Subscriber access provided by BOSTON UNIV
Communication
Nanovelcro: theory of guided folding in atomically thin sheets with regions of complementary doping Yuanxi Wang, and Vincent H. Crespi Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b02773 • Publication Date (Web): 29 Sep 2017 Downloaded from http://pubs.acs.org on October 2, 2017
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Nano Letters is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
Nanovelcro: theory of guided folding in atomically thin sheets with regions of complementary doping Yuanxi Wang∗,†,‡ and Vincent H. Crespi∗,¶,§,k,‡,† †2-Dimensional Crystal Consortium,Pennsylvania State University, University Park, Pennsylvania 16802 ‡Material Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802 ¶Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA §Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA kDepartment of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA E-mail:
[email protected];
[email protected] Phone: +1 (814) 865-7533
1
ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Abstract 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 placement 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 towards a desired final folded structure. Here we provide a theoretical framework for a general methodology towards 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 e.g. 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.
Keywords 2D material, origami, membrane crumpling, density functional theory, molecular dynamics, doping
Folding on the macroscopic scale has a long history in origami and deployable structures. 1 Recent advances in the synthesis of atomically-thin two-dimensional materials such as graphene and monolayer transition metal dichalcogenides present a tempting stage for developing a similar folding technology at the micro/nano-scale. Energetically, folded (or scrolled) structures of two-dimensional materials are favored due to interlayer adhesion, 2–5 although a kinetic barrier may exist due to the curvature of an incipient fold. 6–9 Graphene, for example, can fold in a wide variety of experimental situations, 10 such as bridging of 2
ACS Paragon Plus Environment
Page 2 of 22
Page 3 of 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
adjacent layers under heat treatment 11,12 or electron beam irradiation, 13 mechanical 14 or thermal agitation, 15,16 coordination with ions in solution, 17 growth on curved substrates, 18 partial delamination from modified substrates, 19 deformation by an atomic force microscope (AFM) tip, 20,21 or simply as a by-product of mechanical exfoliation, 22 mechanical cleavage, 23 or post-growth transfer. 24,25 Single-sided functionaliztion or adsorption has also been theoretically studied as a means to induce folds. 26–28 However, these provide a limited degree of control over the placement and sequence of folds. In the absence of nanoscale “fingers” to guide folds, the sheet itself must be structured to prefer certain fold geometries. Something similar has been achieved for 1D biopolymers, both artificially (“staple strands” that exploit the precise base pairing of DNA to deform scaffold DNA into desired shapes 29–32 ) and by nature (protein folding driven by non-bonded interactions that largely favor the adhesion of like-to-like, i.e. hydrophobic residues to each other 33,34 ). The two-color theorem of origami 35 – that the crease pattern of a flat-folded sheet requires only two complementary colors to paint – suggests that a general framework for 2D folding could be formulated by matching complementary regions, as shown in Fig. 1.
1D folding
2D folding
Hydrophobic Hydrophillic Figure 1: Folding of 1D biopolymer, typically governed by hydrophobicity and hydrophilicity, favors adhesion of like-to-like. By contrast, the two-colorable theorem of origami brings regions with different colors into contact in the folded model.
3
ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Here we describe how p-type and n-type doping of 2D sheets 36–46 in selected areas 47,48 could be exploited as two “colors” to guide the sheets into preferred folded shapes where complementarily doped areas maximize their mutual overlap. While ab initio calculations of doped monolayer and bilayer 2D systems 49–58 have been reported, the interaction between complementary dopants in adjacent layers has not yet been investigated as a mechanism of folding control. Similar doping strategies were proposed to achieve the selective docking of molecules. 59,60 We begin by examining the structural energetics of a graphene bilayer with a boron substitution in one layer and a nitrogen substitution in the other, as a function of the lateral √ offset between the dopants, within a 4 × 12 3 supercell. The ground state has the dopants in close proximity 58 as shown in Fig. 2. The layers are then slid relative to each other by discrete amounts to vary the lateral boron-nitrogen separation while always maintaining AB stacking and relaxing other structural parameters at each stage. All density functional theory calculations were performed by the Vienna Ab-initio Simulation Package (VASP) 61,62 with the Perdew-Burke-Ernzerhof exchange-correlation functional 63 and with van der Waals corrections using the semi-empirical DFT-D2 method 64 (details in Supporting Information). The case of minimal boron-nitrogen separation is 0.21 eV more stable (per dopant pair) than the furthest separation examined, as shown by the red curve in Fig. 2. Another common nitrogen dopant geometry known as pyridinic-N (a nitrogen atom bonded to two carbon atoms near a carbon vacancy) p-dopes graphene 52,65 and may offset the n-doping contribution of substitutional nitrogens. However, dopant type selectivity can be achieved both during 66,67 and post-synthesis. 68–70 So long as the two types of N sites can be controllably created, the two-color scheme is still applicable (and could even be implemented with just nitrogen: DFT calculations show that pyridinic-N binds by 0.20 eV with substitutional-N). A similar result is obtained in a semiconducting transition metal dichalcogenide, MoS2 , with doping implemented in two ways. Replacing sulfur with chlorine or phosphorous yields the blue curve in Fig. 2, while replacing molybdenum with rhenium or niobium yields the
4
ACS Paragon Plus Environment
Page 4 of 22
Page 5 of 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
√ green curve, both performed with 4 × 8 3 supercells. The chalcogen dopant sites yield a stronger affinity, 0.21 eV, compared to 0.16 eV for Re/Nb doping. The stronger affinity between chalcogen dopants is likely because they are in direct contact, unlike the metal layers. The metal-doping case does have the advantage of proven experimental accessibility, as substitutional doping of rhenium 71,72 and niobium 73–75 have been confirmed. Experimental reports of sulfur substitution by chlorine 76 and phosphorus are more scarce, although prior theory is available. 77 The ∼0.2 eV p-n affinity for all three cases examined above is substantial, compared to the 0.10 and 0.18 eV interlayer adhesion per bilayer graphene and MoS2 unit cell. 78,79
Figure 2: Interaction between n- and p-dopants in separate layers of bilayer graphene or MoS2 , as a function of their lateral separation. Boron and nitrogen substitutional dopants in bilayer graphene have an attraction of 0.21 eV (red). Chlorine and phosphorous substitutions in bilayer MoS2 have an attraction of 0.21 eV (blue); niobium and rhenium in bilayer MoS2 bind by 0.16 eV (green). The mechanism for this spatial p-n affinity relies on intersheet charge transfer, as we 5
ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
analyze in the following n × n slab geometries. The first four panels of Fig. 3 show the band structures of monolayer graphene with one nitrogen or one boron substitution per 8×8 supercell, compared with band structures of a compensated bilayer, either dilated along z or collapsed into nitrogen-boron proximity. The size of the circles in blue (red) represent the projection of the wavefunction onto the nitrogen (boron) p atomic orbitals. Fermi energies are set to zero (gray horizontal lines) and energy scales are shifted to align vacuum levels across all cases. With pure nitrogen substitution, of course monolayers become n-doped and charge is transferred from nitrogen to graphene (see Supporting Information for a realspace analysis). The opposite is true for boron substitution. For a supercell containing both monolayers, but dilated by 15 ˚ A along z, the band structure resembles superposition of the two monolayer band structures with rigid band shifts: a mere 0.06 electron transfer lowers the electronic potential of the n-doped layer and raises that of the p-doped layer, suppressing further charge transfer. For the collapsed compensated bilayer, the shift in potential for each layer is alleviated by the accumulated opposite charge on the neighboring layer, allowing a 0.39-electron charge transfer from n to p (see differential charge densities in Supporting Information), as estimated by integrating the xy-integrated real space differential charge density ∆ρ(z) in the spaces above and below the partitioning plane where ∆ρ(z) crosses zero. 80 The charge transfer thus estimated, though simple in picture, is smaller than that estimated by integrating differences in band filling, since the wavefunction of a state with a well-defined energy is spatially delocalized; 80 the latter method is not implemented here since the bands do not shift rigidly after charge transfer. The collapsed bilayer system is further stabilized by the gap opening at the crossing point of the two sets of bands, with the Fermi energy lying at the midpoint between the nitrogen and boron levels. This charge transfer creates a built-in electric field, 50,58 separating by ∼0.7 eV the two Dirac points, whose remnants (dashed crossing lines) can be seen in the band structure below and above the band gap. The band structure can also been seen as a perturbation on the signature four-parabola band structure of bilayer graphene, with the two bands closest to the Fermi
6
ACS Paragon Plus Environment
Page 6 of 22
Page 7 of 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
energy developing small band inversions and yielding a gap.
Figure 3: (From left to right) Band structures of graphene with one nitrogen dopant, graphene with one boron dopant, and dilated and collapsed bilayer graphene with complementary doping; all calculated in 8×8 supercells. Blue (red) circles indicate nitrogen (boron) orbital character. The last panel shows the change in band √ structure (from lighter to darker) as the dopant pair slides towards each other in a 4 × 12 3 supercell. √ Having established the presence of interlayer charge transfer, we return to the 4 × 12 3 systems to reveal how interlayer interaction is modulated under sliding. As shown in the last panel of Fig. 3, when boron and nitrogen are in proximity (darker), the negatively charged boron dopant is closer to the positively charged nitrogen in the adjacent layer, lowering the occupied boron levels (red); the reverse applies for the unoccupied nitrogen levels. This shift in potential invites only an additional 5% of intersheet charge transfer but the total energy is lowered significantly due to the more favorable Coulomb interaction. Similar trends in band structures are found in the MoS2 systems with Re/Nb or Cl/P doping, as shown in Fig. 4 with the same color scheme. The charge transfers estimated in real space are larger than the graphene case: 0.55 electrons for the Nb/Re and 0.53 for the 7
ACS Paragon Plus Environment
Nano Letters
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
P/Cl (integrating changes in band filling should give 1 electron in both cases), and laterally localized near the dopants as shown in Supporting Information. The band gap of both cases decreases (upon collapsing the bilayer) due to the charge transfer and further decreases as the p- and n-dopants are slid away from each other, as was the case for graphene, indicating that the p-n affinity is due to the favorable Coulomb interaction when a p-n pair is laterally closest (Fig. 4). For metallic systems such as NbS2 , Mo and Zr dopants do not introduce a significant change in band filling and hence show virtually no charge transfer (
