The weight and density of carbon nanotubes are calculated as a function of their characteristics (inner diameter, outer diameter, and number of walls). The results are reported in the form of diagrams which may be useful to other researchers, in particular in the fields of synthesis/production, materials and composites, health/toxicity studies

Flahaut, Emmanuel

Laurent, Christophe

Peigney, Alain

English

International audienceThe weight and density of carbon nanotubes are calculated as a function of their characteristics (inner diameter, outer diameter, and number of walls). The results are reported in the form of diagrams which may be useful to other researchers, in particular in the fields of synthesis/production, materials and composites, health/toxicity studies

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The weight and density of carbon nanotubes versus the number of walls and diameter

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 Any correspondence concerning this service should be sent to the repository administrator: staff-oatao@inp-toulouse.fr  Open Archive Toulouse Archive Ouverte (OATAO)  OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.  This is an author -deposited version published in: http://oatao.univ-toulouse.fr/  Eprints ID: 4770 To link to this article: DOI:10.1016/j.carbon.2010.04.010 http://dx.doi.org/10.1016/j.carbon.2010.04.010 To cite this version : Laurent, Christophe and Flahaut, Emmanuel and Peigney, Alain The weight and density of carbon nanotubes versus the number of walls and diameter. (2010) Carbon, vol. 48 (n° 10). pp. 2994-2996. ISS N 0008-6223 sepdestheimpin pIcessonin eiceroecE F E R E N C E SThe weight and density of carbon nanotubes versusthe number of walls and diameterCh. Laurent a,*, E. Flahaut b, A. Peigney aa Universite´ de Toulouse, Institut Carnot CIRIMAT, Universite´ Paul-Sabatier, 118 route de Narbonne, 31062 Toulouse cedex 9, Franceb CNRS, Institut Carnot CIRIMAT, Universite´ Paul-Sabatier, 118 route de Narbonne, 31062 Toulouse cedex 9, FranceA B S T R A C TThe weight and density of carbon nanotubes are calculated as a functioistics (inner diameter, outer diameter, and number of walls). The resultform of diagrams which may be useful to other researchers, in particsynthesis/production, materials and composites, health/toxicity studiIn the early years of research on carbon nanotubes(CNTs), many conflicting results have been reported, mainlybesaFpaSmenthsithfaRized PL Emission15202530Processing time (mins)Percentage of individual SWCNTs (%)100 101 102 103020406080100arating the SWCNT bundles into individual tubes. A wiseign of the micro-mixing chamber with consideration offlow field effect should be considered in the future forroving the microfluidization process as a useful techniqueroducing high quality SWCNT dispersions.n summary, a comparison of two distinct SWCNT pro-sing techniques – the microfluidization versus the ultra-ication process has been made. Despite its inefficiencynergy utilization and separation of SWCNT bundles, the[5][6][7]0008-6223/$ - see front mdoi:10.1016/j.carbon.2010* Corresponding author: Fax: +33 561 55 61 63.E-mail address: laurent@chimie.ups-tlse.fr (Ch. Laurent).rmal10rofluidization process, as facilitated by the extremely highrgy dissipation rate, is a useful technique for the highoughput and large-scale production of SWCNT disper-ns. More importantly, the types of flow field rather thanenergy dissipation rate have been identified as a criticaltor in separating the SWCNT bundles into individual tubes.n of their character-s are reported in theular in the fields ofes.cause the authors did not use the same CNTs and CNTmples. It was later fully recognized that several kinds of[1] Cao Q, Rogers JA. Ultrathin films of single-walled carbonnanotubes for electronics and sensors: a review offundamental and applied aspects. Adv Mater 2009;21:29–53.[2] Thess A, Lee R, Nikolaev P, Dai H, Petit P, Robert J, et al.Crystalline ropes of metallic carbon nanotubes. Science1996;273:483–7.[3] Liu T, Luo S, Xiao Z, Zhang C, Wang B. Preparativeultracentrifuge method for characterization of carbonnanotube dispersions. J Phys Chem C 2008;49:19193–202.[4] Liu T, Xiao Z, Wang B. The exfoliation of SWCNT bundlesProcessing Time (mins)No100 101 102 10305 Sonication – PO354Sonication – PO355Microfluidization – PO354Microfluidization – PO355ig. 3 – Effects of ultrasonication and microfluidizationrocesses on the G-band normalized photoluminescencend the degree of separation of dispersions into individualWCNTs. Solid lines are for guidance only.examined by simultaneous Raman scattering andphotoluminescence spectroscopy. Carbon 2009;47:3529–37.Panagiotou T, Mesite SV, Fisher RJ. Production of norfloxacinnanosuspensions using microfluidics reaction technologythrough solvent/antisolvent crystallization. Ind Eng Chem Res2009;48:1761–71.Panagiotou T, Mesite SV, Bernard JM, Chomistek KJ, Fisher RJ.Production of polymer nanosuspensions usingmicrofluidizerTM processor based processes. NSTI Nanotech2008 June 1–5, Boston; 2008.Thumm JR, Lento MA, Higgins JS. Multiple stream highpressure mixer/reactor. US Patent 6221332.atter  2010 Elsevier Ltd. All rights reserved..04.010CNTs do exist, such as single-walled CNTs (SWCNTs), dou-ble-walled CNTs (DWCNTs) and multi-walled CNTs(MWCNTs). Note that some confusion remains because hol-low carbon nanofibers that do not show the particular con-tinuous concentrical structure are sometimes noted CNTs orMWCNTs. It was also taken into account that the differentsynthesis routes produce CNTs with different lengths, crys-tallinity and defect proportion and CNT samples with differ-ent levels of purities (carbon element versus other elementsand CNTs versus other carbon species). However, the factthat a SWCNT and a MWCNT of the same length do nothave the same weight has been neglected until now. Indeed,companies use gross carbon tonnages as CNT productionfigures, and research works, for example on CNT-compositematerials, generally use the term ‘‘CNT content’’ when infact ‘‘carbon content’’ should be used. In this work, we re-port calculations establishing the relations between theweight and the density of CNTs and their geometrical char-acteristics (inner diameter, outer diameter, and number ofwalls). The results are reported in the form of diagramswhich may be useful to other researchers, in particular inthe fields of synthesis/production, materials and compositesand also health/toxicity studies, where the number of CNTsin a given sample is extremely more relevant than theweight itself.The calculations are based on the following hypotheses: (i)the length of the C@C bonds in the curved graphene sheets isthe same than in the planar sheet i.e. dC@C = 0.1421 nm, (ii)the MWCNTs are composed of concentric shells (inter-shelldistance ds–s = 0.3400 nm), (iii) the contribution of the electrondensity to the outer diameter is neglected and (iv) the aspectratio of CNTs is sufficiently high (>1000) to neglect the area ofthe tip surfaces in comparison to the area of the cylindricalsurfaces. As reported earlier [1], the specific surface area ofa SWCNT, whatever its diameter, is that of one side of agraphene sheet, i.e. 1315 m2/g. Thus, the weight of anySWCNT (WSW) of diameter d and length L can be calculatedfrom the surface area of the graphene sheet:WSW ¼ 11315pLd ðgramsÞ ð1ÞWe now consider a MWCNTwith an inner diameter dint, thesame length L and a number of walls n. The surface area ofall the graphene sheets which compose the MWCNT is:SMW ¼ p  L  dint þ ðdint þ 2  dssÞ þ ðdint þ 4  dssÞfþ    þ ½dint þ 2ðn 1Þ  dssg ð2Þwhich can be simplified:SMW ¼ pL ndint þ 2dssXn1i¼0i" #ð3ÞEach graphene sheet has a surfacic weight equal to 1/1315 g/m2 and thus the weight of the MWCNT (n walls, length L)(wMW) can be calculated:WMW ¼ 11315  pL ndint þ 2dssXn1i¼0i" #ð4ÞIn order to simplify the comparison, taking the same lengthfor the two CNTs, the weight of the MWCNT (wMW) of innerdiameter dint (Eq. (4)) is divided by the weight of the SWCNT(Eq. (1)), 1 nm in diameter, giving the ratio R:R ¼ wMW=wðSW;1 nmÞ ¼ ndint þ 2dssXn1i¼0i" #with dint in nm ð5ÞThe volume of one CNT depends on the outer diameter (dout):VMW ¼ pLd2out=4 ð6Þand the weight of the CNT is given by Eq. (4), transformed as afunction of dout as opposed to dint:WMW ¼ 11315  pL ndout  2dssXn1i¼0i" #ð7ÞThe density (dMW) of a MWCNTs is thus:dMW ¼ 1000 wMW=VMW¼ 40001315n=dout  2dssXn1i¼0i !=d2out" #with dout in nm ð8ÞR was plotted versus the number of walls n, for different val-ues of dint (Fig. 1) and the density was plotted versus dout fordifferent number of walls (Fig. 2).For a SWCNT, 1 nm in diameter, R = 1.00. Simply addingone wall, i.e. considering a DWCNTwith dint = 1 nm (solid cir-cle in Fig. 1), results in a strong increase of R (2.68). For aMWCNTwith 10 walls and dint = 5 nm (open circle in Fig. 1),R = 80.60. Thus, the production of 1 ton of (SWCNTs, 1 nm)is equivalent, in terms of the number of CNTs of same length,to the production of 2.68 tons of (DWCNTs, dint = 1 nm) and80.60 tons of (MWCNTs, 10 walls, dint = 5 nm). If one takes into0204060801001201401 2 3 4 5 6 7 8 9 10 11 12 13 14 15Number of wallsR =wMW/w( SW, 1 nm)dint = 1 nmdint = 2 nmdint = 3 nmdint = 5 nmR =wMW/w( SW, 1 nm)Fig. 1 – The ratio R of the weight of a MWCNT of innerdiameter dint and length L to the weight of a SWCNT ofdiameter 1 nm and length L versus the number of walls n,for different values of dint.account that the typical length of MWCNTs and SWCNTS isabout 100 and 10 lm, respectively, there would be a factor ofca. 800 between the respective weight of samples containingthe same number of CNTs. The density (Fig. 2) increases dra-matically when decreasing the diameter, in particular forSWCNTs and DWCNTs. For example, the density of a SWCNT,dout = 3 nm, is equal to 1, whereas it is equal to 1.8 for aDWCNT, dout = 3 nm. Below a certain diameter, the density ishigher than that of graphite. Although this could be coun-ter-intuitive, it reflects the fact that a CNT is a 1D objectwhereas graphite is 2D, with an absence of matter on the lat-eral sides. Note also that the density is lower by a few percentif the CNTs are forming organized bundles, which is not takeninto account here. Therefore, it is clear that the carbon con-tent in a composite material or test sample cannot be trans-lated into the CNTs content without a precise knowledge ofthe geometry of the CNTs in question.Johnson et al. [2] have mentioned that the density of theirMWCNTs is 1.1 as calculated from the microscopic structure.Our calculation from their data (outer diameter 70 nm, 30walls) give 1.12, which is in excellent agreement. Zhan et al.[3] have indeed mentioned that the density of CNTs is a func-tion of both their diameter and their number of shells, butthese authors give no example. The estimated density fortheir SWCNTs is 1.8. We have measured by He pycnometrythe apparent density of one of our samples, consisting mainlyof DWCNTs, with also SWCNTs and CNTs with three walls [4].The obtained value is in the range 1.86–1.94 which is in broadagreement with the expected value of 1.92 calculated usingthe hypothesis that the sample contains only carbon(92 wt.%) and cobalt (8 wt.%, which is overestimated). Notethat since the specific surface area of this sample is equalto 923 m2/g, applying a proper outgassing procedure is veryimportant. Kim et al. [5] have reported that the measureddensity is equal to 1.74 ± 0.16 for two different samples ofCNTs (outer diameters about 15 nm and about 22 nm). Noexperimental details are given on the number of walls otherthan ‘‘a diameter of 15 nm corresponds to about 20 graphitelayers’’. Our calculations from their data give the following re-sults for the two samples: (15 nm, 11 walls, 1725) and (22 nm,17 walls, 1769). Given that their measured density range is1.58–1.90, this represents a good agreement.In conclusion, it is shown that both the weight and densityof CNTs vary over a very wide range depending on the num-ber of walls, inner diameter or outer diameter. The resultsare reported in the form of diagrams which may be usefulto other researchers, in particular in all areas where carboncontent and CNT content should not be confused.R E F E R E N C E S[1] Peigney A, Laurent Ch, Flahaut E, Bacsa RR, Rousset A. Specificsurface area of carbon nanotubes and bundles of carbonnanotubes. Carbon 2001;39(4):507–14.[2] Johnson DF, Craft BJ, Jaffe SM. Adhered supported carbonnanotubes. J Nanoparticle Res 2001;3(1):63–71.[3] Zhan GD, Kuntz JD, Wan J, Mukherjee AK. Single-wall carbonnanotubes as attractive toughening agents in alumina-basednanocomposites. Nat Mater 2003;2(1):38–42.[4] Flahaut E, Bacsa R, Peigney A, Laurent Ch. Gram-scale CCVDsynthesis of double-walled carbon nanotubes. Chem Commun2003:1442–3.[5] Kim SH, Mulholland GW, Zachariah MR. Density measurementof size selected multiwalled carbon nanotubes by mobility-mass characterization. Carbon 2009;47(5):1297–302.0.00.51.01.52.02.53.03.54.04.55 walls1 wallgraphite10 walls20 walls2 wallsDensity0 5 10 15 20 25 30Outer diameter (nm)Fig. 2 – The density (dMW) of CNTs versus the outer diameterfor different number of walls.

Adhered supported carbon nanotubes.

Density measurement of size selected multiwalled carbon nanotubes by mobilitymass characterization.

Gram-scale CCVD synthesis of double-walled carbon nanotubes.

Single-wall carbon nanotubes as attractive toughening agents in alumina-based nanocomposites.

Speciﬁc surface area of carbon nanotubes and bundles of carbon nanotubes.

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The weight and density of carbon nanotubes versus the number of walls and diameter

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