Multi–layer graphene folds supported on a substrate: a variational model
A mathematical model is developed to study the folding behaviour of multi–layer graphene sheets supported on a substrate. The conformation of the fold is determined from variational considerations based on two energies, namely the graphene elastic energy and the van der Waals (vdW) interaction energ...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2020-01-01
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| Series: | Materials Research Express |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2053-1591/abd26b |
| _version_ | 1797746828176785408 |
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| author | Jabr Aljedani Michael J Chen Barry J Cox |
| author_facet | Jabr Aljedani Michael J Chen Barry J Cox |
| author_sort | Jabr Aljedani |
| collection | DOAJ |
| description | A mathematical model is developed to study the folding behaviour of multi–layer graphene sheets supported on a substrate. The conformation of the fold is determined from variational considerations based on two energies, namely the graphene elastic energy and the van der Waals (vdW) interaction energy between graphene layers and the substrate. The model is nondimensionalized and variational calculus techniques are then employed to determine the conformation of the fold. The Lennard–Jones potential is used to determine the vdW interaction energy as well as the graphene–substrate and graphene–graphene spacing distances. The folding conformation is investigated under three different approximations of the total line curvature. Our findings show good agreement with experimental measurements of multi–layer graphene folds from the literature. |
| first_indexed | 2024-03-12T15:42:22Z |
| format | Article |
| id | doaj.art-a932c3ac74744bf39593e0cff7e46fef |
| institution | Directory Open Access Journal |
| issn | 2053-1591 |
| language | English |
| last_indexed | 2024-03-12T15:42:22Z |
| publishDate | 2020-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Materials Research Express |
| spelling | doaj.art-a932c3ac74744bf39593e0cff7e46fef2023-08-09T15:55:19ZengIOP PublishingMaterials Research Express2053-15912020-01-018101500210.1088/2053-1591/abd26bMulti–layer graphene folds supported on a substrate: a variational modelJabr Aljedani0https://orcid.org/0000-0002-8761-5870Michael J Chen1https://orcid.org/0000-0003-1855-7897Barry J Cox2https://orcid.org/0000-0002-0662-7037Faculty of Applied Studies, King Abdulaziz University , Jeddah, Saudi Arabia; School of Mathematical Sciences, University of Adelaide , Adelaide, AustraliaSchool of Mathematical Sciences, University of Adelaide , Adelaide, AustraliaSchool of Mathematical Sciences, University of Adelaide , Adelaide, AustraliaA mathematical model is developed to study the folding behaviour of multi–layer graphene sheets supported on a substrate. The conformation of the fold is determined from variational considerations based on two energies, namely the graphene elastic energy and the van der Waals (vdW) interaction energy between graphene layers and the substrate. The model is nondimensionalized and variational calculus techniques are then employed to determine the conformation of the fold. The Lennard–Jones potential is used to determine the vdW interaction energy as well as the graphene–substrate and graphene–graphene spacing distances. The folding conformation is investigated under three different approximations of the total line curvature. Our findings show good agreement with experimental measurements of multi–layer graphene folds from the literature.https://doi.org/10.1088/2053-1591/abd26bfoldsgrapheneelastic energyvan der Waals energyvariational calculus |
| spellingShingle | Jabr Aljedani Michael J Chen Barry J Cox Multi–layer graphene folds supported on a substrate: a variational model Materials Research Express folds graphene elastic energy van der Waals energy variational calculus |
| title | Multi–layer graphene folds supported on a substrate: a variational model |
| title_full | Multi–layer graphene folds supported on a substrate: a variational model |
| title_fullStr | Multi–layer graphene folds supported on a substrate: a variational model |
| title_full_unstemmed | Multi–layer graphene folds supported on a substrate: a variational model |
| title_short | Multi–layer graphene folds supported on a substrate: a variational model |
| title_sort | multi layer graphene folds supported on a substrate a variational model |
| topic | folds graphene elastic energy van der Waals energy variational calculus |
| url | https://doi.org/10.1088/2053-1591/abd26b |
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