Sorption, Transport, and Structural Evidence for Enhanced Free

Chem. Mater. 2003, 15, 109-123

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Sorption, Transport, and Structural Evidence for Enhanced Free Volume in Poly(4-methyl-2-pentyne)/ Fumed Silica Nanocomposite Membranes T. C. Merkel* Center for Energy Technology, Research Triangle Institute, P.O. Box 12194, Research Triangle Park, North Carolina 27709-2194

B. D. Freeman Department of Chemical Engineering and Center for Energy and Environmental Resources, University of Texas at Austin, 10100 Burnet Road, Austin, Texas 78758-4445

R. J. Spontak Departments of Chemical Engineering and Materials Science & Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905

Z. He and I. Pinnau Membrane Technology and Research, 1360 Willow Road, Menlo Park, California 94025-1516

P. Meakin and A. J. Hill Division of Manufacturing and Infrastructure Technology, CSIRO, Private Bag 33, Clayton, VIC 3168, Australia Received June 17, 2002. Revised Manuscript Received October 2, 2002

In contrast to the performance of traditional filled polymer systems, penetrant permeability coefficients in high-free-volume, glassy poly(4-methyl-2-pentyne) (PMP) increase systematically and substantially with increasing concentration of nonporous, nanoscale fumed silica (FS). For instance, the permeability of PMP containing 40 wt % FS to methane is 2.3 times higher than that of the unfilled polymer. Gas and vapor uptake in the PMP/FS nanocomposites is essentially unaffected by the presence of up to 40 wt % FS, while penetrant diffusion coefficients increase regularly with increasing filler content. This increase in diffusivity is responsible for elevated permeability in the PMP/FS nanocomposites. The addition of FS to PMP augments the permeability of large penetrants more than that of small gases, consistent with a reduction in diffusivity selectivity. Consequently, vapor selectivity in the nanocomposites increases with increasing FS concentration. Activation energies of permeation in PMP decrease with increasing FS content, suggesting that penetrant diffusive jumps require less energy at higher filler concentrations. Positron annihilation lifetime spectroscopy (PALS) reveals that FS subtly increases the free volume in PMP available for molecular transport. The accessible free volume measured by PALS correlates favorably with relative penetrant permeability in the nanocomposites. Transmission electron microscopy confirms that the FS nanoparticles are relatively well dispersed in PMP.

Introduction The identification of new classes of materials with unique properties can profoundly impact existing technologies as well as enable development of entirely new products and processes. This breakthrough potential has led to considerable research into organic-inorganic hybrid materials, which seemingly offer a relatively accessible means for altering the properties of existing materials without requiring synthesis of entirely new chemical species. Through hybridization it is possible to capture the desirable attributes of the organic and inorganic components in a single composite, and possibly to discover new synergistic properties. In molecular

separations, ongoing efforts continue to explore the utility of incorporating porous inorganic particles, such as highly selective zeolites, into dense polymeric membranes to improve gas separation properties.1-5 In theory, such materials might combine the excellent size (1) Jia, M.; Peinemann, K. V.; Behling, R. D. J. Membr. Sci. 1991, 57, 289. (2) Kulprathipanja, S.; Neuzil, R. W.; Li, N. U.S. Patent No. 4,740,219, 1988. (3) Duval, J. M. J. Membr. Sci. 1993, 80, 189. (4) Suer, M. G.; Bac, N.; Yilmaz, L. J. Membr. Sci. 1994, 91, 77. (5) Mahajan, R.; Zimmerman, C. M.; Koros, W. J. In Polymer Membranes for Gas and Vapor Separation: Chemistry and Materials Science; Freeman, B. D., Pinnau, I., Eds.; American Chemical Society: Washington, D.C., 1999; pp 277-286.

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selectivity of zeolites with the desirable mechanical and processing attributes of polymers. In practice, however, attaining this synergy is difficult. Often, hybrid membrane performance is compromised by the formation of relatively nonselective defects caused by dewetting of polymer chains from the surface of micrometer-sized zeolite particles. These problems with zeolite/polymer adhesion, as well as inadequate particle dispersion in the polymer phase, have hindered the development and implementation of such membranes.4,5 In addition to porous zeolite particles, many types of nonporous, inorganic fillers are added to polymers for a variety of reasons, including mechanical and flow property modification, alteration of thermal and electrical conductivity, changing physical appearance, and reducing cost.6 Traditionally, the incorporation of nonporous fillers, such as metal oxides, silicas, or carbon blacks, into polymers reduces gas or vapor permeability. This decreased permeability is the result of a reduction in the amount of polymer through which transport may occur and an increase in the diffusion path length that penetrant molecules experience7,8 as they are forced to take a tortuous course around filler particles to traverse a film. Recently, incorporation of nanoscale, nonporous fumed silica (FS) particles into high-free-volume, glassy poly(4-methyl-2-pentyne) (PMP) has been discovered to increase both gas permeability and organic vapor/ permanent gas selectivity.9,10 For example, addition of 30 wt % FS to PMP simultaneously doubles mixed-gas n-butane/methane selectivity and increases n-butane permeability by a factor of 3 relative to that of pure PMP.9 The fact that both permeability and vapor selectivity increase with FS addition to PMP indicates that these particles modify transport properties without introducing gross defects or large, selectivity-destroying gaps into the membrane. Such defects often allow Knudsen flow,5 which favors preferential permeation of small, permanent gases and thus would lower vapor/ gas selectivity. Since FS particles are nonporous, they do not permeate penetrant molecules as a zeolite might. Rather, they presumably alter PMP chain packing to effect substantial changes in transport properties that are favorable to vapor separations. This approach differs conceptually from previous work in which an attempt is made to harness the separation properties of the filler particles themselves (e.g., zeolites) to enhance the sizesieving ability of the membrane. PMP is a member of a family of substituted acetylene polymers that exhibit poor polymer chain packing in part due to rigid backbones, low interchain cohesion, and bulky substituents.11 These glassy polymers are characterized by low densities, high fractional free volumes, high gas permeabilities, and in some cases, high selectivity for organic vapors over permanent gases.12 Such unusual transport properties make PMP and other polyacetylenes particularly well suited for

vapor separation applications in which polymer membranes that are more permeable to large organic vapors than to small permanent gases are required. Examples of these applications include the removal of higher hydrocarbons from natural gas, organic monomer recovery from mixtures with nitrogen, and hydrocarbon removal from mixtures with hydrogen.13 Currently, poly(dimethylsiloxane) (PDMS), a highly permeable, vapor-selective rubber, is used commercially for membrane-based vapor separations.13,14 The competitiveness of PDMS with conventional separation technologies (e.g., adsorption or condensation systems) is limited primarily by the selectivity of PDMS for organic vapors over permanent gases. Development of membrane materials with improved selectivities would reduce the cost of membrane systems, thereby making them a more attractive option for vapor separation applications.13 The polymer with the highest vapor/permanent gas selectivity is the polyacetylene poly(1-trimethylsilyl-1propyne) (PTMSP).15 However, the industrial utility of this polymer is limited, in part, by its high solubility in many liquid hydrocarbons, which renders it unstable in some of the process environments where its separation properties would be most beneficial. While the vapor selectivity of PMP is less attractive than that of PTMSP, PMP is more solvent-resistant.9,11 Nanocomposites consisting of FS in PMP retain the chemical stability of the base polymer and exhibit improved vapor separation efficacy. The unusual vapor-selective nature of amorphous PMP is partially ascribed to the enormous amount of free volume, or space not occupied by polymer chains, present in this material.11 Generally, as polymer free volume increases, its ability to sieve molecules based on size decreases.16 For solution-diffusion transport in dense polymers with sufficiently high free volume, very low diffusivity selectivity allows larger, more soluble vapors (e.g., n-C4H10) to be more permeable than smaller, less soluble gases (e.g., H2). The vapor selectivity of these high-free-volume glassy materials typically increases with increasing polymer free volume provided that solution diffusion is the dominant transport mechanism (i.e., the material does not have sufficient free volume to permit a significant influence of free phase transport mechanisms such as Knudsen diffusion or Poiseuille flow). In the present work, we report permeability coefficients for several gases and vapors in PMP containing nanoscale FS. In addition, the first values of penetrant solubility in filled PMP are reported which, together with permeation data, permits calculation of penetrant diffusion coefficients. The effect of FS content on these transport parameters and on selectivity is interpreted in terms of the influence of FS on PMP chain packing and free volume. The variation in PMP free volume with FS content is also characterized by positron annihilation lifetime spectroscopy, and FS dispersion in PMP is examined by transmission electron microscopy.

(6) Rothon, R. N. Adv. Polym. Sci. 1999, 139, 67. (7) Barrer, R. M. In Diffusion in Polymers; Crank, J., Park, G. S., Eds.; Academic Press: London, 1968; pp 165-217. (8) van Amerongen, G. J. Rubber Chem. Technol. 1964, 37, 1065. (9) Pinnau, I.; He, Z. U.S. Patent No. 6,316,684, 2001. (10) Merkel, T. C.; Freeman, B. D.; Spontak, R. J.; He, Z.; Pinnau, I.; Meakin, P.; Hill, A. J. Science 2002, 296, 519. (11) Morisato, A.; Pinnau, I. J. Membr. Sci. 1996, 121, 243.

(12) Freeman, B. D.; Pinnau, I. In Polymer Membranes for Gas and Vapor Separations: Chemistry and Materials Science; Freeman, B. D., Pinnau, I., Eds.; American Chemical Society: Washington, D.C., 1999; pp 1-27. (13) Wijmans, J. G.; Helm, V. D. AIChE Symp. Ser. 1989, 85, 74. (14) Wijmans, J. G. U.S. Patent No. 5,089,033, 1992. (15) Pinnau, I.; Toy, L. G. J. Membr. Sci. 1996, 116, 199. (16) Ghosal, K.; Freeman, B. D. Polym. Adv. Technol. 1994, 5, 673.

Free Volume in PMP/FS Nanocomposite Membranes

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Background

and diffusion and the enthalpy of sorption:

Transport in Polymers. The permeability coefficient, P, of a pure penetrant in a polymer film is defined as16

P)

Nl p2 - p1

(1)

where p2 is the feed (or upstream) pressure, p1 is the permeate (or downstream) pressure, l is the film thickness, and N is the steady-state penetrant flux through the polymer film. Permeability is frequently expressed in barrers, where 1 barrer ) 10-10 cm3(STP)‚cm/cm2‚s‚ cmHg. Gas transport in nonporous polymer membranes and in some microporous materials proceeds by a solution-diffusion mechanism for which the permeability coefficient may conveniently be expressed as16

(

)

C2 - C1 ×D P) p2 - p1

(2)

where D is the concentration-averaged effective diffusion coefficient and C2 and C1 are the penetrant concentrations in the polymer at the upstream (p2) and downstream (p1) faces of the membrane, respectively. When the downstream pressure is much less than the upstream pressure, eq 2 may be expressed in the familiar form16

P)S×D

(3)

where S is the solubility coefficient at the upstream pressure, C2/p2. The ideal selectivity of a polymer film for component A relative to component B, RA/B, is defined as the ratio of their permeabilities, which in light of eq 3 may be rewritten as the product of two ratios16

RA/B )

() ( )

PA SA DA ) × PB SB DB

(4)

where the first term on the right-hand side is the solubility selectivity and the second is the diffusivity selectivity. The temperature dependence of permeability, diffusivity, and solubility at temperatures removed from polymer thermal transitions is described as follows:16

( ) ( ) ( )

P ) P0 exp -

EP RT

(5)

D ) D0 exp -

ED RT

(6)

∆HS RT

(7)

S ) S0 exp -

Here, P0, D0, and S0 are pre-exponential constants, EP is the activation energy of permeation, ED is the activation energy of diffusion, ∆HS is the enthalpy of sorption, R is the universal gas constant, and T denotes absolute temperature. As permeability is the product of solubility and diffusivity, the following relationship exists between the activation energies of permeation

EP ) ED + ∆HS

(8)

Transport in Heterogeneous Materials. Numerous theoretical expressions have been developed to explain transport behavior in heterogeneous polymer systems.7 A simple and frequently used model describing permeation in these systems is that of Maxwell, proposed for analyzing the specific resistance of a compound medium composed of a dilute suspension of spheres.17 For a nonporous, impermeable filler dispersed in a continuous polymer matrix, the permeability of the composite is given by

P ) Pp

( ) 1 - φf φf 1+ 2

(9)

where Pp is the permeability of the pure polymer and φf is the volume fraction of filler. According to eq 9, the permeability of the filled polymer is always less than that of the pure polymer and decreases with increasing filler concentration. This reduction in permeability is related to an increase in the tortuosity of the diffusion path, as well as a decrease in penetrant solubility caused by the replacement of polymer, which can sorb penetrant, with nonsorbing filler particles. Despite its simplicity, the Maxwell model captures qualitatively the intuitive expectation that nonporous filler particles reduce permeability. Equation 9 has been used successfully to describe the effect of filler content on permeability in a variety of filled polymers.7,18 Gas solubility in a binary system consisting of filler particles dispersed in a polymer matrix may depend on the concentration of filler particles, as well as their interactions with polymer chains. If a filler is nonporous and interacts favorably with the polymer matrix such that the filler is fully wetted by polymer chains, sorption by the filler is usually negligible.7 In this case, solubility in the filled polymer is equal to the pure polymer solubility times the polymer volume fraction; viz.,7

S ) (1 - φf)Sp

(10)

where Sp is the solubility of a penetrant species in the polymer matrix. Alternately, filler particles can adsorb penetrant molecules, particularly if the particles are not completely wetted by the polymer. This results in the total sorption becoming the sum of two contributions,7

S ) (1 - φf)Sp + φfSf

(11)

where Sf refers to sorption onto the surface of nonporous fillers and, in the case of porous filler particles, into the filler’s pore structure. Additional complexity may be encountered if filler particles cluster together to form interstitial voids or gaps where no polymer can access or, for example, if the filler induces morphological changes in the polymer matrix.18 (17) Maxwell, C. Treatise on Electricity and Magnetism; Oxford University Press: London, 1873; Vol. 1. (18) Barrer, R. M.; Barrie, J. A.; Rogers, M. G. J. Polym. Sci., Part A: Polym. Chem. 1963, 1, 2565.

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Free Volume. Molecular diffusion through a dense polymer depends strongly on the amount of free volume that a material possesses.16 Free volume, whether static voids created by inefficient chain packing or transient gaps generated by thermally induced chain rearrangement, presents diffusing molecules with a low-resistance path for transport. The larger and more numerous these pathways are, the faster molecules migrate through a polymer and vice versa. A quantity frequently used to compare the amount of free volume in polymers is the fractional free volume (FFV), which is defined as

FFV )

Vsp - V0 Vsp

(12)

where Vsp is the polymer bulk specific volume and V0 is the volume occupied by polymer chains. The value of V0 may be calculated from19

V0 ) 1.3Vw

(13)

where Vw is the van der Waals volume, which can be estimated from group contribution methods. We use the method proposed by Bondi19 for this purpose. Within a given family of polymers, penetrant diffusivity and permeability often correlate well with polymer FFV estimated from eq 12.20 Positron annihilation lifetime spectroscopy (PALS) provides an estimate of the size and concentration of both static and dynamic free volume elements in condensed matter (pure or heterogeneous).21 In this technique, a positron is injected into a sample, forms a spin parallel bound state with an electron called opositronium (oPs) and subsequently annihilates with an antiparallel electron of the surrounding medium to form γ rays. The lifetime of an oPs particle depends on the electron density of its local environment, which is sensitive to the size of the free volume element in which it resides. The intensity of oPs annihilations is related to the concentration of accessible free volume elements. Numerous studies point to a strong correlation between PALS accessible free volume and polymer transport properties.20,22,23 Experimental Section Film Preparation. Dense polymer/filler nanocomposite films were prepared by solution-casting mixtures of fumed silica and poly(4-methyl-2-pentyne). Synthesis and characterization information regarding the polymer is provided elsewhere.11 The PMP was dissolved in cyclohexane to form a 1.5 wt % polymer solution, which is near the solubility limit for PMP in this solvent and yields a relatively viscous solution. The high solution viscosity helps to inhibit gravity-driven settling of FS particles during film drying. Nonporous FS powder was then added to the polymer solution. Cab-O-Sil TS(19) Bondi, A. J. Phys. Chem. 1964, 68, 441. (20) Freeman, B. D.; Hill, A. J. In Structure and Properties of Glassy Polymers; Tant, M. R., Hill, A. J., Eds.; American Chemical Society: Washington, D.C., 1998; pp 306-325. (21) Kobayashi, Y.; Haraya, K.; Hattori, S.; Sasuga, T. Polymer 1994, 35, 925. (22) Yampol’skii, Y. P.; Shantorovich, V. P.; Chernyakovskii, F. P.; Kornilov, A. I.; Plate, N. A. J. Appl. Polym. Sci. 1993, 47, 85. (23) Consolati, G.; Genco, I.; Pegoraro, M.; Zanderighi, L. J. Polym. Sci.: Polym. Phys. Ed. 1996, 34, 357.

530, a hydrophobic grade of FS available from Cabot Corporation (Tuscola, IL), was used throughout this study. It has a specific gravity of 2.2 g/cm3 and a BET surface area of 230 m2/g.24 This surface area corresponds to an equivalent spherical primary particle diameter of 13 nm (from geometric considerations: equivalent spherical particle diameter ) 6/(surface area × density)). The TS-530 FS has been chemically treated with hexamethyldisilazane to replace polar hydroxyl surface groups with nonpolar trimethylsilyl surface groups.24 This treatment makes the surface of the silica particles similar in chemical nature to the nonpolar PMP matrix, and together with the small particle size is believed to play an important role in allowing intimate mixing of polymer and filler. The polymer, solvent, and FS were stirred at 18 000 rpm for 10 min in a Waring two-speed commercial blender. The blended mixture was filtered, poured into a casting ring, covered to allow for slow solvent evaporation, and dried at ambient conditions until constant mass was achieved, indicating that all solvent was removed. While the permeation properties and appearance of PMP/ FS nanocomposite films were unchanged if shorter blending times were used (even as short as 30 s), drying conditions had a significant impact on final film properties. For example, if solvent evaporated too quickly, the formation of bubbles in the nascent film resulted in macroscopic defects. Conversely, if solvent evaporation occurred too slowly, FS particles aggregated into a silica-rich phase, especially if there was a mismatch in the polarity of the polymer medium and particle surface groups (i.e., if hydrophilic FS was used rather than hydrophobic FS). The principal factors affecting drying rate were temperature, the solvent partial pressure in the atmosphere immediately above the drying film, and the thickness of the drying film. In this study, the final dry film thickness was 40-50 µm as determined by a precision micrometer, and the drying temperature was 25 ( 2 °C. The casting rings containing blended polymer, FS, and solvent were placed in a casting box that provides quiescent air. The rings themselves were covered with filter paper to further slow the rate of solvent removal. High-free-volume polymers, such as PMP, are known to exhibit permeation properties that are sensitive to polymer processing history and film preparation methods.25-27 Moreover, PMP also demonstrates physical aging behavior.11 Consequently, care was taken when comparing sorption and transport properties of these polymer samples. In this regard, polymer and nanocomposite films were cast under identical conditions from the same batch of PMP. Once PMP and PMP/ FS films were completely solvent-free (after about 72 h), experiments were started. Permeability measurements were conducted over a time period where the decrease in the nitrogen permeability coefficient was less than the uncertainty in the measurements (a maximum of (7% as determined by a propagation of errors analysis28). Similarly, N2 sorption isotherms determined before and after completion of solubility studies were consistent within experimental uncertainty. Throughout this work the concentration of FS in PMP/FS nanocomposite films is reported in weight percent (wt %). However, for comparison with literature data pertaining to transport in filled polymers where fillers of different densities have been used, it is more useful to express filler content on a volumetric basis. Accordingly, the FS volume fraction in PMP has been estimated using pure (24) CAB-O-SIL TS-530 Treated Fumed Silica: Technical Data, Cabot Corporation, 1991. (25) Nagai, K.; Masuda, T.; Nakagawa, T.; Freeman, B. D.; Pinnau, I. Prog. Polym. Sci. 2001, 26, 721. (26) Nagai, K.; Nakagawa, T. J. Membr. Sci. 1995, 105, 261. (27) Nagai, K.; Mori, M.; Watanabe, T.; Nakagawa, T. J. Polym. Sci., Part B: Polym. Phys. 1997, 35, 119. (28) Bevington, P. R.; Robinson, D. K. Data Reduction and Error Analysis for the Physical Sciences, 2nd ed.; McGraw-Hill: New York, 1992.


Chem. Mater., Vol. 15, No. 1, 2003 113

component densities as follows:

φf )

wf Ff wf + (1 - wf) Fp

(14)

Here, Fp and Ff denote the pure polymer and filler densities, respectively, and wf is the filler weight fraction. Permeation Measurements. The pure-gas permeation properties of PMP and FS-filled nanocomposites were determined with a constant pressure/variable volume apparatus.29 The surface area of the film was 13.8 cm2 and gas flow rates were measured with a soap-film bubble flowmeter. Prior to each experiment, both the upstream and downstream sides of the permeation cell were purged with penetrant gas. Permeability coefficients of gases and vapors were determined in the order of increasing penetrant condensability: H2, N2, CH4, C2H6, C3H8, and n-C4H10. When steady-state conditions were achieved, the following expression was used to evaluate permeability:29

P)

l 273 patm dV p2 - p1 TA 76 dt

( )

(15)

where p2 is the upstream pressure, p1 is the downstream pressure (atmospheric pressure in this case), patm is atmospheric pressure (in cmHg), A is the membrane area, and dV/ dt is the volumetric displacement rate of the soap film in the bubble flowmeter. Mixed-gas permeation properties of films were determined with a feed containing 2 vol % n-butane in methane. The feed pressure in these experiments was 11.2 atm and the permeate pressure was atmospheric. The ratio of permeate to feed flow rate, or the stage cut, was always 30 eV were precluded from image formation.31,32 Structure-sensitive images obtained at ∆E settings between 200 and 270 eV energy loss selectively removed electrons inelastically scattered from carbonaceous components, thereby highlighting the siliceous FS particles.33

Results and Discussion where xfeed and xperm refer to the mole fractions of components in the feed and permeate streams, respectively. Sorption Measurements. The solubility of gases in PMP and the FS-filled nanocomposites was measured with a highpressure barometric sorption apparatus.30 Initially, the film to be studied was placed in a sample chamber and exposed to vacuum overnight to remove air gases. Penetrant gas was then introduced into the chamber and allowed to equilibrate. Once the chamber pressure was constant, additional penetrant was introduced and equilibrium was re-established. In this incremental manner, penetrant uptake was measured as a function of penetrant pressure. Sorption equilibrium for all gases was reached within, at most, a few hours. The experimental temperature was maintained within (0.1 °C with a constant temperature water bath. Uptake of n-butane in PMP, in PMP/FS nanocomposites, and on FS powder was measured with a Cahn RG Electrobalance (Bellflower, CA). The balance is serviced by a vacuum system and housed in an insulated box equipped with an air bath temperature regulation system. Approximately 25 mg of sample was placed on the balance and degassed under vacuum. The sample was then exposed to fixed n-butane pressure and mass uptake was monitored as a function of time using a computer equipped with Labtech (Andover, MA) data acquisi(29) Stern, S. A.; Gareis, P. J.; Sinclair, T. F.; Mohr, P. H. J. Appl. Polym. Sci. 1963, 7, 2035. (30) Bondar, V. I.; Freeman, B. D.; Pinnau, I. J. Polym. Sci.: Polym. Phys. Ed. 1999, 37, 2463.

Transmission Electron Microscopy. The distribution of FS particles in PMP containing 15, 30, and 40 wt % FS is visible in the TEM images presented in Figure 1. Consistent with the general network-forming properties of FS,24 some primary particles aggregate into clusters ranging up to a few hundred nanometers in diameter. The clusters evident in Figure 1a-c possess a highly fractal surface, which together with discrete primary particles (see Figure 1d-f) yields a relatively large polymer/filler interface. These TEM images reveal that the number of FS particles, as well as their mean aggregate size, increases with FS concentration (cf., Table 1). Comparison with aggregate sizing discerned from light scattering on dilute FS solutions34 confirms that these particles are well dispersed in PMP. This result is consistent with weak polymer/filler interactions, which is expected based on the relatively nonpolar nature of the PMP matrix and the FS surface. Adequate (31) Reimer, L., Ed. Energy-Filtering Transmission Electron Microscopy; Springer-Verlag: Berlin, 1995. (32) DuChesne, A. Macromol. Chem. Phys. 1999, 200, 1813. (33) Thomann, R.; Spontak, R. J. In Science, Technology, and Education of Microscopy: An Overview; Mendez-Vilas, A., Ed.; Formatex: Badojoz, Spain, in press. (34) Gieger, R. Cabot Corporation, personal communication, 2001.

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Figure 1. A series of energy-filtered TEM images of PMP containing differing concentrations of FS (in wt %): (a, d) 15, (b, e) 30, and (c, f) 40. The insets in the low-magnification images (a-c) are position-matched structure-sensitive images showing the distribution of non-carbonaceous features. Corresponding enlargements of the PMP/FS nanocomposite morphologies are provided in (d-f). Table 1. Mean Aggregate Size of TS-530 FS in PMP system

mean aggregate diameter, nm

PMP PMP containing 15 wt % FSa PMP containing 30 wt % FSa PMP containing 40 wt % FSa dilute fumed silica suspensionb

s 70 110 100 160

a From analysis of TEM images by Scion Image software (Frederick, MD). This program measures the area occupied by each isolated FS species, which may be an individual particle or aggregate of particles, and calculates an equivalent spherical diameter. b From light-scattering experiments performed by Cabot Corporation.34

FS dispersion is important and, as will be shown, consistent with our transport data since highly networked FS might promote defects leading to Knudsen diffusion and the attendant low selectivities, as well as brittle mechanical properties. Density. An intensive property required for estimating FFV by group contribution methods or analyzing sorption data is the mass density of the sample material. For a binary polymer/filler system, the bulk density, F, may be estimated from pure-component properties if volume additivity is obeyed:

F)

1 1 - wf wf + Fp Ff

(17)

The density of PMP/FS nanocomposites was estimated

Figure 2. Density of PMP/FS nanocomposites at 25 °C as a function of FS content. The solid line is the predicted density (i.e., eq 17) based on a measured PMP density of 0.84 g/cm3 and the reported24 FS density of 2.2 g/cm3.

from eq 17 and also measured by gravimetric analysis (i.e., samples of known area and thickness were weighed on an analytical balance). The results are compared in Figure 2, which presents the density of PMP as a function of FS content. The uncertainty in the measured densities is estimated from a propagation of errors analysis suggested by Bevington and Robinson.28 Nanocomposite density, both measured and calculated, increases with FS content, consistent with the fact that FS (2.2 g/cm3)24 has a significantly higher density than


PMP (0.84 g/cm3). The measured densities of PMP containing 30 and 40 wt % FS are somewhat lower than those calculated from the additive model (eq 17). This deviation from additivity suggests that incorporation of FS into PMP increases free volume in the polymer. However, these differences in calculated and measured densities are near to the uncertainty in the measurements, implying that any change in PMP free volume resulting from FS addition is subtle and not easily detected by this method. In the sorption data analysis discussed later in this work, the measured nanocomposite densities are used. However, there is no discernible difference in the results if densities calculated from eq 17 are used instead. Free Volume Characterization. A simple and frequently used means of estimating the fractional free volume of a polymer is the group contribution method (i.e., eq 12). With use of the known filler weight fraction (wf), the measured nanocomposite density (F), and the density of pure filler (Ff), eq 17 may be employed to estimate the density of PMP as a function of filler content. This calculation, of course, assumes that deviations from volume additivity are confined to the polymer phase of the nanocomposite (i.e., filler particle density is constant). The estimated density of PMP in the filled systems, along with literature group contribution values,35 can then be used to calculate the FFV of filled PMP according to eqs 12 and 13. On the basis of this analysis, the FFV of PMP increases at higher FS concentrations. For example, the FFV of PMP increases from 0.22 to 0.28 when the concentration of FS increases from 0 to 40 wt %. This FS-induced increase in FFV is consistent with the observed transport behavior in the filled polymer (as will be demonstrated later). It should be noted, however, that the calculation of FFV by group contribution methods is generally sensitive to sample density measurements, and any variation in PMP FFV with filler content is strictly due to the deviations from volume additivity illustrated in Figure 2. As discussed above, these deviations from additivity are close to the uncertainty in the measurements and, consequently, so is the variation in PMP FFV with filler content. A more sensitive means of probing the effect of FS addition on free volume in PMP is provided by positron annihilation lifetime spectroscopy. Figure 3 presents oPs lifetimes in PMP as a function of FS content. As mentioned previously, the average lifetime of oPs probe particles is related to the average free volume element size in a polymer, with longer lifetimes corresponding to larger free volume elements. While the PALS spectra of most polymers are described by a single oPs lifetime, τ3, some high-free-volume polymers possess a second, longer oPs lifetime, τ4.22 It has been suggested that τ4 corresponds to large, possibly interconnected free volume elements in substituted acetylene polymers such as PMP and PTMSP.23 The PALS analysis of PMP and FS-filled PMP indicates that these materials possess a bimodal distribution of oPs lifetimes. On the basis of the data in Figure 3, the shorter oPs lifetimes (τ3) appear to be nearly independent of FS concentration, whereas the longer lifetimes (35) Van Krevelen, D. W. Properties of Polymers: Their Correlation with Chemical Structure; Their Numerical Estimation and Prediction from Additive Group Contributions; Elsevier: Amsterdam, 1990.

Chem. Mater., Vol. 15, No. 1, 2003 115

Figure 3. Effect of FS content on oPs lifetimes in PMP. PALS spectra have been collected at ambient temperature in a nitrogen environment and modeled as the sum of four decaying exponential terms using the computer program PFPOSFIT. Table 2. Average Free Volume Cavity Radius in PMP and FS-Filled PMP from Positron Annihilation Lifetime Spectroscopy average free volume element radius,a Å system

r3

r4

PMP PMP containing 15 wt % FS PMP containing 30 wt % FS PMP containing 40 wt % FS

2.9 3.3 3.3 3.2

5.7 6.0 6.2 6.4

a Values were calculated from oPs lifetimes using eq 18, which assumes spherical free volume elements.

(τ4) increase monotonically with increasing FS content. This result indicates that large free volume elements in PMP increase in size with increasing FS concentration. If an oPs probe is located at the core of a spherical void, an average free volume element radius, r, can be estimated from the oPs lifetime, τ, as follows,36

[ ()

( )]

1 r 2πr 1 )2 1sin + τ r0 2π r0

(18)

where r0 is the electron layer thickness, estimated to be 1.656 Å.36 With use of eq 18, the data in Figure 3 can be recast in terms of average free volume radii. This analysis indicates that PMP and FS-filled PMP possess small free volume cavities with an average radius of ∼3 Å and larger free volume elements with an average radius ranging between 5.5 and 6.5 Å (cf., Table 2). The total increase in average free volume radius of large elements at high FS concentration is 98%) of free volume in PMP, as well as in the PMP/FS nanocomposites, is located in the larger free volume elements. This result is consistent with previous PALS studies of free volume distribution in other high-flux, glassy polymers.38 The effect of FS content on relative PALS free volume in PMP is illustrated in Figure 4. The quantity on the ordinate of this figure is obtained by calculating (τ33I3 + τ43I4) for each PMP/FS nanocomposite and normalizing the sum by the corresponding value for pure PMP. The error bars shown in this figure are based on propagation of errors from the average error associated with each PALS parameter. The data in Figure 4 indicate that there is negligible change in the PALS accessible free volume in a PMP/FS nanocomposite with 15 wt % FS relative to pure PMP. This result reflects the fact that the increase in large free volume element size (τ4) is offset by a decrease in free volume cavity concentration (I4) as the concentration of FS is increased from 0 to 15 wt %. This may indicate that the initial addition of FS promotes some consolidation of large free volume elements to form a smaller number of even larger cavities. As more FS is added, cavity concentra(37) Shantarovich, V. P.; Kevdina, I. B.; Yampolskii, Y. P.; Alentiev, A. Y. Macromolecules 2000, 33, 7453. (38) Singh, A. Ph.D. Dissertation, North Carolina State University, 1997.

tion remains nearly constant while large free volume elements increase in size, yielding a higher relative free volume. Thus, consistent with group contribution estimates, PALS data confirm that the free volume of PMP increases due to the addition of FS particles. This result suggests that incorporation of FS into PMP could augment transport parameters. Permeability. Figure 5a-f presents pure gas H2, N2, CH4, C2H6, C3H8, and n-C4H10 permeability coefficients in PMP containing 0, 15, and 30 wt % FS as a function of the transmembrane pressure difference, ∆p. Contrary to behavior in traditional filled polymers, the permeability of PMP films is increased by blending nanoscale FS into the polymer. For example, at ∆p ) 3.4 atm, the methane permeability coefficient in PMP containing 30 wt % FS is 130% higher than that in the unfilled polymer. Our permeability coefficients in unfilled PMP are somewhat lower than those previously reported by Morisato and Pinnau11 for this polymer. While the exact reason for this discrepancy is unknown, some scatter in permeability values for high-free-volume polyacetylenes is common. For example, the oxygen permeability of PTMSP, an extremely permeable member of the same family of polymers as PMP, ranges from 2600 to 21 000 barrers at 25 °C depending on polymer processing and film preparation history.39 As illustrated in Figure 5, the permeability coefficients for H2, N2, CH4, and C2H6 in PMP and PMP/FS nanocomposites are either independent of pressure or decrease slightly with increasing ∆p. This behavior is typical for nonplasticizing penetrants in a glassy polymer16 and is consistent with the pressure dependence of permeability reported for these penetrants in PMP.11 In contrast, propane and n-butane permeability coefficients in pure PMP and FS-filled PMP (parts e and f in Figure 5, respectively) increase significantly with increasing ∆p, suggesting penetrant-induced plasticization of the matrix. The permeability coefficient of C3H8 in PMP, for instance, increases by a factor of 2.4 as the upstream propane pressure increases from 2 to 8 atm. These results are characteristic of vapor permeation in glassy polymers and are very similar to the trends previously reported for PMP.11 For the nonplasticizing penetrants other than H2, permeability coefficients decrease slightly with increasing ∆p in the 30 wt % FS sample, while permeability is independent of pressure in PMP containing 0 and 15 wt % FS. For the plasticizing vapors, the increase in propane and n-butane permeability coefficients with increasing ∆p is somewhat smaller for PMP containing 30 wt % FS than for PMP containing 0 and 15 wt % FS. While these results would be entirely consistent with FS increasing accessible free volume in PMP, it is difficult to draw definitive conclusions about this effect given the subtle behavior and experimental uncertainty. (39) Nagai, K. Maku (Membrane) 1997, 22, 206.


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Figure 5. Permeability coefficients for (a) hydrogen, (b) nitrogen, (c) methane, (d) ethane, (e) propane, and (f) n-butane in PMP and FS-filled PMP at 25 °C.

The unusual manner by which FS affects transport in PMP is illustrated in Figure 6, which presents the ratio of methane permeability coefficients in filled PMP to those in pure PMP as a function of FS content. For comparison, permeation data of Barrer et al.18 and Most40 for traditional filled polymer systems and the predictions of the Maxwell model (cf., eq 5) are included in this figure. Methane permeability in FS-filled PMP is approximately 240% higher than that in pure PMP at the highest FS concentration examined. In stark contrast, the data for the filled rubbery polymers are (40) Most, C. F. J. Appl. Polym. Sci. 1970, 14, 1019.

well described by the Maxwell model, which predicts a 35% reduction in permeability at the same filler concentration. In these traditional filled polymer systems, permeability decreases with increasing filler content, partially due to a reduction in the diffusion coefficients.7 This decrease in diffusivity occurs because flexible polymers can accommodate impermeable obstacles without introducing significant amounts of extra free volume (or void space) into the matrix, and the net effect on penetrant transport is an increase in diffusion path length.8 Clearly, this is not the dominant effect in rigid, glassy PMP, where FS addition increases accessible free volume, augments permeability, and as discussed later,

118


Figure 6. Ratio of penetrant permeability in the filled composite, P, to that in the pure polymer, Pp, as a function of filler concentration. The dashed line represents the prediction of the Maxwell model (eq 5). The data represent methane permeation at 25 °C in poly(4-methyl-2-pentyne) containing TS-530 FS (b), ethyl p-aminobenzoate permeation at 27 °C in silicone rubber containing Cabot MS-75 FS (9),40 and propane permeation at 40 °C in natural rubber containing ZnO filler (O).18

Figure 7. Relative PALS accessible free volume (b) and nitrogen permeability (0) in PMP as a function of FS content. Ordinate values are τ33I3 + τ43I4 (or N2 permeability) for the nanocomposites normalized by the corresponding value for pure PMP. PALS data were acquired at room temperature and nitrogen permeability was measured at 25 °C with a feed pressure of 4.4 atm and a permeate pressure of 1 atm.

increases diffusivity. While unusual compared to traditional filled polymers, the increased permeability of FS-filled PMP is consistent with the PALS finding that accessible free volume in the PMP/FS nanocomposites is enhanced. Figure 7 compares relative nitrogen permeability and PALS accessible free volume in PMP as a function of FS content. There is an interestingly strong qualitative agreement between the manner in which both N2 permeability and PALS free volume increase with increasing FS concentration in PMP, suggesting a close correspondence between increasing free volume, as probed by PALS, and enhanced transport properties. Previously, positive deviations from Maxwell’s equation have been observed for some zeolite-filled polymer systems. In these cases, unexpectedly high permeation rates can be attributed to the creation of defects at the polymer/filler interface that allow fast, but relatively

Merkel et al.

Figure 8. Effect of FS content on n-butane permeability and n-butane/methane selectivity of PMP (b, pure PMP; O, filled PMP containing 15, 25, 40, and 45 wt % FS). All data have been collected at 25 °C from mixed-gas experiments with an upstream pressure of 11.2 atm, a permeate pressure of 1 atm, and a feed composition of 2 mol % n-butane in methane. Data for PDMS (2) and PTMSP (9) are provided for comparison.

nonselective, Knudsen diffusion.5 In contrast, as FS is added to PMP, both n-butane permeability and nbutane/methane selectivity increase simultaneously (cf., Figure 8). The relatively large pathways associated with Knudsen diffusion favor methane transport and, if present, would reduce n-butane/methane selectivity.5 Our results indicate that nanoscale FS particles increase free volume in PMP without introducing defects large enough to prevent enhancement in vapor/gas selectivity. To compare the performance of filled PMP, data for PDMS, a commercial vapor-separation polymer, and PTMSP, the material with the most favorable vapor-selective properties known, are also included in Figure 8. As FS content increases, the permeability and vapor selectivity of PMP moves toward the desirable upper right-hand quadrant of Figure 8, approaching the performance of PTMSP and surpassing that of PDMS. Because the selectivity of PMP changes with FS addition, the permeability of different penetrants must be affected to different degrees by the presence of FS. Figure 9 presents permeability enhancement in filled PMP (i.e., the ratio of permeability in filled PMP to that in unfilled PMP) as a function of penetrant size, as characterized by the critical molar volume. For each penetrant, this ratio is greater than 1, indicating that all permeability coefficients are higher in the filled samples than in pure PMP. Most importantly, the permeability ratio increases with increasing penetrant size, indicating that the permeability of larger penetrants (i.e., n-C4H10) increases more than that of smaller gases (i.e., H2) as FS content increases. This phenomenon contributes to the observed increase in vapor/light gas (i.e., n-C4H10/CH4) selectivity with increasing FS content (cf., Figure 8). The simultaneous increase in permeability and vapor selectivity of PMP is consistent with a weakening of the size-sieving ability of the polymer; that is, the difference in diffusion coefficients between large and small molecules decreases as FS content increases. In general, size selectivity of polymers weakens (or decreases) as permeability increases, in accord with the well-known permeability/


Figure 9. Ratio of permeability coefficients in PMP containing 45 wt % FS to those in unfilled PMP at 25 °C as a function of penetrant size. Except for n-butane, all data are from puregas measurements at 4.4 atm upstream pressure and 1 atm downstream pressure. The n-butane datum point is from a mixed-gas experiment with a feed of 2 mol % n-butane in methane at 11.2 atm upstream pressure and 1 atm downstream pressure.

selectivity tradeoff relationship.41 This behavior may be rationalized from free volume considerations as follows: as the free volume in a polymer matrix available for penetrant transport increases, sorbed molecules have a greater likelihood of being in the vicinity of an accessible free volume element and making a diffusive jump. Consequently, penetrant diffusion coefficients increase with increasing polymer free volume. At the same time, as the accessible free volume increases, larger penetrants experience a greater percentage increase in diffusion coefficients than smaller penetrants.20 Thus, as the free volume of a polymer is increased, it loses its ability to discriminate between molecules based on size differences, a desirable result for enhanced vapor selectivity. The permeation data in Figures 8 and 9 are consistent with the PALS findings that incorporation of FS into PMP subtly increases system free volume, thereby increasing diffusion coefficients and weakening diffusivity selectivity, which contributes to higher permeability and vapor selectivity, respectively. Previous studies of filled polymer systems generally report that filler particles have little or no effect on the energetics of penetrant transport.7 The traditional explanation for this observation is that while filler particles typically increase the diffusion path length, they do not alter polymer chain packing or dynamics, and therefore, the energy required to make an individual diffusive jump is unchanged from that in the pure polymer.7 For our systems, transport data suggest that FS particles affect polymer chain packing, implying that activation energies might be influenced by FS content. Figure 10 presents the effect of FS concentration on activation energies of permeation, EP, for several different penetrants in PMP. Consistent with previous results for this polymer,11 penetrant permeability coefficients decrease with increasing temperature, yielding negative EP values. This result is attributed to the fact that the enthalpy of sorption, ∆HS, is exothermic and (41) Robeson, L. M. J. Membr. Sci. 1991, 62, 165.

Chem. Mater., Vol. 15, No. 1, 2003 119

Figure 10. Activation energies of permeation in PMP containing 0, 30, and 40 wt % FS as a function of penetrant critical temperature.

larger in magnitude than the activation energy of diffusion, ED, in high-free-volume PMP.42 As FS concentration is increased in PMP, penetrant activation energies of permeation decrease systematically. From eq 8, this result suggests that FS addition to PMP decreases the enthalpy of sorption, the activation energy of diffusion, or both. Penetrant sorption in a polymer may be described in two thermodynamic steps: (1) penetrant condensation from a gas-phase density to a liquidlike density and (2) mixing of condensed penetrant with polymer chains.16 Consequently, ∆HS may be expressed as the algebraic sum of an enthalpy of condensation, ∆Hcond, and an enthalpy change of mixing, ∆Hmix:16

∆HS ) ∆Hcond + ∆Hmix

(19)

Here, ∆Hmix reflects the energy change associated with breaking penetrant/penetrant and polymer chain/polymer chain interactions to form penetrant/polymer chain interactions. A significant portion of the energy required in this process is that needed to generate gaps in the polymer matrix of sufficient size and shape to accommodate penetrant molecules.16 For sorption in glassy polymers, ∆Hmix is typically small since penetrant molecules can sorb into pre-existing microvoids associated with the glassy state.43,44 Consequently, the magnitude of ∆HS is largely dictated by ∆Hcond, and since the penetrant enthalpy of condensation is unaffected by the sorbing media, it seems reasonable that the presence of FS in PMP will have little effect on ∆HS. If this is the case, the observed decrease in EP upon FS addition to PMP is most likely due to a decrease in ED. This decrease in the activation energy of diffusion for filled PMP is consistent with an opening of the polymer matrix (i.e., an increase in free volume) that facilitates penetrant diffusive jumps. Solubility. Figure 11 presents nitrogen sorption isotherms in PMP, PMP containing 30 wt % FS and (42) Freeman, B. D.; Pinnau, I. Trends Polym. Sci. 1997, 5, 167. (43) Merkel, T. C.; Bondar, V. I.; Nagai, K.; Freeman, B. D.; Yampolskii, Y. Macromolecules 1999, 32, 8427. (44) Yampolskii, Y. P.; Kaliuzhnyi, N. E.; Durgarjan, S. G. Macromolecules 1986, 19, 846.

120


Figure 11. Nitrogen sorption isotherms in PMP (b) and PMP containing 30 wt % FS (O) at 35 °C. For comparison, the following nitrogen sorption results at 35 °C from our laboratories are also included: low-free-volume, glassy polycarbonate [PC] ([), rubbery PDMS46 (0), an amorphous perfluorocopolymer comprised of 13 mol % tetrafluoroethylene and 87 mol % 2,2-bistrifluoromethyl-4,5-difluoro-1,3-dioxole (TFE/ BDD87)43 (2), and PTMSP (9).45

several other polymers43,45,46 studied in our laboratories. Consistent with the extraordinarily large amount of free volume present in PMP, nitrogen sorption levels in this polymer are very high, exceeded only by that in PTMSP, a material that has the highest light gas solubility of all known polymers.47 Interestingly, within experimental uncertainty, nitrogen sorption levels in PMP and PMP containing 30 wt % FS are equivalent. This important result indicates that, in the context of solution-diffusion transport, all of the enhancement in nitrogen permeability with increasing FS content (cf., Figure 5b) is related to augmented nitrogen diffusion coefficients. As demonstrated below, this appears to be a general result applying to penetrant transport in FSfilled PMP. Figure 12 presents methane sorption isotherms in PMP and PMP containing 15 and 30 wt % FS at 25 °C. The isotherms are slightly concave to the pressure axis, which is typical behavior for penetrant sorption in glassy polymers.16 Consistent with the nitrogen data provided in Figure 11, methane sorption data in PMP are independent of FS content, indicating that methane solubility in PMP containing varying amounts of FS is virtually identical to that in the pure polymer. This lack of a measurable difference in methane solubility for PMP and FS-filled PMP suggests three possible explanations: (1) FS sorbs the same amount of methane per unit volume as PMP; (2) FS sorbs a relatively small amount of methane but modifies polymer chain packing in a way that increases PMP sorption capacity to compensate for low sorbing FS particles; or (3) FS sorbs a relatively large amount of methane but modifies polymer chain packing in a manner that decreases PMP sorption capacity to compensate for highly sorbing FS particles. Since FS is nonporous, it can only adsorb (45) Merkel, T. C.; Bondar, V.; Nagai, K.; Freeman, B. D. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 273. (46) Merkel, T. C.; Bondar, V.; Nagai, K.; Freeman, B. D. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 415. (47) Masuda, T.; Iguchi, Y.; Tang, B.; Higashimura, T. Polymer 1988, 29, 2041.

Merkel et al.

Figure 12. Methane sorption isotherms in PMP containing 0 (b), 15 (0), and 30 (4) wt % FS at 25 °C. The concentration of gas sorbed is reported in cm3(STP) of gas per cm3 of material (i.e., PMP + FS for the nanocomposites).

Figure 13. n-Butane sorption isotherms in PMP (b), PMP containing 40 wt % FS (0), and adsorption on FS powder ([) at 25 °C. The dashed line represents the n-butane uptake in PMP containing 40 wt % FS predicted by eq 11.

molecules on its surface, in contrast to a polymer which can also absorb penetrants much like a liquid. On the basis of this fact and recognizing that methane is supercritical at the experimental temperature and would be expected to exhibit little surface adsorption,48 scenario 3 seems unlikely. Differentiating between the remaining two cases is more easily demonstrated with a higher sorbing penetrant, such as n-butane. Displayed in Figure 13 are n-butane sorption isotherms for PMP and PMP containing 40 wt % FS, as well as n-butane adsorption on pure FS powder at 25 °C. The n-butane isotherm for FS is slightly concave to the pressure axis and may be described by an adsorption model such as that given by the Brunauer-EmmettTeller (BET) equation.49 Consistent with the nonporous nature of FS, the amount of n-butane sorbed on the FS particles is substantially lower than that sorbed by PMP at any given pressure. For example, at 0.7 atm, the amount of n-butane sorbed by PMP and FS is 45 and 13 cm3(STP)/cm3, respectively. n-Butane isotherms for (48) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley & Sons: New York, 1984. (49) Brunauer, S.; Emmett, P. H.; Teller, E. J. Am. Chem. Soc. 1938, 60, 309.


Figure 14. Methane concentration-averaged diffusion coefficients as a function of penetrant concentration in the polymer film. Data for PMP containing 0, 15, and 30 wt % FS have been obtained at 25 °C, whereas PTMSP45 and TFE/BDD8743 data have been collected at 35 °C.

PMP and PMP containing 40 wt % FS are concave to the pressure axis, as is generally the case for glassy polymers.50 Similar to the light gas data (i.e., methane and nitrogen), n-butane uptake appears to be unaffected by the presence of FS, as the isotherms for PMP and PMP containing 40 wt % FS are nearly coincident. This result implies that the FS-induced increase in n-butane permeability coefficients is related entirely to enhanced diffusion. The dashed line in Figure 13 represents the predicted n-butane uptake for PMP containing 40 wt % FS based on the pure material sorption capacities and the additive solubility model expressed by eq 11. The measured uptake by PMP containing 40 wt % FS is 24% higher at 0.7 atm than that predicted by the additive model. This result indicates that the heterogeneous nanocomposite has higher sorption capacity than the sum of the sorption capacities of its constituents. As nonporous particles dispersed in PMP, FS should have, at most, its pure powder n-butane sorption capacity. In fact, it would be reasonable to expect that FS would exhibit a lower sorption capacity in PMP since a fraction of the FS particle surface should be wetted by polymer chains, thereby precluding adsorption of n-butane molecules. This scenario would result in a decrease in the expected n-butane uptake of PMP containing 40 wt % FS below that predicted by eq 11. The fact that n-butane solubility is actually higher in the nanocomposite suggests that the presence of FS alters polymer chain packing in a manner that introduces additional sorption sites into the matrix. These sites provide additional accessible free volume where penetrant sorption and transport occur. Diffusivity. From equilibrium sorption and permeation data, penetrant diffusion coefficients in PMP and FS-filled PMP have been calculated according to eq 2. Figure 14 presents methane diffusion coefficients in PMP containing 0, 15, and 30 wt % FS. For comparative purposes, methane diffusion coefficients in two other high-free-volume polymers, PTMSP45 and poly(tetrafluorethylene-co-2,2-bistrifluoromethyl-4,5-difluoro-1,3(50) Vieth, W. R.; Howell, J. M.; Hsieh, J. H. J. Membr. Sci. 1976, 1, 177.

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dioxole) (TFE/BDD87),43 are also included in this figure. Consistent with the relative permeabilities of these polymers,11,43,45 diffusion coefficients in PMP are higher than those in TFE/BDD87, but lower than those in PTMSP. As with the permeation data displayed in Figure 6, an increase in FS content promotes a systematic increase in the diffusivity of methane in PMP. For example, at low pressure (or concentration), methane diffusivities are nearly 150% higher in PMP containing 30 wt % FS than in pure PMP. This increase in diffusion coefficients is entirely consistent with an increase in the free volume of PMP at high FS content. Apparently, any decrease in diffusivity that might have been anticipated due to increased tortuosity in samples containing nonporous FS particles is more than offset by an increase in free volume that permits more facile penetrant diffusive jumps. The slight increase in diffusion coefficients with increasing methane concentration in PMP and the nanocomposites is typical behavior for a nonplasticizing penetrant in a glassy polymer.16 The effect of polymer free volume on penetrant diffusion coefficients is often modeled by the statistical mechanics description of diffusion in a liquid of hard spheres proposed by Cohen and Turnbull.51 This model provides the following expression for penetrant diffusion coefficients:

(

D ) A exp

)

- γv* Vf

(20)

where A is a pre-exponential factor that is weakly dependent on temperature, γ is an overlap factor introduced to avoid double-counting free volume elements, v* is the minimum free volume element size that can accommodate a penetrant molecule (and is closely associated with penetrant size), and Vf is the average free volume in the media accessible to penetrants for transport. This simple model provides a qualitative understanding of the influence of polymer free volume on penetrant diffusion coefficients that is consistent with experimental observations.16 According to eq 20, an increase in polymer free volume is expected to be accompanied by an increase in penetrant diffusion coefficients and a reduction in diffusivity selectivity. Figure 15 presents infinite-dilution diffusion coefficients in PMP and FS-filled PMP as a function of penetrant size, characterized by critical molar volume. According to these data, FS addition to PMP has two important effects: (1) penetrant diffusion coefficients increase systematically with increasing FS content and (2) diffusivity selectivity in PMP weakens progressively as FS concentration increases. As a result of this second effect, the diffusion coefficient of a relatively large penetrant, such as n-butane, increases more as FS concentration increases from 0 to 30 wt % than the diffusion coefficient of a smaller penetrant, such as methane. For example, as FS content increases from 0 to 30 wt %, the infinite-dilution diffusion coefficient of n-butane increases 4 times more than that of methane. This observation is consistent with the predicted effect of increasing polymer free volume on diffusion coefficients provided by the Cohen and Turnbull diffusion model and supports the conclusion that free volume (51) Cohen, M. H.; Turnbull, D. J. Chem. Phys. 1959, 31, 1164.

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Figure 15. Infinite-dilution diffusion coefficients in PMP and FS-filled PMP as a function of penetrant size at 25 °C. The H2 and C2H6 diffusion coefficients in the 15 and 30 wt % FS nanocomposites are calculated from the measured permeability coefficients in these systems and the solubility in unfilled PMP (This calculation assumes no effect of FS on hydrogen or ethane solubility coefficients in accordance with the observed behavior for methane, nitrogen, and n-butane).

increases upon FS addition to PMP. By increasing the free volume in PMP, FS nanoparticles weaken the sizesieving ability of PMP, which consequently enhances vapor selectivity. Physical Aging. High-free-volume polyacetylenes, such as PMP, exhibit substantial physical aging, which results in a decrease in transport parameters over time due to polymer densification.26,52 For instance, nitrogen permeability coefficients in PMP have been reported to decrease by 25% over a period of 29 days.52 Densification of PMP and other polyacetylenes is thought to occur, in part, due to relaxation of nonequilibrium chain conformations and the resulting collapse of large free volume elements.26 This aging phenomenon is detrimental to commercial development of membranes utilizing these polymers since stable transport properties are desirable. The notion that perhaps fine FS filler particles could function as “nanospacers” and mitigate physical aging of PMP motivated an examination of the effect of FS on permeability decline in this polymer. Figure 16 presents nitrogen permeability coefficients in PMP containing 0, 30, and 40 wt % FS as a function of aging time. These data have been collected with a constant pressure-variable volume permeation apparatus at 25 °C from films cast from the same batch of PMP and stored at ambient conditions between measurements. For all three systems, permeability decreases over time, consistent with physical aging. The rate of permeability decline is similar in PMP and the FS-filled nanocomposites, with most of the reduction in flux occurring within the first week after film casting. Beyond this time period, permeability decreases more slowly as the systems appear to approach a quasiequilibrium state. While FS addition does not arrest physical aging in PMP, it does yield materials that exhibit higher permeability than the base polymer (52) Morisato, A.; He, Z.; Pinnau, I. In Polymer Membranes for Gas and Vapor Separation: Chemistry and Materials Science; Freeman, B. D., Pinnau, I., Eds.; American Chemical Society: Washington, D.C., 1999; pp 56-67.

Merkel et al.

Figure 16. Permeability of PMP containing 0, 30, and 40 wt % FS to nitrogen as a function of film aging time. The permeability measurements have been conducted at 25 °C with an upstream pressure of 4.4 atm and downstream pressure of 1 atm. Between measurements the films were stored at ambient conditions.

throughout the aging period examined. For example, after 29 days the permeability of a PMP film to nitrogen was 220 barrers, 36% of its as-cast value. Over a similar time period, the nitrogen permeability coefficient in a PMP film containing 40 wt % FS decreased to 740 barrers, 54% of its as-cast value. Conclusions Penetrant permeability coefficients in high-freevolume, glassy PMP increase systematically with increasing concentration of nonporous, nanoscale FS, in contrast to permeation behavior in traditional filled polymer systems. The increased flux in the PMP/FS nanocomposites is caused entirely by increased penetrant diffusion coefficients, as incorporation of FS into PMP has little impact on gas and vapor solubility. The permeability of PMP to large penetrants is augmented by FS addition more than that of small gases, resulting in favorable increases in vapor selectivity for the nanocomposites. This behavior results from FS weakening the size-sieving capacity of PMP (i.e., the diffusion coefficients of large penetrants increase more than those of small gases upon FS addition). Activation energies of permeation in PMP decrease with increasing FS content, suggesting that penetrant diffusive jumps become energetically easier at higher filler concentrations. These transport results suggest that the nanometer-sized FS particles are able to disrupt packing of rigid, bulky PMP chains, thereby subtly increasing the free volume available for molecular transport. Data from PALS corroborate this effect, indicating that FS addition increases accessible free volume in PMP. Similar to other high-free-volume materials, PMP and PMP/FS nanocomposites possess a bimodal distribution of free volume elements. The larger elements increase in size with increasing FS concentration, and an excellent correlation exists between the effect of FS content on PALS accessible free volume and penetrant permeability in PMP. Transmission electron microscopy of FSfilled PMP reveals that some FS particles aggregate into clusters of up to several hundred nanometers in diameter, that the size and concentration of such aggregates


Chem. Mater., Vol. 15, No. 1, 2003 123

increase with increasing FS content, and that FS particles are relatively well dispersed in PMP.

9901788 and CTS-9803225) and the Department of Energy (DE-FG02-99ER14991).

Acknowledgment. This work has been partially supported by the National Science Foundation (DMI-

CM020672J

Sorption, Transport, and Structural Evidence for Enhanced Free

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