Journal of Thermal Analysis and Calorimetry

, Volume 133, Issue 1, pp 313–319 | Cite as

Enthalpy of formation of carboxylated carbon nanotubes depending on the degree of functionalization

  • E. V. Suslova
  • S. A. Chernyak
  • S. V. Savilov
  • N. E. Strokova
  • V. V. Lunin


Carbon nanotubes (CNTs) with different content of carboxylated groups on their surface (depending on the duration of their treatment with nitric acid) were synthesized. All samples were analyzed by thermal analyses, X-ray photoelectron spectroscopy, Raman and energy-dispersive X-ray spectroscopy, transmission electron microscopy and SBET. The adiabatic bomb calorimetry technique was used for the determination of enthalpy of formation. With the increase in time of treatment from 3 to 9 h, the content of oxygen increased from 7.49 to 8.22 at%. After 15-h treatment in nitric acid, CNTs contained 7.86 at%. The enthalpies of formation of all samples were negative and had nonlinear character. The changes of surface and bulk physicochemical characteristics of oxidized CNTs were analyzed. It was shown that despite decrease in surface enthalpy of formation ∆fH 298(surf.) 0 with the increase in oxygen content, the bulk enthalpy of formation ∆fH 298(bulk) 0 was very sensitive to defectiveness and structure of carbon layers. It resulted in the difficult correlation between oxygen content, morphology, defectiveness and ∆fH 298 0 .


Enthalpy of formation of carbon nanotube Carboxylated carbon nanotubes Bulk enthalpy of formation Surface enthalpy of formation 


In the present time, materials based on carbon nanotubes (CNTs) are widely used as adsorbents [1], supports of catalysts [2], fillers of polymers [3], and materials of electrodes of different energy storage devices [4]. Often, the properties of CNTs determine all characteristics of devices. Thus, the relationship between CNT physicochemical characteristics and functionality plays the particular role.

One of the fundamental parameters characterizing the bulk properties is enthalpy of formation of CNTs. CNTs are metastable phase with positive enthalpy of formation ∆fH > 0. Their enthalpy of formation was experimentally determined earlier in the works [5, 6, 7, 8, 9, 10, 11, 12, 13]. In the work [14], the enthalpy of formation was determined for mixture of CNTs with impurities and was to be found negative.

The value ∆fH strongly depends on degree of materials uniformity, CNT length, thickness of internal and external channel, numbers of carbon layers, defectiveness, impurities, chemical composition, heteroatoms in the structure, adsorbed and functional groups on surface [5, 9]. With the increase in CNT diameters, the enthalpy of formation increases. For example, ∆fH of CNTs with diameter 3–5 nm is equal to 0.018 ± 0.011 kJ mol−1 [13], of those with diameter 130 nm is equal to 9.0 ± 0.8 kJ mol−1 [8], and ∆fH of carbon nanofibers with a thickness 1–4 µm is equal to 16.56 ± 2.76 kJ mol−1 [6]. With the increase in number of carbon layers, the number of possible sp 3 carbon atoms increases, the layers become curved, defectiveness increases and ∆fH grows [5, 10]. For example, the enthalpy of formation of multi-walled CNTs with cylindrical structure is 8.60 ± 0.52 kJ mol−1, while for those with more defective conical structures it equals to 21.70 ± 1.32 kJ mol−1 [6].

The thermodynamic characteristics of the CNTs change with the incorporation of heteroatoms into the CNT composition. With the increase in nitrogen content in CNTs and carbon nanoflakes, the enthalpy of formation decreases [9]. However, this trend also has nonlinear character. The enthalpy of formation is extremely dependent on the nature of these heteroatoms embedded in the structure of the carbon sheets [5].

The different surface groups, as a general rule, stabilize CNT structure because of they are located on the points of defects and breaking of C–C bonds [15]. Earlier, it was established that with the increase in content of functional carboxylated groups in the composition of CNTs, the enthalpy of formation decreases and becomes negative [6]. Similar pattern was also detected for others carbon nanomaterials—for nanodiamond [16] and for bulk coal characterizing decrease in enthalpy of formation with the increase in oxygen content [17]. However, from the presented data in Ref. [6], it follows that oxidized CNTs with equal or simple content of oxygen containing groups have different standard enthalpies of formation and correlation between oxygen content and ∆cH 298 0 has ambiguous character. There are no data about the impact of different functional groups toward the enthalpy of formation and the role of nature of oxidized CNTs. In the present investigation, we tried to estimate the contribution of different functional groups appearing during the oxidation on ∆fH value. The contributions of surface and bulk enthalpy of formation were evaluated at the first time.


CNTs were synthesized via catalytic decomposition of hexane in nitrogen flow (99.999%, Logika Ltd., 500 mL min−1) at 750 °C in a quartz tube reactor. The CNTs were washed in HCl solution during 8 h and then annealed by 4 h at 400 ºC on air for removal of amorphous carbon. CNTs were refluxed with solution of nitric acid (Chimmed, Russia, 99.99%) by 3, 6, 9 and 15 h to achieve different degrees of functionalization [2]. Samples are named CNTs_3, CNTs_6, CNTs_9 and CNTs_15 respectively.

Thermogravimetric analysis (TA) and differential thermal analysis (DTA) were performed using «Netzsch STA 449 PC LUXX» thermal analyzer. The rate of heating was 5 °C min−1 under air atmosphere. The data were used for determination of water content in the samples. Residual content in the samples was evaluated with use of EDX spectroscopy, «JEOL JSM-6390LA» («JEOL Ltd.» , Japan). The relative error of method for determination of hard metals is no more 5%.

X-ray photoelectron spectra (XPS) were recorded using a Kratos Axis Ultra DLD with a monochromatic Al Ka source operated at hν = 1486.6 eV and 150 W (Shimadzu, UK). Overview XPS spectra were obtained by energy transmittance analyzer at 160 eV and 1 eV step (Fig. S1 in the Supplementary data). High-resolution spectra were recorded with the energy bandwidth of the analyzer 40 and 0.05 eV step. Analysis of high-resolution lines of carbon and oxygen spectra and determination of chemical state of atoms were performed using CasaXPS software. The relative error of determination of elements is no more 10%.

TEM images of the samples were obtained using “JEOL 2100F” (200 kV) microscopes. For TEM investigation, the small amount of sample was dispergated in ethanol using ultrasonic bath and a droplet of the suspension was placed on the polymer covered copper grid.

Raman spectra of the samples were registered using a «LabRam HR800 UV» (Horiba Jobin–Yvon, Japan) microscope-spectrometer (5 mW argon laser excitation with 514.5 nm wavelength and 50 × Olympus lens). At least, 4 spectra were obtained for each sample. The relative errors in determination of ratio of D and G lines of samples were different and depended on samples. All spectra were published and discussed early in Ref. [18].

The determination of the heat of combustion was performed on e2k isothermal bomb calorimeter (Digital Data System, South Africa). The energy equivalent of the calorimeter was determined from the combustion of benzoic acid (DDS CAL2k) and graphite. The specific energy of combustion under certificate conditions was (26.456 ± 0.006) kJ g−1 for benzoic acid and (32.89 ± 0.03) kJ g−1 for graphite, that was in line with the reference value of ΔfH0298 of graphite −(32.79 ± 0.13) kJ g−1 [19]. The measurement procedure was the same as previously used for carbon nanotubes [5, 6]. Tablets of carbon ~ 0.4 g were pressed with benzoic acid as internal standard at a ratio of 1:3 and placed into a bomb calorimeter under 30 bar of oxygen (99.7%, Logika Ltd.). For each material, the experiment was repeated at least 5 times to determine the statistical error.

Results and discussion

Content of carbon and oxygen in the composition of CNTs was determined by XPS; the content of water and residual was determined by TA and EDX spectroscopy, respectively (Table 1). The content of residual decreases with the increase in time of oxidized treatment: the included MoO3, MgO and Co particles dissolved because of destruction of CNT walls under action of nitric acid. The content of oxygen was maximum at 9 h of acid treatment.
Table 1

Chemical composition, SBET and ration of D and G Raman lines of samples


C/at% (XPS)

O/at% (XPS)

H2O/wt% (TA)

MgO + MoO3/wt% (EDX)

CoO/wt% (EDX)

SBET/m2 g−1

ID/IG (Raman)

































At the first time, the procedure of calculation of enthalpy of formation of CaHbOc was described in Ref. [20]. For carbonized CNTs, this algorithm was applied at the first time in Ref. [6]. The reaction of combustion of CaHbOc is:
$$ {\text{C}}_{\text{a}} {\text{H}}_{\text{b}} {\text{O}}_{{{\text{c}}({\text{s}}.,\,1\,{\text{atm}} .)}} + \left( {a + \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 4$} b - \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} c} \right){\text{ O}}_{{2({\text{g}}.,\,1\,{\text{atm}} .)}} \to a{\text{CO}}_{{2({\text{g}}.,\,1\,{\text{atm)}}}} + \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} b\,{\text{H}}_{2} {\text{O}}_{{({\text{l}}.,\,1\,{\text{at}}.)}} $$
The first step of algorithm was recalculation of heat of combustion − ∆cU(imp) in specific heat of combustion of CNTs considering that samples contained water and residual—traces of catalysts MgO and MoO3 that was confirmed by XPS and EDX. Washburn correction was made according the formula:
$$ \Delta_{\text{c}} H_{298}^{0} = - \Delta_{\text{c}} U_{{ ( {\text{imp)}}}} + \Delta nRT $$
where ∆n is equal to \(\alpha_{\rm{CO}_2}\)—(a + ¼b − ½c\()_{\rm{O}_2}\), R is gas constant (8.314 J mol−1 K−1), and T is standard temperature (298 K).
Values of standard enthalpies of formation ∆fH 298 0 were calculated according to Hess’s law:
$$ \Delta_{\text{f}} H_{298}^{0} = a\,\Delta_{\text{f}} H_{{298({\text{CO}}_2)}}^{0} - \,\Delta_{\text{c}} H_{{298({\text{CNM}})}}^{0} $$
using the next thermodynamic data:
$$ a{\text{C}}_{{({\text{graphite}},\,1\,{\text{atm}}.)}} + a{\text{O}}_{{2({\text{g}}.,\,1\,{\text{atm}} .)}} \to a{\text{CO}}_{{2({\text{g}}.,\,1\,{\text{atm}})}} , $$
fH 298(graphite, 25 °C) 0  = − 393.51 ± 0.13 kJ mol−1 [19].
The samples CNTs_3, CNTs_6 and CNTs_9 contained Co because of catalytic growth of CNTs in the presence of Co-Mo catalysts. The heat of CoO formation [21] was subtracted from the heat of combustion of CNTs according to equation:
$$ {\text{Co}} + \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} {\text{O}}_{2} \to {\text{CoO}}, $$

fH 298(CoO, 25 °C) 0  = − 237.74 kJ mol−1.

All observed data are presented in Table 2.
Table 2

The calculated values of heat of combustion and enthalpy of formation for oxidized CNTs


− ∆cU/kJ g−1 (exp.)

− ∆cU kJ g−1

(subtraction of H2O, MgO and MoO3)

cH 298 0 /kJ g−1 (CaOc)

fH 298 0 /kJ mol−1


31.88 ± 0.01



9.45 ± 0.01


28.03 ± 0.08



− 24.65 ± 0.21


27.90 ± 0.03



− 16.92 ± 0.16


28.09 ± 0.04



− 19.79 ± 0.17


28.54 ± 0.11



− 13.68 ± 0.24

aData for CNTs taken from Ref. [5]

bErrors are the same for the − ∆cU

It was established earlier that the common correlation between content of carboxylate groups and the enthalpy of formation is linear. With the increase in content of CO2H groups, the enthalpy of formation decreases. However, for the materials with similar oxygen content, it was shown that the value of enthalpy of formation could vary significantly [6]. In the present work, we oxidized the same CNT sample achieving the various degrees of functionalization. The enthalpies of formation of CNTs were negative in all cases and had nonlinear character (Fig. 1).
Fig. 1

Correlation between content of oxygen in different states in carboxylated CNTs and standard enthalpy of formation

Probably, this happens because the oxidation changes not only the surface but also bulk characteristics of CNTs. The oxidation triggers carboxylation of the upper carbon layer and the destruction of the lower layers, as can be seen from the HRTEM images (Fig. 2). It was shown that the content of carbon layers decreased. Non-oxidized CNTs contained 10–15 carbon layers. While the oxidized CNTs gradually lost their structure, the upper layers etched and degraded. These results were previously discussed in details by us in Ref. [2, 18]. After 3 h treatment in nitric acid, CNTs retained their initial structure and upper walls were partially oxidized (Fig. 2b). After 6 h treatment in nitric acid, CNTs became significantly degraded and numerous flections appeared in the stricture (Fig. 2c). After 6 h of treatment, the oxygen content has not increased and new possible sites of oxidation has not observed. After 9 h, CNTs begin to decompose (Fig. 2d). It is important to note that the oxygen content is not increased because the rates of CNT oxidation and CNT defunctionalization become equal [2]. After 15 h, CNTs can lose their initial structure (Fig. 2e).
Fig. 2

HRTEM images of CNTs (a), CNTs_3 (b), CNTs_6 (c), CNTs_9 (d) and CNTs_15 (e)

According to XPS, several types of oxygen atoms were present in the samples (Fig. 3). They were hydroxyl oxygen C–O with a binding energy equal to 533.2–533.3 eV and carbonyl oxygen C=O with a binding energy equal to 531.5–531.6 eV [22]. The C–O and the C=O types of oxygen affect enthalpy of formation nonlinear and replicate the general dependence (Fig. 1).
Fig. 3

XPS spectra of O1 s electrons of investigated samples. Spectra are normalized in proportion to the normalization of the spectra of C1 s electrons

Taking into account that all surface and bulk characteristics change, it seems reasonable to analyze the enthalpy of formation of CNTs as a sum of surface and bulk enthalpy of formation and estimate how each of them can change. Full enthalpy of formation can be represented as the sum of surface and bulk component, according to the formula [5]:
$$ \Delta_{\text{f}} H^{0}_{298} = \Delta_{f} H^{0}_{{ 2 9 8 ( {\text{surf}} . )}} + \Delta_{\text{f}} H^{0}_{{ 2 9 8 ( {\text{bulk)}}}} $$
Physical meaning of the ∆fH 298(surf.) 0 is well demonstrated by the single-walled CNTs and the fullerenes in which the structure is fully formed by single carbon layer. Full enthalpy of formation corresponds to the surface enthalpy of formation. Enthalpy of formation of single-walled CNTs, determined in Ref. [23], was found to be equal to 7 kJ mol−1, in Ref. [24] 9.5 ± 0.4 kJ mol−1 and in the Ref. [12] 4.7 ± 1.3 kJ mol−1. In the case of fullerenes, it was shown that their ∆fH 298 0 is very sensitive to the composition and structure and increases from C76 to C78 and then to C84. However, the energy of the molecule normalized to the carbon atom decreases because the whole structure stabilizes [25].

In the case of multi-walled CNTs and other multilayer carbon structures, more understandable is surface energy that equals to enthalpy of formation normalized to surface area. For example, surface energy was early estimated for carbon nanoflakes and nanodiamond equal to − (0.236 ± 0.005) and − (0.10 ± 0.02) kJ m−2 accordingly [9, 16].

In the present work, we can estimate the enthalpy of the reaction of oxidation of the surface of CNTs. This approach at the first time was proposed in Ref. [5, 26] for nitrogen-doped CNTs. Considering that the bond energy of C–C, C=C, O=O, C–O, C=O (in molecule CO2) and C=O (carboxyl group) are equal to 345.6, 602, 493.6, 331, 799 and 745, respectively [27, 28], we calculated using model Eq. 7 that the enthalpy of formation of 1 mol of oxidized CNT surface was equal to − 1843.6 kJ mol−1:It is obvious that with the increase in oxygen content on the surface of CNTs, the surface becomes more stable. The stabilizing role of the surface and adsorbed groups, however, was implied previously in Ref. [5, 6, 9].
The investigated samples contained adsorbed water which role also should be evaluated. It should be noted that on the surface of oxidized CNTs, the concentration of water was 4–6 times higher compared to non-oxidized CNTs because of increase in polarity of surface and, as a result, the affinity to water. With the increase in water concentration, the enthalpy of formation increased (Fig. 4). A similar dependence was earlier obtained for no functionalized CNTs, which are characterized by an increase in enthalpy with the increase in the concentration of water on their surface (Fig. 4) [5]. Theoretically calculated enthalpy of adsorption of water on the surface of the carbon is equal to 0.22–0.31 eV [29], the heat of sorption of water experimentally obtained is equal to − 37.5 kJ mol−1 for CNTs [30] and oxidized carbon [31]. Probably, water adsorbed on the carboxyl groups through hydrogen bonds and van der Waals forces because of hydrophobic nature of CNTs, then come the filling of pores in the micropore adsorption occurs until it is full. These values are much lower than the heat of condensation [31, 32]. Adsorbed water does not actually stabilize the surface.
Fig. 4

Correlation between of water concentration in the composition of CNTs and carboxylated CNTs and enthalpy of their formation. Correlation between CNTs and their ∆fH 298 0 was plotted with use data [5, 6, 13]

Considering that the surface ∆fH 298(surf.) 0 decreases for samples CNT_3, CNT_6 and CNT_9 with the increase in duration of acid treatment of CNTs, it can be reason to assume that bulk ∆fH 298(bulk) 0 increased. As a rule, a bulk component increases with the increase in degree of CNT defectiveness [5, 6] and with the increase in content of carbon layers [5, 23]. Theoretically, it was predicted that the enthalpy of formation decreases with the increase in length of CNTs [33]. For CNTs assessed in the present work with Raman spectroscopy, it was established that defectiveness decreased: the ratio between intensity of D and G lines ID/IG increased (Table 1). The ratio ID/IG increased for CNT_3, CNT_6 and CNT_9 samples. This indicates a possible graphitization and appearance of sp 2 hybridized carbon atoms. The oxidation process mainly occurs in the places of localization of defects, five and semichronic carbon cycles, and is associated with the washout of impurities and opening the caps [18, 34].

According to XPS, samples contained several types of carbon atoms (Fig. 5). These were sp 2 and sp 3 hybrid atoms of carbon C–C and C=C with binding energy equal to 284.3–284.4 and 285.0 eV, respectively, and also carbon atoms directly binding with oxygen C–O, C=O and O=C–O with binding energy equal to 286.4, 287.2 and 288.6–288.7 eV, respectively [35, 36]. In XPS spectra of C1 s electrons, the ratio between sp 3 :sp 2 carbon atoms also increased. The enthalpies of formation of fragments CC3 (sp 2 ) and CC4 (sp 3 ) calculated based on the enthalpy of formation of bonds C–C and C=C are equal to − 1293.2 and − 1382.4 kJ mol−1, which is in the accordance with the obtained results.
Fig. 5

XPS spectra of C1 s electrons of investigated samples. Spectra are normalized on square of lines

Thus, to understand the trends of the change of enthalpy of formation of carboxylated CNTs, it is necessary to consider all physicochemical characteristics and their changes depending on the time of treatment of CNTs with nitric acid. It is important to estimate not only CNT surface but also change of inner layers and bulk structure. It should be noted that for this reason, a direct comparison of the contributions of surface and bulk components of the enthalpy of formation turns out to be impossible.


The enthalpy of formation was measured for carboxylated CNTs with content of oxygen from 7.49 to 8.22 at%. In all cases, the ∆fH 298 0 was negative. The correlation between oxygen content and ∆fH 298 0 had nonlinear character. Oxygen atoms in the structure of CNTs were in two main forms formed C–O and C=O bonds. We can conclude that the enthalpy of formation carboxylated CNTs is extremely sensitive to both bulk and surface components. With the increase in the concentration of carboxyl groups, the surface enthalpy decreases and the bulk increases due to the degradation of carbon layers under the influence of oxidizing agents.



The authors are grateful to Dr. K. I. Maslakov for XPS experiments. The authors thank M. V. Lomonosov Moscow State University Program of Development for experimental facilities.

Supplementary material

10973_2017_6930_MOESM1_ESM.docx (80 kb)
Supplementary material 1 (DOCX 79 kb)


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • E. V. Suslova
    • 1
  • S. A. Chernyak
    • 1
  • S. V. Savilov
    • 1
  • N. E. Strokova
    • 1
  • V. V. Lunin
    • 1
  1. 1.Department of ChemistryLomonosov Moscow State UniversityMoscowRussia

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