Thermodynamic Properties and Similarity of Stacked-Cup Multiwall

Article pubs.acs.org/jced

Thermodynamic Properties and Similarity of Stacked-Cup Multiwall Carbon Nanotubes and Graphite Gennady J. Kabo,† Eugene Paulechka,*,†,‡ Andrey V. Blokhin,† Olga V. Voitkevich,† Tatsiana Liavitskaya,†,§ and Andrey G. Kabo† †

Chemistry Faculty and Research Institute for Physical Chemical Problems, Belarusian State University, Leningradskaya 14, 220030 Minsk, Belarus ‡ Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, Colorado 80305-3337, Unites States § Department of Chemistry, University of Alabama at Birmingham, Birmingham, Alabama 35294-1240, United States S Supporting Information *

ABSTRACT: The heat capacity of stacked-cup multiwall carbon nanotubes (MWCNTs) was measured in an adiabatic calorimeter over the temperature range of (5 to 370) K. Results are compared with literature data on various samples of CNTs and other carbon allotropes. The relatively large scatter of the heat capacity data for CNTs is discussed. The energy of combustion for MWCNTs was determined by combustion calorimetry, and the enthalpy of formation was found to be ΔfH°m = (0.6 ± 0.9) kJ·mol−1. It is demonstrated that the thermodynamic properties of MWCNTs at T > 200 K are close to those of graphite. Equilibria of the synthesis of MWCNTs were considered.

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significant problems. Belousov et al.11 reported the heat capacity and derived thermodynamic functions at T = 298.15 K based on low-temperature measurements for a material identified simply as “nanotube”. Lytvynenko14 separately described this material as MWCNTs. The results by Nan et al.5 were unphysically small, with reported heat capacities being smaller than the heat capacity of diamond. Lytvynenko14 analyzed the literature data and noted relatively large differences in the available data reaching (3 to 18) × 10−2cp for SWCNTs in the temperature range of (120 to 300) K and (3 to 8) × 10−2cp for MWCNTs in the temperature range of (50 to 300) K. As demonstrated below, the differences between the available data are even larger than noted above. Lytvynenko also derived thermodynamic functions (standard entropies, enthalpies, and Gibbs energies) for SWCNTs and MWCNTs, but the value of these functions is limited due to the large uncertainties. To our knowledge, the enthalpy of formation for CNTs has not been reported. The available thermodynamic properties for this material are insufficient for calculation of chemical equilibria involving CNTs, especially at high temperatures. Determination of thermodynamic properties for CNTs is a complicated problem, as the structure and composition depend on conditions of their synthesis and purification. The material can contain impurities of various nanocarbon phases, catalyst residues, water, functional groups on the edges, and adsorbed

INTRODUCTION Carbon nanotubes (CNTs) are materials that have multiple real and potential applications,1,2 and current production capacities are about 2.7 × 106 kg.1 CNTs are also an interesting and complex subject for fundamental studies. Being one of the carbon allotropes, their properties demonstrate significant deviations from those of diamond, graphite, or fullerenes. Also, CNTs always contain impurities that can affect their properties. Studying the thermodynamic properties of CNTs provides information for characterization of the energy states in this material, calculation of equilibria in their synthesis, functionalization, sorption, solubilization, etc. The first reliable heat capacity measurements for CNTs were reported by Mizel et al.3 The results by Yi et al.,4 published a few months earlier, are unphysically low at T > 150 K, as demonstrated below. The heat capacity has been measured for single-wall CNTs (SWCNTs) and SWCNT bundles,3,5−10 double-wall CNTs (DWCNTs), 6 and multiwall CNT (MWCNTs).3−5,11,12 With the exception of Yi et al.,4 calorimetric techniques were used. In most works, the calorimeters were of the relaxation type, with typical relative standard uncertainties near 5%, as stated by the manufacturer.13 Significantly larger uncertainties were observed for CNTs. For example, the results by Hone et al.9 and Lasjaunias et al.7 obtained on similar samples differed by a factor of 3 near T = 6 K. Most researchers have reported their work in graphical form only, but this has not been a major problem because of the large uncertainties. Adiabatic calorimetry, a potentially more accurate method, has been used in two studies;11,5 however, reported results had © XXXX American Chemical Society

Received: June 25, 2016 Accepted: September 16, 2016

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DOI: 10.1021/acs.jced.6b00525 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Netherlands) using Cu Kα radiation (Ni filter) and a linear PIXcel1D detector, in Bragg−Brentano geometry. Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) were performed with a Netzsch STA 449 Jupiter instrument. About 3 mg of sample was placed in an alumina crucible and heated from (300 to 1273) K at a 10 K· min−1 scanning rate at a flow rate of 60 cm3·min−1 of air + 20 cm3·min−1 of nitrogen. Water can significantly affect the results of combustion calorimetry even at w(H2O) < 10−3, the amount that cannot be reliably detected with routine TGA. Thermal treatment of MWCNTs prior to the measurements leads to changes in the sample mass. To quantify the changes in mass, the measurements of stability in an hour range are required. The long-term thermal stability of the MWCNTs was studied in an air thermostat, providing temperature control to within u(T) = 2 K. A wide-mouth weighing bottle made of glass was annealed and cooled in a desiccator, and ∼1 g of the material was transferred to the bottle and weighed. For weighing, the bottle was covered with a cap. The sample was placed in the thermostat and heated to the desired temperature. After (2 to 7) h, the sample was cooled to room temperature in a desiccator and weighed. Two to five experiments were conducted at each of successively higher temperatures with the same sample. Three samples were studied in parallel. The combustion energies were determined in a combustion calorimeter equipped with a stainless-steel bomb of a 326 cm3 volume.18 The energy equivalent of the calorimeter εcalor = (14604.6 ± 2.9) J·K−1 was determined from five combustion replicates of benzoic acid (K-2 grade, mass fraction purity of 0.99993 specified by the supplier). The initial oxygen pressure in the bomb adjusted to T = 298.15 K was 3.09 MPa. For the adjustment of the data to standard conditions, conventional procedures19 were used. The samples were placed in bags made of 80 μm polyethylene film in a drybox. The polyethylene was assumed to have the formula (CH2)n. The combustion energy of polyethylene Δcuo = −(46337.6 ± 9.6) J·g−1 was determined from the results of eight experiments. Masses were determined with a Mettler Toledo AG 245 balance with a standard uncertainty of 2 × 10−5 g. The HNO3 content in the combustion products was determined by titration with 0.1 mol·dm−3 aqueous KOH solution. Heat capacities were measured with a TAU-10 adiabatic calorimeter (Termis, Moscow).20 A detailed description of the calorimeter construction and the experimental procedures were published earlier.21 Temperature was measured with an Fe/Rh resistance thermometer (R0 = 50 Ω) calibrated on ITS-90 by VNIIFTRI (Moscow). The expanded uncertainty (0.95 confidence interval) of the heat capacity measurements with this instrument was 4 × 10−3cp at T > 20 K and 2 × 10−2cp at T ≈ 5 K.21 The experimental heat capacities were smoothed with polynomial equations, and the root-mean-square deviations of the experimental points from the smoothing curves did not exceed one-half of the uncertainty in the corresponding temperature range. All reported uncertainties correspond to the 95% confidence interval for the normal distribution (coverage factor k = 2) unless specified otherwise.

gases. Clearly, it is highly desirable to make measurements on well-characterized samples with reproducible properties. The latter condition can potentially be satisfied through use of a material produced on an industrial scale. This work continues our activities on thermodynamic characterization of MWCNT-based materials.15 Here, we report the results of the experimental determination of heat capacity and enthalpy of combustion for MWCNTs produced on a tonne scale. The heat capacities and other thermodynamic properties are compared with various CNTs and carbon allotropes. The equilibria of CNT synthesis are considered.

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EXPERIMENTAL SECTION Stacked-cup-type MWCNTs were supplied by Vision Development (Japan). The structural characteristics of the material were reported earlier.15 They were synthesized by catalytic gasphase pyrolysis of hydrocarbons on a Ni(NiO)/MgO catalyst, as described by Tkachev et al.16 Sample characteristics, as stated by the supplier, are indicated in Table 1. To remove metalTable 1. Physicochemical Parameters of MWCNTs, As Stated by the Supplier parameter

value

physical state external diameter/nm average external diameter/nm length, lave/μm specific surface area/m2·kg−1 thermal stability

black powder 10 to 80 50 ≤1 to 2 99 to 100 to 973 K

containing impurities, MWCNTs are typically washed with 30 mass % HNO3,16 which completely removes Mg from the material. Complete removal of Ni is a more challenging problem. When the studied MWCNTs were burned in oxygen or in air, a gray−green residue was observed, indicating the presence of Ni. To determine the nickel content, we applied gravimetric analysis with dimethylglyoxime in a manner similar to that described previously.17 A sample of (0.5 to 3) g mass was burnt at 873 K in a ceramic crucible. The residue was fused with Na2S2O7; however, this did not make it completely watersoluble. The crucible content was quantitatively transferred to a 500 mL beaker with water and treated with a mixture of hydrochloric, nitric, and sulfuric acids on heating. The obtained solution was gently evaporated to a very small volume. Then, 200 mL of water was poured into the beaker, and the mixture was heated on a water bath, followed by dropwise addition of 10 mL of 1 mass % solution of dimethylglyoxime in ethanol with continuous stirring. Addition of a slight excess of NH3 resulted in formation of the bright pink nickel dimethylglyoximate precipitate. The precipitate was aged for at least 2 h. The obtained product was filtered on a glass filter funnel and dried at T = 383 K. The nickel content was deduced from the mass of the precipitate. The result for the calorimetric sample is given later with the sample characterization information. Elemental analysis of the investigated MWCNT sample for C, H, N, and S was carried out with an Elementar Vario El instrument. The reported uncertainties in mass fraction correspond to the 95% interval for normal distribution (k ≈ 2) and characterize repeatability of the data obtained from two to six parallel experiments. X-ray powder diffraction data were collected on an Empyrean diffractometer (Panalytical, The

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RESULTS AND DISCUSSION Sample Characterization. The initial material contained the following mass fractions of the elements: w(C) = (97.16 ± 0.10) × 10−2, w(H) = (0.146 ± 0.011) × 10−2, w(N) = (0.45 ±

B



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0.10) × 10−2, w(Ni) = (0.86 ± 0.02) × 10−2, and S was not detected. The remaining mass fraction of (1.38 ± 0.17) × 10−2 was assigned to O. The mass of the residue left after combustion in air was determined by direct weighing to be (1.07 ± 0.15) × 10−2 of the initial mass. If NiO was the main product of combustion, this would correspond to w(Ni) = (0.84 ± 0.11) × 10−2, which agrees within the uncertainties with the nickel content obtained from the dimethylglyoxime determination, thus confirming the nature of the residue. In MWCNTs, Ni can potentially exist in, at least, three forms: metallic Ni, carbide Ni3C, and oxide NiO. When the NiO/MgO catalyst is exposed to the reducing environment, some nickel ions located close to the surface are reduced and form metallic catalytic centers. However, only a small portion of the Ni2+ ions are transformed.22 When the nickel catalytic centers come into contact with hydrocarbon gases during the induction period, they transform partially or completely into Ni3C.23 It is generally believed that the carbide decomposes during the growth stage;23 however, the carbide may be present to some extent at the carbon−metal interface.23 During treatment with acid, MgO and NiO are normally removed from the material.16 An X-ray powder diffraction pattern for the studied MWCNT contains reflections from metallic Ni but not from NiO (Figure 1).

MWCNTs due to the presence of the carbide phase is less than 2 J·g−1. Heat capacities for Ni3C are not available, but the estimated entropy of formation is 5 J·K−1·mol−1 at 298.15 K (Kelley, as referenced by Richardson26), which indicates that the heat capacity of this compound will be close to that of the (Ni + 3C) mixture. Results of DSC/TGA analysis (Figure 2) showed no notable oxidation of MWCNTs below 800 K and a maximum heat

Figure 2. DSC (blue) and TGA (red) curves for MWCNTs.

effect near 940 K. A long-term stability study, however, revealed a more complex behavior (Figure 3). The material underwent a

Figure 1. X-ray diffraction pattern for the studied MWCNT sample. The ∗ represents peaks of Ni. Other peaks are specific to MWCNTs.

Figure 3. Relative mass change on studying long-term stability of the samples. The lines are provided as guides for the eye only.

Ni clusters remain ferromagnetic even at very small sizes,24 while the carbide is nonferromagnetic. We attempted to separate ferromagnetic and nonferromagnetic fractions of the studied material in its original powder-like state and in a water dispersion using a NdFeB N45 permanent magnet. The entire material was found to be ferromagnetic, which implies that metallic Ni is distributed throughout the material. Such a result further implies that the material contains encapsulated Ni clusters. For evaluation of thermodynamic properties, we assumed that Ni was in the metallic form. Even if Ni3C is formed at the Ni−C interface, this assumption will not introduce significant errors. The following values of the standard molar enthalpy of formation at T = 298.15 K for Ni3C have been reported: (38 ± 7), 25 (34 ± 25), 26 and (20 ± 22) kJ·mol −1 . 27 The corresponding correction to the enthalpy of combustion of

permanent decrease of mass at elevated temperatures, starting near 393 K. Initially, a rapid mass loss was observed, which was found to be reversible and assigned to water adsorption. The relative mass loss extrapolated to zero time was (0.63 ± 0.03) × 10−2. A rapid mass change observed at T = 483 K was followed by insignificant mass changes for more than 10 h. Then, the mass permanently decreased to the end of the series. After the measurements, one of the samples was exposed to air for 16 h and returned (0.33 ± 0.05) × 10−2 of its initial mass. We supposed that the increase in mass, after transfer from a dry atmosphere to air, is caused by adsorption of water. Elemental analysis of the dried initial material and final sample (Table 2) demonstrated that the content of N and O decreased significantly. This is not surprising, as the HNO3 C



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Table 2. Results of Elemental Analysis for MWCNTs, Gram of Element per 100 g of the Initial Material sample initial material initial material (dried) final sample final sample (dried)

C 97.16 97.16 97.18 97.18

± ± ± ±

H 0.10 0.10 0.35 0.35

0.146 0.075 0.107 0.070

± ± ± ±

N 0.011 0.011 0.010 0.010

0.45 0.45 0.22 0.22

± ± ± ±

Ob

Ni 0.10 0.10 0.01 0.01

0.86 0.86 0.86 0.86

± ± ± ±

0.02 0.02 0.02 0.02

1.38 0.82 0.46 0.17

± ± ± ±

0.17 0.17 0.35 0.35

a

Reported expanded uncertainties correspond to 0.95 confidence interval. bDetermined from the difference between one and the sum of mass fractions for other elements.

Table 3. Results for Typical Combustion Experiments at T = 298.15 K (p° = 105 Pa) m (compound)/g m′ (fuse)/g m″ (bag)/g Ti/K Tf/K dTc/K Ei (cont)/J·K−1 Ef (cont)/J·K−1 -m′·U′/J -m″·U″/J dUign/J (Ecalor)·(−dTc)/J (Econt)·(−dTc)/J ΔIBPU/J ΔU(HNO3)/J Δst.stateU/J u°/J·g−1 ⟨u°⟩/J·g−1

0.36138 0.00455 0.09986 298.1131 299.3149 1.1226 14.2 14.5 77.1 4627.3 0.3 −16394.5 −16.2 −16410.4 6.9 12.2 −32340 −32336 ± 12

0.31418 0.00443 0.09589 298.1064 299.1907 1.0021 14.1 14.4 75.1 4406.2 0.3 −14635.8 −14.4 −14649.9 4.8 10.6 −32317

0.30849 0.00508 0.08889 298.1130 299.1673 0.9716 14.1 14.4 86.1 4119.0 0.1 −14189.3 −14.0 −14203.2 2.5 10.3 −32369

0.36338 0.00522 0.09257 298.1047 299.2872 1.1049 14.2 14.4 88.5 4289.5 0.3 −16136.0 −15.9 −16151.6 6.0 12.1 −32351

0.47462 0.00472 0.10037 298.1014 299.5459 1.3748 14.3 14.6 80.0 4650.9 0.2 −20078.1 −20.0 −20097.8 7.2 15.9 −32329

0.30487 0.00518 0.09454 298.1059 299.1685 0.9810 14.1 14.4 87.8 4380.8 0.2 −14327.2 −14.1 −14341.1 6.3 10.3 −32329

0.23894 0.00444 0.09097 298.0974 299.0040 0.8227 14.0 14.3 75.2 4215.3 0.3 −12015.9 −11.8 −12027.3 4.8 8.1 −32326

0.26980 0.00544 0.08931 298.0918 299.0587 0.8870 14.1 14.3 92.2 4138.4 0.3 −12954.9 −12.7 −12967.3 4.2 9.1 −32333

a

mcomp, mfuse, and mfilm are the masses of the sample of the studied compound, cotton fuse, and polyethylene bag adjusted to vacuum conditions (density of the compound is ρ = 2.2 g·cm−3,15 cotton fuse ρ = 1.56 g·cm−3 (data for glucose used as reference),50 polyethylene ρ = 0.90 g·cm−3 as stated by manufacturer); Ti and Tf are the initial and final temperature in the reaction period; ΔTcorr is the corrected temperature increase; εi and εf are the energy equivalents of the contents of the bomb in the initial and final states, respectively; ΔignU is the electrical energy for igniting the sample; εcalor is the energy equivalent of the calorimeter; εcont·(−ΔTcorr) = εi(Ti − 298.15) + εf(298.15 − Ti − ΔTcorr); ΔIBPU is the change of internal energy for the isothermal bomb process; ΔU(HNO3) is the energy required for decomposition of the HNO3 solution formed; Δst.stateU is the energy correction to the standard state (the sum of Washburn’s corrections, for MWCNT cp = 0.74 J·K−1·g−1; (∂U/∂p)T ≈ 0 J·MPa−1·g−1; for polyethylene cp = 2.53 J·K−1·g−1,51 (∂U/∂p)T = −0.3 J·MPa−1·g−1); Δcu° is the standard mass combustion energy of the sample.

treatment of MWCNTs introduces oxygen-containing functionalities on the edges, mostly COOH and NO2. The presence of some hydrogen is expected because cup edges contain C−H moieties after the synthesis in a hydrocarbon atmosphere. Combustion Energy. Before the combustion experiments, the MWCNTs were dried at T = 473 K, which is close to the plateau in Figure 3. If one assumes that, after removal of water, the MWCNT composition changes linearly with mass of the sample, the composition of the material used for combustion experiments is as follows: w(C) = (98.21 ± 0.22) × 10−2, w(H) = (0.074 ± 0.011) × 10−2, w(N) = (0.34 ± 0.06) × 10−2, w(Ni) = (0.87 ± 0.02) × 10−2, w(O) = (0.51 ± 0.26) × 10−2. The standard specific energy of combustion for the sample was experimentally determined to be Δcu° = −(32336 ± 12) J· g−1 (Table 3). Oxidation of Ni to NiO (ΔrU°m = −(238.5 ± 0.5) kJ·mol−128) contributes −(35 ± 1) J/g of the sample. As mentioned above, one would expect the material to have aromatic C−H, COOH, and NO2 groups on the cup edges. To estimate the effect of the functional groups on the energy of combustion, an atom-based group contribution scheme was used. The contribution of an atom was assumed to be independent from its neighbors. For example, the standard energy of combustion for 1,4-dinitrobenzene was presented as

ΔcU ° = 6ΔΔcU °(C) + 4ΔΔcU °(H) + 4ΔΔcU °(O) + 2ΔΔcU °(N)

(1)

where ΔΔcU° is the atomic contribution. The experimental data on solid aromatic compounds presented in Table 4 allowed us to estimate molar contributions of various atoms to ΔcU°: ΔΔcU°(C) = −419 kJ·mol−1, ΔΔcU°(H) = −119 kJ· mol−1, ΔΔcU°(O) = 5.6 kJ·mol−1, ΔΔcU°(N) = 30 kJ·mol−1. Thus, the presence of N, O, and H results in an exothermic Table 4. Experimental Standard Molar Energies of Combustion at T = 298.15 K and p° = 105 Pa for Crystals of Aromatic Compounds Used for the Atomic Group Contribution Scheme

D

crystal

formula

−ΔcU°m/kJ·mol−1

ref

naphthalene anthracene phenanthrene 1-naphthalenecarboxylic acid 2-naphthalenecarboxylic acid 1,4-dinitrobenzene 1-nitronaphthalene 9-nitroanthracene

C10H8 C14H10 C14H10 C10H8O2 C10H8O2 C6H4N2O4 C10H7NO2 C14H9NO2

5152 7053 7036 5136 5123 2899 4985 6905

41, 42 42−44 45, 46 47 47 48 49 49



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Table 5. Thermodynamic Properties of Different Forms of Carbon carbon form

T/K

ΔfH°(T)/kJ·(mol of C)−1

Cp°(T)/J·K−1·(mol of C)−1

So(T) − So(0)/J·K−1·(mol of C)−1

ΔfG°(T)/kJ·(mol of C)−1

32,29

298.15 1000 298.15 1000 298.15 1000 298.15 1000

0 0 0.6 ± 0.9 1.0 ± 0.9 39.1 ± 0.2 37.6 ± 0.2 36.5 ± 0.3 36.6 ± 0.3

8.517 ± 0.009 21.610 ± 0.022 8.842 ± 0.035 22.2 ± 0.4 8.760 ± 0.044 21.35 ± 0.21 8.937 ± 0.045 21.46 ± 0.21

5.74 ± 0.10 24.46 ± 0.10 6.225 ± 0.025 25.5 ± 0.5 7.118 ± 0.036 25.87 ± 0.26 6.467 ± 0.032 25.41 ± 0.25

0 0 0.5 ± 0.9 −(0.1 ± 0.9) 38.7 ± 0.2 36.2 ± 0.4 36.3 ± 0.3 35.6 ± 0.4

graphite

MWCNT fullerene C60 (cr)36 fullerene C70 (cr)36

Following Diky and Kabo,36 we assumed the relative expanded uncertainty in thermodynamic properties equal to 5 × 10−3 at T = 298.15 K and 1 × 10−2 at T = 1000 K; the relative expanded uncertainty of the graphite heat capacity was assumed to be 1 × 10−3.

a

effect of −(79 ± 13) J/g of the sample. The reported uncertainty includes contribution from the uncertainty in the elemental analysis. The standard specific energy of combustion corrected for all non-C elements and reduced to the carbon-only material was determined to be Δc u° =

−(32336 ± 12) + (35 ± 1) + (79 ± 13) 0.9821 ± 0.0022

= ( −32809 ± 73) J·g −1

(2)

The largest contribution to the uncertainty arises from the uncertainty in the carbon content. The uncertainty may be somewhat underestimated due to assumptions used in calculation of the sample composition. The standard molar enthalpy of formation ΔfH°m for the studied MWCNTs at T = 298.15 K, calculated with ΔfH°m(CO2(g)) = (−393.51 ± 0.13) kJ·mol−1,29 is (0.6 ± 0.9) kJ/mol of C. The enthalpy of formation for the studied MWCNTs coincides with that of graphite within the uncertainties and is significantly less positive than the enthalpies of formation for fullerenes (Table 5). Heat Capacity and Thermodynamic Properties of MWCNTs. The sample used for the heat capacity measurements was dried at T = 403 K for several hours. Based on the analyses presented above, the material had the following composition after removal of adsorbed water: w(C) = (97.78 ± 0.10) × 10−2, w(H) = (0.076 ± 0.012) × 10−2, w(N) = (0.45 ± 0.10) × 10−2, w(Ni) = (0.87 ± 0.02) × 10−2, w(O) = (0.83 ± 0.18) × 10−2. The experimental specific heat capacities, cp, of MWCNTs are presented in Figure 4 and Table S1. The results from T = (5 to 83) K were obtained in this study. Heat capacities at higher temperatures were reported earlier.15 For calculation of thermodynamic functions, the experimental heat capacities were corrected for nickel content. The heat capacity of bulk Ni was calculated based on values reported in the literature.30−32 The corrections did not exceed 4.7 × 10−3cp. Below T = 14 K, the corrected heat capacity was found to obey a quadratic dependence on temperature (Figure 5): cp/J·K−1·g −1 = 2.471 × 10−5(T /K)2

Figure 4. Experimental specific heat capacities cp for MWCNTs. Red circles, this work; empty squares, Shevelyova et al.15

Figure 5. Experimental low-temperature specific heat capacities for MWCNTs. Blue line was calculated with eq 3.

amount of catalyst impurities, which are 0.1 mass fraction in some works,5,9,7 and adsorption of helium used to improve heat transfer at very low temperatures.7 For the material studied in this work, the mass fraction of catalyst is relatively low (w(Ni) = 8.6 × 10−3). The adsorption factor is especially important for SWCNTs, which have a very large specific area. The experimental heat capacities for CNTs from the literature are compared to the results of this work in Figure 6. Low-temperature heat capacities have been reported for SWCNTs of (1 to 1.3) nm average diameter.3,9,7,10,6,5 Very

(3)

Deviation of the calculated cp values from the experimental results did not exceed 1.2 × 10−2cp. The T2 dependence of the heat capacity is similar to that observed earlier3 for MWCNTs in the same temperature range. Near T = 5 K, one would expect the heat capacity of CNTs to increase with diameter and decrease with the number of carbon layers.37 Another factor affecting the results is the E



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Figure 6. Relative deviation of heat capacities for CNTs and carbon allotropes available in the literature from MWCNT heat capacities reported in this work (a) below T = 40 K, (b) above T = 40 K: ◆, graphite;33 ◊, diamond;34,35 blue line, recommended heat capacity of fullerene C60 (cr);36 dashed black line, calculated cv for graphene;37 cyan circles, SWCNTs;3 red circles, SWCNTs;9 semifilled circles, SWCNTs;7 crossed circles, SWCNTs;10 green circles, SWCNTs;6 yellow circles, SWCNT;5 green triangles, DWCNTs;6 cyan squares, MWCNTs;3 gray squares, MWCNTs;4 dark blue square, MWCNTs;11 pink squares, MWCNTs;12 yellow squares, MWCNTs.5

Table 6. Smoothed Thermodynamic Properties of MWCNTs (p° = 105 Pa) cp

T/K 0 50 100 150 200 250 298.15 300 370 400b 500b 600b 700b 800b 900b 1000b 1100b 1200b

◦ ΔT 0s

◦ ΔT 0h / T

−(g o(T ) − ho(0)) / T

J·K −1·g −1

◦ Δ f Hm

◦ Δf Gm

J·K −1·g −1

J·K −1·g −1

J·K −1·g −1

kJ·mol−1

kJ·mol−1

0.0 0.0516 0.1580 0.2899 0.4384 0.5933 0.7361 0.7414 0.9367 1.01 1.25 1.44 1.59 1.70 1.79 1.85 1.91 1.95

0.0 0.0284 0.0954 0.1835 0.2870 0.4014 0.5182 0.5228 0.6982 0.774 1.03 1.27 1.51 1.73 1.93 2.12 2.30 2.47

0 0.0186 0.0607 0.1143 0.1766 0.2444 0.3124 0.3150 0.4143 0.4566 0.593 0.720 0.834 0.936 1.03 1.11 1.18 1.24

0 0.0098 0.0347 0.0691 0.1104 0.1570 0.2058 0.2078 0.2839 0.3178 0.434 0.554 0.674 0.792 0.907 1.02 1.13 1.23

0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.8 0.8 0.9 1.0 1.0 1.1

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.1 0.0 −0.1 −0.2 −0.3

Relative expanded uncertainty in heat capacity, entropy, and enthalpy function is 4 × 10−3 below 400 K and about 0.02 at T > 400 K; expanded uncertainty in enthalpies and Gibbs energies of formation is 0.9 kJ·mol−1 (for 0.95 confidence interval). bEstimated using cp(MWCNT)/cp(graphite) = 1.03. a

with the data on MWCNTs of (20 to 30) nm12 is also satisfactory. The heat capacity of MWCNTs obtained in this work is somewhat larger than that of graphite.33,32 The difference is (3.3 to 3.6) × 10−2cp in the temperature range of (300 to 370) K. To estimate thermodynamic properties of MWCNTs at T > 370 K, we assumed that the ratio cp(MWCNT)/cp(graphite) = 1.03 holds. The thermodynamic properties for MWCNTs in the temperature range of (0 to 1200) K calculated from the experimental data obtained in this work and the heat capacity of graphite33,32 are given in Table 6. In the calculations, it was assumed that the material is composed of carbon only. The thermodynamic properties of various allotropic forms of carbon at 298.15 and 1000 K are compared in Table 5. Crystalline fullerenes are less stable than graphite due to the higher enthalpies of formation. It was demonstrated38 that the

large heat capacity differences below 30 K are seen, and these seem too large to be attributable to sample quality alone. Extremely large measurement uncertainties are the more likely cause. Values reported by Xiang et al.6 exceed the theoretical cv for graphene, which is highly improbable based on the theoretical analysis by Popov.37 The heat capacities of SWCNTs and MWCNTs reported by Nan et al.5 in the range of (78 to 398) K are lower than the heat capacity of diamond, which is not possible. A similar problem exists in the results by Yi et al.4 While it is difficult to evaluate measurement quality rigorously, we conclude that the lower results by Mizel et al.3 and Hone et al.9 are preferable. Taking into account the general quality of data reported in the literature, agreement within ∼10% between the present results and those by Mizel et al.3 on MWCNTs of (10 to 20) nm is relatively good. Agreement within ∼20% above T = 30 K F



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thermodynamic instability of crystalline C60 and C70 relative to graphite holds to a temperature of 3000 K and a pressure of 20 GPa. However, in the gas phase, the equilibrium radically shifts toward C60 and C70 due to the large differences in the enthalpy of sublimation for graphite and fullerenes. So, the successful synthesis of C60 and C70 is realized through the hightemperature sublimation of carbon. Enthalpies of formation, heat capacities, and entropies of MWCNTs are very close to those of graphite above T = 200 K. This is physically justified because the distances between the carbon layers in MWCNTs (0.36 nm15) and in graphite (0.3635 nm39) differ insignificantly and the density of MWCNTs, ρ = (2.210 ± 0.022) g·cm−3 at T = 293 K,15 is close to that of graphite39 (ρ = 2.26 g·cm−3). Equilibria of MWCNT Synthesis. The synthesis of MWCNTs by low-temperature catalytic pyrolysis of carboncontaining gases such as CO or hydrocarbons (chemical vapor deposition (CVD) process) has a number of advantages for industrial implementation compared to the discharge arc process and laser ablation synthesis.40 We considered the equilibria of propane thermolysis resulting in formation of MWCNTs at temperatures of T = (500 to 1200) K. This temperature range was selected to cover the temperature interval of (873 to 1173) K normally used for synthesis of MWCNTs by CVD.40 Generally, the process is carried out at ambient or reduced pressure. We conducted simulations at pressures of 0.01 and 0.1 MPa. Initially, we considered various hydrocarbons, H2, and MWCNTs as the potential products. However, during preliminary calculations, it was found that only CH4, H2, and MWCNTs can be present in the equilibrium mixture in significant amounts for any initial hydrocarbon in the considered temperature range. The results of the calculation of the equilibrium compositions for the products of the propane pyrolysis are shown in Figure 7. The reference data for CH4 and H2 were taken from NIST-JANAF tables.32 At T = 500 K, the methane content in the equilibrium mixture at P = 0.1 MPa is 45 mol·kg−1. The content of methane in the equilibrium mixture at T = 900 K and P = 0.1 MPa is reduced to 15 mol·kg−1, which corresponds to ∼0.24 mass fraction. The main components of the equilibrium mixture at 1200 K at this pressure are hydrogen (88 mol·kg−1) and MWCNTs (67 mol·kg−1). Lowering pressure allows one to obtain the same yield of MWCNTs at lower temperatures. Under real conditions, the solid pyrolysis products will contain graphite and other carbon forms in addition to MWCNTs. The relative amounts of various solid products will depend on kinetic factors, which are largely determined by the catalyst selection. The equilibrium of the carbon monoxide disproportionation reaction 2CO(g) ⇆ CO2(g) + C(MWCNT)

Figure 7. Calculated equilibrium composition of the pyrolysis products of propane at a pressure of (a) 0.1 MPa and (b) 0.01 MPa: black circles, MWCNT; red circles, H2; cyan circles, CH4.

K. Analysis of the literature data on heat capacity of CNTs revealed a very large (>20%) data scatter, even near room temperature, that cannot be explained by structural differences. The enthalpy of formation of MWCNTs determined from the combustion calorimetry experiments was found to be equal to zero within the uncertainty. The heat capacity, entropy, and enthalpy of formation of MWCNTs are very close to those of graphite above T = 200 K. This can be explained by the structural similarity of these materials. This behavior means that, under appropriate thermodynamic conditions, the yield of MWCNTs relative to graphite will be defined by kinetic factors. Two examples of the equilibria of MWCNT synthesis were modeled to illustrate selection of the optimal temperature ranges for the process.

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is shifted to the right below T = 900 K. This reaction is exothermic, and the enthalpy factor defines its direction at low temperatures despite a significant decrease in entropy. A high yield of MWCNTs in this reaction is possible at relatively low temperatures, and the reaction is limited only by kinetic constraints.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00525. Experimental specific heat capacities of MWCNTs (PDF)

CONCLUSIONS A sample of stacked-cup MWCNTs was characterized by elemental and thermal analysis. The heat capacity of the material was measured in the temperature range of (5 to 370) G



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This article is, in part, a contribution of NIST and is not subject to copyright in the United States for the author E.P. Trade names are provided only to specify procedures adequately and do not imply endorsement by the National Institute of Standards and Technology. Similar products by other manufacturers may be found to work as well or better.

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Thermodynamic Properties and Similarity of Stacked-Cup Multiwall

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