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Thermodynamic metric geometry and the Fisher-Widom line of simple fluids

Peter Mausbach1, Robin Fingerhut2, and Jadran Vrabec2,*

  • 1Plant and Process Engineering, Technical University of Cologne, 50678 Cologne, Germany
  • 2Thermodynamics and Process Engineering, Technical University of Berlin, 10587 Berlin, Germany

  • *vrabec@tu-berlin.de
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Phys. Rev. E 106, 034136 – Published 28 September, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.034136

Abstract

Two boundary lines are frequently discussed in the literature, separating state regions dominated by repulsion or attraction. The Fisher-Widom line indicates where the longest-range decay of the total pair correlation function crosses from monotonic to exponentially damped oscillatory. In the context of thermodynamic metric geometry, such a transition exists where the Ricci curvature scalar vanishes, R=0. To establish a possible relation between these two lines, R is worked out for four simple fluids. The truncated and shifted Lennard-Jones, a colloid-like and the square-well potential are analyzed to investigate the influence of the repulsive nature on the location of the R=0 line. For the longer-ranged Lennard-Jones potential, the influence of the cutoff radius on the R=0 line is studied. The results are compared with literature data on the Fisher-Widom line. Since such data are rare for the longer-ranged Lennard-Jones potential, dedicated simulations are carried out to determine the number of zeros of the total correlation function, which may provide approximate information about the position of the Fisher-Widom line. An increase of the repulsive strength toward hard sphere interaction leads to the disappearance of the R=0 line in the fluid phase. A rising attraction range results in the nonexistence of the Fisher-Widom line, while it has little effect on the R=0 line as long as it is present in the fluid state.

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Phys. Rev. E 106, 034136– Published 28 September, 2022
  • Received 1 June 2022
  • Accepted 12 July 2022
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