skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Isomorphism in Fluid Phase Diagrams: Kulinskii Transformations Related to the Acentric Factor

Abstract

For a wide class of molecular fluids, the temperature-density phase diagrams exhibit two prominent generic properties: a nearly linear locus, termed the Zeno line, along which the compressibility factor, Z = P/rho RT = 1 (same as an ideal gas), and the widely arching border of the vapor-liquid coexistence region, termed the binodal curve, with gas and liquid branches meeting at the critical point. The Zeno and binodal loci have been known for more than a century, yet only during the past two decades were striking empirical correlations between them recognized. Recently, Kulinskii introduced a remarkably simple projective transformation, wherein the linearity of the Zeno line and its relation to the binodal curve are geometrical consequences of an approximate isomorphism of the fluid with a venerable theoretical model, the lattice gas (equivalent to the Ising spin model). Here we show the Kulinskii transformation is significantly improved in accuracy and scope by using as input, in place of the lattice gas, the original van der Waals equation or simulation results for the Lennard-Jones potential. Moreover, the key parameters in these transformations can be expressed in terms of the acentric factor, introduced by Pitzer to extend corresponding states.

Authors:
;
Publication Date:
Sponsoring Org.:
USDOE Advanced Research Projects Agency - Energy (ARPA-E)
OSTI Identifier:
1211180
DOE Contract Number:  
DE-AR0000170
Resource Type:
Journal Article
Journal Name:
Journal of Physical Chemistry. C
Additional Journal Information:
Journal Volume: 117; Journal Issue: 43; Journal ID: ISSN 1932-7447
Country of Publication:
United States
Language:
English

Citation Formats

Wei, Q, and Herschbach, DR. Isomorphism in Fluid Phase Diagrams: Kulinskii Transformations Related to the Acentric Factor. United States: N. p., 2013. Web. doi:10.1021/jp403307g.
Wei, Q, & Herschbach, DR. Isomorphism in Fluid Phase Diagrams: Kulinskii Transformations Related to the Acentric Factor. United States. https://doi.org/10.1021/jp403307g
Wei, Q, and Herschbach, DR. 2013. "Isomorphism in Fluid Phase Diagrams: Kulinskii Transformations Related to the Acentric Factor". United States. https://doi.org/10.1021/jp403307g.
@article{osti_1211180,
title = {Isomorphism in Fluid Phase Diagrams: Kulinskii Transformations Related to the Acentric Factor},
author = {Wei, Q and Herschbach, DR},
abstractNote = {For a wide class of molecular fluids, the temperature-density phase diagrams exhibit two prominent generic properties: a nearly linear locus, termed the Zeno line, along which the compressibility factor, Z = P/rho RT = 1 (same as an ideal gas), and the widely arching border of the vapor-liquid coexistence region, termed the binodal curve, with gas and liquid branches meeting at the critical point. The Zeno and binodal loci have been known for more than a century, yet only during the past two decades were striking empirical correlations between them recognized. Recently, Kulinskii introduced a remarkably simple projective transformation, wherein the linearity of the Zeno line and its relation to the binodal curve are geometrical consequences of an approximate isomorphism of the fluid with a venerable theoretical model, the lattice gas (equivalent to the Ising spin model). Here we show the Kulinskii transformation is significantly improved in accuracy and scope by using as input, in place of the lattice gas, the original van der Waals equation or simulation results for the Lennard-Jones potential. Moreover, the key parameters in these transformations can be expressed in terms of the acentric factor, introduced by Pitzer to extend corresponding states.},
doi = {10.1021/jp403307g},
url = {https://www.osti.gov/biblio/1211180}, journal = {Journal of Physical Chemistry. C},
issn = {1932-7447},
number = 43,
volume = 117,
place = {United States},
year = {Thu Oct 31 00:00:00 EDT 2013},
month = {Thu Oct 31 00:00:00 EDT 2013}
}