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Macromolecules 2011, 44, 14–16 DOI: 10.1021/ma1024945
Structural Characterization of a Polymer of Intrinsic Microporosity: X-ray Scattering with Interpretation Enhanced by Molecular Dynamics Simulations Amanda G. McDermott,† Gregory S. Larsen,† Peter M. Budd,‡ Coray M. Colina,† and James Runt*,† †
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States, and ‡School of Chemistry, The University of Manchester, Manchester M13 9PL, U.K. Received November 2, 2010 Revised Manuscript Received December 6, 2010 Materials containing networks of pores smaller than 2 nm in diameter, termed microporous by IUPAC convention,1 are of interest for applications including gas storage and separations, adsorption, and catalysis. Rather than relying on templating or cross-linking to induce microporosity, polymers of intrinsic microporosity (PIMs) feature porosity derived from inefficient packing due to a combination of rigid segments and sites of contortion within the macromolecular backbone.2 PIM-1, a polybenzodioxane with a ladder-type structure (see Figure 1), is the most extensively characterized PIM with a Brunauer-Emmett-Teller (BET) surface area of 720-780 m2/g and pores 5.2-10.7 A˚ in size.2-4 The variability in measurements of these key properties is due to the influence of sample processing (thermal history and methanol or gas exposure3) as well as assumptions necessary to interpret data from various characterization techniques. In this paper, we present the first broad scattering vector (q) range X-ray scattering data for PIM-1. We also compare wideangle X-ray scattering (WAXS) patterns with structure factors calculated from molecular dynamics (MD) simulations. In addition to providing a useful validation of PIM simulations, this greatly enhances our understanding of PIM scattering features, building on previous interpretations of WAXS patterns from microporous polymers.5-8 PIM-1 was synthesized as described previously,9 and 100 μm thick films were cast from chloroform solution under ambient conditions. Powder samples were precipitated by adding a solution of PIM-1 (in tetrahydrofuran) to methanol. Prior to scattering measurements, all samples were degassed in a vacuum oven at 120-130 C for at least 24 h. WAXS patterns were collected using a Rigaku DMAXRAPID instrument with an image-plate detector. Small-angle X-ray scattering (SAXS) patterns were collected using a Molecular Metrology instrument with a pinhole camera, multiwire area detector, and sample-to-detector distances of 1.5 and 0.5 m. Both WAXS and SAXS instruments used Cu KR radiation (λ = 1.54 A˚) and yielded isotropic two-dimensional patterns, which were azimuthally averaged into one-dimensional profiles of intensity I(q) vs scattering vector q = 4π(sin θ)/λ. Ultrasmall-angle X-ray scattering (USAXS) patterns were collected with a Bonse-Hart camera using an incident energy of 12 keV (λ=1 A˚) at beamline 32-ID10 of the Advanced Photon Source; these have been desmeared. Backgrounds were subtracted from all scattering patterns. To model PIM-1, chains were grown at a low density to a target length of 10 repeat units and then compressed to a 45-A˚ box with *Corresponding author. E-mail:
[email protected]. pubs.acs.org/Macromolecules
Published on Web 12/09/2010
Figure 1. Chemical structure and representative single-chain conformation of PIM-1.
a realistic density using LAMMPS11 with bonded parameters from GAFF,12 nonbonded parameters from TraPPE,13 and charges from ab initio calculations with Gaussian 0314 and RESP.15 These molecular dynamics simulations are described in detail elsewhere.16 The structure factor S(q) was computed using ISAACS software17 from 10 snapshots acquired during a 500 ps NVT run following compression. The low-q limit of S(q) is defined by the box size: 2π/[(45 A˚)/2] = 0.28 A˚-1. Because a united-atom model was used, S(q) does not include contributions from hydrogen atoms; however, hydrogen is present at a low mole fraction and scatters X-rays much more weakly than heavier elements. The total structure factor for an isotropic system is computed from a Fourier transform of the sum of partial radial distribution functions gAB(r) weighted by atomic X-ray scattering lengths bi and mole fractions ci:17-19 Z SðqÞ ¼ 1 þ 4πr
¥ 0
2
0 1 3 X 1 sin qr 2 4 @ cA bA cB bB gAB ðrÞA- 15 r dr Æb2 æ A, B qr ð1Þ
where gAB(r) represents the probability of finding an atom of species B at a distance r from an atom of species A, normalized to 1 at large distances, and Æb2 æ ¼ ð
X
ci bi Þ2
i
with the index i spanning the atom types present in the simulated structure. We also define partial structure factors SAB(q), similar to the Faber-Ziman definition but scaled by mole fractions and scattering lengths: Z cA bA cB bB 1 þ 4πr SAB ðqÞ ¼ Æb2 æ
sin qr 2 r dr ð2Þ ½gAB ðrÞ - 1 qr 0 ¥
so that SðqÞ ¼
X
SAB ðqÞ
A, B
Low-q intensity is proportional to q-3 over several decades (Figure 2), which is consistent with the limiting case of either a dense mass fractal (D = 3) or a rough, space-filling surface fractal r 2010 American Chemical Society
Communication
Figure 2. Broad q range X-ray scattering data for a PIM-1 film. SAXS (0) and WAXS (;) patterns were scaled so that overlapping q ranges match USAXS data (O), which was desmeared and calibrated on an absolute-intensity scale. For clarity, only every 8th SAXS data point is shown.
(Ds = 3).18 If the spatial distribution of voids (pores) in PIMs at these large length scales is fractal, this must be induced by the same unusual chain statistics that give rise to the large concentration of interconnected free volume; chain statistics in PIMs have yet to be directly investigated. The low-q power law, flat SAXS intensity, and shoulder in the WAXS region are also seen in amorphous, nanoporous activated carbons.20 Although the shoulder or knee feature from 10-1 to 2 A˚-1 should contain information about the pore size distribution, developing a model such as a modified Guinier function to extract this information is complicated by the superimposition of several broad peaks and the presence of a high concentration of pores of poorly defined geometry. Features in WAXS patterns from amorphous polymers are typically limited to one or two amorphous halos, representing distances of closest approach between segments of different chains. Unlike materials with larger, patterned pores, PIMs have no “bulk” phase, only interconnected unoccupied volume. Pore dimensions in PIMs are therefore defined by intersegmental distances. Figure 3 shows that high-resolution WAXS patterns include characteristic peaks at q = 0.89, 1.25, and 1.63 A˚-1. Because these peaks are superimposed on a smooth shoulder not found in nonporous polymers, it is not immediately clear that they should be interpreted as amorphous halos representing intersegmental distances. Weaker features above 2 A˚-1 are related to correlations on the scale of bond lengths; the exaggeration of these features in the calculated S(q) could arise in part from the approximation of atomic scattering lengths as q-independent.17 WAXS patterns from PIMs typically include several broad peaks. Ritter et al. have observed that for polyimide-based PIMs both the degree of microporosity and the relative intensities of amorphous halos, but not their q values, are sensitive to processing conditions.6 Our data (Figure 3) also indicate that for PIM-1 the 1.25 and 1.63 A˚-1 peaks are of higher relative intensity in powders than in films. Methanol treatment significantly increases the permeability of a film, and thermogravimetric measurements suggest that this is due to the removal of adsorbed species that persist after degassing.4 Soaking a film in methanol prior to degassing does not affect the relative peak intensities, but it does increase the low-q intensity of the shoulder. A reduction in the intensity of the scattering shoulder when some pores are occupied is consistent with the idea that scattering in this q range and at smaller q contains information about pore sizes.
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Figure 3. Simulated structure factor S(q) (;) compared to experimental WAXS intensity of PIM-1 samples with three different processing histories: a precipitated powder (O), a solution-cast film (0), and an identical film that was also treated with methanol (Δ). For clarity, only every 50th experimental data point is indicated with a symbol.
S(q) from the simulated sample, which certainly includes no adsorbed species, reproduces the low-q shoulder intensity of a methanol-treated sample and the relative peak intensities of solution-cast films, expected to be closer to equilibrium than precipitated powders. The reproduction of processing-independent WAXS features from the simulated structure indicates that the force-field parameters and structure generation used accurately reproduce intersegmental interactions, crucial in PIMs due to the equivalence of porosity, free volume, and intersegmental distances. Comparing simulated S(q) to a methanol-treated PIM-1 film, there is some excess intensity at the lowest q; this is likely a boxsize effect, an inherent limitation related to periodic boundary conditions. There is also a small, seemingly superfluous peak in S(q) near 0.52 A˚-1. Examining the partial structure factors (Figure 4 and Supporting Information) reveals that there are many positive and negative contributions to this portion of the scattering pattern, which in PIM-1 nearly cancel. When the chemical structure of PIM-1 is modified to include larger spirocenter substituents;one or two phenyl groups instead of two methyl groups21;an additional peak appears here in experimental scattering patterns (unpublished data). It is reasonable to conclude that this simulated structure does not precisely reproduce the history of these experimental samples, but examining partial structure factors can still clarify the meaning of processing-independent scattering features. Figure 4 shows the contribution to the total S(q) from several partial structure factors. SR-R(q) is defined as the sum of all SAB(q) (eq 2) such that A and B are atoms located in rigid segments; SS-S(q) includes contributions from atoms in spirocenters, and SR-S(q) includes cross-terms. Note that S(q) = SR-R(q) þ SR-S(q) þ SS-S(q). Simulations included 10 atom types, and partial structure factors for all pairs are shown in the Supporting Information. The rigid segments overwhelmingly define the shape of the shoulder, a feature that is not present in nonporous polymers and which we conclude contains information about pore sizes. In contrast, spirocenters contribute mainly to the broad peaks superimposed on the shoulder. The lowest-q peak at 0.52 A˚-1 contains contributions from both rigid segments and spirocenters; it represents the correlation between adjacent spirocenters
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Supporting Information Available: Partial structure factors for all 10 atom types in the simulation. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes
Figure 4. Contributions to the total simulated structure factor S(q) (;) from atoms in rigid segments SR-R(q) (O), atoms in spirocenters SS-S(q) (0), and correlations between atoms in the two groups SR-S(q) (-). For clarity, very few data points are indicated with symbols.
along a single chain ∼15 A˚ apart. Notably, neither of the two strongest experimental features (0.89 and 1.25 A˚-1) is an integer multiple of 0.52 A˚-1, suggesting that these represent distances between spirocenters or segments either on different chains or on the same chain, farther apart than the persistence length. Comparing experimental and simulated scattering patterns serves not only to validate the model structure arising from interchain interactions in simulations but also to guide interpretation of experimentally observed scattering features. While correlations between nearest-neighbor segments in nonporous amorphous polymers give rise to one or two amorphous halos against a relatively flat WAXS background, intersegmental distances in PIMs instead contribute to a scattering shoulder, underscoring the fundamental difference in the organization of free volume in these highly permeable polymers. The broad peaks observed superimposed on this shoulder represent characteristic distances between segments or sites of contortion on different chains. Further study will focus on the development of a model to extract pore size distributions from PIM scattering patterns. Acknowledgment. The authors acknowledge the support of the Materials World Network via the National Science Foundation, Division of Materials Research, Award 0908781. Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract DE-AC02-06CH11357; USAXS data were collected at beamline 32-ID by Dr. Jan Ilavsky. We thank Dr. Carin Tattershall, Dr. James Selbie, and Nhamo Chaukura (University of Manchester) for providing samples. A. G. McDermott is supported by a National Science Foundation Graduate Research Fellowship.
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