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Pair correlation function decay in models of simple fluids that contain dispersion interactions.

R Evans1, J R Henderson

  • 1H H Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|August 12, 2011
PubMed
Summary

Dispersion forces in fluids significantly alter correlation function decay. A new pseudo-exponential pole explains complex decay patterns and reveals a pseudo-Fisher-Widom line, crucial for understanding wetting transitions.

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Area of Science:

  • Statistical Mechanics
  • Soft Matter Physics
  • Physical Chemistry

Background:

  • Inter-particle potentials in real fluids are often dominated by attractive dispersion forces, decaying as -r(-6).
  • The direct correlation function's Fourier transform, [Formula: see text], typically exhibits a pole at q=iα(0) for short-ranged potentials, leading to monotonic-exponential decay of the pair correlation function h(r).
  • Understanding the long-range behavior of h(r) is critical for describing fluid properties and phase transitions.

Purpose of the Study:

  • To investigate the impact of -r(-6) decaying potentials on the intermediate- and longest-range decay of the total pair correlation function h(r).
  • To analyze the analytic structure of [Formula: see text] and identify new features introduced by dispersion forces.
  • To determine the implications of these findings for fluid behavior near critical points and for wetting phenomena.

Main Methods:

  • Analysis of the analytic structure of the Fourier transform of the direct correlation function, [Formula: see text], for -r(-6) potentials.
  • Application of the random phase approximation for explicit calculations of h(r).
  • Identification and characterization of a pseudo-Fisher-Widom (pFW) line.

Main Results:

  • The -r(-6) tail replaces the pure imaginary pole with a complex (pseudo-exponential) pole at q=iα(0)+α(1), where α(1) is negative and small.
  • Near the critical point, α(1)∼-α(0)(2), recovering classical Ornstein-Zernike behavior.
  • A pseudo-Fisher-Widom (pFW) line is determined, delineating regions with distinct decay behaviors of h(r): exponentially damped-oscillatory and power-law decay on the high-density side, and sub-dominant damped-oscillatory decay on the low-density side.

Conclusions:

  • The presence of dispersion forces fundamentally alters the analytic structure of correlation functions, leading to previously unidentified pseudo-exponential poles and a pFW line.
  • These findings provide a more accurate description of fluid correlations, especially near critical points and in the context of wetting.
  • The identified pseudo-exponential pole introduces additional terms into the wetting potential, influencing the existence and order of wetting transitions in real fluids.