ms2: A Molecular Simulation Tool for Thermodynamic Properties

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1.5. Self-diffusion coefficients The self-diffusion coefficient Di is related to the mass flux of single molecules within a fluid. Therefore, the relevant Green-Kubo expression is based on the individual molecule velocity autocorrelation function [5] Di = 1 3Ni ∞ 0 dt vk(t)·vk(0) , (15) where vk(t) is the center of mass velocity vector of molecule k at some time t. Eq. (15) is an average over all Ni molecules of componenti in the ensemble, since all contribute to the self-diffusion coefficient. 4
2. Details ofms2 This section provides a closer insight intoms2 and the implemented equations. 2.1. Reduced quantities The simulation programms2 internally uses reduced quantities for its calculations. All quantities are reduced by a reference lengthσR, a reference energyǫR and a reference massmR, respectively. Table 1: Important physical quantities in their reduced form. Note thatε0 indicates the permittivity of the vaccum ε0 = 8.854187×10 −12 A 2 s 4 kg −1 m −3 . length l∗ = l σR energy u∗ = u ǫR mass m∗ = m time t ∗ = t mR ǫR σR mR piston mass Q∗ 4 p =QpσR mR temperature T ∗ = TkB ǫR pressure p ∗ = pσ3 R ǫR density ρ ∗ =ρσ 3 R NA volume V ∗ = V σ 3 R chemical potential ˜µ = µ kBT point charge q∗ 1 q = √ √ 4πε0 ǫRσR dipole moment µ ∗ 1 µ = √ 4πε0 ǫRσ3 R quadrupole moment Q∗ 1 Q = √ 4πε0 ǫRσ5 R diffusion coefficient D∗ D = σ mR/εR viscosity η ∗ = ησ2 R √ mRεR thermal conductivity λ ∗ = 5 kB λσ 2 R mR/εR
Page 1 and 2: ms2: A Molecular Simulation Tool fo
Page 3 and 4: 2. Introduction Due to the advances
Page 5 and 6: 3. Simulation programms2 The simula
Page 7 and 8: sense that the specified chemical p
Page 9 and 10: 3.3.3. Chemical potential The chemi
Page 11 and 12: 3.3.6. Transport properties In ms2,
Page 13 and 14: −0.5 < x, y, z < 0.5. The advanta
Page 15 and 16: Q = 2aq. The electrostatic interact
Page 17 and 18: Programming (OOP). It should be men
Page 19 and 20: motion, kinetic energy calculation,
Page 21 and 22: • PGI pgf95 4 with ”-r8 -fastss
Page 23 and 24: memory scales linearly with the num
Page 25 and 26: Applyingms2par is simple and should
Page 27 and 28: Table 1: Computational demand for t
Page 29 and 30: Table 3: NEC SX8R ”ftrace” prof
Page 31 and 32: i r ij ij Figure 2: Schematic of t
Page 33 and 34: Figure 4: UML class diagram of ms2,
Page 35 and 36: Figure 6: Runtime for the equimolar
Page 37 and 38: (a) (b) Figure 8: ms2 runtime of th
Page 39 and 40: Figure 10: Snapshot of ms2par gener
Page 41 and 42: Figure 12: Snapshot of a ternary mi
Page 43 and 44: [24] Eckl, B., Vrabec, J., and Hass
Page 45 and 46: Supplementary Material to ms2: A Mo
Page 47: The partial derivative of the resid
Page 51 and 52: where u µRF i is its contribution
Page 53 and 54: 3. Modular structure - example The
Page 55 and 56: Table 2 continued Parameter Option
Page 57 and 58: An example for a *.par file is give
Page 59 and 60: Table 4: Parameters and options spe
Page 61: References [1] Allen, M. and Tildes

ms2: A Molecular Simulation Tool for Thermodynamic Properties

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