{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:22:56Z","timestamp":1760239376175,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,10,27]],"date-time":"2020-10-27T00:00:00Z","timestamp":1603756800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["FCT\/MCTES (UIDB\/50006\/2020)"],"award-info":[{"award-number":["FCT\/MCTES (UIDB\/50006\/2020)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["C"],"abstract":"<jats:p>Thermodynamics must be favorable for the growth of carbon nanotubes (CNTs) and graphene to take place, but a kinetic study is required to find the operating mechanism. In fact, thermodynamics indicates whether a reaction is possible; however, the route prevailing is not necessarily the most thermodynamically favorable, but the fastest one. Detailed kinetic studies state that there are three alternative routes operating under different temperature and pressure rates. The modes and rates of diffusion of carbon (C) atoms and noble metals have been known since the 1930s, but proof of C bulk diffusion operating in CNT growth came from detailed kinetic studies performed in the early 1970s, when reversible versus irreversible C formation was discussed with examples. The reason for interstitial C bulk diffusion in transition metals is evidenced based on the values of covalent radius. The reason for operating under steady-state conditions (linearity of the weight versus time) when searching for the operating mechanism is discussed herein. The steady-state C formation process operates sometimes with two different solid phases at each side of the catalyst particle (e.g., Ni and Ni3C), with thicknesses proportional to 1\/D of the respective C bulk diffusivities when the carbon bulk diffusion step is the rate-determining one.<\/jats:p>","DOI":"10.3390\/c6040067","type":"journal-article","created":{"date-parts":[[2020,10,27]],"date-time":"2020-10-27T09:22:45Z","timestamp":1603790565000},"page":"67","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Mechanisms of Carbon Nanotubes and Graphene Growth: Kinetics versus Thermodynamics"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2618-0372","authenticated-orcid":false,"given":"Lu\u00eds Sousa","family":"Lobo","sequence":"first","affiliation":[{"name":"LAQV-REQUIMTE, Department of Chemistry, NOVA School of Science and Technology, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9913-4671","authenticated-orcid":false,"given":"S\u00f3nia A. C.","family":"Carabineiro","sequence":"additional","affiliation":[{"name":"LAQV-REQUIMTE, Department of Chemistry, NOVA School of Science and Technology, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/j.carbon.2013.02.046","article-title":"Current understanding of the growth of carbon nanotubes in catalytic chemical vapour deposition","volume":"58","author":"Jourdain","year":"2013","journal-title":"Carbon"},{"doi-asserted-by":"crossref","unstructured":"Lobo, L.S. (2019). Mechanism of Catalytic CNTs Growth in 400\u2013650 \u00b0C Range: Explaining Volcano Shape Arrhenius Plot and Catalytic Synergism Using both Pt (or Pd) and Ni, Co or Fe. C\u2014J. Carbon Res., 5.","key":"ref_2","DOI":"10.3390\/c5030042"},{"doi-asserted-by":"crossref","unstructured":"Lobo, L.S., and Carabineiro, S.A.C. (2020). Carbon Formation at High Temperatures (550\u20131400 \u00b0C): Kinetics, alternative mechanisms and Growth Modes. Catalysis, 10.","key":"ref_3","DOI":"10.3390\/catal10050465"},{"unstructured":"Lobo, L.S., and Trimm, D.L. (1973). Studies of Carbon Formation on Metals Using a Vacuum Microbalance (1972). Progress in Vacuum Microbalance Techniques, Heyden & Son.","key":"ref_4"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0920-5861(90)85023-H","article-title":"Kinetics of catalytic carbon formation on steel surfaces from light hydrocarbons","volume":"7","author":"Lobo","year":"1990","journal-title":"Catal. Today"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1492","DOI":"10.1039\/tf9605601492","article-title":"Role of nucleation process in the reactions between CO and nickel","volume":"10","author":"Bromley","year":"1960","journal-title":"Trans. Faraday Soc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0008-6223(79)90017-4","article-title":"Kinetics of Gasification of Carbon Deposited on Nickel Catalysts","volume":"17","author":"Bernardo","year":"1979","journal-title":"Carbon"},{"unstructured":"Barrer, R.M. (1941). Diffusion in and Through Solids, Cambridge UP.","key":"ref_8"},{"doi-asserted-by":"crossref","unstructured":"Lobo, S.L., and Carabineiro, S.A.C. (2020). Explaining Bamboo-Like Carbon Fiber Growth Mechanism: Catalyst Shape Adjustments. C\u2014J. Carbon Res., 6.","key":"ref_9","DOI":"10.3390\/c6020018"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1016\/0008-6223(91)90043-I","article-title":"The Dependence of Catalytic Carbon Filament Growth Kinetics upon Gas Phase Carbon Activity","volume":"29","author":"Safvi","year":"1991","journal-title":"Carbon"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/0021-9517(90)90273-M","article-title":"Solubility and Diffusivity of Carbon in Metals","volume":"122","author":"Yang","year":"1990","journal-title":"J. Catal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6104","DOI":"10.1021\/nl501977b","article-title":"Nucleation of Graphene and Its Conversion to Single-Walled Carbon Nanotubes","volume":"14","author":"Picher","year":"2014","journal-title":"Nano Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2149","DOI":"10.1039\/C5NR06873H","article-title":"Towards a general growth model for graphene CVD on transition metal catalysts","volume":"8","author":"Weatherup","year":"2016","journal-title":"Nanoscale"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4431","DOI":"10.1021\/nl300897m","article-title":"Yield and Shape Selection of Graphene nanoislands Grown on Ni(111)","volume":"12","author":"Olle","year":"2012","journal-title":"Nano Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4072","DOI":"10.1021\/jp511069y","article-title":"Substrate-Induced Stabilization and Reconstruction of Zigzag Edges in Graphene Nanoislands on Ni(111)","volume":"119","author":"Palacios","year":"2015","journal-title":"J. Phys. Chem. C"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1063\/1.1710280","article-title":"Rate of Diffusion in Solid Alloys","volume":"8","author":"Mehl","year":"1937","journal-title":"J. Appl. Phys."},{"unstructured":"Budnikov, P.P., and Ginstling, A.M. Principles of solid state chemistry. Reactions in Solids, Gordon and Breach Sci Pub.","key":"ref_17"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1023\/A:1013235300777","article-title":"The Relationship between the State of Active Species in a Ni\/Al2O3 Catalyst and the mechanism of Growth of Filamentous Carbon","volume":"42","author":"Zaikovskii","year":"2001","journal-title":"Kinet. Catal."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S1872-2067(15)60982-2","article-title":"Comparizon of growth mechanisms of undopped and nitrogen doped carbon nanofibers on nickel-containing catalysts","volume":"37","author":"Chesnokov","year":"2016","journal-title":"Chin. J. Catal."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.jcat.2004.03.003","article-title":"Growing Mechanism of CNTs: A kinetic approach","volume":"224","author":"Romeo","year":"2004","journal-title":"J. Catal."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.cattod.2010.03.065","article-title":"Kinetics of carbon nanotubes growth on a Ni-Mg-Al catalyst by CCVD of methane: Influence of catalytic deactivation","volume":"154","author":"Latorre","year":"2010","journal-title":"Catal. Today"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.cattod.2011.02.038","article-title":"Ni.Co-Mg-Al catalysts for hydrogen and carbonaceous nanomaterials production by CCVD of methane","volume":"172","author":"Latorre","year":"2011","journal-title":"Catal. Today"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s00339-005-3256-7","article-title":"In situ measurements and modeling of carbon nanotube array growth kinetics during CVD","volume":"81","author":"Puretzky","year":"2005","journal-title":"Appl. Phys. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1851","DOI":"10.1063\/1.1605793","article-title":"In situ growth rate measurements and length control during CVD of VAMWCNTs","volume":"83","author":"Geohegan","year":"2003","journal-title":"Appl. Phys. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"253105","DOI":"10.1063\/1.1952575","article-title":"High-density vertically aligned multiwalled carbon nanotubes with tubular structures","volume":"86","author":"Kayastha","year":"2005","journal-title":"Appl. Phys. Lett."},{"unstructured":"Lobo, L.S. (1971). Carbon Formation from Hydrocarbons on Metals. [Ph.D. Thesis, Imperial College].","key":"ref_26"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/0008-6223(70)90055-2","article-title":"Metal Oxides as Catalysts for Oxidation of Graphite","volume":"8","author":"McKee","year":"1970","journal-title":"Carbon"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.fuel.2016.06.115","article-title":"Kinetics and mechanism of catalytic carbon gasification","volume":"183","author":"Lobo","year":"2016","journal-title":"Fuel"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"6881","DOI":"10.1021\/acs.energyfuels.6b01051","article-title":"Understanding the Reactions of CO2, NO, and N2O with Activated Carbon Catalyzed by Binary Mixtures","volume":"30","author":"Carabineiro","year":"2016","journal-title":"Energy Fuels"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1081\/CR-100101954","article-title":"Carbon nanofibers: Catalytic synthesis and applications","volume":"42","author":"Geus","year":"2000","journal-title":"Catal. Rev. Sci. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"14095","DOI":"10.1103\/PhysRevB.61.14095","article-title":"Interpretation of Raman spectra of disordered and amorphous carbon","volume":"61","author":"Ferrari","year":"2000","journal-title":"Phys. Rev. B"},{"key":"ref_32","first-page":"1956","article-title":"Temperature Dependence of Raman Scattering from SWCNTs: Undefined Radial Breading Mode Peaks at High Temperatures","volume":"47","author":"Chiashi","year":"2010","journal-title":"Jpn. J. Appl. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"7215","DOI":"10.1039\/C7CP00289K","article-title":"Raman spectra of SWCNTs at high temperatures: Pretreating samples in a nitrogen atmosphere improves their thermal stability in air","volume":"19","author":"Rodriguez","year":"2017","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5106","DOI":"10.1016\/j.carbon.2012.06.051","article-title":"Diameter-dependent kinetics of activation and deactivation in carbon nanotube population growth","volume":"50","author":"Bedewy","year":"2012","journal-title":"Carbon"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/j.jngse.2016.04.027","article-title":"Carbon produced by the catalytic decomposition of methane on Ni: Carbon yields and carbon structure as function of catalytic properties","volume":"32","author":"Salipira","year":"2016","journal-title":"J. Nat. Gas Sci. Eng."}],"container-title":["C"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2311-5629\/6\/4\/67\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:28:52Z","timestamp":1760178532000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2311-5629\/6\/4\/67"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,27]]},"references-count":35,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["c6040067"],"URL":"https:\/\/doi.org\/10.3390\/c6040067","relation":{},"ISSN":["2311-5629"],"issn-type":[{"type":"electronic","value":"2311-5629"}],"subject":[],"published":{"date-parts":[[2020,10,27]]}}}