J. Chem. Eng. Data 2009, 54, 1367–1370
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Thermodynamic Properties of Carbon Nanotubes Zhaodong Nan,*,† Chengzhen Wei,† Qianqian Yang,† and Zhicheng Tan‡ College of Chemistry and Chemical Engineering, Yangzhou University, Yangzhou 225002, China, and Thermochemistry Laboratory, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, P.R. China
Low-temperature molar heat capacities of the carbon nanotubes (CNTs) including single-walled carbon nanotubes (SWNTs) and multiwalled carbon nanotubes (MWNTs) were measured, respectively, by a precision automated adiabatic calorimeter over the temperature range of (78 to 398) K. The observed results demonstrated that the change in the molar heat capacity with thermodynamic temperature was different for the SWNTs and the MWNTs. Polynomial equations of the molar heat capacities as a function of the temperature were fitted by the least-squares method for SWNTs and MWNTs, respectively. Smoothed heat capacities and the changes in thermodynamic functions of the CNTs, such as ∆H ) H(T/K) - H(298.15) and ∆S ) S(T/K) - S(298.15), were calculated on the basis of the fitted polynomials and the relationships of the thermodynamic functions.
Introduction Carbon nanotubes (CNTs) including single-walled carbon nanotubes (SWNTs) and multiwalled carbon nanotubes (MWNTs) have received great interest since their discovery.1,2 CNTs constitute a promising material for use in the aerospace, textile, and electronics industries because this material possesses high chemical and thermal stability, mechanical strength, flexibility, and electrical and thermal conductivity as well as low weight.3-6 In particular, the incorporation of even small amounts of CNTs in other materials can improve the mechanical stabilities and thermal and electrical properties.7-10 However, heat capacities and other thermodynamic functions of CNTs have not been reported, as we know. Heat capacity is one of the more valuable thermophysical quantities to be considered when studying materials. Accurate heat capacity values are needed in many areas of physics, chemistry, and chemical engineering for establishing energy balances, obtaining entropy and enthalpy values, or studying phase transitions. Heat capacities of C60 and C70 have been reported.11,12 Structure changes of C60 and C70 were investigated on the basis of the heat capacities measured at different experimental temperatures. The heat capacities of the CNTs including SWNTs and MWNTs were measured with an adiabatic calorimeter, and the thermodynamic properties of the CNTs were derived in this article. The adiabatic calorimeter has been described and used to measure heat capacities of samples in our previous research.13-15
Experimental Section CNTs were purchased from Shenzhen Nanotech Port, were prepared by the method of chemical vapor deposition (VCD), and contained g 90 % SWNTs and ∼ 98 % MWNTs with a length of (1 to 15) µm. The morphologies of the CNTs were observed by transmission electron microscope (TEM) images, which were taken on a Hitachi model H-800. * Corresponding author. Tel: +86-514-87959896. Fax: +86-514-87959896. E-mail:
[email protected]. † Yangzhou University. ‡ Chinese Academy of Sciences.
Figure 1. TG curves of the CNTs.
The thermogravimetry (TG) measurements of the samples were carried out by a thermogravimetric analysis system (model: TG 209 F1, NETZSSCH, Germany) under nitrogen with a 10 K · min-1 heating rate. The amounts of the samples used for TG analysis were (20.2 and 19.8) mg, respectively, for SWNTs and MWNTs. The flow rate of nitrogen for each of the TG experiments was controlled at 10 mL · min-1. Heat-capacity measurements were carried out in a highprecision automatic adiabatic calorimeter built by Thermochemistry Laboratory, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, described in detail elsewhere.16 The temperature increment in a heating period was (2 to 4) K and the temperature drift was maintained at about 10-3 K · min-1 in equilibrium period. All of the data were automatically acquired through a Data Acquisition/Switch Unit (model: 34970A, Aglient) and processed by a computer. To verify the reliability of the adiabatic calorimeter, we measured the molar heat capacities for the reference standard material R-Al2O3. The deviations of our experimental results from the values recommended by the National Bureau of Standards17 were within ( 0.2 % in the temperature range of (80 to 400) K.
10.1021/je900019f CCC: $40.75 2009 American Chemical Society Published on Web 03/24/2009
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Figure 2. TEM photography of the CNTs: (A) SWNTs and (B) MWNTS. Table 1. Experimental Molar Heat Capacity of the SWNTs and MWNTs T
Cp,m
T
Cp,m
T
Cp,m
T
Cp,m
T
Cp,m
T
Cp,m
K
J · K-1 · mol-1
K
J · K-1 · mol-1
K
J · K-1 · mol-1
K
J · K-1 · mol-1
K
J · K-1 · mol-1
K
J · K-1 · mol-1
78.13 80.96 84.26 87.12 89.92 92.74 95.56 98.39 101.23 105.18 109.06 111.81 114.66 117.52 120.33 123.16 126.01 128.82 131.58 134.38 137.20 139.97 142.72 145.49 148.28 151.05 154.61 158.14 160.89 163.69 166.47 169.22 171.94 174.62 177.34 180.12 182.88 185.63 188.35
0.186 0.308 0.428 0.532 0.633 0.741 0.81 0.88 0.985 1.138 1.282 1.366 1.44 1.565 1.65 1.724 1.817 1.938 2.012 2.111 2.175 2.263 2.35 2.445 2.543 2.579 2.749 2.842 2.883 2.997 3.107 3.191 3.269 3.347 3.422 3.508 3.579 3.644 3.703
191.05 193.73 196.39 199.04 202.31 205.62 208.30 210.97 213.62 216.27 218.91 221.10 223.83 226.55 229.36 232.26 235.17 238.09 241.01 244.47 247.88 250.65 253.41 256.16 258.92 261.67 264.41 267.15 269.89 272.62 275.34 278.07 280.78 283.65 286.51 289.36 292.33 295.31 298.30
301.30 304.30 307.29 310.30 313.31 316.31 319.31 322.31 325.30 328.29 331.27 334.25 337.22 340.19 343.15 346.10 349.05 351.99 354.92 357.83 359.37 363.69 365.17 367.40 370.03 373.29 376.75 379.60 382.15 385.97 389.19 392.23 395.25 398.26
6.112 6.149 6.182 6.241 6.307 6.372 6.432 6.503 6.568 6.602 6.692 6.702 6.781 6.821 6.881 6.922 6.979 7.021 7.073 7.139 7.181 7.214 7.241 7.278 7.328 7.372 7.416 7.46 7.483 7.523 7.608 7.669 7.706 7.762
80.88 84.20 87.13 90.00 92.82 95.59 98.38 101.18 105.14 109.03 111.72 114.50 117.30 120.05 122.81 125.60 128.34 131.11 133.89 136.64 139.35 142.09 144.85 147.58 150.28 153.78 157.24 159.93 162.68 165.41 168.12 170.80 173.47 176.19 178.99 181.77 184.52 187.26
0.0361 0.0712 0.134 0.175 0.224 0.286 0.339 0.41 0.491 0.591 0.639 0.713 0.791 0.891 0.943 0.995 1.102 1.146 1.222 1.279 1.347 1.422 1.499 1.594 1.661 1.757 1.861 1.957 2.031 2.096 2.211 2.293 2.379 2.467 2.549 2.653 2.745 2.829
189.98 192.68 195.36 198.04 200.70 204.00 207.32 210.03 212.72 215.40 218.07 220.72 223.38 226.01 228.74 231.56 234.37 237.20 240.01 243.36 246.64 249.30 251.95 254.60 257.24 259.89 262.53 265.18 267.82 270.45 273.24 276.02 278.80 281.58 284.35 287.26 290.16 293.05
295.93 297.37 300.04 303.06 306.09 309.11 312.12 315.13 318.13 321.13 324.12 327.40 330.38 333.36 336.33 339.30 342.25 345.21 348.15 351.09 354.03 356.96 359.90 362.82 365.74 368.66 371.58 374.50 377.41 380.31 383.22 386.13 389.03 391.93 394.83 397.73
6.247 6.295 6.377 6.453 6.539 6.627 6.703 6.782 6.837 6.948 7.027 7.108 7.195 7.259 7.337 7.414 7.488 7.565 7.637 7.709 7.782 7.849 7.913 7.984 8.046 8.111 8.168 8.236 8.318 8.358 8.422 8.499 8.563 8.626 8.693 8.751
SWNTs 3.801 3.855 3.929 3.993 4.084 4.147 4.207 4.284 4.342 4.402 4.479 4.517 4.585 4.647 4.706 4.769 4.842 4.9 4.943 5.008 5.07 5.129 5.194 5.258 5.307 5.366 5.403 5.486 5.528 5.583 5.628 5.693 5.739 5.799 5.827 5.899 5.929 6.015 6.054
The sample masses of SWNTs and MWNTs used for the calorimetric measurement were 0.67186 and 0.54917 g, respectively, which were equivalent to (0.060000 and 0.045732) mol in terms of the molar mass, M ) 12.0107 g · mol-1.
Results and Discussion Figure 1 shows the TG curves of the CNTs in the temperature range from (25 to 600) °C. The mass % loss was about 1.0 % and 0.6 % for SWNTs and MWNTs, respectively, when the experimental temperature was T e 600 °C. Figure 2 shows TEM photos of the CNTs. Figure 2 demonstrates that the CNTs were dispersed nanotubes and the diameters were about (20 to 40) nm and (30 to 60) nm for SWNTs and MWNTs, respectively.
MWNTs 2.914 3.012 3.077 3.162 3.273 3.381 3.458 3.565 3.675 3.786 3.83 3.936 4.023 4.09 4.208 4.305 4.375 4.454 4.548 4.657 4.748 4.829 4.919 5.011 5.091 5.166 5.25 5.34 5.414 5.499 5.566 5.654 5.749 5.843 5.901 5.999 6.078 6.166
Low-temperature heat capacities of CNTs were measured by the adiabatic calorimeter. All experimental results were listed in Table 1 and plotted in Figure 3. The obtained results showed that the structure of the CNTs was stable over the temperature range of (78 to 398) K; namely, no phase change, association, or thermal decomposition occurred. These results were agreeable with those obtained by TG curves, as given in Figure 1. The 112 experimental points for the SWNTS and the MWNTs, respectively, in the temperature region of (78 to 398) K were fitted by means of the least-squares method. Polynomial equations of the experimental molar heat capacities (Cp,m) versus reduced temperature (X), X ) f(T) ) (T ((T2 + T1)/2))/((T2 - T1)/2) were obtained, where T is thermodynamic temperature and T1 and T2 are the minimum
Journal of Chemical & Engineering Data, Vol. 54, No. 4, 2009 1369
and the maximum temperatures during the calorimetric experiment, respectively. For the SWNTs
δ)
Cp,m/J·K-1·mol-1 ) 0.1376X4 + 0.3051X3 - 1.0438X2 + 3.5028x + 4.890 (1)
fit exptl 2 - Cp,m ) ∑ (Cp,m
(2)
n-1
exptl and where n is the number of experimental points, and Cp,m fit Cp,m represent the molar heat capacity obtained by experimental measurement and the corresponding result calculated from eq 1, respectively.
where T1 ) 78.13 K, T2 ) 398.26 K, and the standard error of this fit is δ ) 0.026 J · K-1 · mol-1. The standard δ of the fits was calculated by the following equation
Table 2. Smoothed Heat Capacities and Thermodynamic Functions of the CNTsa T
Cp,mb
K
-1
80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 298.15 a
∆Hb -1
J · K · mol 0.245 0.429 0.611 0.790 0.968 1.142 1.315 1.485 1.652 1.817 1.980 2.140 2.297 2.452 2.604 2.754 2.902 3.047 3.189 3.329 3.466 3.601 3.733 3.863 3.991 4.116 4.239 4.359 4.478 4.594 4.708 4.820 4.929 5.037 5.143 5.247 5.349 5.449 5.547 5.644 5.740 5.834 5.926 6.017 6.107 6.196 6.284 6.371 6.458 6.543 6.628 6.713 6.797 6.880 6.964 7.048 7.132 7.216 7.300 7.385 7.471 7.557 7.645 7.733 7.823 6.074
-1
J · mol -768.3 -766.6 -764.0 -760.5 -756.1 -750.8 -744.7 -737.7 -729.9 -721.2 -711.7 -701.4 -690.3 -678.4 -665.8 -652.4 -638.2 -623.4 -607.8 -591.5 -574.5 -556.8 -538.5 -519.5 -499.9 -479.6 -458.7 -437.2 -415.1 -392.4 -369.2 -345.4 -321.0 -296.1 -270.6 -244.7 -218.2 -191.2 -163.7 -135.7 -107.2 -78.30 -48.90 -19.04 11.27 42.03 73.23 104.9 136.9 169.4 202.4 235.7 269.5 303.7 338.3 373.3 408.8 444.6 480.9 517.7 554.8 592.4 630.4 668.8 707.7 0
∆H ) H(T/K) - H(298.15). b SWNTs. c MWNTs.
∆Sb -1
∆Hc
Cp,mc -1
J · K · mol -4.093 -4.071 -4.040 -4.000 -3.953 -3.899 -3.839 -3.774 -3.704 -3.630 -3.552 -3.471 -3.386 -3.299 -3.209 -3.116 -3.022 -2.925 -2.827 -2.727 -2.625 -2.522 -2.418 -2.313 -2.206 -2.099 -1.991 -1.882 -1.772 -1.662 -1.551 -1.439 -1.327 -1.215 -1.102 -0.989 -0.875 -0.761 -0.647 -0.533 -0.418 -0.303 -0.188 -0.073 0.043 0.158 0.274 0.390 0.506 0.623 0.739 0.856 0.973 1.090 1.207 1.324 1.442 1.559 1.677 1.796 1.914 2.033 2.152 2.272 2.391 0
-1
-1
J · K · mol 0.019 0.099 0.187 0.281 0.382 0.488 0.601 0.719 0.842 0.969 1.101 1.237 1.377 1.520 1.667 1.816 1.967 2.121 2.277 2.435 2.594 2.755 2.916 3.079 3.242 3.405 3.569 3.732 3.895 4.058 4.221 4.383 4.543 4.703 4.862 5.020 5.176 5.331 5.484 5.636 5.786 5.934 6.080 6.224 6.367 6.507 6.645 6.781 6.915 7.047 7.177 7.305 7.431 7.554 7.676 7.795 7.913 8.029 8.143 8.255 8.366 8.475 8.582 8.689 8.794 6.314
-1
J · mol -647.8 -647.5 -646.8 -645.6 -644.0 -641.8 -639.1 -635.8 -631.9 -627.3 -622.2 -616.3 -609.8 -602.6 -594.6 -585.9 -576.4 -566.2 -555.2 -543.4 -530.9 -517.5 -503.3 -488.3 -472.5 -455.9 -438.5 -420.2 -401.1 -381.3 -360.6 -339.1 -316.7 -293.6 -269.7 -245.0 -219.5 -193.2 -166.2 -138.4 -109.8 -80.55 -50.51 -19.75 11.73 43.91 76.80 110.4 144.6 179.5 215.1 251.3 288.1 325.6 363.7 402.3 441.6 481.5 521.9 562.9 604.4 646.5 689.2 732.4 776.1 0
∆Sc -1
J · K · mol-1 -3.091 -3.088 -3.081 -3.069 -3.052 -3.031 -3.006 -2.977 -2.944 -2.908 -2.867 -2.823 -2.776 -2.725 -2.670 -2.613 -2.553 -2.489 -2.423 -2.354 -2.282 -2.207 -2.130 -2.051 -1.969 -1.885 -1.799 -1.711 -1.621 -1.529 -1.435 -1.339 -1.241 -1.142 -1.041 -0.939 -0.835 -0.730 -0.623 -0.515 -0.406 -0.296 -0.184 -0.072 0.042 0.157 0.273 0.389 0.507 0.625 0.745 0.865 0.986 1.108 1.230 1.354 1.478 1.602 1.728 1.854 1.981 2.108 2.237 2.365 2.495 0
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For the MWNTs
Cp,m/J·K-1·mol-1 ) 0.3477X4 - 0.7319X3 - 0.4793X2 + 5.0884X + 4.521 (3) where T1 ) 80. 88 K, T2 ) 397.73 K, and the standard error of this fit is δ ) 0.014 J · K-1 · mol-1. Figure 3 shows that the changes in the molar heat capacity with respect to experimental temperature were different for the SWNTs and MWNTs. The molar heat capacity of the SWNTs is greater than that of the MWNTs when the temperature is smaller than about 275 K. The molar heat capacities of the SWNTs and the MWNTs are equal to about 5.64 J · K-1 · mol-1 at T ≈ 275 K, but when the temperature is greater than 275 K, the molar heat capacity of the SWNTs is smaller than that of the MWNTs. The smoothed molar heat capacities of the CNTs were calculated, respectively, on the basis of the fitted eqs 1 and 3, and the results are listed in Table 2. The changes in the thermodynamic functions of the CNTs, such as ∆H and ∆S, were also calculated, respectively, according to the following thermodynamic equations
∆H ) H(T/K) - H(298.15) )
∆S ) S(T/K) - S(298.15) )
T Cp,m dT ∫298.15
T ∫298.15
Cp,m dT T
(4)
(5)
The calculated changes in the thermodynamic functions of the CNTs, such as ∆H and ∆S, relative to standard to reference temperature, 298.15 K, are given in Table 2 at 5 K intervals.
Conclusions The thermodynamic properties of the CNTs were investigated in this article. The TG curves of the CNTs showed that the CNTs were stable over the temperature range (25 to 600) °C.
Figure 3. Curves of molar heat capacities of CNTs at different experimental temperatures. 4, SWNTs; O, MWNTs.
The TEM photos of the CNTs demonstrated that the CNTs were dispersed nanotubes (20 to 40) nm and (30 to 60) nm in diameter for the SWNTs and the MWNTs, respectively. The lowtemperature heat capacities of the CNTs were measured by adiabatic calorimetry. The molar heat capacity of the SWNTs is greater than that of the MWNTs when the temperature is less than about 275 K. The molar heat capacities of the SWNTs and the MWNTs are equal to about 5.64 J · K-1 · mol-1 at T ≈ 275 K, but when the temperature is greater than 275 K, the molar heat capacity of the SWNTs is smaller than that of the MWNTs. The function of the molar heat capacity with respect to thermodynamic temperature was established for the SWNTs and MWNTs, respectively. The thermodynamic functions were derived on the basis of the established function and the relationships of thermodynamic functions.
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JE900019F
