Computation of phase equilibria
[CURRENTLY WORKING ON THE PAGE]
The computation of phase equilibria using computer simulation can follow different strategies.
Liquid-vapor equilibria of one component systems
The thermodynamic equilibrium implies, for two phases Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha } and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta } :
- Equal temperature: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_{\alpha} = T_{\beta} }
- Equal pressure: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_{\alpha} = p_{\beta} }
- Equal chemical potential: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\alpha} = \mu_{\beta} }
Independent simulations for each phase at fixed Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T } in the canonical ensemble
The simulations can be carried out either using Monte Carlo or Molecular dynamics techhniques. Let us assume that we have some knowledge on the phase diagram of the system. We could try the following recipe:
- Fix a temperature
- Perform a few simulations in the low density region (where the gas phase density is expected to be)
- Perform a few simulations in the moderate / high density region (where the liquid phase should appear)
- In these simulations we can compute for each density (at fixed T) the values of the pressure and the chemical potentials (for instance using the Widom test-particle method)