Unraveling the Sorption Mechanism of CO2 in a Molecular Crystal

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Unraveling the Sorption Mechanism of CO in a Molecular Crystal without Intrinsic Porosity Nimish Dwarkanath, Sourav Palchowdhury, and Sundaram Balasubramanian J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b05999 • Publication Date (Web): 01 Aug 2019 Downloaded from pubs.acs.org on August 5, 2019

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The Journal of Physical Chemistry

Unraveling the Sorption Mechanism of CO2 in a Molecular Crystal without Intrinsic Porosity Nimish Dwarkanath, Sourav Palchowdhury, and S. Balasubramanian∗ Chemistry and Physics of Materials Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560 064, India. E-mail: [email protected]

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Abstract The facile uptake of CO2 gas in a non-porous molecular crystal constituted by long molecules with carbazole and ethynylphenyl moieties was reported in experiments recently. Herein, the mechanism of gas uptake by this crystal is elucidated using atomistic molecular simulations. The uptake of CO2 is shown to be facilitated by (i) the capacity of the crystal to expand in volume due to weak intermolecular interactions, (ii) the parallel orientation of the long molecules in the crystal and (iii) the ability of the molecule to marginally bend, yet not lose crystallinity due to the anchoring of the terminal carbazole groups. The retention of crystallinity upon sorption and desorption cycles is also demonstrated. At high enough pressures, near-neighbor CO2 molecules sorbed in the crystal are found to be oriented perpendicular to each other.

Introduction The design, synthesis and characterization of porous materials 1–4 to adsorb CO2 is of great research interest in order to reduce its anthropogenic release into the atmosphere. Amine solutions to absorb CO2 at the source of generation been employed for over more than half a century, 5 have nonetheless proved to be energetically expensive among other disadvantages. 6,7 Thus, alternatives to this technology are being actively sought after. In order to capture and regenerate CO2 in an efficient manner, a plethora of material types have been designed and studied. These include: Metal Organic Frameworks (MOFs) 8,9 constructed with metal ions coordinating with organic linkers, Zeolitic Imidazolate Frameworks (ZIFs) 10,11 a subclass of MOFs which are topologically isomorphic to Zeolites and allorganic Covalent Organic Frameworks (COFs). 12–15 ZIFs are microporous materials, many of which are good adsorbents possessing permanent porosity. MOFs are more tailor-made and can either possess micropores which are permanent or which can be activated by an external stimulus through a breathing phenomenon. 16–19 COFs are extended crystals and 2


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possess an advantage of higher gravimetric uptake than other materials categories, due to their all-organic nature, but can suffer from lower isosteric heat of adsorption.

Figure 1: Chemical structure of compounds (A) yl)phenyl)ethynyl)benzene and (B) 1,4-Bis(9H-carbazol-9-yl)benzene.

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1,4-Bis((4-(9H-carbazol-9-


Figure 2: Experimentally determined crystallographic unitcells of (a) A co-crystallized with benzene (A-form-I), 20 (b) crystal of A (A-form-II) 21 and (c) crystal of B. 20 The axes are shown for each unitcell. Labels of aromatic rings (red numerals) of A-form-II will be used in the analyses section in the article.

Nanoporous Molecular Crystals (NMCs) 22–25 are yet another class of nanoporous materials which are comprised of discrete organic molecules with non-covalent intermolecular interactions, unlike COFs which are also purely organic. A NMC could be held together by hydrogen bonding, 26–31 halogen bonding, 29,30,32 π − π interaction, 30 or a combination of these. 27,33 Calixarene based molecular crystals are also being considered for gas storage. 31,34,35 ptert-butylcalix[4]arene (tBC) is the most widely studied calixarene. The tBC molecule has a bowl like structure whose molecular crystal exhibits significant uptake of a variety of 4


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molecules, while retaining its crystal morphology 36–43 as well as by altering it. 36 But even the low density β0 phase of tBC does not contain channels wide enough to accommodate small molecules, also indicated by the negligible Brunauer–Emmett–Teller 44 (BET) surface area from N2 adsorption measurements. 45 Barbour 46 argues that sorption should be the sole criterion for a material to be called porous, thus making tBC porous. GCMC simulations which do not describe the process of guest uptake, but rather describes the thermodynamic equilibrium, show H2 molecules occupying only calixarene “bowls” in the low-density β0 phase of tBC. Other porous materials without apparent pores have also been reported. 25,30,31,47–50 Such materials are said to have “porosity without pores”. 22,46 Molecular Dynamics (MD) simulations of tBC show H2 mostly occupied in the calixarene bowls which occasionally diffuse through tert-butyl groups to another calixarene bowl. 51 Atwood et al. 52 reported a molecular crystal which underwent a phase transition from a high-density phase to a low-density phase by a mere application of CO2 or NO2 pressure. What sets it apart from other NMCs is that it neither contains empty channels nor voids within the constituting molecules, thus truly befitting the phrase “porosity without pores”. However, this phase transition occurs at very high CO2 pressures (at least 10 atm at 298 K). If a molecular crystal constituted by molecules without voids can uptake gas, what is the reason behind it? Can a molecular crystal constituted by flexible molecules, but with no intrinsic porosity take up CO2 ? This question was addressed in a recent work of Braulio Rodriguez-Molina et al. 21 who demonstrated high CO2 uptake (9.0 mmol g−1 ) in a densely packed molecular crystal of 1,4-Bis((4-(9H-carbazol-9-yl)phenyl)ethynyl)benzene, whose molecular structure is shown as A in Figure 1. In the same figure, another molecule B, which is similar to A, but without the intervening phenyl and ethynyl linkers is shown. Molecule A crystallizes in its pristine form as Form-II, the compound which exhibits a high uptake of CO2 . In contrast, the crystal of B does not show any CO2 uptake. PXRD experiments revealed that the crystallinity of A-form-II was preserved even after three sorption-desorption cycles of CO2 .

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A unit cell of A-(form-II) contains two A molecules whose backbones are parallel to each other. In Figure 2(b), it can be observed that phenyl rings labelled 1 and 3 are coplanar while the other (ring 2) is perpendicular to the former. Phenyl rings 1 of two neighboring A molecules are separated by about 5 Å. Phenyl ring 2 of one molecule faces ring 3 of the other in the unitcell, owing to the P -1 spacegroup of the crystal. Likewise, the carbazole group of one molecule with rings 4 and 5 faces the carbazole group with rings 6 and 7 of the other with a separation of about 4 Å. While A-(form-II) is solvent-free, the molecule has also been co-crystallized with the solvent, benzene, in a form denoted as A-(form-I). Through NMR experiments, it was shown that the central phenyl ring in A-form-II was flexible and underwent two-fold motion (either rotation or libration) about the axis along the backbone (Figure 2(b)) at ambient conditions, a process which is absent in the molecules in form-I. Furthermore, it was seen that lowering the temperature to 195 K led to slower dynamics (frequencies lower than 10−4 Hz) of the central phenyl ring in A-form-II. The higher uptake of CO2 at lower temperatures compared to that at 295 K was attributed to the restrained motion of the central phenyl ring at lower temperatures. The flexibility of the backbone of A based on soft ethynyl linkages was also believed to facilitate sorption. Both the accessible and inaccessible pore volumes of A-form-II estimated 53,54 with a probe molecule corresponding to the kinetic radius of CO2 (1.65 Å) is zero. Even if the rotation of the central phenyl ring behaves like a gate opening phenomenon to facilitate the sorption of CO2 , the dense crystal does not contain any pore for CO2 binding. Yet, the experimentally demonstrated uptake of CO2 by this crystal is rather high, which demands explanations on the microscopic mechanism of gas adsorption. Herein, using advanced computational methods, we elucidate the mechanism behind the high uptake of CO2 by the A-form-II crystal at a molecular level and also verify the retention of crystallinity after sorption-desoption cycles. Methods for both the objectives are described in detail in subsequent sections and in the Supporting Information. We also studied CO2 uptake and

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crystallinity of the closely related compound Bis(carbazole-9-yl)phenylene (B). It is of interest to study the B crystal and contrast its behavior against that of A-form-II because of the similarity in their molecular structures. Anticipating our results, we observe both the flexing of the rotor molecule in A crystal and an expansion of the crystal volume upon CO2 sorption. The orientation of the molecules in A being parallel to each other helps it in retaining crystallinity, while B lacks both these crucial attributes – its molecules being shorter, are much less flexible and their non-parallel orientations does not help the retention of crystallinity upon any CO2 uptake.

Methodology The CO2 adsorption isotherm 21 of the A-form-II crystal shows a nearly linear dependence of gas uptake on pressure. Grand Canonical Monte Carlo (GCMC) simulations carried out under constant volume conditions yielded no uptake, consistent with the absence of any intrinsic pore in the crystal. In lieu of constant pressure GCMC simulations, we found it easier to carry out constant pressure molecular dynamics (MD) simulations to study the loading of CO2 and consequent volume expansion of the A-form-II crystal. Subsequently, the results from NPT MD simulations were verified with independent µPT GCMC simulations as well. The experimentally determined adsorption isotherm suggests an uptake of 9 mmol/g of CO2 at 196K and 1 atm which corresponds to two hundred CO2 molecules in a simulation cell containing eighteen unit cells of A-form-II. Molecular Dynamics. The simulation cell consisted of 18 unitcells (3 × 3 × 2 supercell) with a total of 36 molecules of A. We allowed for the uptake of CO2 into it in a phased manner (see Figure 3). Five CO2 molecules were inserted at arbitrarily chosen spaces in the simulation cell with the constraint that they were at least 2.2Å away from any atom of the crystal and from any atom of other CO2 molecules. Later, constant pressure MD simulations

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at 196K were carried out. Subsequent insertions of CO2 molecules were carried out in steps of five molecules, followed by equilibration, until a total of 200 molecules in the simulation cell was reached. The reversibility of the gas uptake was checked as follows. After volume equilibration at each amount of loading, arbitrarily chosen five CO2 molecules were removed and then the volume was re-equilibrated; we call this process as unloading (or depressurizing). Volume equilibration consisted of three consecutive steps: Minimizing the energy of the system with respect to coordinates, a short NVT simulation for 100 ps, followed by NPT simulation in multiples of 5 ns until the volume converged. LAMMPS 55 (version 17 Jan, 2014) was used to perform the MD simulations. For details, refer sections S1.1 to S1.6 of Supporting Information.

Calculation of the PXRD pattern. Powder X-ray Diffraction (PXRD) patterns of the simulated system were calculated at each stage of loading and unloading and compared against experimentally reported data. Further, the retention of crystallinity of the sample was determined by comparing two PXRD patterns at a particular value of pressure — one obtained by iterative pressurization and another by further pressurizing and then depressurizing by five CO2 molecules (illustrated in Figure 3). At a particular pressure, the convergence of the PXRD pattern was confirmed by comparing the same obtained over time. PXRD patterns averaged for 1 ns centered at 3.0 and 4.5 ns for the last 5 ns of the constant NPT trajectory were used for this comparison. RASPA-2.0 56 was used to calculate the PXRD patterns. For details, refer section S1.7 of SI.

GCMC. Grand Canonical Monte-Carlo (GCMC) simulations were performed on the sytems at gas pressures between 0 and 1 atm. The framework coordinates and the simulation cell parameters supplied to the RASPA-2.0 56 program were obtained from the last frame

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Figure 3: Flowchart represents the process of loading (pressurizing) and unloading (depressurizing) of the crystals with with CO2 . Each block represents a volume equilibrated system at its indicated effective pressure (loading). Blocks with solid-line indicate systems obtained by iterative pressurization. Blocks drawn in dashed-line indicate the systems obtained on slight depressurization (by 0.025 atm or removing 5 CO2 molecules) of each iteratively pressurized system. Time-averaged PXRD patterns are compared between the systems connected by a double arrow (↔)

of the NPT trajectory of volume equilibration MD simulation described previously; CO2 coordinates were neglected. These µVT GCMC simulations were performed with a rigid framework and with insertion, deletion, translation and rotation moves of the adsorbate molecules. Furthermore, in order to verify the convergence of volume and to identify effects due to framework flexibility, osmotic ensemble (µPT) GCMC simulations were also independently carried out at each pressure. More information on these simulations are provided in Supporting Information S1.8.

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Results and Discussions Volume Expansion. The expansion of volume of the A-form-II crystal in order to (or upon) uptake CO2 can be rationalized as follows. A unit cell of the A-form-II crystal contains two rotor molecules. Assuming a close packed structure, an estimate of the mean volume of one rotor molecule can be obtained as half of the unit cell volume, which turns out to be 3

774.2 Å . Consider now the form-I crystal in which benzene molecules are co-crystallized along with the carbazole rotor. Again, assuming a close packed structure of form-I crystal, the mean volume occupied by an entrapped benzene molecule in the form-I crystal can be obtained from the volume of its unit cell and the volume of one molecule of A. This value 3

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is 135.3 Å which is very close to its mean volume of 148 Å obtained from the liquid phase of benzene at 20◦ C and 1 atm. Thus, the ratio of molecular volumes of benzene to CO2 is around three. During gas adsorption, we expected the volume of the simulation cell to behave in a manner similar to that of the above observation i.e., for the sorbent CO2 molecule to occupy as much volume in the sorbate A-form-II crystal, as in its neat condensed form. The behavior of volume versus CO2 pressure in the process of loading and unloading in the A-form-II system obtained from MD simulations is shown in Figure 4, where the ordinate is normalized by the average volume of the equilibrated simulation cell at zero loading. The volume of 3 × 3 × 2 unitcells of A-form-II crystal (28726 Å3 ) at zero loading (V0 ) obtained from simulations is within 3% of the experimental value (27870 Å3 ). The green-dotted line is a linear fit to the loading graph with the intercept assumed to be unity. From the value of the slope (=0.3764), we determine the average volume occupied by a CO2 molecule in 3

form-I crystal, as determined from simulations to be 54 Å . For comparison, each CO2 3

molecule occupies 47 and 66 Å in dry ice (1 atm, -78.5◦ C) and in liquid CO2 (1 atm, -37◦ C) respectively. The increase in volume of A-form-II crystal upon CO2 loading is thus consistent with what is expected from the ratio of molecular volumes of benzene and CO2 and that between the volumes of form-I and CO2 loaded A-form-II crystals. In essence, the ability of 10


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the solvent-free A-form-II crystal to expand upon CO2 uptake without loss of crystallinity (vide infra) ‘unravels’ a part of the mystery behind its facile gas uptake even in the absence of intrinsic pores.

Figure 4: Normalized volume of the simulation cell versus CO2 pressure obtained from constant pressure MD simulations. Filled blue and red circles are data from loading and unloading cycles. Evolution of individual lattice parameters are presented in figure S4 of SI.

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Figure 5: Crystal of A at effective CO2 pressures of 0 (a-c), 0.5 (d-f) and 1 atm (g-i) respectively. At each pressure, three different orientations of the crystal are shown. Atoms displayed are obtained after averaging the coordinates over a duration of 20 ns in a constant NVT MD simulation. Simulation boxes are drawn in orange and the cell axes are indicated at bottom-left. Carbon and nitrogen atoms are colored green and blue respectively. Hydrogen atoms and adsorbed CO2 molecules are not shown.

Grand Canonical Monte Carlo Simulations (GCMC). GCMC simulations were also performed to confirm that the volume expansion observed in the MD simulations is not due to any assumptions (in the usage of the experimentally determined isotherm for

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estimating the number of CO2 molecules to be used in simulations), but due to the creation of pores with binding sites. Towards this aim, µVT GCMC simulations were carried out. The initial configurations used in these GCMC simulations were obtained by removing CO2 molecules from the final structures of the NPT MD simulations, at intermediate pressures lying between 0 and 1 atm. The isotherm obtained from such GCMC simulations at 195K closely follows that determined by experiment (Figure 6). The cell volume determined by µPT GCMC simulations (Figure S3(a)) also follows closely that exhibited in Figure 4. The isotherm determined from constant pressure GCMC simulations too agrees well with that obtained from constant volume GCMC simulations and the experimentally determined isotherm (Figure S3(b)). More details of µVT and µPT GCMC simulations are given in section S1.8 of SI.

Figure 6: Sorption isotherms of CO2 at 196 K in A-form-II determined experimentally (solid-blue line) and via GCMC simulations (red circles). Details of GCMC simulations are provided in section S1.8 of SI.

Retention of Crystallinity. The convergence of PXRD patterns was tested and a robust protocol to calculate them from the MD trajectory was identified. The same is presented in SI. Structures of A-form-II obtained during loading and unloading of CO2 were compared through their PXRD calculated at 4.5 ns of the corresponding NPT simulation. Figure S7a 13



shows PXRD patterns at zero loading (solid-red line), obtained for the pure crystal as well as for the crystal obtained by depressurizing from the CO2 -loaded state (dashed-green line). Similarly, in Figure S7b, the solid-red line corresponds to the simulation cell at 0.975 atm obtained by gradual loading and the dashed-green line correponds to the PXRD pattern at the same pressure but obtained by depressurizing the 1 atm configuration by an amount of 0.025 atm (i.e., by removing 5 CO2 molecules from the equilibrated configuration containing 200 CO2 molecules and equilibrating it). The PXRDs of pressurized and depressurized systems at all the intermediate pressures compared well, suggesting closeness of structures and the absence of hysteresis in the simulations. The patterns exhibit sharp features exemplifying the crystallinity of the samples at all CO2 pressures. The experimental CO2 adsorption and desorption isotherms matched, i.e., there was no hysteresis, suggesting that the crystal structure did not change during the process of adsorption and desorption. The PXRD patterns calculated from our simulations demonstrate the recovery of the crystal structure in the same process in a rather direct manner. 21 Crystallinities of systems A and B upon CO2 loading CO2 uptake and creation of pores are concomitant in A-form-II crystal. The system changes its crystal morphology with CO2 pressure but continues to remain crystalline at 1 atm CO2 pressure even after expanding by nearly 40% in volume as compared to its volume at 0 atm. Figures 5(g) to (i) show the A system at 1 atm along three different orientations from which the crystallinity can be discerned. PXRD patterns of A system at three 0.0, 100, 200 cm3 /g uptakes (equivalently 0.0, 0.5 and 0.975 atm pressure) are shown in Figures 7(b), 7(d) and 7(f), respectively. Well defined peaks with high intensities also show that the system remains crystalline at even significantly high uptakes. Similarly, PXRD patterns of B system at three pressures, at CO2 loadings of 0.0, 12.85, 42.85 cm3 /g are shown in Figures 8(b), 8(d) and 8(f), respectively. Although well-defined peaks exist, their intensities are low even though the system is loaded with a far fewer number of CO2 molecules as compared to that in A. The simulation cell at 42.85

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cm3 /g loading is significantly disordered (Figure 8(e)) compared to the system at 0 loading (Figure 8(a)). The differences between crystalline forms of A and of B are better comprehended when the PXRD patterns at various loadings are plotted together. Figures 9(a) and 9(b) show the PXRD at different CO2 loading for systems A and B, respectively.

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(a) Uptake = 0.0 cm3 /g

(b)

(c) Uptake = 100.0 cm3 /g

(d)

(e) Uptake = 200.0 cm3 /g

(f )

Figure 7: First, second and third rows show the time averaged molecular configurations (left) and the corresponding PXRD (right) patterns calculated for A at effective CO2 pressures of 0.0, 0.5 and 0.975 atm respectively. Each pattern is the result of averaging 101 equally spaced patterns calculated between 4.0 and 5.0 ns during the last 5 ns of NPT simulations during volume equilibration. PXRD patterns for the systems obtained during loading are represented in red color while the ones on unloading/depressurizing are represented in dashed green. The cell axes ‘c’ and ‘a’ are represented by the horizontal and the vertical axes respectively. 16 ACS Paragon Plus Environment

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(a) Uptake = 0.0 cm3 /g

(b)

(c) Uptake = 12.85 cm3 /g

(d)

(e) Uptake = 42.85 cm3 /g

(f )

Figure 8: First, second and third rows show the time averaged crystal structures (left) and the corresponding PXRD (right) patterns calculated for compound B at CO2 uptakes of 0.0, 12.85 and 42.85 cm3 /g respectively. Each pattern is the result of averaging 101 equally spaced patterns calculated between 4.0 and 5.0 ns during the last 5 ns of NPT simulations. PXRD patterns obtained for the systems during loading are represented in red color while the ones during unloading/depressurizing are represented in dashed-green. The cell axes ‘c’ and ‘a’ are represented by the horizontal and the vertical axes respectively. 17 ACS Paragon Plus Environment


Figure 9: PXRD patterns calculated for (a) A and (b) B systems at various CO2 pressures. Each pattern is the result of averaging 101 equally spaced patterns calculated between 4.0 and 5.0 ns during the last 5 ns of NPT simulations. The legends indicate the amount of CO2 taken up in mmol/g. At 1 atm pressure, the A system takes up 9 mmol/g of CO2 and remains crystalline in contrast to the B system which loses crystallinity at less than 1/3rd (2.3 mmol/g) uptake of the former.

Structure Description At 1 atm, the volume of the simulation is about 1.37 times that of CO2 -free crystal. The volume increase is not isotropic; lattice parameter a increases by a factor of 1.35 and c by a factor of 1.18 while b shrinks marginally by a factor of 0.96. The angles α and γ increase by about 10 degrees and β by only 4o (Figure S4). In order to understand the change in the microscopic structure and arrangement of A 18


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molecules in the crystal upon CO2 uptake, Radial Distribution Functions (RDF) between centroids of various components (Phenyl rings) of molecule A represented by labels in Figure 2(b) were calculated. The RDF of CO2 with respect to various components of A and with itself (following sections) were also calculated in order to understand the structure and interaction of sorbed CO2 with A molecules and themselves (section S2.3 of SI). Intermolecular RDF of CO2 and A. We now focus on the locations and orientations of CO2 molecules around the rotor in the crystal (see Figure 10a). CO2 molecules are populated most densely near rings 1 and 5. and are present at a distance of 3-4 Å from the rings. The first peak intensity in RDF of CO2 with respect to rings 2, 3, and 4 are smaller than that of its homogeneous density. Hence, the orientations of such CO2 are not important to examine.

(a)

(b)

Figure 10: (a) and (b) show the pair correlation function between centroid of the aromatic ring (ring label indicated by legend) and carbon atom of CO2 molecules. g(r) was obtained by averaging over all A molecules over a 20 ns NVT trajectory at an effective CO2 pressure of 1 atm.

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(a) Ring 1

(b) Ring 2

(c) Ring 3

(d) Ring 4

(e) Ring 5

(f ) Ring 6

(g) Ring 7

Figure 11: (a) to (g) show the normalized probability distribution P r, cos(θ) describing the orientation of CO2 molecules around molecule A. θ is the angle between the backbone of CO2 molecules and the normal to the aromatic ring (ring IDs 1-7) of the 1 molecule. ‘r’ is the distance between the centroid of an aromatic ring and the position of carbon of a CO2 molecule. The labelling of aromatic rings of A are shown in Figure 2b. The distribution is the result of ensemble and timeaveraging 20 ns NVT trajectory of A system at an effective pressure of 1 atm. See Figure 2 for ring labels.

The combined distance and angle distributions of CO2 with respect to the aromatic rings of the rotor molecule in A-form-II crystal at 1 atm CO2 pressure are shown in Figure 11. In the first coordination shell of ring 1, CO2 molecules are oriented at angles between 60o and 90o degree to the unit vector perpendicular to 1, the closest molecules being oriented perpendicular to that unit vector. Thus, the CO2 molecules closest to phenyl ring 1 are aligned along the long axis of the rotor molecule. CO2 molecules are oriented nearly parallel 20


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to the rings 5, 6 and 7 at distances between 3 and 4Å. Intermolecular RDF of CO2 and CO2 .

Figure 12: Normalized probability distribution P r, cos(θ) . θ is the angle between the backbones of CO2 molecules. and ‘r’ is the distance between their carbon atoms. The distribution is the result of ensemble and time-averaging from the 20 ns NVT trajectory of A system at an effective CO2 pressure of 1 atm.

(a)

(b)

Figure 13: Solid-black line: Intermolecular partial radial distribution function (RDF) between carbon and (a) carbon and (b) oxygen atoms of the sorbed CO2 in A system at an effective pressure of 1 atm. Dashed-black lines in (a) and (b) represent the corresponding coordination numbers. The distribution was obtained by averaging around 200 CO2 molecules over a 20 ns NVT trajectory.

The combined distance and angle distributions of CO2 -CO2 shown in Figure 12 demonstrates a high propensity of CO2 molecules to be located within 3.5 Å from each other and 21



Figure 14: Normalized probability distribution of scalar product of CO2 backbone vectors for molecules contributing to the first (black) and second (red) coordination shell of gC−O (r) (Figure 13(b))

with their backbone orientations being parallel to each other. CO2 molecules located farther, i.e., at 4.1 Å however are oriented perpendicular to each other. The distance and orientational distributions are much similar to that found in high pressure, bulk supercritical carbon dioxide. 57 The C-C and C-O pair distribution functions between CO2 molecules are displayed in Figure 13, along with the respective running coordination numbers. The first peak in C-C g(r) (Figure 13a) is rather wide which arises from molecules at different orientations with respect to the central one which is also evident from Figure 12. The first coordination shell extends upto 5.75 Å and the the coordination number is about five, which indicates relatively weaker interaction between CO2 molecules compared to that between CO2 and A. Note that the coordination numbers for CO2 -1 and CO2 -5 at the same distance are 4.9 and 5.7 Å, respectively. Furthermore, at the distance where the first coordination shell of C-C g(r) ends, the CO2 -1 and CO2 -5 g(r) nearly complete two coordination shells (Figure 10). In the C-O g(r) (Figure 13a), the first two peaks with same intensities result from the central CO2 molecule surrounded by CO2 molecules whose axis is perpendicular to the former. A shoulder which appears in g(r) for scCO2 57 appears as a distinct peak in the A system. We believe that the CO2 molecules which are located at the interstitial spaces along the backbones of the A molecules are more likely to align parallel to each other and to the rotor

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as well (black line-Figure(14)). Even in the second coordination shell (i.e. from 3.66 Åto 4.55 Åin Figure 13a), CO2 prefers parallel to perpendicular alignment w.r.t each other, but less dominantly as compared with that in the first coordination shell (red line-Figure 14). Orientations of back bones w.r.t z-axis

Figure 15: Normalized probability distribution of the dot-product of unit vector of the backbones of A (CO2 ) molecules and the z-axis unit vector indicated by black (red) line. The probability distribution of latter is multiplied by a factor of 5 for better visualization. The backbone of an A molecule is defined as the line-segment joining the two of its nitrogen atoms and that of CO2 is defined as the line-segment joining its two oxygen atoms. The distribution was calculated for the system at 1 atm and 196 K (9 mmol/g of CO2 ) from a 20 ns NVT simulation trajectory.

The backbones of molecules of A in the system are quite parallel to each other and are aligned along the z-axis (or the unit cell c axis), as seen from the distribution of the angle between these vectors, shown in Figure 15. A majority of the CO2 molecules are also aligned along the z-axis (See Figure 15). This preferential orientation is due to the narrow pores along the backbone of the A available for CO2 molecules. The other orientation for CO2 which is less preferred is to stay perpendicular to the backbone of the rotor as the normal to the phenyl rings of the rotor molecules lie in the xy-plane. Coplanarity of Phenyl rings of molecule A

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Figure 16: Figure (a) shows a schematic of the three unit vectors u~1 , u~2 and u~3 perpendicular to the phenyl rings 1, 2 and 3, respectively. θ1 and θ2 are the angles between u~1 and u~2 and u~1 and u~3 , respectively. The color plots show normalized probability distributions of cos θ1 and cos θ2 . Figures (b) through (d) are plots for A systems at effective CO2 pressures of 0.0, 0.5 and 1.0 atm, respectively. The probability distribution is a result of averaging over all A molecules over a 20 ns NVT trajectory following volume equilibration. The equivalent plot for A molecule in the experimentally determined form-I crystal structure is presented in (e).

Apart from differences in crystal compositions and structures of form-I and A-form-II, the relative orientations of the three phenyl rings connecting the two terminal carbazole segments of A also differ. In the case of A in form-I, all the three phenyl rings 1, 2 and 3 are coplanar, in contrast with their relative orientations in A-form-II wherein phenyl rings 1

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and 3 are coplanar while the ring 2 is perpendicular to the former (2). The A system at 0.0 atm also shows a similar behavior (Figure 16(b)) but with increase in effective CO2 pressure, the three phenyl rings tend to become coplanar (Figures 16(c) and 16(d)). It is interesting to note that these rings are coplanar in the A-form-I crystal wherein benzene molecules are co-crystallized with A. Bending of molecular backbone of A with CO2 uptake The backbones of A bend and deviate from linearity upon CO2 uptake. To highlight the extent of bending, Figure 5(e) is reproduced in Figure 17(a), highlighting only a few molecules which exhibit considerable deviation from linearity. To quantify the extent of bending, the distribution of scalar products of the unit vector along the bond between triple bonded carbon and ring 2 centroid and that between the triple bonded carbon and ring 3 centroid is calculated and plotted in Figure 17(b). The choice of the unit vectors were made from the fact that the ethynyl linkages with phenyl rings are known to be flexible. 58 The unit vectors are represented by red colored arrows in 17(a). At zero pressure of CO2 , the backbones of A are almost linear. The distribution broadens, i.e., molecules of A bend to a greater extent, almost monotonically with increase in effective CO2 pressure. The mean cos(θ) increases with increasing effective CO2 pressure (Black circles, Figure 17(c)) and saturates beyond a P/P0 value of 0.5. The bending of the backbone of the rotor molecules was also observed, surprisingly in gas phase quantum chemical calculations (see Figure S26 of Supplementary Information of Rodriguez-Molina et al. 21 ). The MD simulations of adsorption in the bulk crystal reported here confirm these findings. A molecules arranged like rods stacked upon each other in A-(form-II) brings a unique feature to the system. The flexiblity of A molecules, specifically the segment between the terminal carbazole groups helps create pores for CO2 molecules to reside and facilitate diffusion. Modest fluxionality combined with strong anchoring of carbazole of one molecule to the carbazole and phenyl rings of the neighbor is responsible for regaining crystallinity upon pressure-depressure cycle (see section on PXRD). This observation is also consistent with

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Figure 17: (a) Configuration of crystal of A molecules highlighting their ‘bent’ nature, at effective CO2 pressure of 0.5 atm. (b) Red arrows: Vectors joining the alkyl carbon bonded to non-central phenyl rings (rings 2 or 3) of molecule A. θ is the angle between the vectors. (c) Probability distribution of cos(θ) at pressures (in atm) indicated by the legend. A bin width of 0.0002 was used in calculating the distribution. (d) Black circles represent the mean value of cos(θ) as a function of pressure. The distribution was obtained by averaging over all the thirty six molecules of A of the 20 ns NVT run, which followed volume equilibration at different effective pressures.

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the experimentally observed lack of hysteresis in adsorption and desorption isotherms. Thus, both these characteristics–backbone flexibility as well as the ability to retain crystallinity upon expansion of cell volume during uptake of CO2 distinguishes the A-form-II crystal of A from that of B and enables the former to adsorb CO2 in a facile manner.

Dynamics Translational and Rotational Dynamics of CO2 . In order to quantify the mobility of CO2 molecules, the Mean Squared Displacement (MSD) versus simulation time for various pressure values were computed and plotted in Figure S9. The CO2 molecules at all effective pressures exhibit diffusion, albeit rather slowely. It can be inferred that the CO2 molecules are not locked in pores. Time-correlation function of the CO2 backbone unitvector (Figure S11) was also calculated for various pressure values and presented in section S2.6 of SI. CO2 molecules exhibit orientational relaxations within the simulation time scales. Rotational Motion of Central Phenyl ring. NMR experiments 21 of the pure Aform-II crystal suggested the flexing of the phenyl rings in the carbazole rotor which can also modulate the gas uptake, although to a much lesser degree than the expansion of the crystal. In-situ NMR experiments were not carried out; however, the librational dynamics of the phenyl rings with increasing CO2 uptake can be determined from our molecular simulations. To understand the dynamics of the central phenyl ring (1), the time auto-correlation function of the unit vector perpendicular to the ring was calculated (see Figure 18). Akin to the behavior of the mean squared displacement, the rate of decay of this time correlation function does not show any systematic dependence on pressure. A complete rotation of the rings is not observed within the duration (20 ns) of the simulation. In fact, the TCF has barely decayed to a value of 0.8 to 0.9 over 10ns. This behavior of the central phenyl ring with CO2 pressure is consistent with its restricted

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behavior in A-form-I which contains entrapped benzene as reported in experiments. 21

Figure 18: Time correlation function of the unit vector perpendicular to the central phenyl ring, 1 (Figure 2(b)). The legend indicates P/P0 .

Conclusions Using molecular simulations, we have delineated the mechanism of gas adsorption in an organic crystal which lacks intrinsic porosity. While at first thought, the facile uptake of CO2 in a non-porous molecular crystal is surprising, the same has been demonstrated here to take place via two chief mechanisms: (a) bending or flexing of the long ethynyl linkages in the molecule. (b) retention of crystallinity while the cell expands to accommodate the gas molecules. The latter is a consequence of the near parallel orientations of these long molecules and their anchoring via the terminal carbazole groups. Our simulations show the librational dynamics of phenyl rings on the rotor molecules to occur in the nanosecond timescales, but the amplitude of rotation is rather small for this dynamics alone to modulate the gas uptake. In this process, we employed a procedure to study sorption in molecular crystals without intrinsic porosity by a combination of Molecular Dynamics (MD) and Grand Canonical Monte Carlo (GCMC) simulations. Its appropriateness was verified by reproducing the CO2 isotherm at 196 K in A-form-II. Using atomistic MD, the time scales required for 228


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fold flips of the central phenyl ring of A molecules could not be achieved; nevertheless, the volume expansion which enables CO2 uptake was observed. By simulating PXRD patterns at various effective pressures of CO2 , we confirmed the retention of crystallinity. We also found an increase in the flexing of the A molecules with CO2 uptake. At high enough pressures, near neighbor CO2 molecules sorbed in the crystal are found to be oriented perpendicular to each other. The crystal of molecule B is experimentally shown not to uptake CO2 ; our simulations too agree with the same. This sample loses its crystallinity with much lower sorption of CO2 , primarily due to the short length of the molecule and to the fact that the molecules are not aligned parallel to each other in the crystalline state. The generality of these observations to all-organic molecular crystals constituted by long rod-like molecules for gas uptake needs to be studied. This will be our objective for the near future.

Description of SI Complete technical details of MD, GCMC simulations and Force Field used; calculation of PXRD patterns; variation of cell parameters with CO2 pressure; demonstration of crystallinity; pair correlation functions of A-A; MSD of CO2 ; reorientational dynamics of the central phenyl rings and CO2

Acknowledgement We thank DST for support. ND acknowledges CSIR for a fellowship.

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Atomistic simulations elucidate the mechanisms of facile CO2 uptake in a non-porous molecular crystal. 82x44mm (300 x 300 DPI)


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Unraveling the Sorption Mechanism of CO2 in a Molecular Crystal

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