DOI: 10.1063/1.4759146. Analytical methods for the mechanics of graphene bubbles

Analytical methods for the mechanics of graphene bubbles

10.1063/1.4759146

Crossref journal-article

AIP Publishing

Journal of Applied Physics (317)

Abstract

When placing a graphene membrane on a substrate, gas molecules may be trapped underneath to form bubbles. The size of a graphene bubble (e.g., diameter and height) depends on the number of gas molecules that are trapped, the elastic properties of graphene, and the interfacial adhesion between graphene and the substrate. A mechanics analysis of such graphene bubbles is conducted via membrane and nonlinear plate theories, so that the interfacial adhesion can be determined directly from measurements of the bubble size. A comparison of the results from these two models establishes that the membrane analysis is sufficient for relatively large bubbles. The adhesion energy of mechanically exfoliated graphene on silicon oxide is extracted from two reported data sets using the simple membrane theory, and the values range from 0.097 to 0.43 J/m2. Moreover, the strain distribution of the graphene bubbles and transport of gas molecules among the bubbles are discussed.

Bibliography

Yue, K., Gao, W., Huang, R., & Liechti, K. M. (2012). Analytical methods for the mechanics of graphene bubbles. Journal of Applied Physics, 112(8).

Authors 4

Kaimin Yue (first)
Wei Gao (additional)
Rui Huang (additional)
Kenneth M. Liechti (additional)

References 40 Referenced 120

10.1021/nl803087x / Nano Lett. (2009)
10.1063/1.3631632 / Appl. Phys. Lett. (2011)
10.1126/science.1191700 / Science (2010)
10.1021/nl203359n / Nano Lett. (2012)
10.1021/nl801457b / Nano Lett. (2008)
10.1038/nnano.2011.123 / Nat. Nanotechnol. (2011)
10.1063/1.3294960 / J. Appl. Phys. (2010)
{'volume-title': 'Thin Film Materials', 'year': '2003', 'key': '2023070423285045300_c8'} / Thin Film Materials (2003)
10.1103/PhysRevB.74.245413 / Phys. Rev. B (2006)
10.1126/science.1157996 / Science (2008)
10.1142/S1758825109000228 / Int. J. Appl. Mech. (2009)
{'key': '2023070423285045300_c12', 'first-page': '311', 'volume': '63', 'year': '1915', 'journal-title': 'Z. Math. Phys.'} / Z. Math. Phys. (1915)
10.1093/qjmam/9.1.84 / Q. J. Mech. Appl. Math. (1956)
10.1023/A:1007314720152 / Int. J. Fract. (1997)
{'year': '1997', 'key': '2023070423285045300_c15'} (1997)
10.1103/PhysRevB.64.235406 / Phys. Rev. B (2001)
10.1088/0022-3727/42/10/102002 / J. Phys. D: Appl. Phys. (2009)
10.1103/PhysRevB.82.235420 / Phys. Rev. B (2010)
10.1007/BF00032362 / Int. J. Fract. (1994)
{'first-page': '333', 'volume-title': 'Theory of Plates and Shells', 'year': '1940', 'key': '2023070423285045300_c20'} / Theory of Plates and Shells (1940)
10.1021/nl070613a / Nano Lett. (2007)
10.1088/0022-3727/44/45/452001 / J. Phys. D: Appl. Phys. (2011)
10.1103/PhysRevB.77.195409 / Phys. Rev. B (2008)
10.1115/1.2722311 / J. Appl. Mech. (2007)
10.1063/1.360255 / J. Appl. Phys. (1995)
10.1063/1.361485 / J. Appl. Phys. (1996)
10.1115/1.2187527 / J. Appl. Mech. (2006)
10.1063/1.3696980 / J. Appl. Phys. (2012)
10.1103/PhysRevB.79.205433 / Phys. Rev. B (2009)
10.1073/pnas.0811754106 / Proc. Natl. Acad. Sci. U.S.A. (2009)
10.1103/PhysRevB.82.201409 / Phys. Rev. B (2010)
10.1103/PhysRevLett.103.046801 / Phys. Rev. Lett. (2009)
10.1038/nphys1420 / Nat. Phys. (2010)
10.1016/j.ssc.2012.04.029 / Solid State Commun. (2012)
10.1021/nl204123h / Nano Lett. (2012)
{'volume-title': 'Materials Science of Thin Films', 'year': '2002', 'key': '2023070423285045300_c36'} / Materials Science of Thin Films (2002)
10.1063/1.3270425 / J. Appl. Phys. (2010)
10.1063/1.3437642 / J. Appl. Phys. (2010)
10.1088/0953-8984/22/48/485301 / J. Phys.: Condens. Matter (2010)
10.1063/1.3656720 / J. Appl. Phys. (2011)

Dates

Type	When
Created	12 years, 10 months ago (Oct. 19, 2012, 7:13 p.m.)
Deposited	2 years, 1 month ago (July 5, 2023, 9:08 a.m.)
Indexed	11 minutes ago (Aug. 28, 2025, 7:44 p.m.)
Issued	12 years, 10 months ago (Oct. 15, 2012)
Published	12 years, 10 months ago (Oct. 15, 2012)
Published Online	12 years, 10 months ago (Oct. 19, 2012)
Published Print	12 years, 10 months ago (Oct. 15, 2012)

Funders 1

National Science Foundation 10.13039/100000001
Region: Americas
gov (National government)
Labels4
1. U.S. National Science Foundation
2. NSF
3. US NSF
4. USA NSF
Awards2
1. CMMI-1130261
2. CMMI-0926851

BibTeX

@article{Yue_2012, title={Analytical methods for the mechanics of graphene bubbles}, volume={112}, ISSN={1089-7550}, url={http://dx.doi.org/10.1063/1.4759146}, DOI={10.1063/1.4759146}, number={8}, journal={Journal of Applied Physics}, publisher={AIP Publishing}, author={Yue, Kaimin and Gao, Wei and Huang, Rui and Liechti, Kenneth M.}, year={2012}, month=oct }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        28
      ]
    ],
    "date-time": "2025-08-28T23:44:40Z",
    "timestamp": 1756424680325,
    "version": "3.41.2"
  },
  "reference-count": 40,
  "publisher": "AIP Publishing",
  "issue": "8",
  "funder": [
    {
      "DOI": "10.13039/100000001",
      "name": "National Science Foundation",
      "doi-asserted-by": "publisher",
      "award": [
        "CMMI-0926851",
        "CMMI-1130261"
      ],
      "id": [
        {
          "id": "10.13039/100000001",
          "id-type": "DOI",
          "asserted-by": "publisher"
        }
      ]
    }
  ],
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2012,
        10,
        15
      ]
    ]
  },
  "abstract": "<jats:p>When placing a graphene membrane on a substrate, gas molecules may be trapped underneath to form bubbles. The size of a graphene bubble (e.g., diameter and height) depends on the number of gas molecules that are trapped, the elastic properties of graphene, and the interfacial adhesion between graphene and the substrate. A mechanics analysis of such graphene bubbles is conducted via membrane and nonlinear plate theories, so that the interfacial adhesion can be determined directly from measurements of the bubble size. A comparison of the results from these two models establishes that the membrane analysis is sufficient for relatively large bubbles. The adhesion energy of mechanically exfoliated graphene on silicon oxide is extracted from two reported data sets using the simple membrane theory, and the values range from 0.097 to 0.43\u2009J/m2. Moreover, the strain distribution of the graphene bubbles and transport of gas molecules among the bubbles are discussed.</jats:p>",
  "DOI": "10.1063/1.4759146",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2012,
        10,
        19
      ]
    ],
    "date-time": "2012-10-19T23:13:54Z",
    "timestamp": 1350688434000
  },
  "update-policy": "https://doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 120,
  "title": "Analytical methods for the mechanics of graphene bubbles",
  "prefix": "10.1063",
  "volume": "112",
  "author": [
    {
      "given": "Kaimin",
      "family": "Yue",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Research Center for the Mechanics of Solids, Structures and Materials, Department of Aerospace Engineering and Engineering Mechanics, University of Texas , Austin, Texas 78712, USA"
        }
      ]
    },
    {
      "given": "Wei",
      "family": "Gao",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Research Center for the Mechanics of Solids, Structures and Materials, Department of Aerospace Engineering and Engineering Mechanics, University of Texas , Austin, Texas 78712, USA"
        }
      ]
    },
    {
      "given": "Rui",
      "family": "Huang",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Research Center for the Mechanics of Solids, Structures and Materials, Department of Aerospace Engineering and Engineering Mechanics, University of Texas , Austin, Texas 78712, USA"
        }
      ]
    },
    {
      "given": "Kenneth M.",
      "family": "Liechti",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Research Center for the Mechanics of Solids, Structures and Materials, Department of Aerospace Engineering and Engineering Mechanics, University of Texas , Austin, Texas 78712, USA"
        }
      ]
    }
  ],
  "member": "317",
  "published-online": {
    "date-parts": [
      [
        2012,
        10,
        19
      ]
    ]
  },
  "reference": [
    {
      "key": "2023070423285045300_c1",
      "doi-asserted-by": "publisher",
      "first-page": "332",
      "DOI": "10.1021/nl803087x",
      "volume": "9",
      "year": "2009",
      "journal-title": "Nano Lett."
    },
    {
      "key": "2023070423285045300_c2",
      "doi-asserted-by": "publisher",
      "first-page": "093103",
      "DOI": "10.1063/1.3631632",
      "volume": "99",
      "year": "2011",
      "journal-title": "Appl. Phys. Lett."
    },
    {
      "key": "2023070423285045300_c3",
      "doi-asserted-by": "publisher",
      "first-page": "544",
      "DOI": "10.1126/science.1191700",
      "volume": "329",
      "year": "2010",
      "journal-title": "Science"
    },
    {
      "key": "2023070423285045300_c4",
      "doi-asserted-by": "publisher",
      "first-page": "617",
      "DOI": "10.1021/nl203359n",
      "volume": "12",
      "year": "2012",
      "journal-title": "Nano Lett."
    },
    {
      "key": "2023070423285045300_c5",
      "doi-asserted-by": "publisher",
      "first-page": "2458",
      "DOI": "10.1021/nl801457b",
      "volume": "8",
      "year": "2008",
      "journal-title": "Nano Lett."
    },
    {
      "key": "2023070423285045300_c6",
      "doi-asserted-by": "publisher",
      "first-page": "543",
      "DOI": "10.1038/nnano.2011.123",
      "volume": "6",
      "year": "2011",
      "journal-title": "Nat. Nanotechnol."
    },
    {
      "key": "2023070423285045300_c7",
      "doi-asserted-by": "publisher",
      "first-page": "026104",
      "DOI": "10.1063/1.3294960",
      "volume": "107",
      "year": "2010",
      "journal-title": "J. Appl. Phys."
    },
    {
      "volume-title": "Thin Film Materials",
      "year": "2003",
      "key": "2023070423285045300_c8"
    },
    {
      "key": "2023070423285045300_c9",
      "doi-asserted-by": "publisher",
      "first-page": "245413",
      "DOI": "10.1103/PhysRevB.74.245413",
      "volume": "74",
      "year": "2006",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2023070423285045300_c10",
      "doi-asserted-by": "publisher",
      "first-page": "385",
      "DOI": "10.1126/science.1157996",
      "volume": "321",
      "year": "2008",
      "journal-title": "Science"
    },
    {
      "key": "2023070423285045300_c11",
      "doi-asserted-by": "publisher",
      "first-page": "443",
      "DOI": "10.1142/S1758825109000228",
      "volume": "1",
      "year": "2009",
      "journal-title": "Int. J. Appl. Mech."
    },
    {
      "key": "2023070423285045300_c12",
      "first-page": "311",
      "volume": "63",
      "year": "1915",
      "journal-title": "Z. Math. Phys."
    },
    {
      "key": "2023070423285045300_c13",
      "doi-asserted-by": "publisher",
      "first-page": "84",
      "DOI": "10.1093/qjmam/9.1.84",
      "volume": "9",
      "year": "1956",
      "journal-title": "Q. J. Mech. Appl. Math."
    },
    {
      "key": "2023070423285045300_c14",
      "doi-asserted-by": "publisher",
      "first-page": "265",
      "DOI": "10.1023/A:1007314720152",
      "volume": "87",
      "year": "1997",
      "journal-title": "Int. J. Fract."
    },
    {
      "year": "1997",
      "key": "2023070423285045300_c15"
    },
    {
      "key": "2023070423285045300_c16",
      "doi-asserted-by": "publisher",
      "first-page": "235406",
      "DOI": "10.1103/PhysRevB.64.235406",
      "volume": "64",
      "year": "2001",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2023070423285045300_c17",
      "doi-asserted-by": "publisher",
      "first-page": "102002",
      "DOI": "10.1088/0022-3727/42/10/102002",
      "volume": "42",
      "year": "2009",
      "journal-title": "J. Phys. D: Appl. Phys."
    },
    {
      "key": "2023070423285045300_c18",
      "doi-asserted-by": "publisher",
      "first-page": "235420",
      "DOI": "10.1103/PhysRevB.82.235420",
      "volume": "82",
      "year": "2010",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2023070423285045300_c19",
      "doi-asserted-by": "publisher",
      "first-page": "21",
      "DOI": "10.1007/BF00032362",
      "volume": "67",
      "year": "1994",
      "journal-title": "Int. J. Fract."
    },
    {
      "first-page": "333",
      "volume-title": "Theory of Plates and Shells",
      "year": "1940",
      "key": "2023070423285045300_c20"
    },
    {
      "key": "2023070423285045300_c21",
      "doi-asserted-by": "publisher",
      "first-page": "1643",
      "DOI": "10.1021/nl070613a",
      "volume": "7",
      "year": "2007",
      "journal-title": "Nano Lett."
    },
    {
      "key": "2023070423285045300_c22",
      "doi-asserted-by": "publisher",
      "first-page": "452001",
      "DOI": "10.1088/0022-3727/44/45/452001",
      "volume": "44",
      "year": "2011",
      "journal-title": "J. Phys. D: Appl. Phys."
    },
    {
      "key": "2023070423285045300_c23",
      "doi-asserted-by": "publisher",
      "first-page": "195409",
      "DOI": "10.1103/PhysRevB.77.195409",
      "volume": "77",
      "year": "2008",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2023070423285045300_c24",
      "doi-asserted-by": "publisher",
      "first-page": "927",
      "DOI": "10.1115/1.2722311",
      "volume": "74",
      "year": "2007",
      "journal-title": "J. Appl. Mech."
    },
    {
      "key": "2023070423285045300_c25",
      "doi-asserted-by": "publisher",
      "first-page": "1614",
      "DOI": "10.1063/1.360255",
      "volume": "78",
      "year": "1995",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2023070423285045300_c26",
      "doi-asserted-by": "publisher",
      "first-page": "7148",
      "DOI": "10.1063/1.361485",
      "volume": "79",
      "year": "1996",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2023070423285045300_c27",
      "doi-asserted-by": "publisher",
      "first-page": "745",
      "DOI": "10.1115/1.2187527",
      "volume": "73",
      "year": "2006",
      "journal-title": "J. Appl. Mech."
    },
    {
      "key": "2023070423285045300_c28",
      "doi-asserted-by": "publisher",
      "first-page": "063513",
      "DOI": "10.1063/1.3696980",
      "volume": "111",
      "year": "2012",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2023070423285045300_c29",
      "doi-asserted-by": "publisher",
      "first-page": "205433",
      "DOI": "10.1103/PhysRevB.79.205433",
      "volume": "79",
      "year": "2009",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2023070423285045300_c30",
      "doi-asserted-by": "publisher",
      "first-page": "7304",
      "DOI": "10.1073/pnas.0811754106",
      "volume": "106",
      "year": "2009",
      "journal-title": "Proc. Natl. Acad. Sci. U.S.A."
    },
    {
      "key": "2023070423285045300_c31",
      "doi-asserted-by": "publisher",
      "first-page": "201409",
      "DOI": "10.1103/PhysRevB.82.201409",
      "volume": "82",
      "year": "2010",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2023070423285045300_c32",
      "doi-asserted-by": "publisher",
      "first-page": "046801",
      "DOI": "10.1103/PhysRevLett.103.046801",
      "volume": "103",
      "year": "2009",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2023070423285045300_c33",
      "doi-asserted-by": "publisher",
      "first-page": "30",
      "DOI": "10.1038/nphys1420",
      "volume": "6",
      "year": "2010",
      "journal-title": "Nat. Phys."
    },
    {
      "key": "2023070423285045300_c34",
      "doi-asserted-by": "publisher",
      "first-page": "1359",
      "DOI": "10.1016/j.ssc.2012.04.029",
      "volume": "152",
      "year": "2012",
      "journal-title": "Solid State Commun."
    },
    {
      "key": "2023070423285045300_c35",
      "doi-asserted-by": "publisher",
      "first-page": "1448",
      "DOI": "10.1021/nl204123h",
      "volume": "12",
      "year": "2012",
      "journal-title": "Nano Lett."
    },
    {
      "volume-title": "Materials Science of Thin Films",
      "year": "2002",
      "key": "2023070423285045300_c36"
    },
    {
      "key": "2023070423285045300_c37",
      "doi-asserted-by": "publisher",
      "first-page": "044301",
      "DOI": "10.1063/1.3270425",
      "volume": "107",
      "year": "2010",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2023070423285045300_c38",
      "doi-asserted-by": "publisher",
      "first-page": "123531",
      "DOI": "10.1063/1.3437642",
      "volume": "107",
      "year": "2010",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2023070423285045300_c39",
      "doi-asserted-by": "publisher",
      "first-page": "485301",
      "DOI": "10.1088/0953-8984/22/48/485301",
      "volume": "22",
      "year": "2010",
      "journal-title": "J. Phys.: Condens. Matter"
    },
    {
      "key": "2023070423285045300_c40",
      "doi-asserted-by": "publisher",
      "first-page": "083526",
      "DOI": "10.1063/1.3656720",
      "volume": "110",
      "year": "2011",
      "journal-title": "J. Appl. Phys."
    }
  ],
  "container-title": "Journal of Applied Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/1.4759146/13435642/083512_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/1.4759146/13435642/083512_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        7,
        5
      ]
    ],
    "date-time": "2023-07-05T13:08:25Z",
    "timestamp": 1688562505000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jap/article/112/8/083512/375385/Analytical-methods-for-the-mechanics-of-graphene"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2012,
        10,
        15
      ]
    ]
  },
  "references-count": 40,
  "journal-issue": {
    "issue": "8",
    "published-print": {
      "date-parts": [
        [
          2012,
          10,
          15
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.4759146",
  "relation": {},
  "ISSN": [
    "0021-8979",
    "1089-7550"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2012,
        10,
        15
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2012,
        10,
        15
      ]
    ]
  },
  "article-number": "083512"
}