Editing Computation of phase equilibria
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Thermodynamic equilibrium implies, for two phases <math> \alpha </math> and <math> \beta </math>: | Thermodynamic equilibrium implies, for two phases <math> \alpha </math> and <math> \beta </math>: | ||
* equal [[temperature]]s: <math> T_{\alpha} = T_{\beta} </math> | * equal [[temperature]]s: <math> T_{\alpha} = T_{\beta} </math> | ||
* equal [[pressure]]s: <math> p_{\alpha} = p_{\beta} </math> | * equal [[pressure]]s: <math> p_{\alpha} = p_{\beta} </math> | ||
* equal [[chemical potential]]s: <math> \mu_{\alpha} = \mu_{\beta} </math> | * equal [[chemical potential]]s: <math> \mu_{\alpha} = \mu_{\beta} </math> | ||
The computation of phase equilibria using computer simulation can follow a number of different strategies. Here we will focus mainly | |||
on [[first-order transitions]] in fluid phases, usually [[Gas-liquid phase transitions |liquid-vapour]] equilibria. | |||
== Independent simulations for each phase at fixed temperature in the [[canonical ensemble]] == | == Independent simulations for each phase at fixed temperature in the [[canonical ensemble]] == | ||
Simulations can be carried out using either the [[Monte Carlo]] or the [[molecular dynamics]] technique. | Simulations can be carried out using either the [[Monte Carlo]] or the [[molecular dynamics]] technique. | ||
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* The simulation results in the two phase region will depend dramatically on the system size (calculations with different number of particles become convenient to check the quality of the phase equilibria results) | * The simulation results in the two phase region will depend dramatically on the system size (calculations with different number of particles become convenient to check the quality of the phase equilibria results) | ||
== Direct simulation of the two phase system== | == Direct simulation of the two phase system== | ||
An example using the [[Lennard-Jones model]], | |||
*[http://dx.doi.org/10.1063/1.1474581 James R. Morris and Xueyu Song "The melting lines of model systems calculated from coexistence simulations", Journal of Chemical Physics '''116''' 9352 (2002)] | |||
and its application to [[water]] | |||
and [[water]] | *[http://dx.doi.org/10.1063/1.2183308 Ramón García Fernández, José L. F. Abascal, and Carlos Vega "The melting point of ice Ih for common water models calculated from direct coexistence of the solid-liquid interface", Journal of Chemical Physics '''124''' 144506 (2006)] | ||
== Gibbs ensemble Monte Carlo for one component systems== | == Gibbs ensemble Monte Carlo for one component systems== | ||
The [[Gibbs ensemble Monte Carlo]] method is often considered as a smart variation of the standard canonical ensemble procedure (See | The [[Gibbs ensemble Monte Carlo]] method is often considered as a 'smart' variation of the standard canonical ensemble procedure (See Ref. 1). | ||
The simulation is, therefore, carried out at constant volume, temperature and number of particles. | The simulation is, therefore, carried out at constant volume, temperature and number of particles. | ||
The whole system is divided into two non-interacting parts, each one has its own simulation | The whole system is divided into two non-interacting parts, each one has its own simulation | ||
box with its own [[periodic boundary conditions]]. | box with its own [[boundary conditions |periodic boundary conditions]]. | ||
This separation of the two phases into different boxes is in order to suppress any influence due to [[interface | interfacial]] effects. | This separation of the two phases into different boxes is in order to suppress any influence due to [[interface | interfacial]] effects. | ||
The two subsystems can interchange volume and particles. The rules for these interchanges are | The two subsystems can interchange volume and particles. The rules for these interchanges are | ||
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[[category: Monte Carlo]] | [[category: Monte Carlo]] | ||
[[category: Computer simulation techniques]] | [[category: Computer simulation techniques]] | ||
== Mixtures == | == Mixtures == | ||
=== Symmetric mixtures === | === Symmetric mixtures === | ||
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temperature. The symmetry in the interactions can be exploited to simplify the calculation of phase diagrams. | temperature. The symmetry in the interactions can be exploited to simplify the calculation of phase diagrams. | ||
== See also== | == See also== | ||
*[[Gibbs-Duhem integration]] | *[[Gibbs-Duhem integration]] | ||
==References== | ==References== | ||
#[http://dx.doi.org/10.1080/00268978700101491 Athanassios Panagiotopoulos "Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble", Molecular Physics '''61''' pp. 813-826 (1987)] | |||
[[category: computer simulation techniques]] | [[category: computer simulation techniques]] |