Graphynes: indispensable nanoporous architectures in carbon flatland

Colossal figure of merit and compelling HER catalytic activity of holey graphyne

Herein, we have conducted a comprehensive study to uncover the thermal transport properties and hydrogen evolution reaction catalytic activity of recently synthesized holey graphyne. Our findings disclose that holey graphyne has a direct bandgap of 1.00 eV using the HSE06 exchange-correlation functional. The absence of imaginary phonon frequencies in the phonon dispersion ensures its dynamic stability. The formation energy of holey graphyne turns out to be - 8.46 eV/atom, comparable to graphene (- 9.22 eV/atom) and h-BN (- 8.80 eV/atom). At 300 K, the Seebeck coefficient is as high as 700 μV/K at a carrier concentration of 1 × 10¹⁰ cm^-2. The predicted room temperature lattice thermal conductivity (κ_l) of 29.3 W/mK is substantially lower than graphene (3000 W/mK) and fourfold smaller than C₃N (128 W/mK). At around 335 nm thickness, the room temperature κ_l suppresses by 25%. The calculated p-type figure of merit (ZT) reaches a maximum of 1.50 at 300 K, higher than that of holey graphene (ZT = 1.13), γ-graphyne (ZT = 0.48), and pristine graphene (ZT = 0.55 × 10^-3). It further scales up to 3.36 at 600 K. Such colossal ZT values make holey graphyne an appealing p-type thermoelectric material. Besides that, holey graphyne is a potential HER catalyst with a low overpotential of 0.20 eV, which further reduces to 0.03 eV at 2% compressive strain.

Unfurling Anion-π Interactions Involving Graphynes

Ever since the inception of anion-π interactions, their nature and functional relevance have intrigued researchers. We address the twin challenge of elucidation of the role of extended conjugation and design of all-carbon neutral anion receptors by computations on the anion-π complexes of the halide ions with graphynes. Leveraging on the extended π-conjugation effects, we unfurl the functional relevance of graphynes as anion receptors using descriptors such as electrostatic potential, quadrupole moments, molecular polarizabilities and binding energies. Further, employing natural energy decomposition analysis, we assert that anion-π interactions are not merely dominated by electrostatic interactions. The polarization components do indeed play a crucial role in governing the binding of the anions to the graphynes.

Multilayer Graphtriyne Membranes for Separation and Storage of CO2: Molecular Dynamics Simulations of Post-Combustion Model Mixtures

The ability to remove carbon dioxide from gaseous mixtures is a necessary step toward the reduction of greenhouse gas emissions. As a contribution to this field of research, we performed a molecular dynamics study assessing the separation and adsorption properties of multi-layered graphtriyne membranes on gaseous mixtures of CO₂, N₂, and H₂O. These mixtures closely resemble post-combustion gaseous products and are, therefore, suitable prototypes with which to model possible technological applications in the field of CO₂ removal methodologies. The molecular dynamics simulations rely on a fairly accurate description of involved force fields, providing reliable predictions of selectivity and adsorption coefficients. The characterization of the interplay between molecules and membrane structure also permitted us to elucidate the adsorption and crossing processes at an atomistic level of detail. The work is intended as a continuation and a strong enhancement of the modeling research and characterization of such materials as molecular sieves for CO₂ storage and removal.

Elucidation of noble gas cluster configurations bound on graphdiyne: A metaheuristic approach

Graphynes are a class of all-carbon two-dimensional membranes that have been intensely researched for various membrane-based technologies on account of their unique pore architectures. Herein, we report an investigation of the mechanism and energetics of adsorption of noble gases (He, Ne and Ar) on graphdiyne (GDY), the most popular form of graphynes. Two global optimization techniques, namely particle swarm optimization (PSO) and differential evolution are employed to predict the putative global minima configurations of rare gas clusters in the size range 1-30 when adsorbed on GDY. We use the 12-6 Lennard-Jones potential to represent the pairwise non-covalent interactions between various interacting atoms. Initially, the gas atoms adsorb as monolayers on GDY at the centers of the triangular pores until all the triangular pores are filled. This is followed by a second layer formation on top of the hexagonal pore centers or on top of the C-C bonds. The findings from the empirical approach are further validated by performing density functional theory calculations on the predicted adsorbed cluster configurations. We have also looked into the adsorption of noble gas clusters on bilayer GDY systems and have found that the intercalation of gas atoms within the bilayers is feasible. Our study suggests that the stochastic nature of the swarm intelligence technique, PSO can assist in an effective search of the potential energy surfaces for the global minima, eventually enabling large-scale simulations.

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.

Modeling the Adsorption of Polycyclic Aromatic Hydrocarbons on Graphynes: An Improved Lennard-Jones Formulation

Research on the development of theoretical methodologies for modeling noncovalent interactions governing the adsorption of polycyclic aromatic hydrocarbons (PAHs) on graphene and other two-dimensional materials is being intensely pursued in recent times. Highly accurate empirical potentials have emerged as a viable alternative to first-principles calculations for performing large-scale simulations. Herein, we report exploration of the potential energy surfaces for the adsorption of cata-condensed and peri-condensed PAHs on graphynes (GYs) using the improved Lennard-Jones (ILJ) potential. Initially, the ILJ potential is parametrized against benchmark electronic structure calculations performed on a selected set of PAH-GY complexes using dispersion-corrected density functional theory. The accuracy of the parametrization scheme is then assessed by a comparison of the adsorption features predicted from the ILJ potential with those computed using electronic structure calculations. The potential energy profiles as well as the single point energy calculations and geometry reoptimizations performed on the minimum-energy configurations predicted by the ILJ potential for a broader range of PAH-GY complexes provided a validation of the parametrization scheme. Finally, by an extrapolation of the PAH adsorption energies on various GYs, we estimated the interlayer cohesion energies for the van der Waals bilayer heterostructures of GYs with graphene to be in the range of 25-50 meV/atom.

Mechanism of Oxygen Reduction Reaction in Alkaline Medium on Nitrogen-Doped Graphyne and Graphdiyne Families: A First Principles Study

Using extensive first principles protocols, a systematic investigation is performed to probe the oxygen reduction reaction (ORR) mechanism on nitrogen (N) doped graphynes (Gys, e. g. αGy, βGy, γGy and 6,6,12Gy) and graphdiyne (Gdy) in alkaline medium. We considered both associative and dissociative pathways, as well as two distinct intermediate forks for each of them depending on the first protonation site(s). Following the dissociative approach, the activation energy to form an O₂ dissociated configuration is found as a function of the distances migrated by the O atoms over the catalyst surface and the amount of charge transferred from the C atoms linked to N. N doped αGy and 6,6,12Gy emerged as the best electrocatalyst comparing both pathways having lowest overpotentials of 0.88 and 0.82 V, respectively. The rate-limiting steps for the two different intermediate routes are observed to be dependent on the first protonation site(s) and related to the desorption of the OH radical from the sp hybridized C atom site(s) linked to N. Hence, the OH adsorption energy is identified as a descriptor for the efficiency of the ORR for the considered systems. The stabilities of the ORR intermediates are further elaborated in terms of pH and electrode potential.

The electronic properties of non-conventional -graphyne nanoribbons

We study the electronic and transport properties of non-conventional graphyne nanoribbons with spin-polarized states, highlighting spin-filtering and spin-switching mechanisms.

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.

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.

Structural, Electronic, and Vibrational Properties of a Two-Dimensional Graphdiyne-like Carbon Nanonetwork Synthesized on Au(111): Implications for the Engineering of sp-sp2 Carbon Nanostructures

Graphdiyne, atomically thin two-dimensional (2D) carbon nanostructure based on sp-sp2 hybridization is an appealing system potentially showing outstanding mechanical and optoelectronic properties. Surface-catalyzed coupling of halogenated sp-carbon-based molecular precursors represents a promising bottom-up strategy to fabricate extended 2D carbon systems with engineered structure on metallic substrates. Here, we investigate the atomic-scale structure and electronic and vibrational properties of an extended graphdiyne-like sp-sp2 carbon nanonetwork grown on Au(111) by means of the on-surface synthesis. The formation of such a 2D nanonetwork at its different stages as a function of the annealing temperature after the deposition is monitored by scanning tunneling microscopy (STM), Raman spectroscopy, and combined with density functional theory (DFT) calculations. High-resolution STM imaging and the high sensitivity of Raman spectroscopy to the bond nature provide a unique strategy to unravel the atomic-scale properties of sp-sp2 carbon nanostructures. We show that hybridization between the 2D carbon nanonetwork and the underlying substrate states strongly affects its electronic and vibrational properties, modifying substantially the density of states and the Raman spectrum compared to the free standing system. This opens the way to the modulation of the electronic properties with significant prospects in future applications as active nanomaterials for catalysis, photoconversion, and carbon-based nanoelectronics.

Enhanced Selective Hydrogen Permeation through Graphdiyne Membrane: A Theoretical Study

Graphdiyne (GDY), with uniform pores and atomic thickness, is attracting widespread attention for application in H2 separation in recent years. However, the challenge lies in the rational design of GDYs for fast and selective H2 permeation. By MD and DFT calculations, several flexible GDYs were constructed to investigate the permeation properties of four pure gas (H2, N2, CO2, and CH4) and three equimolar binary mixtures (H2/N2, H2/CO2, and H2/CH4) in this study. When the pore size is smaller than 2.1 Å, the GDYs acted as an exceptional filter for H2 with an approximately infinite H2 selectivity. Beyond the size-sieving effect, in the separation process of binary mixtures, the blocking effect arising from the strong gas-membrane interaction was proven to greatly impede H2 permeation. After understanding the mechanism, the H2 permeance of the mixtures of H2/CO2 was further increased to 2.84 × 105 GPU by reducing the blocking effect with the addition of a tiny amount of surface charges, without sacrificing the selectivity. This theoretical study provides an additional atomic understanding of H2 permeation crossing GDYs, indicating that the GDY membrane could be a potential candidate for H2 purification.