2752 Journal of The Electrochemical Society, 146 (7) 2752-2761 (1999)S0013-4651(98)10-065-4 CCC: $7.00 © The Electrochemical Society, Inc.

Thermodynamic Study of the Formation of C60 and C70 byCombustion or Pyrolysis

Constantin Vahlas,a,*,z Alina Kacheva,a Michael L. Hitchman,b,* and Philippe Rocaboisb,c

aLaboratoire Interfaces et Matériaux, INPT-CNRS, Ecole Nationale Supérieure de Chimie de Toulouse, 31077 Toulouse, FrancebDepartment of Pure and Applied Chemistry, University of Strathclyde, G1 1XL Glasgow, United Kingdom

An assessment of the available thermodynamic data of gaseous and condensed fullerene C70 is presented. Gibbs energy mini-mization of the gaseous C-H-O-Ar chemical system, including large polyaromatic hydrocarbons and the fullerenes C60 and C70,helps to determine under which conditions C60 and C70 molecules are stable. The influence of the addition of halogen atoms in thegas phase on the improvement of the yield of these two fullerenes in different conditions is investigated by minimizing the Gibbsenergy of the gaseous C-H-F-O-Ar chemical system. The evolution of the yields of the two fullerenes, and of the C70/(C70 1 C60)ratio as a function of temperature, pressure, and C/H ratio in the reactants is illustrated and compared with corresponding experi-mental information from a literature review. In the light of these calculations, the possibility of the direct production of fullerenefilms containing variable amounts of C60 and C70 by a continuous process such as combustion or pyrolysis is discussed.© 1999 The Electrochemical Society. S0013-4651(98)10-065-4. All rights reserved.

Manuscript submitted October 19, 1998; revised manuscript received December 17, 1998. This was Paper 850 presented at theMeeting, of the Society, Boston, MA, November 1-6, 1998.

Although vaporization of graphite with electric arc and resistiveheating are actually the most commonly used methods for the syn-thesis of fullerenes, many other physical or chemical routes have alsobeen used. Physical methods have been reviewed in the book ofKoruga et al.1 Chemical methods of obtaining fullerenes have in-cluded combustion of different precursors such as benzene,2-5 naph-thalene,6,7 acetylene,5,8 and camphor.9 However the investigatedchemical methods or processing conditions do not systematicallyyield fullerenes.10 Formation of fullerenes has also been reportedfrom liquid-spray combustion of hydrocarbons.11,12 The interrela-tionship between C60, soot, and combustion has been discussed byEbert.13 Fullerenes have also been obtained by pyrolysis of varioushydrocarbons,14 particularly of naphthalene15-17 and of its dimerbenzo [k] fluoranthene,18 of decacyclene,19 and of Krätschmer-Huff-man (KH) carbon residues.20 Also, arcing in a cyclopentadiene at-mosphere,21 low pressure chemical vapor deposition (CVD) startingfrom benzene or naphthalene,22 and plasma-enhanced chemicalvapor deposition (PECVD) starting from cyclopentadiene23 havebeen investigated. Fullerenes have, in addition, been produced bypyrolysis of cyclopentadienide metal complexes (ferrocene, nicke-locene, cyclopentadienyl-cobalt dicarbonyl, lithium cyclopentadi-enide).14 The combustion route has been extensively reviewed byHoward et al.4 More recently chemical routes for the production ofC60 with an emphasis on thin films for microelectronic applicationshave been reviewed by Rocabois et al.24 This review pointed out thatfullerene-containing films are currently made by a batch process,which consists of first producing the fullerene, purifying it, and thenfinally depositing it by different evaporation techniques. Althoughthis way of producting C60 layers has given promising results, a directand continuous process of deposition would be less time consumingand/or less expensive. Such a synthetic route could be potentially avery important one for cost-effective large scale production. A step inthis direction was attempted by Mukhopadhyay et al.9 The authorsfirst produced soot by burning camphor and then used its tolueneextract as a precursor in a hot filament CVD setup. In this way theyshowed the feasibility of producing thin films of fullerenes (althoughnot pure) from a natural source using an economic process. Never-theless, removal of soot from a batch reactor is a messy and possiblyhazardous process as has been pointed out by different authors.12,16,25

These conclusions and the fact that scale-up of the electric arc

* Electrochemical Society Active Member.c Present address: Département Physicochimie-IRSID, F-57283 Maizières-les-Metz,

France.z E-mail: cvahlas@ensct.fr

method is problematic,26 led McKinnon in the early nineties27 andRocabois et al. more recently,24 to investigate theoretically the possi-bility of directly producing C60 layers by combustion or pyrolysis.Both authors used equilibrium calculations based on the minimiza-tion of Gibbs energy. They proposed operating conditions underwhich C60 molecules are stable and discussed the possible factors forimproving the expected experimental yield of C60.

Since in the above mentioned processes fullerenes other than C60are also expected to be produced, it would be interesting to includethem in a thermodynamic investigation of the process. Among themany stable fullerenes, C70 which was identified in the very firsttime-of-flight mass spectra together with C60, 28 is the second mostabundant molecule after C60. Furthermore, its processing in the formof thin films is technologically interesting since, for example, it hasbeen shown that nucleation of diamond crystallites is enhanced if apreliminary 50 to 100 nm C70 film is deposited on the surface ini-tially.29 However, in order to consider C70 in a thermodynamic studyfor combustion or pyrolysis, thermodynamic data on solid and gas-eous C70 are needed. If the relative abundance of C60 and of C70 inthe reaction products is also to be investigated, thermodynamic datafor C70 must not only be correct, but also must be coherent withthose of C60.

One point that different authors mention concerning the produc-tion of fullerenes is that the effective participation of heteroatoms(H, O, N) in the process can yield strong carbon-heteroatom bonds,thus inhibiting the formation of all-carbon compounds. Consequent-ly their presence should be deleterious to the formation of fuller-enes,30-32 and so one could conclude that the yield of fullerenes willbe related, among other factors, to the presence of available hetero-atoms in the reactants. This would suggest the need to use ultrapurestarting gases, and the possibility of adding other compounds in thereactive gas to remove the heteroatoms, particularly hydrogen, with-out forming stable species with carbon and this has been discussed.Support for this suggestion is given by the increase of the yield ofC60, when chlorotrifluoromethane CClF3 is added to the gas phaseduring production of fullerenes by a modified graphite evaporationtechnique.31 Nevertheless, this route still has to be optimized inorder to give consistent results, as shown by unsuccessful attemptsto improve the yields of fullerenes using both the 1-chloro and 1-bromo derivatives of naphthalene.18

The introduction in the reactive gas phase of species which formvery stable gaseous compounds with hydrogen has been investigat-ed in different techniques involving production of condensed mate-rials from a gaseous source. Most of these additives have been halo-gens or halogen-containing species. For example, Alexandrov and

Journal of The Electrochemical Society, 146 (7) 2752-2761 (1999) 2753S0013-4651(98)10-065-4 CCC: $7.00 © The Electrochemical Society, Inc.

Hitchman produced silicon nitride thin films by PECVD startingwith silane SiH4 and ammonia NH3. 33 By adding in the reactive gassmall amounts of nitrogen trifluoride NF3, they decreased the totalconcentration of bonded hydrogen in the films and consequentlyimproved their electrical properties. Also, Kim et al. added silicontetrafluoride SiF4 into disilane Si2H6-hydrogen mixtures to depositpolycrystalline silicon films.34-36 They found that fluorine chemistryreduced the amount of hydrogen and oxygen incorporated in thefilms, reduced the amount of powder formation in the gas phase, andhelped the in situ crystallization of the Si films at low temperature.Furthermore, the participation of chlorine-containing compoundsduring silicon dioxide CVD has been investigated, and it has beenshown that it improves the oxide quality by reducing the incorpora-tion of hydrogen-related impurities (Ref. 37 and references therein).Finally, the addition of halogenated compounds in flames has beenrelatively well-studied because of their inhibiting effect (Ref. 38 andreferences therein).

For the production of fullerenes, Richter et al.,38 by adding 4.3%of chlorine Cl2, in benzene/oxygen/argon flames, increased by a fac-tor of 3.5 the quantity of C60 1 C70 obtained, without producinghalogenated fullerenic species. This result was confirmed in a sub-sequent study, where the authors added up to 22% Cl2 in similaracetylene/oxygen/argon flames, although the operating conditions inthe reported experiments did not allow for a direct comparisonbetween depositions with and without Cl2. 39

Following on from these ideas, in the last part of this paper thethermodynamic study is extended to take into account the presenceof a halogen, namely, fluorine, in the reactive species. The choice offluorine is based on the higher stability of the F-H bond (565 kJ/mol)relative to other hydrogen-halogen (example: 431 kJ/mol for the Cl-H), and C-H (example 412 kJ/mol) bonds.40 This choice is also sup-ported by the fact that, in contrast to the previously reported increaseof the yield of fullerenes through the addition of chlorine in flames,the addition of bromine decreases the yield.41 This is not inconsis-tent with the fact that the Br-H bond is weaker (366 kJ/mol) than theC-H bond.

In the present study, an investigation of the gas-phase chemistry isdone using thermodynamic calculations of the homogeneous phase.This approach was originally developed by Spear for CVD processes,but it is generally valid for any process where a thermally activatedgas phase gives a condensed product through a chemical mecha-nism.42 The aim is to get a general view about C60 and C70 yieldswhen varying parameters such as total pressure, temperature, C/H andH/F ratios, rather than describing precisely the effective gas composi-tion in a flame, or in the tail of the flame, or in a pyrolysis process.

The paper is organized in three parts. The constitution of a coher-ent data set for gaseous C60 and C70 is investigated in the first part.Although only homogeneous (gas-phase) calculations are presentedin this study, this first part is completed by also introducing a ther-modynamic assessment of solid C70 together with data on solid C60as proposed by Rocabois et al.24 The aim is to propose the first com-plete thermodynamic description of the two most abundant fullerenesin both gaseous and condensed forms. In the second part, thermody-namic calculations are performed in order to explore the overall yieldof C60 and of C70, and their relative abundance in the gas phase forcommonly adopted processing conditions. In this way, an importantdrawback of the current methods of fullerene generation which is theproduction of mixtures of fullerenes, followed by labor-intensive sep-aration into individual components,18 can be investigated. Finally, asalready mentioned above, the influence of the presence of fluorine onthe calculations is considered, and its effect on the yield of the twofullerenes is discussed. In both the second and the third parts, thecomposition of the gaseous by-products is also investigated.

Thermodynamic Data

In this part the rationale for the creation of the list of the specieswhich are considered in the calculations is presented first, followedby the calculation of the thermodynamic data of gaseous C70 and C60and of solid C70.

Production of fullerenes has been reported to occur through dif-ferent mechanisms involving polyaromatic hydrocarbons (PAHs)and light hydrocarbons such as acetylene C2H2 (see Ref. 22 andreferences therein). Therefore, different PAHs have been consid-ered in the calculations. The criteria for the selection of PAHs, thesources for their thermodynamic data, and a discussion on the wayin which their participation in the equilibrium calculations shouldbe considered have been reported earlier.24 As previously men-tioned24 PAHs are limited to molecules smaller than C94H24. Larg-er molecules (2n > 100) could have been added to the data file.However, the reliability of their thermodynamic data is quite low,43

the knowledge of the mechanisms which govern their productionby pyrolysis is very limited,25 and finally they are unlikely to beprecursors of C60 and of C70.

In addition to PAHs, other hydrocarbons CxHy have been consid-ered in the calculations. The list is restricted, though, to compoundswith 0 < x # 7 and 0 < y # 16, following a discussion which has beenpresented in Ref. 44. This list has been chosen with the aim of achiev-ing representation within the reactive system of possible linear andcyclic groups. Also, since for a given stoichiometry, the higher x is,the greater the number of isomers, the choice within each CxHy groupwas limited to the linear and cyclic isomers with the most negativefree enthalpies within the investigated temperature interval.

In Table I, the species which have been considered in the calcula-tions are listed. The presented data base is incomplete since not all thecompounds which have been reported to participate in combustion orpyrolysis processes have been included. This is mainly due to the lackof thermodynamic data for many of the abundant species which aregenerated from the C-H(-O) system. For example, due to the lack ofthermodynamic data, complex molecules containing a fullerenelinked to an aliphatic chain or to oxygen or fluorine have not beenconsidered in the calculations although their formation in combustionor pyrolysis is not a negligible issue.6,41 For the same reason, no flu-orine-containing hydrocarbons have been considered in the calcula-tions, although it has been reported that, for example, chlorine andbromine present under combustion conditions may yield halogenatedPAHs.25,38 On the other hand, it has been reported that the fullerenesproduced under such conditions contain no halogens, probably due tothe limited thermal or photochemical stability of these compounds orbecause of the impossibility of substituted PAHs to intervene in thefullerene formation mechanism.41 These limitations do not allow fora precise determination of the optimum processing conditions of ful-lerenes through a fluorine-involving chemistry. However, it is re-called that in the present study, the role of fluorine is exclusively in-vestigated in terms of its reactivity toward hydrogen in competitionwith PAHs and light hydrocarbons.

Finally, preliminary calculations help to eliminate highly unsta-ble species, e.g., all long aliphatic chains and CxHyOz compounds.Indeed, one may expect that any large hydrocarbons will be aromat-ic and that oxygenated hydrocarbons probably only occur in flamezones where molecular oxygen is still present and where the tem-perature has not reached its maximum.8

Thus, although the present list of species is far from exhaustive,representatives of the different groups of compounds which havebeen reported to coexist or to compete with fullerenes have beenconsidered in the simulated processes.

Gaseous C70.—The thermodynamic functions of gaseous C70have been derived from its structure and normal mode of vibrationby statistical mechanical calculations applying the harmonic-oscilla-tor, rigid-rotator approximation in the same way as for gaseous C60,presented by Rocabois et al.24 The C70 molecule is considered to bean ellipsoid as proposed by Raghavachari and Rohlfing.45 Using thatwork as a basis, the lengths of the principal axes are determined tobe a 5 b 5 0.33 nm and c 5 0.475 nm. Mass is assumed to be uni-formly distributed on the skin of the ellipsoid. The thickness of theskin is taken as 0.154 nm, i.e., twice the radius r of a covalent car-bon atom. Each moment of inertia Ii (i 5 a, b, c) is calculated as thedifference between the moments of inertia of two ellipsoids whose

2754 Journal of The Electrochemical Society, 146 (7) 2752-2761 (1999)S0013-4651(98)10-065-4 CCC: $7.00 © The Electrochemical Society, Inc.

Table I. C-H-O-Ar(-F) chemical system. List of the gaseous considered species in the calculations.

C1 C4H6, Dimethylacetylene C7H16, 3-Methylhexane C28H14 C66H20 F1O1

C1H1 C4H6, 1,3-Butadiene PAHs C30H12 C80H22 F1O2C1H2 C4H8, 2-Methylpropene C12H10 C30H14 C94H24 F2

C1H3 C4H10, Butane C14H8 C32H12 Fullerenes F2H2C1H4 C5H6, Cyclopentadiene C14H10 C32H14 C60 F2O1C1O1 C5H8, Cyclopentene C16H8 C32H16 C70 F2O2

C1O2 C5H10, 2-Methyl-2-Butene C16H10 C34H12 H1 F3H3C2 C5H12, Pentane C16H12 C34H14 H1O1 F4H4C2H1 C6H6, Benzene C18H10 C34H16 H1O2 F5H5C2H2 C6H8, 1-Methyl-1.3-Cyclopentadiene C18H12 C36H12 H2 F6H6C2H4 C6H10, 2.3-Dimethyl-1.3-Butadiene C20H10 C36H14 H2O1 F7H7C2H6 C6H10, Cyclohexene C20H12 C36H16 H2O2 C1F1C3 C6H10, Trans,trans-2.4-Hexadiene C22H10 C38H14 O1 C1F2C3H4, Methylacetylene C6H12, 2-Methyl-2-Pentene C22H12 C40H14 O2 C1F3C3H4, Allene C6H14, 2-Methylpentane C24H10 C40H16 O3 C1F4C3H6, Propylene C7H8, Toluene C24H12 C42H14 Ar1 C2F2

C3H6, Cyclopropane C7H10, 2-Norbornene C24H14 C42H16 F-species C2F4C3H8, Propane C7H14, Methylcyclohexane C26H12 C48H18 F1 C2F6C4H2, Butadiyne C7H14, Trans-1.2-Dimethylcyclopentane C26H14 C52H18 F1H1 C4F8C4H4, Vinylacetylene C7H16, Heptane C28H12 C54H18 F1H1O1 C6F6

principal axes are respectively a 1 r, b 1 r, and c 1 r, and a 2 r,b 2 r, and c 2 r. For example, Ia is calculated from the expression

[1]

where m 5 1.395932?10221 g, is the mass of one molecule of C70.The values obtained are Ia 5 Ib 5 0.6922149?10222 g nm2, and Ic 50.5675302?10222 g nm2. The product of moments of inertia Im 5IaIbIc is thus calculated to be equal to 0.2719386?10266 g3 nm6.

C70 belongs to the D5h group with the symmetry number s 5 10and a total number of fundamental frequencies of 122. An assign-ment of these frequencies based on a first principles calculation waspresented by Wang et al.46 As for C60, 24 the contribution of excitedelectronic states has been neglected, i.e., only the ground electronicstate with statistical weight of unity has been considered. Based onthe above information the standard entropy So

298.15 is found to be614.123 J/(Kmol) and the heat capacity CP and the free energy func-tion (FEF) referenced to 298.15 K are tabulated between 298.15 and3000 K and are fitted to the following standard polynomials

298.15 K # T # 1000 K

CP 5 136.6958 1 2.4790T 2 1.1231?1023 T 2

2 1.6336?107 T22 J/(K mol)

1000 K < T # 3000 K

CP 5 1655.7326 1 0.0422T 2 6.8231?1026 T 2

2 2.0953?108 T22 J/(K mol) [2]

298.15 K # T # 3000 K

FEF 5 2218212.3906T21 1 3053.5791 2 481.4902 ln(T)

2 0.6739T 1 6.2328 3 1025 T 2 J/(K mol) [3]

The limited information available in the literature and the adoptedassumptions on the C70 molecule do not allow for a more precisedetermination of thermodynamic data. Hence, in contrast to C60whose thermodynamic functions are presented in the next paragraph,only one polynomial has been used to describe the FEF of C70between 298.15 and 3000 K.

To the authors knowledge the standard molar enthalpy of forma-tion, DH8f 298, of gaseous C70 has not been reported in the literatureso far. In the present study, a value of 3130 kJ/mol is proposed forDH8f 298 of gaseous C70, which leads to a ratio of equilibrium partial

Im

b r c rm

b r c ra 5 1 1 1 2 2 1 25 5

2 2 2 2[( ) ( ) ] [( ) ( ) ]

pressures pC70/pC60

5 0.1 at 2100 K and 100 Pa in pure carbon am-bient. This enthalpy value can be compared with the one of3190 kJ/mol calculated by Korobov and Sidorov47 based on anequivalent approach

Gaseous C60.—Data for gaseous C60 have been taken fromRef. 24. The corresponding FEF is calculated to be

298 # T # 500 K

FEF 5 2325099.3635T21 2 2527.9691 1 442.5714 ln(T)

2 1.7966T 1 3.4942?1024 T 2 2 1234355.0348T22 J/(K mol)

500 < T # 1000 K

FEF 5 1985550.4811T21 1 3312.3566 2 483.5726 ln(T)

2 0.6646T 1 8.7235?1025 T 2 1 22249222.334T22 J/(K mol)

1000 < T # 1500 K

FEF 5 2019761.0968T21 1 4185.1727 2 639.4144 ln(T)

2 0.4267T 1 4.1050?1025 T 2 2 1.2952?1023T22 J/(K mol)

1500 < T # 2000 K

FEF 5 1845496.7349T21 1 6622.9039 2 998.9016 ln(T)

2 0.1789T 1 1.2542?1025 T 2 2 1.0053?1023 T22 J/(K mol)

2000 < T # 2750 K

FEF 5 1726418.9240T21 1 7908.0694 2 1180.3027 ln(T)

2 8.6668?1022T 1 4.7110?1026 T2 2 6.9731?1024 T22 J/(K mol)

[4]

Solid C70 and C60.—Two values for DH8f 298 of solid C70, 2555and 2375 kJ/mol were calculated by Beckhaus et al.48 and by Kigob-ayashi et al.,49 respectively. The more recent value of Beckhaus et al.has been chosen in the present assessment because the authors cal-culate a value of DH8f 298 for solid C60 which is also adopted here forcoherency. The heat capacity CP of C70,s is taken as 7/6 times that ofC60,s as given by Rocabois et al., who applied the Kopp-Neuman rulewith respect to graphite. Although CP values of C70,s are proposedthereafter up to 2700 K, it has to be mentioned that the equilibriummelting temperature of solid C70 has been estimated to be 1500 K. 50

The temperature dependency of CP on this basis is then as follows

Journal of The Electrochemical Society, 146 (7) 2752-2761 (1999) 2755S0013-4651(98)10-065-4 CCC: $7.00 © The Electrochemical Society, Inc.

298 # T < 900 K

CP 5 260.4879 1 2.0625T 2 7.8468?1024 T 2

2 18230876.7850T22 J/(K mol)

900 # T # 1400 K

CP 5 1421.0918 1 0.3119880533T 2 6.5535?1025T 2

2 154805252T22 J/(K mol)

1400 < T # 2700 K

CP 5 1643.8936 1 0.0904865339T 2 3.1217?1026 T 2

2223463694T22 J/(K mol) [5]

The standard entropy at 298.15 K, S 8298.15, of solid C70 has beenestimated from its entropy of sublimation at 750 K, DS 8v 750 5126.2 J/K/mol, as was proposed by Sai Baba et al.,51 by using therelation

[6]

From this equation a value of 435.0349 J/(K mol) is obtained forS 8298, which can be compared to the value of 447.014 J/(K mol) cal-culated in Ref. 52. The corresponding temperature dependency ofthe FEF function is given by the relationship

298 # T < 900 K

FEF 5 2223554.7122T21 1 1992.2300 2 260.4879 ln(T)

2 1.0313T 1 1.3078?1024T 2 1 9115438.3925T22 J/(K mol)

900 # T < 1400 K

FEF 5 2885614T21 1 9847.7559 2 1421.0918 ln(T) 2 0.1560T

1 1.0923?1025T 2 1 77402626.0000T22 J/(K mol)

1400 # T < 2700 K

FEF 5 21086594.5315T21 1 11453.1624 2 1643.8936 ln(T)

2 0.0452 T 1 5.2029?1027T 2 1 111731847.1500T22 J/(K mol)

[7]

Data for solid C60 can be taken from Ref. 24 except for DH8f 298 forwhich the value proposed by Beckhaus et al.,48 2327 kJ/mol, is pre-ferred for coherency with the adopted data for solid C70. However,two more recent values for DH8f 298 of solid C60 should be consid-ered.53,54 They are very similar, respectively, 2360 6 10 and 2355 615 kJ/mol, and slightly higher than the one proposed in the presentstudy. The resulting equations for the FEF of C60 are

298 < T # 900 K

FEF 5 7561394T21 1 6938.7991 2 934.1839 ln(T) 2 3.6985T

1 4.6902?1024 T 2 2 32690566.487T22 J/(K mol)

900 < T # 1400 K

FEF 5 5187057T21 1 35110.9594 2 5096.4411 ln(T) 2 0.5594T

1 3.9171?1025T 2 1 277587931.87T22 J/(K mol)

1400 < T # 2700 K

FEF 5 4466285T21 1 40868.4058 2 5895.4720 ln(T) 2 0.1623T

1 1.8659?1026 T 2 1 400702327.26T 22 J/(K mol)

2700 < T # 3000 K

FEF 5 4252678T21 141879.6571 2 6025.0886 ln(T) 2 0.1266T

1 3.3679?1029 T 2 1 468458569.28T 22 J/(K mol) [8]

S S S C C T dT298 298298

750

, , [ )/ ]so

go

v,750o

, ,sP G P5 2 2 2D ∫

ResultsThe GEMINI2 software of Thermodata was used for the mini-

mization.55 Calculations were carried out as a function of tempera-ture within the range (1300 # T # 2700 K), for a total pressure inthe range 102 # ptot # 105 Pa, and for a carbon-to-hydrogen ratio inthe range 0.5 # C/H # 2. Pure carbon equilibrium was also investi-gated. Systematically inert gas dilution was considered and wasfixed at 33 atom % of the quantity of the input carbon atoms, unlessotherwise stated. With this approach it is not possible to directlyinvestigate the influence of the partial pressure of the inert gas on thecomposition of the gas phase. However, as is shown in the next para-graph, variations of this parameter give useful information on theevolution of the yields of the two fullerenes. For the fluorine-con-taining system, calculations were carried out as a function of fluo-rine-to-hydrogen ratio in the reactants 0 # F/H # 1.

The above parametric domains cover most of the experimentallyinvestigated conditions. In particular, the C/H range includes theC/H ratio in naphthalene which is 1.25. This compound is known tohave a strong tendency to soot formation and, due to its molecularstructure, is expected to produce relatively large amounts of PAHswhich promote the formation of fullerenes.6,16 On the other hand,the influence of different hydrocarbons with the same C/H ratio(e.g., C6H6 and C2H2) is not investigated in this work, although it hasbeen reported that the yield of fullerenes processed from C6H6 orfrom C2H2 may be very different.4

Flames with a C/O ratio both higher than 1 2-5,8,38,39,41,56 andlower than 1 2-8,56 have been used for the production of fullerenes incombustion systems. From a thermodynamic equilibrium point ofview, whatever the conditions are, if any excess oxygen (C/O < 1) ispresent initially the main products will be CO and H2O at high tem-peratures (T > 1000 K), and neither soot nor PAHs are formed. Sincethese kinds of compounds do form though, a global equilibrium can-not be reached in a burning process. In the present calculations theC/O ratio was fixed to be equal to 1.25. This value is identical to theone used in our previous investigation24 and is compatible with theconclusions of Richter et al.,5 who propose an optimum value of 1.20in order to reach a maximum fullerene formation. In such a case, andunder the conditions where fullerenes are stable, over 99.9% of theoxygen will be in the form of CO which can then be simply consid-ered as a dilution gas.

Results are presented by means of yield diagrams which illustratethe evolution of the gaseous by-products as a function of one of theinvestigated parameters. The yield of the fullerene Cx (x 5 60, 70) isdefined as the ratio of the number of carbon atoms in a Cx moleculeover the sum of all available carbon atoms except the ones whichform CO. Since with the investigated conditions, as just mentioned,almost all oxygen is in the form of CO, the yield of Cx is given bythe following relation

Yield of Cx 5 xnCx/(Cinput 2 Oinput) [9]

where n is the number of moles of Cx in equilibrium, and Cinput andOinput are, respectively, the initial quantities of carbon and oxygen.

In Fig. 1 is presented the evolution of the yield of C60, C70, andthe C70/(C60 1 C70) molar ratio as a function of temperature, forC/H 5 1 and for four different pressures: 101.3 kPa (1 atm)(Fig. 1a), 10.13 kPa (0.1 atm) (Fig. 1b), 1.013 kPa (0.01 atm)(Fig. 1c), and 0.1013 kPa (0.001 atm) (Fig. 1d). For ease of compar-ison in this as well in the following figure the scale of each axisremains unchanged from one diagram to the other. In all four dia-grams C60 and C70 appear in windows of stability. It is shown laterthat this window is limited by PAHs at low temperatures and main-ly by C2H2 at high temperatures.

As was reported earlier,24 with increasing temperature the C60yield shows a sharp increase, followed by a comparatively slowerdecrease after reaching a maximum. The temperature at which theyield is at a maximum decreases strongly with decreasing total pres-sure. At the same time the maximum yield itself increases. It evenappears that for the investigated conditions and with the assumptions

2756 Journal of The Electrochemical Society, 146 (7) 2752-2761 (1999)S0013-4651(98)10-065-4 CCC: $7.00 © The Electrochemical Society, Inc.

made in this study, at 0.1 kPa almost all of the available carbon, i.e.,that which is not linked to oxygen to form CO, can yield C60.

The yield of C70 shows a comparable behavior to that of C60, i.e.,an approximately bell-shaped form, indicating a window of stabili-ty. However, there are a number of differences between the twofullerenes. For example, the yield of C70 is systematically lower bytwo to three orders of magnitude than that of C60. Then, in contrastto C60, its increase with increasing temperature is less sharp than itsdecrease at higher temperatures, except for p 5 101 kPa. Also, thetemperature corresponding to the maximum yield is systematicallyhigher and is less affected by pressure for C70 than for C60. Indeed,while the maximum yield of C60 is shifted from 2300 to 1500 Kwhen pressure is decreased from 101 to 0.1 kPa, for the same condi-tions that of C70 is only shifted from 2300 to 2150 K. Furthermore,the yield of C70 does not increase with decreasing pressure, but itreaches a maximum value for 10.1 kPa for the four values of pres-sure investigated. The C70/(C70 1 C60) ratio remains at a very lowpercentage in the stability domain of the two fullerenes. It alsoshows a maximum value whose shape becomes more or less sym-metrical with increasing pressure. From these results it can be con-cluded that within the stability domain of C60 and C70, the highestyield in C70 is obtained at high temperature and at an intermediatepressure (,10.1 kPa). However under these conditions the overallyield of fullerenes is low.

In Fig. 2 is presented the evolution of the yield of C60, C70, andthe C70/(C60 1 C70) molar ratio as a function of temperature, for p 510.1 kPa and for four different C/H ratios: 0.5 (Fig. 2a), 1 (Fig. 2b),1.25 (Fig. 2c), and 2 (Fig. 2d). Again, a window of stability for bothfullerenes exists in each diagram. The shapes of the yield for C60 andC70, and of the C70/(C70 1 C60) ratio are comparable to the ones inthe previous figure. With increasing the C/H ratio the yield of bothfullerenes increases but the C70/(C70 1 C60) ratio also increases,

showing that the yield of C70 increases faster than that of C60. ForC/H 5 2, the ratio becomes higher than 0.01. A similar behavior forC60 considered alone, as a function of the C/H ratio, has also beenfound.24 The present results show that not only does the yield of C70behave in the same way, but it is further enhanced by the increase ofthe C/H ratio in the reactants. This suggests that the C70/(C70 1 C60)ratio should be the highest of the highest value of the C/H ratio, i.e.,in a pure carbon ambient. This is indicated in the Fig. 3 which showsthe evolution of the C70/(C70 1 C60) ratio in a reactive phase freefrom hydrogen as a function of temperature for different values ofpressure. This diagram shows that, as in Fig. 1, with increasing tem-perature the C70/(C70 1 C60) ratio increases, but that at low pressure(less than 1 kPa) the ratio comes to a maximum before decreasing:for example, above 2400 K at 0.01 kPa. This maximum value isshifted toward higher temperature with increasing pressure. It is thusexpected that a maximum is attained even above 1 kPa, but for tem-peratures exceeding 2700 K. Figure 3 also shows that the higher thepressure, the higher the content of C70 in the fullerenes at such apoint that C70 might be expected to become the major fullereneunder the conditions investigated at high temperature (>2500 K)-high pressure (>10.1 kPa) conditions.

In Fig. 4 is presented the evolution of the yields of C60 and C70,as a function of the percentage of the number of atoms of an inertgas (Ar) relative to the number of carbon atoms. Although this para-meter only roughly corresponds to the partial pressure of the inertgas, the diagram clearly illustrates the differences in the behavior ofthe two fullerenes: the yield of C60 depends only slightly on the dilu-tion of the reactants, but that of C70 strongly increases with increas-ing dilution at low values, attains a maximum, and then decreasesslowly. This behavior of the yield of C70 is consistent with that foundas a function of pressure, as illustrated in Fig. 1, and where that theC70 yield attained a maximum at about 10.1 kPa. This confirms that

Figure 1. Yield of C60, C70, and C70/(C60 1 C70) molar ratio at equilibrium as a function of temperature, for four different pressures: (a, top left) 101.3 kPa (1atm); (b, top right) 10.13 kPa (0.1 atm); (c, bottom left) 1.013 kPa (0.01 atm); and (d, bottom right) 0.1013 kPa (0.001 atm). C/H 5 1, C/O 5 1.25, Ar 5 33 %.

Journal of The Electrochemical Society, 146 (7) 2752-2761 (1999) 2757S0013-4651(98)10-065-4 CCC: $7.00 © The Electrochemical Society, Inc.

Figure 2. Yield of C60, C70, and C70/(C60 1 C70) molar ratio at equilibrium as a function of temperature, for four different C/H elemental ratios in the reactivegas: (a, top left) 0.5, (b, top right) 1, (c, bottom left) 1.25, and (d, bottom right) 2. P 5 10.1 kPa (0.1 atm), C/O 5 1.25, Ar 5 33 %.

in equilibrium calculations, dilution is comparable (although notcompletely equivalent as has been shown in Ref. 57) to reduction oftotal pressure.

In Fig. 5 are presented the main carbon and hydrocarbon gaseousproducts and their evolution as a function of temperature at 10.1 kPa,and C/H and C/O ratios equal to 1 and to 1.25, respectively; the C60and C70 stability domains are indicated. The stability domain of C70is positioned at the end of that for one PAH (C94H24) and, as waspreviously mentioned, it is shifted toward higher temperatures rela-

Figure 3. C70/(C60 1 C70) ratio as a function of temperature for different val-ues of pressure in a pure carbon ambient.

tive to that of C60. The diagram shows that the window of stabilityof both fullerenes is positioned mainly between PAHs (which arerepresented by C94H24) and C2H2 at low temperatures and C2H2 athigh temperatures. Besides molecular hydrogen H2, which is themain gas, other light hydrocarbons coexist with PAHs, especiallymethane CH4 which is predominant at lower temperature (<1200 K).On the other hand, radicals (e.g., ethynyl, C2H), carbon oligomers(C3), and especially atomic hydrogen coexist with C2H2 at high tem-peratures. Similar calculations have also been performed for thesame conditions but at lower pressure, i.e., in conditions which ex-tend the stability domain of the fullerenes. The results obtained showthat the same situation as that shown in Fig. 5 prevails in terms of thenature of the stabilized species and their relative evolution. However,it should be noted that the stability domain of the fullerenes, and

Figure 4. C60 and C70 yields as a function of the dilution of the reactive gasin Ar. T 5 2000 K, P 5 10.1 kPa (0.1 atm), C/H 5 1, C/O 5 1.25.

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especially that of C60 is extended toward lower temperatures by low-ering at the same time the extent of the domain of C94H24. The upperstability limit of fullerenes is also shifted toward lower temperatureswith decreasing pressure but, as shown in the diagrams of Fig. 1, thetemperature window within which fullerenes are stable is globallyextended. Although the same light species predominate for lowerpressures at high temperature, atomic hydrogen and hydrocarbonradicals (C2H) are favored over C2H2.

The influence of the addition of fluorine in the reactants on thestability of fullerenes is illustrated in the Fig. 6 and 7. In Fig. 6 ispresented the yield of C60 and C70 as a function of temperature forfour different F/H atomic ratios in the reactive gas: 0, 0.4, 0.8, and1, at 10.1 kPa, and C/H and C/O ratios equal to 1 and to 1.25, respec-tively. The addition of fluorine dramatically increases the yield ofboth fullerenes and widens their stability domain, especially that forC60. For example, the yield of C60 shows for F/H 5 1 a plateauextending from 1000 to 2200 K, corresponding to a saturation at amaximum yield. The yield of C70 increases even more strongly thanthat of C60, probably due to the saturation of the latter. With increas-ing F/H ratio, the stability domain of C70 is shifted toward highertemperatures. The change of the F/H ratio from 0 to 1 shifts the max-imum yield of C70 from 0.0008 at 2200 K to 0.0271 at 2750 K whichis the maximum temperature investigated and corresponds to theupper validity limit of the thermodynamic data of C70.

Figure 7 shows the main carbon and hydrocarbon gaseous prod-ucts and their evolution as a function of temperature, calculated witha F/H ratio of 0.8, and under the same conditions as those of Fig. 5.The C60 and C70 stability domains are indicated. Comparison of thetwo diagrams reveals that in the presence of fluorine, the quantitiesof H2, H, C2H2, and other hydrocarbons decrease within the entiretemperature range. The quantity of C94H24 remains unaffected by thepresence of fluorine at low temperatures, with only the upper stabil-ity limit being shifted from 1900 to 1800 K. The decrease of thequantities of all these species makes that additional carbon and hy-drogen atoms are available in the gas phase, allowing for (i) the ex-tension of the stability domain of fullerenes toward lower and high-er temperatures and (ii) the formation of HF in excess.

DiscussionIn this part, the correlation between the different results is con-

sidered, and their validity is discussed in the light of available exper-imental information. However, it has to be recalled that the presenttheoretical study does not exactly simulate a combustion or pyroly-sis process. In addition to the reasons which have already been men-

Figure 5. Main carbon and hydrocarbon gaseous by-products and evolutionof their amount as a function of temperature. P 5 10.1 kPa (0.1 atm), C/H 51, C/O 5 1.25, Ar 5 33%. The C60 and C70 stability domains are indicated.

tioned in the introduction, this is also due to the nonuniform condi-tions in flames, which means that in combustion there are limitationson the investigation of factors which influence the formation of dif-ferent products and, in the present case, of fullerenes. Another pointof concern is the stability of fullerenes in the combustion or thepyrolysis facility immediately after their production. For example, ithas been shown by Ahrens et al.7 that formation of fullerenes in anacetylene flame depends on the flow velocity of the unburned gas:when flow velocity is increased, it causes a decrease in the yield offullerenes. This behavior have been attributed to the oxidation ofreadily produced fullerene (stability limit of C60 in air 5008C 58,59)rather than to a decrease in the rate of formation.7 For the same rea-son, if the readily produced condensed fullerenes and other by-prod-ucts during the principal step of the process are cooled in the air,their initial quantity and composition will be higher than the valueswhich are finally determined ex situ. This could account for the factthat no fullerenes have been reported to form at high temperature, incontrast to their calculated stability as illustrated, for example, inFig. 1b. However, with these points in mind, a knowledge of theparametric domains where formation of fullerenes in the metastable

Figure 6. Yield of C60 and of C70 as a function of temperature for differentF/H atomic ratios in the reactive gas: 0 (a for C60, a for C70), 0.4 (b for C60,b for C70), 0.8 (c for C60, g for C70), and 1 (d for C60, d for C70). P 510.1 kPa (0.1 atm), C/H 5 1, C/O 5 1.25, Ar 5 33%.

Figure 7. Main carbon and hydrocarbon gaseous by-products and evolutionof their amounts as a function of temperature. P 5 10.1 kPa (0.1 atm), C/H 51, C/O 5 1.25, H/F 5 1.25, Ar 5 33%. The C60 and C70 stability domainsare indicated.

Journal of The Electrochemical Society, 146 (7) 2752-2761 (1999) 2759S0013-4651(98)10-065-4 CCC: $7.00 © The Electrochemical Society, Inc.

gas phase is expected to be favored, would still be a guide for thefield of experimental investigations.

One of the main results of this and of previous theoretical studiesfor fullerene production as a function of temperature, is that the yieldof fullerenes is bell-shaped, and that their thermodynamic stabilityplaces them at an intermediate position between PAHs, and low car-bon (C1, C2, C3) radicals and neutral species (C2H2). This result,together with the presence of atomic hydrogen in the gas phase isconsistent with various proposed mechanisms of formation of ful-lerenes in flames. Indeed, Homann’s group2 showed that formationof negative PAH ions, evidenced in time of flight mass spectrometry,occurs within a temperature window, and that the ion concentrationpresents a bell-shaped form as a function of residence time in theflame, i.e., a qualitative similar functional dependence on tempera-ture. Following the so-called zipper reaction model, these polyhedralions are precursors formed in combustion conditions and are in-volved in the initial stages of formation of fullerenes.7,14 Moreover,in the oxidation zone of a flame (i.e., the position where the greaterpart of the fuel is converted in overall exothermic reactions to CO2,CO, H2O, and H2, corresponding to the maximum temperature zone)C2H2 and radicals H, OH, and O are stable . They are present in less-er quantities than the gases previously mentioned as being involvedin exothermic reactions, but in higher quantitites than ethene, PAHs,soot, and fullerenes. After the end of the oxidation zone (i.e., in theregion identified by a luminous yellow color which reveals the for-mation of soot), the temperature decreases with increasing distancefrom the burner, because of heat loss through radiation. In diagramsof Fig. 1 and 2, these two zones correspond, respectively, to the highand to the low temperature regions where C2H2 and C94H24, respec-tively, predominate.

The formation of PAHs at low temperatures can be attributed toan early formation in the flame during the rapid destruction of theinitial hydrocarbon. For the investigated conditions, C94H24, i.e., thecompound with highest number of carbon atoms has been consis-tently stabilized here in the place of other PAHs. This can be attrib-uted to the fact that the larger the molecules are, the closer their ther-modynamic properties are to graphite. Therefore they are very stableand are expected to be found from calculations instead of fullerenes.This thermodynamic behavior has also been experimentally con-firmed by Gerhardt et al.,8 who point out that in hydrocarbon flamesthe mass spectrum of larger PAHs can be described by a Gaussiandistribution, the maximum of which moves to larger masses withincreasing reaction time.

For all conditions, the consumption of the PAHs corresponds tothe steady increase of H atoms in the gas phase. This is consistentwith the fact that the H atom is one of the most important hydrogenabstracting radicals in these flames. In this context, it is worth not-ing that the calculated mole fraction of H at 1800 K is approximate-ly 0.008 which is the same as that one determined experimentallyunder similar conditions.

As has been recalled in Ref. 7, fullerenes are not only formed inthat part of the burned gas which is adjacent to the oxidation zone,but also in a region after the oxidation zone where soot particles startto grow. However, the mechanism for the formation of fullerenes inthis case is assumed to be closely connected with heterogeneousreactions involving incipient soot particles, and for this reason it isnot considered in the present approach.

The calculated sequence of the formation of different gaseousspecies with increasing temperature is compatible with one whichholds for the species formed under combustion conditions, e.g., seethe review by Wiersum.25 According to this review, PAHs can beformed from small hydrocarbons like CH4, which has been shown inFig. 5, to stabilize at low temperatures. Any small PAH formed inthis way is a potential precursor for a larger PAH. Ultimately suchreaction sequences can be considered as going back to even smallercarbon fragments. So, for example, at very high temperatures carbonis expected to be present in atomic form, or to exist as relatively sta-ble C2 species or Cn oligomers. Thus, formation of fullerenes can bethought of as being indirect, due to condensation at lower tempera-

tures (T < 12008C) of Cn oligomers. Although this mechanism isindeed a valid one, the present study showed that there also exists atemperature window above the PAH formation and below that of Cnoligomers, where fullerenes are stable, indicating that a direct for-mation mechanism is possible as well. This route is in agreementwith the results of Kroto’s group16 on an experimental investigationof the formation of fullerenes by pyrolysis of naphthalene. Theauthors proposed that at low temperature high molecular massspecies, namely, C60H38 and C70H42 are produced from naphthalenecondensation. At higher temperature, these are partially dehydro-genated, and finally by further dehydrogenation they collapse to C60and C70, respectively.

The observed bell-shaped curves arising from calculations arealso similar to the ones obtained by Wang et al.12 for the yield of sootproduced from combustion of heptane and benzene. These curves, asillustrated in Fig. 3 of their paper, are slightly asymmetrical, sincetheir decrease at high temperature after the maximum yield has beenattained is shallower than their sharp increase at low temperature.The authors reported that PAHs and fullerenes were identified in thesoots and that the fraction of the former within the soot remainedconstant, independent of the operating conditions. Consequently, itis possible that the yield of fullerenes in their experiments followedthe same behavior, although no relevant information was reported byWang et al.

The calculated maximum yield of the fullerenes under differentconditions would seem to be overestimated compared to observedexperimental results. However, it should be remembered that the cal-culated yield is a thermodynamic yield and thus corresponds tomaintaining the reactive system for an infinite time at the operatingconditions. Indeed, there is evidence39 that in combustion conditionscatalytic effects corresponding to high reaction rates can be neglect-ed, and also the C60 1 C70 yield increases with residence time ofsoot in the flame. Furthermore, extraction of fullerenes occurs in thepost-flame zone. So the actual composition of solid species is theresult of a partial conversion of the generated composition in thehigh-temperature flame zone to the composition corresponding tothe low temperature conditions in the post-flame zone. Phenomenaoccurring in both flame and post-flame zones are kinetically con-trolled. It has been reported that, depending on the burning condi-tions, the net rate of formation of PAHs in the post-flame zone couldbe less than that in the flame zone by more than a factor of 100. For-mation of fullerenes may follow similar trends.

Another major result of the present study is the systematic deter-mination of a stability domain for C70 in addition to that for C60, andof the trends of the evolution of these domains as a function of pro-cessing conditions. It has thus been shown that the overall yielddecreases with increasing pressure. Howard et al.4,56 confirmed thistrend, although they also showed that with increasing pressure theproduction rate increases. The authors pointed out that the decreasein yield for these conditions is somewhat more than offset by theincreased density and, hence, increased rate of mass transfer throughthe combustion chamber for a given burner velocity. The reporteddecrease of the yield of fullerenes for these conditions was also con-firmed by the study of Wang and Cadman11 on the production of C60at 2400 K and ,200 kPa in a shock tube. The nonformation offullerenes at higher pressures (>460 kPa) has even been reported bythese authors. Finally, similar results have been reported by Belzet al.32 who showed a decrease of pressure in an electric arc signifi-cantly increases the yield of fullerenes. The finding here that increas-ing temperature favors the formation of C70 is indirectly supportedby the results of Meilunas et al.29 who reported that, compared toother fullerenes, C70 is more stable in a hydrogen plasma at hightemperatures.

As the present calculations show and Howard et al.4,56 experi-mentally confirmed, the C70/(C70 1 C60) ratio increases (i) whenpressure is increased (Fig. 1 and 3), (ii) when dilution is increased(Fig. 4), and also that the maximum value of this ratio is shiftedtoward higher temperatures relative to the maximum overall yield offullerenes (Fig. 1 and 2). Moreover, the calculated C70/(C70 1 C60)

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ratio in pure carbon is in excellent agreement with the one reportedfor the arc method,60 although this agreement may not be too sur-prising since a C70/(C70 1 C60) ratio equal to 0.1 in pure carbonambient was considered for the estimation of the thermodynamicdata of C70.

Figure 4 shows that the variation of dilution of the reactants hasa direct influence on the yield and on the composition of thefullerenes. Howard et al.4,56 showed that for their investigated con-ditions, i.e., in the case where C70 is the main fullerene, or is at leastcomparable to of C60, this yield goes through a maximum as diluentconcentration varies from 10 to 50%. The present study, indeed, pro-vides evidence that yield attains a maximum, but mainly for the C70evolution which is favored relative to that of C60 (Fig. 4). This holdsfor relatively low dilution values (some tens of percent), whoserange depend on the values of the other processing parameters. Fur-ther increase of the dilution has a minor effect on the relative yieldof the investigated fullerenes. However, it has to be pointed that anincrease of the percentage of inert gas in the reactive mixture de-creases the flame temperature. Through this indirect effect, the in-crease of the dilution favors the yield of C60 over that of C70. Thecombination of these two effects should yield a bell-type curve ofC70/(C70 1 C60) as a function of the dilution of the reactive gas. Re-sults from the work of Richter et al.5 indicate that in conditions com-parable to the ones investigated in this study (C/O 5 1.1, C/H 5 1,p 5 7.6 kPa) the C70/(C70 1 C60) ratio increases with increasingdilution of the reactive gas. The highest percentage of argon in thefresh gas mixture, which was investigated in Ref. 5, was 59%. Thisdilution exceeds the value in Fig. 4 which corresponds to the maxi-mum of the C70/(C70 1 C60) ratio. The observed difference may bedue to kinetic factors and/or to the fact that conditions (especiallytemperature) at the point where the flame-generated soot was col-lected are different from the ones in Fig. 4.

The increase of the C70/(C70 1 C60) ratio with the increasing C/Hratio has been confirmed by Bachmann et al.6 who reported that thisratio is higher in naphthalene (C/H 5 1.25) than in benzene (C/H 51). Finally, the result for the yield of C70 which does not changemonotonically with pressure but presents a maximum at some tenthsof an atmosphere is in agreement with the typical optimum condi-tions for the production of fullerenes by the method of Krätschmerand co-workers.61

In contrast to the striking agreement discussed above betweenexperimental and theoretical investigations, a number of conclusionsdrawn from the calculations seem, a priori, in contradiction to the lit-erature. First, for example, the overall yield of fullerenes calculatedhere appears to be overestimated. However, the present calculationsconcern a metastable equilibrium. Formation of condensedfullerenes is in competition with that of soots and graphite. If in pro-cessing conditions for which the yield of fullerenes is favored, nucle-ation of soot particles and graphite could be avoided, a higherfullerenes yield could possibly be reached. Second, the calculatedvalue of the C70/(C70 1 C60) ratio is often lower than the experi-mentally determined one.3,20,39 This disagreement may be attributedto one or more of the following reasons: (i) the stability of gaseousC70 could be underestimated in the calculations; (ii) the formation ofC70 may be kinetically favored over that of C60; (iii) the relative sta-bility between gaseous C70 and C60 may not be exactly the same asthe one between solid C70 and C60. It should also be noticed that, aswas pointed by Richter et al.,39 the C70/(C70 1 C60) ratio is highlysensitive to processing conditions and to the position of samplingrelative to the flames. The chosen thermodynamic data of the twofullerenes, and especially of C70, may also be responsible of errorsin the calculated ratio, although, based on experimental input, aC70/(C70 1 C60) ratio of 0.1 was considered in pure carbon ambientfor the creation of the thermodynamic functions of C70.

The observed strong enhancement of the yields of both fullereneswhen a halogen atom is added to the reactive gas is confirmed by thepresent calculations. However, it has to be pointed that other com-plex phenomena may also occur for such a case. First, fluorine may,in principle, be incorporated into the products, although the H-F

bond is energetically favored over the C-F bond (their energy is,respectively, 565 and 484 kJ/mol40). Also, as has previously beenmentioned, in a mass spectrometric investigation of fullerene-form-ing flames, Richter et al.41 observed no halogenated fullerenes whenchlorine were added to the fuel. They attributed this fact to a limitedthermal or photochemical stability of these compounds or to theimpossibility of substituted PAHs to intervene into the fullerene for-mation mechanism. Second, as was pointed out by the same groupin another paper,38 the inhibiting role of halogens on the chain reac-tions during combustion is responsible for the decrease of tempera-ture. This effect is probably the origin of the enhanced soot forma-tion for these conditions. The present study does not consider sootformation and, consequently, the effects of this complex phenome-non on the formation of fullerenes, i.e., decrease of temperature andof the availability of carbon for the production of fullerenes, cannotbe taken into account.

It is worth noting that most of the experimentally investigatedconditions up to now have been performed on improvised systems,i.e., burners and associated equipment designed for other purposesand in no way modified for the fullerenes. The conclusions obtainedfrom the present work could therefore be useful for the design of anoptimized system for the production of fullerenes. This resultingprocess should have two major characteristics: (i) it should be con-tinuous and not batch-quantity, as has been pointed out by, amongothers Taylor et al.16; (ii) it should be a multiple-step process, whereproducts of the first step would be recycled in the following ones.This characteristic has been pointed out by different authors as ameans of yield improvement of fullerenes.15,20 The evolution of theyield of the fullerenes with the three major parameters investigatedhere, i.e., temperature, pressure, and C/H ratio, as has been discussedin the previous paragraphs, could be used as a guide for the opera-tion of the sequential steps. For example, an enrichment in fullerenesin the products could be ensured if an increase of the C/H ratio of theinput material is assumed from one step to the next. Appropriatecombinations of temperature and pressure in each step would helpapproach the maximum yield. Furthermore, fine tuning of theseparameters could guide the process toward C60 or C70 enriched prod-ucts. This can be possible due to the remarkable shift between theC60 and C70 peaks, as evidenced in Fig. 1b, 1c, 2c, 2d, and 6.

ConclusionsAn assessment of the available thermodynamic data of gaseous

and of condensed fullerene C70 has been presented. Gibbs energyminimization of the gaseous C-H-O-Ar chemical system includinglarge polyaromatic hydrocarbons and the fullerenes C60 and C70 hasbeen used to determine under which conditions C60 and C70 mole-cules are stable. It has been shown that the yield of fullerenes as afunction of temperature is bell shaped, and that their thermodynamicstabilities place them at an intermediate position between PAH, andlow carbon (C1, C2, C3) radicals and neutral species (C2H2). It wasthus shown that the overall yield increases with decreasing pressureand increasing the C/H ratio in the reactants. A stability domain forC70 in addition to the one of C60 is observed, and it is shifted towardhigher temperatures relative to that for C60. The C70/(C70 1 C60) ratioincreases when pressure and gas-phase dilution is increased. Finally,the maximum value of this ratio is shifted toward higher temperaturesrelative to the maximum overall yield of fullerenes. On the basis ofthe results obtained, the formation and decomposition mechanisms offullerenes has been discussed.

The influence of the addition of halogen atoms in the gas phaseon the yield of the two fullerenes has also been investigated. It hasbeen shown that the addition of fluorine in the reactive gas results inthe formation of HF, in the decrease of hydrocarbons, and conse-quently, in a remarkable increase of the yield and in the extension ofthe stability domain of both fullerenes.

The main question which potentially arises from this type of studyconcerns the degree of reliability of an equilibrium approach for thesimulation of such nonequilibrium processes. A partial answer isgiven by the striking agreement between most calculated trends and

Journal of The Electrochemical Society, 146 (7) 2752-2761 (1999) 2761S0013-4651(98)10-065-4 CCC: $7.00 © The Electrochemical Society, Inc.

experimental evidence from the literature review. It can thus beadmitted that a combination of these two kinds of information is use-ful for discussing the formation mechanism of fullerenes and forunderstanding the observed trends within the framework of produc-tion conditions. The present work shows the possibility of adjustingthe C70/(C70 1 C60) ratio by setting the flame conditions. In the lightof these calculations, the possibility of the direct production offullerene films containing variable amounts of C60 and C70 by a tun-able continuous multistep process has been discussed, and the con-clusions can be used as a guide for the next round of syntheses.

Acknowledgments

We thank Serge Ravaine, CNRS Bordeaux, for help with theselection of crystallographic data of C70, and Professor Wunderlichand his group at ATHAS’s Laboratory, University of Tennessee, forproviding us with their thermodynamic data on C70. A.K. gratefullyacknowledges the European Union for a grant through the TEMPUSSJEP-07316-94 program.

The Institut National Polytechnique de Toulouse assisted in meeting thepublication costs of this article.

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