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=== Narrowest examples === {{multiple image | header = Tube types that are "degenerate" for being too narrow | image1 = nanotube strip +01 000.pdf | caption1 = Degenerate "zigzag" tube type (1,0) | image2 = nanotube strip +02 000.pdf | caption2 = Degenerate "zigzag" tube type (2,0) | image3 = nanotube strip +01 +01.pdf | caption3 = Degenerate "armchair" tube type (1,1) | image4 = nanotube strip +02 +01.pdf | caption4 = Possibly degenerate chiral tube type (2,1) }} {{clear}} If ''n'' and ''m'' are too small, the structure described by the pair (''n'',''m'') will describe a molecule that cannot be reasonably called a "tube", and may not even be stable. For example, the structure theoretically described by the pair (1,0) (the limiting "zigzag" type) would be just a chain of carbons. That is a real molecule, the [[Linear acetylenic carbon|carbyne]]; which has some characteristics of nanotubes (such as orbital hybridization, high tensile strength, etc.) β but has no hollow space, and may not be obtainable as a condensed phase. The pair (2,0) would theoretically yield a chain of fused 4-cycles; and (1,1), the limiting "armchair" structure, would yield a chain of bi-connected 4-rings. These structures may not be realizable. The thinnest carbon nanotube proper is the armchair structure with type (2,2), which has a diameter of 0.3 nm. This nanotube was grown inside a multi-walled carbon nanotube. Assigning of the carbon nanotube type was done by a combination of [[high-resolution transmission electron microscopy]] (HRTEM), [[Raman spectroscopy]], and [[density functional theory]] (DFT) calculations.<ref>{{cite journal | vauthors = Zhao X, Liu Y, Inoue S, Suzuki T, Jones RO, Ando Y | title = Smallest carbon nanotube is 3 a in diameter | journal = Physical Review Letters | volume = 92 | issue = 12 | page = 125502 | date = March 2004 | pmid = 15089683 | doi = 10.1103/PhysRevLett.92.125502 | url = http://juser.fz-juelich.de/record/38262/files/48588.pdf | url-status = live | bibcode = 2004PhRvL..92l5502Z | archive-url = https://ghostarchive.org/archive/20221009/http://juser.fz-juelich.de/record/38262/files/48588.pdf | archive-date = 2022-10-09 }}</ref> The thinnest ''freestanding'' single-walled carbon nanotube is about 0.43 nm in diameter.<ref>{{cite journal | vauthors = Torres-Dias AC |title=From mesoscale to nanoscale mechanics in single-wall carbon nanotubes |journal=Carbon |date=2017 |volume=123 |pages=145β150 |doi=10.1016/j.carbon.2017.07.036 |bibcode=2017Carbo.123..145T |url= http://qmro.qmul.ac.uk/xmlui/handle/123456789/25311}}</ref> Researchers suggested that it can be either (5,1) or (4,2) SWCNT, but the exact type of the carbon nanotube remains questionable.<ref name="Smallest">{{cite journal | vauthors = Hayashi T, Kim YA, Matoba T, Esaka M, Nishimura K, Tsukada T, Endo M, Dresselhaus MS | year = 2003 | title = Smallest Freestanding Single-Walled Carbon Nanotube | journal = [[Nano Letters]] | volume = 3 |issue=7 |pages=887β889 | doi = 10.1021/nl034080r | author-link8 = Mildred Dresselhaus | bibcode = 2003NanoL...3..887H}}</ref> (3,3), (4,3), and (5,1) carbon nanotubes (all about 0.4 nm in diameter) were unambiguously identified using aberration-corrected [[high-resolution transmission electron microscopy]] inside double-walled CNTs.<ref>{{cite journal | vauthors = Guan L, Suenaga K, Iijima S | title = Smallest carbon nanotube assigned with atomic resolution accuracy | journal = Nano Letters | volume = 8 | issue = 2 | pages = 459β462 | date = February 2008 | pmid = 18186659 | doi = 10.1021/nl072396j | author-link3 = Sumio Iijima | bibcode = 2008NanoL...8..459G }}</ref>
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