THERMODYNAMIC PROPERTIES OF FULLERENE NANOSTRUCTURES IN THE RANGE FROM T→ 0 TO 670 K AT STANDARD PRESSURE / ТЕРМОДИНАМИЧЕСКИЕ СВОЙСТВА ФУЛЛЕРЕНОПОДОБНЫХ НАНОСТРУКТУР В ОБЛАСТИ ОТ Т→ 0 ДО 670 К И СТАНДАРТНОМ ДАВЛЕНИИ

Belousov V.P. *, Smirnova N.N.(1), Markin A.V.(1)
Research Institute for Laser Physics, St-Petersburg, 199034, Russia Chemistry Institute, Nizhnii Novgorod State University, 603950, Nizhnii Novgorod, Russia

An unique structure and an exceptional world-while application in practice of fullerene and fullerene structures brought about their continuous intensive research. It was established that trans-formation reactions of graphite to polyhedral clus¬ters of carbon (fullerenes) are nonspontaneous and proceed only under external influence (laser irra¬diation, electric discharge). As a result of synthe¬sis, in all cases a cluster mixture where the number of carbon atoms varies from 32 to 100 and more is formed from a hot carbon plasma [1]. It is worth of note that the total yield of fullerenes is only 0.3 mass % of the graphite used. At present, the meth¬ods of isolation of separate clusters from the treat¬ment products of graphite rods (cathode and anode 'growths') are developed. As a result, on varying the synthesis conditions, the isolation of such phases as multilayer nanotubes and astralenes was successful.
Up to now, precision calorimetric studies of nanotubes and astralenes were not performed. It is difficult to overestimate the urgency and impor¬tance of fundamental thermodynamic data. They can be used in calculations and for the optimization of processes of their preparation and separation. .
In this connection, the goal of the given work is to study the temperature dependence of heat ca¬pacity of nanotube and astralene in the range 6-670 K, to calculate from the data the standard thermodynamic functions Cop (T), Ho (T) - Ho (0) , So (T) and Go (T) - Ho(0) over the range from T→0 to 670 K, to determine fractal dimensions D for them in the heat capacity function of fractal variant of Debye's theory of heat capacity of solids [2], to calculate the standard entropy of formation of crystal astralene and nanotube from graphite at 298.15 K.

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Samples and apparatus

The astralene and nanotube samples were iso¬lated from the treatment products of graphite rods under quasi-stationary conditions in an arc dis¬charge [3]. Further the composition and structure of the samples were examined by microphotography and spectroscopy methods. The appropriate data will be presented in detail in the paper. .
Temperature dependences of the heat capacity were examined in a BKT-3.0 completely auto-mated adiabatic vacuum calorimeter [4] with a dis¬crete heating over the range 6-350 K and an ADKTTM [5] high-precision dynamic calorimeter operating by the principle of triple thermal bridge between 300 and 670 K. As the analysis of calibra¬tion and testing results showed, an uncertainty of Cop measurements at helium temperatures is ±2%, in the range 40-80 K ±0.5%, from 80 to 350 K ±0.2% and within to ±1.5% between 350 and 670 K. As to transition temperatures, the uncertainties are 0.02 K over the range 6-350 K and ±0.2 K be¬tween 350 and 670 K.

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Results and discussion

The heat capacity of astralene (I) and nano-tube (II) increases smoothly with rising tempera¬ture and has no irregular changes and peculiarities. The numerical values of the heat capacity for (I) and (II) virtually coincide within an experimental uncertainty of its determination. Only between 140 and 340 K Cop of (II) is somewhat higher than that of (I) that can be explained with different excita-tion of vibration degrees of freedom of the molecu¬lar skeleton. At T~560 K the heat capacity of both objects stops to depend on temperature. .
It was of interest to treat the low-temperature heat capacity of the objects under study on the base of the multifractal generalization of Debye's theory of the heat capacity of solids. According to the lat¬ter, for solids with a chain structure the relation Cop vs. T at lower temperatures is proportional to T1, in the case of a layer structure to T2 and for a spatial one to T3.In the fractal theory of heat capac¬ity the exponent of T in the heat capacity function (D) is called the fractal dimension. D can be evalu¬ated from the experimental data on the temperature dependence of heat capacity from the slope of the corresponding linear sections of the plot ln Cv against lnT. This follows, in particular, from the equation: .

where N is the number of particles in a molecule, k - the Boltzmann constant, y(D + 1) - y-function, ( D + 1) - the Riemann ^-function, Qmax - the char¬acteristic temperature and D is the fractal dimen¬sion that can be from 1 to 4. The determination procedure of D is described in [2]. For (I) and (II) it was found by eq. (1) that in the range 20-50 K D=2.6 and this corresponds to some structure in¬termediate between layer and spatial ones.
From the data on the temperature dependence of the heat capacity for crystalline astralene and nanotube their thermodynamic functions were cal¬culated in the range from T->0 to 670 K. The en-thalpy Ho(T)-H°(0) and entropy So (T) were estimated by the numerical integration of the rela¬tions Co =f (Т) and Co =f (lnТ) with respect to temperature. The Gibbs function Go(T)-H°(0) was calculated from the values of Ho (T) -H°(0) and So(T) at corresponding temperatures. At T=298.15 K and standard pressure their numerical values are listed in Table. The procedure of the function calculation is demonstrated elsewhere [6]. It should be noted here that in the calculation of the functions from the temperature of the measurement onset to 0 K the known Debye formula was used:

where D - Debye function of the heat capacity; n and eD are adjustable parameters with which eq. range 0-15 K with an uncertainty not exceeding 2 %.
From the absolute values of entropies for car¬bon in the form of graphite, astralene and nanotube their standard entropies of formation at T=298.15 K were calculated. It was found that ASof (I) = -0.079 J/K mol and ASof (II) = 0.5710 J/K mol.

The work was carried out with the financial sup¬port of the Ministry of Science, Industry and Tech-nology of RF.