Calculation of two-temperature plasma composition: II. Consideration of condensed phases

Abstract

The assumption of gaseous species is not always valid in non-LTE plasmas. This requires the consideration of condensed phases in the determination of plasma composition. In this work, we compare two methods for calculating 2T multi-phase plasma composition: the Gibbs free energy minimization method and the entropy maximization method. The latter method is first reported in this work and has the same power as the former method for the calculation of 2T plasma composition taking into account condensed species. Based on these two methods, we present a case study of the multi-phase compositions of N2–Cu, CO2–Cu, and C2F4–Cu plasmas. It is found that the 2T entropy maximization method is less sensitive to the non-equilibrium degree than the 2T Gibbs free energy minimization method. This leads to the large difference between the composition predicted by the two methods, for example, in the phase transition temperature. The case study shows that due to the high electron temperature at large non-equilibrium degree, the ionic species (e.g. Cu+ and C+) can be generated directly from the condensed species (e.g CuF2, Cu2O, Cu, and C). Such ionization does not occur if the copper proportion is very low (e.g only 1%).

Graphite production in two‐temperature non‐LTE plasmas of C4F7N and C5F10O mixed with CO2, N2, and O2 as eco‐friendly SF6 replacements: A numerical study

“…To numerically investigate the formation of condensed phases in arc plasmas (or more generally, thermal plasmas), the essential first step is the calculation of plasma compositions that describe the concentration of species in a plasma, given the plasma state defined by temperature, pressure, volume, and so forth. [ 22 ] For a thermal plasma in the LTE state, there are two commonly used methods of calculating plasma compositions, that is, the methods of mass action law and the Gibbs free energy minimization, respectively, both of which have been verified to be equal in results. [ 23 ] However, for a non‐LTE thermal plasma, due to the complex coupling of the translational kinetic energy between electrons and heavy particles, it is rather difficult to calculate plasma compositions as accurately as for an LTE plasma.…”

“…In a 2T plasma, the distributions of electrons and heavy particles are assumed to be Maxwellian, which are characterized by electron temperature T e and heavy particle temperature T h . According to the work by Zhong et al, [ 22 ] the methods for calculating 2T plasma compositions can be classified into two categories: mass action law methods and extremum searching methods. The former methods include the two described by Potapov [ 24 ] and van de Sanden et al's [ 25 ] mass action laws, respectively.…”

“…In these two methods, plasma compositions are obtained by searching for an extremum in which the corresponding plasma system reaches the minimum Gibbs free energy or maximum entropy. Previous work [ 28 ] showed that the 2T entropy maximization method is less sensitive to the nonequilibrium degree than the 2T Gibbs free energy minimization method, which results in largely different compositions when plasmas depart from thermal equilibrium. Both numerical and experimental works indicate that large difference between T e and T h is rather common in the near‐electrode regions or the arc fringes.…”

“…According to the equilibrium criterion, a thermodynamic system, given temperature and pressure, will reach equilibrium only when the Gibbs free energy G of this system reaches a minimum, which means the differential of G equals zero, that is, d G = 0. [ 28 ] As a result, the plasma compositions can be obtained by searching for the minimum value of G for a plasma system without explicitly defining any chemical reactions, for example, dissociation and ionization. This means the plasma composition computation is converted to an extremum problem, which can be numerically solved by the classical optimization algorithms, for example, the Newton–Raphson method.…”

“…[ 30 ] In such algorithms, the Lagrange multipliers are usually used to construct a nonlinear equation system representing Gibbs free energy minimization, chemical equilibrium, electrical neutrality, and Dalton's law. [ 28 ] As there have been a certain amount of previous works on the optimization algorithms for obtaining plasma compositions, [ 30–33 ] this study does not introduce the implementation of the algorithms in detail. Instead, we focus on how to calculate the Gibbs free energy of a plasma system with various mixtures using the parameters we can obtain from literature or by computation.…”