Modeling Amorphous Microporous Polymers for CO2 Capture and

Review pubs.acs.org/CR

Cite This: Chem. Rev. 2018, 118, 5488−5538

Modeling Amorphous Microporous Polymers for CO2 Capture and Separations Grit Kupgan,†,‡,§ Lauren J. Abbott,∥,# Kyle E. Hart,∥,∇ and Coray M. Colina*,†,‡,§,⊥ †

Department of Materials Science and Engineering, University of Florida, Gainesville, Florida 32611, United States George & Josephine Butler Polymer Research Laboratory, University of Florida, Gainesville, Florida 32611, United States § Center for Macromolecular Science & Engineering, University of Florida, Gainesville, Florida 32611, United States ∥ Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ⊥ Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States

Chem. Rev. 2018.118:5488-5538. Downloaded from pubs.acs.org by KAOHSIUNG MEDICAL UNIV on 06/24/18. For personal use only.

‡

ABSTRACT: This review concentrates on the advances of atomistic molecular simulations to design and evaluate amorphous microporous polymeric materials for CO2 capture and separations. A description of atomistic molecular simulations is provided, including simulation techniques, structural generation approaches, relaxation and equilibration methodologies, and considerations needed for validation of simulated samples. The review provides general guidelines and a comprehensive update of the recent literature (since 2007) to promote the acceleration of the discovery and screening of amorphous microporous polymers for CO2 capture and separation processes.

CONTENTS 1. Introduction 1.1. Carbon Capture Strategies 1.2. Microporous Materials 1.3. Microporous Polymers 1.4. Modeling Materials for CO2 Applications 2. Simulation Methods 2.1. Force Fields 2.2. Monte Carlo (MC) Simulations 2.3. Molecular Dynamics (MD) Simulations 3. Considerations for Modeling Microporous Amorphous Polymers 3.1. Molecular Models of Amorphous Polymers 3.1.1. Approaches for Structure Generation 3.1.2. Structure Equilibration 3.2. Characterization and Validation of Models 3.2.1. Density and Pore Volume 3.2.2. Surface Areas 3.2.3. Pore Size Distributions 3.2.4. X-ray Scattering and Structure Factors 3.2.5. Adsorption Isotherms 3.2.6. Diffusivity 3.2.7. Plasticization 3.3. Interpreting and Guiding Experimental Efforts 3.4. Computational Screening 4. Recent Progress of Polymer Modeling for CO2 Applications

© 2018 American Chemical Society

4.1. Polymers of Intrinsic Microporosity (PIMs) 4.2. Porous Aromatic Frameworks (PAFs) and Hyper-Cross-Linked Polymers (HCPs) 4.3. Conjugated Microporous Polymers (CMPs) 4.4. Thermally Rearranged Polymers (TRPs) 4.5. Mixed-Matrix Microporous Polymers (MMPs) 5. Concluding Remarks and Outlook Associated Content Special Issue Paper Author Information Corresponding Author ORCID Present Addresses Notes Biographies Acknowledgments References

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1. INTRODUCTION We are concerned about the environmental impact of carbon dioxide (CO2) in our atmosphere. The anthropogenic release of CO2 is currently measured at 35 billion tons per year, and the trend is continuously rising worldwide.1 The main source of these CO2 emissions is the burning of fossil fuels (e.g., heating, transportation, and electrical power generation), which

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Received: November 15, 2017 Published: May 29, 2018 5488

DOI: 10.1021/acs.chemrev.7b00691 Chem. Rev. 2018, 118, 5488−5538

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Figure 1. General scheme of CO2 capture strategies during precombustion (left), postcombustion (middle), and oxy-fuel combustion (right). The separation stages are shown in yellow boxes. Precombustion involves high pressure separation of CO2/H2, postcombustion involves low pressure separation of CO2/N2, and oxy-fuel combustion involves low pressure separation of O2/N2.

constitutes 85% of all energy used globally.2,3 Moreover, an increase in atmospheric CO2 concentration can result in serious consequences, such as an escalation of global warming, a rise in sea levels, and an increase in ocean acidity.4−7 Thus, the continued release of CO2 deserves our full attention. Several approaches have been considered to tackle the rapid rise in atmospheric CO2.7−9 One long-term solution to mitigate the harmful impact from CO2 is to utilize clean energy technologies (e.g., solar, wind, hydrogen, and nuclear), but these technologies currently face significant challenges related to cost, scalability, and safety concerns.10,11 The U.S. Department of Energy recently described a framework for CO2 utilization and sequestration technologies that could result in more immediate large-scale reduction of CO2.12 In particular, carbon capture and sequestration technologies are one important area of research being pursued,13−17 which require the development of new solids for adsorption processes and membranes, among others.12 Special attention is being placed on technologies that can be retrofitted onto CO2 point sources,18 including power plants and other industrial processes, which account for about 50% of the total CO2 released in the United States.19,20 Beyond power plants, CO2 separation is important for applications in natural gas, biogas upgrading, and oil recovery.21

content, atmospheric pressure, and an exit temperature of 40− 150 °C,22,23 which necessitate high performance materials and efficient processes. Additionally, existing power plants can be easily retrofitted for postcombustion technology, such that it has a wide applicability.24 Although fuel is typically burned in air, oxy-fuel combustion burns fuel in almost pure oxygen, resulting in a stream of CO2 and water. The process requires an O2/N2 separation unit prior to combustion to facilitate CO2 removal from flue gas, as there is a higher CO2 concentration in the output stream. Moreover, since N2 is not involved in the combustion process, NOx formation is minimized, which reduces the cost of separation. However, oxy-fuel combustion methods currently rely on the costly use of cryogenic distillation to separate O2 from N2. Currently, amine-based systems are the predominant technology for CO2 capture.25−29 The technology has been developed for several decades and is considered wellestablished for industrial use. In this method, CO2 in gas mixtures is captured via reactions with primary, secondary, or tertiary amines in an absorber column (Figure 2). Some commonly employed amine species include monoethanolamine, diethanolamine, piperazine, etc. Afterward, the products of the reactions (carbamate, bicarbonate, etc.) are sent to a stripper column (desorber), where the solution is reheated with steam in order to extract pure CO2 and the recovered amines are subsequently recycled. A similar process can also be applied with other related technologies, such as aqueous ammonia. Although amine-based systems are considered the state-of-theart today and will be a dominant player for the next few decades, they are considered costly and suffer from several drawbacks.25−30 The process requires large sized equipment, and solvent regeneration is relatively energy intensive. The issue is even more problematic for solutions with high water content, as more heat input is required. Amine solutions are also corrosive, which is an environmental concern. Additionally, amine solutions may be unstable at high temperature, which limits the regeneration temperature, lowers solvent lifetime, and is susceptible to evaporation loss. Due to these reasons, other alternatives have been proposed for CO2 capture. Solid adsorbents, such as microporous materials, are an attractive

1.1. Carbon Capture Strategies

Three methods of CO2 separation are typically explored, which include precombustion, postcombustion, and oxy-fuel combustion (Figure 1). For precombustion methods, the gasification and water−gas shift reaction are represented by the conversion step in the diagram. Gasification can produce a syngas stream which contains about 15% CO2, alongside a combination of hydrogen (H2), carbon monoxide (CO), water (H2O), and other impurities. Afterward, a shift reaction with water turns the remaining CO into CO2, which results in about 50% concentration of CO2 in the stream and provides an opportunity for carbon capture. The precombustion method has great potential, yet it has been mainly implemented in integrated coal gasification combined cycle plants.13 Postcombustion methods rely on CO2/N2 separation from exhaust flue gas. Flue gas exiting from the combustion step has low CO2 5489


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the adsorption and desorption of gases within the material. The ability of the adsorbent to effectively separate CO2 at a given set of operating conditions is determined by its adsorption capacity for CO2, as well as its CO2 selectivity. Alternatively, some microporous materials have been shown to be effective for membrane separation processes.35−45 Membranes are traditionally made from nonporous polymers, which have been shown to demonstrate an empirical trade-off relationship between permeability and selectivity for many gas pairs (Figure 3).46,47 Research over the last two decades has focused on surpassing this observed upper bound, and membranes utilizing microporous materials have been shown to improve performance in many cases. Numerous microporous materials have been explored to date for gas adsorption and separation, including both inorganic and organic, as well as crystalline and amorphous. A diagram illustrating some families of microporous materials is presented in Figure 4, many of which have been reviewed extensively in the literature.18,48−63 Common examples of microporous materials are crystalline frameworks with well-defined pore structures, including zeolites,64−66 zeolitic imidazolate frameworks (ZIFs),67 metal−organic frameworks (MOFs),30,68−72 and covalent organic frameworks (COFs).73 Amorphous networks with ill-defined pore structures, like activated carbons74 and carbon molecular sieves (CMSs),75 have also been explored. More recently, research efforts have focused on the design of microporous molecular solids composed of only small molecules, which are typically crystalline but can also be amorphous. These include, for example, nanoporous molecular crystals (NMCs),76,77 porous organic cages (POCs),78,79 and organic molecules of intrinsic microporosity (OMIMs).80,81 In this review, we focus on various classes of network and linear polymers, which offer several advantages over other materials, including chemical diversity, chemical and thermal stability, and potential for competitive manufacturing (e.g., cost-effective, processability, and modularity).82 Note that only a brief

Figure 2. Example of an amine scrubbing unit. The CO2 capture process occurs within the absorber column, while the release of CO2 and solvent regeneration occur within the desorber unit. Adapted with permission from ref 28. Copyright 2015 American Chemical Society.

technology due to the lower energetic penalties associated with the reversible capture and release of CO2 via physisorption. 1.2. Microporous Materials

Microporous materials, which have pores smaller than 2 nm in size,31 are promising candidates for CO2 separation technologies, particularly because their pore sizes are on the order of the molecular dimensions of CO2 and others small gases. Moreover, specific gas−framework interactions can be tuned via the pore structure and chemical functionality for improved CO2 adsorption and separation. Microporous materials are commonly considered for adsorption separation processes due to their large surface areas and corresponding high adsorption capacities.32−34 In pressure swing adsorption (PSA) and temperature swing adsorption (TSA) technologies, operating conditions such as pressure and temperature are used to control

Figure 3. Robeson plot examples for CO2/CH4 (left) and CO2/N2 (right) gas pairs. When gas separation polymers are plotted in terms of permeability (P) and permselectivity (ALPHA), a trade-off relationship between the two can be observed. Desirable polymers should have both high permeability and permselectivity. Empirical upper-bound lines are shown in black, which represent a maximum achievable performance at the time data were collected. The prior upper bound and present upper bound were generated in 1991 and 2008, respectively. Adapted with permission from ref 47. Copyright 2008 Elsevier. 5490


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Figure 4. Diagram of microporous materials for CO2 capture and separations. The microporous materials that are focused in this review are linear polymers, network polymers, and microporous polymer-based composites. Abbreviations: PIs, polyimides; PIMs, polymers of intrinsic microporosity; TRPs, thermally rearranged polymers; PAFs, porous aromatic frameworks; HCPs, hyper-cross-linked polymers; CMPs, conjugated microporous polymers; MMMs, mixed-matrix membranes; MMPs, mixed-matrix microporous polymers; CMSs, carbon molecular sieves; MOFs, metal−organic frameworks; COFs, covalent organic frameworks; OMIMs, organic molecules of intrinsic microporosity; POCs, porous organic cages; NMCs, nanoporous molecular crystals.

or cross-linked structure, linear polymers can achieve significant microporosity, including high surface areas and large gas permeabilities.93,127 Prototypical polymers with high free volume used commonly for membrane separation are poly(trimethylsilyl)propyne (PTMSP) and it variants, which have shown high gas diffusion coefficients as a result of large continuous microvoids.128 Polyimides (PIs) have also been studied more recently, since they show good physical and gas separation properties that can be tuned by the choice of dianhydride and diamine.21,129,130 Thermally rearranged polymers (TRPs) are achieved by thermal rearrangement of PIs post membrane formation and are dense polymeric membranes with ortho-positioned functional groups such as −OH.131,132 They have an interconnected morphology of tuned microvoids that have been shown to be well suited for CO2 gas storage and separation applications.133,134 Polymers of intrinsic microporosity (PIMs)135−138 exploit rigid sites of contortion to generate pore volume, which have been shown to result in relatively high surface areas.139−141 The unique combination of microporosity and solution processability achieved by TRPs and PIMs often yields membranes with improved performance beyond the 2008 Robeson Upper Bound (Figure 3).47 Although most other microporous materials discussed previously are insoluble, they can be incorporated as fillers into a polymer matrix to form solidpolymer mixed-matrix membranes (MMMs),142−145 which usually results in performance surpassing the upper bound. Recently, researchers have explored embedding microporous fillers in a microporous polymer matrix, which we will refer to as mixed-matrix microporous polymers (MMPs).142−145

overview of these polymers is provided, since experimental reviews are widely available elsewhere.82−106 1.3. Microporous Polymers

There are many classes of microporous polymers that are differentiated by their processing and functionalization, which offer opportunities for tuning the structure and properties for specific applications. Hyper-cross-linked polymers (HCPs)107−110 are a class of network polymers that derive porosity by heavily cross-linking polymers in a swollen state in such a way that prevents pores from collapsing once the solvent is removed. Typical examples are synthesized by post-crosslinking of polystyrene111,112 to make the so-called Davankov resins and Friedel−Crafts alkylation of bis(chloromethyl) aromatic monomers.113,114 HCPs that produce an extended conjugated network are termed conjugated microporous polymers (CMPs).115−117 Tailoring the conjugated linker84 and chemical functionality118 have been shown to improve their affinity with CO2. In addition, some CMPs119 exhibit favorable properties for catalysis120 and electroluminescence.121 In the literature, other highly cross-linked polymer networks are sometimes referred to as porous organic polymers (POPs),122 porous polymer networks (PPNs),123 or porous aromatic frameworks (PAFs),124 but these are generally similar to the classes listed above. Although network polymers have exhibited large BET surface areas (e.g., 5,600 m2/g for PAF-1)125 and adsorption capacities (e.g., 4.3 mmol/g or 15.8 wt % CO2 at 1 bar and 298 K for PPN-6-CH2DETA),126 they are inherently insoluble. This presents particular difficulties for processing and may require additional synthetic steps when reforming the material after long-term utilization. Relatively recently, porous linear polymers have been designed using sterically hindered monomer structures with limited degrees of rotational freedom. These high molecular weight linear polymers are solution processable, energy efficient, and industrially attractive. Even without a networked

1.4. Modeling Materials for CO2 Applications

Molecular modeling is a valuable toolset through which we can improve our understanding of the relationship between a material’s chemical structure and the resulting molecular interactions, as well as accelerate the discovery of new materials 5491


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for CO2 capture and separation applications.146−150 Computational studies of crystalline microporous materials with welldefined structures, such as COFs and MOFs, are wellestablished and have led to the development of novel materials with superior gas storage and separation performance.68,70,151−157 Molecular simulations have also been used to study microporous organic molecular solids, including prediction of both crystalline and amorphous structures, as well as dynamics of host−guest interactions.158,159 Amorphous polymeric materials are good candidates for computational modeling due to their functional diversity.82 However, most microporous polymers are amorphous with poorly defined structures and porosity, which poses problems for their design and characterization. Computational studies of these polymers have been limited in part due to the challenges associated with generating physically accurate models of the disordered structures for molecular simulations.160 Here, we aim to discuss the progress of molecular simulations in addressing these challenges. The goal of this review is to discuss the state of the art in the use of molecular simulations for the design and evaluation of amorphous microporous polymers for CO2 capture and separations. Specifically, we define amorphous microporous polymers as disordered organic polymers with measurable surface areas containing mainly persistent and interconnected pores. The majority of the pores should be at least the size of molecular dimension but less than 2 nm, which is the IUPAC upper limit for microporosity. Therefore, conventional nonporous, mesoporous, and macroporous polymers are not included in the discussion. In this review, we first introduce the basic simulation techniques that pertain to CO2 capture and separations. Then, approaches and considerations for generation and validation of simulated samples are discussed. We also provide examples of how simulation results have guided experimental efforts successfully. Afterward, we review the recent progress within the last 10 years in the simulation of microporous polymers with CO2, emphasizing promising material classes such as polymers of intrinsic microporosity (PIMs), porous aromatic frameworks (PAFs), hyper-crosslinked polymers (HCPs), conjugated microporous polymers (CMPs), thermally rearranged polymers (TRPs), and mixedmatrix microporous polymers (MMPs). Lastly, the conclusions, challenges, and future outlook are discussed. The intent is to provide general guidelines and a comprehensive update of the literature to promote acceleration of the discovery and screening of amorphous microporous polymers for CO2 capture and separation processes.

to this review, a system may consist of a matrix (e.g., polymers) and guest molecules (e.g., CO2). The atoms in the system must have appropriate short-range and long-range interactions with other particles within the system. These interactions are called “nonbonded” terms and may include contributions from van der Waals (dispersion), electrostatic, etc. For instance, the functional form for nonbonded interaction commonly includes the Lennard-Jones equation to account for weak interactions and a Coulombic term. Moreover, the atoms that are connected by covalent bonds must be spatially constrained in order for molecules or polymers to acquire the correct conformations. In this case, the set of equations in the force fields are called “bonded” terms, which can include descriptions for bonds, angles, dihedrals, and impropers. For example, the functional form for bonds and angles may be as simple as a harmonic potential. Although the energy of the system can be calculated efficiently using an empirical force field, an average property of interest cannot be obtained from a single state or a single snapshot. In order to obtain an average property, we must sample the system at various configurations and calculate the property of interest for each state. The correct property can be obtained from the ensemble average from these snapshots. In particle-based simulation, different configurations can be explored using molecular dynamics (MD) or Monte Carlo (MC) techniques. In short, MD simulations integrate time based on Newton’s law of motion, such that both thermodynamic and transport properties can be obtained. However, they can more easily be trapped in local minima with kinetically slow processes and can require significant simulation lengths to exhaustively explore a large phase space of possible configurations. To the contrary, MC is time-independent and allows unnatural moves to be performed to achieve new configurations that bypass large energy barriers. Both methods should yield the same value of static properties if different configurations are adequately explored. Depending on a specific application, one method may be more favorable than the other. In the following sections, we provide further details on force fields, MC, and MD methods relevant to atomistic simulation for CO2 capture in polymeric materials. 2.1. Force Fields

Atomistic simulations can be described based on classical mechanics of multiparticle systems by assuming that the molecular systems are made up of particles (e.g., atoms) that interact via both inter- and intramolecular interactions.161,162 Force fields define the functional form and parameters of the potential energy of the system. For an ensemble of N atoms with coordinates rN, the potential energy U, is a sum of contributions from both bonded and nonbonded interactions (eq 1):162

2. SIMULATION METHODS For a small system with hundreds of atoms, we can accurately predict the behavior of the system by accounting for electronic structures of molecules through quantum mechanics (QM) calculations. For modeling CO2 capture in polymers, however, we simply cannot use QM calculations to simulate most of the system sizes that we are interested in due to the limited computational power today. In order to simulate the system size ranges from a few thousands to a few millions of atoms, several approximations are required. Instead of calculating a system’s energy from QM, we can assume that the behavior of molecules can be approximated by a set of empirical equations called force fields. The force field equations are several orders of magnitude less expensive and their parameters are typically derived from QM calculations and/or experiments. Pertaining

U (r N ) = Ubonded + Unon ‐ bonded

(1)

Common force fields for liquids and polymers generally have bonded interactions with terms to describe bonds, angles, and dihedrals between 1−2, 1−3, and 1−4 bonded atoms. For instance, the functional form of the bonded interactions for the Generalized Amber Force Field (GAFF)163 is the following (eq 2): 5492


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∑

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K r(r − req)2 +

bonds

∑ dihedrals

∑

K θ(θ − θeq)2 +

Table 1. CO2 Force Field Parameters for EPM2 and TraPPE Models

angles

Vn [1 + cos(nϕ − γ )] 2

(2)

The force field includes the set of parameters for the given functional form, such as the force constants (Kr, Kθ, and Vn) and equilibrium values (req and θeq) in eq 2, which are specific to the types of atoms involved in the interactions. For liquids and polymers, nonbonded interactions are typically described using a Lennard-Jones (LJ) 12-6 potential for van der Waals interactions and a Coulombic potential for electrostatic interactions (eq 3): Unon ‐ bonded =

⎡ A qiqj ⎤ Bij ij ⎢ ⎥ − + ∑ ⎢ 12 εR ij ⎥⎦ R R ij6 i < j ⎣ ij

model

EPM2175

TraPPE176

εC−C (K) σC−C (Å) εO−O (K) σO−O (Å) qC (e) qO (e) r0,C−O (Å) θ0,C−O−C (deg) interaction type combining rule

28.129 2.757 80.507 3.033 +0.6512 −0.3256 1.149 180.0 LJ12-6 geometric

27.0 2.800 79.0 3.050 +0.700 −0.350 1.160 180.0 LJ12-6 Lorentz−Berthelot

The selection of force fields for CO2 capture and separation in polymers is not always straightforward. Due to the specificity of systems in force field parametrization, the force field used in a simulation should be chosen with care to most accurately model the systems and properties of interest. When possible, simulations should be validated against available experimental data. The properties of microporous polymers that are relevant to CO2 capture and separation include density, pore volume, surface area, pore size distribution, structure factors, etc. For CO2, choosing the most appropriate model also depends on the chemical constituents within the material frameworks, the simulation conditions, and compatibility with other force fields within the system such as the force field for polymers or other molecules. The proper behavior of gases in microporous polymers can be validated using adsorption isotherms and gas diffusion from experiments. Since the decision to apply a specific force field may be ambiguous in some cases, a wellrounded validation using several properties is always advisable, as discussed in section 3.2. Currently, most microporous polymers and their properties can be modeled with reasonable accuracy using the available force fields, granted that they are chosen meticulously. However, there are several issues that should be addressed in order to accelerate the force field usage for atomistic simulation of microporous polymers. First, it is important to note that most of the developed force fields do not employ an extensive amount of thermodynamic, mechanical, and transport properties of polymers as part of their parametrization or validation process. Thus, applying any force fields for polymers is rarely a “ready-to-go” process, since users must perform exhaustive validation themselves. The validation process can be laborious, which is a major difference compared to simulations for proteins or small molecules with very well established force fields. Second, bond formation and bond breaking in microporous polymers using reactive force fields are not widely implemented yet. The use of reactive force fields in polymers has only been developed recently, and examples are limited to only a few polymers. The reactive force fields for polymers could play a significant role for simulating network formation,190−193 controlling mechanical properties,194,195 and degradation at high temperature conditions and in the presence of reactive species.196,197 Lastly, microporous polymers that contain strong charges or ions in the framework for the purpose of enhancing CO2 capture could have potential issues related to force fields. This is because many organic force fields that work well for polymers may not have a complete set of parameters for ionic species. Additionally, although most force fields employ a fixed charge at the center of an atom, some

(3)

Here, A, B, and q correspond to the LJ parameters between atoms i and j and assigned atomic charges, respectively. Again, these parameters are specific to the force field used and are determined based on the types of atoms involved in the interactions. Force field parameters are commonly derived from a training set of small molecules that are representative of the types of systems to be modeled by the force field. The parameter fitting can be matched to higher fidelity quantum mechanics (QM) calculations and/or experimental data.164 For example, force field parameters may be obtained from crystal structures, gasphase geometries, spectroscopy, vibrational frequencies, conformational energies, critical temperatures, cohesive energies, liquid densities, or phase equilibrium data. Force fields have been parametrized to model generic systems such as the Universal Force Field (UFF).165 Many force fields have been optimized specifically for biological and organic molecules, such as the Transferable Potentials for Phase Equilibria (TraPPE),166 Generalized Amber Force Field (GAFF),163 Dreiding Force Field,167 AMBER Force Field,168 CHARMM Force Field,169 and the Optimized Potentials for Liquid Simulations (OPLS).170 Force fields specialized for polymers, which considered polymeric properties during parametrization and validation, are less abundant. Some examples are the Polymer Consistent Force Field (PCFF)171 and the Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS).172 Note that the simulation of polymers is not limited to polymer-based force fields. Often, established force fields can model systems with similar functionalities to those that were involved in the initial parametrization, and these force fields can be modified as necessary to improve accuracy, including charge derivations from first-principles approaches. Additionally, new force fields can be derived from first-principles approaches.173,174 For CO2, several models are available for simulation, including EPM,175 TraPPE,176 exp6,177 and many others.178−185 Among these models, the CO2 molecule may be rigid175,176,179 or flexible180,182 and may include polarizability186,187 or many-body effects.188 These models can produce varying accuracy of thermodynamic properties.189 EPM2 and TraPPE are the most widely used models and their parameters are shown in Table 1. Both models have three sites with partial charges to represent the CO2 quadrupole moment and their parameters were derived from vapor−liquid equilibrium (VLE) data. 5493


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applications require a better description of charge distribution within the system. In such cases, polarizable force fields can be used, which allow redistribution of charges throughout the simulation.198,199 Several examples indicate classical force fields are inaccurate for systems with strong framework/adsorbate interactions, such as MOFs with open-metal sites.200−202 For microporous polymers, systems with additional ions might require a polarizable force field especially if the mobility of ions must be accounted for, which can influence the charge distribution within the framework. A similar situation also applies to highly charged polymers such as polyelectrolytes, poly(ionic liquid)s, and porous ionic polymers (PiPs), which could require reassignment of charges. The improvement in force fields will significantly improve modeling capability of these materials especially for poly(ionic liquids)s and porous ionic polymers (PiPs), which have recently gained significant attention for CO2 capture.203−209

number of gas molecules within the polymer framework defines the equilibrium uptake at a specific condition. There are a few limitations of MC simulations that should be considered in the context of this review. First, the framework of the adsorbent is typically fixed for simplicity. This is warranted to some degree due to the topological complexity of dense amorphous microporous polymers, even with advanced moves. This assumption is only reasonable at low pressures in most systems, due to adsorbent induced changes in the host matrix. Current MC techniques are not adequate to address polymer relaxation in these cases. Thus, adsorbent-induced polymer relaxation must be accounted for using MD (section 2.3). Additionally, holding the framework fixed at high pressures is not recommended since local stresses within the polymer cannot be disregarded. Second, it is also common for simulated adsorption with these MC techniques to occur in both open and closed pores, which may be unrealistic in some cases. Thus, it may be necessary to apply additional constraints to the MC steps to, e.g., block off the inaccessible pores. Finally, it is important to mention that commercial software and popular open-source MC software are available that might be used for polymer applications. These software include, but are not limited to, Material Studio,212 MAPS,213 MCCCS Towhee,214 RASPA,215 and Cassandra.216 The computational efficiency for many of these software for gas adsorption has been recently benchmarked.217

2.2. Monte Carlo (MC) Simulations

In terms of particle-based simulations, MC is a statistical sampling technique based on the generation of random configurations. The randomness that is introduced into the system allows for efficient exploration of microstates, even for kinetically slow processes. New configurations are generated stochastically by introducing Monte Carlo “moves”, such as translation, rotation, insertion, deletion, swap, etc. The system has no time component and no “memory” of previous microstates, except for the last configuration. The newly generated configuration is accepted when the new state is more probable than the previous state.210 If the new state is less probable, the new configuration is accepted with some probability acceptance criteria, which is defined based on the difference between the energy of the “old” and “new” states. If the new state is not accepted, then the previous state is accepted again. For a large number of MC steps, the equilibrium states are the most probable states and the equilibrium properties can be obtained by averaging properties from several configurations, which refers to an ensemble average. A complete discussion on MC simulations can be obtained from molecular simulation textbooks.161,211 For gas capture and separation applications, MC can be used to obtain many relevant properties, such as simulated adsorption isotherms. Two ensembles are usually selected, the grand canonical (μVT) or the constant pressure Gibbs (NPT-Gibbs) ensemble, which are referred to as Grand canonical Monte Carlo (GCMC) and Gibbs ensemble Monte Carlo (GEMC), respectively. GCMC is most widely used and the specification of chemical potential, volume, and temperature are required. During adsorption, the chemical potential is the same between the gas inside the polymeric matrix and the gas in the external reservoir. In other words, gas molecules enter and leave the polymer at equal rates at equilibrium. At high pressures, bulk gas phase simulations should be tested to ensure that the adsorption is performed at the expected condition for a given chemical potential. The MC moves for GCMC may include translation, rotation, insertion, deletion, etc. For GEMC, two simulation boxes are required: one for the polymer and one for the gas phase. Pressure is a direct input for GEMC simulation, which is more convenient than the chemical potential. The volume of the gas box is adjusted until the specified pressure is obtained. Besides translation and rotation moves of gas molecules, GEMC also uses swapping moves for gases between two boxes. At the end of the simulation, the

2.3. Molecular Dynamics (MD) Simulations

MD is a particle-based simulation technique that mimics the motion of atoms and molecules within the system. Contrary to MC, MD is a deterministic or time-dependent technique and therefore can be used to obtain dynamic properties such as diffusivity, viscoelastic properties, etc. MD generates configurations by numerically solving Newton’s equations of motion using an integration scheme such as the velocity-Verlet algorithm. Calculations for the new position and velocity of each particle in the system is discretized into a small time step, which are typically around 1−2 fs in atomistic simulations, based on the force on a particular atom. This force is obtained by differentiating the energy of the system, which is directly related to the force field equations. Although MD can be significantly slower than MC because the system must follow a specific trajectory using a small time step, the implementation is significantly simpler for complex or large molecules, making it practical for simulating polymeric materials. The average properties obtained from an equilibrated MD simulation are equivalent to average properties obtained from an equilibrated MC simulation based on the ergodicity hypothesis, which states that time average and ensemble average are the same. For a detailed discussion on MD techniques, the reader is referred to simulation textbooks.161,211 MD is a versatile tool for simulating CO2 capture and separation in microporous polymers. As discussed in section 3.1, construction and equilibration of microporous polymers in silico rely heavily on MD. When modeling gas diffusivity in an amorphous polymer matrix, MD can be used to obtain meansquared displacements (MSDs), which is directly proportional to the diffusion coefficient of the gas within the framework. MD can also be used to account for sorption-relaxation behavior in materials during gas adsorption. Several studies have used combined or hybrid MC/MD to simulate framework flexibility in crystalline microporous materials during adsorption.215,218−223 However, the technique has yet to be widely 5494


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Figure 5. MC-based polymerization using the recoil growth algorithm. In this algorithm, a short fragment is randomly placed into a simulation box. Next, the new growing direction is attempted until a nonoverlapped configuration is found. If a nonoverlapped configuration is not identified, the chain may retract to a specified length, and the growing process is attempted again. The overall process can be repeated until a fully grown polymer is obtained.

equilibration techniques. Several reviews on modeling approaches are available for amorphous polymers, especially for nonporous, mesoporous, and macroporous polymers.236−239 This section focuses particularly on microporous polymers and discusses the more successful modeling approaches. 3.1.1. Approaches for Structure Generation. The early approach to constructing amorphous polymers was devised by Theodorou and Suter (TS method).240,241 The initial estimate of a polymer structure is built in a periodic box based on probabilities for chain configuration (e.g., tacticity) and chain conformation (e.g., sequence of rotational angles). The probabilities for the MC algorithm were drawn from Flory’s conformational statistics of rotational isomeric state theory (RIS theory).242 One of the most crucial improvements by the TS method was the incorporation of long-range interactions into the RIS conditional probabilities in order to obtain a realistic initial guess. Most importantly, Theodorou and Suter were the first to simulate an amorphous polymer at a high density of a glassy state. The TS method was first used on polypropylene, a relatively simple polymer, yet in the past 30 years it has been successfully used on more complex polymers. In fact, it is still the most widely used approach for constructing amorphous polymer models today. Since its introduction, it has been extended to several types of polymers with a higher degree of complexity than those explored in the original work, including flexible chains in the rubbery state and rigid chains in a glassy state. Many of the polymers presented in section 4 were generated from this TS method.236,237,243−245 The popularity of the method has been facilitated by its incorporation into commercial software, such as Materials Studio212 and MAPS.213 Other MC-based approaches for building polymers include recoil growth,246−248 configurational-biased MC,249−251 connectivity-altering MC,252−254 rotation MC,255,256 latticebased,257 hybrid pivot MC/MD (PMC-MD),258 and random walk polymerization.259,260 A comprehensive discussion of simulations methods for nonmicroporous polymers can be found elsewhere.261 A schematic illustrating a Monte Carlo

used in amorphous microporous polymers. One reason is that most polymer studies performed adsorption at low pressures and assumed that the framework flexibility was negligible in order to avoid expensive MC/MD calculations. A few examples of studies that combined MC and MD for gas capture in polymers are discussed in section 3.2.7. For researchers that are interested in performing MD simulation, commercial software (e.g., Material Studio,212 MAPS,213 Materials Science Suite,224 etc.) and open-source packages such as LAMMPS,225 NAMD,226 DL_POLY,227 GROMACS,228 AMBER,229 and CHARMM230 are available.

3. CONSIDERATIONS FOR MODELING MICROPOROUS AMORPHOUS POLYMERS 3.1. Molecular Models of Amorphous Polymers

The construction of molecular models for amorphous materials is a challenging task because no experimental measurement can provide the precise coordinates of all atoms within the system. As such, advanced techniques are required to generate reasonable starting structures for molecular simulations, which can then be equilibrated. In general, techniques to generate amorphous structures have been divided in the so-called “reconstruction” and “mimetic” approaches.160 On one hand, reconstruction methods create molecular models to match experimental data, such as structure factors or gas adsorption isotherms. Reverse Monte Carlo, for example, optimizes structures iteratively until sufficient agreement with experimental data is achieved.231,232 These types of approaches have been used for several polymeric systems.233−235 However, reconstruction methods are limited to cases where sufficient experimental data is available. One the other hand, the “mimetic” method uses molecular simulations to model processes following, to some extent, the synthesis of the material.160 These approaches are limited and based on our understanding of the chemical and physical processes. As the need to better understand a range of polymeric materials has grown, so has the development of structure generation and 5495


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Figure 6. Polymerization of a linear polymer using the force field assisted random walk algorithm. The new monomer is placed near the previous growing chain. Next, a new bond is generated between the old chain and the new monomer to mimic polymerization. Once a new bond is formed, energy minimization and molecular dynamics are performed to avoid an energetically unfavorable configuration. The process can be repeated until an intended molecular weight of the polymer is achieved (from ref 259, and licensed under CC-BY).

Figure 7. Example of a simulated polymerization for generating an amorphous cross-linked polymer. (i) Monomers are randomly packed into a simulation box with periodic boundary conditions. (ii) Simulated polymerization is performed by connecting linker atoms L1 and L2. (iii and iv) Equilibration and simulated cross-linking is performed by creating bonds between C1 and C2. (v) Equilibration at a predetermined condition, such as 300 K and 1 bar to obtain the final structure. Adapted with permission from ref 287. Copyright 2014 American Chemical Society.

based polymerization using the recoil growth algorithm is shown in Figure 5. In this algorithm, the polymers are generated according to a predetermined angle and dihedral distribution. The monomers are grown sequentially based on Monte Carlo moves through the available space within a simulation box. If an overlap is detected, a few monomers are deleted and regrown at a different starting point. The procedure is repeated until a satisfactory number of polymer chains and molecular weight is obtained and subsequently relaxed. In the force field assisted random walk polymerization, each monomer

can be added to the end of the chain while accounting for interand intramolecular interactions, which leads to bias selfavoiding walks (Figure 6). Energy minimization and MD steps can be executed throughout the chain growth process to ensure that energetically favorable configurations are obtained. In general, all of these procedures can have highly controlled chain length, tacticity, monomer composition, and polydispersity. In these MC approaches, undesirable artifacts during polymer construction such as ring catenations and spearings are 5496


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examples of works that employed simulated polymerizations are discussed in section 4. Several open-source and commercial software are available for building amorphous polymers today. Those freely available to the public include Polymatic,280,288 nuSIMM,289 and pysimm259,290 developed in the Colina group, as well as Polymer Modeler from the Strachan group.260,291 Other packages that have a focus on building polymers include, but are not limited to, Assemble!,292 EMC,293 OCTA,294 and mBuild.563 Additional codes that can aid in constructing polymers include, but are not limited to, LAMMPS,225 Amber,229 HOOMD-blue,295 Moltemplate,296 Avogadro,297 Packmol, 2 9 8 DL_POLY, 2 2 7 VMD, 2 9 9 TopoTools, 3 0 0 Atomsk,301 and ATB.302 Commercial software include, but are not limited to, Material Studio,212 MAPS,213 MedeA,303 Materials Science Suite,224 and SCIGRESS.304 The capabilities of these packages can be widely different and may need to be integrated through pre/post processing in order to complete a specific task. Additionally, they require different levels of expertise and interested users should consult with their manuals directly. 3.1.2. Structure Equilibration. It is essential that atomistic models for amorphous polymeric materials represent the physical molecular arrangement as close as possible to reality to obtain meaningful data. As discussed above, polymeric models are often constructed under conditions that are not realistic for efficient model generation (e.g., lower density packing), and thus, a procedure to translate the initial model to a physically representative model is important. Structure equilibration is an important process for obtaining a final simulated polymeric structure, at specific conditions, that is consistent with experimental properties. The equilibration process is considered to be challenging, especially for amorphous glassy polymers, due to the long relaxation times required. It is worth noting that, although the term equilibrium is commonly used for the relaxation of the molecular structure to a physically representative state, the polymer model is not in true equilibrium. One common strategy to relax the molecular model to a more physically meaningful structure is a sufficiently long molecular dynamics simulation in the canonical ensemble (constant NVT) or isobaric−isothermal ensemble (constant NPT). For example, a polymer model may be created at a low density, then a molecular dynamics NPT simulation at the final pressure and temperature (e.g., 1 atm and 300 K) would be executed until important properties remained stable and appeared to reach an equilibrated state.262 This simple approach works well enough for polymers with flexible backbones and faster relaxation times; however, some models can be trapped in a metastable state and take prohibitively long times to relax.245 As a result, MD-based procedures can be finetuned until the experimental target properties are observed. The strategies can include cycles of stepwise heating/cooling, compression/decompression, variable timesteps, scaling conformational energy, scaling/modifying nonbonded interactions, and adding geometry optimization procedures.262 Note that the extremely high temperatures and pressures typically used in the simulations during equilibration have no physical meaning and are only employed in order for the system to explore new configurations and escape from trapped local minima. Additionally one should consider what model property is being evaluated to determine the accuracy of the model. For example,

prevented by either packing at low density or packing with small molecules (methanol, Si atoms, or CO2).262−265 Modeling polymers with complex topologies and large steric effects, such as those common in microporous amorphous polymers, can be challenging for MC-based construction techniques, particularly as implemented in commercial software packages. For example, the nontraditional ladder backbone of PIMs requires two bonds to be formed with the addition of each new monomer. Using the MC methods in Materials Studio, several studies have generated linear chains of PIMs with only one of the two bonds connected in the ladder backbone, the second bond of which was manually connected after the fact.266 However, this can be a time-consuming and inefficient process for building polymers, particularly in larger simulations or when screening a large number of systems. The connectivity of extensively cross-linked polymer networks also poses difficulties for MC methods. To generate structures of HCPs, for instance, Cooper, Tan, and co-workers constructed representative network clusters that were then packed into periodic simulation boxes to obtain bulk samples.113,140,267−270 In some cases, additional cross-links within the network were added “by hand” after the initial packing of the clusters. As indicated by the authors, these models were often “overly simplistic” with the use of limited representative structures,113 as well as a discontinuity of the network between discrete clusters. These examples highlight the need at the time for polymer construction methods that could be generalized for a broader range of systems and that required less simplistic assumptions when considering complex topologies of extensive networks. Additionally, a generalized methodology would enable an efficient and large-scale automatization of materials construction and screening, which is currently needed. An alternative approach is to perform a simulated polymerization during MD simulations, which is similar to the experimental synthesis to some extent. Generally, monomers are packed into a simulation box and allowed to “react” during MD simulations (Figure 7). It is worth noting that these methods do not actually simulate reactions. That is, they are not implemented with the use of quantum mechanics (QM) or reactive force fields in order to realistically capture the formation or breaking of chemical bonds.271−277 Instead, the reactions are artificially performed by making new bonds when the “reactive sites” are within a specified cutoff.278,279 Other bonding criteria can also be enforced to place restrictions on bonding events280 or mimic monomer reactivities.281,282 A key advantage of simulated polymerization methods is that it can be implemented in the same way regardless of the complexity of connectivities of the polymer system (e.g., linear, cross-linked, branched, and network). This technique can also handle highly rigid and bulky polymers very well, as any overlap will be avoided during the MD steps. In addition, it can be used to help examine effects of processing parameters in comparison with synthetic routes.283,284 Simulated polymerization approaches have become increasingly popular in the literature, particularly as growing computational resources make more intensive MDbased methods more tractable. Initially, these methods were widely used for the simulations of epoxy resins and thermoset polymer.285 Abbott et al. extended the use of simulated polymerization methods to amorphous microporous polymers, demonstrating the generality of their Polymatic code to a broad range of polymer classes, including linear polymers with traditional and ladder backbones,280 as well as network polymers cross-linked in one286 or two steps.287 Several 5497


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system as described by Karayiannis et al.245 This procedure is in contrast with earlier equilibration methods that employed jumps in pressure of several orders of magnitude within a single step, including only one decompression step from a high pressure. This has been shown to work well for simple polymers, but it is not appropriate for amorphous microporous polymers. Another strategy includes multiscale modeling, in which the atomistic polymer system is coarse-grained for equilibration and subsequently reverse-mapped back to the atomistic model after the relaxation process (Figure 8).326−331,564 The advantages of

densities, pore volumes, and structure factors are commonly used as discussed in more detail in section 3.2. One such equilibration method for generating realistic densities for amorphous microporous materials is the so-called compression/decompression or 21-steps equilibration (Table 2).305 One key advantage of this approach is that it does not Table 2. Compression/Decompression Methodologya step 1, 2 3 4, 5 6 7, 8 9 10, 11 12 13, 14 15 16, 17 18 19, 20 21

ensemble NVT, NPT NVT, NPT NVT, NPT NVT, NPT NVT, NPT NVT, NPT NVT, NPT

NVT NVT NVT NVT NVT NVT NVT

conditions

duration (ps)

Tmax, Tfinal Tfinal, 0.02 × Pmax Tmax, Tfinal Tfinal, 0.6 × Pmax Tmax, Tfinal Tfinal, Pmax Tmax, Tfinal Tfinal, 0.5 × Pmax Tmax, Tfinal Tfinal, 0.1 × Pmax Tmax, Tfinal Tfinal, 0.01 × Pmax Tmax, Tfinal Tfinal, Pfinal

50, 50 50 50, 100 50 50, 100 50 50, 100 5 5, 10 5 5, 10 5 5, 10 800

a

Adapted with permission from ref 305. Copyright 2011 American Chemical Society.

require a target property such as density to be defined, which is beneficial for predictive simulations and large-scale screening efforts. The methodology of the compression/decompression scheme includes alternating NVT and NPT cycles at increasing temperatures and pressures, short cycles of restricted decompression, followed by a relatively “long” NPT simulation at the temperature and pressure of interest. As one can infer, the number of cycles, step durations, temperatures, and pressures can be changed as necessary for a given system of interest. The compression/decompression methodology laid out in Table 2 is our recommendation for amorphous microporous polymers based on a thorough analysis of different potential schemes and validation for a variety of systems. Note that it is not required to iterate the scheme until the simulation and experimental densities are matched. Instead, the equilibration process ends when MD simulations are completed as shown in the table (∼1.5 ns) producing microporous polymers with well-relaxed structure. This methodology has been used to equilibrate various amorphous materials, such as PIMs,305−313 polyamides membranes, 314 cross-linked polymers, 287 HCPs,283,284,315 CMPs,316 and many others.80,317−325 The success of the compression/decompression scheme is based on several strategies. The high temperature and pressure are used primarily to relax out the metastable polymer conformations, which for rigid polymers require a significant amount of energy to overcome. We advise that a high temperature, well above the glass transition temperature, should be used to allow adequate fluctuations of the polymer chains during the equilibration. Large pressures are also required to overcome the high energy barriers of rigid polymers and bring the system to realistic densities quickly. It is important that a controlled compression and decompression process is maintained throughout the equilibration, such as through small discretized changes in pressure. In particular, a mild decompression prevents large stress tensor components and high levels of residual stress from being introduced into the

Figure 8. Mapping and reverse-mapping of a polymer system. An atomistic system of polymers can be generated by any method of choice as described in the text. The atomistic model can be mapped into a coarse-grained model to account for the long relaxation time of polymers. After an equilibrated system is obtained from long time simulation (microseconds to milliseconds), backmapping can be performed to obtain the atomistic system capable of providing details at the molecular level. Adapted with permission from ref 335. Copyright 2016 American Chemical Society.

multiscale approaches is that coarse-grained simulations can more easily reach long length- and time-scales important to adequately equilibrate polymeric materials. However, obtaining accurate coarse-grained potentials for chemically specific systems and the algorithms for mapping and backmapping are not always straightforward to implement, particularly as the complexity of the system is increased. It is therefore important that multiscale models are carefully chosen and validated. Nevertheless, multiscale methods are an emerging approach for investigating amorphous microporous polymers and membranes.332−334 For purely atomistic MD-based methods, the main challenge is to choose the appropriate equilibration scheme (relaxation/compression, thermalization, etc.) in order to achieve realistic structures. Currently, atomistic MD-based schemes can be implemented more easily in an automated way, as it works generally for polymers with different levels of topological complexity and does not require potentially timeconsuming development of coarse-grained potentials and mapping algorithms. 3.2. Characterization and Validation of Models

After achieving physically representative molecular models, the structures can be characterized and properties of interest can be measured. When available, comparison with experimental data can provide a validation of the models as well. If simulation 5498


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technique. For instance, PIM-1 films with different thickness and aged time can have densities between 1.061 and 1.092 g/ cm3.266 However, the skeletal density of PIM-1 can range between 1.056 and 1.4 g/cm3.266,337 Moreover, it may not be appropriate to use an “experimental density” as a target due to structural inhomogeneity within amorphous samples.305,338 For example, density at the nanometer scale may not be the same as density at the centimeter scale. Moreover, there are several related definitions of densities that must be considered during the comparison. For instance, density can refer to absolute density (also known as or closely related to true, real, apparent, or skeletal density) or bulk density (also known as envelope density).339 Absolute density uses the volume that excludes all pores and void spaces, while bulk density uses the volume of the whole sample. The absolute and bulk densities are typically obtained experimentally from helium pycnometer and the volume displacement method, respectively. Distinctions are also possible in measurements of pore volume, which may refer to total pore volume or total micropore volume. Pore volume measurements are also dependent on the molecular probe used, meaning that they measure only the pore volume accessible to that probe. Total pore volume and micropore volume are typically calculated from N2 adsorption isotherms using several techniques.339 Recently the use of CO2 adsorption isotherms, as well as other gases, has proven critical for the characterization of micropores.340,341 Densities and pore volume are related by the following equation (eq 4) where ρabs is absolute density, ρbulk is bulk density, and Vpore is pore volume.

models are not in reasonable agreement with experimental data, models should be reconsidered or adjusted as necessary. For example, poor agreement with experiment could be an indication that the chosen force field does not adequately capture the system being studied. In these cases, it may be necessary to test other force fields80,306 or modify the chosen force field to yield more accurate results, such as by including system-specific atomic charges from QM calculations317 or fitting new bonding parameters.173 In addition, incorrect structure or properties in the simulations could be the result of box size effects that have been artificially introduced by the use of simulation boxes that are too small. Alternatively, it is also possible that fundamental assumptions made during the generation of the atomistic models were incorrect, such as the use of ordered models for materials that have shown no longrange order in experimental characterization. All of these factors and others should be considered when evaluating the accuracy of simulations and validating results against experiments. Experimental characterization techniques commonly used on porous materials include several decades in accessible length scales, as shown in Figure 9. It is important to remember that

Vpore 1 1 = − m ρabs ρbulk

(4)

In simulation, bulk density (ρbulk) can be determined directly using the mass within the simulation box divided by the box volume. The pore volume can be determined by the Widom insertion method,342 which uses a helium probe to determine the available spaces within the sample and is consistent with a helium porosimetry measurement. If the simulated microporous polymers do not have pores larger than 2 nm, then the total pore volume is equivalent to the micropore volume (i.e., Vpore = Vtotal = Vmicro). As discussed at the beginning of this section, since experimental and simulated density may not represent a reasonable comparison, we do not recommend that the density be the only property used as validation. Several other properties should be pursued, and thus, the important and relevant techniques for microporous materials are further discussed. 3.2.2. Surface Areas. A common method used to determine the porous material surface area is known as the Brunauer−Emmett−Teller (BET) theory.343 It is typically applied to an adsorption isotherm of nitrogen at 77 K but can also be applied to isotherms for other gases such as CO2. The calculation of the BET surface area is relatively straightforward, which, in part, explains its pervasiveness in the literature. Most commercial equipment has the BET surface area calculation already incorporated in it and facilitates comparison with other materials. The BET theory builds on the Langmuir theory while including multilayer adsorption. In Figure 10a, point B identifies the isotherm’s “knee”, which is believed to correspond to a monolayer coverage of the gas on the material’s surface. Figure 10b shows the process of adsorption, which includes the monolayer formation and pore filling. If these assumptions

Figure 9. Commonly used characterization methods for porous materials.336 For the interest of microporous polymers, studying the porosity with less than 2 nm scale relies on a few indirect techniques, which present a significant challenge when attempting to compare the simulated sample with an experimental sample. Reprinted courtesy of the National Institute of Standards and Technology, U.S. Department of Commerce. Not copyrightable in the United States.

challenges lie in the smallest length scale (50 nm pore sizes) are considered outside the scope for this review. Special attention is given to the simulation-based design and characterization of microporous polymers and their improvements in terms of CO2 storage capacity, adsorbent selectivity, membrane permeability, and membrane permselectivity. Studies on amorphous microporous polymers using molecular simulations that did not involve CO2 are also excluded from this review. Moreover, we mainly focus on several classes of recently emerging materials that are promising for CO2 capture and separations such as polymers of intrinsic microporosity (PIMs), porous aromatic frameworks (PAFs), hyper-cross-linked polymers (HCPs), conjugated microporous polymers (CMPs), thermally rearranged polymers (TRPs), and mixed-matrix microporous polymers (MMPs). Although this review concentrates on the progress made by atomistic molecular simulation of microporous amorphous polymers, we acknowledge the significant progress that has also been made for conventional polymers within the past few decades. Atomistic simulations have been used extensively for more conventional polymers for gas membranes such as polyisoprene, polyethylene, polypropylene, polystyrene, polyester, poly(ether imide), polysulfone, polycarbonate, poly(phenylene oxide), polyimides, polyphosphazenes, siliconcontaining polymers (e.g., PTMSP), polyacetylenes, and Teflon. These types of polymers have been comprehensively reviewed in several book chapters.236,237 It is important to note that the techniques described in the present review can also be applied to these conventional polymers. Many of these works constructed amorphous polymers through atomistic molecular simulations in order to investigate transport and free volume properties, which were found to be beneficial for direct comparison with experimental data.262,460,461 Among these conventional polymers, some polyimides and PTMSP are worth mentioning, since they are considered as high permeable polymers, which is crucial for gas separation 5507


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analyzed using the proposed V_connect and R_max approaches (Hofmann−Heuchel method).263 Both methods relied on a fine grid that contains the information about “free” and “occupied” points. V_connect is determined by connecting “free” grid points based on similar neighbors, which can represent complex shape volume. R_max is determined by assigning “free” grid points based on the nearest local maxima, which represent local volume regions. For instance, R_max may break down complex elongated volumes from V_connect into smaller local sizes. Using the R_max approach, “hole” sizes of about 3 Å were found, in relatively good agreement with PALS measurements.470,471 From the V_connect analysis, large regions of connected free volume were found accessible to a hydrogen atom particle size. The results confirmed the high free volume nature of PIM-1, and similar structural characteristics have also been observed in other high permeability membranes such as PTMSP and Teflon 2400.263 For gas transport in this study, the Gusev−Suter transition state theory (GS-TST)391−393 was used, and the results significantly deviated from experimental values. As mentioned previously, this can be explained since the GS-TST was developed for small penetrants and not for large molecules with strong adsorbent− adsorbate interactions such as CO2. Moreover, CO2 was modeled as a soft, single site, chargeless, Lennard-Jones sphere instead of a more detailed quadrupolar, three site, linear molecule with partial charges. For CO2, the calculated solubility was higher (Scalc = 345 bar−1 versus Sexp = 69 bar−1) and the diffusion coefficient was 1 order of magnitude lower than experimental measurements (Dcalc = 0.22 × 10−8 cm2/s versus Dexp = 26 × 10−8 cm2/s). The analysis of dihedral distributions also showed unexpected in-plane backbone flexibility in the PIM-1 ladder structure. Although this work had some challenges in reproducing experimental values, it became a major influence of subsequent PIMs studies over the next decade. Following the original work,266 several other variations of PIMs with great potentials for gas separation and storage were synthesized and evaluated in silico. Fang et al.377,472 extended the simulation study to several PIM variants, such as PIM without cyano groups (PIM-7) and other functionalizations (e.g., trifluoromethyl, phenylsulfone, and carboxyl groups), and included other characterization methodologies (Figure 21). Instead of employing the GS-TST approach for solubility and diffusivity, the Widom insertion method was used to determine the solubility coefficient, which is equivalent to the Henry’s constant at infinite dilution. The simulated solubility coefficients significantly improved when compared with the values obtained from the GS-TST. The diffusion coefficients were calculated using the Einstein relationship from NVT MD for up to 20 ns and were well within the range reported by previous experimental work (Dexp = 26−120 × 10−8 cm2/s for CO2 in PIM-1).473,474 The trajectories of these MD simulations also showed trapping, jumping, and oscillatory behavior of gases within the polymers. Besides conventional pore characterizations such as FFV, void morphologies, and distributions, they also used radial distribution functions to identify interaction sites between CO2 and specific atoms within the polymers. In a subsequent study,377 they incorporated simulated wide-angle Xray diffraction, in which changes in the patterns indicate alterations in spiro-carbon distance (θ2 = ∼7), microporosity (∼14 < θ2 < ∼21), and chain-to-chain correlations (θ2 > ∼22) as shown in Figure 21. Ab initio calculations were used to determine binding energies (cyano: −8.96 kJ/mol, trifluor-

membranes. Both polyimides and PTMSP can have relatively high free volume with limited conformational changes due to the presence of bulky side group or restricted rotations in the backbone.127 Many polyimides are commercially prevalent, and molecular simulations are continuously being used to study and improve their performance.398,418,419,462−469 New innovations of polyimides with PIMs and TRPs derived from polyimides are discussed in sections 4.1 and 4.4, respectively. For PTMSP, historically, it has been considered one of the most important polymers in membrane applications, since it is an early example of a relatively high free volume polymer with good gas permeability. Although PTMSP possesses significant permeability surpassing the majority of polymeric membranes used in industrial applications, it suffers from significantly low gas selectivity. The use of atomistic molecular simulations to characterize structural and transport properties of these conventional polymers has been already summarized elsewhere;236,237 and thus the reader is referred to these references for further information. 4.1. Polymers of Intrinsic Microporosity (PIMs)

Polymers of intrinsic microporosity (PIMs) with potential for CO2 capture and separations have been explored using molecular simulations by several groups since 2008. Heuchel et al.266 were the first to provide molecular details of PIM-1 through the use of molecular simulations. They constructed three PIM-1 samples where 5 chains of 15 monomers each were packed in a periodic simulation box by using the TS method240,241 (Figure 20). To avoid ring catenation, CH4

Figure 20. In the top panel a PIM-1 repeat unit and atomistic model of a PIM-1 monomer are shown. The tail, head, and terminating hydrogen atoms for the monomer are shown as green, cyan, and yellow, respectively. The bottom panel shows a single polymer chain of 15 monomers that was subsequently used for packing. Adapted with permission from ref 266. Copyright 2008 Elsevier.

molecules were randomly distributed as obstacles, and the density was set to a predetermined value. The structural equilibration was performed using five stages of NVT and NPT MD, including annealing at 600 K, compression at 10 bar, and finally a 1 ns NPT MD at 308 K and 1 bar. The final polymer densities after equilibration and removal of CH4 molecules were compared with experimental densities and were found within an acceptable range (1.06−1.09 g/cm3). According to the authors, the PCFF171 was selected since the COMPASS 2.4172 was unable to sufficiently describe the planarity of this rigid polymer. The distribution of free volume elements was 5508


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Figure 21. (Left) Void morphologies of various PIM variants (PIM-1, TFMPS-PIM, and CX-PIM) are denoted by the blue regions. (Right) Simulated wide-angle X-ray diffraction (WAXDs) in various PIM variants. Adapted with permission from ref 377. Copyright 2011 American Chemical Society.

Figure 22. PIM-1 contains SBI and dioxane groups that can bend and flex to a certain extent. Replacing the backbone with ethanoanthracene (EA) and Tröger’s base unit (TB) groups increase rigidity and can be selective toward small molecules (H2 or O2) over large molecules (N2 or CH4). Adapted with permission from ref 481. Copyright 2013 AAAS.

omethyl: −5.88 kJ/mol, phenylsulfone: −12.52 kJ/mol, carboxyl: −13.29 kJ/mol) and to optimize structures between CO2 and various functional groups. The QM calculation indicated that a CO2-phillic group with a large binding energy, such as the carboxyl group (CX-PIM), should lead to the improvement of CO2/N2 selectivity, which was supported by experimental findings.475 PIMs with ethanoanthracene and Tröger’s base units (PIMEA-TB) have gained special attention, since the substitution significantly increased the rigidity and contortion of the polymer (Figure 22).139 The shape-persistent characteristic of PIM-EA-TB resulted in a higher microporosity, free volume, permeability, and permselectivity for several gas pairs. These promising experimental results have prompted several molecular simulation works for PIMs with Trö g er’s base

units.312,313,476−479 Similar approaches have also been used to construct and evaluate several other PIM variants, such as polyimides-based PIMs (PIM−PIs)312,435,480 and triptycenebased PIMs.312,476 The effects of spiro-centers and backbone modifications, such as functionalization or substitutions of various functional groups and heteroatoms, on CO2 capture and separations performance have also been investigated. Most of these studies confirmed the importance of the polymer chain rigidity, and many have provided recommendations for the design of new CO2 capture materials. Hypothetical PIMs have been synthesized in silico via atomistic simulations and the capability to virtually construct polymers, prior to actual synthesis, is critical for screening processes. For example, the hypothetical sulfur-containing PIMs (sPIMs and soPIMs) have been investigated for CO2/ 5509


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Figure 23. Microstructures and backbone rigidity of various sulfur-containing PIMs obtained from atomistic simulation after equilibration. It can be observed that the pore formation ability of sulfur PIMs is diminished. The porosity also decreases when converting from sulfur to sulfonyl PIM. Adapted with permission from ref 308. Copyright 2013 American Chemical Society.

CH4 separations (Figure 23).308 These PIMs were constructed using a Polymatic simulated polymerization approach instead of the TS method, as it has been shown that the simulated polymerization approach is well suited for ladder polymers. Since these polymers are hypothetical and have not been synthesized in the laboratory, experimental densities are not available as target properties. The study employed a predictive equilibration procedure that does not require experimental densities as an input as shown in Table 2 (21-steps compression/decompression). The sulfonyl-functionalized PIMs (soPIMs) have an improved CO2 loading capacity, heat of adsorption, and selectivity, especially at low pressures, due to an increase in framework polarity. The ability to construct amorphous polymers without experimental data inputs also allows a systematic approach in exploring design principles. In the following work by the same group, they focused specifically on spiro-center size, sulfonyl functionality, backbone length, and backbone functionality, and how these affect membrane permeability and permselectivity.310 The study proposed 14 hypothetical PIMs and evaluated membrane parameters using the solution diffusion model, free volume theory, and GCMC; these techniques preserve the accuracy of predictions and are

significantly faster than conventional MD-based approaches. At the time of publishing, this was the largest number of functionalized PIM structures to be simulated in one study. A novel approach in this study was that membrane permeabilities were calculated entirely from atomistic simulations and compared to experimental values, with the simulations falling within the range of values reported in the literature for PIM-1. Additionally, they concluded that dipolar functionalities and bulky spiro-centers would improve CO2/CH4 separations and higher fractional free volume would improve CO 2 /N 2 separations, some of which has the potential to surpass the 2008 Robeson upper bound.47 Other predictive works included the study of ionic backbone and extra-framework ions in PIMs such as ionomers of intrinsic microporosity (IonomIMs)311,482,483 or hyper-fluorination of PIM-1 (PIM-1f),307 for which, at that time, experimental data were not available. These chemical modification strategies were theoretically promising and, therefore, became ideal candidates for performing predictive simulation and screening by characterizing their structures and separation performance. The structural properties and selectivities from simulations had similar tendencies with the experimental works for both 5510


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Figure 24. Repeat units of (a) PIM-TMN-Trip (2D) and (b) PIM-TMN-SBI (3D). The atomistic structures obtained after energy minimization for PIM-TMN-Trip and PIM-TMN-SBI are shown in panels c and d, respectively. Free volumes obtained from a slice of 1 nm thick of 9 × 9 × 9 nm3 sample for PIM-TMN-Trip and PIM-TMN-SBI are reported in panels e and f, respectively. The free volumes are shown in blue, and the van der Waals surfaces from polymers are shaded in yellow. It can be observed that 2D PIM (PIM-TMN-Trip) has a higher free volume or microporosity than 3D PIM (PIM-TMN-SBI). Adapted with permission from ref 486. Copyright 2017 Macmillan Publishers Ltd.: Nature Materials.

Figure 25. (a) Snapshot from a simulation to study CO2 permeability through PIM-1 using nonequilibrium molecular dynamics. The external force was applied to the left boundary of the box. (b) NEMD trajectories of CO2 and He through PIM-1 as a function of time. Each point represents the location of gas molecules every 0.5 ps. The total time for CO2 is 3.4 ns and 80 ps for He (from ref 421, and licensed under CC-BY).

carboxyPIMs and IonomIMs.376,475,484,485 More recently, molecular simulations were used to construct a new PIM (PIM-TMN-Trip) that is ultrapermeable and highly selective surpassing the 2008 Robeson upper bound47 for H2/CH4, CO2/CH4, CO2/N2, O2/N2, and H2/N2 (Figure 24).486 It is important to note here that the simulations were performed independently from the experiments without target properties, and the results were consistent with experimental measurements such as PSDs, WAXS patterns, permeability, and permselectivity. Additionally, the simulations provided insights

into the understanding of how the concept of 2-dimensional chains can be used to obtain ultrapermeable robust membranes with a higher selectivity. Several creative approaches have been employed to study simulated models, such as polymer swelling in PIMs. Swelling behavior in PIMs induced by gas adsorption has been addressed through atomistic simulations by Hölck et al.412 Hölck and coworkers studied swelling behavior during gas adsorption in glassy polymers including poly(sulfone) (PSU), 6FDA-TrMPD polyimide (PI4), and PIM-1. The swollen polymers were 5511


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Figure 26. (a) Synthesis scheme of TZPIM from PIM-1 using [2 + 3] cycloaddition of aromatic nitrile and sodium azide producing tetrazole group. The atomistic structures of PIM-1 and TZPIM are shown in panels b and c, respectively, where possible hydrogen bonding is identified in TZPIM from molecular simulation. Adapted with permission from ref 386. Copyright 2011 Macmillan Publishers Ltd.: Nature.

constructed by packing the chains with gas molecules of interest at the experimental concentration. The key strategy was the use of the Dual Mode Sorption Model (DM) to predict CO2 and CH4 adsorption isotherms. The DM parameters (i.e., Henry parameter, Langmuir capacity, and affinity parameter) were derived from GCMC adsorption isotherms at unswollen and swollen reference states. The parameters from these two data sets were combined into one isotherm to effectively account for swelling by using a linearly weighted average. Based on this approach, the model was able to reproduce adsorption isotherms for CO2 and CH4 that are in very good agreement with experimental data even at high pressures. As mentioned previously, a combination of MC and MD should help address the sorption-relaxation and swelling behavior of polymeric materials during adsorption. Despite its importance to address swelling, combinations of MC and MD have not been practically implemented so far, due to their high computational costs for polymeric materials. Artificial swelling can also be a cost-effective approach to simulate swelling behavior which has been demonstrated for N2 adsorption in PIMs at 77 K.309 An interesting study on gas permeabilities was carried out by Frentrup et al., 421 where they explicitly modeled gas permeation in a high free volume polymer (PIM-1) and employed nonequilibrium molecular dynamics (NEMD) to study CO2 and He transport within the polymer matrix. The setup mimics the experimental procedure, in which CO2 was permeated through a thin slice of a PIM-1 membrane from a high pressure region to a low pressure region (Figure 25a). The solubility was obtained directly by monitoring the gas concentration within the membrane as a function of pressure, while the permeability was obtained directly as a function of the flux, the pressure drop across the membrane, and the membrane thickness. The simulated data were in good agreement with experimental results. The diffusion of CO2

across the membrane was compared to that of He, which crosses the membrane unimpeded (Figure 25b). In contrast, the relatively strong solid−fluid interactions between the organic matrix and CO2 provided a scenario where the solute has a relatively long residence time within the porous structure and advances at a pace that is roughly 1 order of magnitude slower, adsorbing as pockets of fluid within the cavities of the structure. Analysis of the pathways suggest that molecules within the polymer matrix spend a considerable amount of time in “random walks” throughout the extent of the available free volume. This observation suggests that the transport mechanism deviates from a simple “pore hopping” trajectory expected for a dense polymer as a result of exhibiting highly interconnected porosity. Dense glassy polymers usually exhibit a pore hopping diffusion mechanism, while structured materials with sieving and Knudsen-type separation mechanisms are at the other end of the spectrum. The utilization of molecular simulations as a complementary tool to enhance the fundamental understanding of the materials at the molecular level is pervasive in many experimental works. As discussed in section 3.3, one example is the use of atomistic simulations to interpret small-angle X-ray scattering patterns in order to enhance the understanding of structures of amorphous microporous polymers and their aging process.370,371 In terms of CO2 capture, several examples of such complementarity have been widely demonstrated. For instance, PIM membranes with a functionalized CO2-philic pendant tetrazole group (TZPIMs) can result in a superior CO2 separation performance (Figure 26).386 The atomistic simulation helped identify possible hydrogen-bonding between ether linkages and tetrazole groups in different chains. These hydrogen bonds were hypothesized to prevent polymer swelling induced by CO2. For other materials such as triptycene-based microporous polymers, several studies also used molecular simulation to confirm and 5512


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validate their experimental findings.140,487 The star triptycenebased microporous polymers (STPs) were shown to have high experimental BET surface areas (up to 1990 m2/g) and large CO2 capacity (up to 18.20 wt %) at 1 bar and 273 K.140 Although the simulation confirmed the width of pore channels as experimentally observed, the model overestimated surface area and pore volume due to the noninterconnected packets of occluded free volume. Simulations have also been used to compare samples before and after a specific treatment. For example, experimental studies found that, when a PIM-1 membrane was UV-irradiated, a significant improvement in selectivity of several gas pairs could be achieved.488,489 Atomistic molecular simulations were used to study the van der Waals and Connolly surface before and after treatment of ultraviolet irradiation in the presence of O2. One study argued that the fractional free volumes were significantly reduced due to polymer chain repacking and rearrangement after UV treatment, which improved gas selectivities.488 Simulations of PIMs that did not include CO2 capture could still be valuable to readers and thus are listed here.305,306,309,424,490−492 4.2. Porous Aromatic Frameworks (PAFs) and Hyper-Cross-Linked Polymers (HCPs)

Porous aromatic frameworks (PAFs) and hyper-cross-linked polymers (HCPs) are structurally similar and will be discussed in this section. Several groups have used molecular simulations to aid in the design and characterization of these materials that are promising for carbon capture. A series of PAFs have been modeled in silico based on the computational-led design approach using first-principle calculations and GCMC. Experimentally, PAF-1 was found to be extremely stable with a high BET surface area of 5600 m2/g.125 The optimal number of phenyl ring substitutions that maximize the surface area was initially identified by computer modeling, which subsequently led to the design and synthesis of PAF-1 with competitive CO2 capacity experimentally (1300 mg/g at 298 K and 40 bar), among other porous materials.125 The modification of PAF-1 by introducing various polar groups (e.g., acetonitrile, acetone, ethylamine, and tetrahydrofuran) has also been explored in silico.493 In this work, QM calculations with the MP2/TZVP level of theory were used to optimize the conformations and to calculate binding energies between CO2 and various functional groups (Figure 27). QM-led design suggested that dihydrofuran (DHF_PAF-1) is a good candidate and, indeed, resulted in the highest CO2 capacity (10 mol/kg CO2 at 1 bar and 298 K) and highest selectivities for CO2/CH4, CO2/N2, and CO2/H2 mixtures, among other functional groups considered in the atomistic simulations performed in that work. Computational simulations also guided another improved version of PAF, LiPAF-1, which was made by lithiation in order to enhance adsorption enthalpies.494 Here, atomistic simulations were used to characterize the pore size distribution of the material and to predict gas uptake using GCMC with a Morse potential for the gas molecules. A continuum model, termed Topologically Integrated Mathematical Thermodynamic Adsorption Model (TIMTAM), was used to obtain the potential energy for adsorption, adsorption isotherms, and ligand/cavity size, which allowed efficient exploration of the design space. Exceptionally, it was found experimentally that Li-PAF-1 was able to attain 22%, 71%, and 320% capacity increases for H2, CH4, and CO2, respectively, when compared with PAF-1. In another study, using a highly idealized crystalline model, a screening of PAFs was performed based on the difference of isosteric heats of

Figure 27. (Top) Optimized conformations and binding energy of CO2 with modeled functional groups calculated from the MP2/TZVP level of theory. The functional groups include (a) acetonitrile, (b) acetone, (c) methanol, (d) methyl acetate, (e) dimethylformamide, (f) dimethyl ether, (g) ethylamine, and (h) tetrahydrofuran. (Bottom) Corresponding atomistic structure of DHF_PAF-1. Adapted with permission from ref 493. Copyright 2011 American Chemical Society.

adsorption using GCMC simulations.495 The results showed that the relationship between selectivity and isosteric heats follows the Arrhenius-type equation. Computational studies have also been performed on microporous aromatic frameworks (mPAFs), which were synthesized experimentally based on Friedel−Crafts condensation of tetraphenylmethane (TPM) and formaldehyde dimethyl acetal (FDA).496,497 The simulated and experimental adsorption isotherms deviated significantly, even though the authors498 state that the force field in this work was optimized to correctly describe interactions between CO2 and PAFs. For example, the simulations predicted loading capacities of 125 and 210 cm3(STP)/g at 298 K and 1 and 10 bar, respectively, compared to experimental values of 38 and 136 cm3(STP)/ g.496 This large discrepancy indicates that the model and the experimental findings might be structurally inconsistent. Although PAFs have no long-range crystallographic order, several of the studies mentioned above assumed an idealized or diamond-like structure in their models.125,494−496 The comparison between the ordered PAFs model (idealized) versus the experimentally observed amorphous PAFs showed that various degrees of crystallinity can significantly affect predicted CO2 uptakes and gas selectivities.493 In this particular case, an amorphous model overpredicted CO2 uptake when compared with experimental results, indicating that the model can be further improved. Canti et al.497 explored various methodologies for constructing amorphous mPAFs by using the 5513


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Polymatic simulated polymerization.280 They explored various degrees of monomer complexity to obtain realistic pore size distributions and were able to improve the accuracy of predicted CH4 and CO2 uptake in mPAFs. A variety of HCPs have also employed aromatic-based tetrahedral monomers which are similar to PAFs (e.g., tetrakis(4-ethynylphenyl)methane and 1,3,5,7-tetrakis(4-ethynylphenyl) adamantane). For instance, several porous polymer networks (PPNs) have been shown experimentally to be promising for H2, CH4, and CO2 storage.123,499,500 PPN-4 was found to be one of the best amorphous microporous polymers with respect to BET surface area (6461 m2/g) and CO2 capacity (2121 mg/g at 295 K and 50 bar). Atomistic simulation using the UFF165 yielded surface areas that were consistent with experiments, even though the model was constructed with an idealized crystalline geometry. Selectivities for CO2/N2 and CO2/CH4 for these PPNs were estimated using the IAST. Since PPNs tend to have large CO2 capacity, MC and MD atomistic simulations of amorphous PPNs would be important when evaluating gas selectivity especially at high pressures to account for polymer swelling. Some covalent organic polymers (COPs) used tetrahedral monomers and have been shown experimentally to be inexpensive, thermally stable, and exhibited considerably high CO2 loading and CO2/N2 selectivity (S = 288.1 at 323 K and 1 bar).501 These naturally amorphous materials were modeled as disordered structures, and GCMC calculations were used to obtain CO2 and N2 isotherms. Moreover, quantum chemical calculations with RIMP2 were used to determine binding energies between CO2 and N2 with COPs (Figure 28). Even

experimental and computational approach. For example, microporous polyimides, polyaminals, and poly(Schiff base) networks were found to have high surface areas, high CO2 loading capacity, and favorable CO2 /N2 and CO 2/CH4 selectivity.503−505 High performing HCPs can also be obtained from trifunctional monomers, instead of the tetrafunctional monomers discussed above. The designs have been demonstrated in several COPs that possess many desirable properties as mentioned in the previous paragraph.506,507 Based on a similar design, amide functionalized microporous organic polymers (Am-MOPs) can selectively capture CO2 and have high chemical and thermal stability.508 Density functional theory calculations revealed that the high selectivity was due to the polar amide functional groups along the pore wall resulting in Lewis acid−based interactions with CO2. In other related structures, several hydrophobic polar frameworks were designed to maintain separation performance under harsh and humid conditions.509,510 These hydrophobic polar frameworks can achieve experimentally high CO2 loading, high CO2 working capacity, and good CO2/N2 and H2/CO2 selectivity. The desirable performance came from the hydrophilic− hydrophobic balance within the polymer and preferred configurations forming corrugated channels were obtained from Tight-Binding DFT calculations. Recently, JimenezSolomon et al.511 performed a synergistic study that employed synthesis, characterization, and atomistic simulations to design thin film membranes. Simulated samples of ultrathin polyarylates with enhanced microporosity and H2/CO2 selectivity approaching the Robeson upper bound47 (Figure 29) were constructed using Polymatic280 with the PCFF171 and partial charges obtained from the HF/6-31G* level of theory. The simulated samples were subsequently equilibrated using the 21step compression/relaxation scheme305 (Table 2). The analysis of molecular voids was performed using the Zeo++ software.451 The atomistic molecular simulations not only elucidated the interplay between the interfacial polymerization and the rigidity of the monomers but, moreover, were used to confirm the hypothesis that contorted monomers with noncoplanar orientation were responsible for the enhanced interconnectivity between voids. In addition to desirable gas separation, these polyarylates also demonstrated an outstanding performance for organic solvent nanofiltration. A simple building block with relatively straightforward chemistry can also produce hyper-cross-linked polymers with desirable properties. The reduction in monomer complexity during synthesis can have significant economic impact for industrial use. External cross-linkers have been used experimentally to “knit” several types of rigid aromatic building blocks, producing high surface area HCPs that can be amorphous or 2D layered materials.269,512 Simulations were used to elucidate pore structure and compare the surface energy of polymers constructed from amorphous and crystalline packing. Later, hyper-cross-linked aromatic heterocyclic microporous polymers for CO2 capture and storage were obtained using thiophene (Th-1), pyrrole (Py-1), and furan (Fu-1) with formaldehyde dimethyl acetal as an external cross-linker.270 Experimentally, the highest CO2 selectivity over N2 with remarkable CO2 storage capacity (S = 117 at 273 K) was found with Py-1. In this work, MC simulations were used to obtain a CO2 density map within the frameworks and predict CO2 adsorption along with its distribution of sorption energies. The models for the atomistic molecular simulations were con-

Figure 28. Binding energy between CO2 and representative units in COPs: (a) 1,3,5-triazine, (b) benzene, and (c) sulfur-bridges dimer of triazine and benzene. (d) The figure also shows a GCMC snapshot of CO2/polymer interaction confirming similar binding geometry of CO2 with a triazine-benzene dimer motif. Adapted with permission from ref 506. Copyright 2013 Wiley-VCH.

though COPs are amorphous, efforts have been made to utilize simplified crystalline models of these materials to accelerate the materials prescreening process.502 These simplified models were able to capture the relationship between the linkers’ structures, the polymer topologies, and the subsequent CO2 capacity. Other works, using different tetrahedral monomers, have also found promising materials from a combined 5514


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Figure 29. (a) Simulated structure of a polymer nanofilm produced by interfacial polymerization (TMC, trimesoyl chloride). (b) The choice of phenol monomers (BHPF, TTSBI, DHAQ, and RES) with various degrees of contortion. (c, top) These monomers can produce microporous polymers with various degree of interconnected (green) and disconnected pores (red) and (c, bottom) available spaces for different probe sizes (PAR, polyarylate). Adapted with permission from ref 511. Copyright 2016 Macmillan Publishers Ltd.: Nature Materials.

of systems. Several CMPs have been studied using molecular simulations for carbon capture applications. For example, a tetraphenylethene-based CMP (TPE-CMP) has been shown to have potential for CO2 storage and for light harvesting.519 Atomistic molecular simulations were used to validate the X-ray diffraction patterns, visualize monomer distributions within the resulting pore architecture, and validate CO2 adsorption through GCMC simulations. QM calculations were used to determine optimized geometries and binding energies between CO2 and the polymers fragments, revealing important π−π and hydrogen bonding interactions. The calculated binding energy between CO2 and TPE-CMP was around 30 kJ/mol, which was consistent with the reported experimental value. In this work, it was found that the energy of π−π interactions could be as high as 19 kJ/mol. Atomistic molecular dynamics were also used to obtain spatial density distribution maps of CO2 within the polymeric matrix (Figure 30). Later, the same authors further investigated a variety of conjugated and amorphous microporous polymers.520 A total of 10 simulated samples with diverse chemistries were constructed by building molecular fragments defined as nodes and linkers. The geometry of these building blocks was optimized using the B3LYP/6-31g(d) level of theory. Then, 4−60 oligomers were packed at low density and equilibrated using NVT and NPT MD cycles, and the density was adjusted until the calculated

structed from a combination of clusters, with the COMPASS force field,172 and the results were used to confirm Connolly surface area, Langmuir surface area, and micropore dimensions. In another case, the classic “Davankov-type” hyper-cross-linked polymers have also been investigated through atomistic simulations in terms of gas separation and storage.284 This particular type of HCP, poly(styrene-co-vinylbenzyl chloride-codivinylbenzene), can be synthesized by post-cross-linking by Friedel-Craft alkylation resulting in a highly cross-linked network with high surface area (up to ∼2000 m2/g). For instance, pore size tunability of hyper-cross-linked polystyrenes, using divinylbenzene in the micropore region has been investigated through simulations, a trait that is difficult to quantify in experiments.284 The results showed that, although the micropore size tuning capability was clearly observed, no improvement in gas storage or H2/CO2 selectivity was obtained in this region. Further reading on PAFs and HCPs, outside the context of CO2 separation and storage, can be found elsewhere.113,114,267,283,286,315,332,333,513−518 4.3. Conjugated Microporous Polymers (CMPs)

Conjugated microporous polymers (CMPs) could be considered as a subgroup of HCPs because the monomers typically have high functionalities, resulting in highly cross-linked amorphous structures. However, they are treated separately in this review due to the recent significant interest in these types 5515


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Figure 30. (a) Geometry of CO2 interactions with the framework from MD simulation. (b−e) Spatial density distribution map of CO2 in TPE-CMP at a specific node and linker at 0.1 and 1.0 atm. Adapted with permission from ref 519. Copyright 2014 American Chemical Society.

accessible surface area matched the experimental value. The Xray diffraction patterns showed a reasonable agreement with the experimental data available. The results revealed linear relationships between accessible surface area and density from these microporous polymers. A similar relationship was also reported for several PIMs.309 The slopes of the correlations were varied and can be categorized depending on the chemical constituents such as materials with C, H, and N versus materials with C, H, N, and O. The simulated adsorption isotherms of N2 at 77 K and CO2 at 298 K using GCMC and the calculated isosteric heat of adsorption (Qst) agreed well with experimental data, which indicated, together with the X-ray diffraction patterns, a reasonable representation of the actual materials. Moreover, GCMC revealed that the experimentally observed high values of Qst were related to cooperative capture of CO2 from multiple interaction sites within the polymer through hydrogen bonding, π−π interactions, and Lewis acid−base interactions (Figure 31). In a different CMP study, the multifunctional porous organic polymers (POPs) were designed based on a boron dipyrromethene core (BODIPY) for CO2 and H2 storage by Bandyopadhyay et al.325 These POPs were constructed using the Polymatic simulated polymerization algorithm280 and relaxed using a 21-steps compression and decompression scheme.305 Computational modeling was used to study structure−property relationships in these POPs. For instance, the model identified the effect of backbone rigidity, alkyl groups substituents, and interpenetration of polymer chains on free volume and solvent accessible surfaces. The authors found experimentally that changing the functional group on the repeat unit, from n-octyl to phenyl, resulted in at least a 10-fold increase in BET surface area (73 to 1010 m2/g), and the porosity essentially switched from mesoporous to ultramicroporous. In recent work, cyanovinylene-based microporous

Figure 31. Snapshots from GCMC simulation showing possible interaction sites for CO2 in (a) TSP-1, (b) TSP-2, (c) HCMP-1, and (d) Tr-NPI polymer. Adapted with permission from ref 520. Copyright 2016 American Chemical Society.

polymers have also been shown to be promising for carbon capture (Figure 32).521 These materials have experimentally tunable sorption enthalpies between 20 and 40 kJ/mol based on the content of the functional group. In order to obtain additional insights from simulation, the amorphous networks were constructed by joining monomers with various degrees of complexity, and the porosity was subsequently characterized. The binding energies between CO2 and functional groups of polymers were calculated using DFT. The results showed that CO2 strongly interacts with −CN, CC, and the phenyl ring 5516


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Figure 32. Models for cyanovinylene-based microporous polymers can be built from combining monomer fragments. This figure shows two types of polymers, which are P2 (top) and P6 (bottom). The right part shows the overlay of CO2 diffusion in P2 and P6. It is clearly observed that CO2 molecules were able to diffuse more freely in P2 than in P6 polymer. Adapted with permission from ref 521. Copyright 2017 Wiley-VCH.

Figure 33. Free volume shape analysis. The free volumes were assumed to have geometric shapes ranging between ideal spherical to elliptical profile. The critical characteristics include longer diameter (DL), smaller diameter (DS), least threshold diameter (Dth), and eccentricity of the ellipsoid (DS/ DL). Adapted with permission from ref 533. Copyright 2014 American Chemical Society.

imides (HPI) have been investigated at the molecular level using atomistic simulations.532,533 The solubility and diffusion coefficients were calculated using GCMC and NPT MD with the Einstein relation (eq 9), respectively. The trends for both solubility and diffusivity were consistent with experimental data; however, the accuracy of the diffusivity values deviated by several orders of magnitude depending on the gas. Despite these discrepancies, the structural analysis showed that the interconnected pores were responsible for higher permeability and diffusivity in TR-PBO. In this work, a beneficial approach was the use of an image analysis technique to show that these polymers possess a high fraction of spherical free volume elements based on eccentricity values (Figure 33). From this analysis, the smallest bottleneck in free volume elements was defined from a least threshold diameter and the authors were able to conclude that TR-PBO has elongated pore space and narrow bottlenecks, which corroborated the hourglass-shaped speculation made in the experimental work.131 In the following work, the diffusion of a CO2/N2 mixture in TR-PBO, using molecular dynamics to account for mutual gas diffusion, and

and can be further enhanced from cooperation of several fragments. MD also showed that different building blocks can significantly affect the diffusion coefficient of CO2, which has contributions from both variations in porosity and energy binding sites. Other experimental works have also employed molecular simulations to complement their results, such as the studies of acetylene gas mediated in conjugated microporous polymers (ACMPs),522 perylene based porous polyimides (PPIs),523 and conjugated microporous polythiophenes (PTTT, P-THIDT, and P-DTBDT).524 Many other works on CMPs have also provided useful information regarding structural generation and characterization of the polymeric samples but did not included CO 2 in their evaluations.268,316,525−531 4.4. Thermally Rearranged Polymers (TRPs)

Several studies have relied purely on atomistic simulations to enhance the understanding of the relationship between microstructure of thermally rearranged membranes and its relation with the separation performance. Thermally rearranged polybenzoxazoles (TR-PBO) and hydroxyl-containing poly5517


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Figure 34. (Left) PALS data showing tunability of microcavities in TRPs. (Right) Robeson plot of H2/CO2 showing various TR-PBOs with increasing performance as a function of temperatures. Adapted with permission from ref 134. Copyright 2012 Royal Society of Chemistry.

Figure 35. Void size distribution of PBI/ZIF mixed-matrix membranes (left). Density distribution of H2 (middle) and CO2 (right) in the PBI/1-cage ZIF-7. Adapted with permission from ref 543. Copyright 2012 American Chemical Society.

4.5. Mixed-Matrix Microporous Polymers (MMPs)

competing occupancy was studied at relevant conditions between 35 and 75 °C up to 10 bar.534 The simulated sorption isotherms were obtained using GCMC and the IAST with regression fits from the Langmuir and Dual-Langmuir models. The study accounted for the competitive sorption and diffusion of the CO2/N2 pair and showed that the uptakes and diffusivity can be drastically different in single gas and mixed gas conditions. Many studies have used molecular simulations to complement the understanding of several variations of thermally rearranged polymers for CO2 separations. For instance, some TRPs were shown to have excellent CO2/CH4 separation performance, including polyimides with ortho-positioned functional groups PIOFG-1 and TR-1.132 High CO2 permeability and robust mechanical properties were also found with thermally rearranged benzoxazole membranes spiroTRPBOs.535 In these works, molecular simulations provided free volume distributions, as well as the probability of angle and dihedral distribution at various temperatures, which were related to the mechanical properties and chain conformation. TR-PBOs with different backbone units (m-phenylene, pphenylene, and hexafluoroisopropylidene diphenylene) were also shown to provide the tunability of microcavities as suggested by atomistic simulations and PALS.134 In this work, the membrane with a superior performance for H2/CO2 separation that would exceed the Robeson upper bound was identified (Figure 34).

Mixed-matrix microporous polymer (MMP) materials that combine the advantages of inorganic materials with amorphous polymeric membranes have been experimentally investigated in recent years.536−542 Inorganic materials such as MOFs and zeolites can be highly selective of many molecular species, while polymer supports can lower costs and provide ease of fabrication at a large scale, and at the same time providing separation performance. Molecular simulations have also been used to gain molecular-level insights for these MMPs. One of the earliest works that employed molecular simulation to explore MOF/polymer membranes for H2/CO2 separations was performed by Zhang et al.543 in 2012. In that work, the MOF was represented by a zeolitic imidazolate framework-7 (ZIF-7). Polybenzimidazole (PBI) was chosen as the polymer matrix, and it was built with the PCFF using the TS approach.240,241 Since most simulated ZIFs used a rigid model, the development of a force field was required in this study in order to capture the framework flexibility (especially for the organic linkers). Several nonbonded and bonded parameters were adapted from the AMBER force field with QM derived charges, while equilibrium values were adjusted to reproduce experimentally observed lattice constants. In order to generate the ZIF-7/PBI membrane, the authors slowly created a space within PBI in order for ZIF-7 to be inserted through the use of dummy atoms and adjusting the LJ parameters. The membranes were equilibrated by two stages of MD that involved heating between 573 and 873 K. The simulated results 5518


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handful of molecular simulation studies. A PIM-1/graphene composite was designed with the idea that graphene could enhance permeability and adsorption kinetics for PIMs matrices (Figure 37).549 Interestingly, the model confirmed that structural properties (e.g., density, surface area, and PSD) and CO2 affinity were unaffected when graphene was introduced into PIM-1 in a 1:10 weight ratio. This observation was consistent with experimental CO2 isotherms measurements, in which the loadings were practically the same in the presence or absence of graphene, despite the visually observed change in surface roughness and color within the sample from yellow to black with 1 wt % graphene. Other than graphene, the effect of carbon nanotubes in PIM-1 has also been studied. A study by Golzar et al.550 investigated the role of functionalization in single-walled (SWCNT) and multiwalled carbon nanotubes (MWCNT) in PIM-1. The structural and transport properties evaluated in this work were density, glass transition temperature, X-ray diffraction, fractional free volume, diffusivity, solubility, and permeability. They found that SWCNT and MWCNT functionalization with polyethylene glycol (PEG) could improve membrane performance in terms of CO2 selectivity and permeability. In another molecular simulation study, both MOFs and PIMs were combined in order to improve the performance of the material. Specifically, atomistic simulations were used to gain understanding of the interfacial phenomena between a zeolitic imidazolate framework (ZIF-8) and a PIM-1 polymer (Figure 38).551 Similar to most composite materials, the understanding of the interface between a continuous and a dispersed phase at the molecular-level is paramount, as it can identify the mechanical properties and separation performance of the composite membrane. The study of Semino et al.551 focused on the models at the interface, with a significant effort used for the construction of MOF surfaces using QM calculations and geometry optimization. The PIM-1 polymer was built using the Polymatic simulated polymerization280 and relaxed with the 21steps compression/decompression scheme.305 The interface between ZIF-8 and PIM-1 was generated by bringing the unwrapped polymer in close contact with ZIF-8 and equilibrated in a “piston-like” fashion with MD by allowing the polymer to compress and/or expand in the z direction only. The study found preferential interactions between the −NH group in ZIF-8 and the −CN group in PIM-1, which lead to microvoids at the interface. Moreover, from a density analysis as a function of length in the z direction, it was found that the ZIF-8 presence could affect the structure of PIM-1 for as much as about 20 Å into the polymeric structure. Later the studies were extended to include PIM-EA-TB with ZIF-8 as well as surface defects.552,553 Through a similar analysis, they found that no specific interactions exist between the ZIF-8 and PIMEA-TB in contrast with the findings obtained earlier with PIM1. The role of defects on MOF surface was also negligible in terms of MOF/polymer interactions at the microscopic level.553 Other than ZIF-8, UiO-66 with PIM-1 was also investigated using molecular simulation with special attention at the interface, similar to the studies mentioned above (Figure 39).554 The objective of this study was to improve CO2 capture by efficiently dispersed, properly sized UiO-66 particles and amine-functionalization. From the simulation results, it was observed that amine-functionalized UiO-66 had a significantly larger adhesion energy than nonfunctionalized material (−72.2 versus −55.3 kcal/mol, respectively). Thus, the end result was a

showed that an increase in ZIF-7 content lead to higher fractional free volume (Figure 35, left) and improved mechanical properties, as quantified by geometric insertion and bulk modulus, respectively. Most importantly, the density map of gases from atomistic simulations clearly showed that the increase in permselectivity came from the CO2 being trapped within the ZIF-7 cages while H2 diffusivity was enhanced (Figure 35, middle and right). Other organic−inorganic materials that have been modeled using molecular simulation for CO2 capture include glycol/ZIF8,544 6FDA-DAM/ZIF-8,545 poly(vinyl alcohol)/HKUST-1,546 PEBA/MFI,547 and polyimide/MFI.548 Molecular simulations results from these studies have provided important interfacial phenomena understanding at the atomistic level. For instance, in the glycol/ZIF-8 study,544 the simulation results indicated that glycol can form a highly structured network through hydrogen bonding at the surface of ZIF-8 which was suspected to be the origin of improved CO2 capture efficiency. In the polyimide/MFI study,548 a rigidification of the polymer was observed at the interface with a thickness around 1.2 nm, which can improve CO2/CH4 separation. The densified region was about 30% more selective than the bulk polyimide region. Overall, the PI-MFI sample was about 16% more selective than the PI membrane and was able to surpass the Robeson upper bound for CO2/CH4. In a poly(vinyl alcohol)/HKUST-1 system,546 a coarse-grained model was developed based on atomistic simulations, while the interfacial properties were preserved. The coarse-grained approach is crucial since the MOF particles typically are nanometers to micrometers in size and coarse-graining will eventually allow more realistic membrane simulations in which MOF particles are embedded within the polymer matrix (Figure 36). PIM-based composite membranes have also gained significant attention in the past few years, including less than a

Figure 36. (Top) Polymer/MOF composite consists of poly(vinyl alcohol) and HKUST-1 in atomistic and coarse-grained models. (Bottom) Density profile of atomistic poly(vinyl alcohol) (black), coarse-grained poly(vinyl alcohol) (red), and HKUST-1 (orange). Region A has polymer penetration into MOF and region B is pure polymer. Adapted with permission from ref 546. Copyright 2017 American Chemical Society. 5519


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Figure 37. Visualization of the PIM-1 chain on the graphene sheet. It shows that PIM-1 chains arranged themselves on the graphene sheet in a parallel fashion (from ref 549, and licensed under CC-BY).

Figure 38. (Top) Representation of a MOF/polymer model. The mixed-matrix membrane was prepared by equilibrating a MOF/polymer system, allowing the polymer to compress and expand only in the z direction. (Bottom) The simulations suggested possible preferential interactions between −NH in ZIF-8 with both (a) −CN and (b) −CH3 in PIM-1. Adapted with permission from ref 551. Copyright 2016 American Chemical Society.

mixed-matrix membrane with enhanced selectivity without significant loss of permeability. Composite membranes have also been studied by using atomistic simulation calculations and phenomenological models.555,556 The approach can be cost-effective for predicting gas permeabilities in composite membranes with reasonable accuracy (Figure 40). For instance, a screening study of 360 ZIFs/polymer-based mixed-matrix membranes (15 ZIFs and 24 polymers) for several gas pairs (CO2/CH4, H2/CH4, and H2/ CO2) was performed using GCMC, MD, and continuum modeling, and candidates for the best separation performance were identified.557 A similar approach was also used to investigate the feasibility of using porous organic cages with

polymer matrices for H2/CO2, CO2/N2, and CO2/CH4 separations.558 Specifically, the results showed that the POCsbased mixed-matrix membranes generally have higher estimated permselectivity and could perform either at or higher than the 2008 Robeson upper bound. It is important to note that both of these works utilized theoretical models such as Maxwell and Bruggeman model to estimate permeabilities in their mixedmatrix membranes, because they only considered atomistically the crystalline component of the matrix. It is important to note that these studies did not actually have atomistic structures of the polymer matrix. Organic-based composites of polymer blends and polymers with ionic liquids have also been studied in the past. For 5520


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Figure 39. (a) Models for nonfunctionalized and amine-functionalized UiO-66 with corrugated (UiO-66-A and UiO-66-NH2-A) and flat surface (UiO-66-NH2−B). (b) Top geometry for UiO-66-A and PIM-1 composite. (c) Top geometry for UiO-66-NH2-A and PIM-1 composite. Adapted with permission from ref 554. Copyright 2017 Macmillan Publishers Ltd.: Nature Energy.

separation was recognized only when a nanofiller (ZIF-7) was added to the system. Molecular simulation can also be used to study the miscibility of polymer blends. For instance, the compatibility of commercial polyimides such as Matrimid, Torlon, P84 in hydrolyzed PIM (hPIM-1) was studied by constructing molar Gibbs free energy curves as a function of polymer fraction.562 Recently, ionic polyimides and ionic liquids composite membranes for CO2 capture and purification have been examined using atomistic molecular simulation (Figure 41).207 Three cycles of MC and MD were employed at low pressures to capture the system relaxation, during which gas loading capacity could increase up to 3 times the original uptake at a fixed density. The simulated CO2 and CH4 solubilities agreed well with experimental data across the low pressure range. Moreover, the results showed that the adsorption sites of CO2 and CH4 were shifted between ligand nitrogens and imidazolium ring nitrogens when ionic liquids were introduced into the system, which could affect permeability and selectivity. This work exemplifies the molecular detail that can be obtained from molecular simulations that should assist in the future design of polymer composites for CO2 capture and separations.

Figure 40. Predictability of MOF-based mixed-matrix membrane performance using a combination of atomistic and continuum approaches. The data include H2 (green), CH4 (blue), CO2 (black), and N2 (red) results. The identity line shows the equivalency of permeabilities between simulation prediction and experimental measurements. Adapted with permission from ref 556. Copyright 2016 Wiley-VCH.

5. CONCLUDING REMARKS AND OUTLOOK The impact and potential of atomistic molecular simulations for microporous polymeric materials have been discussed in this review. Significant accomplishments have been made in the past decade relevant to CO2 storage and separations, including new structure generation algorithms of amorphous polymers, equilibration protocols, and strategies for validating the atomistic samples. These achievements have empowered the

example, composite membranes consisting of poly(amide-bethylene oxide) (Pebax), poly(acrylonitrile) (PAN), and poly(trimethylsilyl)propyne (PTMSP) have been constructed using atomistic molecular dynamics.559 It was found that none of the composite membranes have selectivity greater than the pristine Pebax, following the well-known selectivity versus permeability trade-off.560,561 The improvement for CO2/CH4 5521


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Figure 41. (Left) Final structure of an ionic polyimide where the FFV is shown in gold. (Right) Radial distribution functions between CO2 carbon and nitrogen in an imidazolium ring (i-PI, ionic polyimide; IL, ionic liquid). Adapted with permission from ref 207. Copyright 2017 American Chemical Society.

and morphology of polymers. The role of backbone rigidity and bulky side groups and their ability to induce microporosity has been confirmed in many simulation studies, consistent with experimental works. The choice of monomers and how they translate to bulk structures and performance can also be captured through modeling. For instance, there is a significant advantage of using a 2D monomer instead of a 3D monomer for PIMs to produce membranes with exceptional permeability. Additionally, simulations have suggested that monomers that are contorted, rigid, or bulky appear to generate structures with improved CO2 capture and separation performance, as demonstrated in hyper-cross-linked polyarylates and thermally rearranged polymers. Despite the progress mentioned above, several challenges remain for molecular simulations of amorphous microporous polymers. First, the incorporation of polymer flexibility and dynamics of materials in response to CO2 and other guest molecules is one of the key features that should be accounted for. Most studies to date consider the systems as static, which might be an unrealistic assumption, especially at high pressures. In particular, phenomena such as swelling, plasticization, and aging are known to affect the properties of polymers in general. These effects can be significant depending on the rigidity of the amorphous microporous material and the conditions of the experiment. Thus, dynamics of amorphous microporous polymers should be considered when evaluating materials performance. However, this will likely require the development of new and advanced techniques due to the slow dynamics of polymers, especially for large simulation size. For instance, simulating swelling and plasticization at high pressures using atomistic simulations is prohibitively costly to use brute-force MD due to the long time scales of polymer dynamics. For short-time polymer relaxation, it might be possible to use hybrid techniques that combine MC gas adsorption simulations with MD simulations. In this hybrid approach, MC/MD cycles are repeated until equilibrium properties are converged. To empower this type of analysis, software should allow a seamless transition between MC and MD for polymeric materials. By capturing the dynamic response of a polymer to adsorbed CO2 molecules, the structural features of the polymer that limit swelling of CO2 at high pressures may be elucidated. Such insights can be exploited in the design of the next generation of

understanding of different complex problems, leading to significant progress in the design of new materials. Computational methodologies were reviewed, and recent progress on modeling approaches was highlighted. These strategies have facilitated controlled studies of a variety of polymeric materials with different pore structures and topologies. The availability of software has accelerated the progress in this research area, including a better understanding of specific atomic-level detail of the properties of microporous amorphous polymeric materials and mixed-matrices. Simulations have been utilized to help interpret and analyze experimental data including, for example, the assignment of features within small- and wideangle X-ray scattering patterns to structural features within the materials at the molecular level. The complementary approach of experimental and simulation analyses provides a useful understanding of the structures and properties of microporous materials. Moreover, predictive molecular simulations can enable an efficient route to supplement and guide experimental efforts in the design of new materials. A vast array of hypothetical materials can also be screened computationally to pinpoint the most promising structures for a wide variety of applications. Innovative utilization of molecular simulations can lead to significantly improved material performance in experimental studies, as demonstrated by numerous works highlighted in section 4. Exploring various functionalizations of polymers in order to enhance CO2 uptake and selectivity may be synthetically challenging and time-consuming in experiments. However, the testing of these functional groups can be done more rapidly and economically through molecular simulations. For PIMs, improved performance suggested by simulations includes substituting carboxyl, sulfonyl, and tetrazole groups into the framework. The role of ions, such as the incorporation of an ionic functionalized backbone and extra-framework ions, has been shown to lead to better CO2 capture performance. HCPs have also been improved through computational design, resulting in superior materials, such as dihydrofuran PAF, lithiated PAF, and cross-linked polypyrrole. For many of these studies, experimental works have also confirmed the predicted CO2 uptake and selectivities for numerous gas pairs. Besides chemical functionalization, molecular simulations can also provide valuable insights toward the atomistic conformations 5522


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actions correctly. The availability of accurate force fields for polymers that are compatible with force fields used for MOFs, zeolites, etc. is limited. One possible reason is due to the parallel growth of separate communities with different goals. Force fields parameters for such MMP systems have not been developed or extensively validated with experiments, which presents an urgent need. Once reliable force fields for MMP are readily available, molecular simulations of these types of materials will allow for the understanding of the effects of structural characteristics on material properties. For instance, we could model how concentration, structure/shape, and functionality are related to mechanical properties, aging resistance, and gas transport properties of materials. The possible design space of MMP materials is vast, and the frontend screening of these relationships is one area where simulations can provide tremendous value. Fourth, the creation of databases of thousands of amorphous polymeric microporous materials, such as the ones available for MOFs and zeolites, which can empower data mining for CO2 capture and separations, could be attainable within the next 10 years. From the databases, the community can establish and understand general structure−property relationships by combining the wealth of experimental knowledge and the atomistic simulations, leveraged by data mining tools and algorithms. It is important to keep in mind, however, that these databases can only be as good as the data contained within. Therefore, due to the complexity of these simulations, guidelines need to be established across the community to standardize methodologies to ensure that data are reproducible. The guidelines should include, for example, how to determine the minimum box size and the number of independent samples, how to choose and validate force fields, how to check if the parameters are transferable at a specified condition, etc. Additionally, the usefulness and versatility of data generated by computational efforts and laboratory experiments relies on the application of rigorous uncertainty analyses. These suggestions coupled with statistical tools would ensure the consistency and reliability of results, which are essential for useful databases. Although the contributions of molecular simulations of polymeric membranes to the field of CO2 capture and separations are undeniable, meeting the growing needs within the materials genome initiative (MGI) approach will only be possible with the development of high quality molecular simulations of complex polymeric materials. The MGI promotes a convergent interdisciplinary alliance between advance computational, experimental, and data tools, under an integrated research paradigm, which will be crucial to fueling the successful discovery of new materials. State-of-the-art computational approaches and tools are needed in order to accurately measure and predict structure, dynamics, and other relevant properties of microporous polymers using molecular simulations. These abilities to provide accurate and precise measurements and predictions are inherently required to advance the MGI effort. Additionally, open-source packages for molecular simulation that enable collaborative development and add-in contribution from independent groups will further accelerate the MGI goal. The end results will empower many cross-disciplinary collaborations that further enable new avenues for innovation in efficiently solving global challenges. In this review, we have shown several cases where quantitative agreement between carefully conducted simulations and experimental measurements is not only possible, but vital

structures to increase the industrial performance of gas separation polymeric membranes. For example, incorporation of polar functional groups will increase polymer−polymer interactions, which will reduce membrane swelling, but will also increase CO2 uptake by increasing the enthalpy of adsorption, in turn promoting the driving force for swelling. The complex interplay between multiple competing phenomena can be revealed simultaneously by simulations. Developing these quantitative structure−property relationships for polymer flexibility and dynamics in industrially relevant conditions (temperature, pressure, solvents, catalysts, as well as processing conditions) should be an aim of future simulations. Second, to utilize amorphous microporous polymers to their fullest extent, significant efforts in atomistic simulation must be used to address challenging phenomena. For instance, atomistic-detailed mechanisms of selectivities and diffusion of small organic molecules during permeation would provide important insights for the design of microporous polymers. Moreover, the relationship between bulk mechanical properties and the local degrees of freedom at the atomistic scale resolution is in its infancy, and the connection between the two should be established. Molecular simulations of tensile, shear, and dynamic mechanical testing will prove critical for the design of the mechanical properties of amorphous polymeric membranes, MMPs, and hollow fibers. Additionally, polymer and processing histories, such as aging, plasticization, effect of solvent exposure, effect of post-treatment, etc., should be accounted for in the simulation. These factors do have significant influences on the outcome of the microporous structures in experiments, resulting in a wide range of properties, which are not currently being captured systematically through modeling. Third, there have been considerable experimental efforts in recent years to develop mixed-matrix materials combining the advantages of microporous inorganic particles and amorphous polymers. Inorganic materials such as zeolites or MOFs can provide high selectivity for separation applications, while amorphous microporous polymers add the ease of synthesis and reduce cost for large area membrane processing, while still contributing to the separation process. Simulations of MMPs present several challenges as a result of the discrepancies of the size and time scales involved, such as chain mobility, pore blocking, and the sizable polymer−inorganic interface. Such simulations, however, would expedite the discovery of structure−property relationships that would enable the design of MMPs with improved gas separation performance. Even though a handful of works have shown that the potential knowledge that can be discovered from atomistic simulations on this area is vast, there is still a long road ahead. Researchers should be able to study thousands of polymer−inorganic combinations to elucidate the vital physical-chemical factors that control the performance of these systems. Through data mining, this goal could be obtained from a combination of atomistic simulations and experimental work to develop empirical correlations that can be used as predictive tools for de novo materials. Moreover, the fundamental understanding of gas adsorption and permeation properties at the interface of these MMP would require, for example, force field development and parametrization specifically for these organic− inorganic systems. This development is needed to accurately represent the structure and dynamics of the MMPs, where it is of critical importance to describe the polymer−polymer, polymer−inorganic, and inorganic−inorganic atomistic inter5523


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toward the design of the next generation of materials, which is essential for MGI. The following components are crucial to advance the field in the next 10 years: (i) powerful and integrated simulation approaches for in silico synthesis of amorphous polymeric systems and composites, efficient structure relaxation, reliable characterization methods of various properties, and large data analysis/management package; (ii) state-of-the-art and validated force fields; (iii) databases of microporous polymer structures, including predicted and experimental properties with standardized simulation guidelines; and (iv) tools for uncertainty quantification in simulation data and uncertainty propagation of tunable variables to predict outputs and compare with experimental values. These components will certainly accelerate the materials discovery of amorphous microporous polymers, as well as address major challenges discussed previously. With common goals, collaborations between communities with cutting-edge experiments and innovative simulations should be encouraged in order to make effective CO2 capture and separation materials a reality.

Mathematics and earned a Ph.D. in Materials Science and Engineering in 2014 from The Pennsylvania State University advised by Prof. Coray M. Colina. Kyle then joined The Dow Chemical Company in 2014 in the Packaging and Specialty Plastics Materials Science R&D group and is working on delivering innovative and sustainable polyolefin products. Coray M. Colina is Professor of Chemistry and Affiliate Professor of Materials Science and Engineering and Nuclear Engineering at the University of Florida since 2015. She was previously a faculty member ́ at Simón Bolivar University in Caracas, Venezuela and at The Pennsylvania State University, and obtained her Ph.D. at the North Carolina State University with Prof. Keith E. Gubbins. Her current research interests are in atomistic and coarse-grained simulations (including code development and distribution) for functional materials such as polymeric membranes, alternative ionic liquids, hydrogels and bioconjugates.

ACKNOWLEDGMENTS The authors thank Emily Goethe for her assistance in manuscript preparation and editing. This work was financially supported in part by the National Science Foundation (DMR1604376 and ACI-1613155) and the University of Florida Preeminence Initiative. G.K. contribution was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award DE-FG02-17ER16362, as part of the Computational Chemical Sciences Program.

ASSOCIATED CONTENT Special Issue Paper

This paper is an additional review for Chem. Rev. 2017, 117, issue 14, “Carbon Capture and Separation”.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]fl.edu. Tel: +1-352-294-3488.

REFERENCES

ORCID

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Lauren J. Abbott: 0000-0003-3523-9380 Kyle E. Hart: 0000-0002-8158-038X Coray M. Colina: 0000-0003-2367-1352 Present Addresses # AMA Inc., Thermal Protection Materials Branch, NASA Ames Research Center, Moffett Field, CA 94035. ∇ The Dow Chemical Company, 230 Abner Jackson Parkway, Lake Jackson, TX 77566.

Notes

The authors declare no competing financial interest. Biographies Grit Kupgan received his B.S. and M.S. degree in chemical engineering from Oklahoma State University. He is currently a Ph.D. candidate at the University of Florida and working under the supervision of Prof. Coray M. Colina. His research focuses on developing and characterizing amorphous microporous polymers such as hyper-cross-linked polymers and polymers of intrinsic microporosity for gas separation and storage through molecular simulation. Lauren J. Abbott received her Ph.D. in Materials Science and Engineering from The Pennsylvania State University in 2013 under the direction of Prof. Coray M. Colina. She was a postdoctoral appointee at Sandia National Laboratories from 2013 to 2016. Currently, she is a contractor with AMA, Inc. at the NASA Ames Research Center. Her research interests include the use and development of molecular simulation methods to improve understanding of polymeric materials at the nanoscale, in areas such as nanoporous polymers, network polymers, and polymer electrolytes. Kyle E. Hart graduated from Mercyhurst University in 2010 with a B.Sc. in Chemistry with minors in both Computational Science and 5524


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