Surface analysis algorithms in the mardyn program and the ls1 project

Transcription

1 Surface analysis algorithms in the mardyn program and the ls1 project Stuttgart, 15 th December 1 M. T. Horsch

2 Surface tension The virial route Bakker-Buff equation: γ R 2 out in dz z Normal pressure decays at R. Significant decrease of γ due to spherical curvature. Main advantages of the virial route: 2 p 3 out 2 3 2γ Δ dp ( z ) z p in N z ) p ( z ) N ( T Irving-Kirkwood pressure tensor: f ij srij pn( z ) ktρ( z ) 3 4πz r { i, j } S( z ) ij surface tension in units of LJTS fluid.8 Vrabec et al droplet size in molecules Equilibrium analysis (no unstable configurations) Yields the surface of tension radius R = 2γ/Δp.

3 probability density Surface tension The variational route Canonical partition function: ΔF T ln f exp ΔU T 3 4 ΔU, ΔU 2, ΔU O ΔU For small deformations: γ = ΔF/ΔA with A = 4πQ 2 + O(δQ) Nonlinear terms are essential. Tolman length much smaller than based on other methods. Main advantages of the variational route: deviation of ΔU from mean equimolar radius in units of ζ Free energy differences are considered in a direct way. No mechanical equilibrium assumption is applied. γ in units of εζ -2 LJSTS fluid, T =.8 ε (Source: Sampayo et al., 21)

4 Discretization of interfaces Effective radii for a droplet Capillarity radius P = 2γ /Δp, from the Laplace equation and the surface tension in the planar case. Equimolar radius Q, from condition Γ = for the excess density. Laplace radius R = 2γ/Δp, based on a known value of the surface tension for the curved interface. Conservative radius R C for which 2 the excess free energy is 4πR C γ. Radii R(ρ) for a density ρ > ρ > ρ.

5 Discretization of interfaces equimolar radius Q in units of LJTS fluid p from IK pressure tensor (Vrabec et al.) p from density profiles δ lim R Q Q T =.65 T =.75 T =.85 lim Q P η Q capillarity radius P in units of

6 Clustering Cluster critieria for the dispersed liquid phase Molecules with a distance between the centres of mass r ij < r St are regarded as part of the liquid phase (Stillinger). At least n = 4 neighbours are required within a sphere with the radius r St around the centre of mass (ten Wolde-Frenkel). A molecule is liquid if the sphere around its n nearest neigbours has an average density greater than the arithmetic (a n ) or the geometric (g n ) mean between ρ and ρ. n = 5

7 Clustering evaporation rate (reduced) Carbon dioxide T = 237 K = 1.89 mol/l g 2 (geom. mean) a 2 (arithm. mean) a 8 (arithm. mean) ten Wolde-Frenkel Stillinger n 2/3 scaling liquid drop size in number of molecules

8 Population statistics Nucleation in supersaturated vapours Yasuoka and Matsumoto (1998): Canonical MD simulation Limited time interval Conditions change over time liquid drops per nm 3 pressure / kpa NVT with = 1.46 mol/l Higher-level evaluation subsequent to cluster detection: Population statistics, yielding a nucleation rate 1 25 Argon at T = 96.5 K time in units of ns Cluster identification and tracking of growth and decay Evaluation of cluster temperature to analyze the heat transfer

9 Population statistics Requirement for a steady state: Elimination of liquid drops intervention rate (LJ units, natural logarithm) P ( n) n* CNT n exp 2F n exp 2F n LJTS S = T =.7 CNT transposed CNT T T threshold size (molecules)

10 Confined fluid systems 6 5 Poiseuille flow of methane through nanoporous carbon wall d centre wall 6 5 density in units of mol/l velocity in units of m/s y coordinate in units of nm

11 Confined fluid systems Simulation approach LJTS fluid, generic wall model, Dispersive energy ε fw = ζε Equilibrium state Cylindrical meniscus, based on arithm. mean density z coordinate in units of 2-2 =.16 =.13 =.1 =.7 vapour liquid x coordinate in units of

12 Functionality within the ls1 project Main initial application of ls1 mardyn: structure and properties of fluids at interfaces moldy mardyn b b trunk Interfacial profiles planar spherical planar Surface tension virial variational both Cluster detection o arith. mean local ρ local ρ Population statistics o Adsorption o o o Nanoscopic flow o o o