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Enthalpies of sublimation of fullerenes by thermogravimetry
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Enthalpies of sublimation of fullerenes by thermogravimetry Melchor Martínez-Herrera 1 , Myriam Campos, Luis Alfonso Torres, Aarón Rojas ∗ Departamento de Química del Centro de Investigación y de Estudios Avanzados del IPN, Av. Instituto Politécnico Nacional 2508, C.P. 07360, México D.F., Mexico
a r t i c l e
i n f o
Article history: Received 1 June 2015 Received in revised form 1 September 2015 Accepted 1 September 2015 Available online xxx Keywords: Heat capacity Thermal analysis Differential scanning calorimetry Heat of sublimation Cluster
a b s t r a c t The enthalpies of sublimation of fullerenes, as measured in the interval of 810–1170 K by thermogravimetry and applying the Langmuir equation, are reported. The detailed experimental procedure and its application to fullerenes C60 , C70 , C76 , C78 and C84 are supplied. The accuracy and uncertainty associated with the experimental results of the enthalpy of sublimation of these fullerenes show that the reliability of the measurements is comparable to that of other indirect high-temperature methods. The results also indicate that the enthalpy of sublimation increases proportionally to the number of carbon atoms in the cluster but there is also a strong correlation between the enthalpy of sublimation and the polarizability of each fullerene. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Since fullerenes were first isolated in macroscopic quantities in 1990 [1], these carbon clusters structures have gained a main role on the scientific scene. Fullerenes have promoted academic and industrial research that has led to the discovery of many of their interesting physical and chemical properties. Although the research on these nanostructures has expanded rapidly in different directions, many of their fundamental properties remain unknown, such as their thermochemical data, which are useful in the understanding of the energetics of these carbon clusters. The enthalpy of sublimation is one important thermochemical quantity because is essential to deriving the enthalpy of formation in the gas phase of the cluster, which in turn allows us to elucidate the relative stability of these molecules [2]. Some works have attempted to quantify the enthalpy of sublimation of fullerenes [3–21], and they generally considered C60 and C70 [3–17]. In most cases, there was a strong dependence between the enthalpy of sublimation and the applied technique, which made it possible to anticipate discrepancies in the results, e.g. for a specific fullerene, many similar enthalpies of sublimation values have
∗ Corresponding author. E-mail address: [email protected] (A. Rojas). 1 Current address: Departamento de Ciencias Naturales, DCNI, Universidad Autónoma Metropolitana, Cuajimalpa, Av. Vasco de Quiroga 4871, Col. Santa Fe Cuajimalpa, C.P. 05300 México, D.F., Mexico.
been reported at very different temperatures. In consequence, it is important to determine with a single reliable technique, and with high accuracy, the enthalpy of sublimation of the fullerenes C60 , C70 , C76 , C78 and C84 (Fig. 1). In 1998, Price and Hawkins [22] demonstrated that thermogravimetry was a useful technique for determining the enthalpy of sublimation of compounds that have low vapour pressures. In a thermogravimetric device the loss of mass due to the sublimation of a sample was accurately measured, and the vapour pressure was derived by utilizing the Langmuir equation [23]. Thereafter, the enthalpy of sublimation was calculated by correlating the vapour pressure and temperature data through the equation of Clausius–Clapeyron. From that work, substantial research determining vapour pressures and deriving the enthalpy of sublimation of a large variety of compounds with this methodology has been reported and has provided results on the enthalpy of sublimation that are as reliable as those derived from calorimetric methods or by Knudsen effusion [22,24–27]. Given the high sensitivity and large range of operating temperatures in modern thermogravimetric devices, this technique seems to be optimal for measuring the enthalpy of sublimation of fullerenes, for which calorimetric techniques are not applicable because of the inherent low vapour pressure of these compounds and, consequently, the high temperature and long time required for their total sublimation. In this work, thermogravimetry is applied to the systematic determination of the enthalpy of sublimation of fullerenes C60 , C70 , C76 , C78 and C84 , thereby generating results that are comparable in accuracy and precision with those obtained using other
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the sample to be maintained a short lapse at the high experimental temperature of sublimation [24–27]; these characteristics are optimal for studying fullerenes. This methodology is based on the Langmuir equation for determining the vapour pressure through the sublimation process:
dm 1 A
dt
Fig. 1. Structure of the fullerenes studied in this report.
indirect high-temperature measurement techniques. These results indicate that the enthalpy of sublimation is directly proportional to the number of carbon atoms in the fullerene and suggest that there is a strong correlation between the enthalpy of sublimation and the polarizability of each fullerene. 2. Experimental methodology High purity samples of the higher fullerenes C76 , C78 and C84 were obtained from a mixture of higher-order fullerenes containing approximate mole fractions of 0.40 of C84 , 0.20 of C76 , 0.20 of C78 and less than 0.20 of a mixture of C86 , C90 and other higher fullerenes. The mixture was purchased from MER Corporation. Analysis and separation of fullerene C76 , C78 , and C84 was achieved by High Performance Liquid Chromatography (HPLC), by using a Develosil C30-UG-5 analytical and a semi-preparative columns and a Waters 600 HPLC system as described in detail in Ref. [2] and in the Supplementary Information. For separation, 5.0 cm3 of solution of fullerenes was injected in the semi-preparative column utilizing a mixture 63:37 toluene:acetonitrile as mobile phase at the flowrate of 4.7 cm3 min−1 . Simultaneously to separation, assignment of each fullerene to the chromatographic peaks was done by Ultraviolet/Visible (UV/Vis) analysis through a photodiode array detector working at 312 nm. According to this analysis and following the nomenclature of Fowler and Manopolus [28], the resulting fractions of the chromatographic separation were those of the isomer D2 of C76 ; the mixture of isomers C2v (3), C2v (2) and D3 of C78 ; and the mixture of isomers D2 (22) and D2d (23) of C84 , all them in good agreement respect to the spectra reported by Jinno et al. [29]. Before the thermogravimetric experiments, samples of fullerenes C76 , C78 , and C84 were dried by maintaining them in a vacuum stove under a pressure of 0.1 Pa and a temperature of 473 K for 15 h. The chemical structure of these fullerenes was confirmed after isolation by Mass Spectrometry (MS), Infrared (IR) and Ultraviolet/Visible (UV/Vis) spectroscopies. Representative spectra of each cluster are included in the Supplementary Information. Chromatographic separation procedure and spectral analysis allow assign a purity higher than 98% to each fullerene isolated. Samples of fullerenes C60 and C70 were Strem Chemicals commercial products with a mole fraction ≥0.9995 and 0.990, respectively, and were utilized directly from the flask (Table 1). Thermogravimetry by applying the Langmuir equation [22,23] has many advantages with respect to other indirect techniques that are used to quantify the enthalpy of sublimation. These advantages include a smaller sample and a quick experiment, which allows
= p
M , 2RT
(1)
where (dm/dt) is the rate of mass loss at temperature T of a sample with an exposed sublimation area A; p is the vapour pressure of the substance; M is the molar mass; R is the gas constant; and is a constant of vaporization, which should be close to unity under vacuum conditions [23], but is lower than such a value under the experimental conditions of this work. Since the enthalpy of change of phase is the thermochemical quantity that needs to be measured and the vapour pressures are not required, the direct combination of the Langmuir equation with the integrated Clausius–Clapeyron equation leads to the following equation: ln
1/2 1 dm T A
·
dt
·
M
g
=B−
cr Hm (T ) , RT
(2)
where dm/dt is the rate of loss of mass at the temperature T and B is a constant that includes, in turn, all other constant terms from the combined equations, even the constant , whose value is not necessary to know exactly. For the application of Eq. (2), an accurate measurement of the rate of mass loss as a function of temperature is indispensable and can usually be obtained by utilizing a thermogravimetric analyser. In this work, a TA Instruments Q5000IR thermogravimetric device was used for this purpose. The weight range of the thermobalance is 100 mg, with a sensitivity of 0.1 g (precision ± 0.01%) and an operation interval from 298 to 1473 K. The furnace heating is achieved by infrared radiation, with a heating rate of 0.1 to 500 K min−1 and temperature control of ±1.0 K (sensitivity 0.1 K). The purge gas flow through the furnace is controlled in the range of 1.0 to 400 cm3 min−1 by a flow controller that is integrated into the system. The system was calibrated for mass with a standard mass traceable to NIST and certified as (97.938 ± 0.001) mg. Temperature calibration was performed with a certified by the International Confederation for Thermal Analysis and Calorimetry (ICTAC) Curie Point reference materials set, consisting of Ni lot CRM7-40211; Ni0.83 Co0.17 lot CRM8-40211 and Ni0.63 Co0.37 lot CRM9-40211, with respective Curie temperatures of 631.2 ± 1.1 K, 827.4 ± 2.2 K and 1019.4 ± 1.6 K. Preliminary tests in the thermogravimetric device allowed us to establish the best conditions for the scanning rate and nitrogen flow in an experiment to generate well-defined thermogravimetric curves and, consequently, to obtain accurate data for the rate of mass loss as a function of the temperature for each cluster. These experiments showed that masses of 1.0–1.5 mg for C60 , C70 and C84 and a mass from 0.3 mg to 0.5 mg for C76 and C78 , uniformly distributed in the bottom of a 4.6 mm diameter platinum cup located on the dish of the thermobalance, were sufficient to generate continuous and smooth thermogravimetric curves (Fig. 2(a)). These preliminary tests also set up a working temperature range from 363.15 to 1023.15 K as optimal for the scanning in temperature, with heating ramps of 10 K min−1 for C60 , C70 and C84 ; under a nitrogen flow of 25 mL min−1 for C60 and 50 mL min−1 for C70 and C84 . For C76 , the scanning rate was of 10 K min−1 , whereas for C78 , this parameter was 20 K min−1 ; both sets of experiments were performed under a nitrogen flow of 25 mL min−1 . With these purge flow rates, an inert atmosphere of nitrogen gas was maintained around the sample without substantially affecting the vaporization
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Table 1 Source, chemical information and purity data of the fullerenes studied in this work. Formula
M (g mol−1 )a
CAS number
Source
Purity reported by the supplier/mole fraction
Purification method
Purity after purification/mole fraction
C60 C70 C76 C78 C84
720.636 840.742 912.806 936.827 1008.890
99685-96-8 115383-22-7 142136-39-8 136316-32-0 135113-16-5
Strem Strem MER Corp MER Corp MER Corp
0.9995 0.99 0.20b 0.20b 0.40b
None None HPLC HPLC HPLC
0.9995 0.99 >0.98 >0.98 >0.98
a b
Molar masses are computed from the 2011 IUPAC atomic masses recommendation [30]. Approximate mole fraction in the MER higher order fullerenes mixture.
rate of the sample. Under the described experimental conditions, the mass of fullerene lost in a complete thermogravimetric experiment was from 20% to 40%. Non-decomposition of the fullerene after heating was verified by performing a second heating on the same sample and then narrowly reproducing the same thermogravimetric curve in this second scanning. After these experiments, the solubility of the cluster in toluene was checked, and there was no trace of insoluble material; then, the structure of the cluster was verified by mass spectrometry. Once the optimal experimental conditions were found, in a representative thermogravimetric experiment the previously weighed platinum cup was placed in the dish of the thermogravimetric device and it was tared at 313.15 K under a nitrogen flow identical to that of the measurements. Then, the sample of fullerene was uniformly deposited on the bottom of the cup, and its exact mass was quantified by a Mettler-Toledo UMX2 micro-balance with sensitivity of 0.1 g. Subsequently, the crucible with the sample was located in the sample dish of the thermogrametric device, the furnace was closed and its temperature was equilibrated at 363.15 K; after 5 min at this temperature, the scanning for temperature and data acquisition, as controlled by the software Thermal Advantage of the Q5000 device, was started. The temperature was raised until the mass loss of the fullerene, as a result of sublimation process, reached at least 20% of the sample. At the end of the heating, the temperature of the sample was brought to room temperature, and the mass of fullerene lost was confirmed in the UMX2 microbalance, matching that recorded in the thermogravimetric device. For each experiment, the loss of the mass rate (dm/dt) as a function of the temperature T, to substitute in Eq. (1), was computed from data of the respective derivative curve (Fig. 2(b)), which was generated using the Universal Analysis software of the Q5000IR device.
A set of at least four series utilizing the same methodology was performed for each of the fullerene studied in this research. To derive accurate values for the enthalpy of sublimation at 298.15 K from the results obtained at the experimental temperature, reliable data of heat capacity for the solid and gas-phase of the fullerenes are required. In this work, the heat capacity measurements on solids fullerenes C60 , C70 and C84 were performed by DSC with a Perkin Elmer DSC7 calorimeter. The limited sample size of C76 and C78 did not allow for calorimetric measurements on these clusters. The DSC7 calorimeter was previously calibrated in both energy and temperature using certified NIST SRM 2232 Indium. The heat capacity of each fullerene was measured in the range of 293.15–573.15 K at a scanning rate of 10.0 K min−1 . These experiments were performed on samples of approximately 9.0 mg of C60 and C70 , and 4.5 mg of C84 . To minimize the disturbances, measurements were performed under a 5.0 cm3 min−1 nitrogen flow. Prior to the heat-capacity measurements of the fullerenes, the reliability of the DSC7 calorimeter in heat capacity measurements was tested by determining the Cp of a high-purity sample of synthetic sapphire (NIST SRM 720) in a temperature range of 298.15–573.15 K. The values at 298.15 K, 400.15 K and 550.15 K were 77.80 J K−1 mol−1 , 97.37 J K−1 mol−1 and 111.24 J K−1 mol−1 , respectively, which is in agreement with the recommended values of 79.01 J K−1 mol−1 , 96.08 J K−1 mol−1 and 109.67 J K−1 mol−1 [31]. Heat capacity of each fullerene in the gas phase, in the range of 298.15–1000 K, was estimated with Gaussian 98 [32] by utilizing density functional theory (DFT) [33]. The optimized geometries and frequency analysis of each fullerene were computed with the exchange correlation functional B3LYP and the 6-31G* basis [34,35]. The solid phase heat capacity of each fullerene was estimated from 298.15 K to 1000 K based on the results of the estimated
Fig. 2. Representative thermogravimetric curves of (a) percentage of loss of mass as a function of temperature for sublimation experiments; (b) derivative curves used to C60 ; determine the instantaneous loss of mass rate, (dm/dt), as a function of the temperature, applied to calculate the enthalpies of sublimation of the fullerenes. C70 ; C76 ; C78 ; C84 .
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Table 2 a Representative experimental data of the dependence loss mass rate on the inverse of the temperature and the enthalpies of sublimation derived from the thermogravimetric experiments of the fullerenes studied in this work. In this table (dm/dt) is the rate of loss of mass and = (1/A)(dm/dt)(T/M)1/2 , where A is the sublimation area of the sample and M is the molar mass of each fullerene. T (K)
m (mg)
(dm/dt) × 1010 (kg s−1 )
× 104 ((kg K mol)1/2 s−1 m−2 )
C60 , Series 1 2.0016 1.860 3.933 890 1.9890 2.371 5.042 900 1.9724 3.054 6.530 910 1.9513 3.908 8.402 920 1.9243 5.124 11.075 930 940 1.8901 6.432 13.977 950 1.8470 8.027 17.536 960 1.7930 10.022 22.009 1.7260 12.463 27.512 970 1.6428 15.363 34.088 980 1.5401 19.329 43.106 990 1.4095 24.384 54.653 1000 g 2 −1 Series 1: ln = −21195.03/T + 15.96; r = 0.9998; a = 0.1; b = 96.7; cr Hm (945 K)/kJ mol = 176.2 ± 0.8 g Series 2: ln = −21012.09/T + 15.79; r2 = 0.9993; a = 0.2; b = 176.8; cr Hm (945 K)/kJ mol−1 = 174.7 ± 1.5 g Series 3: ln = −20839.68/T + 15.63; r2 = 0.9999; a = 0.1; b = 63.2; cr Hm (945 K)/kJ mol−1 = 173.3 ± 0.5 g Series 4: ln = −21343.84/T + 16.14; r2 = 0.9994; a = 0.1; b = 162.2; cr Hm (945 K)/kJ mol−1 = 177.5 ± 1.3 g Series 5: ln = −21368.42/T + 16.14; r2 = 0.9998; a = 0.1; b = 104.9; cr Hm (945 K)/kJ mol−1 = 177.7 ± 0.9 g Weighted average value: < cr Hm (C60 , 945 K)>/kJ mol−1 = 175.0 ± 0.4 C70 , Series 1 1.0135 0.371 0.727 890.0 1.0107 0.521 1.026 900.0 1.0071 0.674 1.334 910.0 920.0 1.0026 0.857 1.706 0.9965 1.101 2.204 930.0 940.0 0.9888 1.416 2.849 950.0 0.9789 1.907 3.857 960.0 0.9661 2.386 4.851 970.0 0.9502 2.948 6.024 980.0 0.9302 3.710 7.620 990.0 0.9054 4.580 9.455 1000.0 0.8749 5.669 11.763 g Series 1 ln = −22370.30/T + 15.65; r2 = 0.9994; a = 0.2; b = 179.1; cr Hm (945 K)/kJ mol−1 = 186.0 ± 1.5 g 2 −1 Series 2 ln = −23076.63/T + 16.34; r = 0.9965; a = 0.5; b = 432.5; cr Hm (945 K)/kJ mol = 191.9 ± 3.6 g Series 3 ln = −21565.86/T + 14.79; r2 = 0.9997; a = 0.1; b = 111.8; cr Hm (945 K)/kJ mol−1 = 179.3 ± 0.9 g Series 4 ln = −21819.10/T + 15.08; r2 = 0.9971; a = 0.4; b = 372.8; cr Hm (945 K)/kJ mol−1 = 181.4 ± 3.1 g Series 5 ln = −22508.37/T + 15.71; r2 = 0.9993; a = 0.2; b = 182.8; cr Hm (945 K)/kJ mol−1 = 187.1 ± 1.5 g Weighted average value: < cr Hm (C70 , 945 K)>/kJ mol−1 = 182.7 ± 0.7 C76 , Series 1 940.0 0.2830 0.250 0.483 950.0 0.2811 0.301 0.584 960.0 0.2787 0.430 0.838 970.0 0.2756 0.581 1.139 0.2718 0.747 1.472 980.0 990.0 0.2671 0.896 1.775 0.2611 1.110 2.211 1000.0 0.2535 1.400 2.801 1010.0 0.2446 1.611 3.240 1020.0 g 2 −1 Series 1 ln = −23538.35/T + 15.12; r = 0.9931; a = 0.8; b = 742.3; cr Hm (980 K)/kJ mol = 195.7 ± 6.2 g 2 −1 Series 2 ln = −22372.58/T + 13.83; r = 0.9837; a = 1.2; b = 1174.0; cr Hm (975 K)/kJ mol = 186.0 ± 9.8 g Series 3 ln = −22826.10/T + 14.24; r2 = 0.9947; a = 0.7; b = 680.5; cr Hm (985 K)/kJ mol−1 = 189.8 ± 5.6 g Series 4 ln = −22583.42/T + 14.22; r2 = 0.9921; a = 0.7; b = 672.5; cr Hm (970 K)/kJ mol−1 = 187.8 ± 5.6 g Series 5 ln = −22508.37/T + 15.71; r2 = 0.9993; a = 1.7; b = 1660.0; cr Hm (980 K)/kJ mol−1 = 192.6 ± 13.8 g Weighted average value: < cr Hm (C76 , 978 K)>/kJ mol−1 = 190.4 ± 3.1 C78 , Series 1 0.2594 0.500 0.093 900.0 0.2588 1.077 0.203 920.0 0.2583 1.931 0.366 930.0 0.2578 2.348 0.448 940.0 0.2571 2.348 0.450 950.0 0.2562 3.349 0.645 960.0 0.2551 3.883 0.752 970.0 0.2537 4.803 0.934 980.0 0.2520 6.623 1.295 990.0 1000.0 0.2499 7.589 1.492 0.2474 9.400 1.857 1010.0 g Series 1 ln = −23137.44/T + 14.39; r2 = 0.9735; a = 1.3; b = 1272.3; cr Hm (955 K)/kJ mol−1 = 192.4 ± 10.6 g Series 2 ln = −24101.75/T + 16.50; r2 = 0.9772; a = 1.3; b = 1226.1; cr Hm (915 K)/kJ mol−1 = 200.4 ± 10.2 g Series 3 ln = −23048.00/T + 14.64; r2 = 0.9707; a = 1.1; b = 1110.5; cr Hm (890 K)/kJ mol−1 = 191.6 ± 9.2 g Weighted average value: < cr Hm (C78 , 920 K)>/kJ mol−1 = 194.6 ± 5.7 C84 , Series 1 0.9444 0.592 1.154 1060.0 0.9404 0.736 1.442 1070.0 0.9353 0.908 1.787 1080.0
103 K−1 (T)
ln
1.124 1.111 1.099 1.087 1.075 1.064 1.053 1.042 1.031 1.020 1.010 1.000
−7.841 −7.593 −7.334 −7.082 −6.806 −6.573 −6.346 −6.119 −5.896 −5.681 −5.447 −5.209
1.124 1.111 1.099 1.087 1.075 1.064 1.053 1.042 1.031 1.020 1.010 1.000
−9.529 −9.184 −8.922 −8.676 −8.420 −8.164 −7.860 −7.631 −7.415 −7.180 −6.964 −6.745
1.064 1.053 1.042 1.031 1.020 1.010 1.000 9.901 9.804
−9.939 −9.747 −9.387 −9.080 −8.823 −8.636 −8.417 −8.180 −8.035
1.111 1.087 1.075 1.064 1.053 1.042 1.031 1.020 1.010 1.000 9.901
−11.583 −10.805 −10.215 −10.014 −10.009 −9.649 −9.496 −9.278 −8.952 −8.810 −8.591
9.434 9.346 9.259
−9.067 −8.844 −8.630
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Table 2 (Continued) T (K)
m (mg)
(dm/dt) × 1010 (kg s−1 )
× 104 ((kg K mol)1/2 s−1 m−2 )
1090.0 0.9291 1.152 2.277 0.9212 1.462 2.904 1100.0 0.9119 1.734 3.461 1110.0 1120.0 0.9002 2.120 4.250 1130.0 0.8862 2.577 5.188 1140.0 0.8691 3.047 6.163 1150.0 0.8488 3.681 7.477 1160.0 0.8248 4.353 8.881 1170.0 0.7965 5.145 10.543 g Series 1 ln = −25030.39/T + 14.57; r2 = 0.9991; a = 0.2; b = 235.7; cr Hm (1115 K)/kJ mol−1 = 208.1 ± 1.9 g Series 2 ln = −24585.04/T + 14.20; r2 = 0.9980; a = 0.3; b = 345.3; cr Hm (1115 K)/kJ mol−1 = 204.4 ± 2.9 g Series 3 ln = −24,906.25/T + 14.49; r2 = 0.9983; a = 0.3; b = 320.8; cr Hm (1115 K)/kJ mol−1 = 207.1 ± 2.6 g Series 4 ln = −24,851.92/T + 14.52; r2 = 0.9976; a = 0.3; b = 388.4; cr Hm (1115 K)/kJ mol−1 = 206.6 ± 3.2 g Series 5 ln = −24,524.23/T + 14.16; r2 = 0.9985; a = 0.2; b = 202.8; cr Hm (1115 K)/kJ mol−1 = 203.9 ± 2.5 g Weighted average value:< cr Hm (C84 , 1115 K)>/kJ mol−1 = 205.4 ± 1.4
103 K−1 (T) 9.174 9.091 9.009 8.929 8.850 8.772 8.696 8.621 8.547
ln −8.387 −8.144 −7.969 −7.764 −7.564 −7.392 −7.199 −7.026 −6.855
a The sublimation area, A, was calculated as 1.662 × 10−5 m2 from the diameter of the sample cup. Uncertainty of temperature data is ±1.0 K, while uncertainty in mass data is ±1.0 g. Parameters a and b represent the standard deviation of the intercept and slope of the function ln vs 1/T. Dispersion associated to each sublimation enthalpy (xi /i2 )/ (1/i2 ) and value was computed as b R and is a standard uncertainty. The weighted average value and its standard deviation , were calculated as =
(1/i2 )], where xi is each of the N sublimation enthalpy data and its respective standard deviation i [36]. The resulting standard deviation associated to each 2 = [1/ weighted average value of enthalpy of sublimation is a standard uncertainty also.
heat capacity in the gas phase by applying the methodology proposed by Piacente et al. [20]. 3. Results and discussion The smooth and well-defined profile of the thermogravimetric curves (Fig. 2(a)) indicate that fullerenes studied here are enough stable to be sublimed at high temperatures without decomposition. The profiles were similar for all five fullerenes; however, these curves show that a quantifiable loss of mass for C60 and C70 starts at a lower temperature compared with the other fullerenes. The curves also show that the samples lost at least one fifth of its mass in the experimental conditions applied, which allows for an accurate quantification of the mass loss rate as a function of the temperature and can be used to obtain accurate results for the enthalpy of sublimation. Table 2 shows the representative experimental data of the dependence of the loss mass rate with the temperature for the fullerenes as well as the resulting linear equations from each series with uncertainty for the y-intercept a and the slope b , which were both computed as the standard deviation from the best fit, which in turn was calculated as described in Ref. [36]. Dispersion for each sublimation enthalpy value was computed as b ·R and is a
standard uncertainty. Correlation factors in all cases are higher than 0.99, which indicates that despite the wide temperature interval, the slope of the linear dependence ln[(1/A)·(dm/dt)·(T/M)1/2 ] vs 1/T is constant and allows the enthalpy of sublimation to be constant in such an interval. Fig. 3 shows the graphics for the dependence of the rate of loss of mass with the inverse of the temperature for all the fullerenes, and the detailed experimental data sets and results for all series of measurements are provided in the Supplementary Information. Heat capacity data estimated by DFT are reported in Table 3, which includes the heat capacity data for the solid phase measured by DSC to demonstrate the reliability of the calculations. Estimated Cp data for the solid and gas phase of each fullerene were fit to a quadratic equation with a correlation coefficient of 0.999. Table 4 shows the comparison of Cp data at 298.15 K of the solid and gas phase of fullerenes C60 and C70 determined in this work with data found in the literature. Heat capacity of C60 (cr) and C70 (cr) estimated by DFT and measured by DSC in this work, are in acceptable agreement with the results reported in Refs. [37–39] and with the values recommended by Korobov [40] and Diky [14], whose values of Cp for fullerenes are based in analysis of graphics and numerical data of Refs. [41–47]. Similar agreement is found for estimated Cp data of C60 (g) and C70 (g). For higher fullerenes no comparison is
Fig. 3. Rate of loss of mass as a function of the temperature, derived from the thermogravimetric experiments on each fullerene. The C78 series is included in a graphic apart C78 series. for clarity in presentation. (a) 䊐 C60 series; C70 series; C76 series, ♦ C84 series. (b)
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Table 3 Solid and gas phase heat capacities at constant pressure (in J K−1 mol−1 ) of the fullerenes, estimated by DFT procedure applying B3LYP/6-31G* functional and basis. The experimental heat capacities measured by DSCa at P = 80.0 kPab are included to demonstrate the reliability of the estimations on the solid phase. C60
C70
T (K)
Cp (cr) DSC
298.15 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000
535.8 ± 12.7 538.6 648.1 742.0 830.1 917.4
Cp (cr) Theoretical
Cp (g) Theoretical
504.3 508.7 614.7 711.6 798.6 875.7 943.3 1002.5 1054.0 1098.9 1138.0 1172.2 1202.1 1228.4 1251.6 1272.1
487.2 491.6 597.6 694.5 781.4 858.4 926.0 985.0 1036.4 1081.3 1120.3 1154.4 1184.3 1210.5 1233.6 1254.1
Cp (g)/(J K−1 mol−1 ) = −0.00137T2 + 2.83160T − 226.38 Cp (cr)/(J K−1 mol−1 ) = −0.00137T2 + 2.83290T − 209.75
T sub
298.15 K
Cp (cr) Theoretical
298.15 626.8 ± 16.2 592.5 300 630.1 597.6 350 758.3 720.2 400 855.2 832.5 450 924.8 933.4 500 1005.3 1022.9 550 1105.8 1101.5 600 1170.3 650 1230.3 700 1282.6 750 1328.3 800 1368.1 850 1403.1 900 1433.8 950 1460.9 1000 1484.8 −1 340.2 ± 0.3 trs H = (0.075 ± 0.020) kJ mol 401.0 ± 1.9 trs H = (0.215 ± 0.020) kJ mol−1 Cp (g)/(J K−1 mol−1 ) = −0.00158T2 + 3.2789T − 251.75 Cp (cr)/(J K−1 mol−1 ) = −0.00158T2 + 3.2814T − 235.13
Cp (g) Theoretical 575.1 580.2 702.8 814.9 915.6 1005.0 1083.5 1152.2 1212.1 1264.3 1309.8 1349.5 1384.4 1415.0 1441.9 1465.7
g
298.15 K
cr CpdT = −(11.8 ± 0.5) kJ/mol
C78
T (K)
Cp (cr) DSC
Cp (cr) Theoretical
298.15 643.7 649.3 300 350 782.2 903.8 400 1013.1 450 1110.1 500 1195.5 550 600 1270.1 1335.2 650 700 1392.0 1441.5 750 1484.8 800 1522.8 850 1556.2 900 950 1585.6 1611.6 1000 Cp (g)/(J K−1 mol−1 ) = −0.00171T2 + 3.55278T − 269.77 Cp (cr)/(J K−1 mol−1 ) = −0.00171T2 + 3.55548T − 253.15 298.15 K
Cp (cr) DSC
T sub
g
cr CpdT = −(11.3 ± 0.5) kJ/mol
C76
T sub
T (K)
Cp (g) Theoretical
T (K)
626.3 631.8 764.6 886.1 995.3 1092.2 1177.4 1251.9 1316.8 1373.5 1422.9 1466.1 1503.9 1537.1 1566.4 1592.3
298 662.7 300 668.4 350 804.4 400 928.9 450 1040.8 500 1140.2 550 1227.6 600 1304.0 650 1370.8 700 1428.9 750 1479.7 800 1524.1 850 1563.1 900 1597.3 950 1627.5 1000 1654.2 Cp (g)/(J K−1 mol−1 ) = −0.00175T2 + 3.63536T − 271.68 Cp (cr)/(J K−1 mol−1 ) = −0.00175T2 + 3.63814T − 255.06
T sub
g
cr CpdT = −(12.5 ± 0.5) kJ/mol
298.15 K
Cp (cr) DSC
Cp (cr) Theoretical
Cp (g) Theoretical 645.3 650.9 786.8 911.1 1022.9 1122.1 1209.4 1285.7 1352.3 1410.4 1461.0 1505.3 1544.1 1578.2 1608.2 1634.8
g
cr CpdT = -(11.4 ± 0.5) kJ/mol
C84 T (K)
Cp (cr) DSC
Cp (cr) Theoretical
298 740.8 ± 24.1 713.1 753.8 719.2 300 932.1 865.3 350 1026.4 999.0 400 450 1057.7 1119.3 1083.4 1226.1 500 1133.2 1320.2 550 1228.6 1402.5 600 1458.9 1474.3 650 700 1537.0 −1 −1 2 Cp (g)/(J K mol ) = −0.00160T + 3.58385T − 206.92
T sub
298.15 K
g cr CpdT
Cp (g) Theoretical
T (K)
695.7 701.8 847.8 981.4 1101.6 1208.2 1302.1 1384.3 1456.0 1518.6
750 800 850 900 950 1000 1050 1100 1150
Cp (cr) DSC
Cp (cr) Theoretical
Cp (g) Theoretical
1591.7 1639.6 1681.5 1718.4 1751.0 1779.8 1805.3 1828.1 1848.5
1573.2 1620.9 1662.8 1699.5 1731.9 1760.6 1786.1 1808.7 1828.9
Cp (cr)/(J K−1 mol−1 ) = −0.00160T2 + 3.58637T − 190.29
= −(15.0 ± 0.5) kJ/mol
Uncertainty of temperature data of DSC: ±0.2 K. Dispersion associated to each Cp value measured by DSC can be computed as uCp (C60 ) = 0.021 Cp ; uCp (C70 ) = 0.017 Cp and uCp (C84 ) = 0.078 Cp ; was calculated as the standard deviation of at least four measurements (see Supplementary Information) and is a standard uncertainty. b Atmospheric pressure in the laboratory, uncertainty: ±0.130 kPa. a
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M. Martínez-Herrera et al. / Thermochimica Acta xxx (2015) xxx–xxx Table 4 Comparison with literature data of results of solid and gas phase heat capacities at 298.15 K for the fullerenes C60 and C70 . Author C60 (cr) This work This work Steele et al. [37] Jin et al. [38] Rojas-Aguilar [39] Korobov and Sidorov [40] Lebedev et al. [41] Diky and Kabo [14] C60 (g) This work Diky and Kabo [14] C70 (cr) This work This work Diky and Kabo [14] C70 (g) This work Diky and Kabo [14]
Methoda
7
the heat capacity data of Table 3, and then applying the following equation:
Tsub
Temperature interval (K)
Cp (298 K) (J K−1 mol−1 )
cr H(298.15 K) = cr H(Tsub ) −
DSC DFT DSC DSC DSC Review AdC Review
293–573 298–1000 300–800 120–560 293–323 10–1000 5–350 0–1000
535.8 ± 12.7 504.3 556.5 536.9 521.7 520.0b 524.8 525.6
DFT Review
298–1000 0–1000
487.2 498.5
DSC DFT Review
293–573 298–1000 0–1000
626.8 ± 16.2 592.5 625.6
DFT Review
298–1000 0–1000
575.1 585.1
The numerical values for the integral involved in Eq. (3) are also included in Table 3 and have assigned an estimated uncertainty of 0.5 kJ mol−1 , which in turn was included in the dispersion of the result of enthalpy of sublimation at 298.15 K. A summary of the enthalpies of sublimation at the experimental and reference temperature of 298.15 K measured in this work for the fullerenes is shown in Table 5, which also includes comparison with the available data of the literature. For a consistent comparison, literature experimental enthalpies of sublimation were corrected in temperature by the same heat capacity data and prog cedure described and applied in this work, this except when cr Hm (298.15 K) was available in the cited article. Despite the large difference between the experimental and reference temperatures, the results for the correction in temperature are reasonable given that differences in the heat capacities between the solid and gas phases are not substantial. For the results of this work, the enthalpies at 298.15 K are accompanied by expanded uncertainties, which were calculated as ±t, where is the experimental standard deviation and t is Student’s coefficient for a level of confidence of 0.905 [36]. Table 5 and Fig. 4(a) show that once corrected in temperature, the result of enthalpy of sublimation at 298.15 K of 186.3 ± 1.2 kJ mol−1 for C60 , as derived in this work from the thermogravimetric data and Langmuir equation, is consistent with the results derived from the experimental enthalpies of sublimation reported by Mathews [5,7], Dai [8], Sun [10], Piacente [11] and the value recommended by Diky and Kabo [14]. This fact indicates that the methodology here developed generates results sufficiently accurate and can be applied in determining the enthalpy of sublig mation of higher fullerenes. In Fig. 4(a), results of cr Hm (298.15 K) −1 were obtained from polycrystalline for C60 under 180.0 kJ mol mixtures of fullerenes C60 and C70 [3,9] or from a mixture of C60 with Potassium [12], this strongly supports the fact that vapour pressure of pure C60 is affected by the presence of other kind of g fullerene or by impurities. For C70 the result of cr Hm (298.15 K) −1 of 194.5 ± 1.7 kJ mol , is in agreement with the result of Abrefah [6], but is lower than most of the other results. In Fig. 4(b) results
a Method: DSC, Differential Scanning Calorimetry; DFT, Density Functional Theory; AdC, Adiabatic Calorimetry. b Data reported at 300 K.
possible given that in the best of our knowledge there is not heat capacity data reported in the literature for these clusters. For C70 (cr) DSC heat flow and heat capacity curves allowed to detect two reproducible thermal effects, presumably associated to solid-state transitions (see Table 3 and Supplementary Information). The transition found in this work at 340.2 K agrees in temperature with that detected by Zhogova and Lebedev [47] but those authors determined a larger enthalpy for this thermal effect. The transition at 401.0 K has not precedent in the literature, however some authors [14,47] suggest that thermal signals are determined by a greater or lesser number of polymorphic forms of C70 , depending on the sample preparation. The derivation of the sublimation enthalpies at temperature T = 298.15 K was performed using the results of enthalpy of sublimation at the experimental temperature shown in Table 2 and
g
g
g
cr Cp dT
(3)
298.15 K
Fig. 4. Comparison of results of enthalpy of sublimation at 298.15 K for (a) 䊉 fullerene C60 ; (b)
fullerene C70 .
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Table 5 Enthalpies of sublimation at Tsub and at 298.15 K obtained by TGA in this work for the fullerenes and their comparison with values reported in the literature. Author C60 This work Pan et al. [3] Tokmakoff et al. [4] Mathews et al. [5] Abrefah et al. [6] Mathews et al. [7] Dai et al. [8] Popovic et al. [9] Sun et al. [10] Piacente et al. [11] Borisova et al. [12] Pankajavalli et al. [13] Diky and Kabo [14] C70 This work Pan et al. [3] Abrefah et al. [6] Popovic et al. [9] Mathews et al. [15] Baba et al. [16] Piacente et al. [17] Diky and Kabo [14] C76 This work Brunetti et al. [18] Boltalina et al. [19] C78 This work C84 This work Piacente et al. [20] Boltalina et al. [21]
g
g
Methoda
T (K)
Tsub (K)
cr Hm (Tsub ) (kJ mol−1 )
TG KEMS TEAS KEMS KETG KEMS UV/Vis KEMS OA KETB KEMS TMTG Review
890–1000 640–800 400–700 640–787 673–873 600–800 837–995 630–780 683–1123 730–990 560–870 789–907 730–990
945 707 600 727 773 700 916 705 903 860 715 848 860
175.0 167.8 138.5 176.0 159.0 181.4 180.0 158.0 175.0 175.0 159.0 152.3 175.3
± ± ± ± ± ± ± ± ± ± ± ± ±
0.4 5.4 3.8 2.0 4.2 2.3 10.0 3.0 4.0 3.0 3.0 5.3 2.9
186.3 174.9 143.7 183.4 167.2 188.3 190.8 165.0 185.5 182.0 166.2 183.5 183.7
± ± ± ± ± ± ± ± ± ± ± ± ±
1.2c 5.4 3.8 2.0 4.2 2.3 10.0 3.0 4.0 3.0d 3.0 1.0d 5.1d
TG KEMS KETG KEMS KEMS KEMS KETB Review
890–1000 640–800 703–873 670–800 650–850 650–850 783–904 783–904
945 739 788 735 750 750 843 843.5
182.7 179.9 188.0 174.0 196.0 195.7 190.0 189.9
± ± ± ± ± ± ± ±
0.7 9.2 4.0 3.0 2.0 2.3 3.0 3.1
194.5 187.8 196.8 181.1 204.1 203.8 200.0 200.3
± ± ± ± ± ± ± ±
1.7c 9.2 4.0 3.0 2.0 2.3 6.0d 6.1d
TG KETB KEMS
940–1020 834–1069 637–911
978 910 764
190.4 ± 3.1 194.0 ± 4.0 190.0 ± 7.0
202.9 ± 6.2c 206.0 ± 4.0d 198.4 ± 7.0
810–1010
920
194.6 ± 5.7
206.0 ± 11.5c
1053–1153 920–1190 658–980
1115 950 853
205.4 ± 1.4 210.0 ± 6.0 202.0 ± 4.0
220.4 ± 3.0c 225.0 ± 6.0d 212.0 ± 4.0
TG KETB KEMS
cr Hm (298.15 K)b (kJ mol−1 )
a Method: TG, thermogravimetry; KETG, Knudsen effusion associated with thermogravimetry; TEAS, transmission electronic absorption spectroscopy; KEMS, Knudsen effusion associated with mass spectrometry; UV/Vis, ultraviolet/visible spectroscopy; OA, optical Absorption; KETB, Knudsen effusion associated with torsion balance; TMTG, transpiration method associated with thermogravimetry. b Enthalpy of sublimation at 298.15 K was derived from the experimental enthalpy reported by the other authors but applying the same correction in temperature determined in this work. c Dispersion is an expanded uncertainty calculated as ±t, where is the experimental standard deviation and t is Student’s coefficient for a level of confidence of 0.905 [36]. d Value available in the cited reference.
of enthalpy of sublimation under 190.0 kJ mol−1 for this cluster are those obtained also from a polycrystalline mixtures of fullerenes C60 and C70 [3,9]. The results for the enthalpy of sublimation at 298.15 of 202.9 ± 6.2 kJ mol−1 for fullerene C76 and 220.4 ± 3.0 kJ mol−1 for C84 are in the middle of the range of values previously reported in the literature. In the case of C78 , to the best of our knowledge, no experimental value of its enthalpy of sublimation has been previously reported, which thus makes comparison impossible. Large uncertainties in the results of enthalpy of sublimation of C76 and C78 are consequence of the large dispersion in the dependence of the rate of loss of mass with the temperature (Fig. 3). This dispersion is explained by the small mass of sample utilized, the low rate of loss of mass and a possible slight decomposition of the fullerene around 1000 K. This last fact confirms in turn that despite higher fullerenes are thermodynamically more stables than C60 and C70 [2], decomposition of C76 and C78 must be characterized by a lower activation energy. Fig. 5(a) shows the enthalpy of sublimation as a function of the number of carbon atoms and the best fit for this dependence is a second order polynomial with a correlation factor of 0.9987. g The resulting fitted second order equation is cr Hm /(kJ mol−1 ) = 3.366 × 102 − 5.293 × n + 4.650 × 10−2 × n2 , where n is the number of carbon atoms in the cluster. This equation can be useful for deriving the enthalpy of sublimation of a fullerene that is not isolatable in sufficiently high levels to perform a thermochemical study,
such as C86 , at 225.3 ± 2.8 kJ mol−1 . The uncertainty assigned to this magnitude was that of enthalpy of sublimation of fullerene C84 . The strong dependence of the enthalpy of sublimation on the number of carbon atoms suggests that an increasing number of carbon atoms increases the energy that determine the cohesion of the solid. Fig. 5(b) shows the dependence of the enthalpy of sublimation on the polarizability of each molecule of fullerene [48]. The resulting trend is also second order polynomial and has a regression coefficient of 0.9978. This finding confirms that the forces that rule the cohesion of each solid fullerene are dispersion, given that polarizability is a factor that determines the intensity of these forces. 4. Conclusion Thermogravimetry seems to be suitable for determination of reliable values of enthalpies sublimation of fullerenes, given that utilizing this technique and applying the Langmuir equation, the enthalpies of sublimation of C60 , C70 , C76 , and C84 were measured with results in good agreement respect to those reported in literature and with a maximal uncertainty of 3.0%. Despite a larger uncertainty, enthalpy of sublimation not found in literature for C78 , is also reported. From the second order polynomial dependence of the enthalpy of sublimation on the number of carbon atoms established in this work, the enthalpy of sublimation of fullerenes not available or isolatable can be estimated. The enthalpy
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Fig. 5. Dependence of the enthalpy of sublimation on (a) the number of carbon atoms; (b) the polarizability ˛ of the fullerene. Values of ˛ (in Å3 ) were taken from Ref. [48] as 60.8, 73.8, 83.0, 85.7 and 94.4 for C60 , C70 , C76 , C78 and C84 , respectively.
of sublimation of these carbon allotropes showed a polynomial dependence also with the polarizability of the cluster in the range of the fullerenes studied, which suggests an increase in the energy of cohesion in the solid by forces of dispersion and, consequently, with an increase in the molecular volume and surface of the cluster. Acknowledgements The authors are grateful to Conacyt (Mexico) for financial support (grants 47679-Q, 104299 and 128411) and the scholarship of M.M-H. They also thank Patricia Amador for her valuable help in HPLC separation of the clusters and, Iris Ramos-García, Sonia Sánchez-Ruiz, Aurora Vásquez-Badillo and Geiser Cuellar for their valuable support in the spectroscopic analysis of the fullerenes studied here. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.tca.2015.09.001. References [1] W. Krätschmer, L.D. Lamb, K. Fostiropoulous, D.R. Huffmann, Solid C60 : a new form of carbon, Nature 347 (1990) 354–358. [2] A. Rojas, M. Martinez, P. Amador, L.A. Torres, Increasing stability of the fullerenes with the number of carbon atoms: the experimental evidence, J. Phys. Chem. B 111 (2007) 9031–9036. [3] C. Pan, M.P. Sampson, Y. Chai, R.H. Hauge, J.L. Margrave, Heats of sublimation from a polycrystalline mixture of C60 and C70 , J. Phys. Chem. 95 (1991) 2944–2946. [4] A. Tokmakoff, D.R. Haynes, S.M. George, Desorption kinetics of C60 multilayers from Al2 O3 (0001), Chem. Phys. Lett. 186 (1991) 450–455. [5] C.K. Mathews, P.R. Vasudeva Rao, T.G. Srinivasan, V. Ganesan, N. Sivaraman, T.S.L. Lakshmi Narasimhan, I. Kaliappan, K. Chandran, R. Dhamodaran, Preparation and characterization of buckministerfullerene and measurement of its heat of sublimation, Curr. Sci. 61 (1991) 834–838. [6] J. Abrefah, D.R. Olander, M. Balooch, W.J. Siekhaus, Vapor pressure of buckminsterfullerene, Appl. Phys. Lett. 60 (1992) 1313–1314. [7] C.K. Mathews, M.S. Baba, T.S.L. Narasimhan, R. Balasubramanian, N. Sivaraman, T.G. Srinivasan, P.R.V. Rao, Vaporization studies on buckminsterfullerene, J. Phys. Lett. 96 (1992) 3566–3568. [8] S. Dai, L. Mac Toth, G.D. Del Cul, D.H. Metcalf, Ultraviolet-visible absorption spectrum of C60 vapor and determination of the C60 vaporization enthalpy, J. Chem. Phys. 101 (1994) 4470–4471.
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Enthalpies of sublimation of fullerenes by thermogravimetry Melchor Martínez-Herrera 1 , Myriam Campos, Luis Alfonso Torres, Aarón Rojas ∗ Departamento de Química del Centro de Investigación y de Estudios Avanzados del IPN, Av. Instituto Politécnico Nacional 2508, C.P. 07360, México D.F., Mexico
a r t i c l e
i n f o
Article history: Received 1 June 2015 Received in revised form 1 September 2015 Accepted 1 September 2015 Available online xxx Keywords: Heat capacity Thermal analysis Differential scanning calorimetry Heat of sublimation Cluster
a b s t r a c t The enthalpies of sublimation of fullerenes, as measured in the interval of 810–1170 K by thermogravimetry and applying the Langmuir equation, are reported. The detailed experimental procedure and its application to fullerenes C60 , C70 , C76 , C78 and C84 are supplied. The accuracy and uncertainty associated with the experimental results of the enthalpy of sublimation of these fullerenes show that the reliability of the measurements is comparable to that of other indirect high-temperature methods. The results also indicate that the enthalpy of sublimation increases proportionally to the number of carbon atoms in the cluster but there is also a strong correlation between the enthalpy of sublimation and the polarizability of each fullerene. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Since fullerenes were first isolated in macroscopic quantities in 1990 [1], these carbon clusters structures have gained a main role on the scientific scene. Fullerenes have promoted academic and industrial research that has led to the discovery of many of their interesting physical and chemical properties. Although the research on these nanostructures has expanded rapidly in different directions, many of their fundamental properties remain unknown, such as their thermochemical data, which are useful in the understanding of the energetics of these carbon clusters. The enthalpy of sublimation is one important thermochemical quantity because is essential to deriving the enthalpy of formation in the gas phase of the cluster, which in turn allows us to elucidate the relative stability of these molecules [2]. Some works have attempted to quantify the enthalpy of sublimation of fullerenes [3–21], and they generally considered C60 and C70 [3–17]. In most cases, there was a strong dependence between the enthalpy of sublimation and the applied technique, which made it possible to anticipate discrepancies in the results, e.g. for a specific fullerene, many similar enthalpies of sublimation values have
∗ Corresponding author. E-mail address: [email protected] (A. Rojas). 1 Current address: Departamento de Ciencias Naturales, DCNI, Universidad Autónoma Metropolitana, Cuajimalpa, Av. Vasco de Quiroga 4871, Col. Santa Fe Cuajimalpa, C.P. 05300 México, D.F., Mexico.
been reported at very different temperatures. In consequence, it is important to determine with a single reliable technique, and with high accuracy, the enthalpy of sublimation of the fullerenes C60 , C70 , C76 , C78 and C84 (Fig. 1). In 1998, Price and Hawkins [22] demonstrated that thermogravimetry was a useful technique for determining the enthalpy of sublimation of compounds that have low vapour pressures. In a thermogravimetric device the loss of mass due to the sublimation of a sample was accurately measured, and the vapour pressure was derived by utilizing the Langmuir equation [23]. Thereafter, the enthalpy of sublimation was calculated by correlating the vapour pressure and temperature data through the equation of Clausius–Clapeyron. From that work, substantial research determining vapour pressures and deriving the enthalpy of sublimation of a large variety of compounds with this methodology has been reported and has provided results on the enthalpy of sublimation that are as reliable as those derived from calorimetric methods or by Knudsen effusion [22,24–27]. Given the high sensitivity and large range of operating temperatures in modern thermogravimetric devices, this technique seems to be optimal for measuring the enthalpy of sublimation of fullerenes, for which calorimetric techniques are not applicable because of the inherent low vapour pressure of these compounds and, consequently, the high temperature and long time required for their total sublimation. In this work, thermogravimetry is applied to the systematic determination of the enthalpy of sublimation of fullerenes C60 , C70 , C76 , C78 and C84 , thereby generating results that are comparable in accuracy and precision with those obtained using other
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the sample to be maintained a short lapse at the high experimental temperature of sublimation [24–27]; these characteristics are optimal for studying fullerenes. This methodology is based on the Langmuir equation for determining the vapour pressure through the sublimation process:
dm 1 A
dt
Fig. 1. Structure of the fullerenes studied in this report.
indirect high-temperature measurement techniques. These results indicate that the enthalpy of sublimation is directly proportional to the number of carbon atoms in the fullerene and suggest that there is a strong correlation between the enthalpy of sublimation and the polarizability of each fullerene. 2. Experimental methodology High purity samples of the higher fullerenes C76 , C78 and C84 were obtained from a mixture of higher-order fullerenes containing approximate mole fractions of 0.40 of C84 , 0.20 of C76 , 0.20 of C78 and less than 0.20 of a mixture of C86 , C90 and other higher fullerenes. The mixture was purchased from MER Corporation. Analysis and separation of fullerene C76 , C78 , and C84 was achieved by High Performance Liquid Chromatography (HPLC), by using a Develosil C30-UG-5 analytical and a semi-preparative columns and a Waters 600 HPLC system as described in detail in Ref. [2] and in the Supplementary Information. For separation, 5.0 cm3 of solution of fullerenes was injected in the semi-preparative column utilizing a mixture 63:37 toluene:acetonitrile as mobile phase at the flowrate of 4.7 cm3 min−1 . Simultaneously to separation, assignment of each fullerene to the chromatographic peaks was done by Ultraviolet/Visible (UV/Vis) analysis through a photodiode array detector working at 312 nm. According to this analysis and following the nomenclature of Fowler and Manopolus [28], the resulting fractions of the chromatographic separation were those of the isomer D2 of C76 ; the mixture of isomers C2v (3), C2v (2) and D3 of C78 ; and the mixture of isomers D2 (22) and D2d (23) of C84 , all them in good agreement respect to the spectra reported by Jinno et al. [29]. Before the thermogravimetric experiments, samples of fullerenes C76 , C78 , and C84 were dried by maintaining them in a vacuum stove under a pressure of 0.1 Pa and a temperature of 473 K for 15 h. The chemical structure of these fullerenes was confirmed after isolation by Mass Spectrometry (MS), Infrared (IR) and Ultraviolet/Visible (UV/Vis) spectroscopies. Representative spectra of each cluster are included in the Supplementary Information. Chromatographic separation procedure and spectral analysis allow assign a purity higher than 98% to each fullerene isolated. Samples of fullerenes C60 and C70 were Strem Chemicals commercial products with a mole fraction ≥0.9995 and 0.990, respectively, and were utilized directly from the flask (Table 1). Thermogravimetry by applying the Langmuir equation [22,23] has many advantages with respect to other indirect techniques that are used to quantify the enthalpy of sublimation. These advantages include a smaller sample and a quick experiment, which allows
= p
M , 2RT
(1)
where (dm/dt) is the rate of mass loss at temperature T of a sample with an exposed sublimation area A; p is the vapour pressure of the substance; M is the molar mass; R is the gas constant; and is a constant of vaporization, which should be close to unity under vacuum conditions [23], but is lower than such a value under the experimental conditions of this work. Since the enthalpy of change of phase is the thermochemical quantity that needs to be measured and the vapour pressures are not required, the direct combination of the Langmuir equation with the integrated Clausius–Clapeyron equation leads to the following equation: ln
1/2 1 dm T A
·
dt
·
M
g
=B−
cr Hm (T ) , RT
(2)
where dm/dt is the rate of loss of mass at the temperature T and B is a constant that includes, in turn, all other constant terms from the combined equations, even the constant , whose value is not necessary to know exactly. For the application of Eq. (2), an accurate measurement of the rate of mass loss as a function of temperature is indispensable and can usually be obtained by utilizing a thermogravimetric analyser. In this work, a TA Instruments Q5000IR thermogravimetric device was used for this purpose. The weight range of the thermobalance is 100 mg, with a sensitivity of 0.1 g (precision ± 0.01%) and an operation interval from 298 to 1473 K. The furnace heating is achieved by infrared radiation, with a heating rate of 0.1 to 500 K min−1 and temperature control of ±1.0 K (sensitivity 0.1 K). The purge gas flow through the furnace is controlled in the range of 1.0 to 400 cm3 min−1 by a flow controller that is integrated into the system. The system was calibrated for mass with a standard mass traceable to NIST and certified as (97.938 ± 0.001) mg. Temperature calibration was performed with a certified by the International Confederation for Thermal Analysis and Calorimetry (ICTAC) Curie Point reference materials set, consisting of Ni lot CRM7-40211; Ni0.83 Co0.17 lot CRM8-40211 and Ni0.63 Co0.37 lot CRM9-40211, with respective Curie temperatures of 631.2 ± 1.1 K, 827.4 ± 2.2 K and 1019.4 ± 1.6 K. Preliminary tests in the thermogravimetric device allowed us to establish the best conditions for the scanning rate and nitrogen flow in an experiment to generate well-defined thermogravimetric curves and, consequently, to obtain accurate data for the rate of mass loss as a function of the temperature for each cluster. These experiments showed that masses of 1.0–1.5 mg for C60 , C70 and C84 and a mass from 0.3 mg to 0.5 mg for C76 and C78 , uniformly distributed in the bottom of a 4.6 mm diameter platinum cup located on the dish of the thermobalance, were sufficient to generate continuous and smooth thermogravimetric curves (Fig. 2(a)). These preliminary tests also set up a working temperature range from 363.15 to 1023.15 K as optimal for the scanning in temperature, with heating ramps of 10 K min−1 for C60 , C70 and C84 ; under a nitrogen flow of 25 mL min−1 for C60 and 50 mL min−1 for C70 and C84 . For C76 , the scanning rate was of 10 K min−1 , whereas for C78 , this parameter was 20 K min−1 ; both sets of experiments were performed under a nitrogen flow of 25 mL min−1 . With these purge flow rates, an inert atmosphere of nitrogen gas was maintained around the sample without substantially affecting the vaporization
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Table 1 Source, chemical information and purity data of the fullerenes studied in this work. Formula
M (g mol−1 )a
CAS number
Source
Purity reported by the supplier/mole fraction
Purification method
Purity after purification/mole fraction
C60 C70 C76 C78 C84
720.636 840.742 912.806 936.827 1008.890
99685-96-8 115383-22-7 142136-39-8 136316-32-0 135113-16-5
Strem Strem MER Corp MER Corp MER Corp
0.9995 0.99 0.20b 0.20b 0.40b
None None HPLC HPLC HPLC
0.9995 0.99 >0.98 >0.98 >0.98
a b
Molar masses are computed from the 2011 IUPAC atomic masses recommendation [30]. Approximate mole fraction in the MER higher order fullerenes mixture.
rate of the sample. Under the described experimental conditions, the mass of fullerene lost in a complete thermogravimetric experiment was from 20% to 40%. Non-decomposition of the fullerene after heating was verified by performing a second heating on the same sample and then narrowly reproducing the same thermogravimetric curve in this second scanning. After these experiments, the solubility of the cluster in toluene was checked, and there was no trace of insoluble material; then, the structure of the cluster was verified by mass spectrometry. Once the optimal experimental conditions were found, in a representative thermogravimetric experiment the previously weighed platinum cup was placed in the dish of the thermogravimetric device and it was tared at 313.15 K under a nitrogen flow identical to that of the measurements. Then, the sample of fullerene was uniformly deposited on the bottom of the cup, and its exact mass was quantified by a Mettler-Toledo UMX2 micro-balance with sensitivity of 0.1 g. Subsequently, the crucible with the sample was located in the sample dish of the thermogrametric device, the furnace was closed and its temperature was equilibrated at 363.15 K; after 5 min at this temperature, the scanning for temperature and data acquisition, as controlled by the software Thermal Advantage of the Q5000 device, was started. The temperature was raised until the mass loss of the fullerene, as a result of sublimation process, reached at least 20% of the sample. At the end of the heating, the temperature of the sample was brought to room temperature, and the mass of fullerene lost was confirmed in the UMX2 microbalance, matching that recorded in the thermogravimetric device. For each experiment, the loss of the mass rate (dm/dt) as a function of the temperature T, to substitute in Eq. (1), was computed from data of the respective derivative curve (Fig. 2(b)), which was generated using the Universal Analysis software of the Q5000IR device.
A set of at least four series utilizing the same methodology was performed for each of the fullerene studied in this research. To derive accurate values for the enthalpy of sublimation at 298.15 K from the results obtained at the experimental temperature, reliable data of heat capacity for the solid and gas-phase of the fullerenes are required. In this work, the heat capacity measurements on solids fullerenes C60 , C70 and C84 were performed by DSC with a Perkin Elmer DSC7 calorimeter. The limited sample size of C76 and C78 did not allow for calorimetric measurements on these clusters. The DSC7 calorimeter was previously calibrated in both energy and temperature using certified NIST SRM 2232 Indium. The heat capacity of each fullerene was measured in the range of 293.15–573.15 K at a scanning rate of 10.0 K min−1 . These experiments were performed on samples of approximately 9.0 mg of C60 and C70 , and 4.5 mg of C84 . To minimize the disturbances, measurements were performed under a 5.0 cm3 min−1 nitrogen flow. Prior to the heat-capacity measurements of the fullerenes, the reliability of the DSC7 calorimeter in heat capacity measurements was tested by determining the Cp of a high-purity sample of synthetic sapphire (NIST SRM 720) in a temperature range of 298.15–573.15 K. The values at 298.15 K, 400.15 K and 550.15 K were 77.80 J K−1 mol−1 , 97.37 J K−1 mol−1 and 111.24 J K−1 mol−1 , respectively, which is in agreement with the recommended values of 79.01 J K−1 mol−1 , 96.08 J K−1 mol−1 and 109.67 J K−1 mol−1 [31]. Heat capacity of each fullerene in the gas phase, in the range of 298.15–1000 K, was estimated with Gaussian 98 [32] by utilizing density functional theory (DFT) [33]. The optimized geometries and frequency analysis of each fullerene were computed with the exchange correlation functional B3LYP and the 6-31G* basis [34,35]. The solid phase heat capacity of each fullerene was estimated from 298.15 K to 1000 K based on the results of the estimated
Fig. 2. Representative thermogravimetric curves of (a) percentage of loss of mass as a function of temperature for sublimation experiments; (b) derivative curves used to C60 ; determine the instantaneous loss of mass rate, (dm/dt), as a function of the temperature, applied to calculate the enthalpies of sublimation of the fullerenes. C70 ; C76 ; C78 ; C84 .
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Table 2 a Representative experimental data of the dependence loss mass rate on the inverse of the temperature and the enthalpies of sublimation derived from the thermogravimetric experiments of the fullerenes studied in this work. In this table (dm/dt) is the rate of loss of mass and = (1/A)(dm/dt)(T/M)1/2 , where A is the sublimation area of the sample and M is the molar mass of each fullerene. T (K)
m (mg)
(dm/dt) × 1010 (kg s−1 )
× 104 ((kg K mol)1/2 s−1 m−2 )
C60 , Series 1 2.0016 1.860 3.933 890 1.9890 2.371 5.042 900 1.9724 3.054 6.530 910 1.9513 3.908 8.402 920 1.9243 5.124 11.075 930 940 1.8901 6.432 13.977 950 1.8470 8.027 17.536 960 1.7930 10.022 22.009 1.7260 12.463 27.512 970 1.6428 15.363 34.088 980 1.5401 19.329 43.106 990 1.4095 24.384 54.653 1000 g 2 −1 Series 1: ln = −21195.03/T + 15.96; r = 0.9998; a = 0.1; b = 96.7; cr Hm (945 K)/kJ mol = 176.2 ± 0.8 g Series 2: ln = −21012.09/T + 15.79; r2 = 0.9993; a = 0.2; b = 176.8; cr Hm (945 K)/kJ mol−1 = 174.7 ± 1.5 g Series 3: ln = −20839.68/T + 15.63; r2 = 0.9999; a = 0.1; b = 63.2; cr Hm (945 K)/kJ mol−1 = 173.3 ± 0.5 g Series 4: ln = −21343.84/T + 16.14; r2 = 0.9994; a = 0.1; b = 162.2; cr Hm (945 K)/kJ mol−1 = 177.5 ± 1.3 g Series 5: ln = −21368.42/T + 16.14; r2 = 0.9998; a = 0.1; b = 104.9; cr Hm (945 K)/kJ mol−1 = 177.7 ± 0.9 g Weighted average value: < cr Hm (C60 , 945 K)>/kJ mol−1 = 175.0 ± 0.4 C70 , Series 1 1.0135 0.371 0.727 890.0 1.0107 0.521 1.026 900.0 1.0071 0.674 1.334 910.0 920.0 1.0026 0.857 1.706 0.9965 1.101 2.204 930.0 940.0 0.9888 1.416 2.849 950.0 0.9789 1.907 3.857 960.0 0.9661 2.386 4.851 970.0 0.9502 2.948 6.024 980.0 0.9302 3.710 7.620 990.0 0.9054 4.580 9.455 1000.0 0.8749 5.669 11.763 g Series 1 ln = −22370.30/T + 15.65; r2 = 0.9994; a = 0.2; b = 179.1; cr Hm (945 K)/kJ mol−1 = 186.0 ± 1.5 g 2 −1 Series 2 ln = −23076.63/T + 16.34; r = 0.9965; a = 0.5; b = 432.5; cr Hm (945 K)/kJ mol = 191.9 ± 3.6 g Series 3 ln = −21565.86/T + 14.79; r2 = 0.9997; a = 0.1; b = 111.8; cr Hm (945 K)/kJ mol−1 = 179.3 ± 0.9 g Series 4 ln = −21819.10/T + 15.08; r2 = 0.9971; a = 0.4; b = 372.8; cr Hm (945 K)/kJ mol−1 = 181.4 ± 3.1 g Series 5 ln = −22508.37/T + 15.71; r2 = 0.9993; a = 0.2; b = 182.8; cr Hm (945 K)/kJ mol−1 = 187.1 ± 1.5 g Weighted average value: < cr Hm (C70 , 945 K)>/kJ mol−1 = 182.7 ± 0.7 C76 , Series 1 940.0 0.2830 0.250 0.483 950.0 0.2811 0.301 0.584 960.0 0.2787 0.430 0.838 970.0 0.2756 0.581 1.139 0.2718 0.747 1.472 980.0 990.0 0.2671 0.896 1.775 0.2611 1.110 2.211 1000.0 0.2535 1.400 2.801 1010.0 0.2446 1.611 3.240 1020.0 g 2 −1 Series 1 ln = −23538.35/T + 15.12; r = 0.9931; a = 0.8; b = 742.3; cr Hm (980 K)/kJ mol = 195.7 ± 6.2 g 2 −1 Series 2 ln = −22372.58/T + 13.83; r = 0.9837; a = 1.2; b = 1174.0; cr Hm (975 K)/kJ mol = 186.0 ± 9.8 g Series 3 ln = −22826.10/T + 14.24; r2 = 0.9947; a = 0.7; b = 680.5; cr Hm (985 K)/kJ mol−1 = 189.8 ± 5.6 g Series 4 ln = −22583.42/T + 14.22; r2 = 0.9921; a = 0.7; b = 672.5; cr Hm (970 K)/kJ mol−1 = 187.8 ± 5.6 g Series 5 ln = −22508.37/T + 15.71; r2 = 0.9993; a = 1.7; b = 1660.0; cr Hm (980 K)/kJ mol−1 = 192.6 ± 13.8 g Weighted average value: < cr Hm (C76 , 978 K)>/kJ mol−1 = 190.4 ± 3.1 C78 , Series 1 0.2594 0.500 0.093 900.0 0.2588 1.077 0.203 920.0 0.2583 1.931 0.366 930.0 0.2578 2.348 0.448 940.0 0.2571 2.348 0.450 950.0 0.2562 3.349 0.645 960.0 0.2551 3.883 0.752 970.0 0.2537 4.803 0.934 980.0 0.2520 6.623 1.295 990.0 1000.0 0.2499 7.589 1.492 0.2474 9.400 1.857 1010.0 g Series 1 ln = −23137.44/T + 14.39; r2 = 0.9735; a = 1.3; b = 1272.3; cr Hm (955 K)/kJ mol−1 = 192.4 ± 10.6 g Series 2 ln = −24101.75/T + 16.50; r2 = 0.9772; a = 1.3; b = 1226.1; cr Hm (915 K)/kJ mol−1 = 200.4 ± 10.2 g Series 3 ln = −23048.00/T + 14.64; r2 = 0.9707; a = 1.1; b = 1110.5; cr Hm (890 K)/kJ mol−1 = 191.6 ± 9.2 g Weighted average value: < cr Hm (C78 , 920 K)>/kJ mol−1 = 194.6 ± 5.7 C84 , Series 1 0.9444 0.592 1.154 1060.0 0.9404 0.736 1.442 1070.0 0.9353 0.908 1.787 1080.0
103 K−1 (T)
ln
1.124 1.111 1.099 1.087 1.075 1.064 1.053 1.042 1.031 1.020 1.010 1.000
−7.841 −7.593 −7.334 −7.082 −6.806 −6.573 −6.346 −6.119 −5.896 −5.681 −5.447 −5.209
1.124 1.111 1.099 1.087 1.075 1.064 1.053 1.042 1.031 1.020 1.010 1.000
−9.529 −9.184 −8.922 −8.676 −8.420 −8.164 −7.860 −7.631 −7.415 −7.180 −6.964 −6.745
1.064 1.053 1.042 1.031 1.020 1.010 1.000 9.901 9.804
−9.939 −9.747 −9.387 −9.080 −8.823 −8.636 −8.417 −8.180 −8.035
1.111 1.087 1.075 1.064 1.053 1.042 1.031 1.020 1.010 1.000 9.901
−11.583 −10.805 −10.215 −10.014 −10.009 −9.649 −9.496 −9.278 −8.952 −8.810 −8.591
9.434 9.346 9.259
−9.067 −8.844 −8.630
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Table 2 (Continued) T (K)
m (mg)
(dm/dt) × 1010 (kg s−1 )
× 104 ((kg K mol)1/2 s−1 m−2 )
1090.0 0.9291 1.152 2.277 0.9212 1.462 2.904 1100.0 0.9119 1.734 3.461 1110.0 1120.0 0.9002 2.120 4.250 1130.0 0.8862 2.577 5.188 1140.0 0.8691 3.047 6.163 1150.0 0.8488 3.681 7.477 1160.0 0.8248 4.353 8.881 1170.0 0.7965 5.145 10.543 g Series 1 ln = −25030.39/T + 14.57; r2 = 0.9991; a = 0.2; b = 235.7; cr Hm (1115 K)/kJ mol−1 = 208.1 ± 1.9 g Series 2 ln = −24585.04/T + 14.20; r2 = 0.9980; a = 0.3; b = 345.3; cr Hm (1115 K)/kJ mol−1 = 204.4 ± 2.9 g Series 3 ln = −24,906.25/T + 14.49; r2 = 0.9983; a = 0.3; b = 320.8; cr Hm (1115 K)/kJ mol−1 = 207.1 ± 2.6 g Series 4 ln = −24,851.92/T + 14.52; r2 = 0.9976; a = 0.3; b = 388.4; cr Hm (1115 K)/kJ mol−1 = 206.6 ± 3.2 g Series 5 ln = −24,524.23/T + 14.16; r2 = 0.9985; a = 0.2; b = 202.8; cr Hm (1115 K)/kJ mol−1 = 203.9 ± 2.5 g Weighted average value:< cr Hm (C84 , 1115 K)>/kJ mol−1 = 205.4 ± 1.4
103 K−1 (T) 9.174 9.091 9.009 8.929 8.850 8.772 8.696 8.621 8.547
ln −8.387 −8.144 −7.969 −7.764 −7.564 −7.392 −7.199 −7.026 −6.855
a The sublimation area, A, was calculated as 1.662 × 10−5 m2 from the diameter of the sample cup. Uncertainty of temperature data is ±1.0 K, while uncertainty in mass data is ±1.0 g. Parameters a and b represent the standard deviation of the intercept and slope of the function ln vs 1/T. Dispersion associated to each sublimation enthalpy (xi /i2 )/ (1/i2 ) and value was computed as b R and is a standard uncertainty. The weighted average value and its standard deviation , were calculated as =
(1/i2 )], where xi is each of the N sublimation enthalpy data and its respective standard deviation i [36]. The resulting standard deviation associated to each 2 = [1/ weighted average value of enthalpy of sublimation is a standard uncertainty also.
heat capacity in the gas phase by applying the methodology proposed by Piacente et al. [20]. 3. Results and discussion The smooth and well-defined profile of the thermogravimetric curves (Fig. 2(a)) indicate that fullerenes studied here are enough stable to be sublimed at high temperatures without decomposition. The profiles were similar for all five fullerenes; however, these curves show that a quantifiable loss of mass for C60 and C70 starts at a lower temperature compared with the other fullerenes. The curves also show that the samples lost at least one fifth of its mass in the experimental conditions applied, which allows for an accurate quantification of the mass loss rate as a function of the temperature and can be used to obtain accurate results for the enthalpy of sublimation. Table 2 shows the representative experimental data of the dependence of the loss mass rate with the temperature for the fullerenes as well as the resulting linear equations from each series with uncertainty for the y-intercept a and the slope b , which were both computed as the standard deviation from the best fit, which in turn was calculated as described in Ref. [36]. Dispersion for each sublimation enthalpy value was computed as b ·R and is a
standard uncertainty. Correlation factors in all cases are higher than 0.99, which indicates that despite the wide temperature interval, the slope of the linear dependence ln[(1/A)·(dm/dt)·(T/M)1/2 ] vs 1/T is constant and allows the enthalpy of sublimation to be constant in such an interval. Fig. 3 shows the graphics for the dependence of the rate of loss of mass with the inverse of the temperature for all the fullerenes, and the detailed experimental data sets and results for all series of measurements are provided in the Supplementary Information. Heat capacity data estimated by DFT are reported in Table 3, which includes the heat capacity data for the solid phase measured by DSC to demonstrate the reliability of the calculations. Estimated Cp data for the solid and gas phase of each fullerene were fit to a quadratic equation with a correlation coefficient of 0.999. Table 4 shows the comparison of Cp data at 298.15 K of the solid and gas phase of fullerenes C60 and C70 determined in this work with data found in the literature. Heat capacity of C60 (cr) and C70 (cr) estimated by DFT and measured by DSC in this work, are in acceptable agreement with the results reported in Refs. [37–39] and with the values recommended by Korobov [40] and Diky [14], whose values of Cp for fullerenes are based in analysis of graphics and numerical data of Refs. [41–47]. Similar agreement is found for estimated Cp data of C60 (g) and C70 (g). For higher fullerenes no comparison is
Fig. 3. Rate of loss of mass as a function of the temperature, derived from the thermogravimetric experiments on each fullerene. The C78 series is included in a graphic apart C78 series. for clarity in presentation. (a) 䊐 C60 series; C70 series; C76 series, ♦ C84 series. (b)
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Table 3 Solid and gas phase heat capacities at constant pressure (in J K−1 mol−1 ) of the fullerenes, estimated by DFT procedure applying B3LYP/6-31G* functional and basis. The experimental heat capacities measured by DSCa at P = 80.0 kPab are included to demonstrate the reliability of the estimations on the solid phase. C60
C70
T (K)
Cp (cr) DSC
298.15 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000
535.8 ± 12.7 538.6 648.1 742.0 830.1 917.4
Cp (cr) Theoretical
Cp (g) Theoretical
504.3 508.7 614.7 711.6 798.6 875.7 943.3 1002.5 1054.0 1098.9 1138.0 1172.2 1202.1 1228.4 1251.6 1272.1
487.2 491.6 597.6 694.5 781.4 858.4 926.0 985.0 1036.4 1081.3 1120.3 1154.4 1184.3 1210.5 1233.6 1254.1
Cp (g)/(J K−1 mol−1 ) = −0.00137T2 + 2.83160T − 226.38 Cp (cr)/(J K−1 mol−1 ) = −0.00137T2 + 2.83290T − 209.75
T sub
298.15 K
Cp (cr) Theoretical
298.15 626.8 ± 16.2 592.5 300 630.1 597.6 350 758.3 720.2 400 855.2 832.5 450 924.8 933.4 500 1005.3 1022.9 550 1105.8 1101.5 600 1170.3 650 1230.3 700 1282.6 750 1328.3 800 1368.1 850 1403.1 900 1433.8 950 1460.9 1000 1484.8 −1 340.2 ± 0.3 trs H = (0.075 ± 0.020) kJ mol 401.0 ± 1.9 trs H = (0.215 ± 0.020) kJ mol−1 Cp (g)/(J K−1 mol−1 ) = −0.00158T2 + 3.2789T − 251.75 Cp (cr)/(J K−1 mol−1 ) = −0.00158T2 + 3.2814T − 235.13
Cp (g) Theoretical 575.1 580.2 702.8 814.9 915.6 1005.0 1083.5 1152.2 1212.1 1264.3 1309.8 1349.5 1384.4 1415.0 1441.9 1465.7
g
298.15 K
cr CpdT = −(11.8 ± 0.5) kJ/mol
C78
T (K)
Cp (cr) DSC
Cp (cr) Theoretical
298.15 643.7 649.3 300 350 782.2 903.8 400 1013.1 450 1110.1 500 1195.5 550 600 1270.1 1335.2 650 700 1392.0 1441.5 750 1484.8 800 1522.8 850 1556.2 900 950 1585.6 1611.6 1000 Cp (g)/(J K−1 mol−1 ) = −0.00171T2 + 3.55278T − 269.77 Cp (cr)/(J K−1 mol−1 ) = −0.00171T2 + 3.55548T − 253.15 298.15 K
Cp (cr) DSC
T sub
g
cr CpdT = −(11.3 ± 0.5) kJ/mol
C76
T sub
T (K)
Cp (g) Theoretical
T (K)
626.3 631.8 764.6 886.1 995.3 1092.2 1177.4 1251.9 1316.8 1373.5 1422.9 1466.1 1503.9 1537.1 1566.4 1592.3
298 662.7 300 668.4 350 804.4 400 928.9 450 1040.8 500 1140.2 550 1227.6 600 1304.0 650 1370.8 700 1428.9 750 1479.7 800 1524.1 850 1563.1 900 1597.3 950 1627.5 1000 1654.2 Cp (g)/(J K−1 mol−1 ) = −0.00175T2 + 3.63536T − 271.68 Cp (cr)/(J K−1 mol−1 ) = −0.00175T2 + 3.63814T − 255.06
T sub
g
cr CpdT = −(12.5 ± 0.5) kJ/mol
298.15 K
Cp (cr) DSC
Cp (cr) Theoretical
Cp (g) Theoretical 645.3 650.9 786.8 911.1 1022.9 1122.1 1209.4 1285.7 1352.3 1410.4 1461.0 1505.3 1544.1 1578.2 1608.2 1634.8
g
cr CpdT = -(11.4 ± 0.5) kJ/mol
C84 T (K)
Cp (cr) DSC
Cp (cr) Theoretical
298 740.8 ± 24.1 713.1 753.8 719.2 300 932.1 865.3 350 1026.4 999.0 400 450 1057.7 1119.3 1083.4 1226.1 500 1133.2 1320.2 550 1228.6 1402.5 600 1458.9 1474.3 650 700 1537.0 −1 −1 2 Cp (g)/(J K mol ) = −0.00160T + 3.58385T − 206.92
T sub
298.15 K
g cr CpdT
Cp (g) Theoretical
T (K)
695.7 701.8 847.8 981.4 1101.6 1208.2 1302.1 1384.3 1456.0 1518.6
750 800 850 900 950 1000 1050 1100 1150
Cp (cr) DSC
Cp (cr) Theoretical
Cp (g) Theoretical
1591.7 1639.6 1681.5 1718.4 1751.0 1779.8 1805.3 1828.1 1848.5
1573.2 1620.9 1662.8 1699.5 1731.9 1760.6 1786.1 1808.7 1828.9
Cp (cr)/(J K−1 mol−1 ) = −0.00160T2 + 3.58637T − 190.29
= −(15.0 ± 0.5) kJ/mol
Uncertainty of temperature data of DSC: ±0.2 K. Dispersion associated to each Cp value measured by DSC can be computed as uCp (C60 ) = 0.021 Cp ; uCp (C70 ) = 0.017 Cp and uCp (C84 ) = 0.078 Cp ; was calculated as the standard deviation of at least four measurements (see Supplementary Information) and is a standard uncertainty. b Atmospheric pressure in the laboratory, uncertainty: ±0.130 kPa. a
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M. Martínez-Herrera et al. / Thermochimica Acta xxx (2015) xxx–xxx Table 4 Comparison with literature data of results of solid and gas phase heat capacities at 298.15 K for the fullerenes C60 and C70 . Author C60 (cr) This work This work Steele et al. [37] Jin et al. [38] Rojas-Aguilar [39] Korobov and Sidorov [40] Lebedev et al. [41] Diky and Kabo [14] C60 (g) This work Diky and Kabo [14] C70 (cr) This work This work Diky and Kabo [14] C70 (g) This work Diky and Kabo [14]
Methoda
7
the heat capacity data of Table 3, and then applying the following equation:
Tsub
Temperature interval (K)
Cp (298 K) (J K−1 mol−1 )
cr H(298.15 K) = cr H(Tsub ) −
DSC DFT DSC DSC DSC Review AdC Review
293–573 298–1000 300–800 120–560 293–323 10–1000 5–350 0–1000
535.8 ± 12.7 504.3 556.5 536.9 521.7 520.0b 524.8 525.6
DFT Review
298–1000 0–1000
487.2 498.5
DSC DFT Review
293–573 298–1000 0–1000
626.8 ± 16.2 592.5 625.6
DFT Review
298–1000 0–1000
575.1 585.1
The numerical values for the integral involved in Eq. (3) are also included in Table 3 and have assigned an estimated uncertainty of 0.5 kJ mol−1 , which in turn was included in the dispersion of the result of enthalpy of sublimation at 298.15 K. A summary of the enthalpies of sublimation at the experimental and reference temperature of 298.15 K measured in this work for the fullerenes is shown in Table 5, which also includes comparison with the available data of the literature. For a consistent comparison, literature experimental enthalpies of sublimation were corrected in temperature by the same heat capacity data and prog cedure described and applied in this work, this except when cr Hm (298.15 K) was available in the cited article. Despite the large difference between the experimental and reference temperatures, the results for the correction in temperature are reasonable given that differences in the heat capacities between the solid and gas phases are not substantial. For the results of this work, the enthalpies at 298.15 K are accompanied by expanded uncertainties, which were calculated as ±t, where is the experimental standard deviation and t is Student’s coefficient for a level of confidence of 0.905 [36]. Table 5 and Fig. 4(a) show that once corrected in temperature, the result of enthalpy of sublimation at 298.15 K of 186.3 ± 1.2 kJ mol−1 for C60 , as derived in this work from the thermogravimetric data and Langmuir equation, is consistent with the results derived from the experimental enthalpies of sublimation reported by Mathews [5,7], Dai [8], Sun [10], Piacente [11] and the value recommended by Diky and Kabo [14]. This fact indicates that the methodology here developed generates results sufficiently accurate and can be applied in determining the enthalpy of sublig mation of higher fullerenes. In Fig. 4(a), results of cr Hm (298.15 K) −1 were obtained from polycrystalline for C60 under 180.0 kJ mol mixtures of fullerenes C60 and C70 [3,9] or from a mixture of C60 with Potassium [12], this strongly supports the fact that vapour pressure of pure C60 is affected by the presence of other kind of g fullerene or by impurities. For C70 the result of cr Hm (298.15 K) −1 of 194.5 ± 1.7 kJ mol , is in agreement with the result of Abrefah [6], but is lower than most of the other results. In Fig. 4(b) results
a Method: DSC, Differential Scanning Calorimetry; DFT, Density Functional Theory; AdC, Adiabatic Calorimetry. b Data reported at 300 K.
possible given that in the best of our knowledge there is not heat capacity data reported in the literature for these clusters. For C70 (cr) DSC heat flow and heat capacity curves allowed to detect two reproducible thermal effects, presumably associated to solid-state transitions (see Table 3 and Supplementary Information). The transition found in this work at 340.2 K agrees in temperature with that detected by Zhogova and Lebedev [47] but those authors determined a larger enthalpy for this thermal effect. The transition at 401.0 K has not precedent in the literature, however some authors [14,47] suggest that thermal signals are determined by a greater or lesser number of polymorphic forms of C70 , depending on the sample preparation. The derivation of the sublimation enthalpies at temperature T = 298.15 K was performed using the results of enthalpy of sublimation at the experimental temperature shown in Table 2 and
g
g
g
cr Cp dT
(3)
298.15 K
Fig. 4. Comparison of results of enthalpy of sublimation at 298.15 K for (a) 䊉 fullerene C60 ; (b)
fullerene C70 .
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Table 5 Enthalpies of sublimation at Tsub and at 298.15 K obtained by TGA in this work for the fullerenes and their comparison with values reported in the literature. Author C60 This work Pan et al. [3] Tokmakoff et al. [4] Mathews et al. [5] Abrefah et al. [6] Mathews et al. [7] Dai et al. [8] Popovic et al. [9] Sun et al. [10] Piacente et al. [11] Borisova et al. [12] Pankajavalli et al. [13] Diky and Kabo [14] C70 This work Pan et al. [3] Abrefah et al. [6] Popovic et al. [9] Mathews et al. [15] Baba et al. [16] Piacente et al. [17] Diky and Kabo [14] C76 This work Brunetti et al. [18] Boltalina et al. [19] C78 This work C84 This work Piacente et al. [20] Boltalina et al. [21]
g
g
Methoda
T (K)
Tsub (K)
cr Hm (Tsub ) (kJ mol−1 )
TG KEMS TEAS KEMS KETG KEMS UV/Vis KEMS OA KETB KEMS TMTG Review
890–1000 640–800 400–700 640–787 673–873 600–800 837–995 630–780 683–1123 730–990 560–870 789–907 730–990
945 707 600 727 773 700 916 705 903 860 715 848 860
175.0 167.8 138.5 176.0 159.0 181.4 180.0 158.0 175.0 175.0 159.0 152.3 175.3
± ± ± ± ± ± ± ± ± ± ± ± ±
0.4 5.4 3.8 2.0 4.2 2.3 10.0 3.0 4.0 3.0 3.0 5.3 2.9
186.3 174.9 143.7 183.4 167.2 188.3 190.8 165.0 185.5 182.0 166.2 183.5 183.7
± ± ± ± ± ± ± ± ± ± ± ± ±
1.2c 5.4 3.8 2.0 4.2 2.3 10.0 3.0 4.0 3.0d 3.0 1.0d 5.1d
TG KEMS KETG KEMS KEMS KEMS KETB Review
890–1000 640–800 703–873 670–800 650–850 650–850 783–904 783–904
945 739 788 735 750 750 843 843.5
182.7 179.9 188.0 174.0 196.0 195.7 190.0 189.9
± ± ± ± ± ± ± ±
0.7 9.2 4.0 3.0 2.0 2.3 3.0 3.1
194.5 187.8 196.8 181.1 204.1 203.8 200.0 200.3
± ± ± ± ± ± ± ±
1.7c 9.2 4.0 3.0 2.0 2.3 6.0d 6.1d
TG KETB KEMS
940–1020 834–1069 637–911
978 910 764
190.4 ± 3.1 194.0 ± 4.0 190.0 ± 7.0
202.9 ± 6.2c 206.0 ± 4.0d 198.4 ± 7.0
810–1010
920
194.6 ± 5.7
206.0 ± 11.5c
1053–1153 920–1190 658–980
1115 950 853
205.4 ± 1.4 210.0 ± 6.0 202.0 ± 4.0
220.4 ± 3.0c 225.0 ± 6.0d 212.0 ± 4.0
TG KETB KEMS
cr Hm (298.15 K)b (kJ mol−1 )
a Method: TG, thermogravimetry; KETG, Knudsen effusion associated with thermogravimetry; TEAS, transmission electronic absorption spectroscopy; KEMS, Knudsen effusion associated with mass spectrometry; UV/Vis, ultraviolet/visible spectroscopy; OA, optical Absorption; KETB, Knudsen effusion associated with torsion balance; TMTG, transpiration method associated with thermogravimetry. b Enthalpy of sublimation at 298.15 K was derived from the experimental enthalpy reported by the other authors but applying the same correction in temperature determined in this work. c Dispersion is an expanded uncertainty calculated as ±t, where is the experimental standard deviation and t is Student’s coefficient for a level of confidence of 0.905 [36]. d Value available in the cited reference.
of enthalpy of sublimation under 190.0 kJ mol−1 for this cluster are those obtained also from a polycrystalline mixtures of fullerenes C60 and C70 [3,9]. The results for the enthalpy of sublimation at 298.15 of 202.9 ± 6.2 kJ mol−1 for fullerene C76 and 220.4 ± 3.0 kJ mol−1 for C84 are in the middle of the range of values previously reported in the literature. In the case of C78 , to the best of our knowledge, no experimental value of its enthalpy of sublimation has been previously reported, which thus makes comparison impossible. Large uncertainties in the results of enthalpy of sublimation of C76 and C78 are consequence of the large dispersion in the dependence of the rate of loss of mass with the temperature (Fig. 3). This dispersion is explained by the small mass of sample utilized, the low rate of loss of mass and a possible slight decomposition of the fullerene around 1000 K. This last fact confirms in turn that despite higher fullerenes are thermodynamically more stables than C60 and C70 [2], decomposition of C76 and C78 must be characterized by a lower activation energy. Fig. 5(a) shows the enthalpy of sublimation as a function of the number of carbon atoms and the best fit for this dependence is a second order polynomial with a correlation factor of 0.9987. g The resulting fitted second order equation is cr Hm /(kJ mol−1 ) = 3.366 × 102 − 5.293 × n + 4.650 × 10−2 × n2 , where n is the number of carbon atoms in the cluster. This equation can be useful for deriving the enthalpy of sublimation of a fullerene that is not isolatable in sufficiently high levels to perform a thermochemical study,
such as C86 , at 225.3 ± 2.8 kJ mol−1 . The uncertainty assigned to this magnitude was that of enthalpy of sublimation of fullerene C84 . The strong dependence of the enthalpy of sublimation on the number of carbon atoms suggests that an increasing number of carbon atoms increases the energy that determine the cohesion of the solid. Fig. 5(b) shows the dependence of the enthalpy of sublimation on the polarizability of each molecule of fullerene [48]. The resulting trend is also second order polynomial and has a regression coefficient of 0.9978. This finding confirms that the forces that rule the cohesion of each solid fullerene are dispersion, given that polarizability is a factor that determines the intensity of these forces. 4. Conclusion Thermogravimetry seems to be suitable for determination of reliable values of enthalpies sublimation of fullerenes, given that utilizing this technique and applying the Langmuir equation, the enthalpies of sublimation of C60 , C70 , C76 , and C84 were measured with results in good agreement respect to those reported in literature and with a maximal uncertainty of 3.0%. Despite a larger uncertainty, enthalpy of sublimation not found in literature for C78 , is also reported. From the second order polynomial dependence of the enthalpy of sublimation on the number of carbon atoms established in this work, the enthalpy of sublimation of fullerenes not available or isolatable can be estimated. The enthalpy
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Fig. 5. Dependence of the enthalpy of sublimation on (a) the number of carbon atoms; (b) the polarizability ˛ of the fullerene. Values of ˛ (in Å3 ) were taken from Ref. [48] as 60.8, 73.8, 83.0, 85.7 and 94.4 for C60 , C70 , C76 , C78 and C84 , respectively.
of sublimation of these carbon allotropes showed a polynomial dependence also with the polarizability of the cluster in the range of the fullerenes studied, which suggests an increase in the energy of cohesion in the solid by forces of dispersion and, consequently, with an increase in the molecular volume and surface of the cluster. Acknowledgements The authors are grateful to Conacyt (Mexico) for financial support (grants 47679-Q, 104299 and 128411) and the scholarship of M.M-H. They also thank Patricia Amador for her valuable help in HPLC separation of the clusters and, Iris Ramos-García, Sonia Sánchez-Ruiz, Aurora Vásquez-Badillo and Geiser Cuellar for their valuable support in the spectroscopic analysis of the fullerenes studied here. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.tca.2015.09.001. References [1] W. Krätschmer, L.D. Lamb, K. Fostiropoulous, D.R. Huffmann, Solid C60 : a new form of carbon, Nature 347 (1990) 354–358. [2] A. Rojas, M. Martinez, P. Amador, L.A. Torres, Increasing stability of the fullerenes with the number of carbon atoms: the experimental evidence, J. Phys. Chem. B 111 (2007) 9031–9036. [3] C. Pan, M.P. Sampson, Y. Chai, R.H. Hauge, J.L. Margrave, Heats of sublimation from a polycrystalline mixture of C60 and C70 , J. Phys. Chem. 95 (1991) 2944–2946. [4] A. Tokmakoff, D.R. Haynes, S.M. George, Desorption kinetics of C60 multilayers from Al2 O3 (0001), Chem. Phys. Lett. 186 (1991) 450–455. [5] C.K. Mathews, P.R. Vasudeva Rao, T.G. Srinivasan, V. Ganesan, N. Sivaraman, T.S.L. Lakshmi Narasimhan, I. Kaliappan, K. Chandran, R. Dhamodaran, Preparation and characterization of buckministerfullerene and measurement of its heat of sublimation, Curr. Sci. 61 (1991) 834–838. [6] J. Abrefah, D.R. Olander, M. Balooch, W.J. Siekhaus, Vapor pressure of buckminsterfullerene, Appl. Phys. Lett. 60 (1992) 1313–1314. [7] C.K. Mathews, M.S. Baba, T.S.L. Narasimhan, R. Balasubramanian, N. Sivaraman, T.G. Srinivasan, P.R.V. Rao, Vaporization studies on buckminsterfullerene, J. Phys. Lett. 96 (1992) 3566–3568. [8] S. Dai, L. Mac Toth, G.D. Del Cul, D.H. Metcalf, Ultraviolet-visible absorption spectrum of C60 vapor and determination of the C60 vaporization enthalpy, J. Chem. Phys. 101 (1994) 4470–4471.
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