Gibbs-Duhem integration

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History

The so-called Gibbs-Duhem Integration referes to a number of methods that couple molecular simulation techniques with thermodynamic equations in order to draw phase coexistence lines.

The method was proposed by Kofke (Ref 1-2).

Basic Features

Consider two thermodynamic phases: $\alpha ,\beta$, at thermodynamic equilibrium at certain conditions. The thermodynamic equilibrium implies:

• Equal temperature in both phases: $T=T_{\alpha }=T_{\beta }$, i.e. thermal equilbirum.
• Equal pressure in both phases $p=p_{\alpha }=p_{\beta }$, i.e. mechanical equilbrium.
• Equal chemical potentials for the components $\mu _{i}=\mu _{i\alpha }=\mu _{i\beta }$, i.e. material equilibrium.

In addition if we are dealing with a statistical mechanics model, with certain parameters that we can represent as $\lambda$ , the model should be the same in both phases.

Example: phase equilibria of one-compoment system

• Consider that at given conditions of $T,p,\lambda$ two phases of the systems are at equlibrium

References

1. David A. Kofke, Gibbs-Duhem integration: a new method for direct evaluation of phase coexistence by molecular simulation, Mol. Phys. 78 , pp 1331 - 1336 (1993)
2. David A. Kofke, Direct evaluation of phase coexistence by molecular simulation via integration along the saturation line, J. Chem. Phys. 98 ,pp. 4149-4162 (1993)