CH4 Separations by Sulfur-Containing PIMs via

Jun 20, 2013 - Toward Effective CO2/CH4 Separations by Sulfur-Containing PIMs via Predictive ... Grit KupganLauren J. AbbottKyle E. HartCoray M. Colin...
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Toward Effective CO2/CH4 Separations by Sulfur-Containing PIMs via Predictive Molecular Simulations Kyle E. Hart,† Lauren J. Abbott,† Neil B. McKeown,‡ and Coray M. Colina†,* †

Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡ School of Chemistry, Cardiff University, Cardiff, CF10 3AT, U.K. S Supporting Information *

ABSTRACT: Four novel sulfur-containing polymers of intrinsic microporosity (PIMs) were evaluated for use in CO2/CH4 gas separation membranes by means of predictive molecular simulations. It was found that the introduction of sulfur into the monomer backbone provides an extra, less shape-persistent site of contortion, which results in a less porous polymer framework. However, the CO2 adsorption isotherms and isosteric heats of adsorption were greatly increased in sulfonyl-functionalized PIMs. In addition, the 1:1 mixed-gas adsorption selectivity values of sulfonyl PIMs were shown to be enhanced by the highly polar functionality, which was calculated to be 23 at atmospheric pressure, and 50 for the lowest pressures reported. The mixed-gas adsorption selectivity is shown to be exponentially related to the difference between the isosteric heats of adsorption of CO2 and CH4 normalized by the total void space (Δqst/φ), which is referred to as the adsorbility. The results presented in this work should facilitate the purposeful design and screening of new intrinsically microporous polymer membranes with increased CO2/CH4 gas separation performance.

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INTRODUCTION

polymer molecular structure of a high free volume, glassy polymer. Polymers of intrinsic microporosity (PIMs) are a class of glassy polymers that create a large amount of free volume as a result of bulky, rigid, and contorted backbones.9−11 They are typically produced through the reaction of aromatic dihydroxy(e.g., catechol) and dihalogen-based monomers, and the prototypical polymer of intrinsic microporosity, PIM-1, is shown in Figure 1. The resulting polymer is a ladder-type structure with no conformational degrees of freedom, which promotes the formation of free volume through the inefficient packing of the contorted structures. A major advantage of using PIMs for gas adsorption applications is the ability of chemical functionalization of the monomer unit to maximize the adsorbent/adsorbate interactions with a specific gas. Since its inception, PIM-1 has been modified to increase the pore volume and improve the gas selectivity by many techniques including: post treatment of the nitrile group (e.g., conversion to carboxyl,12,13 tetrazole,14,15 thioamide,16 or amidoxime17), cross-linking,18−20 copolymerization,21,22 mixed-matrix membranes,23−28 and purposefully designed monomer units.29−35 A promising route for improving the gas separation properties of PIMs was explored by Guiver and co-workers where sulfur-containing PIMs were synthesized by altering the

The use of polymeric membranes as means toward effective gas separation is an active area of research due to the high demands of industrial processes to mitigate carbon dioxide from significant greenhouse gas producing sources. Polymeric membrane materials offer distinct advantages as potential candidates due to the ease of processability and potential energy savings, as discussed in a number of resources.1−6 However, a fundamental trade-off in membrane performance exists, where there is a balance between high permeability and high selectivity for any given gas pair, as illustrated by the Robeson upper-bound plot.7,8 Permeability is the flux with which any specific gas moves through the polymer membrane, and is dependent on the nature of the permeant species, and the amount of free volume within the framework. Selectivity is the separation of gas pairs, which can be achieved not only by the diffusion through the dense polymeric matrix but also by the differences in solubility of specific gases within the membrane, both of which primarily rely on the physicochemical interactions between the gas species and the polymer. For membranes to be utilized in any gas separation process, both a high permeability and selectivity are required, which results from having a higher diffusivity and solubility of one gas in a mixture. In this study, we aim at understanding and improving the gas separation performance of sulfur-containing polymeric membranes for CO2/CH4 separations by increasing the solubility of the faster gas, CO2, through changes in the © 2013 American Chemical Society

Received: February 15, 2013 Revised: June 6, 2013 Published: June 20, 2013 5371

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Figure 1. Polymers of intrinsic microporosity studied in this work. Functionalized polymers are noted as a prefix to the name parent structure (e.g., sulfur PIM is “sPIM” and sulfonyl PIM is “soPIM”).

halogenated monomer prior to polymerization to contain one36 or two37 sulfone functionalities. Each was successfully incorporated into free-standing copolymer membranes containing varying ratios of sulfonated to nonsulfonated monomers, and it was found that sulfonated membranes showed increased selectivity for O2/N2 and CO2/N2 gas pairs over PIM-1. However, a decrease in permeability was also noted and attributed to the space-filling properties of the sulfone groups. A more recent example of a sulfur-containing monomer has been reported by Guiver and co-workers,38 in which the sulfonyl PIMs are formed by polymerization of oxidized thianthrene units within the backbone of the monomer, presumably to try and limit the space filling effects of the pendant group. Good selectivity was observed, but a reduction in permeability was attributed to the increased distance between spirocenters in the polymer chain. This increase was due to the augmented length of the thianthrene monomer unit, allowing for higher packing efficiency. Examples of sulfur-containing PIMs found in the open literature are usually produced from sulfone-containing monomers, which increase the chances of cross-linking and cyclic formation during polymerization, due to the added steric effects and increased activation of the monomer. Herein, we propose creating thianthrene-containing polymers through the replacement of the catechol monomer with the thiolated equivalent, which may be subjected to a postpolymerization oxidation. For example, a sulfur analogue of PIM-1 may be produced from 5,5′,6,6′-tetrathiol-3,3,3′,3′-tetramethyl-1,1′-spirobisindane and tetrafluoroteraphthalonitrile (sPIM-1, Figure 1), from which a sulfonyl analogue may be generated by subsequent oxidation in either the powder or membrane form (soPIM-1). In this work, we show how this polymer will exhibit enhanced gas selectivity, similar to that described by Guiver and co-workers. Moreover, the presence of large side groups or extended distances between spirocenters is minimized. We also explore sulfur PIM-0 (sPIM-0), see Figure 1, which is derived from a single spirobisindane monomer difunctionalized with thiol and halogen groups such that it can undergo selfpolymerization to form a thianthrene containing ladder polymer. sPIM-0 could then be subjected to the same postpolymerization oxidation as sPIM-1 to give soPIM-0, but

it has the advantage of shorter distances between spirocenters, and so the possibility of enhanced porosity. The structures proposed here are shown in Figure 1, where the sulfur and sulfonyl functionality on the PIM-1 and PIM-0 framework are given. Recently, there has been much effort in the ordered microporous community to develop computationally efficient screening techniques that would, from the vast amount of potential adsorbent material combinations, pinpoint those with the greatest potential.39−43 The issue of having an enormous number of candidates when considering functionality combinations with different parent structures is a shared hurdle between all investigators of adsorbent materials. However for ordered nanoporous materials (i.e, covalent organic frameworks (COFs), metal organic frameworks (MOFs), or zeolites), a known crystal structure exists, which allows for the equilibrium adsorption44 or kinetic separation45 quality of that material to be determined more easily. This is not the case for amorphous polymeric material, where the simulated structure must be generated, then analyzed, for that material’s adsorbing potential to be calculated. It is a goal of this work to reduce the computationally costly adsorbing analysis by developing a model that is a function of only the porosity characteristics of the polymer framework, which correlates strongly to the separation ability of that polymer, similar to recent works on MOFs.46,47 This manuscript is presented as follows: After a description of the computational details used to simulate the sulfur and sulfonyl functionality of PIM-1 and PIM-0 is given, the structures of the sulfur-containing PIMs are characterized and analyzed. Then, the quality of both pure-gas and mixed-gas adsorption is analyzed for carbon dioxide and methane focusing on the effect of the sulfur and sulfonyl functionalities. Finally, a quantitative structure−property relationship model for sulfurcontaining PIMs for CO2/CH4 gas separation is discussed. The work presented here may be used as a means toward more efficient evaluation of the potential CO2/CH4 gas separation quality of PIMs, which should facilitate the intentional design of industrially viable polymeric membranes. 5372

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COMPUTATION DETAILS Simulation Models. The force field chosen to model the atomistic structure of the systems studied here is essential in obtaining meaningful information from the simulation. In all simulations of the polymers presented in this work, bonded interactions were modeled with the generalized Amber force field (GAFF),48 and van der Waals non-bonded interactions were modeled with a 12-6 Lennard-Jones potential (uLJ) using the transferable potential for phase equilibria (TraPPE) parameters.49−52 ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σij σij uLJ = 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ r ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠

framework of a glassy polymer, which was done, in this work, for the two sulfur PIMs and PIM-1. To make the oxidized sulfur (sulfonyl) PIMs, two oxygen atoms were bonded to every sulfur site of the sulfur PIM analogue, followed by a mapping of the partial charge distribution. After energy minimization to relax the new bonds, two low density polymer samples are made from a single polymerization, a sulfur PIM and a sulfonyl PIM, each with a unique charge distribution. This was done to most closely match the experimental technique where a sulfur PIM would be subjected to a postpolymerization oxidation to synthesize the sulfonyl PIM, while simultaneously being more computationally efficient. Since this simulated polymerization algorithm was performed at a low density, the available 21-step MD compression and relaxation scheme was applied.57,58 By this technique, the low density sample is subjected to a cascade of high external pressures and temperatures to generate a final simulation box at an experimental-like density. The compression scheme was performed in LAMMPS60 using the following parameters: Pmax = 5 × 104 bar; Pfinal = 1 bar; Tmax = 600 K; and Tfinal = 300 K. The resulting cubic simulation box length (L) is reported for each PIM in Table 1. A sample LAMMPS input script to run

(1)

In the TraPPE force field, the nonbonded interaction parameters were fit to the vapor−liquid coexistence curve for the single component systems, and have been shown to be accurate for reproducing thermodynamic, adsorptive, and diffusive properties of single components and mixtures. The cross interaction parameters between different atoms were calculated using the Lorentz−Berthelot combining rules,53 such that σij = εij =

1 (σi + σj) 2 εiεj

Table 1. Porosity Properties of the Sulfur-Containing PIMsa

(2)

polymer PIM-163 sPIM-1 sPIM-0 soPIM-1 soPIM-0

(3)

where εij is the depth of the potential between atoms i and j, with σij being the distance at which the separation between two atoms, rij, has a potential of zero. In these simulations the CH4 molecules were modeled with a single sphere, while CO2 was modeled using a 3-site Lennard-Jones potential. It has been shown that adsorption in an ideal slit pore with the more computationally efficient 1-site model of methane is similar to a 5-site model for the regime addressed in this work.54 As such, methane and carbon dioxide simulation parameters are taken from TraPPE−UA49 and −EH,55 respectively. A unique partial charge assignment to the polymer framework was calculated from the electrostatic potential (ESP) using ab initio calculations performed in Gaussian 03.56 Full details for the charge fitting calculations for PIM-1 are provided in Larsen et al.57 and similar calculations were carried out for the sulfur-containing PIMs in this work. For completeness, a summary of this procedure is provided here. In this work, the symmetric repeat unit for all cases was the conjugated backbone from spirocenter to spirocenter, and this repeat unit was capped with charge neutral methyl groups to most closely represent the electronic configuration of the polymer (these repeat units can be found in the Supporting Information). The partial charge distributions of the sulfurcontaining PIMs were then calculated, and are listed in the Supporting Information. Simulated Sample Generation. To generate a realistic polymer, the Polymatic simulated polymerization algorithm was employed,58 which is an open-source code available online.59 This technique involves the virtual “polymerization” of a periodic simulation cell of monomers, which are artificially bonded together in cycles along with molecular dynamics simulations to form long polymer chains. In this work, an initial density of 0.5 g cm−3 and a 6 Å bonding cutoff were used further details of Polymatic can be found elsewhere.58 The result is a computationally efficient route to generate an amorphous

SAgeo (m2g−1) 590 280 330 345 365

± ± ± ± ±

80 60 40 70 110

44.6 51.8 48.5 54.1 49.4

± ± ± ± ±

1.0 1.5 0.5 2.2 0.5

ρsim (g cm−3)

φ

L (Å) 0.417 0.374 0.366 0.389 0.372

± ± ± ± ±

0.010 0.009 0.004 0.014 0.016

0.93 1.01 0.92 1.13 1.03

± ± ± ± ±

0.02 0.02 0.02 0.05 0.02

a

Further details of the simulated samples are reported in the Supporting Information.

the 21-step MD compression and relaxation scheme can be found in Abbott et al.58 All MD simulations use a velocity− verlet algorithm to calculate Newton’s equations of motion with a time step of 1 fs. Nonbonded interactions were calculated with a cutoff distance of 15 Å, and long-range electrostatics were calculated with the particle-particle particle-mesh solver.61 To overcome the problem of statistical uniqueness of a simulated structure, all polymer sample sets consist of 5 independently generated polymeric configurations, from which the properties are calculated as the average and standard deviation of the sample set. To eliminate possible box size effects, all final box lengths were greater than 4 nm.62 The PIM1 model used here for comparison was the simulated sample set presented in Hart et al.63 The complete structure generation procedure used here requires no knowledge of experimental information aside from the chemical structure, and thus is a truly predictive technique to analyze these unsynthesized PIMs. Structural Characterization. Molecular simulations have the unique advantage of providing an atomistically detailed picture of the polymeric structure and pore topology.64 To capitalize on this explicit modeling of pore structure, several characterization techniques can be analyzed. The simulation densities (ρsim) are reported in Table 1, but skeletal densities (ρskel) are a more direct comparison to densities derived through common experimental methods (e.g., helium pycnometry). The simulation density, which considers total mass over total volume in the simulation box, may be converted to skeletal density by accounting for the total geometric pore volume accessible to the gas molecule (Vpore), such that 5373

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Figure 2. (a) Torsional angle distribution around the dioxin/thianthrene ring where 0° denotes planarity and (b) the backbone curling angle as defined by ∠ABC. PIM-1 (solid ▲), sPIM-1 (solid blue ■), sPIM-0 (solid red ●), soPIM-1 (dashed blue □), and soPIM-0 (dashed red ○).

Vpore 1 1 = + m ρsim ρskel

where N and U are the number of particles and the total internal energy in any given configuration, respectively, and ⟨ ⟩ represents a configurational average. While significant deviations from ideality can occur in eqs 5 and 6 at higher pressures, it has been shown that this effect is minimal over the subcritical conditions of these simulations.72 The adsorption selectivity of CO2 with CH4 in a binary mixture is defined as

(4)

where m is the total mass of the simulated sample. The geometric surface area (SAgeo) is measured by the accessible surface of a probe on the surface of the framework, i.e., that outlined by the center of the probe.65 A N2-sized probe (dN2 = 3.681 Å) was used to allow for the comparison with experimental values, which are often calculated from nitrogen adsorption isotherms. The total void volume or “porosity”, φ, is measured by using the TraPPE−UA van der Waals volume of each atom of the polymer and a probe size of 0.0 Å, which gives a measure of the total amount of void space present within the polymer. All calculations were made using PoreBlazer v. 1.2.66 Adsorption Characterization. Simulated adsorption isotherms were measured by using the grand canonical Monte Carlo (GCMC) technique,67 which holds the chemical potential, volume, and temperature constant, while allowing the number of atoms of the adsorbate to fluctuate. During the GCMC simulations, several moves are considered for the gas molecules: creation, deletion, translation, and rotation using the Metropolis scheme, which ensures chemical potential equilibrium between the bulk and adsorbed phases. Fugacities for the pure components and mixtures were calculated using the Peng−Robinson equation of state (PR EoS)68 with the binary interaction parameter of +0.092 for the CH4−CO2 mixture,69 which is valid for the low pressures reported here. A total of at least 15 million moves were attempted during each GCMC simulation with the last half being used for calculating average quantities. These simulations were performed in MCCCS Towhee.70 The total adsorption (ntot) of the simulation may be converted to excess adsorption (nex) by accounting for the total micropore volume (Vpore) of the sample by nex = ntot − Vporeρgas

⎛ x ⎞⎛ y ⎞ CO2 ⎟ CH4 ⎜ ⎟⎟ SCO2 /CH4 = ⎜⎜ ⎟⎜ y ⎝ CO2 ⎠⎝ xCH4 ⎠

where x and y correspond to the molar fraction of species in adsorbed and bulk phases, respectively. In this study, the molar fractions were set to a 1:1 ratio, where a selectivity greater than one represents a preferential adsorption of CO2.

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RESULTS AND DISCUSSION Structural Analysis. An advantage of investigating polymers of intrinsic microporosity through molecular simulations is that the atomistic detail allows for a structural analysis of the pore volume with a level of detail currently unobtainable by traditional experimental techniques. The procedure of structure generation, model characterization, and force fields used here have been shown to accurately simulate structural and adsorption properties of PIM-1 and other polymers under similar conditions, including: densities,57,58 wide-angle X-ray scattering,57,58,63,73 nitrogen,63 methane,57,58 hydrogen,74 and carbon dioxide58 adsorption isotherms, and BET-derived surface areas,63 While the sulfurcontaining PIMs studied here have no experimental evidence with which to compare, as they have not been synthesized at this point, the relatively modest functional change from PIM-1 gives confidence in the accuracy of these predictive structures. The monomeric structures proposed here were purposefully designed to give incremental and controlled changes from each other, such that the difference between polymers could be isolated to a specific structure−property relationship (i.e., PIM1 to sPIM-1 to soPIM-1). When the oxygen atoms are exchanged for sulfur atoms in PIM-1, a distinct difference in the structure on the monomeric level is imposed. While sulfur and oxygen both belong to the chalcogen group of the periodic table, sulfur is a much larger, more polarizable atom, which can expand its valence shell to hold more than eight electrons. These differences not only give rise to different shapes of the

(5)

where ρgas is the bulk density of the gas. However, as the density of the adsorbed gas is much greater than the bulk in the pressures studied here, all adsorption isotherms are reported at the absolute adsorption capacity. The isosteric heat of adsorption, which is the absolute value of the differential enthalpy of adsorption, was calculated during the GCMC simulations with the fluctuation formula71 qst = kBT −

⟨NU ⟩ − ⟨N ⟩⟨U ⟩ ⟨N 2⟩ − ⟨N ⟩⟨N ⟩

(7)

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Figure 3. An atomistic representation of one of the simulation boxes from the set of each PIM taken at the end of the 21-step compression and relaxation scheme. The average simulation box lengths, densities, and porosity characteristics are reported in Table 1. Color scheme: carbon (gray), nitrogen (blue), hydrogen (white), oxygen (red), and sulfur (yellow).

dioxin and thianthrene segments, but also allow for postpolymerization modification of the sulfur-containing PIMs. The change in the monomer backbone structural conformation when sulfur is added is shown in Figure 2a, which is a dihedral histogram describing the bend in the thianthrene unit. For PIM-1, the histogram shows how the dioxin ring exhibits a distribution around 0° (i.e., mostly planar). However, the sulfur PIMs exhibit a much different torsional distribution, where sPIM-1 and sPIM-0 have distributions around 45°. This difference is from the C−S−C equilibrium bond angle (98°) being substantially smaller than C−O−C (119°). This is a result of the loan pair of electrons of the sulfur being more stable in the s orbital, forcing the hybridized sp-bonding orbital to retain more p-bonding character.75 This, in effect, pushes the sulfur atom out of the plane of the ring to minimize the atomic stress, which has been observed in thianthrene molecule crystal structures76 and NMR solution studies.77 On the other hand, the dihedral distribution of the sulfonyl PIMs, while not planar, had a much wider range of values. This is a direct result of the Coulombic interactions of the strong SO dipoles maximizing distances between negative charges. As a result, there is more inherent stress on the sulfur torsion of the sulfonyl PIMs to prefer a planar configuration, which would minimize the Coulombic repulsions of those dipoles. Because of the torsional distribution differences, sulfurcontaining PIMs have a different monomer structural configuration than PIM-1. One example of this effect can be seen in the backbone curling angle distribution of the monomers, as shown in Figure 2b for the PIM-1 series. PIM1 is more planar than either of the sulfur-containing PIM-1 analogues, which exhibited little to no planarity along the backbone. It is interesting to note the differences in distributions of sulfur and sulfonyl PIM-1 curling from PIM1, where sPIM-1 had two distinguishable peaks, at ∼110° and ∼165°. Upon further analysis it was determined that the ∼165° angle represents an “S” monomer backbone configuration,

where the two torsional breaks along the monomer backbone at the sulfur site alternate in direction, while the ∼110° angle represents a “U” configuration. While both sulfur-containing PIM-1’s had both configurations present in the sample and there is a continuous distribution of angles, from this distribution it is clear that sPIM-1 had a greater occurrence of “U” configurations, while soPIM-1 preferred the “S” monomer backbone configuration. Examples of each of the monomeric configurations can be seen in the representative polymer segments shown in Figure 3. Again, this change in the shape of sulfur versus sulfonyl functionality is driven by the Coulombic repulsion of the strong sulfonyl dipoles along the backbone of the chain. From these analyses, it is shown that, while the monomeric configurations of each polymer show tendencies to match their equilibrium configurations (shown in the Supporting Information), there are significant deviations introduced from the packing behavior of these amorphous polymers. Polymers of intrinsic microporosity were created on the premise of including sites of contortion separated by rigid aromatic backbones, and introducing sulfur into the backbone provides an extra site of contortion, as illustrated in the simulated samples of Figure 3. As shown in Table 1, while each of the PIMs studied were in fact microporous, the pore formation ability of sulfur PIMs was diminished compared to PIM-1. The trend in porosity seems to show a decrease when functionalizing to a sulfur or sulfonyl PIM, with the sulfonyl PIMs exhibiting a slightly higher surface area. When considering the backbone dihedral and curling angle distributions of the sulfur-containing PIMs, it is clear that including sulfur into the rigid backbone of PIM-1 introduces more degrees of freedom into the polymer backbone. The sulfur site, being less shape persistent than the spirocenter, permits more freedom of movement through which packing may become more efficient, thus decreasing porosity. While sites of contortion are favorable for pore formation, the stiffness of 5375

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Figure 4. Pure-gas simulated isotherms (left) and isosteric heat of adsorption (right) for CO2 (top) and CH4 (bottom); Legend: PIM-1 (solid ▲), sPIM-1 (solid blue ■), sPIM-0 (solid red ●), soPIM-1 (dashed blue □), and soPIM-0 (dashed red ○).

that site toward prohibiting polymer flexing is essential toward increasing free volume. Therefore, there are two main structural properties of sulfurcontaining PIMs that can be inferred from this analysis. First, there is a disruption of the planar conjugated backbone of PIM1 once sulfur is added, i.e., another site of contortion. Second, there are more conformational degrees of freedom for the backbone to occupy, resulting in a systematic decrease in the pore volume of sulfur-containing PIMs. Through these relationships, it is shown that there is an intimate correlation between structural rigidity and shape persistence of the sites of contortion within the PIM and the ability to form pores. Pure-Gas Adsorption. A possible disadvantage to using linear PIMs similar to the structures shown here for gas adsorption processes is their susceptibility toward CO2 induced plasticization; however, for use in low pressure applications as shown here, this effect is negligible.4,78,79 Therefore, during all adsorption simulations, the polymer matrix was held fixed and rigid, and all of the pore volume was considered accessible to a gas molecule. Experimentally, where adsorption is a kinetic process, the polymer is expected to undergo local and reversible elastic dilations once the gas is introduced into the system,78 which would allow for most of the pore volume to be accessible by opening and closing of pores through those fluctuations. The PIM-1 simulated sample generation method and analysis techniques used here have been validated against available experimental data with respect to adsorbing capacity among other properties for PIM-1,58,63 and the pure-gas adsorption isotherms and the isosteric heats of adsorption at 20 °C for CO2 and CH4 are shown in Figure 4.

The CO2 adsorption (Figure 4a) shows that the different functionalities of PIMs had a strong effect on the adsorbing capacity. The CO2 adsorption was found to have two main regimes, as has been seen with similar adsorbents.80 The low pressure adsorption ( 0.98 for this set of PIMs. While this empirical model fit may be a function of several factors including: the gas pair, the mixture ratio, the techniques used to measure Δqst and φ, the gas feed pressure and temperature, and the class of materials of interest, it is expected that the qualitative relationship between the adsorbility and the gas pair selectivity is robust, as shown here by extension from MOFs to PIMs. The correlation between the adsorbility and the gas selectivity of PIMs has two important implications for the progress of the intentional design of adsorbent materials. First, it provides a design principle from which new structures may be constructed to exploit this relationship. PIM adsorbents should be designed from the monomeric level with functionalities that will simultaneously increase Δqst while slightly decreasing φ to achieve the highest possible selectivity, without consequently compromising the permeability of the membrane. Specifically, the isosteric heat of adsorption should be maximized for one gas in a mixture, which would result in the largest Δqst values. In addition, finding the optimum conditions for a high diffusivity and minimum porosity is desired, and will be the subject of future work. This will maintain a highly permeable and selective membrane, and potentially be an avenue to push high free volume polymeric materials above the current working limits. This was achieved, partially, in this study by incorporating less shape-persistent sulfur sites of contortion to slightly decrease porosity, while introducing the polar sulfonyl groups to increase the isosteric heat of adsorption of CO2. Finally, the adsorbility analysis may be used as a method to determine the adsorption selectivity performance of newly designed PIMs. As a means of screening a large number of potential polymer membrane functionalities, the adsorbility analysis is orders of magnitude more efficient than calculating all of the gas isotherms presented here. However, a realistic simulated polymeric structure is required, which was generated here using Polymatic. Moving forward, the understanding of the adsorbility of a polymer may be exploited, as mentioned above, for the improvement of polymeric membrane performance.

and structures, it is of great importance to develop computationally efficient screening techniques for specific applications. This initiative is being actively pursued in the biomolecular and ordered-microporous adsorption communities and similar advances are necessary in the polymer membrane field. For example, the structure−property relationships of MOFs have begun to be elucidated through a single-factor analysis. By analyzing many MOFs for CO2/H2 and CO2/N2 separations at various conditions, Wu et al.46,47 have reported a strong correlation of the equilibrium adsorption selectivity value with the difference of the isosteric heats of adsorption of the two gases to be separated (Δqst) normalized by the total void volume or “porosity” (φ), a term coined as the adsorbility. In this single factor, Δqst provides a description of the energetic preference of adsorbing one gas over the other, while φ is the fraction of the bulk volume of the polymer framework into which gas may adsorb. This single-factor analysis is important for glassy, large free volume polymers, which have high gas permeabilities, where even slight increases in the sorption selectivity may greatly increase the polymers’ separation performance. For the sulfur-containing PIMs analyzed in this work, a similar correlation is observed between the adsorbility (Δqst/φ) and low pressure selectivity, as shown in Figure 6. The isosteric

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Figure 6. Mixed-gas adsorption selectivity versus adsorbility at 1 kPa (solid) and 100 kPa (dashed) and 20 °C using a 1:1 molar ratio CO2/ CH4. PIM-1 (▲), sPIM-1 (blue ■), sPIM-0 (red ●), soPIM-1 (blue □), and soPIM-0 (red ○).

CONCLUSIONS Through the modeling of sulfur-containing PIMs we have shown that there are two fundamental characteristics that intrinsically microporous materials must possess to facilitate pore formation: (1) sites of contortion separated by rigid units and (2) the rigidity of such sites to prohibit polymer flexing. The sulfur-containing PIMs studied here did exhibit both of these characteristics, but on one hand, the sulfur contortion site promoted more efficient packing, which resulted in decreased porosity. On the other hand, through the analysis of the puregas adsorption isotherms, it was shown here that the slight decrease in porosity, as a result of the polar sulfonyl functionality, only limited the high pressure (>100 kPa) adsorption capacity, while the low pressure adsorption was enhanced. The sulfonyl functionality was shown to increase the enthalpy of adsorption of CO2 without affecting the CH4 adsorption, which in turn greatly increased the 1:1 CO2/CH4 mixed-gas selectivity, with sulfonyl PIM-1 reaching as high as 50 at 1 kPa and 20 °C. Finally, the selectivity data presented here was subjected to the adsorbility analysis, which was extended from previous MOF calculations.47 It was found that the same exponential relationship between the heats of adsorption difference of the

heat of adsorption and porosity are two intimately related characteristics of a polymer membrane, such that a lower φ will increase the amount of interactions of the adsorbent and the pore wall, resulting in a higher Δqst. On the other hand, Δqst may be increased without subsequently decreasing φ by functionalizing the pore wall of the polymer framework with CO2-philic groups with strong polarities. The polar groups on the polymer framework interact with the quadrupole of CO2, facilitating higher qst, as shown for the sulfonyl PIMs in the previous section. However, a key property to study is how the balance of these two factors affects the mixed-gas selectivity of adsorbents. After plotting the selectivity versus the adsorbility of all the sulfur-containing PIMs (Figure 6b), a best fit empirical model was constructed using the form SCO2 /CH4

⎛ Δqst ⎞ B = A⎜ ⎟ + 1.0 ⎝ φ ⎠

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competitively adsorbing gases normalized by the porosity present in the adsorbent and the selectivity under those conditions holds true. This correlative model predicts that for any highly permeable adsorbent, the sorption selectivity may be drastically increased by simultaneously increasing the adsorption interaction with one gas, while slightly decreasing the porosity, through which the sorption selectivity is maximized. Hopefully, this work will facilitate the design of functionalized monomer units to improve the applicability of high free volume polymer membranes for gas separation applications.

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ASSOCIATED CONTENT

S Supporting Information *

Additional structural information and simulation details of the force field parameters for all polymers. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*(C.M.C.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Rupert G. D. Taylor for discussions. In addition, we thank the National Science Foundation (DMR0908781) and EPSRC (EP/G065144/1) for funding. Computational resources were supported in part by the Materials Simulation Center of the Materials Research Institute, the Research Computing and Cyberinfrastructure unit of Information Technology Services. The Penn State Center for Nanoscale Science was supported in part through instrumentation funded by the National Science Foundation (OCI0821527).

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