorporation of titanate nanotubes (TNTs) narrows the free volume pore radius distributionof the membranes. MDS indicates that the segmental chain mobility in the vicinity of the polymer-inorganicinterface is substantially restrained, which creates numerous nanosized voids for molecular transport, anddramatically enhances the fractional free volume (FFV) of the membranes. Quite interestingly, it was foundthat the rubbery membranes can also exhibit simultaneously increased permeability and membrane selectivity,and this unusual phenomenon was tentatively elucidated by relating the separation properties to the freevolume characteristics of the membranes.

Introduction

Since its inception, nanocomposite (hybrid or mixed matrix)materials pave a facile, versatile, and efficient way to endowthe pristine polymers with notably enhanced properties.1-5 Theso-called nanocomposite materials are of hierarchical structuresusually comprising nanosized inorganic “inserts” embeddedwithin a polymer matrix, which ingeniously combines theadvantages of each moiety, rendering superior performance toeach individual phase, e.g., increased permeability, desirablethermal and mechanical properties, specific electrical and opticalproperties, and economical processability.

Nanocomposite materials can be further catalogued as glassypolymer-based and rubbery polymer-based nanocompositematerials. It is found that permeability of certain glassy polymermembranes with nanoinclusions increases with the particlevolume fraction, and they are not subject to the permeability/selectivity trade-off limitation.6 Theoretical explanations of suchphenomenon are ascribed to the polymer chains repelled fromthe inclusion during membrane casting.7,8 To the best of ourknowledge, quite few works set foot on the rubbery polymer-based polymer-inorganic interface structure presently. Inparticular, no successful report has been found to solve the“trade-off” bottleneck between permeability and selectivity.However, nobody will deny that these issues are of greatscientific and technological perspective: First and foremost, theelastomeric and thermoplastic rubbery polymers endow thenanocomposite materials flexible interfacial morphology, whichcan effectively decrease the nonselective voids. Second, mostrubbery polymeric materials have little or no active functionalgroups and are quite difficult to chemically modify viacross-linking9,10 or grafting/copolymerization.11-13 Physical

hybridization seems a “shortcut” to upgrade the properties ofthese inert rubbery polymers.

It is well-recognized that the specific properties of nanocom-posite materials are mainly attributed to the interfacial interac-tions between the inorganic filler and the polymer matrix.14,15

Therefore, the rational design of nanocomposite materialsstrongly depends on penetrating analysis and characterizationof the polymer-inorganic interface structure at microscopicscale or molecular level.16-24 Despite some classical theory ofdiffusion in nanocomposites having been proposed and havingcaptured most of the qualitative physics, these models mainlyfocus on the glassy-polymer-based nanocomposites. In addition,it utilizes density profiles based on theories for polymer solutionsnear flat surfaces whose applicability for polymer melts nearhighly curved surfaces (nanocomposites) is elusive.7,8 Positronannihilation lifetime spectroscopy (PALS), which is able toquantitatively measure the nanosized voids within the matrix,launches new discernment into the microscopic structure ofrubbery nanocomposite materials.6,20 PALS, however, couldonly acquire static free volume characteristics of the materials.In comparison, molecular dynamics simulation (MDS) canpotentially quantify the polymer-inorganic interface and providedynamic information including molecular interactions, chaindynamics, and diffusion behavior of small molecules at themolecular level.25-27 Rational synergy between PALS and MDSwill enable detailed insight into the nanoscale interface structure.

In the present study, we selected rubbery polymer poly(dim-ethylsiloxane) (PDMS) as continuous phase and titanate nano-tubes (TNTs) as dispersed phase. We extensively probed thestructure, morphology, and dynamics of the PDMS-TNTsinterface region by PALS and MDS. The nanocompositemembranes were found to crossover the trade-off hurdle betweenpermeability and membrane selectivity. Although a few studieshave investigated PDMS-based hybrid materials by PALS,28,29

* To whom correspondence should be addressed. E-mail: zhyjiang@tju.edu.cn.

Ind. Eng. Chem. Res. 2010, 49, 12444–1245112444

10.1021/ie101142b 2010 American Chemical SocietyPublished on Web 11/08/2010

the present study mainly features the following: (1) detailedinsight into the nanoscale interface structure was gained bycomplementary information from both PALS and MDS; (2) theunusual separation results were reasonably reconciled bycorrelating the apparent properties to the microscopic structuresof the membranes.

Experimental Section

Materials. Rutile-type titanium dioxide powders were pur-chased from Shanghai Zhuerna High-Tech Powder Material Co.,Ltd., and used without further purification. PDMS oligomer (theviscosity was 5000 mPa · s, and the corresponding averagemolecular weight was about 40 000) ethyl orthosilicate anddibutyltin dilaurate were obtained from Beijing Chemical Co.,Beijing, China. Asymmetric polysulfone (PS) ultrafiltrationmembranes were ordered from Shanghai MegaVision MembraneEngineering and Technology Co., Ltd. N-Octane, thiophene, andn-heptane were supplied by GuangFu Fine Chemical ResearchInstitute, Tianjin, China. Deionized water was used in allexperiments.

Synthesis of TNTs. Titanate nanotubes were synthesized bya hydrothermal method as described by Geng et al.30

Preparation of PDMS-TNTs Nanocomposite Membranes.PDMS, cross-linking agent ethyl orthosilicate, and catalystdibutyltin dilaurate were dissolved into n-heptane to form ahomogeneous solution at room temperature. TNTs were dis-persed in heptane under ultrasound. The PS membrane support(the area of 10 cm ×10 cm) was soaked in deionized water for24 h to remove glycerin and then fully dried to be employed asthe support layer of the composite membrane. The PDMSmembranes were prepared by solution-casting mixtures of thefillers and PDMS/heptane solutions. The mixture was vigorouslystirred to obtain a pseudohomogenous solution. After degassing,the solution was cast onto the PS support at room temperature.The membrane was first dried in air for 24 h and then placed ina 75 °C oven to complete cross-linking and evaporate theresidual solvent. All membrane samples were stored in a dustfree and dry environment before being used in the pervaporationexperiments.

Characterizations. Fourier transform infrared (FT-IR) spectrawere measured using a Nicolet, Magna-IR 560 spectrometerequipped with horizontal attenuated transmission accessories.Pore volume, size distribution, and Brunauer-Emmett-Teller(BET) surface area measurement of the TNTs were performedusing an ASAP 2020 BET system. Scanning electron micro-graph (SEM) images were acquired on a Philips XL-30 M SEMinstrument. The morphology of TNTs was observed with thetransmission electron microscopy (TEM), JEM-100CX II. PALSexperiment was conducted by using an ORTEC fast-fastcoincidence system at room temperature. The integral statisticsfor each spectrum was more than 1 × 107 coincidences. Thespectra were evaluated using “the maximum entropy for lifetimeanalysis” (MELT) program.31 The MELT program automaticallyinverted the lifetime spectrum into a continuous lifetimedistribution using a quantified maximum entropy method.Compared with numerical Laplace inversion method (CONTINprogram),32 it was found that results of MELT were moreaccurate.33 One simply needed to enter the value of the entropyweight E, time resolution, cutoff values, and the time zerochannel of the spectrum. And, then, the MELT program wouldautomatically calculate the results. E was set between 4 × 10-8

and 5 × 10-9; the cutoff value was 5 × 10-3; the time resolutionwas 202 ps; the t0 shift (channels) was 0.690. Three or fourwell-separated peaks could be observed; their characteristic

lifetimes τi and intensities Ii were calculated as the mass centerof and the area below the peaks. τ3 was attributed to orthop-ositronium (o-Ps) pick-off annihilation in the present study,which directly reflected the free volume properties of themembranes. The free volume is assumed as a spherical potentialwell-surrounded by an electron layer of thickness ∆r, and thefollowing expressions were employed to relate lifetime τ3 andradius of free volume holes, r3

34,35

Figure 1. Positron annihilation lifetime spectra in PDMS control and PDMS-TNTs nanocomposite membranes.

Figure 2. Distribution of free volume cavity radius in PDMS control andPDMS-TNTs nanocomposite membranes.

Figure 3. Free volume parameters of the PDMS control and PDMS-TNTsnanocomposite membranes.

τ ) 12[1 - r

r + ∆r+ ( 1

2π) sin( 2πrr + ∆r)]-1

(1)

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010 12445

where ∆r was the electron layer thickness with an estimatedvalue 0.1656 nm. Thus, fractional free volume (FFV) of themembranes could be represented using the values of VF,3I3 inthe present study.

Moreover, it should be noted that positron annihilationmeasurement had strong dependence on the thickness of thesamples. The conventional positron annihilation, due to thepositron energy spectrum being continuous, reflected the com-prehensive/average information from the surface to the substrateof sample materials. For polymeric membranes or thin films,only part of the information was directly related to the bulkmatrix of the samples. Positron annihilation inevitably wouldoccur on the material surface and the substrate, which wouldhave influence on the results to some extent. In the present study,to ensure enough positron annihilation within the bulk matrixof the membranes, PDMS control membrane and nanocompositemembranes were prepared as films (without substrate) withthickness of around 1 mm for the PALS measurement.

Molecular Dynamics Simulation. Molecular dynamicssimulations in this study were carried out using “Forcite” and“Amorphous Cell” module of “Materials Studio”, a powerfulworkstation developed by Accelrys Software Inc. “Universal”force field was employed. For dynamics, the Andersen ther-mostat and Berendsen barostat methods were employed tomaintain a constant temperature and pressure, respectively. Thenonbond cutoff distance was set as 12.5 Å (with a spline widthof 1.0 Å and a buffer width of 0.5 Å). The time step was set as1.0 fs for all dynamics runs. For pure PDMS, the initial atacticpolymer chain consisted of 20 repeat units. The packing modelwith a density of 0.97 g/cm3 containing five PDMS chains wasconstructed by Amorphous Cell module. For PDMS-TiO2

interface, two confined layers of PDMS and TiO2 were contactedand contained in a single layer. The resulting structures weresubsequently optimized by the following procedure. A 5000-step energy minimization (using geometry optimization method)was adopted. And then a 1000 ps MD equilibration run wasperformed in the NPT (T ) 298 K, P ) 1.01 × 105 Pa) ensembleto obtain the equilibrium density. An additional 500 ps NVT (T) 298 K) dynamics was implemented on the end point of theNPT run to obtain the equilibrium molecular structures, and theatomic trajectory of every picosecond was recorded for lateranalysis.

Cross-Link Density Measurement. The cross-link densitywas measured by equilibrium swelling method. The membranes(active layer) were weighed carefully before being immersedin the feed solution at 25 °C. The swollen membrane samples

were taken out from the feed mixture after 24 h and wiped withtissue paper to remove the residual liquid before being weighed.A common simplified method to obtain relative cross-linkdensity was the reciprocal of the swelling index:

where υe was the cross-link density, SI was the swelling index,and m0 and m1 were the weights of the dried and swollenmembranes, respectively.

Pervaporation Experiments. The scheme of the pervapo-ration setup and the configurations of the membrane modulewere reported in our previous literature.36 Feed solution contain-ing 500 µg/g (in terms of sulfur) was pumped into the membranecell with the flow rate of 40 L/h. The temperature of themembrane room was controlled at 30 °C. The pressure in thedownstream side was maintained at <1.0 kPa using a vacuumpump, and the permeate vapor was collected in liquid nitrogentraps. The compositions of the feed solution and permeate wereanalyzed by HP6890 gas chromatography (GC) equipped witha 50 m long PONA (paraffin, olefin, naphthene, and aromatic)capillary column. The temperatures for injector, detector (flameionization detector), and oven were set at 200, 250, and 80 °C,respectively. The pervaporation properties of the membraneswere evaluated by three parameters: permeabilities (Pi), per-meances (Pi/l), and selectivities (Rij) that were related to theintrinsic properties of the membranes.37 The permeability ofcomponent i was

where PiL was a concentration-based permeability of component

i. Ji was the permeation flux of component i. l was the membranethickness. �io

L was the mole fraction of component i in the feedsolution. υi

G was the molar volume of gas i (22.4 L(STP)/mol),and mi was the molecular weight of component i.

When the membrane thickness was not known, membranepermeance (Pi

L/l), a component flux normalized for the drivingforce, could be used, and it was given as

Figure 4. Models of (a) PDMS-bulk and (b) PDMS-TNT interface.

Table 1. Interaction Energies between PDMS and TNTs, kcal/mol

Etotal Epotential Ekinetic

pressure(MPa)

temperature(K)

PDMS -8488.0 -9383.1 895.1 0.098 298.2TNTs -36806.5 -37476.9 670.4 0.086 298.4PDMS-TNTs -45981.9 -47551.1 1569.2 0.099 298.6∆E -687.4 -691.2 3.7

VF,i )4πri

3

3(2)

υe ) 1/SI (3)

SI ) m1/m0 (4)

PiL )

JiυiGl

mi�ioL

(5)

12446 Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010

Membrane selectivity, defined as the ratio of the permeabili-ties or permeances of components i and j through the membrane,is given as follows:

Results and Discussion

Analysis of the Polymer-Inorganic Interface. PALS wasemployed to probe the free volume characteristics of thePDMS-TNTs nanocomposite membranes with different TNTscontent, and the data were summarized in Figure 1-3. Figure1 showed the positron annihilation lifetime spectra in PDMScontrol specimen and PDMS-TNTs nanocomposite membraneswith different TNTs content. The higher the content of TNTsin PDMS, the slower the positron lifetime spectrum decayed,indicating that the FFV of the nanocomposite membranesbecame larger. Figure 2 represented the free volume distributionof the PDMS control specimen and nanocomposite membranesfilled with different TNTs content, both calculated with theMELT program. The incorporation of TNTs narrowed the freevolume pore radius distribution of the nanocomposite mem-branes. As will be further testified by MDS, the TNTs confinedthe segmental chain mobility of PDMS, which made the freevolume pore radius more uniform. From Figure 3, it could beseen that incorporation of TNTs increased the FFV of PDMSmembranes from 0.0293 to 0.039. The FFV was increased byabout 33%. The mean size of the free volume cavities remainedalmost unchanged at around 0.36 nm, so the increase in FFVwith higher TNTs content was ascribed to the increase in thefree volume intensity. This resulted from disruption of thepolymer chain packing due to the presence of nanotubes. Withthe increase of interface areas, significant enhancement of theFFV was observed. Moreover, no larger voids were detectedwhen the content reached 7.5 wt %, suggesting the homogeneousdispersion of TNTs.

To acquire more comprehensive information about thepolymer-inorganic interface, MDS was utilized simultaneously.Equilibrated models of bulk PDMS and PDMS-TNTs interfacewere constructed respectively by Material Studio, as illustratedin Figure. First, the polymer/particle interaction energy wascalculated. According to thermodynamics theory, the interactionenergy ∆E (quoted in kilocalories per mole) of PDMS-TNTscould be calculated as below:

where EPDMS-TNTs was the energy of the PDMS-TNTs layerand ETNTs and EPDMS were the energies of the optimized TNTslayer and PDMS layer, respectively. The calculation resultsof interfacial energy for PDMS-TNTs were summarized inTable 1, which was composed of total, potential, and kineticenergies. Averages were taken over the last 500 ps simulation.The total energy was reduced by 687.4 kcal/mol, and potentialenergy was decreased by 691.2 kcal/mol, while the kineticenergy was slightly increased by 3.7 kcal/mol. Therefore,the addition of TNTs particle to PDMS made the system morestable.

Then, we examined the effects of TNTs on the chain mobilityof the polymer. The mean square displacement (MSD) of the

segmental chains of the bulk and interfacial PDMS werecalculated respectively, and the results were plotted in Figure5a,b. The inserts in Figure 5a,b showed the ln(MSD/(cm2/s))vs ln(t/ps) relations. The straight lines indicated that the modelswere well-equilibrated. Generally, a larger slope of the MSDcurves reflected higher chain mobility. The slope of the dottedMSD of bulk PDMS was larger than that of the interfacialcounterpart. The diffusion coefficients of the segmental chainswere calculated from the slopes of their MSD curves by theEinstein relation38

Figure 5. MSD of (a) PDMS-bulk, (b) PDMS-TNT interface, and (c)segmental chains diffusion coefficient.

PiL

l)

JiυiG

mi�ioL

(6)

Rij )Pi

L

PjL)

PiL/l

PjL/l

(7)

∆E ) EPDMS-TNTs - (EPDMS + ETNTs) (8)

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010 12447

where Di was the diffusion coefficient and ⟨(ri(t) - ri(0))2⟩ wasthe MSD of the i component. The diffusion coefficient ofsegmental chains of the bulk and interfacial PDMS were ca.6.58 × 10-9 and 5.08 × 10-9 cm2/s, respectively, as shown inFigure 5c (statistical average results). The results demonstratedthat the mobility of segmental chains approaching the PDMS-TNTs interface region was substantially restricted/compressed.The current discovery, however, contradicted qualitative ex-pectations based on Hill’s model,7 in which the reduction inpolymer density near interfaces was responsible for the enhanceddiffusivity of penetrants in the interfacial region. MDS indicateda lowering of the mobility possibly due to the complicatedsynergy among diffusion rates and elasticity, as well as naturalconstraints imposed by the surface themselves.

The FFV of the equilibrated bulk and interfacial PDMS weredetected by a hard spherical probe. The penetrant molecules,thiophene and n-octane in the current study, were selected asthe probe molecules which were modeled by spheres with radius2.65 and 3.15 Å, respectively. The Connolly surface wascalculated when the probe molecule with the radius Rp rollingover the van der Waals surface, and free volume was definedas the volume on the side of the Connolly surface without atoms.The fractional free volume was determined by the ratio of freevolume to the total volume of the model. The FFVs of the bulkPDMS were 9.8 and 7.5%, and the FFV of the interfacial PDMSwas increased to 11.8 and 9.0%, using thiophene and n-octaneas probe molecules individually. The increase was mainlyascribed to the rigidification of the interfacial PDMS chains.According to Koros,39 the PDMS-TNTs belongs to the “caseI” hybrid materials. Contrary to the majority of previous work,the rigidified segmental chains generated numerous nanosizedvoids at the polymer-inorganic interface, which considerablyenlarged rather than decreased the FFV of the material.

Characterization of the PDMS-TNTs NanocompositeMembranes. Figure 6a shows the TEM image of the ultimateTNTs. They were around 200-600 nm in length, 6 nm ininternal diameter, and 10 nm in external diameter. The particledensity was estimated to be 3.16 g/cm-3, and the aspect ratiowas about 20-60. The FT-IR spectrum in Figure 7a shows acharacteristic peak at around 498 cm-1 assigning to thestretching vibration of Ti-O together with the peaks at 1635and 3384 cm-1 corresponding to the deformation and stretchingvibration of the adsorbed water. Figure 6b shows the BET resultsof TNTs, which indicated characteristic open end mesoporousstructures. The TNTs possessed a typically large BET surfacearea of about 264 cm2 g-1. BET results demonstrated that theinner diameter with narrow size distribution of TNTs was around6.2 nm. The as-prepared TNTs were then incorporated into thePDMS matrix to fabricate PDMS-TNTs nanocomposite mem-branes with different TNTs weight fractions (0.0, 2.5, 5.0, and7.5 wt %, respectively). FT-IR spectra in Figure 7b showedthat no new characteristic peaks were produced in thePDMS-TNTs nanocomposite membranes, suggesting thatPDMS and TNTs were physically mixed. In addition, in thenanocomposite membranes, a distinct TNTs characteristic peakat 498 cm-1 could not be detected, which was possiblyoverlapped by the broad band of PDMS. However, after TNTsincorporation, the absorption intensities of two characteristicpeaks of PDMS (1080 and 1025 cm-1 peaks in the membranescorresponded to stretching vibrations of Si-O-Si of PDMS)became slightly weaker. The main interfacial interactions

between PDMS and TNTs were hydrogen bonding betweenSi-O-Si and Ti-OH groups. The hydrogen bonding reducedthe amounts of free Si-O-Si groups of PDMS. Since moreinteractions were formed with the increase of the filler content,the intensities of these peaks decreased further.

Figure 8 were the cross-sectional SEM images of PDMScontrol and PDMS-TNTs nanocomposite membranes. Thethickness of the PDMS control and nanocomposite membranescontaining 2.5, 5.0, and 7.5 wt % TNTs were estimated to be15.6, 28.1, 34.4, and 37.5 µm, respectively. It was observedthat individual nanotubes tended to aggregate as bundles withdiameter of ca. 100 nm. Due to the fine adhesion between theactive layer and the support layer,40 no obvious defects wereobserved at the interface of these two layers.

The plot demonstrating cross-link density in PDMS-TNTsnanocomposite membranes as a function of particle loading wasshown in Figure 9. It could be seen that the cross-link densityof the nanocomposite membrane containing 7.5 wt % TNTswas about 2.5 times higher than the PDMS control membrane.The TNTs particles actually acted as additional cross-link sites,which notably increased the cross-link density of the membrane.

Permeability Measurement. Dense membranes are usuallyemployed to separate a mixture of small molecules havingsimilar dimensions. Pervaporation has been used as an effectivedesulfurization method in FCC gasoline.41 Paraffin and olefinwere the main components of FCC gasoline. The content ofparaffin was over 40 wt %. Thiophene and its derivatives werethe main sulfur species in FCC gasoline. As proof-of-principle,

Di ) 16

limtf∞

ddt ∑

i)1

Na

⟨(ri(t) - ri(0))2⟩ (9)

Figure 6. (a) TEM image of TNTs and (b) N2 adsorption-desorptionisotherm and BJH pore size distribution of TNTs.

12448 Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010

we chose n-octane/thiophene binary mixture as a model feedto tentatively validate the proposed methodology.

We first examined the effects of TNTs content on theseparation performance of the membranes by pervaporationprocess, and the results were summarized in Figure 10. Itshowed the variation of permeance, permeability, and membraneselectivity as a function of TNTs loadings (500 µg/g (in termsof sulfur) in the feed, 40 L/h flow rate, 30 °C). It wasdemonstrated that the PDMS control and PDMS-TNTs nano-composite membrane were more permeable to thiophene thann-octane. These membranes were therefore thiophene-selective.A considerable enhancement in permeance was found with theincrease of TNTs content. When the TNTs content reached 7.5wt %, the permeance started to decrease. The permeability,however, was still increased when TNTs content reached 7.5wt %. As shown in Figure 8, this was mostly due to the increaseof the membrane thickness. The membrane selectivity wassimultaneously increased. As proved by PALS and MDS, theincorporation of TNTs into the PDMS matrix significantlyenlarged the FFV. Consequently, the nanocomposite membranescould offer more diffusion paths for those small penetrants.Because the free volume cavity size remained almost unchanged,the selectivity of the membrane was not decreased. To clarify

Figure 7. Characteristic FT-IR spectra of (a) TNTs and (b) PDMS controland PDMS-TNTs nanocomposite membranes.

Figure 8. SEM images of (a) PDMS control and (b-d) PDMS-TNTs nanocomposite membranes with different TNTs content (0-7.5 wt %). The insert ind: nanotube aggregate within PDMS.

Figure 9. Effect of TNTs content on the membrane cross-link density ofPDMS control and PDMS-TNTs nanocomposite membranes.

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010 12449

the relationship between the structure and diffusion behavior,the permeability of thiophene/n-octane in the membranes wascorrelated to the FFV. The plot of the permeability vs the FFVaccording to eq 10 was shown in Figure 11.

where A and B were constant. It could be seen that permeabilityhad an exponential relation to the inverse of FFV, which agreedwell with the prevalent free volume theory.

Conclusions

In the current study, we proposed PALS and MDS combi-native method to probe the microscopic structure and particularlythe interfacial structure of rubbery polymer-inorganic nano-composite materials represented by PDMS-TNTs and toelucidate the successful striding over trade-off hurdle betweenpermeability and selectivity of the nanocomposite membranes.PALS and MDS results indicated that fractional free volume inthe vicinity of the polymer-inorganic interface was significantlyincreased, which was mainly attributed to the variation of chainmobility and the consequent increase of the free volume intensity(the mean size of the free volume cavities kept almostunchanged). It can be envisaged that the reported methodologyof characterizing the polymer-inorganic interface is applicableto a variety of nanocomposite materials.

Acknowledgment

We thank the financial support from the National BasicResearch Program of China (Grant No. 2009CB623404), TianjinNatural Science Foundation (Grant No. 10JCZDJC22600), StateKey Laboratory of Materials-Oriented Chemical Engineeringof Nanjing University of Technology (Grant No. KL09-3), theprogram for Changjiang Scholars and Innovative Research Teamin University (PCSIRT), the Programme of Introducing Talentsof Discipline to Universities (Grant No. B06006). We alsoexpress our gratitude to the R & D Center for PetrochemicalTechnology, Tianjin University for providing access to theMaterial Studio molecular modeling software.

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ReceiVed for reView May 23, 2010ReVised manuscript receiVed October 13, 2010

Accepted October 19, 2010

IE101142B

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010 12451