NanoVelcro: Theory of Guided Folding in Atomically Thin Sheets with Regions of Complementary Doping

Folding has been commonly observed in two-dimensional materials such as graphene and monolayer transition metal dichalcogenides. Although interlayer coupling stabilizes these folds, it provides no control over the <i>placement</i> of the fold, let alone the final folded shape. Lacking nanoscale “fingers” to externally guide folding, control requires interactions engineered into the sheets that guide them toward a desired final folded structure. Here we provide a theoretical framework for a general methodology toward this end: atomically thin 2D sheets are doped with patterns of complementary n-type and p-type regions whose preferential adhesion favors folding into desired shapes. The two-colorable theorem in flat-foldable origami ensures that arbitrary folding patterns are in principle accessible to this method. This complementary doping method can be combined with nanoscale crumpling (by, for example, passage of 2D sheets through holes) to obtain not only control over fold placements but also the ability to distinguish between degenerate folded states, thus attaining nontrivial shapes inaccessible to sequential folding

Theory of Finite-Length Grain Boundaries of Controlled Misfit Angle in Two-Dimensional Materials

Grain boundaries in two-dimensional crystals are usually thought to separate distinct crystallites and as such they must either form closed loops or terminate at the boundary of a sample. However, when an atomically thin two-dimensional crystal grows on a substrate of nonzero Gaussian curvature, it can develop <i>finite-length</i> grain boundaries that terminate abruptly within a monocrystalline domain. We show that by properly designing the substrate topography, these grain boundaries can be placed at desired locations and at specified misfit angles, as the thermodynamic ground state of a two-dimensional (2D) system bound to a substrate. Compared against the hypothetical competition of growing defectless 2D materials on a Gaussian-curved substrate with consequential fold development or detachment from the substrate, the nucleation and formation of finite-length grain boundaries can be made energetically favorably given sufficient substrate adhesion on the order of tens of meV/Ų for typical 2D materials. New properties specific to certain grain boundary geometries, including magnetism and metallicity, can thus be engineered into 2D crystals through topographic design of their substrates

Systematic Enumeration of sp³ Nanothreads

Slow decompression of crystalline benzene in large-volume high-pressure cells has recently achieved synthesis of a novel one-dimensional allotrope of sp³ carbon in which stacked columns of benzene molecules rehybridize into an ordered crystal of nanothreads. The progenitor benzene molecules function as six-valent one-dimensional superatoms with multiple binding sites. Here we enumerate their hexavalent bonding geometries, recognizing that the repeat unit of interatomic connectivity (“topological unit cell”) need not coincide with the crystallographic unit cell, and identify the most energetically favorable cases. A topological unit cell of one or two benzene rings with at least two bonds interconnecting each adjacent pair of rings, accommodates 50 topologically distinct nanothreads, 15 of which are within 80 meV/carbon atom of the most stable member. Optimization of aperiodic helicity reveals the most stable structures to be chiral. We generalize Euler’s rules for ring counting to cover this new form of very thin one-dimensional carbon, calculated their physical properties, and propose a naming convention that can be generalized to handle nanothreads formed from other progenitor molecules

Intrinsic Magnetism of Grain Boundaries in Two-Dimensional Metal Dichalcogenides

Grain boundaries (GBs) are structural imperfections that typically degrade the performance of materials. Here we show that dislocations and GBs in two-dimensional (2D) metal dichalcogenides MX₂ (M = Mo, W; X = S, Se) can actually <i>improve</i> the material by giving it a qualitatively new physical property: magnetism. The dislocations studied all display a substantial magnetic moment of ∼1 Bohr magneton. In contrast, dislocations in other well-studied 2D materials are typically nonmagnetic. GBs composed of pentagon–heptagon pairs interact ferromagnetically and transition from semiconductor to half-metal or metal as a function of tilt angle and/or doping level. When the tilt angle exceeds 47°, the structural energetics favor square–octagon pairs and the GB becomes an antiferromagnetic semiconductor. These exceptional magnetic properties arise from interplay of dislocation-induced localized states, doping, and locally unbalanced stoichiometry. Purposeful engineering of topological GBs may be able to convert MX₂ into a promising 2D magnetic semiconductor

All the Ways To Have Substituted Nanothreads

We describe a general, symmetry-conditioned way of enumerating isomers of saturated singly substituted one-dimensional nanothreads of the (CH)₅E and (CH)₅CR type, where E is a heteroatom and R is a substituent. Four nanothreads  so-called tube (3,0), polytwistane, the zipper polymer, and polymer I, are treated in detail. The methodology, combining symmetry arguments and computer-based enumeration, is generally applicable to isomerism problems in polymers

Controllable Edge Exposure of MoS₂ for Efficient Hydrogen Evolution with High Current Density

MoS₂-based electrocatalysts are promising cost-effective replacements for Pt-based catalysts for hydrogen evolution by water splitting, yet achieving high current density at low overpotential remains a challenge. Herein, a binder-free electrode of MoS₂/CNF (carbon nanofiber) is prepared by electrospinning and subsequent thermal treatment. The growth of MoS₂ nanoplates contained within or protruding out from the CNF can be controlled by adding urea or ammonium bicarbonate to the electrospinning precursors, due to the cross-linking effects of urea and the increased porosity caused by pyrolysis of ammonium bicarbonate allowing growth through pores in the CNF. By virtue of the abundant exposed edges in this microstructure and strong bonding between the catalyst and the conductive carbon network, the composite material exhibits ultrahigh electrocatalytic hydrogen evolution activity in acidic solutions, with current densities of 500 and 1000 mA/cm² at overpotentials of 380 and 450 mV, respectively, exceeding the performance of many reported MoS₂-based catalysts and even commercial Pt/C catalysts. Thus, MoS₂/CNF membranes show potential as efficient and flexible binder-free electrodes for electrocatalytic hydrogen production

All the Ways To Have Substituted Nanothreads

We describe a general, symmetry-conditioned way of enumerating isomers of saturated singly substituted one-dimensional nanothreads of the (CH)₅E and (CH)₅CR type, where E is a heteroatom and R is a substituent. Four nanothreads  so-called tube (3,0), polytwistane, the zipper polymer, and polymer I, are treated in detail. The methodology, combining symmetry arguments and computer-based enumeration, is generally applicable to isomerism problems in polymers

Reversible Intercalation of Hexagonal Boron Nitride with Brønsted Acids

Hexagonal boron nitride (h-BN) is an insulating compound that is structurally similar to graphite. Like graphene, single sheets of BN are atomically flat, and they are of current interest in few-layer hybrid devices, such as transistors and capacitors, that contain insulating components. While graphite and other layered compounds can be intercalated by redox reactions and then converted chemically to suspensions of single sheets, insulating BN is not susceptible to oxidative intercalation except by extremely strong oxidizing agents. We report that stage-1 intercalation compounds can be formed by simple thermal drying of h-BN in Brønsted acids H₂SO₄, H₃PO₄, and HClO₄. X-ray photoelectron and vibrational spectra, as well as electronic structure and molecular dynamics calculations, demonstrate that noncovalent interactions of these oxyacids with the basic N atoms of the sheets drive the intercalation process

ReaxFF Reactive Force-Field Study of Molybdenum Disulfide (MoS₂)

Two-dimensional layers of molybdenum disulfide, MoS₂, have been recognized as promising materials for nanoelectronics due to their exceptional electronic and optical properties. Here we develop a new ReaxFF reactive potential that can accurately describe the thermodynamic and structural properties of MoS₂ sheets, guided by extensive density functional theory simulations. This potential is then applied to the formation energies of five different types of vacancies, various vacancy migration barriers, and the transition barrier between the semiconducting 2H and metallic 1T phases. The energetics of ripplocations, a recently observed defect in van der Waals layers, is examined, and the interplay between these defects and sulfur vacancies is studied. As strain engineering of MoS₂ sheets is an effective way to manipulate the sheets’ electronic and optical properties, the new ReaxFF description can provide valuable insights into morphological changes that occur under various loading conditions and defect distributions, thus allowing one to tailor the electronic properties of these 2D crystals

Spontaneous Formation of Atomically Thin Stripes in Transition Metal Dichalcogenide Monolayers

Whether an alloy is random or ordered can have profound effects on its properties. The close chemical similarity of W and Mo in the two-dimensional semiconductors MoS₂ and WS₂ has led to the expectation that W_<i>x</i>Mo_1–<i>x</i>S₂ is a random alloy. Here we report that triangular monolayer flakes of W_<i>x</i>Mo_1–<i>x</i>S₂ produced by sulfurization of MoO₃/WO₃ are not only nonrandom, but also <i>anisotropic</i>: W and Mo form atomically thin chains oriented parallel to the edges of the triangle, especially around <i>x</i> ∼ 0.5, as resolved by aberration-corrected transmission electron microscopy. First-principles calculations reveal that the binding energies of striped and random alloys are nearly identical but that phase segregation at the growth edge favors one metal over another depending on the local sulfur availability, independent of the composition deeper inside the monolayer. Thus, atomically thin striping is kinetically driven and controlled by fluctuations that couple the local chemical potentials of metals and chalcogenide. Considering the nearly identical electronic properties but very different atomic masses of Mo and W, the resulting striped alloy is electronically isotropic, but vibrationally anisotropic. Phonon anomalies associated with the stripe ordering are predicted, as is an anisotropic thermal conductivity. More generally, fluctuation-driven striping provides a mechanism to produce in-plane subnanometer superlattices within two-dimensional crystals, with broad implications for controlling the electronic, optical, and structural properties of these systems