Beyond equilibrium thermodynamics in the low temperature plasma processor

Abstract

Low temperature plasmas are open driven thermodynamic systems capable of increasing the free energy of the mass that flows through them. An interesting thing about low temperature plasmas is that different species have different temperatures at the same location in space. Since thermal equilibrium cannot be assumed, many of the familiar results of equilibrium thermodynamics cannot be applied in their familiar form to predict, e.g., the direction of a chemical reaction. From the perspective of classical processing governed by thermal equilibrium, examples of highly unexpected gas-phase chemical reactions (CO2 dissociation, NO, N2H4, O3 synthesis) and solid material transformations (surface activation, size-focusing, and hyperdoping) promoted by low temperature plasmas are presented. The lack of a known chemical reaction equilibrium criterion prevents assessment of predictive kinetics models of low temperature plasmas, to ensure that they comply with the laws of thermodynamics. There is a need for a general method to predict chemical reaction equilibrium in low temperature plasmas or an alternative method to establish the thermodynamic admissibility of a proposed kinetics model. Toward those ends, two ideas are explored in this work. The first idea is that chemical reactions in low temperature plasmas proceed toward a thermal equilibrium state at an effective temperature intermediate between the neutral gas temperature and the electron temperature. The effective temperature hypothesis is simple, and surprisingly is adequate for elucidation in some systems, but it lacks generality. The general equation for nonequilibrium reversible–irreversible coupling (GENERIC) is a general beyond equilibrium thermodynamics framework that can be used to rigorously establish the thermodynamic admissibility of a set of dynamic modeling equations, such as a kinetic model, without knowledge of the final state that the system is tending toward. The use of GENERIC is described by way of example using a two-temperature hydrodynamic model from the literature. The conclusion of the GENERIC analysis presented in this work is that the concept of superlocal equilibrium is thermodynamically admissible and may be applied to describe low temperature plasmas, provided that appropriate terms are included for exchange of internal energy and momentum between different species that may have different temperatures and bulk velocities at the same location in space. The concept of superlocal equilibrium is expected to be of utility in future work focused on deriving equilibrium criteria for low temperature plasmas.