Gibbs-Duhem, integration

Most methods for the determination of phase equilibria by simulation rely on particle insertions to equilibrate or determine the chemical potentials of the components. Methods that rely on insertions experience severe difficulties for dense or highly structured phases. If a point on the coexistence curve is known (e.g., from Gibbs ensemble simulations), the remarkable method of Kofke [32, 33] enables the calculation of a complete phase diagram from a series of constant-pressure, NPT, simulations that do not involve any transfers of particles. For one-component systems, the method is based on integration of the Clausius-Clapeyron equation over temperature, 

In some cases, in particular for lattice and polymeric systems, volume change moves may be hard to perform, but particle insertions and deletions may be relatively 

The same pseudo-ensemble concept has been used by Camp and Allen [44] to obtain a pseudo-Gibbs method in which particle transfers are substituted by volume fluctuations of the two phases. The volume fluctuations are unrelated to the ones required for pressure equality (10.7) but are instead designed to correct imbalances in the chemical potentials of some of the components detected, for example, by test particle insertions. 

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]. 

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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... 

Escobedo, F. A. de Pablo, 1. J., Pseudo-ensemble simulations and Gibbs-Duhem integrations for polymers, J. Chem. Phys. 1997,106, 2911-2923... 

In theory, once the activity of an electrolyte in solution is known, the activity of the solvent can be determined by the Gibbs-Duhem integration (see section 2.11). In practice, the calculation is prohibitive, because of the chemical complexity of most aqueous solutions of geochemical interest. Semiempirical approximations are therefore preferred, such as that proposed by Helgeson (1969), consisting of a simulation of the properties of the H20-NaCl system up to a solute... 

The process of calculating the partial molar property of one component from the knowledge of partial molar property of the other component in a binary system, where the integral molar property changes continuously with the composition, is referred to as the Gibbs Duhem Integration. 

Figure 8.7 Estimation of activities of MnO in FeO-MnO system by Gibbs Duhem integration...

Okamoto (1993) and Escobedo and dePablo (1995) relate the pressure to the excess chemical potentials on the basis of a Gibbs-Duhem integration. We integrate... 

The silicon melting line has been determined using a coexistence simulation292 and is able to predict a decrease in Tm with increase in pressure, consistent with experiment. Vega et al.2S9 carry out Gibbs-Duhem integration to determine the coexistence line of water, and the change in the coexistence line... 

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]... 

The n= 12 soft sphere model is the high-temperature limit of the 12-6 Lennard-Jones (LJ) potential. Agrawal and Kofke [182] used this limit as the starting point for another Gibbs-Duhem integration, which proceeded to lower temperatures until reaching the solid-liquid-vapor triple point. The complete solid-fluid coexistence line, from infinite temperature to the triple point, can be conveniently represented by the empirical formula [182]... 

Gibbs-Duhem Integration Tracing Coexistence Lines A. Concept Formalism... 

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