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Entropy-driven stability of chiralsingle-walled carbon nanotubesYann Magnin1*, Hakim Amara2, François Ducastelle2,Annick Loiseau2, Christophe Bichara1†

Single-walled carbon nanotubes are hollow cylinders that can grow centimeters longvia carbon incorporation at the interface with a catalyst. They display semiconductingor metallic characteristics, depending on their helicity, which is determined duringtheir growth. To support the quest for a selective synthesis, we develop a thermodynamicmodel that relates the tube-catalyst interfacial energies, temperature, and the resultingtube chirality. We show that nanotubes can grow chiral because of the configurationalentropy of their nanometer-sized edge, thus explaining experimentally observedtemperature evolutions of chiral distributions. Taking the chemical nature of the catalystinto account through interfacial energies, we derive structural maps and phasediagrams that will guide a rational choice of a catalyst and growth parameters towarda better selectivity.

Electronic properties of single-walled car-bon nanotubes (SWNTs) depend on theirchirality—i.e., the way the SWNTs are rolledalong their axis— which is characterizedby two indices (n, m). Controlling chiral-

ity during the tube’s synthesis would enable usto avoid costly sorting and trigger the imple-mentation of promising applications [such asthe use of SWNT yarns as strong, light, and con-ductive wires (1) or the development of SWNT-based electronics (2)], with the ultimate goal ofovercoming the limitations of silicon. Notablebreakthroughs have been reported (3, 4), andprogress toward carbon nanotube computers(5, 6) has been very rapid. However, selectivesynthesis still appears to be the weak link,though new studies using solid-state catalysts(7–9) have reported a chiral-specific growth ofSWNTs. Detailed mechanisms underlying thisselective growth are still being debated, thusunderlining the need for realistic growth mod-els explicitly including the role of the catalyst.Existing models focus on kinetics (10), neg-lecting the role of the catalyst (11, 12), but failto calculate chiral distributions in line withexperiments. Atomistic computer simulationsemphasize chemical accuracy (13, 14) but needto be complemented with a model so as toprovide a global understanding of the process.In this study, we developed a thermodynamicmodeling of the interface between the tube

and the catalyst to relate its properties tothe resulting chiral distribution obtained dur-ing chemical vapor deposition (CVD) synthesisexperiments.Vapor-liquid-solid and vapor-solid-solid CVD

processes have both been used to grow SWNTs(8), the latter leading to a (n, m) selectivity.Growth can proceed through tangential or per-pendicular modes (15), and ways to control thesemodes have been proposed recently (16). Forspecific catalysts and growth conditions favor-ing the perpendicular mode, a pronounced near-armchair selectivity can be observed (16). In sucha mode, the interface between the tube and thecatalyst nanoparticle (NP) is limited to a line,and a simple model describing the thermo-dynamic stability of the tube-NP system canbe developed. We thus considered an ensembleof configurations of a catalyst NP, possibly ametal or a carbide, in perpendicular contact witha (n,m) SWNT, as in Fig. 1. The total numbers ofcarbon and catalyst atoms are constant. Config-urations differ by the structure of the NP-tubeinterface, defined by (n, m), for which we have(n +m) SWNT-NP bonds, with typically 10 < n +m < 50. On the tube edge, 2m among the bondsare armchair, and (n − m) are zigzag (17). In afirst approximation, the atomic structure of theNP is neglected, and the catalyst appears as asmooth flat surface, in a jellium-like approxi-mation. The interface is then a simple closedloop with two kinds of species: armchair andzigzag contact atoms. Under these conditions,the total energy of the system can be separatedinto three terms

E(n, m) = E0 + ECurv(n, m) + EInt(n, m) (1)

where E0 includes all terms independent of(n, m), such as the energy of the threefold

coordinated carbon atoms in the tube walland the atoms forming the NP. The surfaceenergy of the NP and the very weak surfaceenergy of the tube are also included in E0,because these surfaces are kept constant. Ad-ditionally, ECurv is the curvature energy, andEInt is the interfacial energy. Note that thismodel could possibly also apply in tangentialmode, if the lateral tube-catalyst interactiondoes not depend on (n, m).The (n, m)-dependent energy terms con-

cern the tube curvature and its interface withthe NP. Using density functional theory (DFT)calculations, Gülseren et al. (18) evaluatedthe curvature energy of the isolated tube asECurv ¼ 4 a D�2CNT , where DCNT is the tubediameter and a = 2.14 eV·Å2 per C atom. Weassume that the interfacial energy for a (n, m)tube in contact with the NP surface dependsonly on the number of its 2m armchair and (n,m) zigzag contacts

Eðn;mÞInt ¼ 2mEAInt þ ðn�mÞEZInt ð2Þ

where the armchair ðEAIntÞ and zigzag ðEZIntÞinterfacial energies are given by EXInt ¼ gXG þEXAdh , with X standing for A or Z. The edgeenergy per dangling bond, gXG , is positive be-cause it is the energy cost of cutting a tubeor a graphene ribbon and depends on thetype of edge created. The adhesion energy ofthe tube in contact with the NP, EXAdh, is neg-ative because energy is gained by reconnect-ing a cut tube to the NP. EXInt, the sum of thesetwo terms, has to be positive to create a driv-ing force for SWNT formation. DFT calcula-tions of the edge energies of different edgeconfigurations of a (8, 4) tube (Fig. 2) show nopreferential ordering. We thus assume that alltube-catalyst interfaces with the same numberof armchair and zigzag contacts have the sameenergy.This leads us to introduce the edge config-

urational entropy as a central piece of themodel. We assume that the tube is cut almostperpendicular to its axis, forming the short-est possible interface, for a given (n, m). Weneglect vibrational entropy contributions, whichare essentially the same for all tubes, exceptfor radial breathing modes. Armchair twofoldcoordinated C atoms always come as a pair;thus, this entropy (S) that relates the numberof ways of putting (n − m) zigzag C atoms andm pairs of armchair atoms on n sites (degen-eracy) is

Sðn;mÞkB

¼ ln n !m!ðn�mÞ! ð3Þ

where kB is Boltzmann’s constant. Interfacialenergies can be evaluated using DFT calcula-tions, described in the materials and methods.In agreement with previous studies (17, 19), wefind gAG ¼ 2:06 eV per bond and gZG ¼ 3:17 eVper bond for graphene, and 1.99 and 3.12 eV

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1Aix Marseille Université, CNRS, Centre Interdisciplinaire deNanoscience de Marseille, Campus de Luminy, Case 913,F-13288 Marseille, France. 2Laboratoire d’Etude desMicrostructures, ONERA-CNRS, UMR104, UniversitéParis-Saclay, BP 72, 92322 Châtillon Cedex, France.*Present address: MultiScale Material Science for Energy andEnvironment, MIT-CNRS Joint Laboratory at MIT, Cambridge, MA02139, USA.†Corresponding author. Email: bichara@cinam.univ-mrs.fr

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per bond, respectively, for cutting (6, 6) and(12, 0) tubes. The lower value of gAG is due to therelaxation (shortening) of the C–C bonds ofthe armchair edge that stabilizes it. Adhesionenergies of (10, 0) and (5, 5) tubes on icosa-hedral clusters of various metals, including Fe,Co, Ni, Cu, Pd, and Au, were calculated in (20, 21).Thus, orders of magnitude for interface ener-gies, EXInt, of armchair and zigzag terminationsin contact with typical catalysts can be esti-mated: They lie between 0.0 and 0.5 eV perbond, with EAInt < E

ZInt for these metals. An

example of free energy and corresponding prob-ability distribution is plotted as a function of(n, m) in fig. S1.Instead of focusing on a specific catalytic

system, it is more relevant at this stage tostudy the general properties of the model thatlinks the (n, m) indexes of a SWNT to threeparameters characterizing its CVD growth

conditions—namely, temperature and the in-terfacial energies of armchair ðEAIntÞ and zig-zag ðEZIntÞ tube-catalyst contacts. For each setof parameters, a free energy can be calculated,and its minimization yields the stable (n, m)value. This model displays similarities with asimple alloy model on a linear chair, but thecurvature term, dominant for small diame-ters, and the small and discrete values of nand m prevent it from being analytically sol-vable, except for ground states (i.e., stablestructures at zero kelvin), for which a solu-tion is provided in the materials and methods.We thus define a three-dimensional (3D) spaceof stable configurations in the ðT ; EAInt;EZIntÞcoordinates.Setting T and, hence, the entropy contribu-

tion to zero, the ground states are readily cal-culated and displayed in Fig. 3A. Only armchairor zigzag tubes are found to be stable, sepa-

rated by a line EZInt ¼ 43 EAInt. With increasingtemperature, they become unstable, and atransition toward chiral tubes takes place.Figure 3B is a contour plot of the surface de-fined by the transition temperatures. Abovethis surface, for each set of ðT ; EAInt;EZIntÞ pa-rameters, a chiral (n, m) tube is found sta-ble, defining “volumes” of stability for eachchirality. To explore it, we can cut slices atconstant temperature to obtain an isother-mal stability map (Fig. 3C). In such maps, onlythe most stable (n, m) tube structures areshown, whereas the model yields a distribu-tion of chiralities for each ðT ; EAInt;EZIntÞ point.Within a (n, m) domain, this distribution isnot constant, especially close to the bounda-ries, which are calculated by searching forpoints where the free energies and hence theprobabilities of two competing structures areequal. As illustrated in fig. S1B, around the chi-rality that displays a maximal probability setto 1, neighboring chiralities have non-negligiblecontributions that depend on ðT ; EAInt;EZIntÞ.We can also fix either EAInt or E

ZInt to obtain

temperature-dependent phase diagrams, asin Fig. 4A (for EAInt ¼ 0:15 eV per bond) andFig. 4B (for EZInt ¼ 0:25 eV per bond). As anexample, we can follow the temperature sta-bility of a (6, 6) tube. Figure 4A shows a largestability range with a maximal stability temper-ature rising from 200 to 800 K by increasingEZInt from 0.20 to 0.30 eV per bond, whereas thesecond map, orthogonal to the first one in the3D configuration space, shows an upper temper-ature limit varying from 500 to 700 K, within anarrowerEAInt range. Above the armchair tubes,chiral (n, n − m) tubes become stable start-ing with (n, n − 1) and then with increasing(n − m) values such as (6, 5), (7, 5), etc. Chiraltubes—i.e., tubes different from armchair orzigzag tubes—are stabilized at finite temper-ature by the configurational entropy of thetube edge.An isothermal map calculated at 1000 K is

plotted in Fig. 3C. Chiral tubes are spread alongthe EZInt ¼ 43EAInt diagonal, between armchairand zigzag ones. Small-diameter tubes are sta-bilized for larger values of ðEAInt;EZIntÞ and hencefor weaker adhesion energies of the tube onthe catalyst. Larger-diameter tubes are obtainedfor small values of ðEAInt;EZIntÞ because the en-tropy cannot counterbalance the energy cost ofthe interface, proportional to n + m. A com-parison of maps at 1000 and 1400 K is providedin fig. S3. As shown in movie S1, the effect ofincreasing temperature is to expand and shiftthe stability domain of chiral tubes along andon both sides of the EZInt ¼ 43EAInt diagonal,with a larger spread on the armchair side. Thestability domain of chiralities between central(2n, n) and near-armchair (n, n − 1) expandssubstantially at high temperature. However,the free-energy differences become smaller,leading to broader chiral distributions and thusexplaining the lack of selectivity reported fortubes grown at very high temperature by elec-tric arc or laser ablation methods (22).

Magnin et al., Science 362, 212–215 (2018) 12 October 2018 2 of 4

Fig. 1. From experiments to a model. (A and B) (Top) Postsynthesis transmission electronmicroscopy (TEM) images of a SWNT attached to the NP from which it grew at 1073 K, using eitherCH4 (A) or CO (B) feedstocks, leading to a tangential or perpendicular growth mode, illustrated atthe atomic scale (bottom). TEM images are reproduced from (16) with permission from the RoyalSociety of Chemistry. The experiments and our analysis of the growth modes are described in (16).(C) Sketch of the model, with a SWNT in perpendicular contact with a structureless catalyst.Armchair edge atoms are in red, zigzag ones in blue.

Fig. 2. Key elements of the model.(Top) Different ways of cutting a (8, 4)tube, leading to the formation of zigzag(blue) and armchair (red) undercoordi-nated atoms. For a (8, 4) tube, there are70 different edge configurations withalmost the same energy. (Bottom) For-mation energies of all possible (8, 4)edges, from DFT calculations describedin the materials and methods. Theenergy levels lie within 25 meV per bondand can thus be considered degenerate.

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This very simple model displays a fair agree-ment with literature data, as illustrated in thefollowing examples. Figure 3B suggests a wayto grow either zigzag or armchair tubes, thelatter being metallic for any diameter. For both,growth kinetics is slow, because each new ringof carbon atoms has to nucleate once the pre-vious one has been completed (11, 12). To over-come this nucleation barrier, one should seekregions in the map where such tubes remainstable at high temperature. For armchair spe-cies, this corresponds to the lower right cornerof the map in Fig. 3B, where the adhesion energyof armchair edges is strong and that of zigzagones is weak, and the opposite is true for theinterfacial energies. Such requirements havepossibly been met in high-temperature (1473 K)CVD experiments (23) that also used thiophenein the feedstock. Those experiments might in-dicate that the presence of sulfur at the interfacecould modify the relative interaction strength ofzigzag and armchair edges with the Fe NP.The temperature dependence of the chiral

distributions, measured by photoluminescence(24–26) or Raman and transmission electronspectroscopies (27) in previous studies, seemsmore robust. The maps presented in Fig. 4, Aand B, are consistent with these experiments,showing that armchair or near-armchair chiral-ities [(6, 6) and (6, 5)] are grown at low tem-perature (873 K) and that the chiral distributiongradually shifts toward larger chiral angles [(7, 5),(7, 6), and (8, 4)...] at higher temperatures. Re-ferring to our model, this suggests that Co- andFe-based catalysts used in these experimentscorrespond to interfacial energy values aroundEAInt ¼ 0:15 eV per bond and EZInt ¼ 0:24 eVper bond, as indicated by the dashed boxes inthe maps. A quantitative comparison with fourdifferent sets of experimental data is providedin fig. S2, showing a slight tendency to overes-timate the width of the distributions. This over-

estimation partly results from the fact that weuse a two-parameter thermodynamic model toaccount for experiments that include the var-iability in the catalyst size and chemical com-position and the growth kinetics. Our resultsalso confirm that overlooking metallic tubes inphotoluminescence experiments introduces aserious bias in the resulting chiral distribution.Further, the dependence of the quantum yieldon chiral angles of semiconducting tubes mayalso contribute to underestimating the width ofthe experimental distributions.The present model thus sets a framework for

understanding why a number of experiments,using metallic catalysts in perpendicular growthconditions as discussed in (16), report a near-armchair selectivity. For such catalysts, EAInt isgenerally lower than EZInt (20). At low temper-ature, zigzag or armchair tubes are thermody-namically favored butmay not always be obtained,

owing to kinetic reasons.On the armchair side, ourmodel indicates that near-armchair helicities arethen favored by a temperature increase, becausetheir stability domain is large and they are lesskinetically impaired (11). At even higher temper-atures, tube chiralities tending toward (2n, n)indexes should be stabilized by their larger edgeconfigurational entropy, but their stability do-mains turn out to be narrower in the presentmodel. Taking the atomic structure of the cat-alyst into account in our model could rule outsome neighboring structures and contribute toopen up these domains.Concerning the practical use of these maps,

a first issue is to select the appropriate lo-cation for a catalyst in the ðT ; EAInt;EZIntÞ co-ordinates, so as to favor the desired tube helicity.Looking at Fig. 3C, one can see that the largestand most interesting parameter ranges corre-spond to either metallic armchair tubes or to

Magnin et al., Science 362, 212–215 (2018) 12 October 2018 3 of 4

Fig. 3. Structural maps. (A) Map of the ground states, with armchairtubes in the lower right corner and zigzag ones in the upper left corner,separated by a line EZInt ¼ 43 EAInt. Small-diameter tubes [e.g., (5, 5) and(8, 0)] are obtained for large values of the interfacial energies EInt, whereasstability domains of large-diameter tubes are narrower, with a widthdecaying as 1nðnþ1Þ, and are obtained for small values of EInt. (B) Contour plot ofthe highest temperatures of stability of the ground-state structures,armchair or zigzag. Chiral tubes are found only above this surface,

stabilized by the configurational entropy of the tube’s edge. Armchairand zigzag tubes can remain stable at high temperatures, in thebottom right and upper left corners, respectively. (C) Chiralitymap at 1000 K. Iso-n (iso-m) values are delimited by solid black (dashedblue) lines. Metallic tubes, for which (n − m) is a multiple of 3, areshown in red, and semiconducting ones are flesh colored. Theparameter space for armchair (metallic) and (n, n − 1) and (n, n − 2)(semiconducting) tubes is larger than for other chiralities.

Fig. 4. Chirality phase diagrams. Phase diagrams calculated for constant values of EAInt (A)and EZInt (B). These diagrams would be orthogonal in a 3D plot. The blue dashed boxesindicate possible parameter ranges corresponding to the analysis of growth productsby He et al. (26), based on a photoluminescence assignment of tubes grown using a FeCucatalyst. (6, 5) tubes are reported stable up to 1023 K, (7, 5) and (8, 4) become dominantat 1023 K, and (7, 6) at 1073 K.

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(n, n − 1) and (n, n − 2) semiconducting tubes.A second, more difficult issue is to design acatalyst that would display appropriate EAIntand EZInt values. DFT-based calculations, inthe same spirit as those used in other studies(7, 9, 20, 21, 28), should probably be helpful.However, the evidence of the important roleof the edge configurational entropy calls intoquestion the possibility of explaining the highselectivity reported in (7, 9) on the basis of astructural or symmetry matching. The intrin-sic disorder at the edge could be taken intoaccount by averaging over various atomic con-figurations and using molecular dynamics atfinite temperature.The present model reevaluates the role of

thermodynamics in the understanding of SWNTgrowth mechanisms. It accounts for experimen-tal evidence, such as the near-armchair prefer-ential selectivity, hitherto attributed to kinetics(11), and the temperature-dependent trends inchiralities. It also provides a guide to designbetter, more selective catalysts. However, onemust also consider the importance of kineticsin a global understanding of the SWNT growthprocess. An attempt to combine thermodynamicand kinetic aspects of the growth has beenproposed in (12), but, overlooking the role of theedge configurational entropy, it led to unrealisticchiral distributions. Those resulting from thepresent thermodynamic analysis are slightly

broader than the experimental distributions(fig. S2) but should be narrower if the reportedchirality dependence of the growth kinetics(11) is taken into account. Owing to the highsynthesis temperatures and the very small sizeof the interface, there may be SWNT growthregimes where the atomic mobility and theresidence time of atoms close to the interfaceare large enough to achieve a local thermody-namic equilibrium.

REFERENCES AND NOTES

1. N. Behabtu et al., Science 339, 182–186 (2013).2. A. D. Franklin, Nature 498, 443–444 (2013).3. Q. Cao et al., Science 350, 68–72 (2015).4. D. Zhong et al., Nat. Electron. 1, 40–45 (2018).5. M. M. Shulaker et al., Nature 501, 526–530 (2013).6. M. M. Shulaker et al., Nature 547, 74–78 (2017).7. F. Yang et al., Nature 510, 522–524 (2014).8. M. Li et al., Top. Curr. Chem. 375, 29 (2017).9. S. Zhang et al., Nature 543, 234–238 (2017).10. A. A. Puretzky, D. B. Geohegan, S. Jesse, I. N. Ivanov, G. Eres,

Appl. Phys. A 81, 223–240 (2005).11. F. Ding, A. R. Harutyunyan, B. I. Yakobson, Proc. Natl. Acad.

Sci. U.S.A. 106, 2506–2509 (2009).12. V. I. Artyukhov, E. S. Penev, B. I. Yakobson, Nat. Commun. 5,

4892 (2014).13. A. J. Page, F. Ding, S. Irle, K. Morokuma, Rep. Prog. Phys. 78,

036501 (2015).14. H. Amara, C. Bichara, Top. Curr. Chem. 375, 55 (2017).15. M.-F. C. Fiawoo et al., Phys. Rev. Lett. 108, 195503 (2012).16. M. He et al., Nanoscale 10, 6744–6750 (2018).17. Y. Liu, A. Dobrinsky, B. I. Yakobson, Phys. Rev. Lett. 105,

235502 (2010).18. O. Gülseren, T. Yildirim, S. Ciraci, Phys. Rev. B 65, 153405 (2002).

19. T. Wassmann, A. Seitsonen, A. M. Saitta, M. Lazzeri, F. Mauri,Phys. Rev. Lett. 101, 096402 (2008).

20. F. Ding et al., Nano Lett. 8, 463–468 (2008).21. A. Börjesson, K. Bolton, J. Phys. Chem. C 114, 18045–18050

(2010).22. L. Henrard, A. Loiseau, C. Journet, P. Bernier, Synth. Met. 103,

2533–2536 (1999).23. R. M. Sundaram, K. K. K. Koziol, A. H. Windle, Adv. Mater. 23,

5064–5068 (2011).24. X. Li et al., J. Am. Chem. Soc. 129, 15770–15771 (2007).25. H. Wang et al., J. Am. Chem. Soc. 132, 16747–16749 (2010).26. M. He et al., J. Am. Chem. Soc. 132, 13994–13996 (2010).27. M. Fouquet et al., Phys. Rev. B 85, 235411 (2012).28. F. Silvearv, P. Larsson, S. Jones, R. Ahuja, J. A. Larsson,

J. Mater. Chem. C 3, 3422–3427 (2015).

ACKNOWLEDGMENTS

Funding: Support from the French research funding agency (ANR)under grant 13-BS10-0015-01 (SYNAPSE) is gratefullyacknowledged. C.B. thanks P. Müller for stimulating discussions.Author contributions: C.B. designed the project; Y.M., H.A.,F.D., and C.B. developed the model; and all authors contributed tothe data analysis and manuscript preparation. Competinginterests: The authors declare no competing interests. Data andmaterials availability: All data are available in the main text orthe supplementary materials.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/362/6411/212/suppl/DC1Materials and MethodsFigs. S1 to S3References (29–35)Movie S1Data S1 and S2

21 March 2018; accepted 8 August 201810.1126/science.aat6228

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Entropy-driven stability of chiral single-walled carbon nanotubesYann Magnin, Hakim Amara, François Ducastelle, Annick Loiseau and Christophe Bichara

DOI: 10.1126/science.aat6228 (6411), 212-215.362Science

, this issue p. 212Sciencenanotube edge. The model should be useful in helping to guide nanotube growth parameters to enhance selectivity.carbon nanotubes. The model explains the origin of nanotube chirality in terms of the configurational entropy of the

developed a thermodynamic model for the growth of single-walledet al.their growth are still not fully known. Magnin Despite progress in growing single-walled carbon nanotubes of specific size and chirality, the factors that control

The twisted carbon nanotube story

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