Thermodynamic modeling of carbon nanoparticle C32 heating in the nitrogen environment

Using computer thermodynamic modeling, the behavior of carbon nanoparticles was studied C32when heated in nitrogen atmosphere at pressure 105 Pa. Modeling was carried out using a software package TERRA. Experiment temperature range – from 273 to 3373 κ. A graph of the carbon balance in the system is constructed C32-N2, physical and chemical processes are described. The equilibrium constants of reactions with the allocation of temperature ranges are calculated and graphs of the dependence of the equilibrium constants of reactions on temperature are given.


Introduction
Knowledge of the temperature stability of carbon nanoparticles is necessary both for the development of technologies for the production and purification of carbon nanoparticles, and for their application [1].
Thermodynamic modeling consists in a thermodynamic analysis of the equilibrium state of the system as a whole [2].

Calculation Method
The calculations used the TERRA software package. Calculations of the phase composition and characteristics were carried out using the reference database [3][4][5][6].

Simulation results and discussion
In the range of 2373-2673 К there is an increase in the amount of C5N gases from 4% tо 84%. At a temperature of 2673 K, an inflection point is observed. In the temperature range from 2673 to 3373 K, the C5N content decreases and amounts to 28%. This is caused by a sharp increase in С3, СNС, С5 gases.
At high temperatures, an increase in other gases and a solid solution containing С28 is observed in the system, but their content, in comparison with others, is small and does not exceed 4%.
In the system under consideration, physicochemical processes occur, which can be divided into three groups, shown in Table 1. For the reaction equations given in Table 1, the equilibrium constants of the reactions of the С32-N2 system were calculated. The calculation was performed according to an analytical equation of the form where Ki is the equilibrium constant of reactions occurring in the С32-N2 system, Аi is coefficient affecting the position (shift) of lnKi relative to the reciprocal temperature, Bi is coefficient influencing the angle of inclination lnKi relative to the reciprocal temperature. The coefficients Аi and Bi of the reactions are calculated using the least squares method, coefficient of determination R 2 is determined and presented in Table 2.  Figure 2 (c) shows graphs of the dependences of the equilibrium constants of the reactions of the С32-N2 system on 1/T in the temperature range of 1873-3373 K (reaction numbers are given in Table 2).

Figure 2.
Graphs of the dependences of the equilibrium constants of reactions of the С32-N2 system on 1/T.
In Figure 2, the positions of the graphs show the magnitude and nature of the temperature dependence of the equilibrium constants of reactions. They are represented by analytical equation (1). In this equation, Аi is the coefficient that affects the position of the straight line relative to the axis of the abscissas. The larger this coefficient, the higher the graph is in the figure and the reaction is more strongly shifted towards the formation of reaction products.
The Bi coefficient indicates the angle of inclination between the reaction constant graph and the abscissas axis. The larger this coefficient, the stronger the reaction proceeds with increasing temperature.
The approximation values given in Table 2 indicate a deviation from a linear relationship. The percentage deviation for reactions 1 and 2 reaches 19%.

Conclusions
In this work, a computer experiment was conducted by the method of thermodynamic modeling to study the thermal properties of С32 carbon nanoparticles. Simulation data show that in the temperature range from 273 tо 973 К, the content of С32(s) carbon solid solution in the С32-N2 system is 100%, with a temperature increase, its percentage decreases. Most reactions occur at a temperature of 2073 K and higher. An analysis of the processes shows that С32 fullerene in a nitrogen atmosphere is thermally stable up to 2273 K. The main reaction products are gases C5N, C4N, С3, С5, CNC, and C2N2.