MD simulation of methane in nanochannels COCIM, Arica, Chile M. Horsch, M. Heitzig, and J. Vrabec University of Stuttgart November 6, 2008
Scope and structure Molecular model for graphite and the fluid-wall interaction Scalability of the MD simulation Poiseuille/Couette flow of methane through graphite channels Cluster criteria for systems with vapor-liquid coexistence Vapor-liquid equilibria of methane under confinement Contact angle dependence on the fluid-wall interaction
Methane confined in a nanochannel z Poiseuille flow: The fluid is accelerated in z direction Couette flow: x y The walls are accelerated in z direction Contact angle: Meniscus perpendicular to the z axis
State of the art: system size Vishnyakov et al. 1999 L 1,5 nm Langmuir 15: 8736 Werder et al. 2001 L 7,5 nm Nano Lett. 1: 697 Diameter / number of particles Sokhan et al. 2002 L 2,8 nm N wall = 2000 J. Chem. Phys. 117: 8531 Cui und Cochran 2004 L 200 nm (ρ Ionen 0,02 mol/l) Mol. Sim. 30: 259 Dimitrov et al. 2007 L 20 σ LJ 6 nm N fluid = 25000 PRL 99: 054501 Present work 2008 L up to 75 nm N up to 4,8 million
Scaling with isotropic domain decomposition Molecular dynamics code Mardyn (developed by the ls 1 project): n P x runtime / N x time steps [µs] 100 50 20 10 wall fluid+wall fluid 1 3 6 14 32 64 150 number of concurrent processes n P N = 450000 N = 3000n P N = 32000n P
State of the art: potential models fluid wall fluid-wall Vishnyakov et al. 1999 3CLJQ rigid Steele Langmuir 15: 8736 (CO 2 ) (10-4-3) Werder et al. 2001 SPC Walther et al. LJ Nano Lett. 1: 697 (water) (carbon) Sokhan et al. 2002 LJ Tersoff-Brenner LJ J. Chem. Phys. 117: 8531 (carbon) Liu und Wang 2005 SPC rigid LJ Phys. Rev. B 72: 085420 (water) Dimitrov et al. 2007 LJTS LJTS, elastic LJTS PRL 99: 054501 (LJTS LJ, truncated and shifted at r ij = 2,5σ) Present work 2008 LJTS Tersoff LJTS (also: springs)
Reparametrization of the Tersoff potential U(bond length) Bond length Tersoff potential: 1.461 Å Actual graphite: 1.421 Å RDF new old 1.46 1.47 length in units of Å More adequate potential parameters for graphite: Cutoff Attraction 1.35 1.40 1.45 1.50 radius in units of Å Repulsion R = 2.0 Å (1.8 Å) S = 2.35 Å (2.1 Å) µ = 2.275 Å -1 (2.2119 Å -1 ) λ = 3.587 Å -1 (3.4879 Å -1 )
Integration time step U [ev] p [kpa] t [ps] A time step of 1 fs leads to an acceptable accuracy.
Uniform acceleration (PI controller) Poiseuille, v target = 10 m/s, τ = 3 ps, L = 15 nm, liquid CH 4 at 166 K flow velocity in units of m/s 60 40 20 0-20 -40 2 τ aɺ = v v τvɺ target current a z mean over 50 ps 0 40 80 120 160 time in units of ps 60 40 20 0-20 -40 acceleration in units of nm/ns 2
Fluid-wall interaction Lennard-Jones energy parameter: fluid density in units of mol/l Lennard-Jones size parameter: 40 30 20 10 0 ε σ FW FW = ξ ε = η σ ξ = 0.075 η = 1 ξ = 0.160 η = 1 ξ = 0.353 η = 0.947 ξ = 0.497 η = 0.957 Wang et al. Kalra et al. 2 3 4 5 6 y coordinate in units of nm FF FF T = 0.95 ε/k ρ = 1.005 ρ
MD simulation of Couette flow
Poiseuille and Couette flow: velocity profile T = 0.95 ε/k, ρ = 1.005 ρ, v target = 10 m/s, ξ = 0.353, η = 0.9466 (Wang et al.) 10 5 0 v z [m/s] 0.60-0.75 ns 1.05-1.20 ns y [nm] v z [m/s] 10 5 0.45-0.60 ns 0.60-0.75 ns y [nm] 0 10 20 30 Couette flow 0 5 10 15 Poiseuille flow
Comparison of cluster criteria criterion a 2 criterion g 2
Dependence of the contact angle on ξ y [σ] 8 6 4 T = 0,73 ε/k B 75 o ξ = 0,16 ξ = 0,10 105 o y [σ] 8 6 4 2 80 o 120 o T = 1,00 ε/k B ξ = 0,11 ξ = 0,14 5 6 z [σ] 8 10 z [σ]
Conclusion System size: acceptable scaling of Mardyn, L up to 75 nm easily possible the system geometry requires (at least static) load balancing Flow simulations: were carried out in the canonical ensemble unknown interaction parameters ξ and η Vapor-liquid interface: dependence of the contact angle on ξ was studied suitable criterion for the interface: ρ ρ ' ρ '' J. Chem. Phys. 128: 164510 Phys. Rev. E 78: 011603