Gibbs-Duhem integration method

Once a state point of coexistence is established, additional state points can be determined expeditiously through application of the Gibbs-Duhem integration method [48,85,86]. In this approach a differential equation for the coexistence line is used to guide the establishment of state points away from the known coexistence point. The most well known such formula is the Clapeyron equation [41]... 

Summary of Applications of Gibbs-Duhem Integration Method"... 

The Gibbs-Duhem integration method excels in calculations of solid-fluid coexistence [48,49], for which other methods described in this chapter are not applicable. An extension of the method that assumes that the initial free energy difference between the two phases is known in advance, rather than requiring it to be zero, has been proposed by Meijer and El Azhar [51]. The procedure has been used in [51] to determine the coexistence lines of a hard-core Yukawa model for charge-stabilized colloids. 

Kofke D A 1993 Gibbs-Duhem integration a new method for direot evaluation of phase ooexistenoe by moleoular simulation Mol. Phys. 78 1 331-6... 

Kofke, D. A., Gibbs-Duhem integration a new method for direct evaluation of phase coexistence by molecular simulation, Mol. Phys. 1993, 78, 1331-1336... 

While the main driving force in [43, 44] was to avoid direct particle transfers, Escobedo and de Pablo [38] designed a pseudo-NPT method to avoid direct volume fluctuations which may be inefficient for polymeric systems, especially on lattices. Escobedo [45] extended the concept for bubble-point and dew-point calculations in a pseudo-Gibbs method and proposed extensions of the Gibbs-Duhem integration techniques for tracing coexistence lines in multicomponent systems [46]. 

There are many different routes for calculating phase equilibria that are covered in detail in other chapters of this volume thermodynamic scaling Monte Carlo (chapter by Valleau), Gibbs-Duhem integration along coexistence lines (chapter by Kofke), and pseudo-ensemble methods (chapter by de Pablo and Escobedo). Thus these methods are not discussed here. 

Kofke, D. A. (1993) Gibbs-Duhem Integration A New Method for the Direct Evaluation of... 

III. THE NPT+ TEST PARTICLE METHOD, GIBBS-DUHEM INTEGRATION AND PSEUDO-ENSEMBLES... 

Interesting connections between many of the methods discussed in the present chapter have been pointed out by Escobedo [54,55]. In particular, Escobedo suggests that Gibbs-Duhem integration, pseudo-ensembles, and the NPT + test particle method can be considered as low-order approximations of a histogram reweighting approach. 

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