Details
| Original language | English |
|---|---|
| Article number | 015021 |
| Journal | 2D Materials |
| Volume | 6 |
| Issue number | 1 |
| Early online date | 4 Dec 2018 |
| Publication status | Published - Jan 2019 |
Abstract
Thin adhesive films can be removed from substrates, torn, and folded in distinct geometries under external driving forces. In two-dimensional materials, however, these processes can be self-driven as shown in previous studies on folded twisted bilayer graphene nanoribbons produced by spontaneous tearing and peeling from a substrate. Here, we use atomic force microscopy techniques to generate and characterize the geometrical structure of naturally self-grown folded nanoribbon structures. Measurements of nanoribbon width and interlayer separation reveal similar twist-angle dependences possibly caused by the anisotropy in the bilayer potential. In addition, analysis of the data shows an unexpected correlation between the height of the folded arc edge - parameterized by a radius R - , and the ribbon width, suggestive of a self-growth process driven by a variable cross-sectional shape. These observations are well described by an energy minimization model that includes the bilayer adhesion energy density as represented by a distance dependent Morse potential. We obtain an analytical expression for the radius R versus the ribbon width that predicts a renormalized bending rigidity and stands in good agreement with experimental observations. The newly found relation between these geometrical parameters suggests a mechanism for tailored growth of folded twisted bilayer graphene- a platform for many intriguing physics phenomena.
Keywords
- graphene folds, graphene ribbons, twisted bilayer grapheme
ASJC Scopus subject areas
- Chemistry(all)
- General Chemistry
- Materials Science(all)
- General Materials Science
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
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In: 2D Materials, Vol. 6, No. 1, 015021, 01.2019.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Linking interlayer twist angle to geometrical parameters of self-assembled folded graphene structures
AU - Rode, Johannes C.
AU - Zhai, Dawei
AU - Belke, Christopher
AU - Hong, Sung Ju
AU - Schmidt, Hennrik
AU - Sandler, Nancy
AU - Haug, Rolf J.
N1 - Funding information: The authors acknowledge financial support from the DFG within the priority program SPP 1459, the School for Contacts in Nanosystems, the ‘Fundamentals of Physics and Metrology’ initiative (JCR, CB, SJH, HS, and RJH), and NSF-DMR 1508325 (DZ and NS). This work was partially performed at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611 (NS). JC Rode acknowledges support from the Hannover School for Nanotechnology. The authors thank Peter Behrens and Hadar Steinberg for helpful discussion.
PY - 2019/1
Y1 - 2019/1
N2 - Thin adhesive films can be removed from substrates, torn, and folded in distinct geometries under external driving forces. In two-dimensional materials, however, these processes can be self-driven as shown in previous studies on folded twisted bilayer graphene nanoribbons produced by spontaneous tearing and peeling from a substrate. Here, we use atomic force microscopy techniques to generate and characterize the geometrical structure of naturally self-grown folded nanoribbon structures. Measurements of nanoribbon width and interlayer separation reveal similar twist-angle dependences possibly caused by the anisotropy in the bilayer potential. In addition, analysis of the data shows an unexpected correlation between the height of the folded arc edge - parameterized by a radius R - , and the ribbon width, suggestive of a self-growth process driven by a variable cross-sectional shape. These observations are well described by an energy minimization model that includes the bilayer adhesion energy density as represented by a distance dependent Morse potential. We obtain an analytical expression for the radius R versus the ribbon width that predicts a renormalized bending rigidity and stands in good agreement with experimental observations. The newly found relation between these geometrical parameters suggests a mechanism for tailored growth of folded twisted bilayer graphene- a platform for many intriguing physics phenomena.
AB - Thin adhesive films can be removed from substrates, torn, and folded in distinct geometries under external driving forces. In two-dimensional materials, however, these processes can be self-driven as shown in previous studies on folded twisted bilayer graphene nanoribbons produced by spontaneous tearing and peeling from a substrate. Here, we use atomic force microscopy techniques to generate and characterize the geometrical structure of naturally self-grown folded nanoribbon structures. Measurements of nanoribbon width and interlayer separation reveal similar twist-angle dependences possibly caused by the anisotropy in the bilayer potential. In addition, analysis of the data shows an unexpected correlation between the height of the folded arc edge - parameterized by a radius R - , and the ribbon width, suggestive of a self-growth process driven by a variable cross-sectional shape. These observations are well described by an energy minimization model that includes the bilayer adhesion energy density as represented by a distance dependent Morse potential. We obtain an analytical expression for the radius R versus the ribbon width that predicts a renormalized bending rigidity and stands in good agreement with experimental observations. The newly found relation between these geometrical parameters suggests a mechanism for tailored growth of folded twisted bilayer graphene- a platform for many intriguing physics phenomena.
KW - graphene folds
KW - graphene ribbons
KW - twisted bilayer grapheme
UR - http://www.scopus.com/inward/record.url?scp=85059246162&partnerID=8YFLogxK
U2 - 10.1088/2053-1583/aaf1e7
DO - 10.1088/2053-1583/aaf1e7
M3 - Article
AN - SCOPUS:85059246162
VL - 6
JO - 2D Materials
JF - 2D Materials
SN - 2053-1583
IS - 1
M1 - 015021
ER -