Thermodynamic Properties of Gaseous Plasmas in the Limit of Extremely Low Temperature

TL;DR

This paper investigates the zero-temperature and zero-density limit of gaseous plasma thermodynamics, revealing a universal stepped 'ionization stairs' structure in equations of state linked to binding energies and intrinsic energy scales.

Contribution

It demonstrates that in the zero-temperature limit, plasma thermodynamics universally form a stepped structure determined by binding energies, providing a basis for rigorous quasi-chemical modeling.

Findings

Universal stepped 'ionization stairs' structure in EOS at T→0

Thermodynamic parameters form a 'thermodynamic spectrum'

Limiting form explains shell oscillations in plasma EOS

Abstract

Limiting structure of thermodynamic functions of gaseous plasmas is under consideration in the limit of zero temperature and density. Remarkable tendency, which was claimed previously (Iosilevskiy and Gryaznov, 1985) is carried to extreme. Both equations of state, thermal and caloric ones obtain in this limit identical stepped structure ("ionization stairs") for plasma of any single element when this limit (T -> 0, n -> 0) is carried out at fixed value of chemical potential for electrons (or atoms). The same stepped structure is valid for plasma of mixtures or compounds. This structure appears within a fixed (negative) range of chemical potential of electrons bounded below by value of major ionization potential of element and above by the value depending on sublimation energy of substance. Binding energies of all possible bound complexes (atomic, molecular, ionic and clusters) in its ground state are the only quantities that manifest itself in meaningful details of this limiting picture as location and value of every step. The sublimation energy this collection ("intrinsic energy scale"). All thermodynamic differential parameters (heat capacity, compressibility, etc.) obtain their remarkable betta-like structures in the zero-temperature limit ("thermodynamic spectrum"). All "lines" of these "spectrum" are centralized just at the elements of the intrinsic energy scale. The limiting EOS stepped structure of gaseous zero-Kelvin isotherm is generic prototype of well-known "shell oscillations" in EOS of gaseous plasmas at low, but finite temperature. This limiting form of plasma thermodynamics could be used as a natural basis for rigorous deduction of quasi-chemical approach ("chemical picture") in frames of temperature (not density!) asymptotic expansion around this reference system.