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

Abstract

The turbidity (\(\tau \)) measurements of Güttinger and Cannell (Phys Rev A 24:3188–3201, 1981) in the temperature range \(28\,\text {mK}\le T-T_{c}\le 29\,\text {K}\) along the critical isochore of homogeneous xenon are reanalyzed. The singular behaviors of the isothermal compressibility (\(\kappa _{T}\)) and the correlation length (\(\xi \)) 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 (\(\Delta \rho _{LV}\)). The excellent agreement observed for \(\tau \), \(\kappa _{T}\), \(\xi \), and \(\Delta \rho _{LV}\) 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.