Gibbs Project

LJ-mixtures

Results of the program were compared with already published theoretical and simulation results for binary and ternary LJ-mixtures. On this page results for different runs are given in form of graphs and report files which contain the "technical data" of the simulation and the averages (only of the last simulation block). To perform a good test for convergence it was attempted to start the simulations "far away" from the expected equilibrium points. However it should be noticed that during reproducing the results for the ternary LJ-mixtures the equilibrium points could not be approached from every point in the two phase region. The reason for this are density fluctuations in the GEMC-NPT ensemble which can move the simulated point out of the two phase region especially when the simulation is started from marginal points of the two phase region. Number densities are given in A^-3, and volumes in A³.

Contents

• Binary monatomic LJ-mixture
• Ternary monatomic LJ-mixture
  

• Final results
  A qualitative comparison (with existing graphs) was carried out:
  
• Reduced pressure vs. mole fraction of component 1
• Reduced pressure vs. reduced densities
  
• Performance of the runs:
1. GEMC-NPT run at P^* = 0.2:
   The run was started in the two phase region from a feed with an initial number density
   rho = 0.6/A³ and concentration z = 0.5.
   The starting concentration lies approximately on the middle of the tie line between the equilibrium concentrations, the starting density is close to the equilibrium density of the vapor phase.
   Progress:
• Number density vs. configuration
• Concentrations vs. configuration
• Volume vs. configuration
  

Report file


2. GEMC-NVT run at V = 2000 A³:
   This run was started from the same initial conditions like the GEMC-NPT run. Note that a different point on the phase envelope is approached since the total volume (and not the pressure) remains constant during the simulation.
   Progress:
• Number density vs. configuration
• Concentrations vs. configuration
• Volume vs. configuration
  

Report file

Ternary LJ mixtures
Reproduction of results of Tsang et al. in Fluid Phase Eq., 107, 31-43 (1995) for a system with Sigma₂/Sigma₁ = 0.75, Sigma₃/Sigma₁ = 0.5, Epsilon₂/Epsilon₁ = 0.75, Epsilon₃/Epsilon₁ = 0.5 at T^* = 1.0 and P^* = 0.20 by GEMC-NPT runs with N = 1000 LJ atoms.
The equilibrium number densities and concentrations were also compared with the values of an EOS for the LJ-fluid. For obtaining the following results long runs (2000000 - 5000000 configurations) were necessary to ensure that densities, concentrations and volumes were equilibrated. The results were obtained by averaging over the last 10⁶ steps of the simulation.

• Final results:
• Graphs:
• Equilibrium number densities vs. concentration of component 1 in the liquid phase in comparison with an EOS
• Equilibrium concentrations of components 1 and 2 in comparison with an EOS
• Numbers

Tsang et al.	x1	x2	rho*liq.	y1	y2	rho*vap.
Binary 1	0.59(1)	0.0	0.59(3)	0.14(2)	0.0	0.048(2)
Ternary 2	0.56(2)	0.100(3)	0.60(3)	0.14(2)	0.100(2)	0.056(3)
Ternary 3	0.45(1)	0.259(9)	0.58(3)	0.110(8)	0.243(6)	0.063(3)
Ternary 4	0.35(1)	0.450(9)	0.58(3)	0.10(1)	0.45(1)	0.083(5)
Ternary 5	0.21(1)	0.69(1)	0.54(3)	0.062(6)	0.72(1)	0.107(1)
Binary 6	0.102(4)	0.898(4)	0.48(4)	0.038(3)	0.962(3)	0.158(1)
Gibbs Project	x1	x2	rho*liq.	y1	y2	rho*vap.
Binary 1	0.589(8)	0	0.588(6)	0.14(2)	0.0	0.048(3)
Ternary 2	0.54(2)	0.102(2)	0.60(1)	0.12(1)	0.099(3)	0.052(3)
Ternary 3	0.464(9)	0.246(4)	0.584(8)	0.117(6)	0.254(4)	0.065(1)
Ternary 4	0.343(7)	0.45(1)	0.57(1)	0.092(4)	0.45(1)	0.0794(9)
Ternary 5	0.212(5)	0.683(6)	0.53(2)	0.064(4)	0.714(5)	0.110(3)
Binary 6	0.096(1)	0.904(1)	0.49(1)	0.034(2)	0.966(2)	0.150(5)

• Performance of the runs (selection):

Ternary 3	Initial conditions
Densities (A-3)	rhoI = 0.80, rhoII = 0.40
Concentrations	z1 = 0.30, z2 = 0.25

The starting concentrations of this run lie approximately on the middle of the tie line between the equilibrium densities. The starting number densities of the phases lie closer to the expected equilibrium densities. Note that it takes about 2000000 MC steps to equilibrate the volume while densities and concentrations are equilibrated much earlier. Convergence was also achieved for runs starting from the same concentrations and almost equal densities rho_I = 0.81 and rho_II = 0.79. However by starting with this densities from concentrations lying on the tie line left to the point z₁ = 0.26, z₂ = 0.25 the system was moved out of the two phase region.
Progress:

• Number density vs. configuration
• Concentrations vs. configuration
• Volume vs. configuration

Report file

Ternary 4	Initial conditions
Densities (A-3)	rhoI = 0.851, rhoII = 0.684
Concentrations	z1 = 0.21, z2 = 0.45

The starting concentrations of this run lie approximately on the middle of the tie line between the equilibrium densities. The starting number densities of the phases lie by the same distance away from their equilibrium values. Volume, compositions and densities of the system are equilibrated after 1000000 MC steps.
Progress:

• Number density vs. configuration
• Concentrations vs. configuration
• Volume vs. configuration

Report file

Ternary 5	Initial conditions
Densities (A-3)	rhoI = 0.8, rhoII = 0.6
Concentrations	z1 = 0.13, z2 = 0.70

The starting concentrations of this run lie approximately on the middle of the tie line between the equilibrium densities. The starting number densities of the phases lie by the same distance away from their equilibrium values. Volume, compositions and densities of the system need about 2500000 MC steps to equilibrate.
Progress:

• Number density vs. configuration
• Concentrations vs. configuration
• Volume vs. configuration

Report file

Page last modified by Johannes, August 1st 1996
Page created by Johannes, March 9th 1996