Gibbs-Duhem integration: Difference between revisions
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* Equal temperature in both phases: <math> T = T_{\alpha} = T_{\beta} </math>, i.e. thermal equilbirum. | * Equal temperature in both phases: <math> T = T_{\alpha} = T_{\beta} </math>, i.e. thermal equilbirum. | ||
* Equal pressure in both phases <math> p = p_{\alpha} = p_{\beta} </math>, i.e. mechanical equilbrium. | * Equal pressure in both phases <math> p = p_{\alpha} = p_{\beta} </math>, i.e. mechanical equilbrium. | ||
* Equal chemical potentials for the components <math> \mu_i = \mu_{i\alpha} = \mu_{i\beta} </math>, i.e. | * Equal chemical potentials for the components <math> \mu_i = \mu_{i\alpha} = \mu_{i\beta} </math>, i.e. ''material'' equilibrium. | ||
In addition if we are dealing with a statistical mechanics model, with certain parameters that we can represent as <math> \lambda </math> , the | In addition if we are dealing with a statistical mechanics model, with certain parameters that we can represent as <math> \lambda </math> , the | ||
Revision as of 11:34, 2 March 2007
CURRENTLY THIS ARTICLE IS UNDER CONSTRUCTION
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: , at thermodynamic equilibrium at certain conditions. The thermodynamic equilibrium implies:
- Equal temperature in both phases: , i.e. thermal equilbirum.
- Equal pressure in both phases , i.e. mechanical equilbrium.
- Equal chemical potentials for the components , i.e. material equilibrium.
In addition if we are dealing with a statistical mechanics model, with certain parameters that we can represent as , the model should be the same in both phases.
References
- 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)
- 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)