QUANTUM AND DIMENSIONAL EFFECTS IN CARBON NANOMATERIALS 1
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N. A.Vinnikov , A. V. Dolbin , V. B. Esel'son , V. G. Gavrilko , V. G. Manzhelii , S. N. Popov , B. Sundqvist 1
B. Verkin Institute for Low Temperature Physics and Engineering, 47 Lenin Ave., 61103 Kharkov, Ukraine 2 Department of Physics, Umea University, SE - 901 87 Umea, Sweden
At present the development, property investigations and commercial applications of new carbon nanosystems are among the top priority trends of the world science and sciencebased technologies. Recently the authors have obtained fundamentally novel results pointing to a quantum character of carbon nanosystems at low temperatures. They are as follows. 1. A negative thermal expansion of fullerite has been observed at low temperatures, which suggests the tunnel origin of the rotational states of C60 molecules. Impurities introduced into the voids of the C60 lattice affect drastically both the magnitudes and the sign of the thermal expansion of the system [1]. 2. Quantum diffusion of 3He, 4He, Ne atoms and H2 molecules in C60 has been detected by investigating the sorption – desorption kinetics of gases at low temperature [2-4]. The method was a direct measurement of the pressure of these gases contacting a C60 powder in a closed volume. 3. An isotopic effect has been detected in the investigation of the thermal expansion of C60 doped with methane and deuteromethane. The effect is caused by the tunnel rotation of the CH4 and CD4 molecules in the octahedral interstitials of the C60 lattice [5]. 4. The low temperature coefficient of the thermal expansion of bundles of single-walled carbon nanotubes in the radial direction has been measured for the first time [6]. Negative values of the thermal expansion were observed be low 5.5 K. This novel phenomenon is a manifestation of the lowest-frequency part of the vibrational spectrum of nanotubes at low temperatures. The spectrum is characterized by a negative Gruneisen coefficient, which is typical of bending vibrations of two – dimensional systems. As the temperature increases above 5.5 K, the negative values of the thermal expansion typical for two-dimensional systems change into positive ones characteristics of three-dimensional objects. 5. Saturation of nanotube bundles with gas impurities triggers an intensive increase in the radial thermal expansion of bundles of carbon nanotubes, which is attributed to the influence of the gas impurity molecules on the bending vibrations of the system. Because of the geometrical features of SWNT bundles, their saturation with an impurity leads to the formation of one-dimensional chains of the impurity molecules in the grooves of the bundles. This structural reordering of the impurity molecules produces a peak in the temperature dependence of the radial thermal expansion coefficient [7]. 6. Experimental evidence has been obtained for the first time which suggests tunneling of 4He and 3He atoms in bundles of single-walled carbon nanotubes [8,9]. This results in a considerable increase in the magnitudes of the negative radial thermal expansion of the 4He-SWNT and 3He-SWNT systems at T<3.7 and 7K, respectively. An unexpectedly large isotopic effect has been observed due to the higher probability of tunneling of 3He atoms. The results obtained point to the importance of the influence of quantum effects upon the structure and properties of new carbon nanomaterials. The above results lead us to expect that a controllable introduction of impurities (including quantum ones) will enable modification of the properties of carbon nanosystems in a wide temperature interval. Following illustrations briefly demonstrate our results.
Our experimental setup Low temperature capacitance dilatometer 11 1
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Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with 3He
Large negative values of Gruneisen coefficient are strong evidence for the tunneling nature of the negative thermal expansion
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ΔCCD4, J/K mol
-1 -5
α, 10 ,K
0.6 0.4
C60+50% CH4
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Т, K
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T, K
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The ΔСCD4 contribution in heat capacity of CD4-C60 solution
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T, K
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Temperature dependence of the thermal expansion coefficients of Kr-doped fullerite С60
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The temperature dependence of the 4He and 3He diffusion coefficients in fullerite С60
Pure C60
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Doped C60
-50 -100
γ
-150 -200
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l2 D≈ _ 6τ
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He
He
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T,K
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Rotational tunnelling of C60 molecules can lead to a negative Gruneisen coefficients and negative thermal expansion [A. N. Aleksandrovskii, A. S. Bakai, A. V. Dolbin, et al. Low Temp. Phys. 29, 324 (2003)]
The measurement was made on (1) heating (▲,●) and (2) cooling ( ) the sample (3) – pure C60 (heating and cooling).
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Tetrahedral cavities Octahedral cavities
He 10
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T, К 3Не
(filled symbol); 4Не (open symbol); circle – octahedral interstitial site, square – tetrahedral interstitial site)
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C60+50% CD4
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- 3Не - SWNT, molar 3He concentration ~9.4%; - 3Не – SWNT, after a partial removal of the 3He impurity at 11 К; 1 -4Не - SWNT, molar 4He concentration 9.4% ;2 - Н2- SWNT;3 - Хe-SWNT; 4 - pure SWNT .
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C tr (E=112.6K) C lib (E=51 K) C tunn C calc
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ΔC(CD4) experiment
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D, cm /s
CH4 molecules
Pure С60
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Resolution - 2⋅10-9 см.
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Low temperature part of dilatometer: 1-the coaxial line, 2, 11 - the vacuum wire , 3 - the housing of the small movings sensor, 4 - the sylphon, 5 - the sapphire tip of a stock, 6 - the thermal switch, 7 - the differential thermocouple, 8 - the heater, 9- the cold wire of the thermal switch, 10 - the metal housing, 12 - the timing screw, 13 - the springs, 14 - the capacitive sensor of the small movings, 15 - the membrane block, 16 - the copper stock, 17 - the sapphire hemisphere, 18 - the investigated sample, 19 - the thermometers, 20 - the sapphire stage, 21 - aluminium foil, 22 - sapphire pyramids.
The impurities CH4 and CD4 substantially decrease the thermal expansion coefficients compared with the values of for pure fullerite. The effect is much stronger in the system CH4–C60. The observed feature is attributed to the contribution of tunneling СН4 rotation of CH4 and CD4 molecules localized in СD4 octahedral interstices of the crystal lattice of fullerite C60 to the thermal expansion of the solutions. The tunneling probability is higher for
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α, 10 K
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1. Yu.A.Freiman, Fiz.Nizk.Temp., v.9, 657 (1983) 2. F.W. Sheard, In: AIP Conference Proceedings, №3, Thermal Expansion - 1971, Eds. : M.G. Graham, H.E. Hagy, N.Y. , pp. 151-154 (1972)
αr , 10 K
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‐ average С60 crystal grain size (~1 um); τ ‐ diffusion characteristic time As the temperature is lowered from 292 K to 79.3 K, the diffusion coefficients reduce, which indicates a predominance of thermally activated diffusion of helium in C60. On a further decrease to T = 10 K the diffusion coefficients increase over an order of magnitude. Below 8 K the diffusion coefficients are temperature-independent. This suggests a tunnel character of 4He and 3He diffusion in C60.
Квантовая диффузия в нерегулярных кристаллах / Ю. М. Каган, Л. А. Максимов, 39 с. табл. 21 см, М. ИАЭ 1983
References [1] A.N. Aleksandrovskii et al, Low temperature thermal expansion of pure and inert gas-doped C60, Fiz. Nizk. Temp. 29, 432 (2003) [Low Temp. Phys. 29, 324(2003)]. [2] A. V. Dolbin et al, Kinetics of 4He gas sorption by fullerite C60. Quantum effects. Fiz. Nizk. Temp. 36, 1352 (2010), [Low Temp. Phys. 36, 1091 (2010)]. [3] A. V. Dolbin et al, Kinetics of the Sorption of 3He by C60 Fullerite. The Quantum Diffusion of 3He and 4He in Fullerite. JETP Letters, 93, pp. 577–579 (2011) [4] A. V. Dolbin et al, Diffusion of H2 and Ne impurities in fullerite C60. Quantum effects Fiz. Nizk. Temp. 38, (2012) (to be published). [5] A. V. Dolbin et al, Thermal expansion of deuterium methane solutions in fullerite C60 at low temperatures. Isotopic effect, Fiz. Nizk. Temp. 35, 299 (2009) [Low Temp. Phys. 35, 226 (2009)]. [6] A.V. Dolbin et al, Radial thermal expansion of single-walled carbon nanotube bundles at low temperatures. Fiz. Nizk. Temp. 34, 860 (2008). [Low Temp. Phys. 34, 678 (2008)]. [7] A. V. Dolbin et al, Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures. Fiz. Nizk. Temp. 35, 613 (2009) [Low Temp. Phys. 35, 484 (2009)]. [8] A. V. Dolbin et al, Quantum effects in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with 4He.Fiz. Nizk. Temp. 36, 797 (2010) [Low Temp. Phys. 36, 635 (2010)]. [9] A. V. Dolbin et al, Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with 3He. A giant isotope effect. Fiz. Nizk. Temp. 37, 685 (2011) [Low Temp. Phys. 37, 544 (2011)].