Design Elements for Enhanced Hydrogen Isotope Separations in Barely Porous Organic Cages.

Barely porous organic cages (POCs) successfully separate hydrogen isotopes (H2/D2) at temperatures below 100 K. Identifying the mechanisms that control the separation process is key to the design of next-generation hydrogen separation materials. Here, ab initio molecular dynamics (AIMD) simulations are used to elucidate the mechanisms that control D2 and H2 separation in barely POCs with varying functionalization. The temperature and pore size dependence were identified, including the selective capture of D2 in three different CC3 structures (RCC3, CC3-S, and 6ET-RCC3). The temperature versus capture trend was reversed for the 6ET-RCC3 structure, identifying that the D2 and H2 escape mechanisms are unique in highly functionalized systems. Analysis of calculated isotope velocities identified effective pore sizes that extend beyond the pore opening distances, resulting in increased capture in minimally functionalized CC3-S and RCC3. In a highly functionalized POC, 6ET-RCC3, higher velocities of the H isotopes were calculated moving through the restricted pore compared to the rest of the system, identifying a unique molecular behavior in the barely nanoporous pore openings. By using AIMD, mechanisms of H2 and D2 separation were identified, allowing for the targeted design of future novel materials for hydrogen isotope separation.

Introduction

Hydrogen isotope species (H2/D2) are needed for multiple applications across science and industry, including proton nuclear magnetic resonance,[1] neutron moderators in nuclear reactors,[2] isotope tracing,[3−5] and neutron scattering techniques.[6] A wide variety of porous materials have been explored for H2 separation from mixed gas streams for hydrogen storage[7−10] but H2/D2 separation continues to be a challenge. The nearly identical chemical nature of hydrogen isotopes provides unique challenges in separation, which cannot be achieved through traditional methods such as molecular sieving.[11] Traditionally, hydrogen isotope separation has been achieved through electrolysis of heavy water extracted through the Girdler-sulfide process[12] or by cryogenic distillation at 24 K.[13] These processes are energy intensive and are currently driven primarily via precious metal (Pd and Pt)-based adsorption systems.[14−16]

Recently, isotopic separation has been approached using nanoporous materials for size or adsorption sieving.[17] These separation processes include kinetic quantum sieving (KQS),[18] which is derived from quantum interactions during the diffusion of gas through pores in the material, and chemical affinity quantum sieving (CAQS),[19] which is dependent on quantum effects resulting in enhanced chemical adsorption. Previous work investigating the use of porous materials based on KQS and CAQS for hydrogen isotope separations includes barely nanoporous carbons,[20] zeolites,[21] metal–organic frameworks,[22] and graphene materials.[23]

Among these nanoporous materials, barely nanoporous carbons composed of porous organic cages (POCs) have shown to have a combination of both high D2 selectivity and uptake.[20] Specifically, the CC3 series of POCs synthesized in a cocrystal provide the best combination of high uptake and selectivity at temperatures between 30 and 77 K.[20] The porous organic chiral imine cage, CC3, is formed by cycloimination of 1,3,5-triformylbenzene and (1R,2R)-1,2-diaminocyclohexane.[24] Further functionalization of the parent CC3 cage results in the modification of the cage pore to create the reduced CC3 cage (RCC3) and ethylidene-functionalized CC3 cage (6ET-RCC3).[20,25] The phenomenon of KQS becomes relevant when the de Broglie wavelength, λ = h/mvr, of a gas molecule is comparable in size to the pore diameter of a material, resulting in a reduced transversal motion of the molecule.[18,20] The KQS effect that occurs in POCs and other nanoporous materials is temperature-dependent and localized to the individual small molecule of interest. However, when applying flexible framework materials, the effects of temperature and flexibility are coupled. Lower temperatures induce a lower motion of the POC and result in smaller pore window sizes in functionalized 6ET-RCC3. Due to the smaller pore windows at low temperatures, the KQS effect is amplified. Not only is KQS more effective at low temperatures for isotopic pairs but also the decreased motion of the separation material at low temperatures further restricts light isotope motion through the reduced pore window size. The higher adsorption temperature range for CC3 POCs compared to current cryogenic distillation methods results in lower energy consumption and expense to achieve isotopic purity of D2 from an H2/D2 stream.[23] Experimentally, the results demonstrate that in a temperature range of 30–77 K, there was a dependence of KQS on the temperature, and at lower temperatures, the heavier D2 is retained in larger quantities. The effect of KQS is also enhanced in CC3 variants through the choice of functionalization. The standard pore size of CC3 is ∼4.5 Å compared to ethylidene-functionalized 6ET-RCC3, which has a pore diameter of ∼1.9 Å.[20] The combination of temperature and choice of functionalization provides increased separation and selectivity of hydrogen isotopes and highlights the tunability of POCs for chemical separations.

While hydrogen isotope separation has been identified as the process for high D2 selectivity and uptake, the fundamental mechanisms of atomic interactions have not been identified. Atomic level mechanisms in porous materials have been successfully investigated through the use of high-performance computing and ab initio molecular dynamics (AIMD) simulations.[26−28] AIMD simulations combine classical MD simulations with density functional theory (DFT) electronic structure calculations at each time step. The use of AIMD also provides the opportunity to directly monitor the temperature-based effects of hydrogen isotopes in CC3 POCs. Previous calculations have utilized grand canonical Monte Carlo (GCMC) and classical MD methods to identify hydrogen isotope equilibrium distributions and path integral MD using a single H2 or D2 molecule.[20] To gain a deeper insight into mechanisms of hydrogen isotope separation, AIMD is applied to study the specific mechanisms of hydrogen isotope interactions with three CC3 POCs: RCC3, CC3-S, and 6ET-RCC3. The evaluation of multiple CC3 POCs allows for the identification of the effect of temperature and functionalization on hydrogen isotope motion.

By studying the unknown temperature-dependent structure–property relationships that exist in a series of CC3 barely nanoporous carbons,[20] the design of new hydrogen isotope separation materials can be achieved. Selective separation of hydrogen isotopes in nanoporous sieves via size and weight will enable the design of future low-cost and energy-efficient purification processes.

Computational Methods

Three unique CC3 POC structures (RCC3, CC3-S, and 6ET-RCC3) were investigated using DFT as implemented in the Vienna ab initio simulation package (VASP) code[29,30] in a plane wave basis set[31,32] with projector-augmented wave potentials and a closed shell electronic structure.[33,34] A 600 eV cutoff energy was used and converged to a force accuracy of 1 × 10–4 eV/atom at the gamma point for k-point sampling. A Gaussian smearing of 0.1 eV was used for smearing of electron occupation. The generalized gradient approximation exchange–correlation functional of Perdew, Burke, and Ernzerhof was used along with the DFT-D2 method of Grimme as a van der Waals correction.[35−37] Similar methods have been used in the evaluation of porous metal–organic frameworks for investigation of structural, adsorption, and optical properties.[38−41] Initial structures were taken from published crystal structures,[20] and snapshots of the three POC structures are presented in Figure and highlighted functionalization is shown in the Supporting Information, Figure S1. DFT calculations have limitations when applied to isotopic species, making ground-state energy comparisons difficult due to calculated energies being dependent on the number of valence electrons within the simulation. For H2 and D2 calculations, one electronic structure calculation is needed to compute the electronic energy of both isotopes. To distinguish H2 and D2 molecules, the D atom was modeled using the H potential and by modifying the mass to 2 a.u. However, upon the introduction of temperature, dynamic simulations of isotopes result in unique behaviors and allow for identification of isotopic-dependent classical behavior.

Figure 1

Initial POC geometric structures for (A) RCC3, (B) CC3-S, and (C) 6ET-RCC3. Atoms are represented by C (brown), N (blue), and H (white).

Following POC geometry optimization, a single H2 or D2 molecule or a H2 and D2 pair was placed in the center of the POC structure. A microcanonical ensemble (NVE) was used to optimize the POC + gas system with a 0.5 fs time step, and the velocities rescaled every 10 steps for 4000 steps using the same computational parameters as the initial equilibration.[28] Using the structures calculated during NVE, the AIMD trajectories continued with canonical ensembles (NVT) performed to simulate the model at the desired temperature and are used for data analysis. Four different temperatures (30, 50, 77, and 100 K) were selected based on the reported experimental conditions.[20] The NVT calculations utilized the Nose–Hoover[42,43] thermostat and were performed for 20,000 steps with a 0.5 fs time step, resulting in a 10 ps trajectory for analysis. The AIMD trajectories were calculated in triplicate by randomizing the D2 or H2 molecule starting position within the POC pore cavity. This resulted in 12 AIMD trajectories for both D2 and H2 with three trajectories at each temperature. All data presented as an average value are taken over three AIMD trajectories for each temperature, unless specified, and contain the standard error of the values. During all AIMD trajectories, the simulation model was a single POC placed in the center of the unit cell, and all atomic positions were allowed to move without constraint. Trajectory analysis of pore aperture was calculated via the cross product, , where S is the area of the aperture defined by the vectors a and b. Vectors a and b are defined by atomic coordinates of functional groups and visualized in Figures S2 and S3. Determination of gas location relative to the POC was calculated using the center of mass of both the POC and gas molecule of interest. The distance between the gas and POC center of mass was then compared to the distance required to be outside any POC window, resulting in identification of an exit event.

Results and Discussion

To identify the fundamental mechanisms of isotope selectivity in barely nanoporous CC3 POCs, AIMD calculations of H2/D2 interaction and escape from the POCs are simulated to identify spontaneous interactions between the molecule and the POC structure. Additionally, a series of CC3 POCs with a range of functionalization are used to identify the molecular selectivity due to changes in pore size. The three POCs studied include CC3-S, RCC3, and 6ET-RCC3 which have decreasing pore aperture due to functionalization and have been previously identified as POCs of interest in hydrogen isotope separation.[20] Techniques for MD simulations are highly dependent on sample size. For AIMD trajectories, the trajectory provides a highly accurate chemical interaction sampling for gas species within the POC structures. Of interest are the individual interaction events that occur between the gas and POC, which are provided at a higher level of chemical accuracy than classical MD trajectories. The AIMD evaluation of hydrogen isotope separation focuses on diffusion and pore exit or entrance mechanisms of H2 and D2 gas molecules to identify how POC functionalization influences isotope motion. Results are presented in the order of increasing functionalization POCs (CC3-S, RCC3, and 6ET-RCC3) for single hydrogen isotopes (H2/D2).

Energetic Response of POC to Gas Loading

To identify relative structural stability of gas concentration within the pore volume, the functionalized 6ET-RCC3 POC was loaded with three, five, seven, or ten H2 gas molecules, respectively, and optimized. The optimized energies provide relative stability in the POC framework as a function of gas concentration loaded into the POC. An initial geometry optimization identifies an average energy change in the simulation of −6.84 eV/H2 molecule added to the POC (see data in Table S1). To specify how the POC cage is structurally changing under various gas loadings, comparison of the POC energies was performed. Following the optimization of all gas-loaded POCs, the gas molecules are removed, and a single point energy calculation was performed, Table .

Table 1

Energy of the 6ET-RCC3 Cage as a Function of Gas Loading and Relative Energy Changes as a Function of Gas Concentration

empty and gas-loaded 6ET-RCC3 cage energies
# of H2	total energy (eV)	dE vs empty (eV)	dE per H2 (eV)
0	–1307.27
3	–1307.28	–0.01	–0.004
5	–1307.15	0.12	0.024
7	–1307.09	0.18	0.026
10	–1307.02	0.25	0.025

Results indicate a small energetic preference (−0.01 eV) for 6ET-RCC3 containing up to three H2 molecules. However, for higher gas loadings (3+ H2 molecules), the change in energy increases, indicating a non-thermodynamically favored system. Given the small volume within the 6ET-RCC3 pore and the difficulty of H2 to move through the functionalized pore windows, higher gas loadings are expected to be a non-equilibrium state of the material. Therefore, the maximum number of gas molecules in the 6ET-RCC3 cage is less than three, and here, we have focused on 1–2 total gas molecules in the POC structures.

Selectivity Dependence on the Functionalization of CC3 POCs

The primary difference among the modeled POC structures is the added chemical functionality to the parent CC3 POC. The functionalization of POCs changes the size of the aperture, resulting in a smaller pore window size for gas escape. Here, the parent POC is the CC3-S model, while RCC3 and 6ET-RCC3 are the functionalized POCs. The geometries that determine the aperture size are described in detail in the Supporting Information, Figures S2 and S3. Calculation of the aperture area provides insights into mechanisms of gas diffusion and selectivity as a function of temperature. CC3-S and RCC3 POCs have no and minimal functionalization, respectively. With minimal functionalization, the pore area is dependent on the flexibility of the POC framework. The calculated pore areas for CC3-S and RCC3, Figure , show a linear dependence between the area and temperature with the area decreasing with increasing temperature.

Figure 2

Average pore aperture areas calculated for CC3-S and RCC3 across all temperatures (30, 50, 77, and 100 K) for D2 (blue)- and H2 (red)-containing models.

As atomic motion increases at higher temperatures, a negative linear trend in the pore area is expected. In the larger bulk material formed from POC cages, the individual units organize themselves into a structured packing. To investigate the role of POC motion, a semi-restricted RCC3 model was simulated to approximate a covalently bonded POC structure and test the hypothesis that the rotation of the POC cage due to weak van der Waals bonding is a factor in controlling hydrogen isotope separation, Supporting Information. The semi-fixed RCC3 aperture areas showed a minimal decrease in response to temperature, Figure S4, indicating restricted pore motion in response to terminal fixing. The full detail of the semi-fixed RCC3 simulations is presented in the Supporting Information. In the CC3-S parent POC, the pore aperture area is relatively consistent across the calculated temperatures ranging from 26.89 ± 0.01 Å2 at 30 K to 26.77 ± 0.02 Å2 at 100 K across the D2 and H2 models. The reduced RCC3 POC has a larger pore area fluctuation at higher temperatures resulting in areas of 26.76 ± 0.01 Å2 at 30 K to 26.44 ± 0.05 Å2 at 100 K across D2 and H2 models. The non-functionalized CC3-S shows slightly larger pore apertures compared to the reduced RCC3, indicating a decreasing pore aperture with increasing POC functionalization. In contrast to CC3-S and RCC3, the functionalized 6ET-RCC3 has a much smaller aperture area, between 7.3 and 8.8 Å2, and has an opposite temperature, Figure .

Figure 3

Visualization of a pore aperture in 6ET-RCC3 (left) with the aperture coordinates (green dots) and the calculated aperture plane (red triangle) shown. The average pore aperture of 6ET-RCC3 with either D2 (blue) or H2 (red) in the pore at 30, 50, 77, and 100 K. Atom colors are consistent with Figure .

The 6ET-RCC3 functionalization is unique in which the functional groups protrude into the POC cavity and pore opening, resulting in the greatly reduced aperture area. Since the functional group directly determines the aperture area, the POC framework fluctuation is not the determining factor in pore opening areas as seen in CC3-S and RCC3. However, the functional group responds to temperature in the same manner as the CC3-S and RCC3 frameworks. The increased motion of the functional group due to temperature results in a larger pore opening size, changing from 7.98 ± 0.47 to 8.23 ± 0.55 Å2 for D2 and 7.93 ± 0.42 to 8.27 ± 0.49 Å2 for H2. This area dependence on functionalization and temperature is a key indicator of gaining size control into a POC pore via the choice of temperature. Another key feature of functionalization in 6ET-RCC3 is that not all apertures are functionalized in the same manner. There are four pore apertures and six functional groups, with two apertures having two methyl groups and one H, while the other two apertures only have one methyl group and two H. The visualization in Figure shows an aperture with two methyl groups and one H. When comparing the larger and smaller apertures in 6ET-RCC3, the calculated global averages along all AIMD trajectories are 7.64 ± 0.18 Å2 and 8.53 ± 0.19 Å2 for the smaller and larger pore apertures, respectively. The averages of all four 6ET-RCC3 pores are plotted in Figure S7. In all escape events along the calculated 6ET-RCC3 trajectories, the H2 or D2 isotope exited only through the larger apertures with only one methyl group. This difference of ∼1 Å2 in aperture size demonstrates how a small a change in functionalization results in the passage of H isotopes through the POC aperture. The smaller size of the most functionalized pore apertures of 7.64 ± 0.18 Å2 indicates the potential pore opening barrier for possible molecular isotope diffusion through a POC material.

The pore aperture size has been hypothesized as the primary driver of H isotope selectivity, and the temperature dependence of POC material behavior and aperture area can be analyzed to understand H isotope mobility along AIMD trajectories. An indicator of temperature-dependent molecular selectivity is how frequently the H2 or D2 molecule exits the POC structure. Observation along all AIMD trajectories of CC3-S, RCC3, and 6ET-RCC3 provides an average number of exit or entrance events of H2 or D2 per trajectory for all simulated temperatures, Figure .

Figure 4

Averaged number of exit or entrance events per AIMD trajectory along calculated for CC3-S (red), RCC3 (blue), and 6ET-RCC3 (green) at temperatures of 30, 50, 77, and 100 K.

The observed exit and entrance events are averaged over three AIMD trajectories at each temperature. The behavior of both D2 and H2 shows similar trends in the functionalized 6ET-RCC3. As 6ET-RCC3 has a greatly reduced pore aperture, exit and entrance events were less frequently observed on the calculation time scale. Over a total of six AIMD trajectories, no D2 exit events were observed at 30 and 50 K, while 1 and 2 events were observed for 77 and 100 K, respectively. Similarly, H2 exit and entrance events in 6ET-RCC3 were minimal with 1 event occurring at 30, 50, and 77 K each and 2 events at 100 K. All observed events were exit events and did not include any re-entry of the H2 into the POC.

A unique observation is seen for POCs containing a D2 molecule in the minimally functionalized RCC3. A higher number of total exit and entrance events occur at lower temperatures of 30 K (6 events) and 50 K (9 events) compared to 77 K (2 events) and 100 K (1 event), Figure . As RCC3 and CC3-S have similar pore aperture areas, it would be expected to see similar behaviors in the D2 ability to move in and out of the POC. However, D2 was observed to be consistent for temperatures of 30 K (5 events), 77 K (6 events), and 100 K (5 events) with a single lower value at 50 K (1 event). The functionalized pores, even minimally as in RCC3, are expected to produce a small selectivity for the heavier D2 isotope compared to that of H2. The ability of D2 to enter and exit RCC3 also agrees with experimentally determined D2 uptake in the material.[20]

The number of entrance and exit events that occurred for H2 in CC3-S and RCC3 exhibited inverted behavior compared to D2. For RCC3, H2 has a low value of 2 exit and entrance events at 50 K and 3 at 77 K, while low and higher temperatures have 5 and 8 events for 30 and 100 K, respectively. For the nonfunctionalized CC3-S, H2 was observed to have a higher number of entrance and exit events at 30 K (4 events) and 50 K (7 events) compared to the higher temperatures of 77 K (2 events) and 100 K (1 event). To further examine D2 and H2 mobility in and out of the studied POCs, the relative time percentages of the gases can be analyzed, Figure .

Figure 5

Average time D2 (left) or H2 (right) spends outside the POC pore for CC3-S (red), RCC3 (blue), and 6ET-RCC3 (green) at temperatures of 30, 50, 77, and 100 K.

The time of an isotope molecule spent outside of the POC pore along the AIMD trajectories provides information that has two dependencies. Time spent outside the pore indicates the ability of the gas to exit the pore. This first indication provides initial identification of which isotope/POC/temperature environments may lead to idealized isotope behavior. The second indication from the time outside the pore is in conjunction with known exit and entrance events. Exit events are observed along a trajectory and the time outside the pore is high, which indicate that the gas does not re-enter the POC.

The number of exit and entrance events in the functionalized 6ET-RCC3 is low, Figure , and the corresponding time spent outside the pore is also low for a temperature of 30 and 50 K. However, for a temperature of 77 and 100 K, where exit events were observed, the time outside the pore is above 40% for both D2 and H2. The high values of time outside the pore indicate that once gas has exited 6ET-RCC3, it does not re-enter.

The more accessible CC3-S and RCC3 POCs show that gases spent more time outside the pore on average compared to that of 6ET-RCC3. The non-functionalized CC3-S has a low value of time outside the pore for D2, indicating that the isotope prefers to stay inside the pore at temperatures below 77 K. For H2 in CC3-S, the isotope spends more than 60% of the trajectory outside of the pore at temperatures of 50, 77, and 100 K. This agrees with the number of exit and entrance events observed, highlighting that the lighter H2 isotope moves more freely through the open POC. It also indicates that D2 is more likely to move throughout RCC3 at low temperatures compared to H2. Interestingly, the D2 molecule is observed to spend outside of the pore of RCC3 at temperatures of 30, 50, and 77 K compared to CC3-S. In contrast, H2 does not show a drastic change in time outside the pore between CC3-S and RCC3 across any temperatures. Further investigation of comparative behavior of D2 and H2 was calculated for a single mixed gas trajectory in CC3-S, RCC3, and 6ET-RCC3. The resulting trajectories containing both H2 and D2 resulted in the exit of one isotope molecule and no re-entry, Figure S9, agreeing with the DFT-calculated energies for gas concentrations in the POC pore. Full discussion of the mixed H2 and D2 trajectories is presented in the Supporting Information.

Gas Escape Mechanisms for Single Gas Trajectories

For material prediction and design, understanding the fundamental mechanisms by which hydrogen isotopes enter and exit POCs during adsorption processes is critical. Analyzing the calculated AIMD trajectories provide atomistic information on isotope motion as the H2 and D2 gas molecules exit and enter the POCs. Snapshots along two AIMD trajectories show both H2 and D2 exiting the CC3-S POC, Figure S12.

The largest impact of KQS is exhibited at low temperatures for POCs with functionalized pore windows with the smallest pore diameters. To compare the temperature-dependent behavior of H2 and D2 motion in functionalized POCs, velocities of isotope gases have been organized as a function of temperature and gas location in CC3-S, RCC3, and 6ET-RCC3. An example is shown for H2 in POC 6ET-RCC3 at 100 K in Figure .

Figure 6

Velocity of an H2 isotope in 6ET-RCC3 at 100 K plotted as a function of distance from the POC center with localized regions labeled as in pore, exiting, and outside pore.

In the AIMD simulations, the gas position was divided into three regions: (i) in the pore, (ii) exiting/entering the pore, and (iii) outside the POC. The distances used to separate the distinct regions have been visually highlighted in Figure with vertical red lines. The distinct regions where a gas molecule is located within a POC directly effects the gas-POC interaction energy and ability to be displaced.[44,45] To identify isotope behavior along the AIMD trajectories, the velocity of the gas molecule was calculated and plotted as a function of distance from the POC center with Figure , highlighting the H2 gas molecule sampled along the 6ET-RCC3 at 100 K trajectory. The three distinct POC regions were defined by distance from the POC center: 0–2.65 Å in the pore, 2.65–5.75 Å approaching or exiting the POC, and greater than 5.75 Å is outside the pore. In Figure , the thickness or shading of the plotted velocity indicates the amount of time the gas sampled each location. This is highlighted by the darker plot in the pore and outside the POC. As the H2 isotope approaches the exit a clear decrease in velocity is identified near 2.65 Å, Figure . The reduction in velocity as the isotope reaches the pore aperture indicates the barrier for the isotope to exit the POC. The region of approach/exit in Figure is light as the H2 molecule exited the POC and never re-entered. If the gas does not exit the pore, only distances less than 3 Å from the POC center are sampled. The small pore aperture concentrates the spatial sampling by the isotopic gases to inside and outside the POC and does not allow the gases to stay within the pore opening.

In the case of the open POCs of CC3-S and RCC3, the isotopes can sample not only inside and outside of the POC but also the spatial regions in the pore openings. To illustrate the difference of open pore apertures compared to the functionalized 6ET-RCC3, the H2 path at 30 K in CC3-S POC has been visualized, Figure .

Figure 7

H2 distance from the center of the POC (left) and velocity plotted as a function of distance from the POC (right) in CC3-S at 30 K. Effective pore exits are represented by dashed horizontal and vertical red lines for the same distance, 6 Å, in both plots. The calculated distance of the average minimum of pore opening distance from the center of the POC (left, green dashed line).

Along one AIMD trajectory of H2 in CC3-S, the H2 molecule samples all specified regions of the simulation while having multiple exit and entrance events. The distance of the H2 molecule as a function of distance from the POC center is plotted in Figure (left). In the plot, a horizontal dashed red line indicates an effective pore exit distance. The plotted red line is labeled an effective pore exit as the calculated distances from the center of the POC to the center of the pore opening range between 3.15 and 3.29 Å in CC3-S (green horizontal line). The H2 molecule sample distances from the pore between 3.3 and 6.0 Å correspond to molecule interaction with the edges of the pore opening and N atoms at the corners of the pore opening. The H2 and D2 molecules were also observed to be able to move beyond the identified pore aperture plane, ∼6.25 Å, but still be retained by the POC. This behavior was observed for both H2 and D2 molecules, indicating an attractive interaction between the gas and POCs that is not dependent on isotopic species. In correlation, the velocity as a function of distance from the POC center, Figure (right), shows a similar velocity feature as observed in 6ET-RCC3, Figure . As the H2 molecule nears the pore exit and is retained, a large sampling of slow velocities is calculated. Just beyond the effective pore exit, the velocity sampling is minimal and the plot narrows. This feature of small velocity sampling is not distributed across a long exit distance as seen in 6ET-RCC3, Figure , but is identifiable. The ability of non-functionalized or minimally functionalized POCs to retain H2 or D2 molecules inside the pore from beyond the aperture plane enhances the uptake ability and capacity of the material. Overall, the variation in the average isotope velocities during exit and entrance events across multiple functionalized POCs provides information to predict H2/D2 separation in future isotope pairs.

For all POCs studied, the velocities of both H2 and D2 have been calculated for the specific regions of inside the pore, Vin, exiting/entering the pore, Vexit, and outside the pore, Vout (Figure ). As described above in Figures and 7, the distances for each region of the POC vary between the functionalized 6ET-RCC3 and CC3-S and RCC3. The cutoff values used for 6ET-RCC3 POC were Vin < 3.5 Å, 3.5 Å < Vexit < 4.0 Å, and 4.0 Å < Vout. For the CC3-S and RCC3 POCs, the distance values for the velocity regions were Vin < 5.5 Å, 5.5 Å < Vexit < 6.0 Å, and 6.0 Å < Vout. For the non-functionalized CC3-S, the D2 velocities are lowest at 77 K, while for H2, they are the highest velocities. Overall, the H2 velocities were faster than D2 on average throughout all temperature trajectories. Since the CC3-S POC has the largest pore opening, the lower mass of H2 will allow it to move more freely through the system.

Figure 8

Calculated average isotope velocities for D2 (left) and H2 (right) in CC3-S, RCC3, and 6ET-RCC3 at varying positions of the simulation cell. Velocities are plotted for regions, where the isotope is in the POC (Vin, blue), outside the POC (Vout, red), and when exiting or entering the POC (Vexit, green).

In the reduced RCC3 POC, the trends in D2 and H2 velocities are modified compared to CC3-S. For D2, the fastest velocities are calculated to be 0.0127 ± 0.006 Å/fs at 50 K and reduce with increasing temperature. This trend of faster velocities for D2 at lower temperatures matches the reported experimental trend.[20] The H2 molecule velocities show a linear trend with temperature, with velocities increasing as the temperature increases, due to its lower mass compared with D2. While both CC3-S and RCC3 have larger pore openings, the trends from calculated velocities show unique differentiable behavior of D2 and H2.

In the functionalized 6ET-RCC3, the velocities of D2 and H2 have similar behavior when inside the POC pore. One feature that stands out is the number of exit events for both D2 and H2 compared to the velocities inside and outside of the POC. The values of D2Vexit were calculated to be 0.018 ± 0.007 Å/fs compared to an average velocity of 0.010 ± 0.002 Å/fs for Vin and 0.013 ± 0.004 Å/fs for Vout. The H2 values of Vexit are 0.020 ± 0.005 Å/fs compared to 0.012 ± 0.003 Å/fs for Vin and 0.017 ± 0.006 Å/fs for Vout. The increased velocity of both H2 and D2 isotopic molecules when moving through the restricted pore apertures indicates a unique molecular behavior when exiting the pore opening compared to being inside or outside the POC. The expectation of KQS is that an isotopic dependence exists between H isotopes, resulting in velocity differences when moving through restricted volumes. As both D2 and H2 were calculated to have increased velocities when exiting the 6ET-RCC3 pore at 77 and 100 K, further trajectory calculations would be required until sampling can occur for exit events of D2 and 30 and 50 K to provide the best comparison of exit velocities between D2 and H2 as a function of temperature. However, it is known that the classical treatment utilized along the AIMD trajectories do not account for known zero-point energy corrections and quantum effect utilized in more expensive calculation methods. This leaves opportunity for improvement and further refinement of results in future work. The results from the velocity analysis along multiple trajectories and POCs showed differentiable behavior between two hydrogen isotopes at varying temperature environments. The utilization of AIMD presents data that provides chemically accurate calculations, which fills the gap between classical MD and GCMC methods and restricted path integral calculations.

Conclusions

A series of AIMD calculations were completed with focus to address unknown temperature-dependent structure–property relationships, which exist between a series of CC3 barely nanoporous carbons and H2/D2 for design of new isotope separation materials. The simulations identified POC material responses to temperature, resulting in decreased pore apertures for RCC3 and CC3-S, whereas the functionalized 6ET-RCC3 increased as temperature increased. This identification highlights that a cage can be designed to have variable pore sizes given a set temperature through material functionalization. Analysis of D2 and H2 exit and entrance events indicated that D2 had preferred ability to move through RCC3 at low temperatures, while H2 had preferred ability at high temperatures. This observation indicates that in a co-crystal material that comprise multiple POCs, D2 can move through minimally functionalized pores and interact with the isotopic-selective functionalized POCs. Velocity analysis identified barrier distances, which control H2 and D2 interactions with POCs. In CC3-S and RCC3, observed interactions outside the pore aperture plane help the POC retain the gases and increase uptake within the material. For the functionalized 6ET-RCC3, the narrow pore aperture results in a longer path through the pore to exit the POC, resulting in identified experimental selectivity of D2. POC functionalization resulted in isotopic velocity dependence, highlighting unique behavior of H2 and D2 within the POCs and indicating separation by using KQS with a dependence on temperature. In the functionalized 6ET-RCC3, both H2 and D2 were observed to have higher velocities when exiting the POC pore compared to either inside or outside the POC. The increased Vexit highlights unique molecular behavior in the spatially confined region of the POC. The result of functionalization-dependent selectivity can be further exploited and tuned for specific isotopic separation and selectivity. Through the application of AIMD calculations, mechanisms of H2 and D2 separation were identified, allowing for targeted design of future novel materials for hydrogen isotope separation.