Crossover Equation of State Models Applied to the Critical Behavior of Xenon

• Published in: Journal of statistical physics 2015-03, Vol.158 (6), p.1379-1412
• Main Authors: Garrabos, Y., Lecoutre, C., Marre, S., Guillaument, R., Beysens, D., Hahn, I.
• Format: Article
• Language: English
• Subjects: Chemical Sciences; Material chemistry; Mathematical and Computational Physics; Physical Chemistry; Physics; Physics and Astronomy; Quantum Physics; Statistical Physics and Dynamical Systems; Theoretical
• ISSN: 0022-4715; 1572-9613
• DOI: 10.1007/s10955-014-1157-x

The turbidity ( τ ) measurements of Güttinger and Cannell (Phys Rev A 24:3188–3201, 1981 ) in the temperature range 28 mK ≤ T - T c ≤ 29 K along the critical isochore of homogeneous xenon are reanalyzed. The singular behaviors of the isothermal compressibility ( κ T ) and the correlation length ( ξ ) predicted from the master crossover functions are introduced in the turbidity functional form derived by Puglielli and Ford (Phys Rev Lett 25:143–146, 1970 ). We show that the turbidity data are thus well represented by the Ornstein–Zernike approximant, within 1 % precision. We also introduce a new crossover master model (CMM) of the parametric equation of state for a simple fluid system with no adjustable parameter. The CMM model and the phenomenological crossover parametric model are compared with the turbidity data and the coexisting liquid–gas density difference ( Δ ρ L V ). The excellent agreement observed for τ , κ T , ξ , and Δ ρ L V in a finite temperature range well beyond the Ising-like preasymptotic domain confirms that the Ising-like critical crossover behavior of xenon can be described in conformity with the universal features estimated by the renormalization-group methods. Only 4 critical coordinates of the vapor–liquid critical point are needed in the (pressure, temperature, molecular volume) phase surface of xenon.