Transmission of Helium Isotopes through Graphdiyne Pores: Tunneling versus Zero Point Energy Effects

Revisiting Numerical Solutions of Weakly Bound Noble Gases' Vibrational Energy Levels Modeled by the Improved Lennard-Jones Potential

We revisit the numerical solutions of vibrational eigenstates of weakly bound homonuclear and heteronuclear noble gas pairs by applying a Fortran program based on the Numerov method. The harmonic, Lennard-Jones (LJ), Morse, Tang-Toennies (TT), and Improved Lennard-Jones (ILJ) potential models have been implemented to represent the potential energy curves (PECs). The obtained vibrational energies spectrum was tested on the experimental data and accurate ab initio calculations at CCSD(T)/CBS level. The vibrational eigenvalues and eigenfunctions can be reproduced accurately within the ILJ potential model. Moreover, considering the calculated lifetime of van der Waals (vdW) complexes, the implementation of ILJ rather than standard LJ potential model has a significant impact on the systems dynamics by providing more representative atomic trajectories when the function is incorporated in force fields for molecular dynamics (MD) simulations. Overall, the ILJ function is the best suited potential model for the representation of vibrational motions and the determination of vibrational energy levels of weakly bound systems, both at equilibrium and non-equilibrium conditions.

Sodium into γ-Graphyne Multilayers: An Intercalation Compound for Anodes in Metal-Ion Batteries

The bulk synthesis of γ-graphyne has been recently achieved and evidenced a multilayered structure, which suggests its potential exploitation as a substitute of graphite-based anode materials for metals heavier than lithium (Li). In fact, each of its regular pores of sub-nanometric size features an optimal environment for hosting a single sodium (Na) ion, as reported here by means of accurate electronic structure calculations. We show that the graphyne/Na ion coupling mimics that found on the graphene/Li ion in terms of metal-single layer interaction and equilibrium distance. More importantly, in contrast to what is found for graphite, we demonstrate that graphyne intercalation compounds with Na are thermodynamically stable and feature an optimal storage capacity of 372 mAh·g-1. These findings, together with a limited crystal structure expansion upon Na intercalation, a low metal diffusion barrier as well as high electrical conductivity, pave the way to the development of novel graphyne-based anodes for efficient Na-ion batteries.

Separation of oxygen from nitrogen using a graphdiyne membrane: a quantum-mechanical study

Efficient separation of oxygen and nitrogen from air is a process of great importance for many industrial and medical applications. Two-dimensional (2D) membranes are very promising materials for separation of gases, as they offer enhanced mass transport due to their smallest atomic thickness. In this work, we examine the capacity of graphdiyne (GDY), a new 2D carbon allotrope with regular subnanometric pores, for separating oxygen (16O2) from nitrogen (14N2). A quantum-mechanical model has been applied to the calculation of the transmission probabilities and permeances of these molecules through GDY using force fields based on accurate electronic structure computations. It is found that the 16O2/14N2 selectivity (ratio of permeances) is quite high (e.g., about 106 and 102 at 100 and 300 K, respectively), indicating that GDY can be useful for separation of these species, even at room temperature. This is mainly due to the N2 transmission barrier (∼0.37 eV) which is considerably higher than the O2 one (∼0.25 eV). It is also found that molecular motions are quite confined inside the GDY pores and that, as a consequence, quantum effects (zero-point energy) are significant in the studied processes. Finally, we explore the possibility of 18O2/16O2 isotopologue separation due to these mass-dependent quantum effects, but it is found that the process is not practical since reasonable selectivities are concomitant with extremely small permeances.

Gas permeation through graphdiyne-based nanoporous membranes

Nanoporous membranes based on two dimensional materials are predicted to provide highly selective gas transport in combination with extreme permeance. Here we investigate membranes made from multilayer graphdiyne, a graphene-like crystal with a larger unit cell. Despite being nearly a hundred of nanometers thick, the membranes allow fast, Knudsen-type permeation of light gases such as helium and hydrogen whereas heavy noble gases like xenon exhibit strongly suppressed flows. Using isotope and cryogenic temperature measurements, the seemingly conflicting characteristics are explained by a high density of straight-through holes (direct porosity of ∼0.1%), in which heavy atoms are adsorbed on the walls, partially blocking Knudsen flows. Our work offers important insights into intricate transport mechanisms playing a role at nanoscale.

2D nanoporous membranes are predicted to provide highly selective gas transport in combination with extreme permeance. Here authors demonstrate gas separation performance and transport mechanisms through membranes of graphdiyne, a quasi 2D material with a graphene-like structure.

Molecular hydrogen isotope separation by a graphdiyne membrane: a quantum-mechanical study

Graphdiyne (GDY) has emerged as a very promising two-dimensional (2D) membrane for gas separation technologies. One of the most challenging goals is the separation of deuterium (D₂) and tritium (T₂) from a mixture with the most abundant hydrogen isotope, H₂, an achievement that would be of great value for a number of industrial and scientific applications. In this work we study the separation of hydrogen isotopes in their transport through a GDY membrane due to mass-dependent quantum effects that are enhanced by the confinement provided by its intrinsic sub-nanometric pores. A reliable improved Lennard-Jones force field, optimized on accurate ab initio calculations, has been built to describe the molecule-membrane interaction, where the molecule is treated as a pseudoatom. The quantum dynamics of the molecules impacting on the membrane along a complete set of incidence directions have been rigorously addressed by means of wave packet calculations in the 3D space, which have allowed us to obtain transmission probabilities and, in turn, permeances, as the thermal average of the molecular flux per unit pressure. The effect of the different incidence directions on the probabilities is analyzed in detail and it is concluded that restricting the simulations to a perpendicular incidence leads to reasonable results. Moreover, it is found that a simple 1D model-using a zero-point energy-corrected interaction potential-provides an excellent agreement with the 3D probailities for perpendicular incidence conditions. Finally, D₂/H₂ and T₂/H₂ selectivities are found to reach maximum values of about 6 and 21 at ≈50 and 45 K, respectively, a feature due to a balance between zero-point energy and tunneling effects in the transport dynamics. Permeances at these temperatures are below recommended values for practical applications, however, at slightly higher temperatures (77 K) they become acceptable while the selectivities preserve promising values, particularly for the separation of tritium.

In pursuit of accurate interlayer potentials for twisted bilayer graphynes

Recent explorations of twist in bilayer graphene and the discovery of superconducting phases at certain magic angles have laid the groundwork for a new branch in materials science called twistronics. However, theoretical studies on twisted layered materials are impeded due to the computational expense associated with first-principles calculations. Empirical force field approaches that include anisotropic terms to describe interlayer interactions have come to the fore as excellent alternatives to deal with such a stumbling block. Taking a cue from these formulations, herein, we describe our pursuit of capturing the interlayer interactions in bilayer graphynes with atomistic empirical potentials. The choice of the potentials, namely the improved Lennard-Jones potential and Hod's interlayer potential, is motivated by the objective of bringing out the role of anisotropy explicitly. Empirical parameters for both the potentials are calibrated against dispersion-corrected DFT calculations that are performed to incorporate the stacking, sliding and twisting features of the bilayer configurations. Although the isotropic improved Lennard-Jones potential is able to describe the interlayer stacking of graphynes, it is inadequate to account for the interlayer twist properties. The anisotropic Hod's interlayer potential portrays the interlayer twisting energy profiles of the benchmark DFT calculations with a reasonable accuracy. Our potential formulations can bestow impetus to the research on the homo- and hetero-bilayer structures of graphynes and other two-dimensional materials.

Isotopic separation of helium through graphyne membranes: a ring polymer molecular dynamics study

Microscopic-level understanding of the separation mechanism for two-dimensional (2D) membranes is an active area of research due to potential implications of this class of membranes for various technological processes. Helium (He) purification from the natural resources is of particular interest due to the shortfall in its production. In this work, we applied the ring polymer molecular dynamics (RPMD) method to graphdiyne (Gr2) and graphtriyne (Gr3) 2D membranes having variable pore sizes for the separation of He isotopes, and compare for the first time with rigorous quantum calculations. We found that the transmission rate through Gr3 is many orders of magnitude greater than Gr2. The selectivity of either isotope at low temperatures is a consequence of a delicate balance between the zero-point energy effect and tunneling of ⁴He and ³He. In particular, a remarkable tunneling effect is reported on the Gr2 membrane at 10 K, leading to a much larger permeation of the lighter species as compared to the heavier isotope. RPMD provides an efficient approach for studying the separation of He isotopes, taking into account quantum effects of light nuclei motions at low temperatures, which classical methods fail to capture.

Graphenylene and inorganic graphenylene nanopores for gas-phase 4He/3He separation: kinetic and steady-state considerations

Selective membrane-based separation of light isotopes is considered to be possible based on the quantum phenomena. In this regard, the role of two mass-dependent effects, quantum tunneling and zero-point energy (ZPE), is realized to be consequential for selective separation of helium isotopes using appropriate membranes. In the present study, the efficiency of two analogous nanoporous membranes, graphenylene (GP) and inorganic graphenylene (IGP), for gas phase separation of 3He and 4He has been theoretically investigated. Since the performance of the studied membranes is extremely influenced by the close competition between both quantum tunneling and zero-point energy (ZPE) effects, high precision in the calculations is required to provide more realistic theoretical predictions. The current study attempts to provide such predictions by applying domain-based local pair natural orbital coupled cluster theory (DLPNO-CCSD) to obtain the accurate helium-pore interaction potential, based on which the tunneling rates, as well as the exact (anharmonic) bound levels for the vibration of helium in the pore plane, are calculated. From the analysis of the obtained results, the performance of the GP and IGP nanopores has been investigated in both kinetic competition and steady-state conditions in the temperature range of 10-200 K. The results of this study indicate that harmonic oscillator approximation significantly overestimates the efficiency of the studied nanopores for helium isotope separation. Based on our accurate calculations, both GP and IGP nanopores provide almost similar selectivities in kinetic competition conditions (Stot4/3 ≈ 3 at T = 50 K); however, the predicted permeance for GP (10-8 mol m-2 s-1 bar-1) is about 100 times higher than that predicted for IGP under the same conditions. Under steady-state conditions, IGP has been shown to be more efficient than GP, since it provides acceptable values of separation factor at higher temperatures.

Helium Isotopes Quantum Sieving through Graphtriyne Membranes

We report accurate quantum calculations of the sieving of Helium atoms by two-dimensional (2D) graphtriyne layers with a new interaction potential. Thermal rate constants and permeances in an ample temperature range are computed and compared for both Helium isotopes. With a pore larger than graphdiyne, the most common member of the γ-graphyne family, it could be expected that the appearance of quantum effects were more limited. We find, however, a strong quantum behavior that can be attributed to the presence of selective adsorption resonances, with a pronounced effect in the low temperature regime. This effect leads to the appearance of some selectivity at very low temperatures and the possibility for the heavier isotope to cross the membrane more efficiently than the lighter, contrarily to what happened with graphdiyne membranes, where the sieving at low energy is predominantly ruled by quantum tunneling. The use of more approximate methods could be not advisable in these situations and prototypical transition state theory treatments might lead to large errors.

Multiscale Design of Graphyne-Based Materials for High-Performance Separation Membranes

By varying the number of acetylenic linkages connecting aromatic rings, a new family of atomically thin graph-n-yne materials can be designed and synthesized. Generating immense scientific interest due to its structural diversity and excellent physical properties, graph-n-yne has opened new avenues toward numerous promising engineering applications, especially for separation membranes with precise pore sizes. Having these tunable pore sizes in combination with their excellent mechanical strength to withstand high pressures, free-standing graph-n-yne is theoretically posited to be an outstanding membrane material for separating or purifying mixtures of either gases or liquids, rivaling or even dramatically exceeding the capabilities of current, state-of-art separation membranes. Computational modeling and simulations play an integral role in the bottom-up design and characterization of these graph-n-yne materials. Thus, here, the state of the art in modeling α-, β-, γ-, δ-, and 6,6,12-graphyne nanosheets for synthesizing graph-2-yne materials and 3D architectures thereof is discussed. Different synthesis methods are described and a broad overview of computational characterizations of graph-n-yne's electrical, chemical, and thermal properties is provided. Furthermore, a series of in-depth computational studies that delve into the specifics of graph-n-yne's mechanical strength and porosity, which confer superior performance for separation and desalination membranes, are reviewed.

The Accelerating World of Graphdiynes

Graphdiyne (GDY), a 2D allotrope of graphene, is first synthesized in 2010 and has attracted attention as a new low-dimensional carbon material. This work surveys the literature on GDYs. The history of GDYs is summarized, including their relationship with 2D graphyne carbons and yearly publication trends. GDY is a molecule-based nanosheet woven from a molecular monomer, hexaethynylbenzene; thus, it is synthesized by bottom-up approaches, which allow rich variation via monomer design. The GDY family and the synthetic procedures are also described. Highly developed π-conjugated electronic structures are common important features in GDY and graphene; however, the coexistence of sp and sp² carbons differentiates GDY from graphene. This difference gives rise to unique physical properties, such as high conductivity and large carrier mobility. Next, the theoretical and experimental studies of these properties are described in detail. A wide variety of applications are proposed for GDYs, including electrocatalysts and energy devices, which exploit the carbon-rich nature, porous framework, and expanded π-electron system of these compounds. Finally, potential uses are discussed.

4He/3He separation using oxygen-functionalized nanoporous graphene

Various oxygen-functionalized graphene nanopores were modeled to investigate their ⁴He/³He separation performances under both kinetic competition and steady state conditions.

Potential models for the simulation of methane adsorption on graphene: development and CCSD(T) benchmarks

Different force fields for the graphene-CH4 system are proposed including pseudo-atom and full atomistic models. Furthermore, different charge schemes are tested to evaluate the electrostatic interaction for the CH4 dimer. The interaction parameters are optimized by fitting to interaction energies at the DFT level, which were themselves benchmarked against CCSD(T) calculations. The potentials obtained with both the pseudo-atom and full atomistic approaches describe accurately enough the average interaction in the methane dimer as well as in the graphene-methane system. Moreover, the atom-atom potentials also correctly provide the energies associated with different orientations of the molecules. In the atomistic models, charge schemes including small charges allow for the adequate representation of the stability sequence of significant conformations of the methane dimer. Additionally, an intermediate charge of -0.63e on the carbon atom in methane leads to bond energies with errors of ca. 0.07 kcal mol-1 with respect to the CCSD(T) values for the methane dimer. For the graphene-methane interaction, the atom-atom potential model predicts an average interaction energy of 2.89 kcal mol-1, comparable to the experimental interaction energy of 3.00 kcal mol-1. Finally, the presented force fields were used to obtain self-diffusion coefficients that were checked against the experimental value found in the literature. The no-charge and Hirshfeld charge atom-atom models perform extremely well in this respect, while the cheapest potential considered, a pseudo-atom model without charges, still performs reasonably well.

Graphynes: indispensable nanoporous architectures in carbon flatland

Theoretical design and experimental realization of novel nanoporous architectures in carbon membranes has been a success story in recent times. Research on graphynes, an interesting class of materials in carbon flatland, has contributed immensely to this success story. Graphyne frameworks possessing sp and sp2 hybridized carbon atoms offer a variety of uniformly distributed nanoporous architectures for applications ranging from water desalination, gas separation, and energy storage to catalysis. Theory has played a pivotal role in research on graphynes, starting from the prediction of various structural forms to the emergence of their remarkable applications. Herein, we attempt to provide an up-to-date account of research on graphynes, highlighting contributions from numerous theoretical investigations that have led to the current status of graphynes as indispensable materials in carbon flatland. Despite unsolved challenges in large-scale synthesis, the future appears bright for graphynes in present theoretical and experimental research scenarios.

Quantum tunneling of thermal protons through pristine graphene

Engineering of atomically thin membranes for hydrogen isotope separation is an actual challenge which has a broad range of applications. Recent experiments [M. Lozada-Hidalgo et al., Science 351, 68 (2016)] unambiguously demonstrate an order-of-magnitude difference in permeabilities of graphene-based membranes to protons and deuterons at ambient conditions, making such materials promising for novel separation technologies. Here we demonstrate that the permeability mechanism in such systems changes from quantum tunneling for protons to quasi-classical transport for heavier isotopes. Quantum nuclear effects exhibit large temperature and mass dependence, modifying the Arrhenius activation energy and Arrhenius prefactor for protons by more than 0.5 eV and by seven orders of magnitude correspondingly. Our findings not only shed light on the separation process for hydrogen isotope ions passing through pristine graphene but also offer new insights for controlling ion transport mechanisms in nanostructured separation membranes by manipulating the shape of the barrier and transport process conditions.

Carbon Nanotubes Immersed in Superfluid Helium: The Impact of Quantum Confinement on Wetting and Capillary Action

A recent experimental study [ Ohba, Sci. Rep. 2016, 6, 28992 ] of gas adsorption on single-walled carbon nanotubes at temperatures between 2 and 5 K reported a quenched propagation of helium through carbon nanotubes with diameters below 7 Å despite the small kinetic diameter of helium atoms. After assessing the performance of a potential model for the He-nanotube interaction via ab initio calculations with density functional theory-based symmetry adapted perturbation theory, we apply orbital-free helium density functional theory to show that the counterintuitive experimental result is a consequence of the exceptionally high zero-point energy of helium and its tendency to form spatially separated layers of helium upon adsorption at the lowest temperatures. Helium filling factors are derived for a series of carbon nanotubes and compared to the available experimental data.

A Novel Nanoporous Graphite Based on Graphynes: First-Principles Structure and Carbon Dioxide Preferential Physisorption

Ubiquitous graphene is a stricly 2D material representing an ideal adsorbing platform due to its large specific surface area as well as its mechanical strength and resistance to both thermal and chemical stresses. However, graphene as a bulk material has the tendency to form irreversible agglomerates leading to 3D graphitic structures with a significant decrease of the area available for adsorption and no room for gas intercalation. In this paper, a novel nanoporous graphite formed by graphtriyne sheets is introduced; its 3D structure is theoretically assessed by means of electronic structure and molecular dynamics computations within the DFT level of theory. It is found that the novel layered carbon allotrope is almost as compact as pristine graphite but the inherent porosity of the 2D graphyne sheets and its relative stacking leads to nanochannels that cross the material and whose subnanometer size could allow the diffusion and storage of gas species. A molecular prototype of the nanochannel is used to accurately determine first-principles adsorption energies and enthalpies for CO₂, N₂, H₂O, and H₂ within the pores. The proposed porous graphite presents no significant barrier for gas diffusion and shows a high propensity for CO₂ physisorption with respect to the other relevant components in both pre- and postcombustion gas streams.