On the calculation of equilibrium thermodynamic properties and the establishment of statistical-thermodynamically-consistent finite bound-state partition functions in nonideal multicomponent plasma mixtures within the chemical model

Abstract

The problem of the calculation of equilibrium thermodynamic properties and the establishment of statistical-thermodynamically consistent finite bound-state partition functions in nonideal multicomponent plasma systems is revised within the chemical picture. The present exploration accompanied by the introduction of a generalized consistent formulation, in terms of the solution of the inverse problem, clears ambiguities and gives a better understanding of the problem on top of pointing out weaknesses and inaccuracies/inconsistencies buried in widely used models in literature.

Equation-of-state, critical constants, and thermodynamic properties of lithium at high energy density

“…This minimization can be achieved iteratively through using optimization algorithms [12][13][14] or by casting the set of minimization Page6 equations, analytically, into the form of nonideal Saha-like equations which can then be solved using techniques and algorithms developed for this purpose [15,16]. A brief discussion of the advantages and disadvantages of both techniques for the minimization of the function can be found in [17].…”

“…The evaluation of the internal partition function for the composite structured particles has been thoroughly discussed and investigated in Refs [17,[29][30][31][32]]. An essential concern in modeling thermodynamic equilibrium at high density is associated with the need to consistently and smoothly truncate the internal partition functions of the ensemble of bound states.…”

Tables of equation-of-state, thermodynamic properties, and shock Hugoniot for hot dense fluid deuterium

“…The model takes into consideration the dissociation equilibrium of diatomic molecules and ionization equilibrium of dissociated species with special interest given to the phenomena of pressure dissociation and pressure ionization. The model also implements a recently proposed formulation for the establishment of statistical-thermodynamically-consistent finite electronic partition functions [35][36][37] where an occupational probability is prescribed in advance to assure a smooth truncation of the electronic partition function and manifestation of the phenomenon of pressure ionization. A similar formulation and analogous occupational probability is also introduced and used to smoothly truncate the vibrational-rotational molecular partition function of deuterium molecules.…”

Response to “Comment on ‘On the ionization equilibrium of hot hydrogen plasma and thermodynamic consistency of formulating finite partition functions’ ” [Phys. Plasmas 17, 124705 (2010)]

“…Nevertheless, we find this to be completely irrelevant as we do not use such an approximation, and in fact we strongly criticized it in Ref. 7 showing that it wipes out the basic requirement of the dependence of w k on the individual excited states.…”

“…It is important also to note that in Ref. 7, we showed also mathematically that for the case of a separable F conf , statistical-thermodynamic consistency requires the IPF to be independent of the occupation numbers with no guarantee of the finiteness of the IPF in such a case.…”