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Computing the starting state for Gibbs-Duhem integration.

A van 't Hof1, S W de Leeuw, C J Peters

  • 1Physical Chemistry and Molecular Thermodynamics, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands.

The Journal of Chemical Physics
|February 14, 2006
PubMed
Summary

This study assesses methods for computing initial values for Gibbs-Duhem integration in chain molecule mixtures. The Npbeta+test molecule method and overlapping-distributions difference method are highlighted for accurate vapor-liquid equilibria calculations.

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Area of Science:

  • Thermodynamics
  • Physical Chemistry
  • Computational Chemistry

Background:

  • Gibbs-Duhem integration requires initial values for numerical integration of the Clapeyron equation.
  • Accurate computation of these initial values is crucial for applying Gibbs-Duhem integration across diverse systems and conditions.
  • Vapor-liquid equilibria in binary mixtures of chain molecules present specific challenges.

Purpose of the Study:

  • To investigate and assess methods for computing the initial coexistence point and initial slope of the Clapeyron equation for Gibbs-Duhem integration.
  • To introduce and evaluate the Npbeta+test molecule method with overlapping distributions for determining the initial coexistence point.
  • To compare different methods for calculating the initial slope of the Clapeyron equation, focusing on reliability and applicability.

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Main Methods:

  • NVbeta Gibbs ensemble and the novel Npbeta+test molecule method with overlapping distributions for initial coexistence point calculation.
  • Widom method, overlapping-distributions difference method, and a difference method for computing the initial slope of the Clapeyron equation.
  • Development of a new bias method for efficient composition sampling in semigrand-canonical simulations of chain molecules.

Main Results:

  • The Npbeta+test molecule method with overlapping distributions is applicable where the NVbeta Gibbs ensemble fails, despite higher computational cost.
  • The Widom method and overlapping-distributions difference method yield correct initial slope values.
  • The overlapping-distributions difference method is identified as the most reliable for determining the initial slope due to result reliability assessment.
  • The new bias method significantly improves composition sampling for chain molecules in simulations.

Conclusions:

  • The Npbeta+test molecule method and overlapping-distributions difference method provide robust approaches for obtaining necessary initial values for Gibbs-Duhem integration.
  • The developed bias method enhances computational efficiency for simulating complex molecular systems.
  • These advancements facilitate more accurate and reliable thermodynamic property predictions for mixtures of chain molecules.