Ionomers of Intrinsic Microporosity: In Silico Development of Ionic

Oct 1, 2014 - This work presents the predictive molecular simulations of a functionalized polymer of intrinsic microporosity (PIM) with an ionic backb...
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Ionomers of Intrinsic Microporosity: In Silico Development of IonicFunctionalized Gas-Separation Membranes Kyle E. Hart and Coray M. Colina* Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *

ABSTRACT: This work presents the predictive molecular simulations of a functionalized polymer of intrinsic microporosity (PIM) with an ionic backbone (carboxylate) and extra-framework counterions (Na+) for CO2 gas storage and separation applications. The CO2-philic carboxylate-functionalized polymers are predicted to contain similar degrees of free volume to PIM-1, with Brunauer− Emmett−Teller (BET) surface areas from 510 to 890 m2/g, depending on concentration of ionic groups from 100% to 17%. As a result of ionic groups enhancing the CO2 enthalpy of adsorption (to 42−50 kJ/mol), the uptake of the proposed polymers at 293 K exceeded 1.7 mmol/g at 10 kPa and 3.3 mmol/g at 100 kPa for the polymers containing 100% and 50% ionic functional groups, respectively. In addition, CO2/CH4 and CO2/N2 mixed-gas separation performance was evaluated under several industrially relevant conditions, where the IonomIMs are shown to increase both the working capacity and selection performance in certain pressure swing applications (e.g., natural gas separations). These simulations reveal that intrinsically microporous ionomers show great potential as the future of energy-efficient gas-separation polymeric materials.

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through unsaturated metal sites5 or with an anionic framework containing impregnated metal ions.6,7 Molecular simulations of ion-containing MOFs combined with charge-balancing extraframework ions exhibited outstanding adsorption selectivity for CO2/H2 (1800), CO2/CH4 (80), and CO2/N2 (500), with projected CO2 enthalpy of adsorption of 58 kJ/mol.8 However, zeolites and MOFs have yet to meet the criteria necessary for industrial use in CO2 capture technologies (e.g., requiring high regeneration temperatures, lack of stability, etc.).9 Alternatively, organic microporous materials are a class of gas adsorption materials that exhibit high physicochemical stability as a result of a composition of lightweight, covalently bound framework structures,10 and several examples of ionic-functionalized microporous organic materials have recently been synthesized.11,12 A sulfonic acid-containing porous polymer network (PPN), PPN-6-SO3H, was neutralized with Li+ to produce PPN-6-SO3Li,13 which exhibited CO2 adsorption of 3.7 mmol/g at 100 kPa and 295 K, with CO2/N2 adsorption selectivity of 414. An amorphous carbon material with high Ndoping and extra-framework K+ ions (8.6 wt %) was synthesized and exhibited adsorption uptake at 298 K of 1.62 and 4.04 mmol/g at 10 and 100 kPa, respectively. The addition of K+ ions improved the CO2 enthalpy of adsorption from 27 to 59 kJ/mol and exhibited a CO2/N2 adsorption selectivity of 48

INTRODUCTION Significant research efforts have been devoted toward designing a microporous material that would have a maximized solubility for CO2 and minimized solubility for all other species (e.g., N2, CH4, or H2), which would increase the energy efficiency of several industrial separation processes.1 Due to the quadrupolar nature of CO2, this may be accomplished by addition of polar groups in the polymer matrix, thus facilitating high adsorption at lower pressures or concentrations. For example, it was shown for microporous polymer networks that the chemical composition of the framework dictates CO2 uptake, where the enthalpy of adsorption was greatly enhanced with polar acidic functionalities.2 To fully exploit the polymer−CO2 electrostatic interactions, the polar acidic functionalities can be metalized, which creates an exposed ionic functional group with extra-framework metal ions. Physisorbent materials with ionic moieties have exhibited excellent CO2 adsorption and separation performance, which so far have been focused on networked microporous materials. The CO2 adsorption and separation performance of cationexchanged zeolites has been well studied,3 where the negative charge resulting from a substitution of SiO4 tetrahedra by AlO4− is compensated by extra-framework alkali or alkaline earth metal ions. For example, recent experimental works have synthesized zeolite NaKA (10 at. % K+) that exhibited CO2/N2 adsorption selectivity greater than 1100 with CO2 uptake of 4 mmol/g at 100 kPa and 298 K.4 Similarly, metal organic frameworks (MOFs) can exploit electrostatic interactions © 2014 American Chemical Society

Received: July 9, 2014 Revised: September 15, 2014 Published: October 1, 2014 12039

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at 10 kPa.14 A carboxyl-functionalized porous aromatic framework (PAF-26-COOH) was highly metalized (85%) with Li+, Na+, K+, or Mg2+. Depending on the impregnated metal, the ion-functionalized PAFs exhibited CO2 enthalpy of adsorption of 31−35 kJ/mol and adsorption selectivity values of 24−73 for CO2/N2 and 5−9 for CO2/CH4.15,16 To summarize, introduction of ionic functionalities has been shown to improve CO2 storage capacity and adsorption selectivity over N2 and CH4 for a wide variety of microporous materials. Moving forward, it will be advantageous to design a microporous material that retains its solution processability, and thus we aim to extend this functionalization to microporous linear polymers (i.e., non-networked microporous polymers). Polymeric materials with ionic functional groups (e.g., carboxylate or sulfate groups) covalently attached to the backbone are referred to as ionomers;17 however, traditional ionomers are not microporous due to the presence of a flexible backbone. On the other hand, polymers with rigid and contorted backbone units that prohibit rotational motion along the backbone, known as polymers of intrinsic microporosity (PIMs),18 retain the ability to be functionalized with polar acidic groups while exhibiting significant amounts of pore volume due to inefficiently packed chains. PIMs with metal ions incorporated into the framework have been synthesized, but these materials were chemically cross-linked into an insoluble networked structure.19,20 For example, metalloporphyrin units can be incorporated into PIMs, which produced a networked polymer containing bound metal ions (e.g., Co2+ and Fe2+) with relatively high surface areas (500−1000 m2/g)21 and large gas uptake capacity, although only H2 isotherms were reported.22 In addition, a linear PIM, PIM-7, was combined with bis(benzonitrile)palladium(II) dichloride to create a crosslinked PIM-7/Pd2+ networked polymer with a Brunauer− Emmett−Teller (BET) surface area of 650 m2/g, where the phenazine unit was a ligand for the coordination of metal ions.23 However, creating a non-networked polymeric material with extra-framework metal ions that has the potential to exhibit favorable gas storage and separation properties has proven a challenging endeavor. As a result, predictive molecular simulations have the distinct advantage of systematically analyzing candidate materials, and they will be used in this work as a means toward exploring ionic-functionalized PIMs. Here we present results for a high free volume linear polymer with an ionic functionality, which exploits the electrostatic interactions between the framework and CO2 with the objective of maximizing gas physisorption and mixed-gas separation performance. Carboxylate-functionalized PIMs neutralized with extra-framework cations were originally proposed by McKeown et al.,24 but to our knowledge they have yet to be explored experimentally. The ionic-functionalized polymers of intrinsic microporosity represent a unique class of the next generation of gas-separation polymers, which are referred to as ionomers of intrinsic microporosity, or IonomIMs. A representative IonomIM studied in this work is shown in Figure 1c, which was analyzed by means of predictive molecular simulations. A sodium cation was chosen as a representative extra-framework cation in this work, as divalent cations may lead to extensive cross-linking, creating an insoluble polymer.23 Here, we show that IonomIMs are a viable extension of PIMs that greatly improve upon the gas-separation performance under several industrially relevant conditions, specifically high CO2 loading capacity and selective CO2/CH4 and CO2/N2 gas separations.

In addition, the improved gas-separation ability of IonomIMs is compared with leading MOF and zeolite materials, illustrating specific applications where these polymers exhibit superior performance. Finally, the design principles developed here will allow for further synthetic development of this novel class of highly effective adsorbent polymeric material.

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SIMULATION DETAILS

Molecular Models. There are three monomers used in the simulations presented here: PIM-1 (Figure 1a), carboxyPIM-1 (Figure

Figure 1. Chemical structures of (a) PIM-1, (b) carboxyPIM-1, and (c) ionomer of intrinsic microporosity, IonomIM-1.24 (d) Random copolymers of IonomIM-1 and PIM-1 are referred to as “co-IonomIM1 (x),” where x is the mole fraction of IonomIM-1 units in the copolymer. 1b), and IonomIM-1 (Figure 1c). In addition to the polymers constructed out of 100% of each monomer, a random copolymer was simulated: co-IonomIM-1 (x) (Figure 1d), which was designed to represent polymeric samples that are not completely hydrolyzed.25 For the copolymer, x denotes the mole fraction of IonomIM-1 content, while the PIM-1 concentration is equal to 1 − x. For example, coIonomIM-1 (20%) contains 20% IonomIM-1 units and 80% PIM-1 units. Four copolymers were simulated, which varied the content of IonomIM-1: 50%, 33%, 20%, and 17%. The force fields used in this work are a combination of generic and transferable force fields. For the bonded interactions of the polymer framework, the generalized Amber force field (GAFF)26 was used. The nonbonded interactions of the polymer were modeled using the united atom transferable potential for phase equilbria (TraPPE-UA),27 which utilizes a Lennard-Jones 12-6 potential. For the Na+ ion, the Dreiding 12040

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force field parameters were used28 with a +1 atomic charge, as this represented a conservative adsorption capacity compared with several generic force fields (shown in Supporting Information) and has been shown to accurately produce experimental adsorption isotherms for simulations of MOFs.29 To calculate the atomic partial charge distribution, the carboxyPIM-1 and IonomIM-1 chemical repeat units were subjected to ab initio calculations at the HF/6-31G* level of theory, followed by a restrained electrostatic potential (RESP)30,31 charge fitting procedure. For the purpose of the partial charge calculation, a symmetric repeat unit of the PIM was defined as spirocenter to spirocenter. For the IonomIM-1 unit, the extraframework Na+ ions were omitted from the charge fitting calculations, and the net charge of the monomer was set at −1. Large-scale atomic/ molecular massively parallel simulator (LAMMPS) data files for the monomers of the PIMs simulated in this study are available for download,32 which includes all force field information. The molecular models of the gases simulated in this study, CO2, CH4, and N2, were represented with the TraPPE force field.33,34 The cross interaction parameters between different atoms were calculated by use of the Lorentz−Berthelot combining rules. Structure Generation. There are two distinct steps in the structure generation of an amorphous linear polymer: (1) artificially polymerizing a periodic box of monomers at low density and (2) compressing and relaxing the polymerized sample. The open-source simulated polymerization algorithm Polymatic35,36 was used for virtual synthesis of the polymers. Initially, a low density (ρ0 = 0.2−0.4 g/cm3) periodic box is randomly packed with 150 chemical repeat units. For the random copolymers, the corresponding ratio of the monomer composition was packed randomly into the box, keeping the 150 monomer total. For example, in the co-IonomIM-1 (20%) structure, the initial box was packed with 30 chemical units of IonomIM-1 and 120 chemical units of PIM-1 randomly, and the polymerization was allowed to proceed without bias (i.e., generating a random copolymer). After the initial box of monomers is packed, Polymatic then subjects the monomers to successive steps of artificial bonding. In addition to orientational bonding criteria and additional charges on bonding-capable chain ends (qpolym = ±0.5e), a bonding length cutoff of 7 Å was used. The virtual polymerization was finished after a search for 500 ps for acceptable bonds. In order to avoid hindering the artificial polymerization, the Na+ charge was removed, and the Lennard-Jones potential of all atoms was cut and shifted at 5 Å. More information on the implementation and used of Polymatic can be found in ref 36. Next, the polymerized sample was compressed and relaxed through a molecular dynamics procedure to create an equilibrated final density. For this, a 21-step molecular dynamics compression and relaxation scheme was used.36,37 This scheme uses successively higher external temperatures (Tmax = 1000 K) and pressures (Pmax = 5 × 104 bar) followed by a stepwise decompression to generate a simulated sample at the conditions of interest (Tfinal = 300 K, Pfinal = 1 bar). All molecular dynamics simulations were run on the LAMMPS38 software by use of a velocity-Verlet algorithm with a time step of 1 fs. For nonbonded interactions, a cutoff distance of 15 Å was used, with the long-range electrostatics calculated with the particle−particle particle− mesh solver. A sample LAMMPS input script of this procedure is available in the Supporting Information of ref 36. In all cases, five independently generated samples were used to calculate the average and standard deviation of the characteristics of interest for each polymer. Model Characterization. To evaluate the resulting simulated polymeric samples as viable gas-separation materials, porosity calculations and pure- and mixed-gas adsorption simulations were performed. To determine the amount of porosity, the surface area according to BET theory39 applied to N2 adsorption isotherm at 77 K (SABET), the simulation density (ρsim), and the fractional free volume (f) were calculated. The procedure for applying BET theory to the average simulated adsorption isotherm of PIMs is described in detail in ref 40. The simulation density is the total mass of the polymeric sample over the volume of the sample box including all pore volume. The fractional free volume is calculated as the difference between the

specific volume (Vsp) and the volume occupied by the polymer molecules (VW):

f = Vsp − 1.3VW

(1)

including a factor of 1.3 based on the packing density of a molecular crystal at 0 K. VW is geometrically calculated from the van der Waals volume of each atom in the sample. All geometric calculations of surface area and free volume used the Pore Blazer41 software, with example input scripts included in ref 42. The pure- and mixed-gas grand canonical Monte Carlo (GCMC) adsorption simulations were calculated by use of Towhee software43 at 20 °C, with the input chemical potentials being calculated from the Peng−Robinson equation of state.44 The polymer model was held rigid during the adsorption simulations. The number of MC moves was 3 × 107, with the last half being used to calculated equilibrium values. The trial moves allowed during the GCMC simulations were addition of gas molecules, deletion of gas molecules, and translation of gas molecules or Na+ ions. The adsorption simulations are reported by an absolute adsorption capacity and enthalpy of adsorption, with the enthalpy of adsorption calculated during the GCMC simulations via the fluctuation formula:45

qst = kBT −

⟨NU ⟩ − ⟨N ⟩⟨U ⟩ ⟨N 2⟩ − ⟨N ⟩⟨N ⟩

(2)

where kB is the Boltzmann constant and N and U are the number of particles and total internal energy in any configuration, respectively.

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RESULTS AND DISCUSSION In this study, we show the implications on gas adsorption and separation of including an anionic functionality onto the backbone of a porous ladder polymer, PIM-1. The ability of the microporous ionomer to create surface area is discussed, followed by the CO2 adsorption capacity. To provide a structural description of the interactions between covalently bound ionic group, extra-framework cation, and adsorbed CO2, radial distribution functions are then presented and discussed. Additionally, the results of screening the ion-containing PIMs for CO2 permeability and CO2/CH4 and CO2/N2 ideal permeation selectivity are provided. Finally, the mixed-gas separation performance of the IonomIMs in four industrial study cases are presented and their performance is compared to several leading microporous materials, which highlights specific areas in which ionic-functionalized PIMs exhibits favorable gas adsorption and separation potential. Porosity. Significant insight into the relative performance of gas adsorption and separation materials can be gained from quantification of the microporosity within the framework. Three common measurements are shown in Table 1: surface area derived by use of BET theory (SABET), simulation density (ρsim), and fractional free volume ( f). In addition, a representative simulation box of the ionic-functionalized PIMs Table 1. Porosity Properties of IonomIMs and Other Simulated PIMs polymer 40

PIM-1 soPIM-147 carboxyPIM-1 IonomIM-1 co-IonomIM-1 co-IonomIM-1 co-IonomIM-1 co-IonomIM-1 12041

(50%) (33%) (20%) (17%)

SABET (m2/g)

ρsim (g/cm3)

f (%)

830 574 652 513 743 848 861 890

0.933 (0.017) 1.150 (0.027) 1.018 (0.011) 1.117 (0.030) 0.993(0.023) 0.948 (0.029) 0.936 (0.032) 0.920 (0.020)

24.3 (1.3) 20.6 (1.9) 20.8 (0.8) 17.3(2.1) 23.2 (1.8) 25.5 (2.2) 25.5 (2.4) 26.6 (1.6)

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is shown in Figure 2, which illustrates the amorphous, microporous structure of the void space within the IonomIM.

Figure 3. CO2 adsorption isotherms of IonomIM-1 (red squares), coIonomIM-1 (50%) (green diamonds), co-IonomIM-1 (17%) (purple inverted triangles), and carboxyPIM-1 (gray circles, dashed line) simulated in this work as a function of pressure at 20 °C, compared with PIM-147 (black circles, solid line). Error bars represent the standard deviation of five samples, and all simulated isotherms are provided in Supporting Information.

Figure 2. Example model of an ionic-functionalized PIM used in this study: simulation box of co-IonomIM (20%) sample set after GCMC CO2 adsorption simulation at 20 °C and 100 kPa, which shows polymer structure (yellow), Na+ ions (blue), and adsorbed CO2 (red). The simulation box length is 50 Å and it contains 5310 polymer beads, 60 Na+ ions, and 215 CO2 gas molecules.

adsorption capacity when compared to PIM-1. CarboxyPIM-1 exhibited only marginal improvements on low-pressure CO2 uptake upon PIM-1, and the polar sulfonyl-functionalized PIM1 (soPIM-1),47 shown in Supporting Information, outperformed only the lowest percentage ionic-functionalized polymer, co-IonomIM-1 (17%). Thus, IonomIM-1 copolymers are shown here to be promising potential adsorption materials with high CO2 uptake. Below atmospheric pressure, CO2 loading of the IonomIMs correlates with ionic group content, where IonomIM-1 exhibited exceptionally strong adsorption. At 10 kPa, the partial pressure of CO2 in some gaseous mixtures, IonomIM-1 exhibited a 230% increase in uptake versus PIM-1 at 1.7 mmol/g (∼7.4 wt %), which was similar to ionic Ndoped microporous carbon14 and exceeded conventional monoethanolamine (MEA) solution scrubbing CO2 capacity of 5.5 wt %.48 Upon increasing pressure, up to 250 kPa, the low relative microporosity of IonomIM-1 limited the adsorption capacity as the polymer sample was nearing saturation. In this regime, the co-IonomIM-1 copolymers, which had lower ion content but higher degrees of free volume, exhibited the highest CO2 loading. At 100 kPa, co-IonomIM-1 (50%) exhibited a 40% increase in CO2 adsorption capacity over PIM-1 at 3.3 mmol/g, and as such, the introduction of an ionic functionality improved the CO2 adsorption performance of PIM-1 at both low- and ambient-pressure conditions. Enthalpy of adsorption (qst), shown in Figure 4, also correlated directly with ionic group concentration, where IonomIM-1 and copolymers containing 50%, 33%, 20%, and 17% ionic content exhibited enthalpies of adsorption at zero loading of 49.8, 46.0, 45.6, 42.8, and 41.7 kJ/mol, respectively. These values represent a significant enhancement over PIM-1, 29.5 kJ/mol, and outperform experimental values for Li+-PPN (35.7 kJ/mol)13 and Na+-PAF (35.0 kJ/mol)16 materials. The enthalpy of adsorption for IonomIM-1, 49.8 kJ/mol, is comparable to the values obtained for cation-exchanged zeolites such as NaY (49 kJ/mol).49 Thus, the ionic functionality was

As the nitrile functionality on PIM-1 is hydrolyzed to carboxyPIM-1, the amount of microporosity within the framework decreases as a result of the increased polymer framework interactions, which agrees with experimental observation.46 When the carboxylic acid functionality is then subjected to ionomerization to produce the sodium salt, IonomIM-1, the strong polymer−polymer Coulombic interactions cause a further collapse of the microporosity, resulting in a sample with 513 m2/g surface area and only 17% fractional free volume. As the percentage of ionic groups is decreased, the ability of the framework to maintain larger amounts of porosity is improved, as exhibited by the co-IonomIM-1 structure with 50%, 33%, 20%, and 17% ionic groups, which had BET surface areas of 743, 848, 861, and 890 m2/g, respectively. Interestingly, when the ionic content was below 50%, the partially hydrolyzed copolymer exhibited similar BET surface areas to PIM-1. This suggests that, given a sufficiently low ionic content, the carboxylate functional groups promote inefficient packing and overcome the increase in polymer association interactions to yield materials with free volumes similar to PIM-1, 23−26%. Thus, it is shown that intrinsically microporous ionomers will maintain a significant amount of microporosity that is inversely proportional to the carboxylate content, yielding a highly functionalized polymer framework suitable for gas adsorption and separation applications. CO2 Adsorption. To evaluate the CO2 adsorption capacity of these microporous polymers, grand canonical Monte Carlo simulations were executed, which calculate the equilibrium loading of gas within the framework at a constant chemical potential, volume, and temperature. The simulated adsorption isotherms up to 250 kPa at 20 °C of the porous ladder polymers are shown in Figure 3. All intrinsically microporous polymers in this study have increased low-pressure CO2 12042

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Figure 4. CO2 enthalpy of adsorption of IonomIMs simulated in this work as a function of pressure at 20 °C, compared to previous simulations of PIM-1.47 Symbols represent same materials as in Figure 3; coIonomIM-1 (33%) is shown by blue triangles.

effective at increasing electrostatic interactions between the polymer framework and CO2, which is encouraging for gas storage applications. The adsorption capacity of the ionicfunctionalized PIMs, which exceeded 3 mmol/g at 1 bar and 293 K, is among the highest observed for any high free volume linear polymer50 and approaches the extraordinary capacities achieved for networked polymers51 and porous coordination polymers.52 Therefore, the IonomIMs presented in this work exhibit excellent performance for both low- and ambientpressure CO2 adsorption, with the optimum loading capacity tunable depending on the fraction of ionic groups included within the polymer framework, highlighting the potential of intrinsically microporous ionomers as industrially viable CO2 adsorption, sequestration, and capture materials. Characterization of Na+. To characterize the interactions between the IonomIM, Na+ ions, and adsorbed CO2 gas, radial distribution functions (RDFs), gij(r), were calculated. RDFs give the probability of finding atom i a distance r from atom j compared to the ideal gas distribution. After CO2 gas adsorption, molecular dynamics simulations in the canonical ensemble (NVT) were run in LAMMPS at 293 K for 500 ps, and all RDFs were averaged over 10 configurational snapshots. The results of two characteristic RDFs are shown in Figure 5. In Figure 5a, the RDF of the central carbon of the carboxylate functional group interacting with Na+ ion is presented. The strong peak at ∼3.3 Å corresponds to Na+ ion associating with negatively charged oxygens on the carboxylate group and increases in intensity with decreasing ion content, which is a result of the increasing concentration of ions. Interestingly, nearly all Na+ ions associate with a carboxylate group for each polymeric system, and some of these ion pairs aggregated together during the compression and relaxation scheme to form ionic clusters, as shown in Supporting Information. These clusters would act as physical cross-links of the polymeric material and are shown to decrease in frequency with decreasing ion concentration. Figure 5b shows the RDF of Na+ ions interacting with oxygen atoms on the adsorbed CO2, with two distinct peaks, B1 and B2, at ∼3 and ∼5 Å, respectively. Again, as the ion content is decreased, the peak intensity of Na+−CO2 increases. In the lower ion content IonomIMs, Na+ ion is an energetically favorable site that is preferentially adsorbed. This is consistent with the enthalpy of adsorption data shown in Figure 4, where the co-IonomIMs exhibit enhanced enthalpy of adsorption at low loading, which rapidly declines as the Na+ ions are no

Figure 5. Radial distribution functions (RDFs) of (a) carboxylate− Na+ and (b) Na+−CO2, with (c) schematic of representative carboxylate−Na+−CO2 coordination, which highlights three important correlative distances: A, B1, and B2. Distance A is shown in panel a as carboxylate C to Na+, which is ∼3.3 Å. Distances B1 and B2 are shown in panel b as Na+ to each O in an adsorbed CO2 molecule, which are ∼3 and ∼5 Å, respectively. An adsorption pressure of 1 kPa is shown; however, the distances are consistent with 100 kPa pressure, which is shown in Supporting Information. Shown are IonomIM-1 (dashed red line), co-IonomIM-1 (50%) (solid green line), and co-IonomIM-1 (33%) (dot−dashed blue line).

longer accessible, and at high loading they exhibit similar qst to PIM-1. The B1 peak distance results from the negatively charged oxygen that adsorbs onto the Na+ ion, while the B2 peak location provides information on the orientation of CO2 molecules. Since the location of the B2 peak is further, ∼5 Å, this suggests that CO2 adsorbs onto the Na+ ion in an orientation that is not perpendicular. This effect has been observed experimentally in IR spectroscopy of cationexchanged zeolites, which demonstrated a preference of the physisorbed CO2 to orient linearly by ion−dipole interaction.53 When the average distances of B1 and B2 and the length of a CO2 molecule are considered, the CO2 statistically orients at ∼100° angle in these simulations, with the breadth of the peaks indicating some degree of thermal fluctuations. Figure 5b shows results at 1 kPa, but the results are consistent with the 100 kPa RDFs shown in Supporting Information. This means that the Na+ ions remain associated with the carboxylate group during the adsorption simulations and are not solvated by increasing loading of CO2 (up to 100 kPa), which is in contrast to what has been observed in ionic MOF simulations at higher pressures (10 bar).8 Finally, Figure 5c provides a representation of what is occurring during CO2 adsorption at the ionic functionalities, which is consistent with the RDFs and experimental results of cation-exchanged zeolites. Na+ ions associate strongly with the carboxylate functionality along the 12043

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previous simulations and performed near the UB for each gas pair, as shown in Supporting Information. Therefore, the ideal gas-separation performance of ionicfunctionalized PIMs was relatively unaffected by the ionic groups, because it was a function of f in the system; however, for industrial applications, it is the mixed-gas separation ability that determines the energy efficiency of a polymeric membrane. As such, several application-based case studies of mixed-gas separation were evaluated and are discussed in the following section. Adsorption Evaluation Criteria. In an effort to place the real gas-separation performance of the newly proposed IonomIMs in context with other leading microporous materials for industrial CO2-separation applications, the previously proposed adsorption evaluation criteria were simulated.5 Practically, microporous materials can be used to separate CO2 in pressure- or vacuum-swing applications, PSA or VSA, which rely on different adsorption capacities of gas as the pressure swings from high to low. PSA and VSA differ only in the adsorption (Pads) and desorption (Pdes) pressure regimes, which for PSA are 5 and 1 bar and for VSA are 1 and 0.1 bar, respectively. There are four gas mixture compositions and adsorption/desorption conditions evaluated, as shown in Table 2.

backbone of the polymer. Upon adsorption, CO2 molecules preferentially adsorb on Na+ ions and orient themselves nearly linearly, which maximizes electrostatic interactions between the quadrupole of CO2 and the Na+ ions. Permeability Screening. Recently, through molecular simulations of hypothetical gas-separation polymers, our group has developed an efficient screening methodology that calculates gas permeability and permselectivity.42 This allows for the gas-separation performance of simulated polymers to be compared against the Robeson upper bound (UB)54 for a given gas pair. The permeability coefficient (P) is separated into the solubility (S) and diffusivity coefficients (D) according to the solution-diffusion model, P = SD. The solubility is calculated from pure-gas GCMC simulations at 293 K and 100 kPa and the diffusivity is calculated by use of an empirical model55 based on free volume theory. Further details of this screening procedure are given in Supporting Information. Permeability, calculated from the screening methodology, is shown in Figure 6 as a function of fractional free volume, f, for

Table 2. Mixed-Gas Adsorption/Desorption Conditions5 Studied in This Work case

application

mixture composition

1

natural gas purification by PSA landfill gas purification by PSA landfill gas separation by VSA flue gas separation by VSA

CO2/CH4 = 10:90 CO2/CH4 = 50:50 CO2/CH4 = 50:50 CO2/N2 = 10:90

2 3

Figure 6. Estimated permeability of CO2 at 1 bar as a function of the fractional free volume ( f) for ionic-functionalized PIMs (open red squares) and previous simulation data for non-ionic-functionalized PIMs (open black circles).42 Each data point represents one of the five simulation boxes of each sample set, with average values being reported in Supporting Information. Also shown is the empirical model fit (eq 3) to nonionic PIMs (solid black line) and ionicfunctionalized PIMs (dashed red line).

4

Pads = 5, Pdes = 1 Pads = 5, Pdes = 1 Pads = 1, Pdes = 0.1 Pads = 1, Pdes = 0.1

For each case, there are two essential criteria to assess the effectiveness of the potential adsorbent material: working CO2 capacity (ΔNCO2) and sorbent selection parameter (Ssp). In addition, the results of all five adsorbent criteria proposed are reported in Supporting Information (CO2 uptake, working CO2 capacity, regenerability, adsorption selectivity, and sorbent selection parameter). The working CO2 capacity is calculated as

CO2. The nonionic PIMs of ref 42 are shown as black circles, and the ion-containing PIMs simulated here are shown as red squares. Both sets of simulation data were fit to the empirical relationship: P = α* exp(βf )

pressure conditions (bar)

ads des ΔNCO2 = NCO − NCO 2 2

(4)

with N being the absolute loading capacity at the condition of interest. The sorbent selection parameter is calculated as

(3)

where α* and β are empirical constants of 0.319 and 38.27, respectively, from ref 42, with β being related to the size of the gas molecule.55 When CO2 permeability performance is compared, the relationship between permeability coefficient and fractional free volume of the material was similar for ionic and nonionic PIMs. Thus, the estimated screening performance suggests that gas permeability is a function of fractional free volume in the framework, regardless of functionality. This supports the conclusions of our previous work: that even with strongly CO2-philic functionalities, the diffusivity is most influential on gas-permeation performance.42 Similar results were also obtained for CH4 and N2 permeation, shown in Supporting Information. In addition, the ideal permeation selectivity of CO2/CH4 and CO2/N2 was also consistent with

2 des Ssp = (αiads / j ) /(αi / j )(ΔNi / ΔNj)

(5)

where i and j are the two gases in the mixture and αi/j = (Ni/ Nj)/(yi/yj), with y being the molar ratio of gas in the bulk phase. To simulate these industrially applicable conditions, mixed-gas adsorption grand canonical Monte Carlo simulations were carried out at 293 K for all four cases. These gas mixture compositions and adsorption evaluation criteria have been used in a number of computational and experimental screening investigations of ordered network microporous materials, which have aided in pinpointing the materials with excellent performance for each condition.5,56 For the first time, this work compares the performance of highly functionalized PIMs to that of zeolites, MOFs, and porous organic polymers (POPs) 12044

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Figure 7. Sorbent selection parameter, Ssp, versus working capacity of gas, ΔNCO2, calculated for previously proposed5 evaluation criteria of adsorbed materials (Table 2): (a) case 1, natural gas purification by PSA, CO2/CH4 10:90 mixture; (b) case 2, landfill gas purification by PSA, CO2/CH4 50:50 mixture; (c) case 3, landfill gas separation by VSA, CO2/CH4 50:50 mixture; and (d) case 4, flue gas separation by VSA, CO2/N2 10:90 mixture. Simulated microporous polymers were PIM-1 (black circles), soPIM-147 (gray squares), carboxyPIM-1 (gray circles), IonomIM-1 (red squares), coIonomIM-1 (50%) (green diamonds), coIonomIM-1 (33%) (blue triangles), coIonomIM-1 (20%) (gold squares), and coIonomIM-1 (17%) (purple inverted triangles). For context, experimental data points are shown from ref 5 and experimental data referenced therein: zeolites (△), MOFs (×), POPs (+), and activated carbons (▽). For each case, a leading microporous material from experiments is highlighted (open red squares): case 1, Mg-MOF-74;57 case 2, HKUST-1;58 case 3, CUK-1;59 and case 4, ZIF-78.60

the polymer framework correspondingly increased the selection performance while decreasing the working capacity. While HKUST-158 was shown experimentally to exhibit a significant CO2 working capacity, as a result of open metal sites, the intrinsically microporous polymers outperformed all materials for the sorbent selection parameter in case 2, which spanned from 69 for PIM-1 to 324 for IonomIM-1. Therefore, for pressure-swing applications (cases 1 and 2), the ionicfunctionalized PIMs have the potential to improve the efficiency of both natural gas purification and landfill gas separation, where the electrostatic interactions between CO2 and ionic groups facilitated excellent mixed-gas adsorption selectivity. For vacuum-swing applications (cases 3 and 4), the lower total adsorption pressure has the advantage of limiting the plasticization susceptibility of a polymeric membrane, which may occur at higher pressures. However, as the adsorption partial pressure of CO2 in case 3 was similar to case 1 at ∼0.5 bar, the effect of ion functionality was similar, where the partially ionic microporous polymers increased both working capacity and selectivity of CO2/CH4 (Figure 7c). CUK-159 exhibited the highest sorbent selection parameter observed experimentally for case 3 at 359; however, IonomIM-1 exhibited an Ssp value almost twice that of CUK-1 at 664. It was suggested in a previous study that 50 kJ/mol is an optimum enthalpy of adsorption for case 3 separation,5 which is supported by the excellent performance of IonomIM-1 (49.8 kJ/mol). For flue gas separation (CO2/N2 in case 4; Figure 7d), it is unlikely that PIMs will compete with the high sorbent

and highlights several specific areas in which PIMs outperform these leading gas-separation materials. Gas-separation performances of the simulated ionomers for all cases are shown in Figure 7 and compared to experimental performance of several leading microporous materials. These plots illustrate the sorbent selection parameter (Ssp) and working CO2 capacity (ΔNCO2), both of which should be maximized for improved gas-separation performance: that is, the best materials for any condition will exist in the upper-right corner. Cases 1 and 2 both refer to applying a pressure-swing application for separating CO2 from CH4 at different mixture ratios, 10:90 and 50:50, respectively. For case 1 (Figure 7a), the ionic-functionalized PIMs exhibited an increase in both working capacity of CO2 and sorbent selection parameter, with IonomIM-1 exhibiting a selection performance almost 20 times as effective as PIM-1 with values of 144 and 8, respectively. IonomIM-1 is projected to surpass the high sorbent selection parameter observed experimentally for MgMOF-74,57 which displayed an Ssp value of 82 as a result of the unsaturated Mg2+ sites facilitating high CO2 enthalpy of adsorption (43 kJ/mol). In case 2 (Figure 7b), the partial pressure of CO2 is higher (2.43 bar), which limits the working capacity as the ion content is increased; however, the enhanced CO2 enthalpy of adsorption of the IonomIMs again improved the selection ability of the polymer framework by an order of magnitude. Interestingly, a direct tradeoff is observed between ΔNCO2 and Ssp in case 2, where increasing the ion content of 12045

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Langmuir selection parameters achieved by MOFs or the high working capacities of zeolites. For example, ZIF-7860 exhibited similar working capacity but the Ssp was an order of magnitude higher. On the other hand, the IonomIMs did slightly increase the working CO2 capacity while maintaining the selection ability observed for PIM-1, suggesting that the IonomIMs may be an effective alternative to include in mixed-matrix membranes61 for flue gas separations. In all cases, the partially metalized polymers, co-IonomIMs, exhibited Ssp values between those of PIM-1 and IonomIM-1, with the increasing content following a direct trend between the two. This suggests that, for the selection conditions shown here, the desired value of the selection parameter may be tailored by designing materials with a specific ion content (i.e., a controllable synthetic design principle). Outstandingly, while some zeolites and MOFs did exhibit a higher working capacity of CO2, the hypothetical IonomIMs exhibited a higher sorbent selection parameter than all MOFs and zeolites for gasseparation applications involving CO2/CH4, including a large data set of hypothetical MOFs.56 These results emphasize that ionomers of intrinsic microporosity are a promising class of next-generation polymeric materials, which excel in both CO2 loading capacity and mixed-gas selectivity of several industrial gas-separation applications.

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

Article

S Supporting Information *

Additional text and equations, 10 figures, and five tables with details of molecular models used for porosity characterization; BET adsorption isotherms of N2 at 77 K; CO2 adsorption of IonomIM-1 with different Na+ force fields; adsorption isotherms and enthalpy of adsorption for CO2, CH4, and N2 at 293 K; Dual Mode model parameters for simulated adsorption isotherms; additional radial distribution functions; schematic representation of physical cross-link and frequency distribution of coordination number; gas-separation performance and permeability model fit parameters of simulated PIMs; simulation details and results of screening CO2 permeability and ideal permeation selectivity of CO2/CH4 and CO2/N2; and simulation details and results for simulating mixed-gas adsorption evaluation criteria for the four cases. This material is available free of charge via the Internet at http://pubs.acs. org/. Corresponding Author

*E-mail [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Lauren J. Abbott and James Runt for helpful discussions. In addition, we thank the National Science Foundation (DMR-1310258) 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. This work was supported in part through instrumentation funded by the National Science Foundation through Grant OCI-0821527.

CONCLUSIONS The gas adsorption potential of a novel class of ionicfunctionalized high free volume polymeric materials was analyzed via predictive molecular simulations. Ionomers of intrinsic microporosity (IonomIMs) displayed similar microporosity to PIM-1 for partially hydrolyzed systems (coIonomIMs); however, as a result of the increased polymer− polymer interactions, the amount of free volume for IonomIM1 decreased. As a result of introduction of highly CO2-philic ionic groups, the CO2 loading capacity increased for both lowand ambient-pressure ranges for the co-IonomIMs, while IonomIM-1 significantly increased the low-pressure adsorption uptake. This is a result of Na+ ions associating with carboxylate groups and creating an energetically favorable adsorption site for the partially negative oxygen atoms of CO2, which enhanced the enthalpy of adsorption from that of PIM-1 (30 kJ/mol) to 42−50 kJ/mol for the ion-containing polymers. Through computational screening of permeability and ideal permselectivity, all co-IonomIM polymer materials are projected to perform near the Robeson upper bound for both CO2/CH4 and CO2/N2, as the permeability was dictated by the amount of free volume in the system, which was consistent with previous results. In addition, several mixed-gas case studies of separating CO2 from CH4 or N2 were simulated, where the ioncontaining polymer increased both working CO2 capacity and selectivity for natural gas purification and landfill gas separation. Most importantly, PIMs are shown here to outperform the selection performance of several leading MOFs, zeolites, POPs, and activated carbons, highlighting the real potential these polymers have in CO2/CH4 application-based gas separations. In conclusion, ionomers of intrinsic microporosity are excellent candidates for highly functionalized polymeric membranes for gas-separation applications, as shown by the promising performance predicted by these molecular simulations. The design principles provided will allow for further synthetic endeavors of this novel class of highly effective adsorbent polymeric materials.

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REFERENCES

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